help please!!!!!!!!!!!

1) The Combination, Probability is (5C2 x 12C3) / 30C5

2) The Combination, Probability is (C(4,7) x C(2,5)) / C(6,12)

3) The Combination, Probability is (C(3,5) x C(3,5)) / C(6,10)

4) The Permutation, Probability is 1 / P(50,3)

1) This situation is describing a combination because the order in which the students are chosen does not matter. The probability of randomly choosing 2 blonde girls and 3 dark-haired boys can be found as follows:

Number of ways to choose 2 blonde girls out of 5 = C(5, 2) = 10

Number of ways to choose 3 dark-haired boys out of 12 = C(12, 3) = 220

Total number of ways to choose 5 students out of 30 = C(30, 5) = 142,506

Probability = (10 x 220) / 142,506 = 0.0154

Therefore, the probability of randomly choosing 2 blonde girls and 3 dark-haired boys if 5 students are randomly chosen to be class representatives is 0.0154.

2) This situation is describing a permutation because the order in which the smartphones are sold matters. The probability that exactly four of the first six sold have cracked screens can be found as follows:

Number of ways to choose 4 cracked screens out of 7 = C(7, 4) = 35

Number of ways to choose 2 intact screens out of 5 = C(5, 2) = 10

Number of ways to arrange the 6 chosen smartphones = P(6, 6) = 720

Probability = (35 x 10 x P(6, 6-4)) / P(12, 6) = 0.078

Therefore, the probability that exactly four of the first six sold have cracked screens is 0.078.

3) This situation is describing a combination because the order in which the songs are listened to does not matter. The probability that exactly three country songs are listened to can be found as follows:

Number of ways to choose 3 country songs out of 5 = C(5, 3) = 10

Number of ways to choose 3 pop songs out of 5 = C(5, 3) = 10

Total number of ways to choose 6 songs out of 10 = C(10, 6) = 210

Probability = (10 x 10) / 210 = 0.476

Therefore, the probability that exactly three country songs are listened to is 0.476.

4) This situation is describing a permutation because the order in which the hurdlers finish matters. The probability of randomly choosing the correct finishing order of the first, second, and third place for the hurdlers out of 50 contestants can be found as:

Probability = 1 / P(50, 3) = 1 / 117,600

Therefore, the probability of randomly choosing the correct finishing order of the first, second, and third place for the hurdlers out of 50 contestants is approximately 0.0000085.

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Answer: x < 4

Step-by-step explanation:

    The graph uses an open circle, this means we will use the < or > symbol because it is not equal to.

    The open circle is on the 4.

    The arrow goes to the left of 4, meaning it is equal to values less than 4.

    Our inequality:

              x < 4

The statement that is true if the measures of the sides of the original square is that each side of the original square is 4 times the length of each side of the scale model. That is option B.

To determine the dimensions of the original square is through the formula of the scale factor. That is;

Scale factor = original scale/scale model

The given scale factor = 4

the dimensions of square model = 8

Therefore the original dimensions of the square = 4×8 = 32ft

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The percentage of people those who have the disease and are tested positive are calculated to be approximately 91.06%.

The table shows the number of people testing positive and negative for a certain disease, categorized by those who have the disease and those who do not.

To find the percentage of those who have the disease and tested positive, we need to divide the number of people who have the disease and tested positive by the total number of people who have the disease, and then multiply by 100 to express the result as a percentage.

From the table, we can see that the number of people who have the disease and tested positive is 112.

The total number of people who have the disease is 123.

Therefore, the percentage of those who have the disease and tested positive is:

(112/123) x 100% = 91.06%

Therefore, approximately 91.06% of those who have the disease tested positive.

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Answer:

75.4mm

Step-by-step explanation:

Circumference is the distance around a circle (just like perimeter, but a special word just for circles)

You find circumference by this formula:

C = pi•d

where d is the diameter.

They gave you the diameter in your problem, 24mm

C = pi•24

C = 75.39822

Rounded to the nearest tenth is 75.4mm

(also 24pi is a perfectly good, exact answer or 75.40mm if you need it rounded to two decimal places)

The margin of error for the proportion of all U.S. adults who think things are on the wrong track for 90% confidence is approximately 2.2%.

