Answers
In the triangle, the values are p=10.3, [tex]\angle Q=19.5\textdegree[/tex] and [tex]\angle R = 112.5\textdegree[/tex].
What is trigοnοmetric functiοn?The functiοns οf an angle in a triangle are knοwn as trigοnοmetric functiοns, cοmmοnly referred tο as circular functiοns. In οther wοrds, these trig functiοns prοvide the relatiοnship between a triangle's angles and sides. There are five fundamental trigοnοmetric functiοns: sine, cοsine, tangent, cοtangent, secant, and cοsecant.
Here in the given triangle PQR, [tex]\angle P = 48\textdegree[/tex] , q=5 and r=13.
Now using law of cosine fοrmula,
=> [tex]p^2=q^2+r^2-2qr.cos\angle P[/tex]
=> [tex]p^2=5^2+13^2-2.5.13.cos 48\textdegree[/tex]
=> [tex]p^2=25+169-130cos48\textdegree[/tex]
=> [tex]p^2=107[/tex]
=> p = 10.3
Now using law of sine then,
=> [tex]\frac{p}{sinP}=\frac{q}{sinQ}[/tex]
=> [tex]sinQ=\frac{q sinP}{p}[/tex]
=> [tex]sin Q= \frac{5sin 48\textdegree}{10.3}[/tex]
=> sin Q = 0.344
=>[tex]\angle Q = 19.5\textdegree[/tex]
Now sum οf all angles in triangle is 180°. Then,
=>[tex]\angle P+\angle Q+\angle R = 180\textdegree[/tex]
=> [tex]\angle R = 180-48-19.5=112.5\textdegree[/tex]
Hence the answers are p=10.3, [tex]\angle Q=19.5\textdegree[/tex] and [tex]\angle R = 112.5\textdegree[/tex].
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Related Questions
what is the margin of error, using a 95% confidence level, for estimating the true population proportion of adult office workers who have worn a halloween costume to the office at least once? (round to the nearest thousandth)
Answers
For example, if the estimated population proportion of adult office workers who have worn a Halloween costume to the office at least once is 0.25 and the sample size is 400, the margin of error would be calculated as follows:
[tex]ME = 1.96*sqrt((0.25*(1-0.25))/400) = 0.032.[/tex]
The margin of error is 0.032. This means that if you were to survey a sample of adult office workers about the proportion of them who have worn a Halloween costume to the office at least once, the results of the survey would be within plus or minus 0.032 of the true population proportion 95% of the time.
To calculate this margin of error,
use the following formula:[tex]ME = 1.96*sqrt((p*(1-p))/n)[/tex] where p is the estimated population proportion and n is the sample size.
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calculate the average growth rate from the following growth rates. (round your intermediate calculations at least to 4 decimal places and final answer to 2 decimal places.) 1.50% 1.60% .20% .20% 3.20%
Answers
The average growth rate is 1.34%, which is calculated by the sum of the growth rates divided by the number of growth rates.
To calculate the average growth rate, we need to add up the given growth rates and then divide by the number of growth rates.
1. First, add up the given growth rates: 1.50% + 1.60% + .20% + .20% + 3.20% = 6.70%
2. Next, divide the sum by the number of growth rates: 6.70% / 5 = 1.34%
3. Finally, round the answer to 2 decimal places: 1.34%
Therefore, the average growth rate is 1.34%.
Answer: 1.34%.
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What is the solution to the system of equations? x=6y+24 and 2x+3y=3
Answers
Answer:
Below
Step-by-step explanation:
2x + 3y =3 since x = 6y+24 put that in for 'x'
2 ( 6y+24) + 3y = 3
12 y + 48 + 3y = 3
15 y + 48 = 3
15 y = -45
y = -3 <======use this value of 'y' in one of the equations to calculate the corresponding 'x' value :
x = 6y + 24
x = 6(-3) + 24
x = 6
What is 8 multiplied by 16?
Answers
Answer:
Step-by-step explanation:
128
The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction pi Over 2 EndFraction (t + 2)) + 5. Which of the following is the graph of this equation?
Answers
The graph of the equation, which looks like the below diagram.
What is the term graph means?The term "graph" can refer to a visual representation of data or information, typically in the form of a diagram or chart. Graphs can be used to show relationships or patterns between different sets of data.
The given equation is:
h = 3 sin(π/2(t + 2)) + 5
This is a sinusoidal function with an amplitude of 3, a period of 4, a phase shift of -2, and a vertical shift of 5.
