in a class, there are 4 freshman boys, 6 freshman girls, and 6 sophomore boys. how many sophomore girls must be present if sex and class are to be independent when a student is selected at random?

Equation that we can use to find the amount of money, p, Roman Rounds normally charges for a large pizza is 12(p - 2) = 192.

Let's use p to represent the normal price of a large pizza from Roman Rounds. Since Mr. Mosley ordered 12 large pizzas and received a $2 discount on each, he paid a total of $192. We can use this information to set up the following equation:

12(p - 2) = 192

In this equation, 12 represents the number of large pizzas that were ordered, and (p - 2) represents the discounted price of each pizza. The left side of the equation gives us the total amount that Mr. Mosley paid for the pizzas. By setting this expression equal to 192, we can solve for p, the normal price of a large pizza from Roman Rounds.

To solve for p, we first distribute the 12 on the left side of the equation:

12p - 24 = 192

Next, we add 24 to both sides of the equation:

12p = 216

Finally, we divide both sides of the equation by 12:

p = 18

Therefore, the normal price of a large pizza from Roman Rounds is $18.

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Answer:

ferris wheel: 2

roller coaster: 4

Step-by-step explanation:

Variables

y = ferris wheel tickets

x = roller coaster tickets

Two equations

5y + 4x = 26

5y + 3x = 22

Using Elimination (minus the top and bottom)

We get:

x = 4 (because 5y - 5y is zero, 4x - 3x is x, and 26 - 22 is 4)

Since the roller coaster price is know, you can sub it into any of the two equations and fine ferris wheel price.

5y + 3(4) = 22

5y + 12 = 22

5y = 10

y = 2

Therefore:

ferris wheel charges 2 tickets

roller coaster charges 4 tickets

Answer:

Step-by-step explanation:

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

Vince works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 16 strands of lights to decorate 2 bushes and 1 tree. This afternoon, he strung lights on 3 bushes and 4 trees, using a total of 44 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Vince use on each?

Vince decorated every bush with

strands of lights and every tree with

strands.

Answer:

the area of the isosceles triangle is approximately 104.49 cm^2.

Step-by-step explanation:

The perimeter of the triangle is 100 cm, so we can write an equation using the lengths of the sides:

x + x + (x + 10) = 100

3x + 10 = 100

3x = 90

x = 30

So the equal sides of the triangle have length 30 cm and the side that is 10 cm greater has length 40 cm.

To find the area of the triangle, we can use the formula for the area of an equilateral triangle:

Area = (sqrt(3) / 4) * (side length)^2

Area = (sqrt(3) / 4) * 30^2

Area = (sqrt(3) / 4) * 900

Area = (sqrt(3) / 4) * 30 * 30

Area = (sqrt(3) / 4) * 900

Area = (30 * sqrt(3)) / 2

Area = 45 sqrt(3)

The mean of Y is 103 dollars. The standard deviation of X is 64.8 dollars

The mathematical expression that we would have to use i the representation of Y is Y = 60X - 5.

How to solve for the mean of Y

Y = exp(Y)

= 60 * EXP(X) - 5

the expected value of x is 1.8

= 60 * 1.8 - 5

= 103 dollars

then we have to solve for the standard deviation of Y

standard deviation of x = 1.08

= 60 * 1.08

= 64.8 dollars

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To find the average value of a function on an interval dividing the definite integral [tex]\int\limits^a_b f{(x)} \, dx[/tex] by the length of the interval.

The definition of average value of a function is -"The average value of a function is the height of the rectangle that has an area that is equivalent to the area under the curve of the function."

When there's a need to find the average value of a function, rather than adding up numbers we can just integrate, and instead of dividing by the number of values we can just divide by the length of the interval.

Adding values → Integration

Number of values → Length of the interval

When we use the length of the interval it makes more sense as we all know intervals have an infinite number of values, so it is more appropriate to use the length of the interval instead.

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mZDAE is a line segment that connects the midpoints of line segments BA and CE. In the diagram, its coordinates are (66⁰, 52%).

It will take Daniel approximately 2 hours and 52 minutes (172.066 minutes) to complete the triathlon.

To estimate how long it will take Daniel to complete the triathlon, we can calculate the time it will take him to complete each leg of the race and add them together.