To calculate the margin of error, we first need to find the standard error, which can be calculated using the formula:
Standard Error = Square Root [ (p * q) / n ]
where p is the proportion of the sample who said things are on the wrong track (0.747), q is the complement of p (1 - p, which is 0.253), and n is the sample size (1997).
Plugging in the values, we get:
Standard Error = Square Root [ (0.747 * 0.253) / 1997 ] = 0.014
To find the margin of error at 90% confidence, we need to multiply the standard error by the z-score corresponding to 90% confidence, which is 1.645.
Margin of Error = 1.645 * 0.014 = 0.022 or approximately 2.2%

Hence, we can say with 90% confidence that the true proportion of all U.S. adults who think things are on the wrong track is between 72.5% and 77.0% (74.7% ± 2.2%).

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Answer: First one

Step-by-step explanation:

You have to include a question or a link to thw question so qe could solve it.

The following are the values for the segments of the triangles:

4). a = 6.5

5). x = 2.7

6). x = 7.8 and y = 7.2

Using the proportionality theorem for calculating for the triangle segments as follows:

4). YZ/ZW = XY/XW

a/12 = 12/22

a = (12 × 12)/22 {cross multiplication}

a = 6.2

5). BC/CD = AB/AD

x/(7 - x) = 5/8

8x = 5(7 - x) {cross multiplication}

8x = 35 - 5x

8x + 5x = 35

13x = 35

x = 2.7

6). KL/LM = NK/NM

y/(15 - y) = 23/25

25y = 23(15 - y)

25y + 23y = 345

48y = 345

y = 7.2

x = LM so;

x = 15 - y

x = 15 - 7.2 = 7.8.

Therefore, the values for the segments of the triangles are:

4). a = 6.5

5). x = 2.7

6). x = 7.8 and y = 7.2

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Answer: 4cm² 

Step-by-step explanation:

To find the area of a triangle, we can use the formula:

Area: (base x height) ÷ 2

In this case, the base of the triangle is 4cm and the height of the triangle is 2cm. We simply replace the values with the variables in the formula. So, we get:

Area: (4cm x 2cm) ÷ 2

Area: 8cm² ÷ 2

Area: 4cm² 

Therefore, the area of the triangle is 4cm².

Answer: 40% of her budget

Step-by-step explanation:

The area of the composite figure is

321 square m

The area is calculated by dividing the figure into simpler shapes.

The simple shapes used here include

Area of triangle = 1/2 x base x height

height = √(22² + 15²) = 16

= 1/2 x 15 x 16

= 120 square m

Area of quarter of circle = 1/4 x π x r²

= 1/4 x π x 16²

= 201 square m

Total area

= 201 square m + 120 square m

=  321 square m

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Olivia plans to spend $44 on each nephew and $54 on each sister, for a total of $250 on presents.

What is variables?

In mathematics, a variable is a symbol or letter that represents a value that can change or vary. Variables are commonly used in algebraic expressions and equations to denote unknown values that need to be determined, or to represent values that can change in a given situation.

For example, in the equation y = 2x + 3, x is a variable that can represent any number, and y is the value that results from multiplying x by 2, adding 3, and solving for y. In this case, x can be any number, so it is a variable.

Let's start by assigning some variables to represent the amounts Olivia spends on each present. Let's call the amount she spends on each nephew "n" and the amount she spends on each sister "s". We know that Olivia has 2 nephews and 3 sisters, so we can write:

2n + 3s = 250

We also know that Olivia wants to spend $10 more on each sister than she spends on her nephew. In other words, the amount she spends on a sister is $10 more than the amount she spends on a nephew:

s = n + 10

Now we can substitute this expression for "s" into the first equation to get:

2n + 3(n + 10) = 250

Simplifying this equation, we get:

5n + 30 = 250

Subtracting 30 from both sides, we get:

5n = 220

Dividing both sides by 5, we get:

n = 44

So Olivia plans to spend $44 on each nephew. Using the equation s = n + 10, we can see that she plans to spend $54 on each sister.

To check that this solution works, we can verify that the total amount Olivia plans to spend on presents is equal to $250:

2(44) + 3(54) = 88 + 162 = 250

Therefore, Olivia plans to spend $44 on each nephew and $54 on each sister, for a total of $250 on presents.

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Therefore, the image of the point (0, -7) after a dilation by a scale factor of 4 centered at the origin is (0, -28).

In mathematics, a scale factor is a numerical value that describes how much an object has been scaled or resized. It is the ratio of the size of the image to the size of the original object. Scale factors can be applied to two-dimensional or three-dimensional objects, and can be used to describe enlargements (scaling up) or reductions (scaling down) of the object.

