B is the midpoint of AC. C is the midpoint of AD. Find the coordinates of B and D given the coordinates of A (-2,5) and the coordinates of C (8,7). ​

The table with the correct values for A, B and C are,

Black 9 36 63 90

White 13 52 91 130

A proportional relationship is defined as follows:

⇒ y = kx.

In which k is the constant of proportionality.

Here, The input and output variables for this problem are given as follows:

Input:     number of black keys.

Output:  number of white keys.

Hence, The constant k is obtained as follows:

91 = 63k

k = 91/63

k = 13/9.

So, The equation is,

⇒ y = 13x/9.

Hence, the values are given as follows;

For A:

when x = 9,

y = 13 × 9 / 9

y = 13

For B:

when x = 36,

y = 13 x 36/9

y = 52.

For C:

when x = 90,

y = 13 x 90/9 = 130.

Thus, First table is correct.

Learn more about proportional relationships visit:

brainly.com/question/7723640

#SPJ1

The question is concerned with the merry-go-round that revolves two times in one minute, and the distance of Jack and Bob from its center. It's important to know how to calculate the circumference of a circle, which is 2πr, where "r" is the radius of the circle and "π" is a constant value approximately equal to 3.14, but you can also use your calculator for accurate results.

Let's first find the distance that Jack travels in one minute.

Since the merry-go-round revolves 2 times in one minute and Jack is 10 feet from the center, Jack will travel a distance equal to the circumference of a circle with a radius of 10 feet twice in one minute.

Therefore, the distance Jack travels in one minute is given by; Distance = 2(πr) = 2(π)(10) ≈ 62.8 feet.

Next, let's find the distance Bob travels in one minute.

Since the merry-go-round revolves 2 times in one minute and Bob is 14 feet from the center, Bob will travel a distance equal to the circumference of a circle with a radius of 14 feet twice in one minute.

Therefore, the distance Bob travels in one minute is given by;

Distance = 2(πr) = 2(π)(14) ≈ 87.92 feet.

To know more about distance visit:

https://brainly.com/question/13034462

#SPJ11

a) The average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. b) The estimated coefficients of REDS and TRAINS in the regression model are 1.3353 (REDS). c) The absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis.

a) To find the average estimated time in minutes for Bill to drive to work when he leaves on time at 6:30 and there are no red lights and no trains at the crossroad to wait, we substitute the values into the regression model:

TIME = -19.9166 + 0.3692(DEPART) + 1.3353(REDS) + 2.7548(TRAINS)

Given:

DEPART = 0 (as he leaves on time at 6:30)

REDS = 0 (no red lights)

TRAINS = 0 (no trains to wait for)

Substituting these values:

TIME = -19.9166 + 0.3692(0) + 1.3353(0) + 2.7548(0)

    = -19.9166

Therefore, the average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. However, it's important to note that negative values in this context may not make practical sense, so we should interpret this as Bill arriving approximately 19.92 minutes early to work.

b) The estimated coefficients of REDS and TRAINS in the regression model are:

1.3353 (REDS)

2.7548 (TRAINS)

Interpreting the coefficients:

- The coefficient of REDS (1.3353) suggests that for each additional red light, the estimated time to drive to work increases by approximately 1.3353 minutes, holding all other factors constant.

- The coefficient of TRAINS (2.7548) suggests that for each additional train Bill has to wait for at the crossing, the estimated time to drive to work increases by approximately 2.7548 minutes, holding all other factors constant.

c) To test the hypothesis that each train delays Bill by 3 minutes, we can conduct a hypothesis test.

Null hypothesis (H0): The coefficient of TRAINS is equal to 3 minutes.

Alternative hypothesis (Ha): The coefficient of TRAINS is not equal to 3 minutes.

