At a local college, only 60% of students live off campus. Of those who live off campus, 58% of those students get a part-time job. Of those who live on campus, 67% work part-time. The tree diagram shows how the college students are divided into subgroups.

What is the percentage of students who live off campus and do not have a part-time job?

42.6%
34.8%
25.2%
24.3%

The value of the unknown side y for the given triangle will be 46.15.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

The sine law, also known as the law of sines, states that the ratio of a triangle's side length to the sine of its opposite angle is constant for all three sides. It's sometimes referred to as the sine rule.

We have to find the value of the side as y.

Apply Sin law in the given triangle,

SinA/a=SinB/b=SinC/c

Sin42/31=sin85/y

0.6691/31=0.9962/y

y=30.8822/0.6691

y=46.15

Thus, the value of the unknown side y for the given triangle will be 46.15.

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Answer:

12

Step-by-step explanation:

The given triangles are congruent following the side angle side (SAS) congruency .

Given,

∴ ∠ A = ∠ B = ∠ C = ∠ D =90°

In Δ ABC and Δ CDA

AB =  CD

∠ BAC= ∠ DAC

AB= AD

∴ By Side Angle Side congruent property

Δ ABC ≅ Δ CDA

Congruent refers to figures that are similar in all respects, primarily in terms of size and shape. Congruence describes how two congruent figures relate to one another.

The relationship between two figures that are congruent is referred to as congruence. Let's talk about the triangle SAS congruence now. We don't necessarily need to look into all the sides and angles to determine whether the two triangles are identical.

Triangles must be congruent to mean,

There are no different comparable angle pairs.

It is equal on all comparable sides.

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Equation for each situation are A = 59 -7t and B = 34 -2t and t<5 is the interval of time.

Two or more expressions with an Equal sign is called as Equation.

Snowman A starts at 59 inches and decreases height at 7 inches per hour.

The height can be represented as A = 59 -7t

Snowman B starts at 34 inches and decreases height by 2 inches per hour. That height can be represented by B = 34 -2t

A is taller than B.

A > B

59 -7t > 34 -2t

add 7t-34

25 > 5t

Divide by 5

5 > t

A will be taller than B when t < 5.

Hence,  A = 59 -7t and B = 34 -2t are equation for each situation and t< is the interval.

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Answer:

is that geometry

Step-by-step explanation:

By solving linear inequation, it can be calculated that

x = 60 , y = 70 is one possible solution.

What is linear inequation?

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by <, >, ≤, ≥

A one degree inequation is known as linear inequation

Let the number of tacos sold be $x and the number of burrito sold be $y

He only has enough supplies to make 130 tacos or burritos.

x + y [tex]\leq[/tex] 130 ... (1)

He sells each taco for $4.25 and each burrito for $8.50.

Isaac must sell a minimum of $850 worth of tacos and burritos each day.

4.25x + 8.5y [tex]\geq[/tex] 850

x + 2y [tex]\geq[/tex] 200 ... (2)

The inequalities has been solved graphically

One possible solution is x = 60, y = 70

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Using the Central Limit Theorem for proportions, the correct option is:

E. The statistic is biased.

What is Central Limit Theorem?

The central limit theorem in probability theory proves that, even if independent random variables are not normally distributed in themselves, in many cases, when they are added together, their properly normalised sum tends toward a normal distribution.

The central limit theorem states that the distribution of the sample means will be roughly normally distributed if you have a population with mean and standard deviation and take sufficiently large random samples from the population with replacement.

The Central Limit Theorem establishes that for a proportion p in a sample of size n:

- The expected value is[tex]$\mu=p$[/tex].

- The standard error is [tex]$s=\sqrt{\frac{p(1-p)}{n}}$[/tex]

In this problem, the expected value is different of the expected of [tex]$\mu=p$[/tex], hence, the statistic is biased, and the correct option is [tex]$\mathbf{E}$[/tex].

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Answer:

g= 7-3e / 4 - 9e

Step-by-step explanation:

I assume you need to solve for g. Please let me know if that is not the case

The y-intercepts for the models are equal to 13.2.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all

Any two different points on a line can be used to calculate the slope of any line.

A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

Hence, The y-intercepts for the models are equal to 13.2.

