How many different words can be formed with the letters SCHOOL? (The words formed do not have to be real words.)

Answer:

(7,5)

Step-by-step explanation:

The transformation that would produce an image with vertices B"(-2, 1), C"(3, 2), D"(0, -1) from the original vertices B(-3,0), C(2, -1), D(-1, 2) is the transformation (x,y) → (X + 1, y + 1).

By applying the transformation (x,y) → (X + 1, y + 1), each point's x-coordinate is shifted one unit to the right (X = x + 1), and each point's y-coordinate is shifted one unit upward (Y = y + 1). This results in the image with the given coordinates B"(-2, 1), C"(3, 2), D"(0, -1).

The other transformations listed do not match the given image coordinates and would not produce the desired result.

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Answer:

(x, y) → (x, −y) → (x + 1, y + 1)

Step-by-step explanation:

Reflect the vertices over the x-axis by applying the transformation (x, y) → (x, -y):

B'(-3, 0) → B'(-3, 0)

C(2, -1) → C(2, 1)

D(-1, 2) → D(-1, -2)

Translate the reflected vertices by (1, 1):

B'(-3, 0) → B″(-3 + 1, 0 + 1) → B″(-2, 1)

C(2, 1) → C″(2 + 1, 1 + 1) → C″(3, 2)

D(-1, -2) → D″(-1 + 1, -2 + 1) → D″(0, -1)

So, the correct sequence of transformations is:

(x, y) → (x, -y) → (x + 1, y + 1)

(Image provided for more proof)

Answer:

72

Step-by-step explanation:

Answer:

d) 3

Step-by-step explanation:

7x+4=25

7x=21

X=3

Answer: D. 3

Step-by-step explanation:

Given

7x+4=25

Subtract 4 on both sides

7x+4-4=25-4

7x=21

Divide 7 on both sides

7x/7=21/7

x=3

Hope this helps!! :)

Please let me know if you have any questions

15.49 =  3w + 10.99 & b = 3w + p

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

Answer:

12.566

12.6 (simplified to the tenths)

12.57(simplified to the hundredths)

Step-by-step explanation:

The diameter of a circle is always double of the radius

π is always ≈ 3.14

π * 2^2 = π * 4  ≈ 12.566

Answer:

Width = 6 m and lenght = 7 m

Step-by-step explanation:

Let x be the width of the rectangle.

lenght = 2x - 5

Perimeter means the addition of all sides of the rectangle.

Thus, x + x + 2x - 5 + 2x - 5 = 26

2x + 2x + 2x = 26 + 10

6x = 36, x= 6

Therefore, width is 6 m and lenght is 2 (6) -5 == 7 m

Hope it helps :)

Mark it as the brainliest answer pls :)

There are 144 possible sequences of chip colors.

We can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.

Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:

Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144

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Answer:

A

Step-by-step explanation:

-1/4,5/8

Answer:

it's the top one

Step-by-step explanation:

the x coordinate is -1/4 and the y coordinate is 5/8

Answer:

Step-by-step explanation:

19x - 5y = 5

slope intercept form y=mx+b b is the constant

Add y to the other side to make it positive : 19x = 5 + 5y

subtract 5 from each side: 19x -5 =5y

Divide both sides by 5 to get y by itself: (19/5)x - 1 = y

Rewrite: y= (19/5)x -1

The value of  Q(x) =   x² - 1  

R(x) = 4

What is Long Division?

Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.

By long Division method:

                        x² - 1            

                     _______________________________

         (3x - 4) | 3x³ - 4x² - 3x

                       3x³ - 4x²

                       _________________

                            0 - 0   - 3x      

                                       - 3x + 4  

                                ___________________

                                          0  + 4

Q(x) =   x² - 1  

R(x) = 4

Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1  ) + 4

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Answer:

1. Sides 1 and 2 are congruent so sides 3 are also congruent

2. Since angles D and R are the same and the two sides are the same, the triangles are the same

The solutions of the given differential equation are y(x) = e^(-7x) and y(x) = 0. To determine which functions are solutions of the differential equation y'' + 14y' + 49y = 0, we can substitute each function into the equation and check if it satisfies the equation.

The functions that satisfy the equation are the solutions.

