twenty professiional athlets were asked what age did you graduate from college the responses are displayed in the histogram below

Explanation:

Let the regular price of the dress = y

20% off sale = 0.20

Discounted price= 0.2 × y

Rachel saved = $45

This means after removing the discount from the regular price, she saved $45

45 = regular price - Disounted price

45 = y - 0.2y

45 = 0.8y

divide both sides by 0.8:

45/0.8 = 0.8y/0.8

y =56.25

The regular price

Answer:

18

Step-by-step explanation:

3z + 4z +4 -2 -5z

Combine like terms

3z + 4z  -5z  +4-2

2z+2

Let z=8

2*8 +2

16+2

18

Answer:

18

Step-by-step explanation:

When z=8

Substitute 8 wherever u see z

3(8)+4(8)+4-2-5(8)

24+32+4-2-40

18

The Length of the springs of the two pogo sticks will never be equal.

A pogo stick is an apparatus used for jumping off the ground. The pogo stick uses a spring to store energy when a user jumps on it. The spring is released when the user jumps off the ground.

The length of the spring is compressed when the user jumps on the pogo stick and non-compressed when not in use. The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after 8 seconds can be described by the function (0) = 2sine+√2.

Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)The non-compressed length is given by y = √2. When the pogo stick's spring is equal to its non-compressed length, the difference in length of the spring will be zero.2sine+√2 = √22sine = 0sine = 0The solutions to this equation are obtained by finding the values of θ for which sine = 0.

Therefore, the values of θ are given by:θ = nπwhere n is an integer.

Part B: If the angle was doubled, that is 0 became 20, what are the solutions in the interval [0, 2π)?How do these compare to the original function? (5 points)When the angle is doubled, the equation becomes:2sin2θ+√2 = √2By simplifying the equation, we obtain:2sin2θ = 0sin2θ = 0The solutions to this equation are obtained by finding the values of 2θ for which sine = 0.

Therefore, the values of θ are given by:θ = 0, π, 2πPart C: A toddler is jumping on another pogo stick whose length of its spring can be represented bythe function g(e)-1-cos² e+√2. At what times are the springs from the original pogo stick and thetoddler's pogo stick lengths equal? (5 points)The length of the spring of the toddler's pogo stick can be represented by the function g(e) = -1 - cos² e+√2.

The length of the spring of the original pogo stick is given by the function f(θ) = 2sinθ+√2.To find the times when the two springs are equal, we need to solve the equation:g(e) = f(θ)-1 - cos² e+√2 = 2sinθ+√2cos² e = 2sinθ2cos² e = sin2θ2(1-sin² e) = sin2θ2 - sin² e = sin2θsin² e + sin2θ = 1sin² e = 1 - sin2θ

Therefore, the equation reduces to:-1 - (1 - sin2θ) + √2 = 2sinθ + √2sin2θ = 0, sin2θ = -2The equation has no solutions since the value of sin2θ is less than or equal to 1.

Therefore, the length of the springs of the two pogo sticks will never be equal.

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Step-by-step explanation:

there is nothing missing. this is a complete proof.

yes, the various steps are correct.

Answer:

D.) <V is an obtuse angle that measures 112.

yw ig

Answer:

D

Step-by-step explanation:

yes

Answer:

way too long

Step-by-step explanation:

jk, 3 hours and 55 minutes

Answer:

you dont really want the smoke

Step-by-step explanation:

Answer:

871 and 1/2 ft.  

We have the next data

70,89,75,36,80

First we will calculate the mean

(70+89+75+36+80)/5=70

mean=70

Then we will calculate the Median

36,70,75,80,89

median =75

Then we will calculate the mode because any value is repeated all the values given are the mode

mode:70,89,75,36,80

Range

89-36=53

Range =53

Answer:

0.06

Step-by-step explanation:

0.06 is = to 6% because the percentage is out of 100 and 0.06 is out of a 100.

Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

Answer:

it's better to use a table method

Step-by-step explanation:

start from -2 to 2 insert these x values to your formula

Answer:

Step-by-step explanation:

y=20+15x

so x is slope

slope = 15

and when x =0 Y=20

for graph is starting from (0, 20) (1,35) (2,50)

Good luck!!

Answer:

148.59

Step-by-step explanation:

Inflation is kind of similar to interest and with that bieng said we can (kind of ) use the same formula

the time between 2034 and 2014 is 2034-2014= 20

100(1.02)²⁰=148.5947396

which we can round to 148.59

148.5 is the cost in 2034 of an item that costs $100 in 2014

Simple interest is a quick and easy method of calculating the interest charge on a loan

\(A=P(1+r)^{t}\)

where A is the Actual amount

P is Initial amount

t is time period

r is rate of interest

Given,

The rate of inflation measures the percentage increase in the price of consumer goods

The rate of inflation in the year 2014 was 2% per year.

2% is converted to decimal by dividing with 100

2/100=0.02

The time gap between 2014 and 2034 is

2034-2014=20 years

The initial amount is 100

A=100(1+0.02)²⁰

A=100(1.02)²⁰

A=100×1.485

A=148.5

Hence 148.5 is the cost in 2034 of an item that costs $100 in 2014.

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Answer:

2100

Step-by-step explanation:

The number of days that this solution will probably last would be = 8 days.

To calculate the number of days the solution will last the following is taken into consideration.

The parameters given which are not in ml should be converted to ml as follows;

2 Oz of Lidocaine to ml = 2×29.6=59.2ml

½tsp of banana flavouring;

= 1/2×4.92

= 2.5ml

Therefore the total volume of the solution = 100+59.2+2.5 = 161.7ml

But 2×10 = 1 day

20ml = 1 day

161.7ml = X

Make X the subject of formula;

X = 161.7/20

= 8.1

= 8 days.

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Answer:

15 is 25% of 60

Step-by-step explanation:

15 x 4 = 60

25% x 4 = 100%

Answer:

I think that might be 60

Step-by-step explanation:

The area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The area of the triangle can be determined by using the midpoint formula, which states that the area of an isosceles triangle is equal to half the product of the two base lengths multiplied by the height.

In this case, the midpoint of the triangle is (3,0). This means that the triangle's base lengths are equal to 6 (the difference between the x coordinates of the midpoint and the two endpoints, 3-(-3)) and the height is equal to 6 (the difference between the y coordinates of the midpoint and the two endpoints, 3-(-3)).

Therefore, the area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

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The total measurements of the roof in square feet as required to be determined in the task content is; 2649 ft².

It follows from the task content that the total area of the roof as given in the task content is to be determined.

On this note, the area of the roof is the total area of the 71ft by 39 ft rectangle minus the area of the shaded region with dimensions 15 ft by 8 ft.

Therefore;

Area = (71 × 39) - (15 × 8)

= 2649 ft².

Ultimately, the total area measure of the roof in square feet is; 2649 square feet.

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The correct answer is C) 54.34°.

Answer:

h(1)= -90 h(n)=h(n-1) ⋅ 6

Step-by-step explanation:

Im smart :D

Answer:

\(12.56m\)

Step-by-step explanation:

\( \frac{180}{360} \times 2\pi \: r \\ \frac{1}{2} \times 2 \times \pi \times 4 \\ = 12.56m\)

Answer:

this answer is attached to the picture

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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The derivatives of the functions are now listed:

19) f'(x) = 3

23) f'(x) = 2 · x - 6 · x²

25) g'(x) = - 1 / [2 ·√(9 - x)]

27) g'(t) = - 2 / 3

In this case we have four functions, whose first derivatives must be found by means of derivative rule. Now we present the result of each expression along with the corresponding derivative rules:

19) f(x) = 3 · x - 8 → f'(x) = 3                                         Differentiation for the addition of two functions / Derivative of a power / Derivative of the product of a power and a constant / Derivative of a constant

23) f(x) = x² - 2 · x³ → f'(x) = 2 · x - 6 · x²                     Differentiation for the subtraction of two functions / Derivative of a power / Derivative of the product of a power and a constant

25) g(x) = √(9 - x) → g'(x) = - 1 / [2 ·√(9 - x)]                Differentiation of the square root / Chain rule

27) g(t) = 1 - 2 · t / 3 + 1 → g'(t) = - 2 / 3                       Differentiation for the addition of two functions / Derivative of a power / Derivative of the product of a power and a constant / Derivative of a constant

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The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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Answer:

I need help with this as well.

