The expression sin(2x) − sinx is equivalent to 2sin (3x/2) sin(x/2) therefore option (D) is correct.
Recall the formula of sine
[tex]\sin x-\sin y=2 \sin (\frac{x+y}{2}) \sin (\frac{x-y}{2})[/tex]
How to find the equivalent expression?The given expression is sin (2x) − sin x.
Apply the formula
[tex]\sin (2x) - \sin x =2 \sin (\frac{2x+x}{2}) \sin (\frac{2x-x}{2})[/tex]
[tex]=2 \sin (\frac{3x}{2}) \sin (\frac{x}{2})[/tex]
Hence the expression is equivalent to 2sin (3x/2) sin(x/2)
brainly.com/question/8120556
Learn more about trigonometric expressions here- brainly.com/question/11234923
#SPJ2
A flower store has 25 daisies and 15 tulips. It puts the same number of flowers in each of 5 bouquets.
Which statement can be used to fill in the blank space?
The statement is option (A) ∠ ADB and ∠CBD satisfies the alternate interior angle theorem.
What is a rectangle?A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
The diagram below shows the rectangle ABCD.
The diagonals AC and BD are drawn.
From the diagram,
According to alternate interior angle theorem, [tex]\angle ADB[/tex] and [tex]\angle CBD[/tex] are alternate interior angles .
Hence we can conclude that the statement is option (A) ∠ ADB and ∠CBD satisfies the alternate interior angle theorem.
Learn more about the rectangles here
https://brainly.com/question/1380651
#SPJ3
If you flip a fair coin 5 times, what is the probability that you will get exactly 3 tails?
The probability of getting exactly 3 tails when flipping a fair coin 5 times is 0.3125, or [tex]\( 31.25\% \)[/tex]. This means that in about 31.25% of the cases, when flipping a fair coin 5 times, exactly 3 of those flips will result in tails.
To find the probability of getting exactly 3 tails when flipping a fair coin 5 times, we can use the binomial probability formula. In a binomial experiment like this, where there are only two possible outcomes (heads or tails) and each trial is independent and has the same probability of success (50% for a fair coin), we can use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1-p)^{n-k} \][/tex]
Where:
- P(X = k) is the probability of getting exactly k successes (tails, in this case).
- n is the number of trials (5 flips).
- k is the number of successes (3 tails).
- p is the probability of success on each trial (0.5 for a fair coin).
- (1-p) is the probability of failure on each trial.
Substituting the given values into the formula:
[tex]\[ P(X = 3) = \binom{5}{3} \times (0.5)^3 \times (1-0.5)^{5-3} \][/tex]
[tex]\[ P(X = 3) = \binom{5}{3} \times 0.5^3 \times 0.5^2 \][/tex]
[tex]\[ P(X = 3) = \frac{5!}{3!(5-3)!} \times 0.5^3 \times 0.5^2 \][/tex]
[tex]\[ P(X = 3) = \frac{5 \times 4}{2 \times 1} \times 0.125 \times 0.25 \][/tex]
[tex]\[ P(X = 3) = 10 \times 0.125 \times 0.25 \][/tex]
[tex]\[ P(X = 3) = 0.3125 \][/tex]
So, the probability of getting exactly 3 tails when flipping a fair coin 5 times is 0.3125, or [tex]\( 31.25\% \)[/tex].
This means that in about 31.25% of the cases, when flipping a fair coin 5 times, exactly 3 of those flips will result in tails.
a total of 32 students have entered a spelling contest. There are 6 medals for first through sixth place that will be awarded. In how many different ways can the medals be awarded?
Final answer:
There are 27,405,5040 different ways the medals can be awarded to the 32 students.
Explanation:
In this problem, we need to find the number of different ways the 6 medals can be awarded to the 32 students. To solve this, we can use the concept of permutations. There are 32 students competing for the first medal, so there are 32 choices for that medal. Once the first medal is awarded, there are 31 students remaining to compete for the second medal, so there are 31 choices for that medal. We continue this process until all 6 medals have been awarded. Therefore, the total number of different ways the medals can be awarded is 32 * 31 * 30 * 29 * 28 * 27 = 27,405,5040.
Which statement best explains whether △JKL is congruent to △MNP?
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.
△JKL is not congruent to △MNP because there is no sequence of rigid motions that maps △JKL to △MNP.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the x-axis followed by a rotation of 180° about the origin.
Two triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. In triangle J K L, the vertex labeled as J lies on begin ordered pair negative 4 comma 2 end ordered pair. The vertex labeled as K lies on begin ordered pair negative 2 comma 3 end ordered pair. The vertex labeled as L lies on begin ordered pair negative 2 comma negative 1 end ordered pair. In triangle M N P, the vertex labeled as M lies on begin ordered pair 4 comma 0 end ordered pair. The vertex labeled as N lies on begin ordered pair 2 comma negative 1 end ordered pair. The vertex labeled as P lies on begin ordered pair 2 comma 3 end ordered pair.
