The solutions of the equation in the interval `[0, 2π)` are `π/3` and `3π/4`.Hence, the required answer is `(π/3, 3π/4)` in comma-separated form.
Given that `cos(θ) - sin(θ) = (2/1) sin(2θ)`, find `θ`.Solution:As we have been given `cos(θ) - sin(θ) = (2/1) sin(2θ)`, we know that we can apply double angle formulae to convert `2θ` to `θ`.`sin(2θ) = 2sin(θ)cos(θ)`∴ `cos(θ) - sin(θ) = (2/1) sin(θ)cos(θ)`⇒ `2 sin(θ) cos(θ) - sin(θ) + cos(θ) = 0`⇒ `sin(θ) (2 cos(θ) - 1) - cos(θ) (2 cos(θ) - 1) = 0`⇒ `(sin(θ) - cos(θ)) (2 cos(θ) - 1) = 0`Therefore, `sin(θ) - cos(θ) = 0` or `cos(θ) = 1/2`Solving `sin(θ) - cos(θ) = 0` gives `θ = 3π/4` (Since `sin(3π/4) = 1/√2` and `cos(3π/4) = -1/√2`)Solving `cos(θ) = 1/2` gives `θ = π/3` (Since `cos(π/3) = 1/2`)Therefore, the solutions of the equation in the interval `[0, 2π)` are `π/3` and `3π/4`.Hence, the required answer is `(π/3, 3π/4)` in comma-separated form.
Learn more about Equation in the interval
brainly.com/question/13551568
#SPJ11
A cylinder has volume of 45 \displaystyle \piπ and radius 3. What is the height?
A cylinder has volume of 45 and radius 3, the height of the cylinder is 5 units.
The formula for the volume of a cylinder is given by V =
[tex]\pi r^2 h,[/tex]
where V is the volume, r is the radius, and h is the height.
In this case, we know that the volume is 45
[tex]\pi[/tex]
and the radius is 3. We can plug these values into the formula and solve for the height:
[tex]45 \pi = \pi (3)^2 h[/tex]
Simplifying the right-hand side of the equation:
Dividing both sides by 9
[tex]h = \frac{45 \pi}{9 \pi} = 5[/tex]
learn more about volume of cylinder here:
https://brainly.com/question/6204273
#SPJ4
Chapter 5 Lesson 1 Adding and Subtracting Polynomials
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]
To know more about polynomials visit:
brainly.com/question/29135551
#SPJ1
The ratio of cows to sheep on a farm is 3 to 7. There are 90 cows on the farm.
How many sheep are on the farm?
If the ratio of cows to sheep is 3:7, then there are 210 sheep on the farm if there are 90 cows.
How to calculate the number of sheep on the farm?The first step is to write out the parameters:
The ratio of cows to sheep on the farm is 3:7.There are 90 cows on the farm.Now, the number of sheep on the farm can be calculated as follows:
The next step is to divide the number of sheep by the number of cows/sheep= 3/7The next step is to multiply this fraction by 90= 7/3 × 90= 630/3= 210Hence there are 210 sheep on the farm
Read more on ratio here https:/:/brainly.com/question/29277355
#SPJ1
Counting with combinations Question A pizza place has 15 different toppings listed for its customers to choose from. How many different pizzas can be made with 5 toppings each, without repeating the toppings?
The number of different pizzas that can be made with 5 toppings each, without repeating the toppings, after counting the combinations, is 3003.
To find the number of different pizzas that can be made with 5 toppings each, without repeating the toppings, we can use the combination formula:
C(n , r) = n! / (r! * (n-r)!)
Where:
n = the total number of toppings available (15)
r = the number of toppings on each pizza (5)
So, substituting the values into the formula, we get:
C(15,5) = 15! / (5! * (15-5)!)
C(15,5) = 15! / (5! * 10!)
C(15,5) = 3003
Therefore, the number of different pizzas that can be made with 5 toppings each, without repeating the toppings is 3003.
To know more about Counting Combinations, click the link below:
https://brainly.com/question/22855614#
#SPJ11
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 .
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.
To learn more about geometric distribution from the given link
https://brainly.com/question/10164132?
#SPJ1
A school supply company is giving away free chalkboards to promote their dust-free chalk. The company can spend up to $2,500 on the chalkboards. If each chalkboard costs the company $5, how many chalkboards will they be able to give away?