We can use the t-test to test this hypothesis. The t-value is calculated as:

t-value = (coefficient of TRAINS - hypothesized value) / standard error of coefficient of TRAINS

Given:

Coefficient of TRAINS = 2.7548

Hypothesized value = 3

Standard error of coefficient of TRAINS = 0.1390

t-value = (2.7548 - 3) / 0.1390

       = -0.2465 / 0.1390

       ≈ -1.7733

Using a significance level of 5% (or alpha = 0.05) and looking up the critical value for a two-tailed test, the critical t-value for 230 degrees of freedom is approximately ±1.9719.

Since the absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that each train delays Bill by 3 minutes.

To know more about hypothesis visit:

brainly.com/question/30404845

#SPJ4

Step-by-step explanation:

Use z-score table to find the z-score that corresponds to .7000   ( 70%)

approx   .525   s.d.  above the mean

  .525  * 10 =  5.25  points above 100   = 105.25

Options b, d, and e are the true statements about the substitution method.

b. It is useful to solve the integral ∫2x sin x^2 dx.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

e. It is based on the chain rule for derivatives.

The true statements about the substitution method are:

b. It is useful to solve the integral ∫2x sin x^2 dx.

The substitution method is commonly used to simplify integrals and make them easier to evaluate. It can be applied to various types of integrals, including the given example.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

The substitution method involves making a substitution in the integral by introducing a new variable. This formula represents the fundamental principle of substitution, where the derivative of the substituted function appears in the integral.

e. It is based on the chain rule for derivatives.

The substitution method is based on the chain rule of derivatives. By making an appropriate substitution, the integral can be transformed into a new form that corresponds to a derivative of a simpler function.

Therefore, options b, d, and e are the true statements about the substitution method.

To know more about substitution refer here:

https://brainly.com/question/29383142#

#SPJ11

Answer:

x = 7

Step-by-step explanation:

CONCEPT :

Here, we will use the below following steps to find a solution using the transposition method:

\(\begin{gathered}\end{gathered}\)

SOLUTION :

To solve this equation, we'll use this given concept :

\(\begin{gathered} \qquad{\twoheadrightarrow{\sf{3(x - 5) = 6}}}\\\\\qquad{\twoheadrightarrow{\sf{(3 \times x) - (3 \times 5) = 6}}}\\\\\qquad{\twoheadrightarrow{\sf{(3x) - (15) = 6}}}\\\\\qquad{\twoheadrightarrow{\sf{3x - 15 = 6}}}\\\\\qquad{\twoheadrightarrow{\sf{3x = 6 + 15}}}\\\\\qquad{\twoheadrightarrow{\sf{3x =21}}}\\\\\qquad{\twoheadrightarrow{\sf{x = \dfrac{21}{3}}}}\\\\\qquad{\twoheadrightarrow{\sf{x = 7}}}\\\\\qquad{\star{\underline{\boxed{\sf{\purple{x = 7}}}}}}\end{gathered}\)

Hence, the value of x is 7.

\(\rule{300}{2.5}\)

Hey ! there

Answer:

Step-by-step explanation:

In the question we are given with an equation that is 3 ( x - 5 ) = 6 . And we're asked to solve the equation that means we have to find the value of x .

Solution : -

\( \dashrightarrow \qquad \: 3(x - 5) = 6\)

Step 1 : Solving parenthesis by using distributive property that means multiplying 3 with x as well as - 5 :

\( \dashrightarrow \qquad \: (3 \times x) - (3 \times 5) = 6\)

Simplifying it ,

\( \dashrightarrow \qquad \: 3x - 15 = 6\)

Step 2 : Adding 15 to both sides :

\( \dashrightarrow \qquad \: 3x - \cancel{15 }+ \cancel{15 }= 6+ 15\)

On cancelling -15 with 15 , We get :

\( \dashrightarrow \qquad \: 3x = 6 + 15\)

Step 3 : Adding 6 and 15 :

\( \dashrightarrow \qquad \: 3x = 21\)

Step 4 : Now to make our variable isolate , dividing with 3 on both sides :

\( \dashrightarrow \qquad \: \dfrac{ \cancel{3}x}{ \cancel{3}}= \cancel{\dfrac{21}{3} }\)

On further calculations , We get ,

\( \dashrightarrow \qquad \: \purple{ \underline{\boxed{\frak{ x = 7}}}} \quad \star\)

Verifying : -

Atlast , we are checking our answer by substituting the above value of x in given equation . So ,

Therefore , our solution is correct .