To graph this function, we can plot a few points and connect them with a smooth curve. For example, we can choose some values of t and calculate the corresponding values of h:
t = -4: h = 2
t = -3: h = 5
t = -2: h = 8
t = -1: h = 5
t = 0: h = 2
t = 1: h = -1
t = 2: h = 2
t = 3: h = 5
t = 4: h = 8
Using these values, we can sketch the graph of the function. The amplitude is 3, so the maximum height of the ball is 3 units above and below the vertical shift of 5. The period is 4 seconds, since the frequency is 2π/B = 4. The phase shift is to the left by 2 seconds. Therefore, the graph of the equation is as follows:
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Complete question is:
1. Construct symmetric and antisymmetric matrices from \[ A=\left[\begin{array}{ccc} -1 & 0 & 2 \\ 4 & 6 & 0 \\ 0 & 0 & 1 \end{array}\right] \] 2. Is the following matrix antisymmetric? \[ B=\left[\be
Answers
Answer:78.9
Step-by-step explanation:
78.9x 0896968
A 5 foot girl is standing in the Grand Canyon, and she wants to estimate the height (depth) of the canyon. The sun casts her shadow 9 inches along the ground. To measure the shadow cast by the top of the canyon, she walks the length of the shadow. She takes 280 steps and estimates that each step is roughly 3 feet. Approximately how deep is the Grand Canyon?
Answers
The estimated depth of the Grand Canyon would be approximately 467 feet.
First we need to calculate the height of the girl in inches. Since a foot is equal to 12 inches, the girl's height would be 5 x 12 = 60 inches. If the girl's shadow is 9 inches, then the ratio between the girl's height and her shadow is 60/9 or 6.6667 (rounded to 4 decimal places).Now, if the girl's shadow is 9 inches long, and she takes 280 steps to reach the end of it, and each step is approximately 3 feet long, then the total distance she has covered would be 280 x 3 = 840 feet.
The distance from the girl to the canyon is the height of the canyon. If we multiply the distance covered by the girl, which was 840 feet, by the ratio between the girl's height and her shadow length, which was 6.6667, we will get the height of the canyon. Therefore, the height of the Grand Canyon can be estimated to be 840 x 6.6667 = 5600 inches (rounded to the nearest whole number), which is equivalent to approximately 467 feet. Answer: The estimated depth of the Grand Canyon would be approximately 467 feet.
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$2,800 is invested in an account earning 2.8% interest (APR), compounded daily. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answers
Using the compound interest formula the percentage of growth per year (APY), to the nearest hundredth of a percent is 2.82%.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
To calculate the value of the account after t years, we can use the formula for compound interest -
[tex]A = P(1 + \frac{r}{n} )^{(nt)}[/tex]
where -
A is the final amount
P is the principal amount
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, P = 2800, r = 0.028 (since the APR is 2.8%), n = 365 (since the interest is compounded daily), and we want to find A as a function of t.
So the function that represents the value of the account after t years is -
[tex]f(t) = 2800 \times \big(1 + \frac{0.028}{365} \big)^{(365 \times t)}[/tex]
We can simplify this function by using the fact that 0.028/365 is a constant.
Let's call this constant "k" -
k = 0.028/365
Then we can rewrite the function as -
[tex]f(t) = 2800 \times (1 + k)^{(365 \times t)}[/tex]
Rounding all coefficients to four decimal places, the final function is -
[tex]f(t) = 2800 \times (1 + 0.000077)^{(365 \times t)}[/tex]
To calculate the annual percentage yield (APY), we can use the formula -
[tex]APY = (1 + \frac{r}{n} )^{(n-1)}[/tex]
where r is the annual interest rate and n is the number of times the interest is compounded per year.
In this case, r = 0.028 and n = 365. So the APY is -
[tex]APY = (1 + 0.028/365)^{365 - 1} = 0.02824...[/tex]
Rounding to the nearest hundredth of a percent, the APY is 2.82%.
Therefore, the APY value is obtained as 2.82%.
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Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.
x.....................f(x)....................g(x)
1995 $69,682.50 $72,429.27
2000 $78,943.50 $79,967.77
2005 $88,204.50 $88,290.88
2006 $90,056.70 $90,056.70
2007 $91,908.90 $91,857.83
2010 $97,465.50 $97,480.27
A) f(x) is exponential; an exponential function increases more slowly than a linear function.
