Please help me guys please

Answer:

Step-by-step explanation:

The value of y is given in equation 2

Putting value of y = 3x in equation 1

Y = - x + 4

3x = - x + 4

Bringing like terms on one side

3x + x = 4

4x = 4

x = 4/4 = 1

Now putting value of x = 1 in equation 2

Y = 3x

Y = 3(1) = 3

The answers are as follows 1. The slope of the regression line predicting the number of accidents from the posted speed limit is -0.510 (approx). 2. The y-intercept of the regression line predicting the number of accidents from the posted speed limit is 150.43 (approx). 3. The predicted number of reported accidents for a posted speed limit of 10 mph is 145.

1. The slope of the regression line predicting the number of accidents from the posted speed limit: Given, Posted Speed Limit: 51, 47, 41, 38, 21, 20Reported Number of Accidents: 27, 26, 21, 16, 17, 11

The scatter plot for the given data is: The equation of the regression line is y = ax + b, where y is the dependent variable, x is the independent variable, a is the slope of the line, and b is the y-intercept of the line.

Therefore, Slope (a) of the regression line can be found by: Slope (a) = [n(∑xy) - (∑x)(∑y)] / [n(∑x²) - (∑x)²]Here, n is the number of data points∑x = 218, ∑y = 118∑xy = 4448, ∑x² = 9950n = 6. Therefore, slope of the regression line is: Slope (a) = [6(4448) - (218)(118)] / [6(9950) - (218)²] = -0.510 (approx)

Hence, the slope of the regression line predicting the number of accidents from the posted speed limit is -0.510 (approx).

2. The intercept of the regression line predicting the number of accidents from the posted speed limit: The slope of the regression line has already been found in the above question.

Now, we can find the y-intercept of the regression line by using the slope (a) and the following formula: y-intercept (b) = (∑y - a(∑x)) / n. Here, n is the number of data points∑x = 218, ∑y = 118a = -0.510

Therefore, the y-intercept of the regression line predicting the number of accidents from the posted speed limit is: y-intercept (b) = (118 - (-0.510)(218)) / 6= 150.43 (approx)

Hence, the y-intercept of the regression line predicting the number of accidents from the posted speed limit is 150.43 (approx).

3. Predict the number of reported accidents for a posted speed limit of 10mph: Using the equation of the regression line:y = ax + by = -0.510x + 150.43Putting x = 10, we get:y = -0.510(10) + 150.43= 145.4 (approx)

Rounding to the nearest whole number, the predicted number of reported accidents for a posted speed limit of 10 mph is 145.

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Answer:-12x

Step-by-step explanation:

just trust me on this

The probability of losing less than $72 in total is 0.68.

To find the probability of losing less than $72 in total, we need to first calculate the expected loss for each game and then use the law of total probability to find the overall probability.

First, let's calculate the expected loss for each game. The expected loss for the first game is 36 * -2 = -72, and the expected loss for the second game is 50 * -1.5 = -75.

Now, we need to use the law of total probability to find the overall probability of losing less than $72 in total. The law of total probability states that the probability of an event occurring is the sum of the probabilities of the event occurring under each possible condition. In this case, the possible conditions are losing less than $72 in the first game and losing less than $72 in the second game.

So the overall probability of losing less than $72 in total is:

P(losing less than $72) = P(losing less than $72 in first game) + P(losing less than $72 in second game) - P(losing less than $72 in both games)
= (36/100) + (50/100) - (36/100) * (50/100)
= 0.36 + 0.5 - 0.18
= 0.68

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We integrate each component separately over the given limits of t. Evaluating the integral for each component will yield the final result of the line integral of F along the line segment C from (0, 0, 0) to (4, 3, 2).

A line integral is a way to calculate the work done by a force along a curve. In this case, we have the vector field F = xeyz and the curve C, which is the line segment from (0, 0, 0) to (4, 3, 2). The line integral of F along C can be written as ∫CF · dr, where dr is the differential vector along the curve.

To evaluate this line integral, we parameterize the curve C. Since C is a line segment, we can use a linear parameterization. Let's denote the parameter as t, ranging from 0 to 1. We can express the coordinates of C as x = 4t, y = 3t, and z = 2t.

Next, we need to find the differential vector dr along curve C. Taking the derivatives of the parameterized equations with respect to t, we obtain dx = 4dt, dy = 3dt, and dz = 2dt. Hence, dr = (dx, dy, dz) = (4dt, 3dt, 2dt).

Substituting these values into the line integral, we have ∫CF · dr = ∫CF(x, y, z) · (4dt, 3dt, 2dt). Simplifying the expression, we get ∫C(4xeyz dt, 3xeyz dt, 2xeyz dt).

