Following shows (sin 7x)/sin x = 64(cos x)^6 - 80(cos x)^4 +24(cos x)^2 - 1:
12sin^3 x - 8sin^
To show that (sin 7x)/sin x is equal to 64(cos x)^6 - 80(cos x)^4 + 24(cos x)^2 - 1, we can use trigonometric identities and algebraic manipulation.
Let's start with the left-hand side of the equation:
(sin 7x)/sin x
Using the trigonometric identity for sin(A + B):
sin(A + B) = sin A cos B + cos A sin B
We can rewrite sin 7x as sin (6x + x):
sin (6x + x) = sin 6x cos x + cos 6x sin x
Now we can substitute sin 7x with sin 6x cos x + cos 6x sin x:
(sin 6x cos x + cos 6x sin x)/sin x
Next, we can simplify this expression by dividing both terms by sin x:
(sin 6x cos x)/sin x + (cos 6x sin x)/sin x
The sin x term cancels out, leaving us with:
sin 6x cos x + cos 6x
Now, we can use the double-angle identity for sin 2A:
sin 2A = 2sin A cos A
To rewrite sin 6x cos x, we can treat it as sin 2A with A = 3x:
sin 6x cos x = 2sin 3x cos 3x
Next, we can use the triple-angle identity for sin 3A:
sin 3A = 3sin A - 4sin^3 A
To rewrite sin 3x, we can treat it as sin A with A = x:
sin 3x = 3sin x - 4sin^3 x
Substituting this into our expression:
2sin 3x cos 3x = 2(3sin x - 4sin^3 x) cos 3x
Expanding further:
= 6sin x cos 3x - 8sin^3 x cos 3x
Now, we can use the double-angle identity for cos 2A:
cos 2A = cos^2 A - sin^2 A
To rewrite cos 3x, we can treat it as cos A with A = x:
cos 3x = cos^2 x - sin^2 x
Substituting this into our expression:
6sin x cos 3x - 8sin^3 x cos 3x = 6sin x (cos^2 x - sin^2 x) - 8sin^3 x (cos^2 x - sin^2 x)
Expanding further:
= 6sin x cos^2 x - 6sin x sin^2 x - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
Now, we can use the Pythagorean identity for sin^2 x + cos^2 x:
sin^2 x + cos^2 x = 1
To rewrite sin^2 x, we can subtract cos^2 x from both sides:
sin^2 x = 1 - cos^2 x
Substituting this back into our expression:
= 6sin x (cos^2 x - (1 - sin^2 x)) - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
= 6sin x (2sin^2 x) - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
= 12sin^3 x - 8sin^
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Los lados de un triangulo miden, en cm, tres numeros enteros consecutivos. Encuentra la longitud de los tres lados
There are infinitely many possible solutions for the lengths of the three sides of the triangle.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
If we call x the length of the smallest side, then the other two sides are x+1 and x+2 (since they are three consecutive integers). According to the triangle inequality, the sum of any pair of sides must be greater than the length of the third side.
Therefore, we have:
x + (x+1) > (x+2) (and also x + (x+2) > (x+1) and (x+1) + (x+2) > x)
Simplifying each inequality, we get:
2x + 1 > x + 2 (and also 2x + 2 > x + 1 and 2x + 3 > x)
Which gives:
x > 1
So the smallest side must be greater than 1 cm.
Now, to find the length of the three sides, we can choose any value greater than 1 for x. For example, if we take x=2, then the three sides are:
2 cm, 3 cm, and 4 cm
If we take x=3, then the three sides are:
3 cm, 4 cm, and 5 cm
And so on. Therefore, there are infinitely many possible solutions for the lengths of the three sides of the triangle.
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Find the interquartile range (IQR) for the data. 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22
The interquartile range for the data 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22 is 14.
