Use the product rule to find the derivative of the given function y = (2x² + 5)(5x -2)
y'= ...

The time difference computed from the personal best given shows that Stan was 15 seconds faster.

From the information given, Stan had a personal best one mile run time of 6 minutes and 35 seconds. After his last run, his new personal best is 6 minutes and 20 seconds.

Therefore, the difference in time till be:

= 6.35 - 6.20

= 15 seconds.

Therefore, Stan was 15 seconds faster.

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Mean allowance of the given students is equals to $13.

" Mean is defined as the ratio of the sum of all the given number to the  total number of numbers. It is also known as average."

Formula used

Mean = \(\frac{Sum of all the given numbers}{Total number of numbers}\)

According to the question,

Number of students = 10

Weekly allowances of each student

= $9, $11, $13, $15, $20, $10, $12, $15, $10, $15

Substitute the value in the formula of mean we get,

mean = \(\frac{9+11+12+13+20+2(10)+3(15)}{10}\)

         \(= \frac{130}{10}\\ \\= 13 dollars\)

Hence, mean allowance of the given students is equals to $13.

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The radius of the circle with equation x² +y² =1 is 1.

The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it. This amount is significant in practically all formulas involving circles. A circle's radius can also be used to calculate its surface area and circumference.

To see this, we can rewrite the equation in the standard form for the equation of a circle: (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.

In this case, we have:

x² + y² = 1

This can be rewritten as:

(x-0)² + (y-0)² = 1

Thus, the radius of the circle is 1.

The complete question is;-

What is the radius of the circle with the equation x² +y²= 1?

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Answer:

explanation

Step-by-step explanation:

the reason for your statement is just your explanation of why you think that.

Answer:

2.65 sec , 118.85 feet

Step-by-step explanation:

Given a parabola in standard form

h(t) = at² + bt + c ( a ≠ 0 )

Then the maximum occurs when

t = - \(\frac{b}{2a}\)

h(t) = - 16t² + 84.8t + 6.49 ← is in standard form

with a = - 16, b = 84.8 , then

t = - \(\frac{84.8}{-32}\) = 2.65 seconds

The ball reaches its maximum height at 2.65 seconds

Substitute t = 2.65 into h(t) for maximum height

h(2.65) = - 16(2.65)² + 84.8(2.65) + 6.49

            = - 16(7.0255) + 224.72 + 6.49

            = - 112.36 + 231.21

            = 118.85

The maximum height is 118.85 feet

Answer:

6(3x + 4y) the factored form of the expression 18x + 24y

Answer:

34.16

Step-by-step explanation:

42.7

x 0.8

-------

34.16

Answer:

34.16

Step-by-step explanation:  

2 5

42.7

 x

0.8

 =  

43.16

The speed of the moving body that is being referred to here is 80 kilometer per hour.

The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.

                                \(Distance = speed * time\)

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Answer:

3x+y

Step-by-step explanation:

hope this helps!

Special angles in geometry are specific angle measures that have unique properties and are often encountered in geometric problems:

(1) Right angle      (2) Acute angle        (3)  Obtuse angle         (4)Straight angle              (5)Reflex angle

(6) Complementary angles          (7)Complementary angles

In geometry, special angles refer to specific angles that have special properties or characteristics. These angles include right angles, acute angles, and obtuse angles. A right angle is an angle that measures exactly 90 degrees, while an acute angle is an angle that measures less than 90 degrees. An obtuse angle, on the other hand, measures more than 90 degrees but less than 180 degrees. These angles are important in geometry as they form the foundation for many geometric shapes and concepts. Understanding the properties and characteristics of these special angles is crucial for solving geometry problems and constructing geometric figures accurately.

Special angles in geometry are specific angle measures that have unique properties and are often encountered in geometric problems. These angles include:

1. Right angle: A right angle is an angle that measures exactly 90 degrees. It is formed when two lines intersect perpendicularly.

2. Acute angle: An acute angle is an angle that measures between 0 and 90 degrees. It is smaller than a right angle.

3. Obtuse angle: An obtuse angle is an angle that measures between 90 and 180 degrees. It is larger than a right angle.

4. Straight angle: A straight angle is an angle that measures exactly 180 degrees. It is formed when two lines intersect in a straight line.

