donald surveyed 16 students at his school and found that 8 of them planned to take auto shop as their next elective. what is the experimental probability that a randomly selected student plans to take auto shop? write your answer as a fraction or whole number. p(auto shop)

The angle of elevation of the Sun is approximately 23.85 degrees.

This problem can be solved using the tangent trigonometric ratio.

If we call "x" the angle of elevation of the Sun, then we can write:

tan(x) = height of the tree / length of the shadow

tan(x) = 32.5 / 75

To find the value of x, we can take the inverse tangent (tan⁻¹) of both sides of the equation:

x = tan⁻¹ (32.5 / 75)

x ≈ 23.85 degrees

Therefore, the angle of elevation of the Sun is approximately 23.85 degrees.

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The Sample space includes all possible combinations of the three types of sour candies, taking into account that there can be multiple candies of the same type in the bag.

The correct sample space for the sour candies in the bag is:

Sample space = {lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape}

Each element in the sample space represents a different possible outcome of selecting a sour candy from the bag. The sample space includes all possible combinations of the three types of sour candies, taking into account that there can be multiple candies of the same type in the bag.

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The correct sample space for the sour candies in the bag is (c)  Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

from the question, we have the following parameters that can be used in our computation:

3 lemon-lime, 6 watermelon, and 5 grape sour candies

The correct sample space for the sour candies in the bag is the list of items in the bag

So, we have

Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

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Therefore, Diego has 1.8 kilograms of carrots left.

Diego initially had 3 kilograms of carrots. He used 0.8 kilograms for the soup and 0.4 kilograms (400 grams) for the carrot cake.

So the total amount of carrots he used is:

0.8 + 0.4 = 1.2 kilograms

To find out how many kilograms of carrots he has left, we can subtract the amount he used from the initial amount:

3 - 1.2 = 1.8 kilograms

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The measure  f the angle of depression is 66 degrees

To determine the value of the angle, we need to know that there are six different trigonometric identities.

These identities are enumerated as;

From the information given, we have that;

The adjacent side = 60 meters

The opposite side = 135 meters

Using the tangent identity, we have that;

tan θ = 135/60

Divide the values, we have;

tan θ = 2. 25

Find the tangent inverse of the value

θ = 66. 0 degrees

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Note: The information given does not require diagrams and thus is self - explanatory.

Answer:

Sure. Here are the values that you requested:

Future Value: The future value of the investment is $1,388,903.23.

Interest Earned: The total interest earned is $1,263,903.23.

Number of Payments: The total number of payments is 160 (40 years * 4 quarters/year).

Average Balance: The average balance of the account is $432,203.28.

Here is the formula that I used to calculate the future value of the investment:

FV = PV * (1 + r)^n

Where:

FV is the future value

PV is the present value (the initial deposit)

r is the interest rate

n is the number of years

In this case, the present value is $2,500, the interest rate is 2%, and the number of years is 40.

FV = 2500 * (1 + 0.02)^40 = 1388903.23

Here is the formula that I used to calculate the interest earned:

Interest = FV - PV

In this case, the future value is $1,388,903.23 and the present value is $2,500.

Interest = 1388903.23 - 2500 = 1263903.23

Here is the formula that I used to calculate the number of payments:

Number of Payments = Years * Periods/Year

In this case, the number of years is 40 and the number of periods per year is 4.

Number of Payments = 40 * 4 = 160

Here is the formula that I used to calculate the average balance of the account:

Average Balance = (PV + FV)/2

In this case, the present value is $2,500 and the future value is $1,388,903.23.

Average Balance = (2500 + 1388903.23)/2 = 432203.28

Step-by-step explanation:

The total number of possible passwords can be calculated by finding the number of possible combinations for each character position in the password and multiplying them together.

Since each character can be an uppercase letter or a digit, there are a total of 36 possible characters (26 letters + 10 digits). The number of passwords that do not contain any digits can be found by calculating the number of possible passwords with only uppercase letters (26 possible characters) and then multiplying it by the number of possible positions in the password (6 to 8 characters).  Therefore, the total number of possible passwords is: 36⁶ + 36⁷ + 36⁸ - 26⁶ - 26⁷ - 26⁸
= 2,176,782,336 + 78,364,164,096 + 2,821,109,907,456 - 308,915,776 - 8,031,810,176 - 208,827,064,576
= 2,584,618,967,360
So there are a total of 2,584,618,967,360 possible passwords that meet the given criteria.