How to find the interquartile range (IQR)?1. Arrange the data in ascending order (order the data set from smallest to largest): 2, 3, 4, 4, 5, 6, 7, 8, 12, 16, 17, 18, 18, 20, 22
2. Determine the median (Q2):
The IQR is a measure of variability that represents the range of the middle 50% of the data. To find it, we need to first calculate the median of the entire data set. Since we have an even number of data points, we take the average of the two middle values:
Median = (8 + 12) / 2 = 10
Next, we need to find the median of the lower half of the data set (also called the first quartile, or Q1). To do this, we take the median of the values below the overall median:
Q1 = (4 + 4) / 2 = 4
Finally, we find the median of the upper half of the data set (also called the third quartile, or Q3). To do this, we take the median of the values above the overall median:
Q3 = (18 + 18) / 2 = 18
3. Find the lower quartile (Q1):
The lower half of the data has 7 points, so the median of the lower half is Q1. Q1 is the 4th value, which is 4.
4. Find the upper quartile (Q3):
The upper half of the data also has 7 points, so the median of the upper half is Q3. Q3 is the 12th value, which is 18.
5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1
= 18 - 4
= 14.
The interquartile range (IQR) for the given data is 14.
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You spin the spinner, flip a coin, then spin the spinner again. Find the probability of not spinning a 5. Flipping tails, then spinning a 5. Write your answer as a traction in simplest form
The probability of not spinning 5 is 81/200.
What is the probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: You spin the spinner, flip a coin, then spin the spinner again.
We have to find the probability of not spinning a 5. Flipping tails, then spinning a 5.
P(not spinning a 5) = 9/10
P(heads)= 1/2 because there is an equal chance to get heads or tails
P(not spinning a 5)= same as before, 9/10 (independent events).
= [tex]\frac{9}{10}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{10}[/tex]
= [tex]\frac{81}{200}[/tex]
Hence, the probability of not spinning 5 is 81/200.
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Please Help. All I have been getting is bot answers, and I actually need help with this. Thanks.
1. Two neighbors are each hosting a party. The first neighbor orders 5 large pizzas, each with a diameter of 16 inches. The second neighbor orders 9 small pizzas, each with a diameter of 12 inches. In terms of area, which party has more pizza? Explain. Show all work.
2. A toy train set has a circular track piece. The inner radius of the piece is 6 cm. One sector of the track has an arc length of 33 cm on the inside and 55 cm on the outside. What is the width of the track?
1. The second party has more pizza in terms of area
2. The width of the track is approximately 3.50 cm.
How to find which party has more pizza?1. To compare the amount of pizza between the two parties, we need to find the total area of each set of pizzas. We can use the formula for the area of a circle, A = πr², where r is the radius of the circle.
For the large pizzas, the diameter is 16 inches, so the radius is 8 inches. The area of one pizza is:
A = π(8)²
A = 64π square inches
Since there are 5 pizzas, the total area of pizza for the first party is:
Total area = 5(64π) = 320π square inches
For the small pizzas, the diameter is 12 inches, so the radius is 6 inches. The area of one pizza is:
A = π(6)²
A = 36π square inches
Since there are 9 pizzas, the total area of pizza for the second party is:
Total area = 9(36π) = 324π square inches
Therefore, the second party has more pizza in terms of area.
How to find width of the track?2. We can start by finding the length of the arc of the sector. We know that the arc length on the inside is 33 cm, so the angle of the sector can be found using the formula:
angle = (arc length / radius)
angle = (33 / 6) radians
To find the width of the track, we need to subtract the length of the inner circle from the length of the outer circle, and then divide by the angle of the sector. Let's call the width of the track "x". Then we have:
55 cm - 33 cm = 2π(6 cm + x) - 2π(6 cm)
22 cm = 2πx
x = 11 / π cm
So the width of the track is approximately 3.50 cm.
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Tamekia and Marsha mow lawns during the summer to earn money. Tamekia determined that she can earn between $6. 00 and $6. 25 per hour. Marsha estimates that she earns between $7. 50 and $8. 00 per hour. About how much more money will Marsha earn than Tamekia if they each work 22 hours?
