Twenty students are standing in line to buy food at a football game. The first three students
spend a total of $24. on food.
a. How much do the first three students spend on food per person? [1 point)

The equation of the line that is parallel to y=-5x+6 and passes through the point (-4,-1) is y = -5x-21.

Given data :

Here, given equation of line is y = -5x+6

Required line is parallel to this given line, so we can say that the slope is same for the lines.

General equation of a line be y = mx+c ,  where m is the slope

Comparing given equation with this equation we get,

m = -5

The required line also passes through the point (-4, -1)

Now, we know that,

m = (y2-y1)/(x2-x1).

⇒ -5 = (-1 - Y ) / ( -4 - x )

⇒ -5 = y + 1 / x + 1

⇒ y+1 = -5x-20

⇒ y = -5x-21

Hence the equation proved.

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Answer:

boottom left middle left and top right

Step-by-step explanation:

Answer:

B: 4/5

Step-by-step explanation:

Here, we simply go on to express the ratios of each of the options in its smallest form

2/3 is already in it’s smallest form

4/5 cannot be divided further

4/6 is same as 2/3

8/12 is same as 2/3

Answer:

C= 150.8 I hope this helped! Also I used Google because I didn't know.

Step-by-step explanation:

Answer:

5) 75.36ft

6) 150.72mm

Step-by-step explanation:

Bc, you need to multiply 24 * 3.14 and you'll get 75.36.

Answer:

28°

Step-by-step explanation:

1. We can see that ∠GFH has two smaller angles within it: ∠1 and ∠2. Given that m∠GFH is 53° (the whole thing), and m∠2 is 25° (a part of it), we just have to subtract 25 from 53 to get the measure of ∠1.

Therefore, m∠1 = 28°.

More than twice as many roast beef sandwiches as the deli sold over the course of five months.

Let the tuna sandwich sold by deli be 'x'

Then, tuna sandwich for 5 months-

1st month - x1

2nd month - x2

3rd month - x3

4th month - x4

5th month - x5

Then,

Selling of roast beef sandwich is 3 times more than tuna sandwich.

Then, roast beef sandwich for 5 months-

1st month -3x1

2nd month - 3x2

3rd month -3x3

4th month - 3x4

5th month - 3x5

Thus, the difference is-

Difference = (3x5 + 3x4 + 3x3 +  3x2 + 3x1) - (x1 + x2 + x3 + x4 + x5)

Difference  = 2x1 + 2x2 + 2x3 + 2x4 + 2x5

Thus, more than twice as many roast beef sandwiches as the deli sold over the course of five months.

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Answer:

Step-by-step explanation:

At 7:00 am Wesley complete his third shift if Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hour shifts option (C) is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

Wesley and two of his friends are driving cross country nonstop and have agreed to take driving in 7-hour shifts.

Wesley’s first shift starts at 6:00 am

6:00 am = 6h 0m

= 6 + 7

= 13 h = 1:00 PM (Wesley's starts to rest)

Wesley will take a rest for 14 hours (7 + 7)

First shift = 7 + 14 = 21

Second shift = 7 + 14 = 21

Third shift = 7 = 7

= 21 + 21 + 7 = 49

= 49/24 = 2 days + 1 hour

6h + 1h = 7h = 7:00 am

Thus, at 7:00 am Wesley complete his third shift if Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hour shifts option (C) is correct.

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We will substitute this value of sin²x in our expression which will give;6 tan²x(1 - sin²x)6 tan²x(1 - (1 - cos²x))6 tan²x cos²x.

We need to simplify the given expression which is given below;

6 tan2 x − 6 tan2 x sin2 x

In order to solve this expression, we will first write it in a factored form which will be;

6 tan²x(1 - sin²x)

We know that the identity for sin²x is;sin²x + cos²x = 1

Which can be rearranged to give;

sin²x = 1 - cos²x

Now we will substitute this value of sin²x in our expression which will give;6 tan²x(1 - sin²x)6 tan²x(1 - (1 - cos²x))6 tan²x cos²x.

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True. The multiplicity of a root r of the characteristic equation of matrix A is indeed called the algebraic multiplicity of r as an eigenvalue of A.

The characteristic equation of a square matrix A is obtained by subtracting λI (where λ is an eigenvalue and I is the identity matrix) from A and taking its determinant. The roots of this equation are the eigenvalues of matrix A.

