The Mathemagicians are about to reach our GOOOOAAAAALLLLLL. Can you reach yours?
Which of these three sets of transformations will score a goal? If the ball lands on a vertex with a player, the play fails. (All plays start at (0,4))

The polygon has 21 sides whose interior angle are in Arithmetic Progression (A.P.)

The interior angles of a polygon are in an arithmetic progression (A.P) if the difference between any two consecutive angles is constant. To find the number of sides in a polygon given its smallest angle and the common difference of its interior angles, we can use the formula:

n = (180° - smallest angle) / common difference + 1, where n is the number of sides in the polygon.

In this case, the smallest angle is 100° and the common difference is 4°, so the number of sides can be calculated as follows:

n = (180° - 100°) / 4° + 1 = (80°) / 4° + 1 = 20 + 1 = 21.

Therefore, the polygon has 21 sides. It is important to note that a polygon with 21 sides is called an icosikaihenagon, which is a highly unusual and exotic shape, as most polygons have a smaller number of sides.

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Answer:

absol value is 7 so pick the option that is 7.

Step-by-step explanation:

Hope this helps plz hit the crown :D

Answer:

(a) The conclusion of the test if null hypothesis is rejected is that we conclude that the null hypothesis that the defendant is not guilty is false and the defendant is found guilty and should be convicted.

(b) The consequence of a Type I error would be that an innocent defendant was found guilty and will be hanged but in actual he was not guilty.

(c) The conclusion of the test if we fail to reject the null hypothesis is that we conclude that the null hypothesis is true and the defendant is not guilty. The defendant should be set free.

(d) The consequence of a Type II error would be that a guilty defendant was set free but in actual it is found guilty and should be convicted.

Step-by-step explanation:

We are given the following hypothesis below;

Null Hypothesis, \(H_0\) : The defendant is not guilty.

Alternate Hypothesis, \(H_A\) : The defendant is guilty.

(a) The conclusion of the test if null hypothesis is rejected is that we conclude that the null hypothesis that the defendant is not guilty is false and the defendant is found guilty and should be convicted.

(b) Type I error states that the null hypothesis is rejected given the fact that null hypothesis was true.

So, here the Type I error would be to conclude that the defendant is guilty but in fact it was not guilty.

Hence, the consequence of a Type I error would be that an innocent defendant was found guilty and will be hanged but in actual he was not guilty.

(c) The conclusion of the test if we fail to reject the null hypothesis is that we conclude that the null hypothesis is true and the defendant is not guilty. The defendant should be set free.

(d) Type II error states that the null hypothesis is accepted given the fact that null hypothesis was false.

So, here the Type II error would be to conclude that the defendant is not guilty but in fact it was found guilty.

Hence, the consequence of a Type II error would be that a guilty defendant was set free but in actual it is found guilty and should be convicted.

Answer:

x < -4

Step-by-step explanation:

-64/16 = -4

Answer:

Step-by-step explanation:

LCD (15,20) = 60

\(\frac{2}{15}\) + \(\frac{1}{20}\) = \(\frac{8}{60}\) + \(\frac{3}{60}\) = \(\frac{11}{60}\)

Answer:

2/15 + 1/20 = 11/60

Step-by-step explanation:

1. Find the least common denominator or LCM of the two denominators:

15 and 20.

Steps to find LCM:

1. Find the prime factorization of 15

15 = 3 × 5

2. Find the prime factorization of 20

20 = 2 × 2 × 5

3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 3 × 5

LCM = 60

2. Next, find the equivalent fraction of both fractional numbers with denominator 60.

For the 1st fraction, since 15 × 4 = 60,

2/15 = 2 * 4 / 15 * 4 = 8/60

Likewise, for the 2nd fraction, since 20 × 3 = 60,

1/20 = 1 * 3 / 20 × 3 = 3/60

Add the two like fractions:

8/60 + 3/60 = 8 + 3/60 = 11/60

Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.

To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.

The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.

To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).

Payback Period = Cost of Education / Annual Increase in Earning Potential

Payback Period = $36,000 / $18,262

The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.

If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.

In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.

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The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answer: 4,6

Step-by-step explanation:

The factored form is (5x+2)(x-4).

What is factorization?

A number, matrix, or polynomial may be broken up or decomposed into factors that, when multiplied together, produce the original number, matrix, etc. This process is known as factorization or factoring.

Here, we have

Given:  5 x squared minus 18 x minus 8

we have to find the factored form.

= 5x² - 18x - 8

= 5x² - 20x + 2x - 8

= 5x(x-4) + 2(x-4)

= (5x+2)(x-4)

Hence, the factored form is (5x+2)(x-4).

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Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

Answer:

  $2496

Step-by-step explanation:

You want to know the cost of carpeting a 18 ft by 24 ft room with carpet that costs $52 per square yard.