If they each work 22 hours, Marsha will earn about $35.75 more than Tamekia.
To compare how much more money Marsha will earn than Tamekia, we can use the averages of their respective hourly rates and then multiply by the number of hours worked.
Tamekia's average hourly rate: ($6.00 + $6.25) / 2 = $6.125
Marsha's average hourly rate: ($7.50 + $8.00) / 2 = $7.75
Now, we'll multiply their average hourly rates by the number of hours worked, which is 22 hours.
Tamekia's total earnings: $6.125 x 22 = $134.75
Marsha's total earnings: $7.75 x 22 = $170.50
Finally, we'll subtract Tamekia's earnings from Marsha's earnings to find the difference:
$170.50 - $134.75 = $35.75
So, Marsha will earn about $35.75 more than Tamekia if they each work 22 hours.
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Marsha will earn $38.50 more than Tamekia if they each work 22 hours.
Toad and Toadette just had their first little toadstool! Toad's family is known to be purebred dominant for red spots on their white cap. Everyone was shocked when Little Toad was born with a white cap with white spots instead of red. Toadette is very upset as she thinks the Mushroom Kingdom Hospital accidentally switched babies. Is this true? Did the hospital really switch babies? Choose either "yes" or "no" and defend your answer.
No, it is not necessarily true that the hospital switched babies.
What happened there?Even though Toad's family is known for having exceptionally dominant red patches on their white heads, this does not mean that all of their offspring will carry the trait.
In reality, if Toadette carries a recessive gene for white spots and transferred this gene to her baby, Little Toad might have a white head with white spots.
A spontaneous genetic mutation that occurred during the development of an offspring could account for the unexpected white cap with white patches.
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Construct angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm. ii, Construct M the midpoint of XZ where XYZ= 60o. iii, Measure YM.
i) The angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm is constructed.
ii) M the midpoint of XZ where XYZ= 60 is constructed.
iii) The measure of YM is 6.3 cm
Firstly, you are asked to construct an angle XYZ where XY= 8.3 cm and YZ= 11.9 cm. To construct an angle, we need to follow a few steps.
Draw a line segment XY of length 8.3 cm.
At point Y, draw a ray YZ extending in the direction of Z.
Using a compass, draw an arc of radius 11.9 cm from point Y, intersecting the ray YZ at point Z.
The angle XYZ is the angle formed by the line segments XY and YZ.
Now, you need to construct the midpoint M of XZ. The midpoint of a line segment is the point that divides it into two equal parts. To construct the midpoint, we follow these steps:
Draw a line segment XZ joining points X and Z.
Using a compass, draw an arc of radius greater than half of XZ from point X.
Using the same radius, draw another arc from point Z intersecting the first arc at point P.
Draw a line through points X and P, and another line through points Z and P. These two lines will intersect at the midpoint M of line segment XZ.
Finally, you are asked to measure angle YM. To measure an angle, we use a protractor.
Draw a line segment YM.
Place the protractor at point Y with the base line of the protractor aligned with line segment YZ.
Read the angle measurement where line segment YM intersects the protractor.
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The number line shows all of the possible values of m.
-2 -1 0 1 2 3 4 5 6
Create an inequality that represents all of the possible values of m.
The inequality that represent all the possible value shown in the number line for the m is -2 ≤ m ≤ 6 where m is an integer
The possible values on the number line is -2,-1,0,1,2,3,4,5,6
All the values are integers so the possible inequality can be formed is in which the value of m can be greater than or equal to -2 and less than equal to 6.
Inequalities are the mathematical expressions in which both sides are not equal it tells the relation between two values.
It can be represented the form
-2 ≤ m ≤ 6 where m is an integer
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The given question is incomplete complete question is :
The number line shows all the values passible values of m.
create an in equality that represents all the possible value of m.