B) f(x) is exponential; f(x) increased more overall than g(x).
C) g(x) is exponential; g(x) has a higher starting value and higher ending value.
D) g(x) is exponential; an exponential function increases faster than a linear function.
Answers
D) g(x) is exponential; an exponential function increases faster than a linear function.
Determining exponential expression:To determine which function is exponential, find the rate of change between the different years for each function.
An exponential function will have a constant rate of change over time, while a linear function will have a constant slope.
Looking at the table, we can calculate the rate of change between each year for both f(x) and g(x).
Here we have
x f(x) g(x)
1995 69,682.50 72,429.27
2000 78,943.50 79,967.77
2005 88,204.50 88,290.88
2006 90,056.70 90,056.70
2007 91,908.90 91,857.83
2010 97,465.50 97,480.27
Calculate the rate increase the both cases
From f(x)
For the years 1995 to 2000
= [78,943.50 - 69,682.50 ]/ 69,682.50 x 100 = 13.3%
For the years 2000 to 2005
= [88,204.50 - 78943.50]/ 78943.50 × 100 = 11.73
For g(x)
For the years 1995 to 2000
= [ 79,967.77 - 72,429.27]/ 72,429.27× 100 = 10.40
For the years 2000 to 2005
= [ 88,290.88 - 79,967.77]/79,967.77 × 100 = 10.40
Here we can observe that the rate of increase in g(x) is constant whereas in f(x) the rate of increase is decreasing
Hence we can conclude that
D) g(x) is exponential; an exponential function increases faster than a linear function.
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ANSWER FOR BRANLIEST
Which of the following is an irrational number?
Answers
-5<-0.2
Since that is true it satisfies the equation
Solution:
To help pay for culinary school, Austin borrowed money from his credit union. He took out a personal, amortized loan for $56,000 , at an interest rate of 5.25% , with monthly payments for a term of 15 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find Austin's monthly payment. (b) If Austin pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) If Austin pays the monthly payment each month for the full term, find the total amount of interest he will pay.
Answers
The required answers are a) P ≈ $441.59, b) $79,486.20, c) $23,486.20.
How to find monthly payment?(a) To find Austin's monthly payment, we can use the formula for the monthly payment on an amortized loan:
P = (A * r) / (1 - (1 + r)^(-n))
where:
P = monthly payment
A = loan amount = $56,000
r = monthly interest rate = 5.25%/12 = 0.004375
n = total number of payments = 15 years * 12 months/year = 180
Plugging in these values, we get:
P = (56000 * 0.004375) / (1 - (1 + 0.004375)^(-180))
P ≈ $441.59
Therefore, Austin's monthly payment is $441.59.
(b) If Austin pays the monthly payment each month for the full term, he will make 180 payments. So his total amount to repay the loan is:
Total amount = Monthly payment * Number of payments
Total amount = $441.59 * 180
Total amount ≈ $79,486.20
Therefore, Austin will repay a total of $79,486.20 over the 15-year term.
(c) To find the total amount of interest Austin will pay, we can subtract the original loan amount from the total amount he will repay:
Total interest = Total amount - Loan amount
Total interest = $79,486.20 - $56,000
Total interest ≈ $23,486.20
Therefore, Austin will pay a total of approximately $23,486.20 in interest over the 15-year term.
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The diagram shows a triangle.
Answers
Answer:
x = 11
Step-by-step explanation:
1) Put our angles into an equation
We know that all these angles in the triangle must add up to 180 so to put it simply we can write it as...
6x + x + 47 + x + 45 = 1802) Simplify
To simplify what we have been given so far, we have to collect like terms.
8x + 92 = 1803) Solve the equation
To solve this equation we have to isolate the x and to do this we have to get rid of the 92 and the 8. To get rid of these we have to subtract 92 from both sides and divide 8 from both sides!
8x + 92 - 92 = 8x = 888x ÷ 8x = x = 11This means x = 11
Hope this helps, have a lovely day! :)
Answer:
See below.
Step-by-step explanation:
We are asked to find the value of x.
First, we should know that a Triangles' angles adds up to 180° due to the Triangle having 3 sides.
Since a Triangles' angles add up to 180°, we can set all of the angles' combined sum equal to 180°.
Our Equation:
[tex]6x+x+45+x+47=180[/tex]
We can begin solving for x.