The dimensions of the room in yards are (18 ft)/(3 ft/yd) = 6 yd, by (24 ft)/(3 ft/yd) = 8 yd.

In square yards, the area is ...

  (6 yd)(8 yd) = 48 yd²

The cost of one square yard of carpet is $52, so the cost of 48 square yards will be 48 times as much.

  (48 yd²)($52/yd²) = $(48·52) = $2496

The total price to carpet the floor is $2496.

__

Additional comment

We're reluctant to call this the total price, as there are usually additional charges for tax, carpet pad, delivery, installation, removal and disposal of old flooring, and possibly additional materials such as tack strips or thresholds. Repairing mold or water damage, or leveling the floor, can also add cost.

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Answer:

0.9986 = 99.86% probability that you win less than 40

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

The probability of winning a slot machine is 5% and you are going to play 500 pulls.

This means that \(p = 0.05, n = 500\)

Mean and Standard deviation:

\(\mu = E(X) = np = 500*0.05 = 25\)

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734\)

What’s the probability that you win less than 40?

Using continuity correction, this is P(X < 40 - 0.5) = P(X < 39.5), which is the pvalue of Z when X = 39.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{39.5 - 25}{4.8734}\)

\(Z = 2.98\)

\(Z = 2.98\) has a pvalue of 0.9986

0.9986 = 99.86% probability that you win less than 40

Giant one method: It is the method in which we multiply any fraction and we get an equivalent fraction.

For example:

1/2 x 1 (giant one) can also be written as:

=> 1/2 x 8/8

=> 8/16

It is also the method in which we divide any fraction and we get an equivalent fraction.

For example:

21/30 ÷ 1 (giant one) can also be written as:

=> 21/30 ÷ 3/3

=> 7/10

Solving the question:

2/1 ÷ 3/11

Solving this we get

=> 2 x 11/3 = 22/3

Multiplying giant one (1) through the giant one method.

=> 22/3 x 1 (giant one)

Multiplying both numerator and denominator by 3.

=> 22/3 x 3/3

=> 66/9

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The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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Answer:

Linear

The 500 hundred gallons is adding up by the hours. Linear- first difference.

The approximate height of the pole in centimeters is 17,500 centimeters.

We have,

Let's start by calculating the total length of the pole, which is buried plus the part that protrudes from the ground.

We know that the part that protrudes is 25 meters and that it represents one-seventh of the total length.

25 = L/7

where L is the total length of the pole.

We can solve for L by multiplying both sides of the equation by 7:

L = 7 x 25

  = 175 meters

Now we need to convert this length to centimeters.

Since 1 meter is equal to 100 centimeters,

175 meters x 100

= 17,500 centimeters

Therefore,

The approximate height of the pole in centimeters is 17,500 centimeters.

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The complete question.

The Clarisse company, dedicated to the telephone business, is expanding its coverage, due to this, it is placing poles, where the seventh part of a pole is buried, and protrudes 25 meters from the ground. Calculate the approximate height of the pole in centimeters.

Answer:

\(\huge\boxed{\sf r = 5}\)

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

\(\rule[225]{225}{2}\)

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

Answer: you need to add

Step-by-step explanation: I would ask your teacher to help you understand the lesson.  

The vοlume οf the prism is 14 cubic feet.

A three-dimensiοnal structure having six rectangular faces is called a prism. It is alsο knοwn as a rectangular cubοid οr a rectangular parallelepiped.

The prism is cοmpletely filled with 1750 cubes that have an edge length οf 1/5 ft. This means that the vοlume οf each cube is \((1/5)^3 = 1/125\) cubic feet.

Tο find the vοlume οf the prism, we can divide the tοtal vοlume οf the cubes by the number οf cubes:

Vοlume οf prism = (Vοlume οf οne cube) x (Number οf cubes)

Vοlume οf prism = (1/125) x 1750

Vοlume οf prism = 14 cubic feet

Therefοre, the vοlume οf the prism is 14 cubic feet.

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Answer: 8.24%

Step-by-step explanation:

To calculate the annual percentage rate (APR) and the effective annual rate of interest on Aruna's investment, we need to know the following information:

The initial investment amount (Rs 150,000)

The final investment amount (Rs 168,925)

The time period of the investment (18 months)

The frequency of interest payments (every 3 months)

The interest earned on the investment is the difference between the final investment amount and the initial investment amount. In this case, the interest earned is:

Rs 168,925 - Rs 150,000 = Rs 18,925.

Calculate the interest rate per period: To find the interest rate per period, divide the interest earned by the initial investment amount and multiply by the number of periods per year. In this case, the interest rate per period is:

(Rs 18,925 / Rs 150,000) * (4 periods per year) = 0.08%.