Pls help now with algebra 2 picture provided
The inverse function of f(x) = ∛(8x) + 4 is f^-1(x) = 1/8(y - 4)^3
Calculating the inverse function of f(x) = ∛(8x) + 4To find the inverse function of f(x), we need to solve for x in terms of f(x).
To find the inverse function of f(x) = ∛(8x) + 4, we can follow these steps:
Step 1: Replace f(x) with y:
y = ∛(8x) + 4
Step 2: Solve for x in terms of y:
y - 4 = ∛(8x)
Cube both sides:
(y - 4)^3 = 8x
x = 1/8(y - 4)^3
Step 3: Replace x with f^-1(x):
f^-1(x) = 1/8(y - 4)^3
Therefore, the inverse function of f(x) is f^-1(x) = 1/8(y - 4)^3
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In circle N with \text{m} \angle MQP= 44^{\circ}m∠MQP=44 ∘ , find the angle measure of minor arc \stackrel{\Large \frown}{MP}. MP ⌢. M P N Q
In a circle with a 44 degree central angle, the minor arc MPQ's angle measure is 316 degrees.
We must first get the measure of the central angle MNQ that intercepts this arc in order to determine the measure of the minor arc MPQ. Because minor arc MPQ and minor arc MP are next to each other, their sum equals the minor arc MPNQ's measure.
MPNQ = MPQ + arc MP
If we substitute 44 degrees for the minor arc's measurement (MP), we obtain,
∠MPQ + 44 = 360
When we solve for MPQ, we obtain, ∠MPQ = 360 - 44
MPQ equals 316 degrees. As a result, 316 degrees is the minor arc MPQ's measure.
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Help with problem in photo
Check the picture below.
Solve for "B" I tried it the way I solved the rest of the equations but I can't get it
Answer:b=30
Step-by-step explanation:
Alternate angles are the same so the angle opposite 30=125
125+30=155.but angles on a straight line=180
So we subtract 180-155 which leaves us with 25 for the top angle in the triangle.Angles in a triangle must add to 180 so we do, 125+25=150
180-150=30
The dive tank managers at seaside scuba center try to keep their recreational scuba tanks filled with air at a pressure of approximately 3,000 pounds per square inch (psi). the maximum acceptable pressure for a tank is 3,300\psi , and the minimum acceptable pressure is 2,600 psi. which inequality expresses the complete range of acceptable pressures, p, in psi, for the scuba tanks?
The complete range of acceptable pressures, p, for the scuba tanks is 2,600 psi ≤ p ≤ 3,300 psi to ensure safe and enjoyable diving experiences.
Maintaining the correct pressure in scuba tanks is critical for safe and enjoyable diving experiences. If the pressure is too low, the diver may not have enough air to complete the dive and may be at risk of running out of air.
If the pressure is too high, the tank could rupture or explode, posing a significant danger to the diver. It is essential to keep the pressure within the acceptable range of 2,600 psi to 3,300 psi.
This means that the pressure of the scuba tanks must be greater than or equal to 2,600 psi and less than or equal to 3,300 psi.The inequality that expresses the complete range of acceptable pressures, p, in psi, for the scuba tanks is 2,600 psi ≤ p ≤ 3,300 psi.
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Mr. Vara is designing post caps in the shape of a square pyramid for a fence that he just built in his backyard. The caps are solid wood and each one has a volume of 94. 5 cubic centimeters
The height of the wooden post cap is approximately 11.34 centimeters.
To find the height of the wooden post cap, we need to use the formula for the volume of a square pyramid which is V = (1/3) Bh, where B is the area of the base and h is the height. Since we know that each post cap has a volume of 94.5 cubic centimeters, we can plug this into the formula to get:
94.5 = (1/3) B h
We also know that the base of the pyramid is a square, so the area of the base is equal to s², where s is the length of one side. Since we don't know the length of the side or the height of the pyramid, we need to use another piece of information. Let's assume that the fence posts are all the same height and that the caps fit snugly on top of them. If we measure the height of the fence post, we can use this to find the height of the cap.
