A witness at the scene of a hit-and-run accident saw that the car that caused the accident had a license plate with only the letters I, R, L, T, O, and A. Find the probability that the license plate starts with a T and ends with an R.

Answer:

1-100

Step-by-step explanation:

The number of times you write 2 as a factor of 552 is 3 times.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given numerical expression is 23·24.

Here, equivalent expression is 552

Factor of 552 is

2×2×2×3×23

Therefore, the number of times you write 2 as a factor of 552 is 3 times.

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Answer:

it will grow by 1.44 people

Step-by-step explanation:

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Answer:

no because she would get the same total if she added it before or after

Step-by-step explanation:

the length of side x = 12.5.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, we have,

From the given figure, we get.

These two figures are similar.

so, we have,

8/x=y/5 ............(1)

10/15=4/z ......(2)

8/15=y/z .....(3)

Solving we get,

x=12.5

Hence,  the length of side x = 12.5.

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Answer:

the green and the yellow

Answer:

x = 61

Step-by-step explanation:

Supplementary angles sum to 180°

sum the 2 angles and equate to 180

2x + 6 + x - 9 = 180 , that is

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61

The measure of angles ∠CDE and ∠EDF which are supplementary are 128° and 52° respectively.

Two angles are said to be complementary when their sum is 90°

We know two angles are supplementary when their sum is 180°.

Given that ∠CDE and ∠EDF are supplementary.

Also given m∠CDE is (2x + 6)° and m∠FDE is (x - 9)°.

∴ ∠CDE +  ∠EDF = 180°.

(2x + 6)° + (x - 9)° = 180°.

(2x + x + 6 - 9)° = 180°.

(3x - 3)° = 180°.

3x = 183°.

x = 51°.

So, m∠CDE = (2×61 + 6)° = 128° and m∠EDF = (61 - 9)° = 52°.

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To write a cosine equation to represent the height of a passenger on the Ferris Wheel at any time, we can start by determining the key parameters involved.

Given:

Maximum height of the Ferris Wheel: 30 m

Time for one complete revolution: 4 minutes

Passengers board 2 m above the ground at the bottom of the revolution

To create a cosine equation, we can use the general form: h(t) = A * cos(B * (t - C)) + D

Where:

A represents the amplitude (half the vertical distance between the maximum and minimum values)

B represents the frequency (the number of cycles or revolutions per unit of time)

C represents the phase shift (horizontal shift of the waveform)

D represents the vertical shift (shift of the waveform up or down)

In this case, the maximum height is 30 m, so the amplitude (A) is 30/2 = 15 m. The Ferris Wheel takes 4 minutes to complete one revolution, so the frequency (B) is 2π/4 = π/2.

To determine the phase shift (C), we need to find the time at which the passenger starts boarding the Ferris Wheel. Since the passengers board 2 m above the ground at the bottom of the revolution, we can consider this as the starting point. Thus, the phase shift is 0.

Lastly, the vertical shift (D) is 2 m above the ground level where passengers board.

Putting it all together, the cosine equation representing the height of a passenger on the Ferris Wheel at any time (t) in minutes is:

h(t) = 15 * cos((π/2) * (t - 0)) + 2

Simplifying:

h(t) = 15 * cos((π/2) * t) + 2

This equation describes the height of a passenger on the Ferris Wheel as a function of time.

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There are 21 unique ways the first and second place ribbons can be awarded.

The given information can be solved using permutations. The total number of ways the first and second place ribbons can be awarded is: `7P2`The formula for permutation is given by:nPr = n!/(n-r)!Where, n is the total number of objects and r is the number of objects to be arranged in a permutation.

As per the given question, n = 7 (number of contestants) and r = 2 (number of ribbons).Therefore, the total number of ways the first and second place ribbons can be awarded is:7P2 = 7!/(7-2)! = 7!/5! = 7 x 6/2 x 1 = 21Thus, there are 21 unique ways the first and second place ribbons can be awarded.

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The required volume of the given solid is (√16 - r²) -(-√16 - r²).

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

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Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

Answer: (-6,-9)

Step-by-step explanation: you probably don't wanna read this but in case someone asks you about it- first start by putting the first equation into graphing form, turning it into 2y=-3x+12.

then you can go ahead and multiply the second equation by two to get 2(y=1/2x-6), which is 2y=x-12.

next, just subtraction! 2y=-3x+12 minus 2y=x-12!