Swim:

Distance = 0.93 miles

Speed = 2.2 mph

Time = Distance / Speed = 0.93 miles / 2.2 mph = 0.4236 hours = 25.416 minutes

Bike:

Distance = 24.8 miles

Speed = 17.8 mph

Time = Distance / Speed = 24.8 miles / 17.8 mph = 1.3933 hours = 83.6 minutes

Run:

Distance = 6.2 miles

Speed = 5.9 mph

Time = Distance / Speed = 6.2 miles / 5.9 mph = 1.0508 hours = 63.05 minutes

Total time = Swim time + Bike time + Run time

Total time = 25.416 minutes + 83.6 minutes + 63.05 minutes

Total time = 172.066 minutes

Therefore, it took  172.066 minutes which is approximately equal to 2 hours and 52 minutes by Daniel to complete the triathlon.

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The values in the missing observation are:

X1    X2

76 22  

82 25

91 32

101    41

88 28

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x1 x2

76 22  

82 __

91 32

__    41

88 28

The difference between each row are:

76 - 22 = 54

82 - 25 = 57

91 - 32 = 59

101 - 41 = 60

88 - 28 = 60

We see that,

57 - 54 = 3

59 - 57 = 2

60 - 59 = 1

60 - 60 = 0

So,

The difference between the numbers is consecutive as 3, 2, 1, 0.

Thus,

The missing values of X1 and X2 are 101 and 25.

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Answer:

35 m

Step-by-step explanation:

I will assume the goal is not to waste any wood.  We need to find a common length that will allow each piece of wood to be divided into whole pieces with nothing left over.  The shortest plank is 70 m, but that length will cause a loss of 35 m on the 105m plank, and also 35m on the 175m plank after two 70m sections have been cut off (175 - 140 = 35).

Looking at the actual lengths, one might spot that they are all evenly divisible by 35.  See the table below.  The numbers under "35" are the result of the length divided by 35.  They are all whole numbers.  We can cut each plank into 35m sections and have none left over.

Length (m) 35 (factor)

  70                  2 planks

  105          3 planks

  175          5 planks

This will result in 10 35m planks.  

No need to plank me.

The answer option which is not a characteristic of a plane include the following: C. thickness.

In Mathematics, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Additionally, two (2) planes intersect at a line.

Generally speaking, there are different characteristics of a plane and these include the following:

In this context, we can reasonably infer and logically deduce that thickness is not a characteristic of a plane.

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Complete Question:

Which of the following is NOT a characteristic of a plane?

A. length

B. flat surface

C. thickness

D. width

Answer:

The answer is 15 and 22

Step-by-step explanation:

KHAN

The measures of angles C and D are 70° and 100°, respectively.

Understanding angles is a fundamental concept in geometry. A quadrilateral is a polygon with four sides, and its angles are essential to determining its properties.

Let's start by labeling the angles in the quadrilateral. We know that two angles measure 100° and 90°, so let's label them as A and B, respectively. The other two angles, which we are trying to find, can be labeled as C and D.

Now, we are given that the ratio of angles C and D is 7:10. This means that we can write the following equation:

C/D = 7/10

We can use this equation to solve for one of the angles. Let's choose angle C. We can rewrite the equation as:

C = (7/10)D

We also know that the sum of the angles in a quadrilateral is 360°. Therefore, we can write another equation:

A + B + C + D = 360°

We can substitute the values we know into this equation and solve for angle D:

100° + 90° + (7/10)D + D = 360°

Simplifying the equation:

(17/10)D = 170°

D = 100°

Now that we know the value of angle D, we can use the equation we derived earlier to find the value of angle C:

C = (7/10)D = (7/10) x 100° = 70°

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The radius line intersects the circle at (4, 8) because the tangent line's slope, which is -1/3, is perpendicular to the radius line's slope of (0, 8), which is 0.

1. Use m = 0 to calculate the slope of the line through point (12, 0).

2. Calculate the radical line's angle between the origin and the tangent point: m = ∞

3. To determine the location where the line touches the circle, use the relationship between the slopes: M2 = -1/M1 = -1/0 = - since M1 M2 = -1

4. To determine a point's coordinates, use the equation for a circle: (x - 8)2 + (y - 8)2 = 82, so (4, 8) (4, 8)

We can use the relationship between the slopes of the tangent line and the radical line from the origin to the tangent point to determine the location where the line contacts the circle. Since the tangent line crosses through point (12,0), its slope is equal to zero. Since the radical line slopes at m2 =, m1 m2 = -1. Accordingly, m2 = -1/m1 = -1/0 = -∞.The coordinates of the spot where the line touches the circle can then be determined using the equation for a circle. (x - 8)2 + (y - 8)2 = 82 is the equation for a circle having the origin as its center and a radius of 8. The coordinates of the place where the line intersects the circle are (4, 8), which can be obtained by substituting in the values for m1 and m2.

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The IQR of the data is 10 years and option B is the correct answer.

The dispersion of the middle 50% of the sample is measured by the interquartile range, or IQR, which is the difference between the top and lower quartiles.