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Answer:

Interest rate = 7 percent

Step-by-step explanation:

i = prt

r = [tex] \frac{i}{pt} [/tex]

r = [tex] \frac{1400}{20000 \times 1} [/tex]

r = 0.07

0.07 x 100 = 7

Answer:

(x/4)+10

Step-by-step explanation:

Quotient=division, so x/4

Increased by 10, so (x/4)+10

Answer:

Step-by-step explanation:

The scatter plot shows positive correlation because as the plotted values of x increase, the values of y generally increase.

When x and y both increase, you have a positive correlation. When one increases and the other decreases then you have a negative correlation.

Answer:

f = 3

g = -1

h = 6

r = 18

Step-by-step explanation:

Box 1

f(x) = [tex]2x^{4}[/tex]-[tex]12x^{3}[/tex]+[tex]16x^{2}[/tex]+4x+15 with x = 3

f(3) = [tex]2(3^{4)}[/tex] - [tex]12(3^{3} )[/tex] + [tex]16(3^{2})[/tex]+ 4(3) + 15

Reorder

Evaluate

Multiply

3f = 2 x 81 - 12 + 27 +16 x 9 + 12 +15

3f = 162 - 324 + 144 + 12 + 15

3f =  9

3  ÷  3

f = 3

Box 1

g(x) = [tex]3x^{3}[/tex] - [tex]16x^{2}[/tex] - 7x - 36 with x = 6

g(6) = [tex]3(6^{3} )[/tex] - [tex]16(6^{2})[/tex] - 7(6) - 36

g6 = 3 x 216 - 576 - 42 - 36

g6 = -6

6   ÷ 6

g = -1

Box 2

h(x) = [tex]5x^{3}[/tex] - [tex]2x^{2}[/tex] - 3 with x = -1

h(-1) = [tex]5(-1^{3} )[/tex] - [tex]2(-1^{2})[/tex] -3

h-1 = -5 + 2 -3

h-1 = -6

-1    ÷  - 1

h = -6

Box 2

r(x) = [tex]4x^{4}[/tex] - [tex]9x^{2}[/tex] + 5x - 2 with x = 2

r(2) = [tex]4(2^{4} )[/tex] - [tex]9(2^{2} )[/tex] + 5(2) - 2

r2 = 64 - 36 + 10 - 2

r2 = 36

2   ÷  2

r = 18

The equation of line parallel to y = -3 passing through (2,6) is y = 6

The slope-intercept form of straight line is used to find the equation of line. It is given as y =mx + b

where m is a slope of line

b is y-intercept

According to the question,

The required line is parallel to line y = -3

Slope of given line : m₁

m₁ = 0

When two lines are parallel to each other then their slopes are equal

Therefore , slope of required line is m₂ =  m₁ = 0

Also , given that the line is passing through the coordinate (2,6)

So , 6 = 0(2) + b

=> b = 6

Substituting the values of slope and intercept

y = 6 is required equation of line

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Answer: d.) 6

Step-by-step explanation:

Since Chris runs 1. 2 as fast as his usual running speed, he runs at 5 km/h, and so will take 6 hours to complete the 30 km run. Since Pat runs at 11. 2 times her usual speed.

The expression for 60 decreased by twice Jenny's score 60 - 2x.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Let Jenny's score be x.

Twice Jenny's score will be 2x.

Therefore, the expression will be:

= 60 - 2x

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y=1/3x+4 is the equation of line passing through (3, 5) and parallel to -x+3y=6

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

-x+3y=6

3y=6+x

Divide both sides by 3

y=2+1/3x

y=1/3x+2

slope is 1/3

In parallel lines the slope will remain same

We need to find the equation of line passing through (3, 5) and parallel to 3y=6+x

5=1/3(3)+b

5=1+b

b=4

Hence, y=1/3x+4 is the equation of line passing through (3, 5) and parallel to -x+3y=6

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Answer: A

Step-by-step explanation: To solve this problem, we can set up a system of equations to represent the information given in the problem. Let x represent the cost of a plate of spring rolls, y represent the cost of a plate of chicken tenders, and z represent the cost of a plate of pretzel dippers.

The first group spent $23 on 2 plates of chicken tenders and 1 plate of pretzel dippers, so the equation for this group is:

2y + z = $23

The second group spent $30.75 to buy 3 plates of spring rolls and 1 plate of chicken tenders, so the equation for this group is:

3x + y = $30.75

The third group spent $22.25 on one of each appetizer, so the equation for this group is:

x + y + z = $22.25

Now that we have three equations, we can use algebraic techniques to solve for the value of x, which represents the cost of a plate of spring rolls.