Answer:

85% acid

Step-by-step explanation:

The amount of acid is 83.75 milliliters

The percentage of the resulting mixture of acid is 67%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

A chemist mixes 100 milliliters of a solution that is 75% acid with 25 milliliters of a solution that is 35% acid.

This means,

75% of 100 milliliters = 75/100 x 100 = 75 milliliters

35% of 25 milliliters = 35/100 x 25 = 8.75 milliliters

Now,

The amount of acid is (75 + 8.75) = 83.75 milliliters

The percentage of the resulting mixture of acid.

= 83.75 / (100 + 25) x 100

= 83.75/125 x 100

= 67%

Thus,

The amount of acid is 83.75 milliliters

The percentage of the resulting mixture of acid is 67%

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

Answer:

x = 3

y = 6

Step-by-step explanation:

2x = x + 9

x = 3

y = 2 * 3

y = 6 .    Hope this help teehee :D

Answer:

Your answer is 93.3.

Step-by-step explanation:

\(53-\)\((-40) = 93.3\)

The probability that the sum of the claim representing damage to the house and the claim representing the rest of the property is more than 1 is 0.1875.

We need to find P(X+Y > 1), where X and Y are the portions of the claim representing damage to the house and the rest of the property, respectively.

We can find this probability by integrating the joint density function f(x,y) over the region where X+Y > 1. This region is the triangular region with vertices at (0,1), (1,0), and (1,1). Thus, we have:

P(X+Y > 1) = ∫∫R f(x,y) dA

where R is the region described above.

Breaking the integral into two parts, we have:

P(X+Y > 1) = ∫0^1 ∫1-x^2^4-x dy dx + ∫1^2 ∫0^2-x f(x,y) dy dx

Evaluating the integrals, we get:

P(X+Y > 1) = 0.1875

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ11

The board of directors for Procter and Gamble is concerned that only

19% of the people who use toothpaste buy Crest toothpaste. A marketing

director suggests that the company invest in a new marketing campaign

which will include advertisements and new labeling for the toothpaste.

The research department conducts product trials in test markets for one

month to determine if the market share increases with new labels.

PROCTOR and GAMBLE had only 19% of the people who use toothpaste

buy Crest toothpaste. Hence, it was worried about the market share of

the toothpaste it had been producing. The marketing director suggested

that the company invest in a new marketing campaign which will include

advertisements and new labeling for the toothpaste. The research

department conducted product trials in test markets for one month to

determine if the market share increases with new labels. This is an

effective approach because new labels attract customers easily. By

changing or improving the way that a product is labeled or packaged,

companies can influence the likelihood of a purchase by making the

product look more appealing or professional. Therefore, after changing

the labeling, the market share of Crest Toothpaste will increase.

LEARN MORE ON PROCTOR & GAMBLE AT: https://brainly.com/question/17151793

#SPJ11

The rate of change, in square inches per second, of the area of the region at the instant when R is 44 inches and r is 33 inches is

8363 square inches

The rate of change is the derivative, the rate of change is calculated by differentiation the area

formula for area of concentric circle is given by

Area A = π(R^2 - r^2) =

R = radius of the inner circle

r = radius of the outer circle

δA/δt = δA/δRδr * δRδr/δt

δA/δt = π * (2RδR/δt - 2rδr/δt)

δA/δt = π * 2(R * δR/δt - r * δr/δt)

where R = 44 and δR/δt = 22

r = 33 and δr/δt = -11

= 2π(44 * 22 - 33 * -11)

= 2π (968 - -363)

=  2π (1331)

= 2662π

= 8362.9196 square inches

Learn more about rate of change here:

https://brainly.com/question/8728504

#SPJ1

Answer:

LMK and QPM

Step-by-step explanation:

When two lines are crossed by another line (called the transversal), the angles in matching corners are called corresponding angles.