The given data is:  2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.

The median of the data is:

M = 15 + 1 /2 = 16/2 = 8th value.

M = 10

Ignoring the median divide the data into two parts.

The lower quartile median is 4th term:

Q1 = 5

The upper quartile median is 12th term:

Q2 = 15

IQR = Q2 - Q1

IQR = 15 - 5 = 10 years.

Hence, the IQR of the data is 10 years and option B is the correct answer.

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The college will have about 640 students who prefer pie. We can calculate percentages based on the student sampling of 225 students (assuming it was a completely random sample, and not one taken just from a specific group, such as football players at half-time).

What is random sample?

To make a prediction, we need to assume that the preferences of the 225 students surveyed are representative of the entire student population of 4,000. We can use the proportion of students who prefer pie in the sample to make an estimate.

The proportion of students who prefer pie in the sample is:

                36/225 = 0.16

We can use this proportion to estimate the number of students who prefer pie in the entire population:

                       4,000 x 0.16 = 640

Therefore, the best prediction about the slices of pie the college will need is that the college will have about 640 students who prefer pie. So the option "The college will have about 640 students who prefer pie" is the correct statement.

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The inequality that represents the least number of days after Monday that Joseph needs to run to reach his goal is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex]  ≤ 6

Number of miles that Joseph run on Monday = [tex]2\frac{1}{2}[/tex] miles

Number of miles that Joseph run each day after that = [tex]1\frac{1}{3}[/tex] miles

The inequality is the mathematical statement that shows the relationship between two expression using an inequality symbol. The inequality symbols are less than, greater than, less than or equal and greater than or equal.

Then the inequality will be

[tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex]  ≤ 6

Where x is the number of days after Monday that Joseph needs to run to reach his goal

Therefore, the inequality is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex]  ≤ 6

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The approaches to building a multiple linear regression model is option (C) Backward elimination

Here the multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain

We know the independent variable is the variable that does not depends on any other variables

Here the given elimination methods is eliminating insignificant ones until only significant ones remain

In the backward elimination method starts with explanatory variables in the regression model then starts to eliminates the least significant ones will eliminates one by one

Therefore, the suitable approach is backward elimination method

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The second statement in your question is the correct response.

What is the sampling distribution?

A sampling distribution is the probability distribution of a statistic (such as the sample mean or sample proportion) based on all possible random samples of a fixed size from a population.

The following statement must be true for an estimator of a population parameter to be unbiased:

The expected value of the estimator is equal to the population parameter.

Hence, the second statement in your question is the correct response.

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[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Total cards = 52

Total diamond cards = 13

So, probability of getting a card of diamond,

P(diamond) = 13/52 = 1/4

Now,

Total cards with number seven = 4

So, probability of getting a seven,

P(seven) = 4/52 = 1/13

Answer:

it's simple 4 that is 100% the correct answer

Answer:

In the expression -17 + (-b) + (-25), the coefficient is a number that multiplies a variable. In this case, the coefficients are -17, -1 (which multiplies the variable "b"), and -25.

Step-by-step explanation:

Answer:

2d-6

Step-by-step explanation:

Since the d is doubled you are multipling then subtracting 6 from the result

Answer: 167.55 cm.

Step-by-step explanation:

Cone volume formula is V=1/3hπr².

Substitute...

V= 1/3 (10) (π) (4)^2

V= 53 1/3 π

V= 167.55 cm

Hope this helps!

MM

Answer:

Step-by-step explanation:

Convers 95 min into hours

95/60 = 1.58 Hours

Sara can read 19 pages per hour

Total pages in 95 min or 1.58 hours =

19 * 1.58 = 30.02

Rounding off to nearest whole number- 30

Hope it helps

Answer:

7x

Step-by-step explanation:

That would be   ( -2x )(-5) + -3x(1) = 10x - 3x = 7x

Her percentage difference in programming in accordance with the statement is 40%.

It is discussing speed. the velocity at which the position of an object shifts in any direction. Speed is defined as the ratio of the distance traveled to the time required to cover that distance. Speed can be stated as a number since it just has to have 1 element and no magnitude.

You may use the following format to get Rhetta's increased typing speed in percentages:

(New Values - Originally Value) / (Original Value x 100) = Percent Increase

Calculating the percentage increase is as follows: Percentage Point Equals (56 - 40) / 40 x 100 Equals 40% in this instance, where the previous value was 40 words every minute and the new number was 56.

Rhetta was now 40% faster at typing.

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Answer: $3,500

Step-by-step explanation: 15000-5000=10000

0.7*10,000=700.

700*5=$3,500