Therefore , the solution of the given problem of unitary comes out to be the school supply business may distribute 500 chalkboards.
An unitary method is what?By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified in the expression will also be identified, or both crucial procedures will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.
Here,
Assuming each chalkboard costs the company $5 and they can spend up to $2,500 on the chalkboards:
Number of chalkboards Equals Total allowable spending / Chalkboard cost
=> Chalkboard count = $2,500 / $5
=> 500 chalkboards are present.
Consequently, the school supply business may distribute 500 chalkboards.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
A bridge is 440 metres long. There are four parts to the bridge. Assuming
each part is the same length, how long is each part of the bridge?
Answer:If the bridge is divided into four equal parts, then the length of each part can be found by dividing the total length of the bridge by 4. Therefore:
Length of each part = Total length of the bridge / Number of parts
Length of each part = 440 m / 4
Length of each part = 110 m
Therefore, each part of the bridge is 110 metres long.
Step-by-step explanation:
Calculate 7234 divided by 48 using the long division method
Answer: The quotient is 150 with a remainder of 34
Step-by-step explanation:
A car travels 330km at an average speed of 110 km/h how long does it takes the car to cover the distance
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
28 heart pancakes serve 20
people at the Valentine's Day
brunch. At this rate, how
many pancakes will you
probably need for a table of
5 people?
Answer:The answer is 7 pancakes, I think.
Step-by-step explanation:
28:20
?:5
Divide 28 by 20.
You get 1.4 because every person eats 1.4 .
Multiply 1.4 by 5. You give all of the five people 1.4 pancakes each.
The total will be 7 pancakes.
2 of 52 of 5 Items
10:40
Skip to resources
Question
All eighteen of Mrs. Gordon’s math students scored low on a test, so she gave them a retest.
Both tests had a median score of 78
The original test had a range of 20
The retest had a range of 2.
Which statement is true based on the given information?
Responses
A The mean score for the retest is greater than 80.The mean score for the retest is greater than 80.
B The highest score on the original test is less than 98.The highest score on the original test is less than 98.
C At least one students scored a 78 on the retest.At least one students scored a 78 on the retest.
D One of the students scored 100 on the retest.One of the students scored 100 on the retest.
Option B is the true statement based on the given information by solving the method of average.
What is average?In mathematics, the average (also called the arithmetic mean) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of values in the set.
Since both tests had a median score of 78, we know that there were nine scores below 78 and nine scores above 78 on each test.
If the original test had a range of 20, that means the highest score was 20 points above the lowest score. Therefore, the lowest score on the original test was 78 - 10 = 68, and the highest score was 68 + 20 = 88.
If the retest had a range of 2, that means the highest score was only 1 point above the lowest score. Therefore, the lowest score on the retest was 78 - 1 = 77, and the highest score was 77 + 2 = 79.
We don't know the mean score for either test, so we cannot determine if option A is true or false. We also don't know if any student scored exactly 78 on the retest, so we cannot determine if option C is true or false. Finally, we know that the highest score on the retest is 79, so option D is false.
To know more about Average visits:
https://brainly.com/question/24057012
#SPJ1
the double number line shows the relationship between the number of minutes and the number of pages that a printer prints. How many pages does the printer in
4
1
2
minutes?
Answer:
Step-by-step explanation:
Find the missing term of the following arithmetic sequence.
...3, , 27, ...
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, ...
What is 8 multiplied by 16?
Answer:
Step-by-step explanation:
128
Subtract
−
10
�
2
−
10
�
−10x
2
−10x from
−
2
�
2
−
10
�
−2x
2
−10x.
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])
Tο learn mοre about Algebraic expression from given link.
https://brainly.com/question/953809
#SPJ1
Complete Answer:
Subtract the expression [tex]$(-10\div(2-10x^{2}))-(-2\div(2-10x^{2}))$[/tex]
HELP PLS DUE IN FIVE MINS I NEED HELP STRESSING TIMES
The number of hazardous waste sites in State Y in the year 2000 was 21.
How to determine the number of Hazardous Waste SiteLet n be the number of hazardous waste sites in State Y.
Based on the problem statement, we have
2n - 8 = 34
So, we have
2n = 42
Divide
n = 21
Hence, the waste sites in State Y in the year 2000 was 21.