Here,

To find the image of the point (0, -7) after a dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) is the original point, (x', y') is the image of the point after dilation, k is the scale factor, and the dilation is centered at the origin.

In this case, the original point is (0, -7), the scale factor is 4, and the origin is (0, 0). Plugging these values into the formula, we get:

(x', y') = (4 * 0, 4 * (-7))

Simplifying, we get:

(x', y') = (0, -28)

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Step-by-step explanation:

tan (40) = 1250 / x

x = 1250 / tan 40 = 1490 ft

A model that could model the probability of a student participating is a model in which 3 out of 4 outcomes represent a success.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The participation rate in this problem is of 75%, which represents the probability of a success, hence we want to model an experiment in which 3 out of 4 outcomes represent a success.

One possible example is using numbers from 1 to 4, in which:

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The equation of the line with slope -1.5 and passing through origin in slope intercept form is given by y = -1.5x + 0

Slope of the line = -1.5

and one of the coordinates is at the origin.

let us consider the coordinate of the origin as ( x₁ , y₁ ).

Use the point-slope form of a linear equation to write the equation of the line as,

y - y₁= m(x - x₁)

where m is the slope

and (x₁, y₁) is the point on the line.

(x₁, y₁) =  (0, 0)

Since the line passes through the origin.

Substituting the values, we get,

⇒ y - 0 = -1.5(x - 0)

Simplifying, we get,

⇒ y = -1.5x

Here,

y = -1.5x + 0

y-intercept is 0

Therefore , the equation of the line in slope intercept form is equal to y = -1.5x + 0.

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The given question is incomplete, I answer the question in general according to my knowledge:

Given the line:

The slope of the line is -1. 5 and one of the coordinate is at the origin .Write the equation of the line in slope intercept form.

The transformations that maps triangle A onto triangle B are given as follows:

Examples of transformations are given as follows:

We note that the triangles have different orientations, hence the triangle A was reflected over the line y = 2.

The side lengths on triangle B are half the side lengths on triangle A, hence there was a dilation with a scale factor of 0.5.

Then the x-coordinates of the triangles had it's signal exchanged, meaning that the graph was reflected over the y-axis.

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The factors of n are 4y³, xy, and 8. So the correct options are:

Finding a number's prime factors in a way that the original number may be divided equally by them is known as prime factorization.

To find the factors of n, we need to consider all possible combinations of the prime factors 2, x, and y.

The factors of n can be found by taking all possible combinations of the exponents of the prime factors 2, x, and y, as long as the exponents are less than or equal to their respective powers in the prime factorization of n.

From the given prime factorization of n, we know that the powers of 2, x, and y are 5, 1, and 4, respectively.

Therefore, the possible factors of n are:

2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32

x⁰ = 1, x¹ = x

y⁰ = 1, y¹ = y, y², y³, y⁴

Now we can check which of the given numbers are factors of n:

Therefore, the factors of n are 4y³, xy, and 8. So the correct options are:

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The area of the circle Z is 72.1 square cm and the length of the segment XV is 9 cm

Given that

Arc XY = 40 degrees

This means that

∠V = 1/2 * 40 degrees

∠V = 20 degrees

The angle in a semicircle is a right-angle

So, we have

∠X = 90 degrees

So, we calculate the length VZ using

cos(V) = XV/2VZ

This gives

cos(20) = 9/2VZ

So, we have

VZ = 9/[2 cos(20)]

Evaluate

VZ = 4.79

The area is calculated  using

Area = πVZ²

So, we have

Area = π * 4.79²

Evaluate

Area = 72.1

Hence, the area is 72.1 square cm and the length XV is 9 cm (given)

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The total number of routes possible is 6227020800, under the given condition that a overnight express company must include thirteen cities on its route, assuming that it does matter in which order the cities are included.

For this given question in order to find the accurate answer we have to perform calculations based on the principles of factorial operation.
The total  number of different routes possible, considering  that it matters in which order the cities are included  is 13!
The factorial of 13 is evaluated
13! = 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 6227020800
The total number of routes possible is 6227020800, under the given condition that a overnight express company must include thirteen cities on its route, assuming that it does matter in which order the cities are included.

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The work done in each of the cases is:

B) W =  8,400 N*m

C) W = 17,500 N*m

The work can be defined by the product between the force and the distance translated.