Calculate the APR: The APR is the interest rate per period multiplied by the number of periods in the investment. In this case, the APR is:

0.08% * 18 months = 8%.

The effective annual rate of interest takes into account the compounding of interest over time. To calculate the effective annual rate of interest, we use the formula:

(1 + r/n)^n - 1, where r is the interest rate per period and n is the number of compounding periods per year.

In this case, the effective annual rate of interest is:

(1 + 0.08%/4)^4 - 1 = 8.24%.

So the annual percentage rate (APR) is 8% and the effective annual rate of interest is 8.24%

Answer:

Height of Flagpole: 24.03 feet

Length between tip of flagpole and tip of shadow: 46.67 feet

Step-by-step explanation:

So the angle of elevation (31°) is facing directly opposite of the flagpole. The shadow of the flagpole (40 ft) is adjacent to the angle of elevation. Therefore, the tangent function incorporates both the opposite and adjacent sides of the right triangle created. We would then make the equation and solve for the height of the flagpole which is the opposite side (h in this case):

tanθ = opposite/adjacent

tan(31°) = h/40

40tan(31°) = h

24.03442476 = h

h ≈ 24.03

Therefore, the height of the flagpole is about 24.03 ft.

As for your bonus question, the length of the tip of the flagpole to the tip of the shadow would be the hypotenuse of the triangle created, which can easily be found using the Pythagorean Theorem (using exact values):

a² + b² = c²

(40tan(31))² + (40)² = c²

577.6535736 + 1600 = c²

2177.6535736 = c²

46.66533589 = c

c ≈ 46.67

Therefore, the length from the tip of the flagpole to the tip of the shadow is 46.67 ft.

Answer:The answer is: D y=5x²-5x-30

Step-by-step explanation:

Answer:

Graph B

Step-by-step explanation:

Hope I helped!

 Graph given option B will be the answer.

 This question is incomplete without the options, find the graphs attached.

Parent function for the given expression → \(y=2^x\)

If the graph of \(y=2^x\) is reflected across x-axis, the new function will be,

\(y=-2^x\)

Further the inverted function is translated down by 1 unit on y-axis then the image function will be,

\(y=-2^x-1\)

 Hence, the graph given in option B will be the answer.

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Answer: 9

Step-by-step explanation:

4x²-7x+7   f(2)=4*(2)^2-7(2)+7=16-14+7=9

A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:

a. Revenue Function:

Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.

The revenue function can be formulated as:

Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)

In equation form:

Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

b. Constraints:

The constraints for the availability of ingredients can be formulated as follows:

Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280

Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300

Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80

Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250

Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190

Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

c. Solve the system of linear inequalities using E x c e l Solver:

To solve the system of linear inequalities using E x c e l Solver, follow these steps:

1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:

| | A | B |

|-----|-----------|-----------------|

| 1 | Cakes | Selling Price |

| 2 | Cake 1 | $9 |

| 3 | Cake 2 | $12 |

| 4 | Cake 3 | $4 |

| 5 | Cake 4 | $5 |

| 6 | Cake 5 | $8 |

| | | |

| | | Formula |

| 9 | Milk | 280 |

| 10 | Sugar | 300 |

| 11 | Eggs | 80 |

| 12 | Flour | 250 |

| 13 | Cream | 190 |

2. In cell B16, enter the formula for the revenue:

=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11

3. In cell B18, enter the formula for the milk constraint:

=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6

4. In cell B19, enter the formula for the sugar constraint:

=7×B2 + 4×B3 + 5×B4

5. In cell B20, enter the formula for the egg constraint:

=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6

6. In cell B21, enter the formula for the flour constraint:

=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6

7. In cell B22, enter the formula for the cream constraint:

=4×B2 + 5×B4 + B5 + 3×B6

8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:

=B2

9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:

=B3

=B4

=B5

=B6

10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.

11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).

12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).

13. Click on the "Add" button in the "Subject to the Constraints" section.

14. In the Constraint window, select the range B18:B22 for the constraint cells.

15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.

16. Set the Solver options as desired, and click on the "Solve" button.

E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.

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1. It is false that when non-Standard unit used is small few unit's are

needed .

2. Objects with different shapes can have the same volume. True

3. Length, width and height and multiplied to find volume of a rectangular prism. True

4. It is false that volume is measured in square unit.

5. It is true that Volume is a measure of the amount of space inside an object.

6. The formula for volume of a rectangular prism is V = l × w × h. True

7. It is true that Standard units give a consistent and accurate measure of a container.

8. It is false that Non-Standard units cannot be used to measure volume.

9. Volume is measured in cubic units. True

Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.

Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).

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Answer:

x=4.697636

Step-by-step explanation:

Step 1: Multiply both sides by x.

Step 2: Multiply both sides by x^2.