Write a few sentences explaining how to determine whether a relation shown in a table or a graph is a function.

Answer:

A) each donut costs $0.65

B) the price for 1 and 1/2 dozen of donuts (18 donuts) is $11.70

Step-by-step explanation:

For a you have to divide $7.80 by 12 (since its a dozen) and thats how you get $0.65

For b you have to multiply the price of each donut ($0.65) by the 1 and 1/2 dozen (18 donuts) and thats how you get $11.70

A) The price per donut is approximately $0.65, and B) the cost of 1 and 1/2  dozen donuts is $11.70.

Certainly, let's break it down:

A) To find the price per donut, divide the total cost by the number of donuts in a dozen:

  Price per donut = $7.80 / 12 ≈ $0.65

B) Calculate the cost of 1 dozen:

  Cost of 1 dozen = $7.80

  Now, for [tex]\( \frac{1}{2} \)[/tex] dozen, multiply the price per donut by 6 (half of 12):

  Cost of [tex]\( \frac{1}{2} \)[/tex] dozen = $0.65 × 6 = $3.90

  Add the cost of [tex]\( \frac{1}{2} \)[/tex] dozen to the cost of 1 dozen:

  Total cost for 1 and [tex]\( \frac{1}{2} \)[/tex] dozen = $7.80 + $3.90 = $11.70

In summary, A) the price per donut is approximately $0.65, and B) the cost of 1 and [tex]\( \frac{1}{2} \)[/tex] dozen donuts is $11.70.

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Answer:

Pitcher 1/3 gallon = 4/12 gallon

Jug 3/4 = 9/12 gallon

So, it will take 2 pitchers plus 1/12 of a gallon to fill the jug.

Step-by-step explanation:

Lucio spent a total of $5.37 on candy by purchasing 1.7 pounds of gummy bears at $1.88 per pound and 0.8 pounds of caramels at $2.72 per pound, and then summing both costs.

To calculate the total cost of candy that Lucio is buying, we compute the cost of each candy type separately and then add those costs together. He buys 1.7 pounds of gummy bears at $1.88 per pound and 0.8 pounds of caramels at $2.72 per pound.

For the gummy bears: 1.7 pounds × $1.88 per pound = $3.196

For the caramels: 0.8 pounds × $2.72 per pound = $2.176

To find the total cost, we add the cost of gummy bears and caramels. Therefore, the total cost is $3.196 + $2.176 = $5.372. After rounding to two decimal places, we conclude that Lucio spent a total of $5.37 on candy.

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Answer:

D

Step-by-step explanation:

Lets look at the numbers

sqrt(4) = 2  which is a rational number

sqrt(5)   cannot be simplified, it is an irrational number

-6/5  a ratio of integers, which is the definition of a rational number, so it is a rational number

3.5 = 35/10  a ratio of integers, which is the definition of a rational number, so it is a rational number

.555555 = 5/9   a ratio of integers, which is the definition of a rational number, so it is a rational number

Rational numbers:  sqrt(4), -6/5, 3.5  , .5555(repeating)

Irrational numbers: sqrt(5)

Answer: D

Step-by-step explanation:

(1 & 2/3) ft = (1 ft) + (2/3 ft)

(1 & 2/3) ft = 12 inches + 12*(2/3) inches

(1 & 2/3) ft = 12 inches + 8 inches

(1 & 2/3) ft = 20 inches

If the tree grows 5 inches per year, then it will take 4 years to get to 20 inches since 5*4 = 20. You can also divide to get 20/5 = 4.

So it takes 4 years for the tree to grow 1&2/3 feet tall.

Answer:

4 years

Step-by-step explanation:

Okay, so basically write a proportion

5 inches/per year

Then, find out how many inches are in  1 2/3 feet

1 2/3 = 1 8/12

Meaning there 1 2/3 feet is 1 foot and 8 inches. We know a foot is 12 inches. so then you just add 12 + 8 which is 20

Now going back to your proportion

5 inches/ per year =20 inches/x years

We know 5 goes into 20 4 times. Meaning to get to 20, your'e going to have to multiply the numerator by 4. But whatever you do to the numerator, you must do to the denominator. So multiply 1 x 4 which is 4 meaning it is going to take 4 years for the tree to grow 1 2/3 feet.

Hello!

The number of tickets is dependent on age, so age is the independent variable.