Combine Like Terms:
[tex]8x+92=180[/tex]
Subtract 92 from both sides:
[tex]8x=88[/tex]
Divide by 8:
[tex]\frac{8x}{8} = \frac{88}{8} \\x = 11.[/tex]
Our final answer is x equals 11.
Aija and John both have Only Fans pages in which they receive income based on the number of monthly subscriptions.
In 2022, Aija had 560 paid monthly subscribers, each paying $14. John earned $76,000, in the last 8 months of 2022, with each monthly subscriber paying $19. Who made more money in 2022 with their page? Who has more subscribers? What recommendations would you give to your peers who may be considering creating an Only Fans account?
Applying the SOLVE strategy
“S” - What is the problem asking you to find?
“O” - What facts are necessary for you to answer the problem?
“L” - What operations, steps, or plans can you use to obtain your answer?
“V” - Demonstrate your work by showing your steps.
“E” - Look at your answer. Does it make sense? Did you answer all parts of the problem?
Answers
Answer: S - The problem is asking us to find who made more money in 2022 with their Only Fans page and who has more subscribers. It also asks for recommendations for peers considering creating an Only Fans account.
O - The necessary facts to answer the problem are the number of paid monthly subscribers and the amount each subscriber pays for Aija and John.
L - To find out who made more money in 2022 with their Only Fans page, we can calculate the total income for Aija and John by multiplying the number of paid monthly subscribers by the amount each subscriber pays and then by the number of months. To find out who has more subscribers, we can compare the number of paid monthly subscribers for Aija and John.
V - Aija’s total income in 2022 = 560 subscribers * $14/subscriber * 12 months = $94,080 John’s total income in 2022 = $76,000 John’s number of subscribers = $76,000 / ($19/subscriber * 8 months) = 500 subscribers
E - Aija made more money in 2022 with her Only Fans page than John. Aija also has more subscribers than John. As for recommendations for peers considering creating an Only Fans account, it is important to carefully consider the potential risks and benefits before making a decision. It is also important to research and understand the platform’s terms of service and community guidelines.
A classic rock radio station claims to play and average of 50 minutes of music every hour. However, it seems like every time you turn to this station, there is a commercial playing. To investigate their claim, you randomly selected 12 different hours during the next week and recorded the number of minutes of music played during each of the 12 hours. Here are the number of minutes of music in each of these hours: 44 49 45 51 49 53 49 44 47 50 46 48 Is there evidence that the mean number of hours of music played each hour is less than what the radio station advertises? Interpret the p-value in the context of the problem. If an error has been committed, explain which type of error it could be.
Answers
So the convincing evidence that the radio station plays less than
[tex]50\ min\ of\ music\ per\ hour[/tex]. Here we have to see graph and chart.
How to get convincing evidence that radio station play less?Parameter of Interest, [tex]\mu = the\ true\ average\ number \ minutes\ of\ music \ played\ every \ hour.[/tex]
Null Hypothesis, [tex]H_{o} : \mu = 50[/tex]
Alternative Hypothesis, [tex]H_{a} : \mu < 50[/tex]
[tex]Conditions\ of\ test :[/tex]
[tex]Random :[/tex] A random sample of [tex]hours[/tex] was selected.
[tex]Independent:[/tex] There are more than [tex]10(12) = 120\ hours[/tex] of music played during the week.
[tex]Normal:[/tex] We do not know if the population distribution of the music [tex]times[/tex] is approximately Normal and we don’t have a large (big) sample size, so we will graph the data and look for any departures from Normality.
Level of Significance, [tex]\alpha = 0.05\ Significance\ level[/tex]
[tex]n = 12, df = 11, \bar x = 47.9, S_{x} = 2.81[/tex]
1- var Stats:
[tex]\bar x= 47.9166[/tex] , [tex]\Sigma\ x = 575[/tex], [tex]\Sigma\ x^{2} = 27639[/tex], [tex]Sx = 2.81096[/tex], [tex]\sigma x = 2.69129[/tex]
[tex]t = \frac{\bar x- \mu_{o}}{ \frac{S_{x} }{\sqrt{n} } }[/tex]
[tex]t = \frac{47.9- 50}{ \frac{2.81 }{\sqrt{12} } }[/tex]
[tex]= - 2.59[/tex]
T test :
[tex]\mu < 50, t = -2.5674, p=.013, \bar x = 47.9166, S_{x} = 2.81, n = 12[/tex]
P-value (Use correct probability notation.) [tex]P-value = P(t < -2.59) = 0.0126[/tex]
Since the [tex]P-value(.013)[/tex] is less than [tex]\alpha =.05[/tex], we reject the null hypothesis.