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Answer:

a ) -1

Step-by-step explanation:

[tex]\frac{1}{64} = 4^{2s-1} . 16^{2s+2}\\ 4^{-3} = 4^{2s-1+4s+4}\\ 4^{-3} = 4^{6s+3}\\ 6s + 3 = -3\\6s = -6\\s = -1[/tex]

The Length of side AB is approximately 72.4 cm.

To draw triangle ABC, we can start by drawing a straight line AB and then drawing a perpendicular line segment BC that meets AB at a 90-degree angle. This gives us a right triangle where angle B is 90 degrees. Finally, we can draw a line segment AC to connect points A and C, making sure that the length of AC is 25 cm since that is given in the problem.

To label the parts of the triangle, we can use the following conventions:

- Side AB is the hypotenuse of the right triangle and is opposite the right angle B.

- Angle A is opposite side AC, and angle C is opposite side BC.

Using this labeling convention, we can write:

- AB is the hypotenuse.

- AC is the side opposite angle A.

- BC is the side opposite angle C.

To find the length of AB, we can use the trigonometric ratio for the sine of angle A:

sin A = opposite / hypotenuse

sin 18 = AC / AB

Multiplying both sides by AB, we get:

AB * sin 18 = AC

Substituting the value of AC as 25 cm, we get:

AB * sin 18 = 25

Dividing both sides by sin 18, we get:

AB = 25 / sin 18

Using a calculator, we can evaluate this to get:

AB ≈ 72.4 cm (rounded to the nearest tenth)

Therefore, the length of side AB is approximately 72.4 cm.

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Based on the fictitious study of gender and ear piercing in high school students, we can conclude that the sample provides evidence that is too weak to conclude that gender and ear piercing are dependent in the population of high school students. Gender and ear piercing for high school students may be independent.

The study did not provide strong evidence that gender and ear piercing for high school students are dependent. In addition, the differences between observed and expected counts could be attributed to chance variation that occurs in random samples of high school students when gender and ear piercing are independent.

Therefore, the conditions are not met for use of the chi-square test of independence, and we cannot draw a conclusion based on this data.

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Answer:

3rd layer: 450

2nd layer: 300

1st layer: 150

Total: 900

Step-by-step explanation:

got it correct!

The total volume of the three-layer gelatin dessert is 900 cm³.

The space occupied within the boundaries of an object in three-dimensional space is known as volume.

To calculate the volume of each layer, we multiply the length, width, and height of each layer.

The volume of the bottom layer:

Volume = length × width × height

Volume = 15 cm × 10 cm×3 cm

Volume = 450 cm³

The volume of the middle layer:

Volume = length×width × height

Volume = 15 cm× 10 cm ×2 cm

Volume = 300 cm³

The volume of the top layer:

Volume = length×width × height

Volume = 15 cm × 10 cm× 1 cm

Volume = 150 cm³

To find the total volume, we add up the volumes of each layer:

Total Volume = 450 cm³ + 300 cm³ + 150 cm³

Total Volume = 900 cm³

Hence, 900 cm³ is the total volume of the three-layer gelatin dessert.

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Answer:$7.50

Step-by-step explanation:The original cost of the sandals is $30 and the discount if is 75%.That means only 25% of the original cost of the sandals remain so we do 30x.25=$7.50

The probability of getting tails on the 41st flip remains the same as any other individual flip: 0.5 or 50%.

When you flip a fair coin, there are two possible outcomes: heads (H) or tails (T). Since it's a fair coin, each outcome has an equal probability of occurring, which is 0.5 or 50%.

Now, let's consider the scenario you mentioned. You have already flipped the coin 40 times, and each time it landed on heads (H). In this case, the probability of getting heads on each of those 40 flips is (0.5)⁴⁰, which is an incredibly small probability because it's unlikely to get heads on 40 consecutive flips of a fair coin.