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Answer:

a^4+2ab^2+b^4+a^16+2ab^8+b^16

Step-by-step explanation:

(a^2+b^2)^2+(a^8+b^8)^2

(a^2+b^2)^2=(a^2+b^2)(a^2+b^2)

=a^2(a^2+b^2)+b^2(a^2+b^2)

=a^4+(ab)^2+(ba)^2+b^4

=a^4+2ab^2+b^4

(a^8+b^8)^2=(a^8+b^8)(a^8+b^8)

=a^8(a^8+b^8)+b^8(a^8+b^8)

=a^16+(ab)^8+(ba)^8+b^16

=a^16+2ab^8+b^16

(a^2+b^2)^2+(a^8+b^8)^2=(a^4+2ab^2+b^4)+(a^16+2ab^8+b^16)

the answer is a^4+2ab^2+b^4+a^16+2ab^8+b^16

i think it is simplified answer

The height of the rectangular pyramid is 16 units.

To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:

Volume = (1/3) * base area * height

Given that the volume of the rectangular pyramid is 512 units^3, and the length of the rectangular base is 8 units and the width is 12 units, we can find the base area:

Base Area = length * width = 8 * 12 = 96 units^2

Now we can substitute the values into the volume formula:

512 = (1/3) * 96 * height

To solve for the height, we can isolate it by multiplying both sides of the equation by 3/96:

512 * 3/96 = height

Simplifying the right side of the equation:

16 = height

The rectangular pyramid is 16 units tall as a result.

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Answer:

The correct answer is a = 44.

Step-by-step explanation:

To solve this problem, we need to isolate the variable (a) on one side of the equation. Our first step should be to subtract 6 from both sides, which gives us:

6 + a/2 - 6 = 28 - 6

a/2 = 22

Next, we should multiply both sides by 2 to cancel out the fraction on the left side of the equation and get the variable a alone.

a/2 * 2 = 22 * 2

a = 44

Therefore, the answer to your question is a = 44.

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The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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Answer: (-2,-2)

Step-by-step explanation:

Start at finding the y-intercept(-3) then do rise over run with -2x

Rise over run is count up/down then left/right

Answer:

D, Circle

Step-by-step explanation:

All the other shapes are 3D and have a volume.

Answer:

It looks like the Bears have the higher wins, as they won 40 games while the Bulls won only 32 games.

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

The speed of the river is 7.5 kilometers per hour.

Let the speed of boat in still water = u = 14 km/h

Let the speed of river = v = x km/h

Upstream speed = u - v = 14 - x

Downstream speed = u + v = 14 +x

Distance paddled upstream = \(D_{1}\) = 5 km

Distance paddled downstream = \(D_{2}\) = 10 km

Time taken (upstream) = \(T_{1}\) = \(\frac{D_{1} }{u-v}\)

Time taken (downstream) = \(T_{2}\) = \(\frac{D_{2} }{u+v}\)

According to question,

        \(T_{1}\) = \(T_{2}\)

      \(\frac{D_{1} }{u-v}\) = \(\frac{D_{2} }{u+v}\)

     \(\frac{5}{14-x}\) = \(\frac{10}{14+x}\)

5(14 + x) = 10(14 - x)

   14 + x = 2(14 - x)

   14 + x = 28 - 2x

  x + 2x = 28 - 14

        3x = 14

          x = \(\frac{14}{3}\)

          x = 7.5

Hence, Speed of river is 7.5 km/h.

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Jax bought 92 trees to satisfy these three conditions.

To find the number of trees Jax bought, we can start by setting up a system of equations based on the given conditions:

Let's say the number of trees Jax bought is 'x'.

Condition 1: Jax had enough trees to plant 8 equal rows and one tree died.
So, the number of trees after one tree died is (x - 1).

Condition 2: Jax had enough trees to plant 9 equal rows after one tree died.
Therefore, (x - 1) should be divisible by 9.

Condition 3: Jax had enough trees to plant 10 equal rows after one tree died and another tree was stolen.
So, the number of trees after two trees were lost is (x - 2).

Therefore, (x - 2) should be divisible by 10.

By solving these equations simultaneously, we can find the value of 'x'.

(x - 1) should be divisible by 9, and (x - 2) should be divisible by 10. The least common multiple of 9 and 10 is 90.

So, (x - 2) should be equal to 90.

Therefore, x - 2 = 90
Simplifying the equation, we get:
x = 92

Hence, Jax bought 92 trees to satisfy these three conditions.

By finding the least common multiple of 9 and 10, which is 90, we can set up the equation (x - 2) = 90.

Solving for x, we get x = 92. Therefore, Jax bought 92 trees to satisfy all three conditions.