Let's say that the height of the fence post is 10 centimeters. We can use this to find the area of the base:
B = s² = (10/2)² = 25 square centimeters
Now we can plug this into the formula:
94.5 = (1/3) (25) h
Simplifying this equation, we get:
h = (94.5 * 3) / 25 = 11.34 centimeters
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3 square root y to the second power
The expression for the given statement is √3².
We have,
The expression that can be written from the statement.
3 square root = √3
Second power of x = x²
Now,
We can write the expression as,
= √3²
Thus,
The expression for the given statement is √3².
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
On the first day it was posted online, a music video got 1880 views. The number of views that the video got each day increased by 25% per day. How many total views did the video get over the course of the first 16 days, to the nearest whole number?
Answer:
The answer to your problem is, 259,644
Step-by-step explanation:
an = 1880 ( it 25% [tex])^{t}[/tex]
= 1880 x (1.25[tex])^{t}[/tex]
ai = 1880, r will equal 1.25
Sn = [tex]\frac{aill-r^{4} }{l = r}[/tex]
[tex]S_{16}[/tex] = [tex]\frac{1880(l-1.25^{16}) }{l - 1.25}[/tex]
= 259,644
Thus the answer to your problem is, 259,644
how many minutes are required for 175 gpm to pass the entire 1500-foot length of a 12-inch diameter pipeline
To calculate the time required for 175 gallons per minute (gpm) to pass through a 1500-foot length of a pipeline with a 12-inch diameter, we can follow these steps:
Convert the diameter from inches to feet:
12 inches = 12/12 = 1 foot
Calculate the cross-sectional area of the pipeline using the formula for the area of a circle:
Area = π *[tex](radius)^2[/tex]
Radius = diameter/2 = 1/2 = 0.5 feet
Area = π *[tex](0.5)^2[/tex] = 0.785 square feet
Convert the flow rate from gallons per minute (gpm) to gallons per second (gps):
175 gpm = 175/60 gps
Calculate the velocity of the flow using the formula:
Velocity = Flow rate / Cross-sectional area
Velocity = (175/60) / 0.785 = 3.56 feet per second (rounded to two decimal places)
Calculate the time required to pass the entire 1500-foot length of the pipeline using the formula:
Time = Distance / Velocity
Time = 1500 / 3.56 = 421.35 seconds (rounded to two decimal places)
Convert the time from seconds to minutes:
421.35 seconds = 421.35/60 minutes = 7.02 minutes (rounded to two decimal places)
So, it would take approximately 7.02 minutes for a flow rate of 175 gpm to pass through the entire 1500-foot length of a 12-inch diameter pipeline.
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At appliance store, 37% of customers purchase a wahing machine. 11 % of customers buy both a wahsing machine. 11% of customers buy both waher and a dryer. Find the probability that a customer who buys a washer also buys a dryer
The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.
To find the probability that a customer who buys a washer also buys a dryer, we need to use conditional probability.
Let's start by finding the probability of a customer buying a washer and a dryer, which is given as 11%.
Now, we know that 11% of customers buy both a washer and a dryer. We also know that 37% of customers buy a washer.
Using these two pieces of information, we can find the probability of a customer buying a dryer given that they have already bought a washer. This is the conditional probability we are looking for.
The formula for conditional probability is:
P(D | W) = P(D and W) / P(W)
where P(D | W) is the probability of buying a dryer given that a washer has already been purchased, P(D and W) is the probability of buying both a dryer and a washer, and P(W) is the probability of buying a washer.
Substituting the values we have:
P(D | W) = 0.11 / 0.37
P(D | W) = 0.297
The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.
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A man borrows birra 800 for 2 years at a simple interest rate of 20 percent. What's the total amount that nyatta be repaid
The man needs to repay a total of 1120 birra after 2 years.