Expanding this expression, we can obtain the Maclaurin series for the given function f(x) = 8x cos((1/7)x^2).

To obtain the Maclaurin series for the function f(x) = 8x cos((1/7)x^2), we can expand the function using the Maclaurin series for cosine. The Maclaurin series for cosine is given by:

cos(x) = Σ(-1)^n (x^(2n)) / (2n)!

Substituting (1/7)x^2 for x in the Maclaurin series for cosine, we get:

cos((1/7)x^2) = Σ(-1)^n ((1/7)x^2)^(2n) / (2n)!

Simplifying further, we have:

cos((1/7)x^2) = Σ(-1)^n (1/7)^(2n) (x^(4n)) / (2n)!

Now, multiplying the Maclaurin series for cosine by 8x, we get:

f(x) = 8x * cos((1/7)x^2) = 8x * Σ(-1)^n (1/7)^(2n) (x^(4n)) / (2n)!

To know more about Maclaurin series,

https://brainly.com/question/31972602

#SPJ11

Answer:

  20/k

Step-by-step explanation:

Given a rate of k pages in 20 minutes, you want to know the rate in minutes per page.

To find the rate in minutes per page, divide minutes by pages:

  (20 min)/(k pages) = (20/k) min/page

Answer:

2.15

Step-by-step explanation:

I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):

(-1/4)*(-8.6)

= (8.6/4)

= 2.15

Answer:

I need help with his question too but I don’t know the answer

Step-by-step explanation:

Answer:

(2, - 1 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , thus

O(- 1, - 2 ) → (2, - 1 )

Answer:

8n+7

Step-by-step explanation:

The value of \(f^{-1}(6)\) is \(-3\).

Given:

The function \(f\) has an inverse and \(f(-3)=6\).

To find:

The value of \(f^{-1}(6)\).

Explanation:

If a point \((a,b)\) lies on the function \(f(x)\), then the point \((b,a)\) must lies on the inverse function \(f^{-1}(x)\).

According to the given value \(f(-3)=6\), the point \((-3,6)\) lies on the function \(f(x)\). So, the point \((6,-3)\) must be lies on \(f^{-1}(x)\).

\(f^{-1}(6)=-3\)

Therefore, the value of \(f^{-1}(6)\) is \(-3\).

Learn more:

https://brainly.com/question/17148722

The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

Learn more about integral here: brainly.com/question/18125359

#SPJ11

Answer:

The correct answer is B.2 plz mark as brainliest.

Step-by-step explanation:

Using Laplace transforms the solution to the initial value problem y'' - 2y' + y = 0 is y(t) = (t - 1)y(0) + y'(0)e^t, where y(0) and y'(0) are the initial conditions.

To solve the initial value problem y'' - 2y' + y = 0, we can use the method of Laplace transforms.

Take the Laplace transform of both sides of the differential equation. Using the linearity property of Laplace transforms and the derivative property, we have:

s^2Y(s) - sy(0) - y'(0) - 2(sY(s) - y(0)) + Y(s) = 0

Simplify the equation by rearranging terms and grouping:

s^2Y(s) - 2sY(s) + Y(s) - sy(0) + 2y(0) - y'(0) = 0

Substitute the initial conditions into the equation:

s^2Y(s) - 2sY(s) + Y(s) - sy(0) + 2y(0) - y'(0) = 0

Solve for Y(s) by factoring and isolating it:

(Y(s)(s^2 - 2s + 1)) - (sy(0) - 2y(0) + y'(0)) = 0

Y(s) = (sy(0) - 2y(0) + y'(0)) / (s^2 - 2s + 1)

Y(s) = (s - 1)y(0) + y'(0) / (s - 1)^2

Apply the inverse Laplace transform to find the solution y(t):

y(t) = (t - 1)y(0) + y'(0)e^t

Therefore, the solution to the initial value problem y'' - 2y' + y = 0 is y(t) = (t - 1)y(0) + y'(0)e^t.