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To evaluate the specific values of the derivative of the function f(x) = 3x^(1/4)(x^3 - 7), we need to calculate f'(x) and substitute the given values.

To find the derivative of f(x), we apply the product rule and the power rule of differentiation. The derivative of f(x) is given by:

f'(x) = 3x^(1/4) * d/dx(x^3 - 7) + (x^3 - 7) * d/dx(3x^(1/4))

Using the power rule and the derivative of a constant, we can simplify the expression to:

f'(x) = 3x^(1/4) * (3x^2) + (x^3 - 7) * (3/4)x^(-3/4)

Simplifying further, we have:

f'(x) = 9x^(9/4) + (3/4)(x^3 - 7)x^(-3/4)

Now, we can evaluate the specific values of the derivative:

(a) For x = 1, we substitute x = 1 into f'(x):

f'(1) = 9(1)^(9/4) + (3/4)((1)^3 - 7)(1)^(-3/4)

      = 9 + (3/4)(-6)

      = 9 - 9/2

      = 9/2

Therefore, f'(1) = 9/2.

(b) For x = 4, we substitute x = 4 into f'(x):

f'(4) = 9(4)^(9/4) + (3/4)((4)^3 - 7)(4)^(-3/4)

To evaluate this value, you can plug in the given values and perform the calculations.

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In a case whereby a ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the time the ball is thrown will it strike the​ ground at t = 2.5 or -3.5.

Height of building = 140 ft

Initial velocity, u = 16 ft/sec

the equation given is

h = -16t² -16t +140

h(t) = -16t² -16t +140

AT h(t) = 0 , We can divide by -2 and have

(8t² + 8t - 70) = 0

8t² + 8t - 70 = 0

Then if we solve with quadratic equation formula where  a=8, b=8, c=- 70 then the root will be -7/2 and 5/2 then  t = 2.5 or -3.5

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complete question;

A ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the height of the ball h in feet after t seconds is given by the equation h equals negative 16 t squared minus 16 t plus 140. how long after the ball is thrown will it strike the​ ground?

\(Draw\ \overline {AB}\perp\overline {CD}\ at\ point \ A.\)

To find the state matrices X_1, X_2, and X_3, we can use the transition probability matrix P and the initial state matrix X_0.

P = [0.6 0.2 0.1

0.3 0.7 0.1

0.1 0.1 0.8]

X_0 = [0.1 0.2 0.7]

To calculate X_1, we multiply the transition probability matrix P with the initial state matrix X_0:

X_1 = P * X_0

To calculate X_2, we multiply P with X_1:

X_2 = P * X_1

Similarly, to calculate X_3, we multiply P with X_2:

X_3 = P * X_2

Performing these matrix multiplications will give us the state matrices X_1, X_2, and X_3.

Note: Since the provided matrix P has a dimension of 3x3 and the initial state matrix X_0 has a dimension of 1x3, the resulting state matrices X_1, X_2, and X_3 will also have a dimension of 1x3.

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To find the state matrices X₁, X₂, and X₃ given the transition probabilities matrix P and the initial state matrix X₀, we can apply matrix multiplication repeatedly.

P = [0.6 0.2 0.1

0.3 0.7 0.1

0.1 0.1 0.8]

X₀ = [0.1

0.2

0.7]

To find X₁, we multiply P with X₀:

X₁ = P * X₀

To find X₂, we multiply P with X₁:

X₂ = P * X₁ = P * (P * X₀)

To find X₃, we multiply P with X₂:

X₃ = P * X₂ = P * (P * (P * X₀))

Performing the matrix multiplications, we get:

X₁ = [0.6 0.2 0.1] * [0.1

0.2

0.7] = [0.06 + 0.04 + 0.07

0.03 + 0.14 + 0.07

0.01 + 0.02 + 0.56]

X₁ = [0.17

0.24

0.59]

X₂ = [0.6 0.2 0.1] * [0.17

0.24

0.59] = [0.048 + 0.048 + 0.059

0.023 + 0.168 + 0.059

0.007 + 0.048 + 0.472]

X₂ = [0.155

0.25

0.527]

X₃ = [0.6 0.2 0.1] * [0.155

0.25

0.527] = [0.042 + 0.031 + 0.053

0.021 + 0.175 + 0.053

0.006 + 0.05 + 0.422]

X₃ = [0.126

0.249

0.478]

Therefore, the state matrices are:

X₁ = [0.17

0.24

0.59]

X₂ = [0.155

0.25

0.527]

X₃ = [0.126

0.249

0.478]

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Answer:

x=2/3

Step-by-step explanation:

25-(3x+5)=2(x+8)+x

25-3x-5=2x+16+x

20-3x=3x+16

20-3x-3x=16

20-6x=16

6x=20-16

6x=4x=4/6

simplify

x=2/3

Answer:

x=2/3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

Hello,

R(2)=-2

Step-by-step explanation:

\(F(x)=q_1(x)*x+0 \ , \ F(0)=0 \\F(x)=q_2(x)*(x+1)+1\ , \ F(-1)=1\\\\F(x)=q_3*x*(x+1)+(a*x+b)\\\\if\ x=0\ then\ F(0)=0=a*0+b \Longrightarrow\ b=0\\\\if\ x=-1\ then\ F(-1)=1=a*(-1)+b \Longrightarrow\ a=-1\\\\\\R(x)=ax+b=-x\\R(2)=-2\\\)

Step-by-step explanation:

the answer is in the image above

A school gymnasium can hold 256 people for an awards banquet. There will be 10 staff members in attendance. The principal is trying to determine how many guests each award recipient can invite if each invites the same number of people (p).

There are 41 award recipients. The principal's calculations are shown as follows:41p + 10 < 256 41p < 256 - 10 = 246 p < 246/41 p < 6, so p = 5Award recipients are able to invite more than 100 guests if the number of award recipients is less than or equal to 20. Since there are 41 award recipients, each can invite no more than 5 guests. The total number of guests that can be accommodated is:41(5) + 10 = 205 + 10 = 215Therefore, the calculations made by the principal are correct.

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Only two options are necessarily true for the triangle,

m∠r > 90°

m∠s + m∠t < 90°

In any triangle, the sum of the three angles is 180 degrees. If m∠r > m∠s + m∠t, then angle r must be the largest angle in the triangle. Additionally, the sum of the other two angles (s and t) must be less than 90 degrees.

Option m∠s = m∠t is not necessarily true because the two angles could be different and still add up to be less than m∠r. Options m∠r > m∠t, m∠r > m∠s, and m∠s > m∠t are not necessarily true and depend on the specific values of the angles in triangle RST.

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Answer:

  (b)  Both vertical and horizontal reflection

Step-by-step explanation:

The figure will be a horizontal reflection of itself about any vertical line through two of the smaller 6-pointed stars.

The figure will be a vertical reflection of itself about any horizontal line through two of the smaller 6-pointed stars.

  the pattern has both vertical and horizontal reflection

__

Additional comment

A pattern will have horizontal reflection if there exists a vertical line about which the pattern can be reflected to itself. That is, there exists one (or more) vertical lines of symmetry.

Similarly, the pattern will have vertical reflection if there is a horizontal line about which the pattern can be reflected to itself. Such a line is a horizontal line of symmetry.

Answer:

27720

Hope its right :)

Step-by-step explanation:

Answer:

202.5

Step-by-step explanation:

Start by finding the area of the triangle part using the lengths of 9 , 9 , and 5

That gives you 22.5

Then find the area of the rectangle part using the sides of 20 and 9

This gives you 180

When you add them you get 202.5

I hope that this helps!!

a) The 90% confidence interval for the population mean is approximately (21.52, 23.48).

b) The 95% confidence interval for the population mean is approximately (21.322, 23.678).

c) The 99% confidence interval for the population mean is approximately (20.926, 24.074).

To develop confidence intervals for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

where the standard error is equal to the sample standard deviation divided by the square root of the sample size.

a) For a 90% confidence interval, we need to find the critical value corresponding to a confidence level of 90%. The critical value can be obtained from the t-distribution table with (n-1) degrees of freedom. Since the sample size is 56, the degrees of freedom is 56-1 = 55.

From the t-distribution table, the critical value for a 90% confidence interval with 55 degrees of freedom is approximately 1.671.

The standard error can be calculated as:

Standard Error = sample standard deviation / sqrt(sample size)

Standard Error = 4.4 / sqrt(56)

Standard Error ≈ 0.5882

Now we can calculate the confidence interval:

Confidence Interval = 22.5 ± (1.671 * 0.5882)

Confidence Interval = 22.5 ± 0.9816

Confidence Interval ≈ (21.52, 23.48)

b) For a 95% confidence interval, the critical value for 55 degrees of freedom is approximately 2.004 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.004 * 0.5882)

Confidence Interval = 22.5 ± 1.178

Confidence Interval ≈ (21.322, 23.678)

c) For a 99% confidence interval, the critical value for 55 degrees of freedom is approximately 2.678 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.678 * 0.5882)

Confidence Interval = 22.5 ± 1.574

Confidence Interval ≈ (20.926, 24.074)

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Answer:

13.72 cm

Step-by-step explanation:

Perimeter of the given figure = sum of all sides

40 = x + 9.7 + 16.58

40 = x + 26.28

x = 40 - 26.28

x = 13.72 cm