To calculate the total amount to be repaid, we need to find the simple interest first.
The formula for simple interest is:
Simple Interest = (Principal Amount) x (Interest Rate) x (Time Period)
Here, the principal amount is 800 birra, the interest rate is 20% (or 0.20 as a decimal), and the time period is 2 years.
Plugging these values into the formula:
Simple Interest = (800) x (0.20) x (2) = 320 birra
Now, to find the total amount to be repaid, we add the simple interest to the principal amount:
Total Amount = Principal Amount + Simple Interest = 800 + 320 = 1120 birra
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To find the quotient of 4. 082 and 10,000, move the decimal point in 4. 082
Choose.
places to the
Choose.
The Quotient of 4.082 and 10,000 is 0.0004082.
Find the qoutient of 4. 082 and 10,000?
To find the quotient of 4.082 and 10,000, we need to move the decimal point in 4.082 four places to the left, since there are four zeros in 10,000.
So, we get:
4.082 ÷ 10,000 = 0.0004082 is the answer.
Explanation.
To find the quotient of 4.082 and 10,000, we need to divide 4.082 by 10,000. When we divide by a number that is a power of 10, we can simplify the calculation by moving the decimal point to the left as many places as there are zeros in the divisor.
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What is the length of the segment indicated by the question mark
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4[/tex]
In 2012, gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that random samples of 100 respondents were selected from both vermont and hawaii. From the survey, vermont had 65. 3% who said yes and hawaii had 62. 2% who said yes. What is the value of the sample proportion of people from vermont who exercised for at least 30 minutes a day 3 days a week?
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653 or 65.3%.
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week can be calculated as follows:
sample proportion = number of people who exercised / total number of people sampled
From the information given, we know that a random sample of 100 respondents was selected from Vermont, and 65.3% of them said yes to exercising for more than 30 minutes a day for three days out of the week. Therefore:
number of people who exercised in Vermont = 65.3% of 100 = 0.653 x 100 = 65.3
So the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is:
sample proportion = 65.3 / 100 = 0.653
Therefore, the value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653 or 65.3%.
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25 points! if 1000 raffle ticket are sold for $1 each and there are ten $20, five $50, and one $100 prize, what is the expected value of a ticket?
The expected value of a ticket in this raffle is $12.50.
We have to given that;
1000 raffle ticket are sold for $1 each and there are ten $20, five $50, and one $100 prize.
Now, For the expected value of a ticket, we need to multiply the probability of winning each prize by the amount of each prize, and then add up those values.
Hence, In this case, there are a total of 16 prizes as,
⇒ (10 $20 prizes, 5 $50 prizes, and 1 $100 prize),
Thus, the probability of winning any one prize is,
⇒ 1/16
So, the expected value of a ticket would be:
= (10/16) $20 + (5/16) $50 + (1/16) x $100
= $12.50
Therefore, the expected value of a ticket in this raffle is $12.50.
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The volume of a pyramid is 51 cubic centimeters. The area of the base is 17 square centimeters What is its height?
Given hjk and rst what is tan (r)
12/13
5/12
12/5
5/13
The expression simplifies to sin(r)/cos(r) because of the trigonometric identity for the tangent function.
How can simplify the given expression?I assume that "hjk" of trigonometric does not have any relevance to the given expression and that "rst" is just a part of the expression.
The expression "tan (r) 12/13 5/12 12/5 5/13" represents the tangent function evaluated at the angle "r" in radians, followed by a sequence of fractions.
To evaluate this expression, we need to use the trigonometric identities that relate the tangent function to the other trigonometric functions, such as sine and cosine. Specifically, we can use the following identity:
tan(r) = sin(r) / cos(r)
We can use this identity to write the expression as:
sin(r) / cos(r) * 12/13 * 5/12 * 12/5 * 5/13
Next, we can simplify the expression by canceling out common factors in the numerators and denominators. For example, we can simplify 12/13 * 13/12 to 1 and 5/13 * 13/5 to 1. After simplification, the expression becomes:
sin(r) / cos(r) * 1 * 1 * 1 * 1
Simplifying further, we get:
sin(r) / cos(r)
Therefore, the expression "tan (r) 12/13 5/12 12/5 5/13" simplifies to "sin(r) / cos(r)".