Let's substitute each function into the given differential equation and check if it holds true.

a. y(x) = xe^(-7x):

Taking the first and second derivatives of y(x):

y'(x) = e^(-7x) - 7xe^(-7x)

y''(x) = -14e^(-7x) + 49xe^(-7x) - 7e^(-7x)

Substituting these derivatives into the differential equation:

(-14e^(-7x) + 49xe^(-7x) - 7e^(-7x)) + 14(e^(-7x) - 7xe^(-7x)) + 49(xe^(-7x)) = 0

Simplifying:

-14e^(-7x) + 49xe^(-7x) - 7e^(-7x) + 14e^(-7x) - 98xe^(-7x) + 49xe^(-7x) = 0

-7e^(-7x) = 0

The equation is not satisfied, so y(x) = xe^(-7x) is not a solution.

We can perform a similar analysis for the remaining functions:

b. y(x) = e^(7x): Not a solution.

c. y(x) = -7x: Not a solution.

d. y(x) = x^2e^(-7x): Not a solution.

e. y(x) = xe^(7x): Not a solution.

f. y(x) = e^(-7x): Solution.

g. y(x) = 0: Solution.

Therefore, the solutions of the given differential equation are y(x) = e^(-7x) and y(x) = 0.

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Answer: Large Box: 18.75 kilograms

Small Box: 15.75 kilograms

Step-by-step explanation:

l=large box. s=small box

5l+3s=141

7l+9s=273

(5l+3s=141)*3

15l+9s=423    ==> subtract this equation

7l+9s=273   ==> subtract this equation

8l=150 ==> subtract the two above equations

l=150/8

l=18.75

5(18.75)+3s=141

93.75+3s=141

93.75+3s=141.00

3s=47.25

s=15.75

Large Box: 18.75 kilograms

Small Box: 15.75 kilograms

Answer:

Answer is option a) 4/5

Here value of opposite side is 40

And the value of hypotenuse is 50

Step-by-step explanation:

\( \sin(C) = \frac{opposite \: side \: }{hypotenuse} \\ = \frac{40}{50} \\ = \frac{4}{5} \)

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Answer: Infinitely many solutions

Answer:

Below

Step-by-step explanation:

15x + 3y = 27     divide through by 3 to get

5x + y = 9    <====== this is the same equation as the first one so they are the SAME line ....meaning INFINITE solutions

The final amount of the investment is $852.88

The formula for the compound interest is given by:

A = P(1 + r/n)^(nt)

Where:

In this case, P = $700, r = 5% = 0.05, n = 2 (semi-annually compounded), and t = 4 years.

Plugging in the values, we get:

A = 700(1 + 0.05/2)^(2*4)

= 700(1.025)^8

= $852.88 (rounded to two decimal places)

Therefore, the final amount after 4 years is $852.88

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Answer:

4x+3y-23=0

Step-by-step explanation:

4x+3y-23=23-23

4x+3y-23=0

Answer:

2.08

Step-by-step explanation:

Answer:

this is the answer okkkkkkkkkkkkkkkk

Answer:

81 and 324

Step-by-step explanation:

total units->3+12=15

1u=405÷15=27

3u=27×3=81

12u=27×12=324

Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

a) Vf(x, y, z) = [2xy+8x, x²+4yz-14y+184y, 2y²+2yz].

b)  Therefore, (2, 1, -1) is not a stationary point of f.

c) The Hessian of f at the point (2, 1, -1) is 32.

(a) The vector gradient Vf of f at the point (x, y, z) is given by

[Vf(x, y, z)]=[(2xy+8x, x²+4yz-14y+184y, 2y²+2yz)].

Therefore, we get

Vf(x, y, z) = [2xy+8x, x²+4yz-14y+184y, 2y²+2yz].

(b) A point (a, b, c) is a stationary point of the function f if Vf(a, b, c)=0.

If we substitute x=2, y=1, and z= -1

in Vf(x, y, z) = [2xy+8x, x²+4yz-14y+184y, 2y²+2yz],

we get Vf(2, 1, -1) = [4, -42, 2], which is not zero.

If we substitute x=2,

y= 1, and

z= -1 in

Vf(x, y, z). we get Vf(2, 1, -1) = [4, -42, 2], which is not zero.

Therefore, (2, 1, -1) is not a stationary point of f.

(c) The Hessian Hf(x, y, z) of f is given by

Hf(x, y, z)=|fx² fxy fxz ||fxy fy² fyz ||fxz fyz fz² |

Substituting x=2,

y=1, and

z= -1,

we get Hf(2, 1, -1)=|8 6 -4 ||6 4 0 ||-4 0 4 |=32.