You get -4x=24, which leaves you to divide both sides by -4 to get x=-6!

now to put in x for the solution, you take a equation(either one) and put in x

[y=1/2(-6)-6]

[y=-3-6]

[y=-9]

so your points are (-6,-9)

Answer:

C: 125

Step-by-step explanation:

First of all we can see that one angle is 55 degrees. Due to the fact it is on a straight line, we can assume to angle directly on the left of it, 6 is 180-55. Because a straight line is 180 degrees and we already have 55 degrees filling it. So if we do that, we can see that angle number 6 is 125 degrees. Which if we use the corresponding angles theroem, we get that angle number 1 is also 125 degrees. And because number 1 and x are corresponding angles, x is also 125 degrees. There are many ways to do it but I did this way the fastest. I challenge you to try to find another way to solve it.

Hope this helps!

Answer:

y = -½x + 7

Step-by-step explanation:

To write the equation of the line in slope-intercept form, y = mx + b, find the slope value (m) and the y-intercept value (b).

Using any two points on the line, say (0, 7) and (2, 6):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 7}{2 - 0} = \frac{-1}{2} \)

Slope (m) = -½

y-intercept (b) = 7 (this is where the y-axis is cut across by the line)

To write the equation, substitute m = -½, and b = 7 into y = mx + b.

Thus:

y = -½x + 7

Answer:

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

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

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

Step-by-step explanation:

• George's Height, = 1.75 meters

We know,

Let's convert:

Then,

• Martha's Height, = 160 cm

We know,

Let's convert:

In millimeters,

George is 1750 mm

Martha is 1600 mm

Difference in height = 1750 - 1600 = 150 mm

Thus,

To find the area bounded above by y = 3x and below by y = 4x^2, we need to calculate the definite integral of the difference between the upper and lower curves over the appropriate interval.

The intersection points of the two curves can be found by setting them equal to each other:

3x = 4x^2

Rearranging the equation:

4x^2 - 3x = 0

Factoring out x:

x(4x - 3) = 0

So, x = 0 or x = 3/4.

To determine the area, we integrate the difference between the curves from x = 0 to x = 3/4:

Area = ∫[0, 3/4] (3x - 4x^2) dx

Evaluating the integral:

Area = [3/2 * x^2 - 4/3 * x^3] from 0 to 3/4

Plugging in the upper limit:

Area = (3/2 * (3/4)^2 - 4/3 * (3/4)^3) - (3/2 * 0^2 - 4/3 * 0^3)

Simplifying:

Area = (9/32 - 27/256) - 0

Area = 9/32 - 27/256

Finding a common denominator:

Area = (72/256 - 27/256)

Area = 45/256

Therefore, the area bounded above by y = 3x and below by y = 4x^2 is 45/256.

Hence, the correct answer is option B) 45/64.

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Answer:

The answer is C.

Step-by-step explanation:

4 x 12 is how much money per worker per hour. 20 x 160 is how much the cost for the concrete. Adding them gets you the total cost.

Hope this helped!

The equation that can be used to describe the contractor’s total cost, C, if the project takes h hours to complete is C = (4 × 12)h + (20 + 160)

Given:

Number of workers = 4

Earnings of each work = $12

Yards of concrete = 20 cubic yards

Cost per cubic yards = $160

let

C = total cost

h = number of hours needed to complete the project

C = (Number of workers + Earnings of each work)number of hours + (Yards of concrete + Cost per cubic yards)

C = (4 × 12)h + (20 + 160)

Therefore, the equation that can be used to describe the contractor’s total cost, C, if the project takes h hours to complete is C = (4 × 12)h + (20 + 160)

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To determine the percentage of times the machine will dispense more than 7.1 oz of coffee, we need to calculate the z-score and find the corresponding area under the normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / σ

where x is the value we're interested in (7.1 oz), μ is the mean (7.6 oz), and σ is the standard deviation (0.5 oz).

Let's calculate the z-score:

z = (7.1 - 7.6) / 0.5

z = -0.5 / 0.5

z = -1

Now we need to find the area under the normal distribution curve for a z-score of -1. We can use a standard normal distribution table or a statistical calculator to find this area.

The area corresponds to the probability that the machine will dispense more than 7.1 oz.

Using a standard normal distribution table, we can find that the area to the left of z = -1 is approximately 0.1587. Since we're interested in the area to the right (more than 7.1 oz), we subtract this value from 1:

P(X > 7.1) = 1 - 0.1587

P(X > 7.1) ≈ 0.8413

Therefore, the vending machine will dispense more than 7.1 oz approximately 84.13% of the time.

