If the total amount given the original price and tax or tip are 123.28,7. 5%, the total amount including tax is $132.52.
To find the total amount given the original price and tax or tip, we need to add the amount of tax or tip to the original price.
In this case, the original price is $123.28 and the tax is 7.5%. To find the amount of tax, we can multiply the original price by the tax rate expressed as a decimal.
Tax = 0.075 x $123.28 = $9.24
Therefore, the amount of tax is $9.24. To find the total amount, we simply add the original price and the amount of tax:
Total amount = $123.28 + $9.24 = $132.52
Note that if the 7.5% was a tip instead of a tax, we would calculate it in the same way by multiplying the original price by the tip rate expressed as a decimal.
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ANSWER FOR BRANLIEST
Which of the following is an irrational number?
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.
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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A health expert evaluates the sleeping patterns of adults. Each week, she randomly selects 50 adults and calculates their average sleep time. Over many weeks, she finds that 5% of average sleep time is less than 9 hours and 5% of average sleep time is more than 9.4 hours.
What are the mean and standard deviation (in hours) of sleep time for the population?
The mean and standard deviation of sleep time for the population are 9.2 hours and 8.225 hours.
What does "normal distribution" mean?In statistics and probability theory, the normal distribution is a continuous probability distribution that is often utilised. Due to its distinctive form, it is sometimes referred to as the bell curve or the Gaussian distribution. Many statistical and data analysis techniques, such as confidence intervals, regression analysis, and hypothesis testing, all make use of the normal distribution. It is well recognised that many real-world occurrences, like heights, weights, and IQ scores, follow a normal distribution, making it a useful tool for data analysis and interpretation.
Given that, 5% of average sleep time is less than 9 hours.
The z-score for the lower 5% percentile is z = -1.645.
Similarly, for upper 5th percentile we have z = 1.645.
The z-score is given as:
z = (x - μ) / σ
For the lower 5th percentile:
-1.645 = (9 - μ) / σ
For the upper 5th percentile:
1.645 = (9.4 - μ) / σ
Adding the two equations we have:
-1.645σ = (9 - μ)
1.645σ = (9.4 - μ)
0 = 18.4 - 2μ
μ = 9.2 hours.
Substitute the value of μ:
1.645σ = (9.4 - 9.2)
1.645σ = 0.2
σ = 8.225
Hence, the mean and standard deviation of sleep time for the population are 9.2 hours and 8.225 hours.
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I need help with number 3 ASAP please! cos^2u- cos u sec u= cot^2 u
PLEASE I NEED HELP
Answer:
cosx
Step-by-step explanation:
using the identity
• sin² = 1 - cos²x
cos²x + cosx - 1 + sin²x
= cos²x + cosx - 1 + 1 - cos²x ← collect like terms
= cos x
What is the area of a trapezoid with base lengths 8 in and 10 in and a
height of 9 in?
Answer: 81 inches
Step-by-step explanation:
Area of a trapezoid is … Area= 1/2(b1+b2)h
So if we plug it in
Area = 1/2(8+10)9
= 1/2(18)9
= 9(9) = 81
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.
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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Estimating Proportions The quality control people at your company have tested a sample of 450 widgets and found that 23 were defective. What is your interval estimate (confidence interval) for the average proportion of defective widgets (choose your confidence level)?
At a confidence level of 95%, the interval estimate for the average proportion of defective widgets is approximately 0.020 to 0.082.
To find the confidence interval for the proportion of defective widgets, we can use the formula:
CI = p ± z*(sqrt(p*(1-p)/n))
where:
p = proportion of defective widgets in the sample
z* = the z-value for the desired confidence level
n = sample size
The z-value depends on the desired confidence level. For example, if we want a 95% confidence level, we would use a z-value of 1.96 (from the standard normal distribution table).
Plugging in the values given in the problem, we get:
p = 23/450 = 0.0511
n = 450
z* = 1.96 (for a 95% confidence level)
sqrt(p*(1-p)/n) = sqrt(0.0511*(1-0.0511)/450) ≈ 0.016
Therefore, the 95% confidence interval for the proportion of defective widgets is:
CI = 0.0511 ± 1.96*0.016
= (0.020, 0.082)
This means we are 95% confident that the true proportion of defective widgets in the population is between 0.020 and 0.082.
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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%
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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$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.
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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How do I get full marks on this question?
Therefore , the solution of the given problem of triangle comes out to be y + y√2 and y - y√2. are the two possible numbers for x.