Think of it as a y = mx equation. In this equation, x is the input, and y changes depending on the value of x inputted.

In this situation, y is the number of tickets, as y changes depending on the age x inputted. x is age, the independent variable.

Answer:

Its C) the number of tickets

Step-by-step explanation:

Answer:

Point-Slope form:  [tex]y+1=-\frac{6}{15}(x+5)\\[/tex]

standard form:  [tex]2x+5y=-15[/tex]

Step-by-step explanation:

The standard form is given by: [tex]Ax+By=C[/tex]

The point-slope form is given by: [tex]y-y_1=m(x-x_1)[/tex]

point [tex](10,-7)[/tex] as point [tex](x_2,y_2)[/tex]

Let's find the slope:

[tex]m=\frac{-7-(-1)}{10-(-5)}=-\frac{6}{15}[/tex]

1. So, point slope form can be written as:

[tex]y-(-1)=-\frac{6}{15}(x-(-5))\\y+1=-\frac{6}{15}(x+5)\\[/tex]

2. Rearranging this equation and bringing all x's and y's to one side and the number to another side will give us the standard form. So:

[tex]y+1=-\frac{6}{15}x-2\\y+\frac{6}{15}x=-2-1\\y+\frac{6}{15}x=-3[/tex]

But A, B, and C (standard form) needs to be integers, so to get rid of the denominator , we multiply the whole equation by 15. So we have:

[tex]y+\frac{6}{15}x=-3\\15y+6x=-45[/tex]

We can factor out a 3, so it becomes:

[tex]15y+6x=-45\\5y+2x=-15[/tex]

So standard form is [tex]2x+5y=-15[/tex]

Answer:

4.5%

Step-by-step explanation:

Find interest rate by using the formula I=P⋅i⋅t, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

I = $720, P = $2000 and t = 8 years, so

I = P*i*t

i = I/P*t

i = 720 / 2000 * 8

i = 0.045 = 4.5% per year

The interest rate, calculated with the simple interest formula, for an investment of $2000 that grows to $2720 over 8 years is 4.5%.

The subject is about determining the interest rate for an investment in a simple interest account. The formula for calculating simple interest is: Interest = Principal x Rate x Time (I = PRT). In this case, the principal (P) is $2000, the time (T) is 8 years, and the interest (I) earned is the difference between the final balance and the initial deposit, which is $2720 - $2000 = $720.

To find the rate (R), we rearrange the formula to: R = I / (P x T). Plugging in the numbers, we get: R = $720 / ($2000 x 8) = 0.045, or 4.5% when expressed as a percentage.

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Answer:

Option A is correct

[tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]

Step-by-step explanation:

Given that:

70% of x.

⇒[tex]\frac{70}{100} \times x[/tex]

⇒[tex]\frac{7x}{10}[/tex]

Option A:

[tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]

⇒[tex]\frac{3x}{4}-\frac{x}{20}[/tex]

⇒[tex]\frac{60x-4x}{80}[/tex]

⇒[tex]\frac{56x}{80}[/tex]

Simplify:

⇒[tex]\frac{7x}{10}[/tex]

Option B:

[tex]3(\frac{x}{4})-(\frac{x}{10})[/tex]

⇒[tex]\frac{3x}{4}-\frac{x}{10}[/tex]

⇒[tex]\frac{30x-4x}{40}[/tex]

⇒[tex]\frac{26x}{40}[/tex]

Simplify:

⇒[tex]\frac{13x}{20}[/tex]

Option C:

[tex](\frac{x}{2})+(\frac{x}{10})[/tex]

⇒[tex]\frac{6x}{10}[/tex]

Simplify:

⇒[tex]\frac{3x}{5}[/tex]

Option D:

[tex](\frac{x}{2})+\frac{1}{2}(\frac{x}{4})[/tex]

⇒[tex]\frac{x}{2}+\frac{x}{8}[/tex]

⇒[tex]\frac{5x}{8}[/tex]

Therefore, only option which is equivalent to 70% of x is, Option A i.e  [tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]

Answer:

a

Step-by-step explanation:

Check out the attached image below. It shows the bar graphs of each school. As you can see in figure 2 (Cleveland highschool), the data is more spread out compared figure 1. So this has a higher standard deviation. The standard deviation measures spread. The larger the standard deviation is, the more spread out the values will be. It can be thought of as a measure of how distant each value is from the mean.