△JKL is congruent to △MNP because it can be mapped to △MNP through a reflection across the y-axis and a translation 2 units up.
Explanation:To determine if △JKL is congruent to △MNP, we need to see if a series of rigid motions (rotations, reflections, translations) can map △JKL exactly onto △MNP. Looking at the positions of the vertices for both triangles, we can observe that if we carry out a reflection of △JKL across the y-axis (changing the sign of the x-coordinates) and then translate the reflected △JKL 2 units upward (+2 to the y-coordinates), we end up getting the vertices for △MNP. Therefore, △JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis and a translation 2 units up. This option is not given explicitly in the original options, but this explanation provides the correct transformational sequence.
Learn more about Triangle Congruence here:https://brainly.com/question/20521780
#SPJ11
Match the statement to the property it shows
Order 0.40mm, 40mm , 0.4 mm, and 0.004mm from most to least precise
One number is 3 more than twice another number. if the sum of two number is 39, find the two numbers
(X+3)^2-x^2=39 x^2+6X+9-x^2=39 6x+9=39. 6x=30 x =5 x+3=8
If the product of a number and negative −3 is subtracted from the number, the result is 11 more than the number. find the number.
Formula to find volume of a right triangular prism
Garrick gets paid $4.70 an hour with time-and-a-half for overtime (over 40 hours) How much did he earn one week when he worked 48 hours?
A. $195.05
B. $220.90
C. $230.30
D. $188
pleeeaaase explain your process on how you got to that answer you picked
Help please pre calculus
What is the domain of the function f(x)=4x-16
A right triangle has a hypotenuse that measures 65 in. and one side that measure 16 in. what is the length of the remaining side of the triangle?
Amy deposited dimes and quarters into the coinstar machine at her local grocery store. The total money she deposited was $11.35.
What is the slope of the line that passes through the points (-1, 2) and (-4, 3)?
Answer: -1/3
Step-by-step explanation:
Slope is the difference between the y coordinate points divided by the x coordinate points
We have (-1, 2) and (-4, 3)
Slope = 3 - 2/ -4 - (-1)
Slope = -1/3
What is the equations of the quadratic function with a vertex (4, -4) and a point at (3, -6)?
Kara bought a new dress. the original price of the dress was $65.50. there was a 15% discount on the dress. how much did kara pay for the dress?
Final answer:
Kara will pay $55.68 for the dress after a 15% discount is applied to the original price of $65.50.
Explanation:
Kara wants to buy a dress with an original price of $65.50, and there is a 15% discount on it.
To find out how much Kara will pay for the dress after the discount, we first need to calculate the amount of the discount.
To do this, we convert the percentage to a decimal by dividing by 100 (15% = 0.15) and then multiply it by the original price of the dress.
The amount of the discount is:
$65.50 × 0.15 = $9.825.
To find out the final price that Kara pays, we subtract the discount from the original price:
$65.50 - $9.825 = $55.675.
However, stores usually round the price to the nearest cent, so Kara would pay $55.68 for the dress after the discount is applied.
Use the chart to multiply the binomial by the trinomial (y+3)(y^2-3y+9) What is the product? y3 + 27 y3 – 27 y3 – 6y2 + 27 y3 + 6y2 + 27
A typical running track is an oval with 74-m-diameter half circles at each end. a runner going once around the track covers a distance of 400 m . suppose a runner, moving at a constant speed, goes once around the track in 1 min 40 s. what is her centripetal acceleration during the turn at each end of the track?
Answer:
Her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]
Step-by-step explanation:
Total distance covered in one round , D= 400 m
Time taken to cover one round , T = 1 min 40 s = 100 sec
Speed of runner , [tex]V=\frac{D}{T}=\frac{400}{100}\, \frac{m}{s}= 4.0\, \frac{m}{s}[/tex]
Now centripetal acceleration is given by
[tex]a_c=\frac{V^{2}}{R}[/tex]
where [tex]V= 4.0\frac{m}{s}[/tex]
[tex]Radius, R= \frac{Diameter}{2}=\frac{74}{2}m=37\, m[/tex]
[tex]\therefore a_c=\frac{4^{2}}{37}\, \frac{m}{s^{2}}=0.432\, \frac{m}{s^{2}}[/tex]
Thus her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]
The centripetal acceleration of runner at each end of track is [tex]\boxed{0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .
Explanation:
It is given that the diameter of oval track that consists of two half circles at each end is [tex]74{\text{ m}}[/tex] .
The distance runner runs once around the track is [tex]400{\text{ m}}[/tex] . The runner covers one round of track in [tex]1{\text{ m}}[/tex] and [tex]40{\text{ s}}[/tex] .
Our aim is obtain the value of centripetal acceleration for runner at each track.