A triangle is exactly what?If a polygon has at least one additional segment, it is a hexagon. Its form is a straightforward rectangle. Something like this can only be distinguished from a regular triangular by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
Due to the similarity of the two triangles in the diagram, we can create an equation and solve for x using the ratios of respective sides.
Assuming that the line segment's length is x, we can construct the following equation:
=> (2x + y) / x = x / y
=> (2x + y) y = x²
=> 2xy + y² = x²
=> x² - 2xy - y² = 0
This quadratic equation in x has the coefficients a = 1, b = -2y, and c = -y2 in it. The quadratic algorithm yields:
=> x = [2y ± √((2y)² - 4(1)(-y²))] / 2(1)
=> x = [2y ± √(4y² + 4y²)] / 2
=> x = [y ± y√2]
Therefore, y + y√2 and y - y√2. are the two possible numbers for x.
The two triangles in the illustration are thought to be comparable.
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Classify the quadrilateral. Justify
your reasoning
Answer:
The quadrilateral is a square. A quadrilateral is a polygon with four sides. There are many types of quadrilaterals such as parallelogram and rhombuses. A rhombus is a parallelogram with four congruent sides. The plural of a rhombus is rhombi. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. A square is a rhombus becasue it has 4 congruent sides and angles
Step-by-step explanation:
Hope this helps!!
In circle K with
m
∠
J
K
L
=
60
m∠JKL=60 and
J
K
=
17
JK=17 units find area of sector JKL. Round to the nearest hundredth.
Answer:
KL=43
Step-by-step explanation:
JKL=60, jk=17, KL=43
B) Which other two triangles (from A, B, C and D) are congruent to each other? Please help!
A) by mere observation, the triangles from A, B, C, and D that is congruent or similar to Triangle E is Triangle C.
B) The other two triangles that are congruent to each other are Triangles A and B.
What does it mean for two triangles to be congruent?Two triangles are considered congruent if they have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal.
In other words, if you were to superimpose one triangle onto the other, they would match up perfectly. The concept of congruence is important in geometry, as it allows us to make precise statements about the relationship between different figures and their properties.
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Full Question:
See the attached image.
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
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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what is the answer I am stumped
Answer: Repost this with the question (not just the graph) attached.
Step-by-step explanation: Please attach the question, otherwise I cannot help you:)
A system of two linear equations has no solution. The first equation is -7x + y = 3. select the second equation that will make this system have no solution.
A. 3x+y=3
B. -7x+y=-10
C. 3x+y=-7
D. 4x+y=3
Answer:
It's B.
Step-by-step explanation:
To make the given system of linear equations have no solution, we need the second equation to be inconsistent with the first equation. This means that the two equations must be parallel lines, and they cannot intersect at any point.
We can see that the first equation -7x + y = 3 has a slope of 7, since it can be written in slope-intercept form as y = 7x + 3. Therefore, to create a parallel line with the same slope of 7, we can choose the second equation to be:
B. -7x + y = -10
This equation has the same slope of 7 as the first equation, but it intersects the y-axis at a different point (-10 instead of 3). Therefore, the two lines are parallel and do not intersect, so the system of equations has no solution
Hope this helps you! I'm sorry if it doesn't. If you need more help, ask me! :]
Describe in practical terms the meanings of f^(-1)(0.7), f^(-1)(0.5),f^(-1)(0.2)
In practical terms, the meanings of f^(-1)(0.7), f^(-1)(0.5),f^(-1)(0.2) are as follows:f^(-1)(0.7): This means the value of x for which f(x) = 0.7. Here, f^-1 is the inverse function of f. It returns the value of the input x for which the output of the function is 0.7. In other words, if y = f(x), then f^(-1)(y) = x. Hence, f^(-1)(0.7) means the input value of x for which the function returns 0.7 as the output.f^(-1)(0.5): This means the value of x for which f(x) = 0.5. Similarly, the inverse of the function f, f^-1, returns the value of the input x for which the output of the function is 0.5.f^(-1)(0.2): This means the value of x for which f(x) = 0.2. Here, f^-1 is the inverse function of f. It returns the value of the input x for which the output of the function is 0.2. Hence, f^(-1)(0.2) means the input value of x for which the function returns 0.2 as the output.
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Very Urgent Urgent Urgent
Answer:
Step-by-step explanation:
a False
b True
c True
d Falce
e True
f True
g False
h True
i True
j False
k True
l True
The diagram shows a triangle.
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.
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
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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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! :______
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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a plane flying horizontally at an altitude of 1 mile and a speed of 580 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station. (round your answer to the nearest whole number.)
The rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station is 656 mi/h (rounded to the nearest whole number).
To solve this problem, we can use the equation
rate = distance/time.
We know the distance and the time, so we can calculate the rate:
rate = 5 mi/ 1 hour
= 5 mi/3600 sec
= 5/3600 mi/sec
= 0.00138889 mi/sec.
Multiplying this by 3600 to convert it to mi/h gives us 656 mi/h.
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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?
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:
pls help with my Algebra 2
Answer: second graph,and upper curve is right answer .
Step-by-step explanation: just put X= 0,1,2,..
and you get Y. and those are the dots which you have to see that are on that graph.
Malik measured the middle school and made a scale drawing. He used the scale 8 inches = 6 feet. What is the scale factor of the drawing?
Therefore, the scale factor of the drawing is 4/3.
What is scale factor?In mathematics, the scale factor is the ratio between two corresponding measurements in different scales. It is a measure of how much a figure or object has been scaled up or down, compared to its original size. The scale factor is often used in geometry and is particularly useful when creating scale drawings or models. A scale drawing is a drawing that is proportional to the actual size of the object it represents, but is scaled down or up by a certain factor to fit on a piece of paper or to make it easier to work with. The scale factor is used to determine the relationship between the measurements of the original object and the measurements of the scaled-down or scaled-up version.
Here,
To find the scale factor of the drawing, we need to determine the ratio of the length in the drawing to the actual length.
Here, the scale is given as 8 inches = 6 feet. This means that every 8 inches in the drawing represents 6 feet in real life.
To find the ratio of the length in the drawing to the actual length, we can set up a proportion:
8 inches / 6 feet = x inches / y feet
where x is the length in the drawing that corresponds to a length of y feet in real life.
To solve for x, we can cross-multiply and simplify:
8 inches * y feet = 6 feet * x inches
8y = 6x
x = (8/6) y
x = (4/3) y
This means that the length in the drawing is (4/3) times the length in real life.
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The question is in the image below
I am stuck on Part 2, and where it says 2 that's all I got
Grade 8
The equation has no solution as 10 + x ≠ 5 + x
When the value of x is 2, the equation also have no solution as 12 ≠ 7
What are algebraic expressions?Algebraic expressions are simply defined as expressions that are composed of terms, variables, constants, factors and coefficients.
These algebraic expressions are expressions that are identified with arithmetic operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFrom the information given, we have;
6 + x + 4 = 2 + x + 3
collect the like terms, we have
10 + x = 5 + x
But we know that 5 is not equal to x and thus, the equation has no solution
Now, let's substitute the value of x as 2, we have;
10 + 2 = 5 + 2
This gives;
12 = 7
This is not true and thus, the equation has no solution
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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)
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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Let X be a normal random variable with mean 209 units and standard deviation 7 units. Answer the following questions, rounding your answers to two decimal places.(a) What is the probability that X will be less than 201 units, P(X<201)?(b) What is the probability that X will be within 8units of the mean?(c) The probability is 0.04 that X will be more than how many units?
196.75 units
Answer:(a) P(X < 201) = 0.0099(b) P(201 < X < 217) = 0.9544(c) P(X > 227.12) = 0.04Explanation:Given that, X be a normal random variable with mean 209 units and standard deviation 7 units.We need to find the following.(a) P(X < 201)(b) P(201 < X < 217)(c) P(X > x) = 0.04.(a) We know that,When X is a normally distributed variable with mean μ and standard deviation σ,thenZ = (X - μ) / σ is a standard normal variable.Then,P(X < 201) = P(Z < (201 - 209) / 7)= P(Z < -1.14)Using the z-tables, the probability is 0.0099.(b) We need to find the probability that X will be within 8 units of the mean. Therefore,X will be within 8 units of the mean, if 201 < X < 217.Therefore,P(201 < X < 217) = P((X - μ)/σ) < (217 - 209)/7) - P((X - μ)/σ) < (201 - 209)/7)= P(0.57 < Z < -0.57)Using z-tables, P(0.57 < Z < -0.57) = 0.9544(c) We need to find the value of X such that P(X > x) = 0.04.Then,P(Z > (X - μ)/σ) = 0.04P(Z < -1.75) = 0.04Using z-tables, P(Z < -1.75) = 0.04By using the standard normal distribution tables, the value of -1.75 corresponds to 0.0401.Therefore,-1.75 = (X - 209)/7-12.25 = X - 209X = 209 - 12.25X = 196.75Therefore, the probability is 0.04 that X will be more than 196.75 units.
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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?
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
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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