How to determine the solution to the equationGiven that
6x + 1.6 = 58
Apply the subtraction property
6x = 56.4
Apply the division property
x = 9.4
The equation of a bar diagram, and the solutionHere, we have the bar diagram
Adding the terms in the bar, we have
n + n + n + 8 = 53
3n + 8 = 53
Apply the subtraction property
3n = 45
Apply the division property
n = 15
Hence, the bar equation is 3n + 8 = 53
Read more about equation at
https://brainly.com/question/18831322
#SPJ1
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?
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.
Learn more about Estimated
brainly.com/question/17961193
#SPJ4
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
(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.
For more such questions on Polygon: brainly.com/question/12729233
#SPJ4
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.
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
Learn more about absolute value inequality on https://brainly.com/question/30201926
#SPJ1
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?
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.
Malik and his mom are planting vegetables in their garden. Malik has finished planting 7 rows of carrots so far and is planting new rows at a rate of 5 rows per hour. His mom has finished 10 rows of tomatoes and will continue planting at 2 rows per hour. Once they have an equal number of carrot and tomato rows, they will take a break and decide what to plant next.
a. How many hours will it take for them to plant the same number of vegetable rows? How many rows will they each have completed?
The number of hours it will take for them to plant the same number of vegetable rows is equals to one hour. Total twelve rows of vegitables they will each have completed.
We have, Malik and his mom are planting vegetables in their garden.
For Malik : he has finished planting 7 rows of carrots and his planting rate = 5 rows per hour.
For his mom : She has finished 10 rows of tomatoes and continue.
Her planting rate = 2 rows per hour.
Let they finish an equal number of carrot and tomato rows in "x hours". That is we can wright the provide information in equation form : Malik plants 5 rows of vegitable per hour, so he will plant 5x rows in x hours. Similarly, his mother will plant 2x rows of vegitables in x hours. Thus, after x hours, (Malik) 7 + 5x = 10 + 2x (mom)
Simplify the above equation,
=> 5x - 2x = 10 - 7
=> 3x = 3
=> x = 1
So, x = 1 be the hours it will take for them to plant the same number of vegetable rows. Now, total rows they will each have completed = 7 + 5×1 = 12 rows or 10 +2×1
= 12
Thus, total 12 rows they finally completed.
For more information about equation, visit :
https://brainly.com/question/18831322
#SPJ4
What is the solution to the system of equations? x=6y+24 and 2x+3y=3
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
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?
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.
Learn more about inequalities on;
https://brainly.com/question/24372553
#SPJ1
Using the side lengths of △pqr and △stu, which angle has a sine ratio of ? ∠p ∠q ∠t ∠u
The angle that has the sine ratio, 4/5, is: A. Angle P.
Sine Ratio:
The sine ratio is the ratio of the side opposite the hypotenuse of a right triangle to a given reference angle. When the ratio is found using the opposite and the hypotenuse, we call it the sine ratio rather than the tangent ratio.
Example:
Then we say that the sine of 45 degrees is equal to 0.707. In short, we can use the notation sin instead of sine and write sin(45 degrees) = 0.707
In general, the sine of angle A = leg length of opposite angle A / hypocenter
sin(A ) = opposite / hypotenuse
Given:
sine ratio of 4/5, then it means:
Opposite side (side directly opposite to the reference angle) = 4
Hypotenuse (longest side) = 5.
Thus, in the image given, using P as the reference angle, the sine ratio of P is:
QR/PQ
= 16/20 = 4/5
Therefore, the angle with the sine ratio of 4/5 is: A (P)
Complete Question:
Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?
A. P
B. Q
C. T
D. U
Learn more about Angle:
https://brainly.com/question/28451077
#SPJ4
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.
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].
To learn more about graph, visit:
https://brainly.com/question/11803331
#SPJ1
The surface area of this cube is 216 square centimeters. What is the volume?
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!
Which choices are equivalent to the expression below? Check all that apply.
√-16
A. -√16
B. i√16
C. -4
D. 4i
The answer fοr the imaginary expressiοn is 4i (οptiοn D)
What is imaginary expressiοn?Imaginary numbers are numbers that are nοt real. We knοw that the quadratic equatiοn is οf the fοrm ax² + bx + c= 0, where the discriminant is b²-4ac. In imaginary expressiοn οr number the discriminant becοmes negative οr less than 0.