(d) If Hf(a, b, c) > 0 and fx(a, b, c) > 0, then (a, b, c) is a local minimizer of f.

If Hf(a, b, c) < 0 and fx(a, b, c) < 0, then (a, b, c) is a local maximizer of f.

If Hf(a, b, c) < 0, but fx(a, b, c) > 0 or Hf(a, b, c) > 0, but fx(a, b, c) < 0,

then (a, b, c) is a saddle point of f.

We have already found the value of Hf(2, 1, -1), which is positive.

We can also see that fx(2, 1, -1) = 2xy+8x

= 2(2)(1)+8(2)

= 20 > 0.

Therefore, (2, 1, -1) is a local minimizer of f.

d)  (2, 1, -1) is a local minimizer of f.

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Answer:

a = 55° and b = 60°

Step-by-step explanation:

→ Remember 2 key points about angles

→ Angle a is alternate to 55° so using the 2nd point,

a = 55°

→ Remember the fact that angle in a triangle add up to 180°

55°  + 65° + b = 180°

→ Collect the whole numbers

120° + b = 180°

→ Minus 120° from both sides to isolate b

b = 60°

The solution is : the measures of angles A and B are:

A = 55° and B = 60°

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

We know that 55+ b+ other angle = 180 since they make a straight line

The other angle = 65 since they are alternate interior angles

55+ B+ 65 = 180

Combine like terms

120 + B = 180

B = 60

A + B + 65 = 180

interior angles of a triangle must equal 180 degrees

A +60+ 65 =180  

Combine like terms

A +125 = 180

A = 55

Hence, The solution is : the measures of angles A and B are:

A = 55° and B = 60°

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The 90% confidence interval for the mean capacitance of this type of capacitor is (0.216, 0.238).

To find a 90% confidence interval for the mean capacitance of this type of capacitor, we will need to use the formula for confidence intervals. The formula for a confidence interval is:

Sample mean +/- Margin of error

Where the margin of error is calculated using the formula:

Z * (Standard deviation / sqrt(sample size))

Since we are given a 95% confidence interval, we can assume that the Z-value for a two-tailed test is 1.96. We can also assume that the standard deviation is unknown and use the sample standard deviation as an estimate. We are not given the sample size, so we cannot calculate the margin of error directly.

However, since we want to find a 90% confidence interval, we can use the fact that the margin of error for a 90% confidence interval will be smaller than the margin of error for a 95% confidence interval. We can use the margin of error from the 95% confidence interval and adjust it accordingly.

Using the formula for the margin of error, we get:

1.96 * (standard deviation / sqrt(sample size)) = 0.014

We can rearrange this formula to solve for the sample size:

sample size = (1.96 * standard deviation / 0.014)^2

Without knowing the standard deviation, we cannot calculate the sample size directly. However, we can estimate the standard deviation by using the range of the 95% confidence interval. The range is the difference between the upper and lower bounds:

range = 0.241 - 0.213 = 0.028

We can assume that the standard deviation is approximately equal to the range divided by 4. This is a rough estimate, but it should be good enough for our purposes.

standard deviation = range / 4 = 0.028 / 4 = 0.007

Now we can calculate the sample size:

sample size = (1.96 * 0.007 / 0.014)^2 = 49

So we would need a sample size of 49 to obtain a 90% confidence interval with the same margin of error as the 95% confidence interval. We can now use this sample size to calculate the margin of error for a 90% confidence interval:

1.645 * (0.007 / sqrt(49)) = 0.011

Finally, we can calculate the 90% confidence interval for the mean capacitance using the formula:

Sample mean +/- Margin of error

= 0.227 +/- 0.011

= (0.216, 0.238)

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Step-by-step explanation:

Probabibility = 1/6 * 1/6 = 1/36 = 2.77%.

A race car with wheels with diameter 66 cm must turn 1,088,000 times to cover a 300 km race. This is because the circumference of a wheel is equal to its diameter multiplied by pi, which is approximately 3.14.

So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.

The circumference of a circle is equal to its diameter multiplied by pi, which is approximately 3.14. So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.

In other words, the car must turn its wheels 1,445 times to cover the race distance. This is a lot of turns, but it is possible for a Formula 1 car to do this. The cars are designed to be very efficient and to have very low rolling resistance, which means that they can turn their wheels very quickly without losing too much energy.

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Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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