Step-by-step explanation:

The coordinates of point Q in terms of a, b, and c are (2b+2a, 2c) and SQ and PR bisect each other because the midpoints are same.

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

Let us find coordinates if T using midpoint formula

T=(2b+2a/2, 2c+0/2)

T=(b+a, c)

Now let us find coordinates of Q using midpoint formula

Xs+Xq/2=Xt

0+Xq/2=Xt

Xq = 2b+2a

Ys+Yq/2=Yt

Yq/2=C

Yq=2c

The coordinates of Q are (2b+2a, 2c)

To verify that SQ and PR bisect each other they share the same midpoint

For SQ = (0+2b+2a/2, 0+2c/2)

Midpoint is (b+a, c)

For PR =(2b+2a/2, 2c+0/2)

Midpoint is (b+a, c)

They have same midpoints, so they bisect each other

Hence,  the coordinates of point Q in terms of a, b, and c are (2b+2a, 2c) and SQ and PR bisect each other because the midpoints are same.

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Answer:

0.17 °/s

Step-by-step explanation:

Since the ladder is leaning against the wall and has a length, L and is at a distance, D from the wall. If θ is the angle between the ladder and the wall, then sinθ = D/L.

We differentiate the above expression with respect to time to have

dsinθ/dt = d(D/L)/dt

cosθdθ/dt = (1/L)dD/dt

dθ/dt = (1/Lcosθ)dD/dt where dD/dt = rate at which the ladder is being pulled away from the wall = 2 ft/s and dθ/dt = rate at which angle between wall and ladder is increasing.

We now find dθ/dt when D = 16 ft, dD/dt = + 2 ft/s, and L = 20 ft

We know from trigonometric ratios, sin²θ + cos²θ = 1. So, cosθ = √(1 - sin²θ) = √[1 - (D/L)²]

dθ/dt = (1/Lcosθ)dD/dt

dθ/dt = (1/L√[1 - (D/L)²])dD/dt

dθ/dt = (1/√[L² - D²])dD/dt

Substituting the values of the variables, we have

dθ/dt = (1/√[20² - 16²]) 2 ft/s

dθ/dt = (1/√[400 - 256]) 2 ft/s

dθ/dt = (1/√144) 2 ft/s

dθ/dt = (1/12) 2 ft/s

dθ/dt = 1/6 °/s

dθ/dt = 0.17 °/s

The number of steps they climbed can be represented by positive

From the question, we understand that they climbed up

Upward movements are usually represented by the positive sign

This means that:

Steps = 125 or +125

Hence, the number of steps they climbed can be represented by positive

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The image coordinates of K′ if the preimage is reflected across y = −7 is (-4, -8)

Based on the given question, we have certain variables that can be utilized for our calculations.

K = (-4, -6)

First, find the equation of the reflection line

The reflection line is y = -7.

This can be expressed as

y = a = -7

The image of the reflection is then calculated as

K' = (x, -(y + 2|a|))

Replace the given or established values in the equation mentioned earlier, resulting in the following expression

K' = (-4, -(-6 + 2 * 7))

Evaluate

K' = (-4, -8)

Hence, the image coordinates of K′ are (-4, -8).

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The probability that a mouse leaves first and then a bat is given as follows:

14/55.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

As the animal is not replaced, the probabilities for this problem are given as follows:

Hence the probability is given as follows:

4/11 x 7/10 = 2/11 x 7/5 = 14/55.

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