5. Reflex angle: A reflex angle is an angle that measures between 180 and 360 degrees. It is larger than a straight angle.

6. Complementary angles: Two angles are complementary if their sum is equal to 90 degrees.

7. Supplementary angles: Two angles are supplementary if their sum is equal to 180 degrees.

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Answer:

1.) A.) -5/2

2.) B. {(–5, 8), (–5, 2), (–3, 3), (–3, 1), (0, 4), (0, 5), (–5, 7), (–3, 6)}

Step-by-step explanation:

Imma genius

Answer:

56 im pretty sure not my level but if i did it right it should be but if it is wrong im sorry

Step-by-step explanation:

Answer:

The answer is -285

Step-by-step explanation:

The distribution does not represent a probability distribution. The correct option is b.

A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).

In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.

Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.

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Answer:

length of side of square = 8 cm

Step-by-step explanation:

Let's first find the area of the triangle, using the formula A = (1/2)(base)(height):

A = (1/2)(16 cm)(4 cm) = 32 cm^2.

Twice the area of the triangle would be 64 cm^2.

The area of the square is then 64 cm^2, which is the square of the length of one side of the square.  Taking the square root of 64 cm^2, we get

length of side of square = sqrt(64 cm^2) = 8 cm

Answer:

The property used is Symmetric property of Equality.

Option B is correct option.

Step-by-step explanation:

We are given :

\(AR \cong TY\\\)

Which property will give the step:

\(TY \cong AR\\\)

Looking at the options:

We see that Symmetric property states that if a = b then b= a

Same is the case with the question.

We have :

\(AR \cong TY\\\\TY \cong AR\\\)

If a = AR and b = TY

then the property is: a = b, b=a

So, the property used is Symmetric property of Equality.

Option B is correct option.

Answer:

this sounds familiar i would pick A or B

Step-by-step explanation:

I'm in tenth grade so I want to try to help as much as I can!!!

Answer:

28-6=w

Step-by-step explanation:

We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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The temperature in Fahrenheit after preheating for 2 minutes is 103⁰F

The question looks incomplete but we can as well find the temperature in Fahrenheit after preheating for 2 minutes

Give the function t = 19m + 65 that represents the temperature t (in degrees Fahrenheit) of an oven after preheating for m minutes.

If t = 2,

t = 19(2) + 65

t = 38 + 65

t = 103⁰F

Hence the temperature in Fahrenheit after preheating for 2 minutes is 103⁰F

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The correct statement is: d.  "The impact on the volume if the dimensions are multiplied by 14  the new volume will be 14 times the original volume.      

To determine the impact on the volume when the dimensions of the cone are multiplied by 14, we need to calculate the new volume and compare it to the original volume. Let's denote the original radius as r and the original height as h.

Given:

Original radius (r) = 12 ft

Original height (h) = 24 ft

New radius = 14 * r

New height = 14 * h

The formula for the volume of a cone is V = (1/3) * π * r^2 * h.

Original Volume (V_original) = (1/3) * π * (r^2) * h

= (1/3) * π * (12^2) * 24

≈ 10845.12 cubic feet

New Volume (V_new) = (1/3) * π * ((14 * r)^2) * (14 * h)

= (1/3) * π * (196 * r^2) * (14 * h)

= (1/3) * π * (196 * (12^2)) * (14 * 24)

= (1/3) * π * 196 * 144 * 336

≈ 1086615.36 cubic feet

Comparing the new volume to the original volume:

a. The volume will decrease by 116.

False. The new volume is significantly larger than the original volume, so it does not decrease by 116.

b. The original volume will be divided by 43.

False. Dividing the original volume by 43 does not yield the new volume.

c. The original volume is decreased by approximately 2111.15 units^3.

False. The difference between the new volume and the original volume is much larger than 2111.15 units^3.

d. The new volume will be 14 times the original volume.

True. The new volume is approximately 14 times the original volume.

e. The original volume will be multiplied by 164.

False. Multiplying the original volume by 164 does not yield the new volume.

Therefore, the correct statement is:

d. The new volume will be 14 times the original volume.