There is convincing evidence(proof) that the radio station plays less than [tex]50\ min\ of\ music\ per\ hour[/tex].
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The surface area of this cube is 216 square centimeters. What is the volume?
Answers
Answer:
[tex]216cm^3[/tex]
Step-by-step explanation:
Surface area of a cube is [tex]6 * s^2[/tex]
[tex]6 * (s)^2 = 216cm^2\\s^2 = 36cm^2\\s = 6cm[/tex]
Now we have a value of the side we can get the volume.
Volume = [tex]s^3\\[/tex]
[tex]= (6cm) ^ 3[/tex]
[tex]= 216cm^3[/tex]
Hope this helps!
Brainliest and a like is much appreciated!
ravel leisure magazine provides an annual list of the best hotels in the world. the magazine provides a rating for each hotel along with a brief description that includes the size of the hotel, amenities, and the cost per night for a double room. a sample of of the top-rated hotels in the
Answers
The Ravel Leisure Magazine's annual list of the best hotels in the world is a content-loaded resource that provides valuable information for travelers. Each hotel on the list is rated and includes a brief description of the size. Here is a sample of the top-rated hotels on the list: The Ritz-Carlton, The Peninsula and The Four Seasons
The Ritz-Carlton, Bali: This luxurious hotel boasts a stunning beachfront location, spacious suites, and top-of-the-line amenities, including a spa and multiple dining options. The cost per night for a double room is $450.
The Peninsula, Hong Kong: This iconic hotel offers unparalleled views of Victoria Harbour, along with world-class amenities, such as a rooftop infinity pool and award-winning restaurants. The cost per night for a double room is $700.
The Four Seasons, Paris: This elegant hotel is located in the heart of Paris and features opulent rooms, a Michelin-starred restaurant, and a spa. The cost per night for a double room is $800.
These are just a few examples of the top-rated hotels on the Ravel Leisure Magazine's annual list. Each hotel offers a unique experience for travelers, making it a valuable resource for planning a leisure trip.
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7. Allen believes 3 possible outcomes in a game are equally likely to occur.
Outcome
Number of times
observed
#1 #2 #3
4 14 2
Which conclusion BEST supports the data?
Answers
Looking at the data, we see that outcome #2 occurred much more frequently than the other outcomes (14 times out of 20 total trials). This suggests that outcome #2 may not be equally likely to occur as the other outcomes.
Therefore, the best conclusion supported by the data is that Allen's assumption that the 3 outcomes are equally likely to occur may not be accurate.
Calculate 7234 divided by 48 using the long division method
Answers
Answer: The quotient is 150 with a remainder of 34
Step-by-step explanation:
Chapter 5 Lesson 1 Adding and Subtracting Polynomials
Answers
Polynomial [tex]-4x^2y[/tex] is called a monomial of degree 3 and a polynomial [tex]3x^4 - 2x^3 - 5x^2 + 6x - 12[/tex] is a quintic polynomial.
What is a pοlynοmial?In mathematics, a pοlynοmial is an expressiοn cοnsisting οf variables (usually represented by letters), cοefficients (usually represented by numbers), and expοnents (usually represented by nοn-negative integers).
The variables and cοefficients are cοmbined using the arithmetic οperatiοns οf additiοn, subtractiοn, multiplicatiοn, and raising tο pοwer tο create terms, which are then cοmbined using additiοn and subtractiοn tο create the pοlynοmial.
1) The polynomial [tex]-4x^2y[/tex] has a degree of 3 and a single term, so it is called a monomial of degree 3.
2) The polynomial [tex]3x^4 - 2x^3 - 5x^2 + 6x - 12[/tex] has a degree of 4 and five terms, so it is called a polynomial of degree 4 and five terms, or simply a quintic polynomial.
3) The polynomial [tex]x^2 + 5x - 4[/tex] has a degree of 2 and three terms, so it is called a polynomial of degree 2 and three terms, or simply a quadratic polynomial.
To write each polynomial in standard form, we need to arrange the terms in descending order of degree. In standard form, the polynomial starts with the highest degree term and ends with the constant term, with the coefficients of the terms arranged in descending order.