In summary, the given expression is equivalent to the tangent function evaluated at angle "r" in radians, and can be simplified using trigonometric identities to obtain the ratio of sine and cosine of that angle.
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Sheila is an agriscientist shopping in a grocery store. In the produce section, she
picks several apples, a couple lemons, a large tomato, and a cucumber. From a
biological perspective, which of these produce items would Sheila MOST likely
classify as a fruit?
the apples and lemons
the apples, lemons, and cucumber
the lemons and tomato
all of the produce items
The cucumber is also considered a vegetable due to its culinary usage in salads and savory dishes.
What are vegetables?Vegetables are edible plants that are commonly used as a food source. They are a primary source of vitamins, minerals, fiber, and other nutrients that are important for maintaining good health.
From a biological perspective, Sheila would most likely classify the apples and lemons as fruits. In botanical terms, fruits are the mature ovary of a flowering plant, containing seeds. Both apples and lemons contain seeds and develop from the ovary of a flower, so they are classified as fruits. The tomato and cucumber, on the other hand, are classified as vegetables.
While the tomato also develops from the ovary of a flower and contains seeds, it is considered a vegetable in culinary terms due to its savory flavor and common usage in savory dishes.
Therefore, The cucumber is also considered a vegetable due to its culinary usage in salads and savory dishes.
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A. y=sin(x+ TT/2)
C. y = sin x
Find the equation.
NEL
2
B. y=sin(x + TT)
D. y=sin(x-TT/2)
The sine function graphed is defined as follows:
C. y = sin(x).
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(Bx).
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.(as the function crosses it's midline at the origin, it has no phase shift).
The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:
2A = 2
A = 1.
The period is of 2π/3 units, hence the coefficient B is given as follows:
B = 3.
Then the equation is:
y = sin(3x).
Meaning that option C is the correct option for this problem.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Use the order of operations to find the value of the expression. 12 ÷ 2 × 3 − ( 7 − 5 ) a. 0 b. 6 c. 16 d. 19
Answer:
Step-by-step explanation:
12 ÷ 2 × 3 − ( 7 − 5 )
= 6 × 3 - 2 (since 7 - 5 = 2)
= 18 - 2
= 16
Answer is C
The value of the expression is 16.
What is the value of the expression 12 ÷ 2 × 3 − (7 − 5) using the order of operations?The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), is a set of rules used to determine the sequence in which calculations are performed.
In this case, we start with the parentheses first: 7 - 5 = 2. Then, we perform multiplication and division from left to right: 12 ÷ 2 = 6, 6 × 3 = 18. we subtract the result of the parentheses: 18 - 2 = 16. Therefore, the answer is c. 16.
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4) what is the perimeter of the
trapezoid in simplest radical form?
helpp
The perimeter of the trapezoid in simplest radical form is 2(1 + 5√6).
The perimeter of the trapezoid = sum of sides
We know that 54 = 2 × 3 × 3 × 3
= 2 × 3³
24 = 2 × 2 × 2 × 3
= 2³ × 3
Perimeter = 2 + √54 + √54 + 2√24
= 2 + 2√54 + 2√24
= 2 + 2√(2 × 3³) + 2√(2³ × 3)
= 2 + 2 × 3√(2×3) + 2 × 2√(2 × 3)
= 2 + 6√(6) + 4√(6)
= 2 + 10√(6)
= 2(1 + 5√6)
Therefore, the perimeter of the trapezoid in simplest radical form is 2(1 + 5√6).
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Given question is incomplete, the complete question is below:
what is the perimeter of the trapezoid in simplest radical form?