First, we can solve the second equation for y:

y = $30.75 - 3x

Substituting this expression for y into the first equation, we get:

2($30.75 - 3x) + z = $23

Solving for x, we find that x = $7.75.

Therefore, the cost of a plate of spring rolls is $7.75, so the answer is A.

The equation of a line is y = 2x - 4. If the equation is changed to y = 2x - 2, how will the graph of the line change?

A The line will become less steep.

B The line will shift right 2 units.

C The line will shift up 2 units.

D The line will shift left 2 units.

E The line will shift down 2 units.

The value of the inequality is ( 45/4 , 19/4 )

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

According to the given information

Number of hours spent in washing cars = x

Number of hours spent in clearing tables = y

Amount paid per hour for washing the car = $7

Amount paid per hour for clearing the tables = $15

Earnings

7x + 15y ≥ 150

x + y ≤ 16

7x + 15y = 150 ........ (i)

x + y = 16 ........(ii)

Multiply (ii) by 7

7x + 7y = 112 ..... (iii)

Subtract (i) and (iii)

8y = 38

y = 19/4

Putting the value of y in (ii)

x + 19/4 = 16

x = 16 - 19/4

x = 45/4

The value of the inequality is ( 45/4 , 19/4 )

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If a square has an area of 450 square inches then according to Area = 2(length of a side), the length of one side of that square will be 225 inches.

The formula of Area of a Square is ,

area = side × side = side² square units

whereas the perimeter of square is = 4 x side

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at right angles or at 90 degrees.

let the length of a side of a square is x

area of square is = 450 square inches

as area of square is found as

Area = 2(length of a side)

2x = 450 square inches

x =450/2

x=225 inches

so the length of each side of square is 225 inches.

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Answer: -2.2y - 1.8

Step-by-step explanation:

Combine like terms

1.2y+(-3.4y)

4.5+(-6.3)

-2.2y - 1.8

The probability distribution that she or he is on duty on Saturday or Sunday will be 0.7

What is probability distribution ?

A frequency distribution that has been idealised is a probability distribution.

An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each potential value of a variable appears.

The probability of occurrence of a value determines how frequently it appears in a sample. Probability is a value between 0 and 1 that indicates the likelihood that something will happen:

A value will occur more frequently in a sample the higher its likelihood.

The probability of a value is more particularly the relative frequency in an indefinitely large sample.

Probability distributions are theoretical since it is not feasible to obtain infinitely large samples in practise.

Let the people work on Sunday = sun = 4

Let the people work on Saturday = sat = 3

total no. of doctors are 10

so the probability distribution of people work on either Sunday or Saturday will be :

= Sun + sat / total no of doctors

= 3+4/10

=0.7

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Answer:

Step-by-step explanation:    3?    

The values of as shown in the isosceles triangle x is 55°

An isosceles triangle is a type of triangle that have two equal sides.

To calculate the value of x in the isosceles triangle, we use the formula below.

Note: The sum of the angle in a triangle is 180°.

Formula:

Where:

From the image,

Given:

Substitute these values into equation and solve for x

Hence, the values of x is 55°

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The number of subscribers in 2008 will be 110845988.

From the information, in 1985, there were 285 cell phone subscribers in the small town of glenwood. the number of subscribers increased by 75% per year after 1985.

It should be noted that the number of years between 1985 and 2008 will be:

= 2008 - 1985

= 23 years.

Therefore, the number of subscriber in 2008 will be:

= 285 × (1 + 75%)^23

= 285 × 1.75^23

= 285 × 388933.29

= 110845988

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It explains that people don't want to donate their organs in opt out  because the probability of non donation public are greater.

As we know people who wants to donates their is organs opt out are approximately around 15 %

And we also know that people who don't want to donate their organs are approx. 90 %

In countries such as Australia, laws make organ donation the default option at the time of death, and so people must explicitly “opt out” of organ donation. In these so-called opt-out countries, more than 90% of people register to donate their organs.

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Answer:

567.06 in.²

Step-by-step explanation:

The mat is a semicircle.

The straight side is a diameter.

d = 38 in.

r = d/2 = 19 in.

Area of circle = πr²

Area of semicircle = πr²/2

A = 3.14159 × (19 in.)² / 2

A = 567.06 in.²