4) [tex]x^3 + 3x^2 - 5x - 4[/tex]
5) [tex]-x^5 + 4x^4 + 2x^3 + 2x - 7[/tex]
6) [tex]-x^2 + 5x + 9[/tex]
To combine like terms and write each expression in standard form, we need to simplify the coefficients of each variable to obtain the sum of the like terms:
7) [tex]-5y + 3y^2 + 2y - 2y^2 - 9[/tex]
=[tex](3y^2 - 2y^2) + (-5y + 2y) - 9[/tex]
=[tex]y^2 - 3y - 9[/tex]
8) [tex]-2x^2 + x + 5x^3 + 4x + 2x^2[/tex]
= [tex]5x^3 + 3x[/tex]
9) [tex]x^2 - 5 + 2x + x^2[/tex]
= [tex]2x^2 + 2x - 5[/tex]
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For each of the following quadrilaterals, select all the properties that must be true. All sides congruent Two pairs of parallel sides Only one pair of parallel sides Four right angles (a) Trapezoid (b) Rectangle (c) Parallelogram
Answers
(a) Trapezoid: Only one pair of parallel sides
(b) Rectangle: All sides congruent, Four right angles
(c) Parallelogram: Two pairs of parallel sides
(a) Trapezoid: Only one pair of parallel sides must be true. A trapezoid is defined as a quadrilateral with at least one pair of parallel sides, but the other two sides may or may not be congruent.
(b) Rectangle: All sides congruent and Four right angles must be true. A rectangle is a special case of a parallelogram where all angles are right angles and all four sides are congruent.
(c) Parallelogram: Two pairs of parallel sides must be true. A parallelogram is defined as a quadrilateral with two pairs of parallel sides. The opposite sides are congruent and parallel, but the adjacent sides may or may not be congruent.
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Can someone help with this question fast!?!?!
Trying to get better at doing word problems like this is would help a lot.
In the summertime, the local school district tries to conserve electricity by adjusting the air conditioning temperatures. During the day the lowest the air conditioning can reach is 75° F, at night it is turned up to 92° F so the building does not reach temperatures over 92° F. Staff cannot work in the building when the temperature is above 92° F.
Write an inequality to represent the acceptable temperatures the building can reach. Describe the graph of the inequality completely.
Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent.
In July, the air conditioning broke and the temperature of the building rose to 103° F. Would the staff have been able to work in the building on this day? Why or why not?
Answers
The acceptable temperatures the building can reach can be represented by the following inequality:
75°F ≤ temperature ≤ 92°F
How to explain the inequalityThis inequality states that the temperature must be greater than or equal to 75°F, but less than or equal to 92°F. Any temperature within this range is acceptable.
To graph this inequality, we can use a number line with 75 and 92 marked as endpoints, and shade the region in between the two endpoints, including the endpoints themselves. This shaded region represents all the acceptable temperatures the building can reach, as shown below:
|-------|-------|-------|-------|-------|------> Temperature (°F)
70 75 80 85 90 95
<------ Shaded Region
In this graph, the shaded region between 75 and 92 represents all the temperatures that are acceptable for the building. Any temperature outside of this region is not acceptable and would cause the building to be too hot for staff to work in.
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Very Urgent Urgent Urgent
Answers
Answer:
Step-by-step explanation:
a False
b True
c True
d Falce
e True
f True
g False
h True
i True
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Please help with this statistics problem.A traffic light at a certain intersection is green 45% of the time, yellow 10% of the time, and red 45% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial.A.) Find P(X=3).B.) Find P(X<=3)C.) Find μX .D.) Find σ2/x .
Answers
The variance οf X is 2.716.
What is geοmetric distributiοn?The geοmetric distributiοn is a discrete prοbability distributiοn that describes the number οf independent trials required tο achieve the first success in a series οf Bernοulli trials (i.e., a sequence οf independent binary events with a fixed prοbability οf success).
In the geοmetric distributiοn, the prοbability οf success οn each trial is denοted by p, and the prοbability οf failure (i.e., nοt achieving the desired οutcοme) is denοted by q = 1 - p. The randοm variable X represents the number οf trials required tο achieve the first success, and its probability distribution can be expressed as:
P(X = k) = [tex]\mathrm{q^{(n-1)}}[/tex] × p
This is a prοblem abοut a discrete prοbability distributiοn called the geοmetric distributiοn. The prοbability οf an event οccurring οn the first trial is p, and the prοbability οf the event nοt οccurring οn the first trial is q = 1 - p. The prοbability that the event will οccur οn the nth trial is then given by:
P(X = n) = [tex]\mathrm{q^{(n-1)}}[/tex] × p
where X is the randοm variable representing the number οf trials required fοr the first οccurrence οf the event.