Imaginary numbers are the numbers that give a negative number when squared. In οther wοrds, we can say that an imaginary number is basically the square rοοt οf a negative number which dοes nοt have a tangible value.
√-16
=√16i² [since i²= -1]
= 4i
Hence the value οf the imaginary number is 4i
To know more about imaginary number from the link.
https://brainly.com/question/13039076
#SPJ1
Answer: 4i and i√16
Step-by-step explanation: Just did it.
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
Answer:78.9
Step-by-step explanation:
78.9x 0896968
Will Luke pass the quiz? Luke's teacher has assigned each student in his class
an online quiz, which is made up of 10 multiple-choice questions with 4 options
each. Luke hasn't been paying attention in class and has to guess on each
question. However, his teacher allows each student to take the quiz three times
and will record the highest of the three scores. A passing score is 6 or more
correct out of 10. We want to perform a simulation to estimate the score that Luke
will earn on the quiz if he guesses at random on all the questions.
a. Describe how to use a random number generator to perform one trial of the
simulation
The dotplot shows Luke's simulated quiz score in 50 trials of the simulation.
Simulated quiz score
Starnes & Tabor, The Practice of Statistics, 6e, o 2018
Bedford, Freeman & Worth High School Publishers
b. Explain what the dot at 1 represents.
c. Use the results of the simulation to estimate the probability that Luke passes
the quiz
d. Doug is in the same class and claims to understand some of the material. If he
scored 8 points on the quiz, is there convincing evidence that he understands
some of the material? Explain your answer.
Simulation shows Luke's quiz score in 50 trials with a minimum passing score of 6. Probability of passing is about 0.1. Strong evidence that Luke understands some material as getting a score of 8 by guessing is highly unlikely.
Step 1: The teacher plans to give a multiple-choice test consisting of 10 questions with four answer options each. To conduct one trial of the simulation, a random number generator will be used. To pass the test, the student needs to answer at least six questions correctly. Since each question has four options, the probability of guessing the correct answer is one out of four. To simulate guessing, ten numbers will be generated between one and four, where one represents a correct answer and 2, 3, 4 represent incorrect answers.
Step 2: The dot plot provided illustrates the simulated quiz score of Luke through 50 trials. Each dot on the plot corresponds to a single trial. One dot, specifically the one located at 1, represents a simulated quiz score of one. This implies that in one of the simulation trials, Luke answered only one out of ten questions correctly.
Step 3: We must determine the likelihood of Luke passing the quiz, which contains 10 multiple-choice questions with four answer choices each, requiring a minimum of 6 correct answers to pass. In the dot plot depicting 50 trials of the simulation, the dots represent the quiz score, and 5 of the 50 trials resulted in a score of 6 or more. Thus, the probability of Luke passing the quiz is approximately 0.1 or 1/10.
Step 4: We need to determine whether there is sufficient evidence to support the claim that Doug has an understanding of some of the material.
Step 5: The dot plot displays the simulated quiz score over 50 trials when a person is guessing the answers to the questions. We can infer that it is highly improbable to obtain a quiz score of at least 8 by randomly guessing, as there are no dots above or to the right of 8 on the plot. This suggests that there is compelling evidence that the person understands some of the subject matter, as it is unlikely that they guessed correctly on all questions.
Learn more about Probability here: brainly.com/question/30034780
#SPJ4
The missing figure is in the image attached below
what is the maxuim number of possible extreme values for the function f(x)=x^4+x^3-7x^2-x+6
Answer:
The maximum number of possible extreme values for a fourth-degree polynomial function like f(x) = x^4 + x^3 - 7x^2 - x + 6 is 3.
To determine the number of extreme values, we can find the derivative of the function f(x) and set it equal to zero to solve for critical points.
f(x) = x^4 + x^3 - 7x^2 - x + 6
f'(x) = 4x^3 + 3x^2 - 14x - 1
Setting f'(x) = 0, we can solve for critical points:
4x^3 + 3x^2 - 14x - 1 = 0
Using numerical methods like the cubic formula or numerical approximation techniques, we can find that there are three real roots for this equation, which correspond to the critical points of f(x).
Since f(x) is a fourth-degree polynomial, we know that it has at most four critical points. Therefore, the maximum number of extreme values for f(x) is three, which can be achieved if the function has two local maxima and one local minimum or one local maximum and two local minima.