However, the key point is that each coin flip is an independent event. The outcome of one flip does not affect the outcome of the next flip. So, regardless of the previous 40 flips landing on heads, the probability of getting tails on the 41st flip is still 0.5 or 50%. The coin has no memory of the previous flips and doesn't "know" that it needs to "balance out" the previous heads with a tails.

Therefore, the probability of getting tails on the 41st flip remains the same as any other individual flip: 0.5 or 50%.

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The required area of the trapezoid PQRS is 144+72√3 square units. Option A is correct.

Area of trapezoid PQRS = [PQ+RS]/2 * QB

We are given PQ=18, QR = 24

The vertical line from Q to line SR is given as,
sin30 = V/24
V = 12
And horizontal measure over SR is given as,
cos30 = H/QR
H = 12√3

The length of QR is given as,
QR = 6 + 12√3

Area of trapezoid PQRS = [PQ+RS]/2 * QB
                                        = [18+6+12√3]/2*12
                                        = 144+72√3

Thus, the required area of the trapezoid PQRS is 144+72√3 square units.

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The average speed for this part of the journey is 6 m/s.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for this problem are given as follows:

Change in distance of 90 - 30 = 60 m.

Change in time of 10 - 0 = 10 s.

Hence the average speed for this part of the journey is given as follows:

60/10 = 6 m/s.

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Answer:

Rotate 'r' anticlockwise to form 315° angle with the positive x-axis. The tan of 315 degrees equals the y-coordinate(-0.7071) divided by x-coordinate(0.7071) of the point of intersection (0.7071, -0.7071) of unit circle and r.

Step-by-step explanation:

basicly what I said

Answer:

The function f(x) = cos^2x + sin^2x is not a straight line, but rather a constant function that always evaluates to 1 for any value of x.To see why this is the case, recall the trigonometric identity that states that the square of the cosine of an angle added to the square of the sine of the same angle equals 1:cos^2x + sin^2x = 1Since this identity holds for all values of x, it follows that f(x) = 1 for all x. Therefore, the graph of this function is a horizontal line at y = 1, not a straight line.

Step-by-step explanation:

1. It will cost Dave $646.62 to refill his truck's fuel tank.

2. The cost of concrete for Greg's driveway will be $9,720.

3. Total cost of the topsoil needed from suppliers is $726.90 from Holland Growers and $919.55 from Night Growers.

A refill refers to filling something again with more of same thing such as fuel, water etc.

We need to convert the fuel capacity of Dave's truck from gallons to liters.

1 US gallon = 3.78541 liters

So, 180 US gallons will give us:

= 180 * 3.78541 liters

= 681.37 liters

We will calculate total cost of refilling Dave's truck which is:

= 681.37 liters * 0.949 dollars/liter

= $646.62013

= $646.62.

2. To get volume of concrete needed, we will convert thickness of the driveway from inches to meters. 4 inches is equal to 0.1 meters.

The volume of the driveway is:

V = l x w x h

V = 20m x 36m x 0.1m

V = 72 cubic meters

The cost of the concrete for the driveway is:

= Volume x Price per cubic meter

= 72 cubic meters x $135/cubic meter

= $9,720.

3. To get total cost of the topsoil, we have to calculate volume of soil required for each planter box:

Volume = Length x Width x Depth

Volume = 44" x 24" x 18"

Volume = (44/36) yards x (24/36) yards x (18/36) yards

Volume = 1.22 yards³

Since she needs to build 35 planter boxes, the total volume of soil required is:

= 1.22 yards³ x 35

= 42.7 yards³

The cost from Holland Growers will be:

= Total Volume x $17/yd

= 42.7 yards³ x $17/yd

= $726.90

The cost from Night Growers will be:

= Total Volume x $21.50/yd²

= 42.7 yards³ x $21.50/yd²

= $919.55.

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The increasing the difference between sample means will result in a larger t statistic. This means that the difference between the two sample means is more likely to be statistically significant and less likely to be due to chance.

the t statistic is calculated by taking the difference between the sample means and dividing it by the standard error of the difference. When the difference between sample means increases, the numerator of the t statistic increases, while the denominator (the standard error) remains relatively constant. This leads to a larger t statistic and a smaller p-value, indicating stronger evidence against the null hypothesis.

increasing the difference between sample means has a significant effect on the independent-measures t statistic. It increases the strength of the evidence against the null hypothesis, making it more likely that the difference between the two groups is real and not due to chance.