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Answer:

1. measure of angle E is 90 degrees

2. Measure of angle F + measure of angle G is 90 degrees

Step-by-step explanation:

Angle E is 90 degrees because it is marked as a right angle (the square)

A triangle has 180 degrees so if E is 90 degrees then the other 2 also have to equal 90 degrees

The value of Stigma notation to represent the sum of the first five terms of the sequence is -65.

The sequence can be written as : -5, -9, -13, ...

To find the sum of the first five terms of the above sequence, we need to apply the formula of Stigma notation that can be defined as the sum of the terms in a sequence. We can use Stigma notation to represent the sum of the first five terms of the given sequence. We will use the letter "n" to represent the number of terms we will use in the sequence. Then the given sequence can be represented as: S₅ = -5 - 9 - 13 - 17 - 21.To find the value of Stigma notation, the given formula can be used: Stigma notation can be defined as :∑a_n = a₁ + a₂ + a₃ + a₄ + a₅ + ... + a_n, where n represents the number of terms that are included in the sequence. To find the sum of the first five terms of the sequence: S₅ = -5 - 9 - 13 - 17 - 21We have n = 5 because we are finding the sum of the first five terms of the sequence .Therefore, ∑a₅ = -5 - 9 - 13 - 17 - 21= -65

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Answer:

Step-by-step explanation:

y - 8 = -2/3(x + 3)

y - 8 = -2/3x - 2

y = -2/3x + 6

Answer:

4*10^7

Step-by-step explanation:

If it is a single digit then round up the number

7 represents the number of spaces the decimal travels to make the given number a single digit.

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

Step-by-step explanation:

\(\frac{2}{9}=\frac{2*3}{9*3}=\frac{6}{27}\\\\\frac{2}{9}=\frac{2*4}{9*4}=\frac{8}{36}\\\\\frac{2/2}{9/2}=\frac{1}{4.5}\)

Answer:

1.47 times 10 to the power of -3

Step-by-step explanation:

8th grade math I'm guessing lol

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis.

A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.

A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

The alternative and null hypotheses are listed below.

Lack of hypothesis H0: μ = 13

Ha: 13 Alternative Hypothesis

Statistical test, z = (xbar - mu)/(sigma/sqrt(n))

z = (11 - 13)/(8/sqrt(50))

z = -1.77

Region of Rejection

For α= 0.05, this is a left-tailed test.

Z has a critical value of -1.645.

Therefore, if z -1.645, reject H0 and accept the null hypothesis.

P-value Approach

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis

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Step 1. The expression that we have is:

And we need to solve for v.

Step 2. To solve this problem we use the following rule for absolute value expressions:

In our case:

Step 3. The final step to solve is to subtract 4 to all parts of the expression:

Answer:

The drama club must sell at least 74 student tickets in order to meet the show's expenses.

Let's denote the number of student tickets sold as "S".

We know that each student ticket sells for $7.50, so the total revenue from student ticket sales is 7.50S dollars.

We are also given that each adult ticket sells for $10, and 37 adult tickets were sold. Therefore, the revenue from adult ticket sales is 10 * 37 dollars.

The total revenue from ticket sales must be at least $920 to cover the show's costs. Therefore, we can set up the equation:

7.50S + 10 * 37 ≥ 920

Now, we can solve this equation to find the range of possible values for S:

7.50S + 370 ≥ 920

7.50S ≥ 920 - 370

7.50S ≥ 550

S ≥ 550 / 7.50

S ≥ 73.33

Since the number of student tickets must be a whole number, the smallest possible value for S is 74. Therefore, the drama club must sell at least 74 student tickets in order to meet the show's expenses.

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Answer:

16 i think

Step-by-step explanation:

The x-intercept will be at (16,0) and the y-intercept at (0, 6).

We have to solve for y by substituting 0 as the value of x. This will be:

24x + 64y = 384

24(0) + 64y = 384

64y = 384

y = 384/64

y = 6

We have to solve for x by substituting 0 as the value of y. This will be:

24x + 64y = 384

24x + 64(0) = 384

24x = 384

x = 384/24

x = 16

Answer:

The x-intercept, at the point (16, 0) indicates the choice to produce fruit for 16 minutes. In 16 minutes, producing 24 cans of fruit a minute, all 384 cans for the order will be completed. The zero for the y-value represents that no time is spent producing cans of vegetables.

Step-by-step explanation:

sample response edg 2021