To learn more about differential equations visit:

https://brainly.com/question/28099315

#SPJ11

The complete question is,

use the Laplace transforms to find the solution y(t) to the initial value problem  y'' - 2y' + y = 0

The volume of the solid that lies within both the cylinder is 4π/3

We can use cylindrical coordinates to solve this problem. In cylindrical coordinates, we have:

x = r cos θ

y = r sin θ

z = z

The equation of the cylinder is:

x^2 + y^2 = 4

Substituting in the expressions for x and y, we get:

r^2 cos^2 θ + r^2 sin^2 θ = 4

r^2 = 4

So the cylinder has radius 2 and height h.

The equation of the sphere is:

x^2 + y^2 + z^2 = 9

Substituting in the expressions for x and y, we get:

r^2 + z^2 = 9

So the sphere has radius 3.

To find the volume of the solid that lies within both the cylinder and the sphere, we need to integrate the function 1 over this region:

V = ∫∫∫ dV

In cylindrical coordinates, the volume element is:

dV = r dr dθ dz

The limits of integration are:

0 ≤ r ≤ 2

0 ≤ θ ≤ 2π

-√(9 - r^2) ≤ z ≤ √(9 - r^2)

So we have:

V = ∫∫∫ dV

V = ∫₀² ∫₀²π ∫_{-√(9 - r^2)}^{√(9 - r^2)} r dz dθ dr

V = ∫₀² ∫₀²π 2r√(9 - r^2) dθ dr

V = 2π ∫₀² r√(9 - r^2) dr

We can make the substitution u = 9 - r^2, du = -2r dr, and write:

V = -π ∫₉¹ √u du

V = -π [2/3 u^(3/2)]₉¹

V = -π [2/3 (9 - 1/3)]

V = 4π/3

So the volume of the solid that lies within both the cylinder and the sphere is 4π/3.

Learn more about volume here

brainly.com/question/17056637

#SPJ11

An equation that is parallel to the line 32x-y=15 is y = 32x - 47.

y' = 4x³

m = slope of tangent line =slope of the given line = 32

y' = 32 at the tangent point

4x³ = 32

x = 2

y = 2⁴+ 1 = 17

The tangent point is (2,17)

Tangent line:

y = 32x + b

17 = 32(2) + b

b = -47

y = 32x - 47

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

A straight line has a slope of f'(c), where f' is the derivative of f, and is said to be tangent to a curve at a point x = c if it passes through the point (c, f(c)) on the curve. Space curves and curves in n-dimensional Euclidean space have a similar definition.

To learn about Tangent:

https://brainly.com/question/4470346

#SPJ4

We were given that:

At equilibrium, we have:

Answer: 99,999

Step-by-step explanation:

Answer:P= 16 + 2\|65 units; A= 56 units2

Step-by-step explanation:

The scatterplot shows that the prediction of the height in centimeters of a student with a weight of 64 kilograms is 156cm.

It should be noted that a scatterplot simply means a type of data display which shows the relationship between two numerical variables.

From the complete question, the prediction of the height in centimeters of a student with a weight of 64 kilograms is 156cm. This was illustrated in the scatterplot.

Learn more about scatterplot on:

https://brainly.com/question/6592115

Answer: 2

Step-by-step explanation:

2.5(6x-4)=10+4(1.5+0.5x) [Work out the brackets]

15x-10=0+6+2x [Solve]

15x-10=16+2x [Convey the terms]

15x-2x=16+10 [Add up the same terms and calculate]

13x=26 [Divide both parts]

x=2

Answer:

x = 2

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

2.5(6x - 4) = 10 + 4(1.5 + 0.5x)

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 20 does indeed equal 20.

∴ x = 2 is a solution of the equation.