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Answer:

Anything you want

Step-by-step explanation:

This is a problem where you have your own choice about whether you agree or disagree with the choice.

Answer:

307.5 milliliters

Step-by-step explanation:

Ratio 3:15, 1:5

61.4 is 1 un 1:5

61.5 x 5= 307.5

307.5 milliliters

The value of a = 1/3 and b = 2.

We can expand the given expression using the binomial theorem:

Binomial theorem statement that for any positive integer n the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form in the sequence of terms, the index r takes on the successive values 0, 1, 2,…, n.

Equation.

(2-x)(1+ax)⁶ = (2-x) × [1 + 6a x + 15a² x² + ...]

Multiplying this out gives:

(2-x)(1+ax)⁶ = 2 + (6a-2x) x + (15a² - 12ax + x²) x² + ...

Comparing the coefficient of x and x² with the given expansion we get:

6a - 2 = 0 (coefficient of x)

15a² - 12a + 1 = b (coefficient of x²)

From the first equation, we get:

6a = 2

a = 1/3

Substituting this value of a into the second equation, we get:

15(1/3)² - 12(1/3) + 1 = b

5 - 4 + 1 = b

b = 2

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Answer:

y = (3/2)x + 1

Step-by-step explanation:

straight line equation format is y -y1 = m(x - x1)

where y1 is y-coordinate of a point, x1 is x-coordinate of the same point, m is the slope (gradient).

slope of y - 4 = -2/3 (x - 6) is -2/3, since that's the number before x.

this means that slope of perpendicular line = -(1/ (-2/3)) = 3/2.

it passes through (-2, -2)

equation is y - -2 = 3/2 (x - - 2)

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

subtract 2 from both sides

y = (3/2)x + 1

The value of the variable x is 7

Point of tangency is described as the point where tangent meets the circle.

It is perpendicular to the radius of the circle, with which it intersects

From the information given, we have that;

BD = 46

CD = x² - 3

Since tangent lines are equal

We have that;

46 = x² - 3

collect the like terms, we get;;

x² = 46 + 3

Add the values

x² = 49

Find the square root of both sides, we have;

x = √49

Find the value

x = 7

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The perimeters and areas of each figures are

Given that all curves are semicircles or quadrants., we have

Figure 1

The area is calculated as

Area = 1.6 * 2.8

Area = 4.48 m²

The perimeter is calculated as

Perimeter = 2 * (1.6 + 2.8) + 3.14 * 1.6/2

Perimeter = 11.312 meters

Figure 2

The area is calculated as

Area = 50 * 68

Area = 3400 cm²

The perimeter is calculated as

Perimeter = 2 * (50 + 68) + 3.14 * 50

Perimeter = 393 centimeters

Figure 3

The area is calculated as

Area = 3.14 * 5² + 2 * 3.14 * (5/2)² * 1/2

Area = 98.125 m²

The perimeter is calculated as

Perimeter = 2 * 3.14 * 5 + 2 * 1/2 * 3.14 * 5/2

Perimeter = 39.25 meters

Figure 4

The area is calculated as

Area = 3.14 * (4.6/2)²/2 + 3.14 * (2.3)²/4

Area = 12.46 cm²

The perimeter is calculated as

Perimeter = 3.14 * (4.6/2) + 3.14 * (2.3)/4

Perimeter = 9.03 centimeters

Figure 5

The area is calculated as

Area = 3.14 * (15)²/2 + 2 * 3.14 * (5)²/2 - 3.14 * (5)²/2

Area = 392.5 cm²

The perimeter is calculated as

Perimeter = 3.14 * (15) + 2 * 3.14 * (5)/2 - 3.14 * (5)/2

Perimeter = 54.95 centimeters

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Answer:

x= 52° and y= 142°

Step-by-step explanation:

x combined with angle next to it make a right angle, so you can find x by subtracting 38 from 90. y would be 90 plus 52 because the other angle is the same as x.