Answer:

IT HAS THE NEGATIVE SIGN BY THE 9

Step-by-step explanation:

Answer:

The value of square root -9 is not -3 because -9 is a negative number which will then have to be turned into a postive. So, the square root of -9 is 3.

Step-by-step explanation:

To solve the system of equations x - y = 7 and 0.5x + y = 5, convert both to y = mx + b form, graph them, and identify the intersection point as the solution.

To solve the system of linear equations:

we aim to express each equation in the

y = mx + b

form, where

m

is the slope and

b

is the y-intercept, to make them easy to graph.

Rearrange the first equation to isolate y:

The second equation rearranges to:

Both equations are now in a form where they can be graphed easily.

When these equations are graphed, the point where they intersect is the solution to the system. For simplicity, this explanation does not involve the actual graphing, but you can use graph paper or a graphing calculator:

The intersection point gives the solution to the system.

Answer: 585.15

Step-by-step explanation:

Subtract 20 from 169

Once you do so you should get 149%

figure out what $235 + 149% is then you should get five hundred eighty five dollars and fifteen cents ($585.15)

Answer:

B. The total price depends on the number of crates

Step-by-step explanation:

We can immediately rule out C & A because the two factors in the graph are crates and total price. So both the number of crates and total price will be part of our answer, but pumpkins aren't shown on the graph at all.  

This leaves us with B & D. Using common sense we know that the number of crates isn't going to change if the total cost changes but rather the total cost will change depending on how many crates you buy.

I hope that helps u understand & answers ur question! (If u have a question about anything I just said lmk and I'll be glad to tell u what I mean)

Good luck! :)

Answer:

5/8

Step-by-step explanation:

62.5% = 62.5/100

       =0.625

=0.625/1 x 1000/1000

=625/1000

=5/8

Answer:

None

Step-by-step explanation:

it says that there are no late fees after the 15th day

Answer:

32767

Step-by-step explanation:

the geometric sequence 2^{n-1}

and you have to find the sum of the first 15 term of the sequence

The next term is double the previous term, so that the [tex]n[/tex]-th term is given recursively by

[tex]\begin{cases}a_1=1\\a_n=2a_{n-1}&\text{for }n>1\end{cases}[/tex]

This rule tells us that

[tex]a_2=2a_1[/tex]

[tex]a_3=2a_2=2^2a_1[/tex]

[tex]a_4=2a_3=2^3a_1[/tex]

and so on, with the explicit rule

[tex]a_n=2^{n-1}a_1=2^{n-1}[/tex]

for [tex]n\ge1[/tex].

If 512 is the [tex]k[/tex]-th term in the sequence, then

[tex]512=2^{k-1}\implies\log_2512=\log_22^9=\log_22^{k-1}\implies9=k-1\implies k=10[/tex]

Final answer:

In the geometric progression 1, 2, 4, ..., the 9th term is 512, determined by the formula for the nth term of a geometric progression.

Explanation:

The question asks us to find the term in a geometric progression where the value is 512. A geometric progression (GP) is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the ratio. In the given geometric progression 1, 2, 4, ..., each term is obtained by multiplying the previous term by 2. To find which term is 512, we can use the formula for the nth term of a GP, which is a_n = a_1 × r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

Since a_1 is 1 and r is 2, we have: 512 = 1 × 2^(n-1). Simplifying this gives us 2^9 = 512, which means the 9th term of the sequence is 512. Therefore, 512 is the 9th term in the given geometrical progression.

Answer:

6(4a+3b-5)

Step-by-step explanation:

They all share a common factor of 6 so we can factor out the six, 6(4a+3b-5)

Answer:

2a+b=5/2

Step-by-step explanation:

given the expression

24a + 12b - 30

Step one :

To solve this we need to look for a common factor

Here 6 is a common factor

So divide all through by 6

24a/6+12b/6-30/6

4a+2b-5

4a+2b=5

Step two :

We can still factor 2 out for the terms with variables

2(2a+b)=5

2a+b=5/2

Answer: 6*Q= 6Q or 6*Q= y

Step-by-step explanation:

The product is the answer to a multiplication problem, therefore 6*Q will be the first part.

The second part will be the answer. Normally, this would be represented just by 6Q, but you can use another letter to represent it. We'll use y for an example.