The algebraic multiplicity of an eigenvalue r refers to the number of times r appears as a root of the characteristic equation. In other words, it represents the multiplicity of r as a solution of the equation.

The algebraic multiplicity provides information about the behavior of the eigenvalue r within the matrix A. If the algebraic multiplicity of r is greater than 1, it means that r is a repeated eigenvalue and there exist multiple linearly independent eigenvectors associated with it. On the other hand, if the algebraic multiplicity is 1, r is a simple eigenvalue, indicating that there is only one linearly independent eigenvector corresponding to r.

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Answer:

20/4 = 5ml

Step-by-step explanation:

Answer:

(0, 1 )

Step-by-step explanation:

Given the 2 equations

y = 2x + 1 → (1)

y = 5x + 1 → (2)

Substitute y = 5x + 1 into (1)

5x + 1 = 2x + 1 ( subtract 2x from both sides )

3x + 1 = 1 ( subtract 1 from both sides )

3x = 0 , then

x = 0

Substitute x = 0 into either of the 2 equations for corresponding value of y

Substituting into (1)

y = 0 + 1 = 1

solution is (0, 1 )

Answer:

(Please see attachment)

Step-by-step explanation:

Points on the graph:

(-1.5, 4.5), (3.5, 3.5)

Graph of points (-1.5, 4.5) and (-3.5,3.5) is given in attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given points are minus one point five comma four point five and minus three point five comma three point five.

(-1.5, 4.5) and (-3.5,3.5)

A coordinate plane is a tool used for graphing points, lines, and other objects

To point these points first we have to consider two lines, horizontal line and vertical line.

The horizontal line is called as X axis and vertical line is called as Y axis.

Then we have to pair (-1.5, 4.5) and (-3.5,3.5) with (x, y) coordinates.

Hence the given graph is the required answer.

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Answer:

y = - \(\frac{1}{4}\) x - 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x - 2 ← is in slope- intercept form

with slope m = 4

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{4}\) , then

y = - \(\frac{1}{4}\) x + c ← is the partial equation

to find c substitute (4, - 11 ) into the partial equation

- 11 = - \(\frac{1}{4}\) (4) + c = - 1 + c ( add 1 to both sides )

- 10 = c

y = - \(\frac{1}{4}\) x + (- 10) , that is

y = - \(\frac{1}{4}\) x - 10 ← equation of line

The hospital uses the quadratic model to predict the number of births

The equation of the quadratic model is f(x) = 4 x^2 -43 x +178, and the number of births for month 8 is 90

To determine the quadratic model, the make use of a graphing calculator, that has the following calculation summary

A quadratic model is represented as:

\(y= ax^2 + bx + c\)

So, we have:

\(y = 4.339 x^2 -43.461 x +178.3\)

Approximate

\(y = 4 x^2 -43 x +178\)

Rewrite as:

\(f(x) = 4 x^2 -43 x +178\)

At the 8th month, we have x = 8.

So, the function becomes

\(f(8) = 4 * 8^2 -43 *8 +178\)

\(f(8) = 90\)

Hence, the number of births for month 8 is 90

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Answer:

4

-43

178

90

Step-by-step explanation:

yep

Step-by-step explanation:

If x + y = 0, then x = -y

Hence they are additive inverse to each other. (b)

c, d, and e. this is because c equals 21, d equals 27, and e equals 9

Answer: 4/10

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

flip 5/6 to become 6/5 then cross reduce then cross multiply

Answer:the equation of the horizontal line passing through (4,7) is y=7 . Note − The equation of a vertical line is always of the type x=k and hence the equation of the vertical line passing through (4,7) is x=4 .

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

\(\dfrac{7}{9}\)

Step-by-step explanation:

\(\dfrac{2}{3}=\dfrac{2\cdot 3}{3\cdot 3}=\dfrac{6}{9} \\\\\\\dfrac{6}{9}+\dfrac{1}{9}=\dfrac{7}{9}\)

Hope this helps!

Answer:

Step-by-step explanation:

\(\frac{2x3}{3x3} \\\)

multiplying by three because you want the denominator same as the other.