Answer:

x = 52° and y = 142°

Step-by-step explanation:

38 + x + the right angle are on straight line.

angles on straight line add up to 180.

so x = 180 - 90 - 38 = 52.

y is the big angle, not the 90.

again, angles on straight line:

y = 180 - 38 = 142

The space within the cylinder not taken up by the three tennis balls can be found by first determining the volume of the cylinder and the total volume of the three tennis balls.

The volume of the cylinder is given by the formula:

V_cylinder = πr^2h

where r is the radius and h is the height. Substituting the given values, we get:

V_cylinder = π(1.39)^2(8.6) = 50.168 cubic inches

The total volume of the three tennis balls can be found by multiplying the volume of one tennis ball by three. The volume of a tennis ball can be approximated by the formula for the volume of a sphere:

V_ball = (4/3)πr^3

where r is the radius. Since the circumference of a tennis ball is 8 inches, we can solve for the radius using the formula:

C = 2πr

8 = 2πr

r ≈ 1.27 inches

Substituting this value, we get:

V_ball = (4/3)π(1.27)^3 ≈ 8.48 cubic inches

Therefore, the total volume of the three tennis balls is:

V_total = 3V_ball = 25.44 cubic inches

Finally, we can find the amount of space within the cylinder not taken up by the tennis balls by subtracting the total volume of the tennis balls from the volume of the cylinder:

V_not_taken_up = V_cylinder - V_total = 50.168 - 25.44 = 24.728 cubic inches

Therefore, the amount of space within the cylinder not taken up by the tennis balls is approximately 24.728 cubic inches.

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The polynomial with degree 4 and the given zeros is f(x) = ((x+2)² + 25)(x-4)²

If a polynomial has complex zeros with non-zero imaginary parts, then the complex conjugate of each complex zero must also be a zero of the polynomial with the same multiplicity.

Therefore, the zeros of the polynomial with degree 4 are:

-2-5i, -2+5i, 4, and 4 (with multiplicity 2).

To find the polynomial, we can start by writing out the factors corresponding to each zero:

(x - (-2-5i))(x - (-2+5i))(x - 4)²

Simplifying the factors, we get:

((x+2)+5i)((x+2)-5i)(x-4)²

Expanding the factors, we get:

((x+2)² - (5i)²)(x-4)²

((x+2)² + 25)(x-4)²

Thus, the polynomial with degree 4 and the given zeros is:

f(x) = ((x+2)² + 25)(x-4)²

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The correct expression to solve for the amount of time it takes to drain the hot tub is: A) (9t - 9)(5t - 7)

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

By using the sum-product pattern, we have the following:

45t² − 108t + 63

45t² − 63t - 45t + 63

By writing the common factor from the two pairs, we have the following:

(45t² − 63t) - (45t + 63)

9t(5t - 7) - 9(5t - 7)

By rewriting in factored form, we have the following:

(9t - 9)(5t - 7)

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The population of the city  in 2020 is approximately 255 100

To find the population in 2020 we first need to find the population in 2015 after the 7% growth from 2010.

Population in 2015 = 246 000 + 0.07 x 246 000 = 263,220

we need to find the population in 2020 after the 3% decrease from 2015

Population in 2020 = 263 220 - 0.03 x 263,220 = 255 027.6

Rounding to the nearest 100 people the population in 2020 is approximately 255 100

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angles that differ by a multiple of 2π have the same terminal point, because they complete the same number of full circles around the unit circle.

The terminal point determined by an angle in standard position (i.e., with the initial side along the positive x-axis) is the point where the terminal side of the angle intersects the unit circle. Here are the terminal points determined by π/2, π, −π/2, and 2π:

The angle π/2 (90 degrees) has a terminal point at (0, 1), which is the point on the unit circle that is directly above the origin.

The angle π (180 degrees) has a terminal point at (-1, 0), which is the point on the unit circle that is to the left of the origin.

The angle −π/2 (-90 degrees) has a terminal point at (0, -1), which is the point on the unit circle that is directly below the origin.

The angle 2π (360 degrees) has a terminal point at (1, 0), which is the point on the unit circle that is to the right of the origin.

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