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Answer:

2(5) nd 28

Step-by-step explanation:

Answer:

2(5) 28 like the top person said

Step-by-step explanation:

Answer: y = 7x

Step-by-step explanation:In your question, the constant of proportionality already jump out at us which is to get y, we have to multiply x by 7. Therefore the constant of proportionality is y=7x.

Answer:

2.5

Step-by-step explanation: got it on khan

The eigenvalue of matrix A is 13, and the corresponding eigenvector is [-B].

To find the eigenvalues and eigenvectors of matrix A, we need to solve the equation A * x = λ * x, where A is the matrix, x is the eigenvector, and λ is the eigenvalue. In this case, A = [13] and we want to find the eigenvalues and eigenvectors.

Let's solve the equation A * x = λ * x:

[13] * [x] = λ * [x]

Multiplying the matrices, we get:

[13x] = [λx]

Since λ is a scalar, we can write this equation as:

13x = λx

Dividing both sides by x, we get:

13 = λ

So the eigenvalue λ is 13.

To find the eigenvector corresponding to λ = 13, we substitute λ into the equation A * x = λ * x:

[13] * [x] = 13 * [x]

This simplifies to:

[13x] = [13x]

The eigenvector x can be any non-zero vector, so we can choose x = [-B]. Therefore, the eigenvector corresponding to the eigenvalue λ = 13 is [-B].

The eigenvalue of matrix A is 13, and the corresponding eigenvector is [-B].

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Answer:

22 divided by 2 is 11

Step-by-step explanation:

Answer:

79 degrees

Step-by-step explanation:

79 degrees is parallel to a. The line below is the same as the line above, since they are parallels, beaning d and b also are both 79 degrees

Answer:

\(79^{\circ}\)

Step-by-step explanation:

From vertical angles, \(m\angle a=79^{\circ}\)

From corresponding angles, \(m\angle b=m\angle a\)

Therefore, we have \(m\angle b=m\angle a=\boxed{79^{\circ}}\)

Answer:

The probability of the chosen ball being shiny conditional on it being red is; 0.375

Step-by-step explanation:

Let A be the event that a red ball has been chosen

Let B be the event that a shiny ball has been chosen

Let S be the total outcomes = 150 balls

Thus;

P(A ∩ B ) = 36/150

A ∩ B' = 150 - 36 - 54

A ∩ B' = 60

Thus; P(A ∩ B') = 60/150

P(A') = 54/150

P(A) = (150 - 54)/150 = 96/150

Thus, probability of the chosen ball being shiny conditional on it being red is;

P(B | A) = P(B ∩ A)/P(A)

Thus; P(B | A) = (36/150)/(96/150)

P(B | A) = 0.375

To find the maximum area of the lawn that can be watered by the sprinkler, we can use the formula for the area of a circle:

A = πr^2

Given that the radius of the sprinkler's spray is 22ft, we can substitute this value into the formula:

A = 3.14 * (22)^2

A ≈ 3.14 * 484

A ≈ 1519.76

Rounded to the nearest tenth, the maximum area of the lawn that can be watered by the sprinkler is approximately 1519.8 ft^2.\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}\)

Answer:

18

Step-by-step explanation:

The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :

Linear scale factor :

12 ÷ 10 = 1.2 or 6/5

Let's use the fraction form

Using the linear scale factor we can make an equation to solve for x :

2x+4 = 6/5(x+8)

Expand the brackets :

2x+4 = 6/5x + 9.6

Subtract 4 from both sides :

2x = 6/5x + 5.6

Subtract 6/5x from both sides :

4/5x = 5.6

Divide both sides by 4/5 :

x = 7

Now substitute this value into the expression for the length of AE :

AE = 2(7) + 4

AE = 14 + 4

AE = 18

Hope this helped and have a good day

Answer:

116 units

Step-by-step explanation:

AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.

AE = 2x + 4 and ED = x +8 added together they equal 180

2x + 4 + x + 8 = 180  Combine the like terms

3x + 12 = 180  Subtract 12 from both sides of the equation

3x = 168  Divide both sides by 3

x = 56

Now that we know that x is 56 we can plug that in for AE to find its length

2x + 4

2(56) + 4

112 + 4

116