A.) Find P(X=3).
The car encοunters a red light fοr the first time οn the third day. Therefοre, we need tο calculate the prοbability that the car encοunters a green light οn the first twο days and a red light οn the third day:
P(X=3) = (0.45)¹ × (0.45)¹ × (0.10)¹ = 0.02025
B.) Find P(X ≤ 3)
Tο find the prοbability that the car encοunters a red light οn οr befοre the third day, we can sum the prοbabilities fοr X = 1, X = 2, and X = 3:
P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)
= 0.45 + 0.450.55 + 0.450.55^2
= 0.92775
C.) Find μX
The mean οf the geοmetric distributiοn is given by:
μX = 1/p
where p is the prοbability οf the event οccurring οn any given trial. In this case, p is the prοbability οf encοuntering a red light, which is 0.45.
μX = 1/0.45
≈ 2.22
D.) Find σ²ₓ
The variance οf the geοmetric distributiοn is given by:
σ²ₓ = q/p²
where p is the prοbability οf the event οccurring οn any given trial, and q is the prοbability οf the event nοt οccurring οn any given trial. In this case, p is the prοbability οf encοuntering a red light, which is 0.45, and q is the prοbability οf encοuntering a green οr yellοw light, which is 0.55.
σ²ₓ = 0.55/0.45²
≈ 2.716
Therefοre, the variance οf X is apprοximately 2.716.
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The Belmont race track known as “Big Sandy” is 1½ miles long. In 1973, Secretariat won the Belmont Stakes race in 2 minutes and 30 seconds. Assuming he ran on “Big Sandy”, what was his unit speed?
im doing a test in class HELP ME! :______
Answers
In response to the query, we can state that Therefore on "Big Sandy," equation Secretariat's unit speed was roughly 0.05454 miles per hour.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
Secretariat's unit speed can be calculated using the following formula:
Unit speed = distance ÷ time
We are aware that Secretariat covered a distance of 112 miles, or 12 furlongs (1 furlong equals 1/8 mile). Also, we are aware of his timing, which was 2 minutes and 30 seconds, or 150 seconds.
Hence, after entering the values, we obtain:
Unit speed equals 150 seconds over 12 furlongs.
Unit speed = 0.08 furlongs per second
This needs to be multiplied by the conversion factor of 0.681818 to get miles per hour (mph):
Furlong speed equals 0.08 furlongs per second, or 0.681818 miles per hour.
Speed in miles per hour is 0.05454
Therefore on "Big Sandy," Secretariat's unit speed was roughly 0.05454 miles per hour.
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Write the whole or mixed number as an improper fraction 18 7/10 a. 126
/10 b. 25/10 c. 197/10 d. 187/10
Answers
The mixed fraction 18 7/10 can be changed to the improper fraction 187/10. The correct answer is Option "D".
Here, The number 18 is the whole-number. The number 7 is in the numerator and the number 10 is in the denominator.
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction. Improper fraction is solved and simplified form of the mixed fraction. so, 2 1/3 is a mixed fraction 7/3 is the Improper fraction.
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Subtract
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10
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2
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−10x
2
−10x from
−
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−2x
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Answers
The final result of the subtraction is: -4 ÷ (1 - 5[tex]x^{2}[/tex])
What is Algebraic expression ?
A cοmbinatiοn οf variables and cοnstants is an algebraic expressiοn.
To subtract the expression:
(-10 ÷ (2 - 10[tex]x^{2}[/tex])) - (-2 ÷ (2 - 10[tex]x^{2}[/tex])))
we need to first simplify the denominator by factoring out a common factor of 2:
2 - 10[tex]x^{2}[/tex]= 2(1 - 5[tex]x^{2}[/tex])
Now we can write the expression as:
(-10 ÷ [2(1 - 5[tex]x^{2}[/tex])]) - (-2 ÷ [2(1 - 5[tex]x^{2}[/tex])])
which simplifies to:
(-5 ÷ [1 - 5[tex]x^{2}[/tex]]) - (-1 ÷ [1 - 5[tex]x^{2}[/tex]])
Using the fact that subtracting a negative is the same as adding a positive, we can rewrite this as:
(-5 + 1) ÷ [1 - 5[tex]x^{2}[/tex]]
which equals:
-4 ÷ [1 - 5[tex]x^{2}[/tex]]
Therefore, the final result of the subtraction is: -4 ÷(1 - 5[tex]x^{2}[/tex])
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Complete Answer:
Subtract the expression [tex]$(-10\div(2-10x^{2}))-(-2\div(2-10x^{2}))$[/tex]
On your basketball team, the starting players'
scoring averages are between 6 and 10 points
per game. Write an absolute value inequality
describing the scoring averages of the players.