  \(\frac{6}{9}\)

+ \(\frac{1}{9}\)

Add the numerators and keep the denominator the same - the denominator never gets added by the way. You only multiply them to get the denominators to equal

\(\frac{7}{9}\)

Answer:

\(\displaystyle f(x)=-\frac{2}{3}(x+2)(x-3)^2\)

Step-by-step explanation:

The graph corresponds to a cubic function of the form:

\(f(x)=a(x-p)(x-q)(x-r)\)

Where p, q, and r are the zeros of f(x).

We can clearly see there are only two crossings through the x-axis. That is because one of the roots is repeated (multiple).

Thus, the roots are p=-2, q=r=3

Substituting into the function:

\(f(x)=a(x+2)(x-3)(x-3)\)

\(f(x)=a(x+2)(x-3)^2\)

The value of a can be found by using the y-intercept seen on the graph (0,-12):

\(-12=a(0+2)(0+3)^2\)

Operating:

\(-12=18a\)

Thus:

\(a = -12 / 18 = -2/3\)

The function is now complete:

\(\mathbf{\displaystyle f(x)=-\frac{2}{3}(x+2)(x-3)^2}\)

Answer:

5

Step-by-step explanation:

double 5 is 10

10+3=13

13 multiplied by 4=52

Answer:

The average height difference between randomly selected girls and boys is 5.5 inches. The standard deviation of the difference in height is about 4.18808 inches.

Step-by-step explanation:

Just subtract the girls' average from the boys' average to find the average difference between any girl and boy.

Calculate the variance from the given standard deviations (square the SD). Add the variances and find the square root of that sum. (SD = square root of Var).

The standard deviation is only able to be calculated when the two variables are independent.

The variances are added and not subtracted because finding a different average doesn't mean that the data that is being observed also has a different deviation (also there isn't really a situation where you would subtract the Var).

Answer:

20,701 feet

Step-by-step explanation:    

29,028-8,327= 20,701

Answer:

8 : 5

Step-by-step explanation:

white socks 8

brown socks 5

Answer:

8:5

Step-by-step explanation:

cause

white= 8

brown=5

white:brown

8:5

Find the difference between the starting and ending values:

    72 - 60 = 12

Divide that difference by the starting value:

    12 ÷ 60 = 0.2

Convert that to a percent:

   0.2 = 20%

The number of teachers increased by 20%.

The key is to divide the difference by the original number, not the ending number.

Answer: 1 7/10

Step-by-step explanation:

Answer:

1 \(\frac{1}{10}\)

Step-by-step explanation:

Multiply the whole numbers first.  1 x 1 = 1

Then do the fractions.  \(\frac{1}{5}\) X \(\frac{1}{2}\).  Multiply the two top numbers then multiply the two bottom numbers.  1 x 1 = 1  and  5 x 2 = 10 so this part equals \(\frac{1}{10}\).

Putting it together you get 1 \(\frac{1}{10}\).

The odds in favor of the event occurring are 8:1.

The odds in favor of an event occurring can be calculated by dividing the probability of the event occurring by the probability of the event not occurring. In this case, the probability that the event will occur is 8/9, and the probability that the event will not occur is 1/9. To determine the odds in favor of the event occurring, we divide the probability of the event occurring by the probability of the event not occurring, which gives us 8/1 or simply 8:1.

In probability theory, odds are a way of expressing the likelihood of an event happening. They can be calculated by comparing the probability of an event occurring to the probability of the event not occurring. In this case, if the probability that an event will occur is 8/9, it means that out of nine equally likely outcomes, eight are favorable to the event occurring.

To calculate the odds in favor of the event occurring, we divide the probability of the event occurring (8/9) by the probability of the event not occurring (1/9). This gives us a ratio of 8:1, indicating that the event is highly likely to occur. In other words, for every one unfavorable outcome, there are eight favorable outcomes.

Understanding odds is essential in various fields, such as gambling, statistics, and risk assessment. It allows us to assess the likelihood of certain outcomes and make informed decisions based on the probabilities involved. By knowing the odds in favor of an event occurring, we can evaluate the potential risks and rewards associated with it.

Learning more about probability and odds can provide valuable insights into decision-making processes and help in assessing uncertainties. It is an essential tool for professionals working in fields that involve risk analysis, such as finance, insurance, and scientific research. By understanding how to calculate and interpret odds, individuals can make more informed choices and mitigate potential risks effectively.

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