The expression for centripetal acceleration is shown below.
[tex]{a_c}=\frac{{{v^2}}}{R}[/tex] …… (1)
Here, [tex]v[/tex] is the speed of the runner and [tex]R[/tex] is the radius of track.
The speed of the runner is the ratio of distance she takes to cover the track to the time taken by her.
The time in seconds is calculated as,
[tex]\begin{aligned}t&=60{\text{ s}}+40{\text{ s}}\\&=100{\text{ s}}\\\end{aligned}[/tex]
The distance covered is [tex]400{\text{ m}}[/tex] , so the speed calculated is shown below.
[tex]\begin{aligned}{\text{speed}}&=\frac{{{\text{distance}}}}{{{\text{time}}}}\\&=\frac{{400{\text{ m}}}}{{100{\text{ s}}}}\\&=4{\text{ }}{{\text{m}}\mathord{\left/{\vphantom {{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}[/tex]
The radius of track calculated is shown below.
[tex]\begin{aligned}R&=\frac{d}{2}\\&=\frac{{74{\text{ m}}}}{2}\\&=37{\text{ m}}\\\end{aligned}[/tex]
Substitute [tex]4[/tex] for [tex]v[/tex] and [tex]37[/tex] for [tex]R[/tex] in equation (1) to obtain the centripetal acceleration [tex]{a_c}[/tex] .
[tex]\begin{aligned}a_{c}&=\frac{(4\text{ m/s})^{2}}{37\text{ m}}\\&=\frac{16}{37}\text{ m/s}^{2}\\&=0.432\text{ m/s}^{2}\end{aligned}[/tex]
Therefore, the centripetal acceleration [tex]{a_c}[/tex] is [tex]0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}[/tex] .
Thus, the centripetal acceleration of runner at each end of track is [tex]\boxed{0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .
Learn More:
1. Centripetal Force https://brainly.com/question/6372960
2. Velocity and Momentum https://brainly.com/question/11896510
3. Centripetal force on orbit https://brainly.com/question/7420923
Answer Details:
Grade: High School
Subject: Physics
Chapter: Circular Motion
Keywords:
Track, running, diameter, circle, runner, distance, moves, constant, speed, centripetal, acceleration, force, motion, uniform, radius, velocity and oval.
what does at least mean in a word problem less than or greater than
The gym trainer is purchasing some new weights and a new balance bar. The weights cost $4.50 each. The balance bar costs $78. The trainer has $156. What is the greatest number of weights the trainer can purchase?
Question 13 options:
17
18
20
24
Mr. Blair is taking his family to the Great Wolfe Lodge. There are 10 people going to the Great Wolfe Lodge, and they need 3 rooms. Mr. Blair pays $110 for each of the three rooms. He gives each person including himself an allowance of money to spend. Mr. Blair has budgeted $530 for the rooms and the spending money he gives each family member. How much money did he allow in the budget for each member to spend?
Question 14 options:
$15.00
$20.00
$43.00
$53.00
The greatest number of weights the trainer can purchase is 17.
Explanation:To find the maximum number of weights the trainer can purchase, we need to divide the trainer's total budget by the cost of each weight.
Step 1: Find the cost of weights per trainer's budget: $156 - $78 = $78
Step 2: Divide the cost of weights by the cost of each weight: $78 / $4.50 = 17.33
Since you cannot purchase a fraction of a weight, the trainer can purchase a maximum of 17 weights.
Q is the midpoint of PR R is the midpoint of QS Prove: PR = QS
Proving that PR = QS
Given: Q is the midpoint of PRThe midpoint of a segment: PQ = QR
Given: R is the midpoint of QS
The midpoint of a segment: PQ = QR
The addition property of Equality : QR + RS = PQ + QR
Therefore, PR = QS
To learn more, visit the link below:
brainly.com/question/13457564
What is the least common multiple of 18, 16, and 9?
A box of books has a mass of 4.10 kilograms for every meter of its Height . Convert this ratio into pounds per foot.
Answer:
0.498 on edg
Step-by-step explanation:
help with pythagorean theorem!! BRAINLIEST ANSWER
x^2 +x^2 = C^2
x^2 +x^2 = 15^2
x^2 + x^2 = 225
225/2 = 112.5 = x^2
sqrt(112.5) = 10.6066
round answer as needed
note the answer can also be written as 15sqrt(2)/2
Plz I need help asap:
Parallelogram CDEF is shown below.
Find the length of the segments and the measure of the angles: CF, FE, ∠D, and ∠E.
Simplify 4a + 8b - 6b + 2a
Answer:
The answer is 6a+2b
Step-by-step explanation:
hope it's helpful :)
Form the union for the following sets.
R = {10, 15, 20}
S = {20, 25}
R ∪ S =
A. { }
B. {20}
C. {10, 15, 25}
D. {10, 15, 20, 25}
Solve this questionhhhhhhhh