W = Force*Distance

So, if there is a force of 120N and the vehicle moves 70 meters, the work done is:

W = 120N*70m = 8,400 N*m

C) Similar case to the above one, here the force is F = 3.5 KN = 3,500N

And the distance is d = 15m

Then in this case the work done is:

W = 3,500N*15m = 17,500 N*m

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Answer:

10feet

Step-by-step explanation:

Calculate the length from the base of the stair to the walls of the house.

We have the ladder extend 2 feet beyond the edge of the roof so 28-2=26feet

Let x is the length from the base of the stair to the wall of the house

(26)²=(24)²+x²

x²=(26)²-(24)²=676-576=100

x=√100=10feet

So the length from the base of the stair to the wall of the house is 10 feet.

The angle in degrees at the center of Aron's slice of cake is (A / (A + K + G)) × 360 degrees.

Assuming that the cake is divided into three slices, with each slice having a size proportional to the age of each person, let A, K, and G represent the ages of Aron, Kai, and Grace, respectively. Then, the total size of the cake can be represented as A + K + G.

Let x be the size of Aron's slice of cake. Then, Kai's slice of cake is (K / (A + K + G)) × 360 degrees, and Grace's slice of cake is (G / (A + K + G)) × 360 degrees.

Since the total angle at the center of the cake is 360 degrees, we can write

x + (K / (A + K + G)) × 360 degrees + (G / (A + K + G)) × 360 degrees = 360 degrees

Simplifying this equation, we get

x = (A / (A + K + G)) × 360 degrees

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The expected number of assignments for Ms. Clea's advisory class in a day is 1.4.

The probability distribution can be written in a table as follows:

When Number of assignments 0,1,2,3, probability will be 0.3, 0.2, 0.3, 0.2 respectively.

To find the expected value, we can use the formula:

Expected value = Σ (number of assignments × probability)

where the sum is taken over all possible values of the number of assignments.

So, the expected value is:

Expected value

[tex] = (0 \times 0.3) + (1 \times 0.2) + (2 \times 0.3) + (3 \times 0.2) \\ = 0 + 0.2 + 0.6 + 0.6 \\ = 1.4[/tex]

Therefore, the expected number of assignments for Ms. Clea's advisory class in a day is 1.4.

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Answer: 3%

Step-by-step explanation:

We can use this equation to solve for the simple interest:

        A = P(1 + rt)

We will substitute our known values and solve:

➜ A = final amount ($5,000 + $600 = $5,600)

➜  P = initial balance ($5,000)

➜  r = interest rate (solving for r)

➜  t = time (4 years)

        A = P(1 + rt)

        5,600 = 5,000(1 + (r)(4))

        [tex]\frac{5,600}{5000}[/tex] = 1 + (r)(4)

        1.12 = 1 + 4r

        0.12 = 4r

        4r = 0.12

        r = 0.03

        r = 3%

If Jackson has  [tex]4\frac{1}{2}[/tex]  pounds of salt to fill in containers that hold 1/4 a pound then he fill 18 containers.

Given that Jackson has [tex]4\frac{1}{2}[/tex] pounds of salt

He has to fill in containers that hold 1/4 a pound

We have to find the number of containers to fill  [tex]4\frac{1}{2}[/tex] pounds of salt.

To find containers we have to divide  [tex]4\frac{1}{2}[/tex] pounds of salt by 1/4

[tex]4\frac{1}{2}[/tex]/1/4

(9/2)×4

36/2= 18

Hence, 18 contains can Jackson fill, option D is correct.

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A linear equation of the trend line (line of best fit) that models the data point contained in the table is y = 1.875x - 12.25.

In order to determine a linear equation of the trend line (line of best fit) that models the data point contained in the table (see attachment), we would have to first calculate the slope as shown below.

In Mathematics and Geometry, the slope of any linear equation can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided about the servers' collected tips (in dollars) with respect to customers, we have the following parameters:

Substituting the given points into the formula, we have;

Slope, m = (91 - 76)/(42 - 34)

Slope, m = 15/8

Slope, m = 1.875

At point (34, 76), the equation of this line is given by:

y - y₁ = m(x - x₁)

Where:

By substituting the data points, we have;

y - 76 = 1.875(x - 34)

y - 76 = 1.875x - 63.75

y = 1.875x - 63.75 + 76

y = 1.875x - 12.25

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Check the picture below.