Answers
The absolute value inequality describing the scoring averages of the players is -6 <= x - 5 <= 6
What is absolute value?The absolute value or modulus of a real number |0|=0}
If we remove the absolute value symbols from the following inequality
|expression| < value
then we get the following compound inequality
-value < expression < value
This is a basic property of absolute value inequalities that needs to be memorized. (If one understands absolute value to be a distance from zero on the Real number line, then this property is self-explanatory.)
Therefore, the inequality
|x - 5| <= 6
becomes the following compound inequality, once we use the property above to remove the absolute value symbols.
-6 <= x - 5 <= 6
Well, this process is reversible. I mean, once we come up with the numbers 5 and -6 and 6, and we write
-6 <= x - 5 <= 6
it's simply a matter of rewriting it using absolute value form
|x - 5| <= 6
So, now the question becomes: where did the -6, 6, and 5 come from?
Let x be a particular starter's scoring average.
Given: 4 <= x <= 10
The average of the endpoints of this given range of scoring averages is 15. I mean, the average of the lowest scoring average (4) and the highest scoring average (10).
Subtracting this average from each part in the given compound inequality above gets us to
-6 <= x - 5 <= 6
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Find the missing term of the following arithmetic sequence.
...3, , 27, ...
Answers
Answer:
We can find the common difference by subtracting the first term from the second term, or the second term from the third term:
27 - 3 = 24
So the common difference is 24.
To find the missing term, we can add the common difference to the second term:
27 + 24 = 51
Therefore, the missing term in the sequence is 51.
The complete sequence is:
3, 27, 51, ...
On July 1, Mr Taylor owed $6,000. On the first of each of the following months he repaid $400.
a) list the amount owed by Mr. Taylor on the 2nd of each month starting with July 2
b) explain why the amount owed each month forms an arithmetic sequence
Answers
a) July 2- $5600, August 2- $5200, September 2- $4800, October 2- $4400, November 2- $4000
b) The amount owed each month forms an arithmetic sequence because it decreases by the same amount ($400) each month.
For the month of July, the amount owed is
6,000 - 400(1-1) = 6,000 - 400(0) = 6,000 - 0 = $6,000.
For the month of August, the amount owed is
6,000 - 400(2-1) = 6,000 - 400(1) = 6,000 - 400 = $5,600.
For the month of September, the amount owed is
6,000 - 400(3-1) = 6,000 - 400(2) = 6,000 - 800 = $5,200.
For the month of October, the amount owed is
6,000 - 400(4-1) = 6,000 - 400(3) = 6,000 - 1,200 = $4,800.
For the month of November, the amount owed is
6,000 - 400(5-1) = 6,000 - 400(4) = 6,000 - 1,600 = $4,400.
The amount owed by Mr. Taylor on the 2nd of each month starting with July 2 is as follows: July 2- $5600, August 2- $5200, September 2- $4800, October 2- $4400, November 2- $4000. This forms an arithmetic sequence because each month the amount owed decreases by the same amount of $400.Arithmetic sequences are collections of integers where each term following the first is created by adding a predetermined constant to the term before it. In this case, the constant is $400 because each month the amount owed is decreased by $400. An arithmetic sequence can be written as a mathematical expression, with the nth term being expressed as an + d(n-1). In the case of Mr. Taylor, the initial amount (a) is $6,000 and the common difference (d) is -$400 because the amount owed decreases each month. Therefore, each month the amount owed is expressed as 6,000 - 400(n-1).
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A car travels 330km at an average speed of 110 km/h how long does it takes the car to cover the distance
Answers
Answer:
3 hours
Step-by-step explanation:
to find the time the formula is
time=distance/speed
time=330km/110km/h
(the km will cancel out as it appears it the numerator and denominator)
time=330/110h
(330/110=3)
time=3hours
When rearranged, time = distance / speed
330 / 110 = 3
3 Hours