6*Q= 6Q

or

6*Q= y

Step-by-step explanation:

ANSWER: 6*q

Answer:

1

Step-by-step explanation:

You can only make one because once an angle is given, the only possibility is to connect the two sides. You can't change it to an obtuse triangle with that.

Everyone else will be a congruent to the first one triangle.

SAS stands for "side, angle, side" and means that we have two congruent triangles where we know two sides and the included angle are equal.

The formula of a slope m:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (0, -1) and (5, -2). Substitute:

[tex]m=\dfrac{-2-(-1)}{5-0}=\dfrac{-2+1}{5}=-\dfrac{1}{5}[/tex]

Answer:

slope = 0

Step-by-step explanation:

To find the slope when you have 2 points, we use the formula

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

m = (-5--5)/(18--2)

   = (-5+5)/(18+2)

   = 0/20

The slope is zero

This a horizontal line, because the y values do not change

By using the properties of angle bisectors and congruent triangles, we can demonstrate that ABCD has both pairs of opposite sides parallel, proving it is a parallelogram.

Proof that ABCD is a Parallelogram

To prove that quadrilateral ABCD is a parallelogram:

DE bisects AC, meaning D is the midpoint of AC, and E is the midpoint of BD.

Since <1 is congruent to <2, triangles ADE and CDE are congruent by the Angle-Side-Angle (ASA) criterion.

If these triangles are congruent, then AD = DC and AE = EC by corresponding parts of congruent triangles (CPCTC).

Since DE bisects AC and BD, triangles ADE and CDE are mirror images.

Consequently, AD is parallel to BC, and AB is parallel to CD.

Because opposite sides are congruent and parallel, we conclude that ABCD is a parallelogram.

The distance between points PQ is [tex]2\sqrt{10}[/tex].

The midpoint of PQ is [tex]( 4, 3)[/tex].

Given that,

The points are P(7, 4) and Q(1, 2).

We have to determine,

The distance between the points and,

The midpoint of PQ.

According to the question,

To calculate the distance between two points by using distance formula;

[tex]Distance \ formula = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }[/tex]

Where,  [tex]x_1 = 7 , y_1 = 4 , x_2 = 1 , y_2 = 2[/tex]

Substitute the values in the formula;

[tex]PQ = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }\\\\PQ = \sqrt{(1-7)^2 + (2-4)^2 }\\\\PQ = \sqrt{(-6)^2 + (-2)^2 }\\\\PQ = \sqrt{36+ 4 }\\\\PQ = \sqrt{40}\\\\PQ = 2\sqrt{10}[/tex]

And, The midpoint of PQ calculated by using formula;

[tex]Midpoint \ of \ PQ = (\dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2} )[/tex]

Where,  [tex]x_1 = 7 , y_1 = 4 , x_2 = 1 , y_2 = 2[/tex]

Substitute the values in the formula;

[tex]Midpoint \ of \ PQ = (\dfrac{7+1}{2} ,\dfrac{4+2}{2} )\\\\Midpoint \ of \ PQ = (\dfrac{8}{2} ,\dfrac{6}{2} )\\\\Midpoint \ of \ PQ = (4,3)[/tex]

Hence, The distance between points PQ is [tex]2\sqrt{10}[/tex].

The midpoint of PQ is [tex]( 4, 3)[/tex].

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Answer:

Yes. The statement is absolutely True

Step-by-step explanation:

Answer:

Yes the statement is true for real numbers.

Step-by-step explanation:

Yes. Every real number has two qualities: a sign and a distance from zero

Real numbers are points along a continuous infinite number line with its midpoint at 0.

These have a sigh either positive or negative. Like the numbers less than zero, or on the left side of zero on a number line are negative and the numbers on the right are positive.

Answer:

Stock Yield = [tex]\frac{Annual Dividend}{Current Stock Price}[/tex]

Step-by-step explanation:

Stock yield is found by the annual dividend divided by the current stock price.

There is an inverse relationship between the stock yield and the current  stock price.

For example, let's assume we have some shares of Company ABC, which pays $1.20 per share in annual dividends and the current stock price is $12.00, then by using the formula above we can calculate the stock yield of the Company ABC as,

Stock Yield  of company ABC = [tex]\frac{Annual Dividend}{Current Stock Price}[/tex]

                                                  = [tex]\frac{\$1.20}{\$12.00}[/tex]

                                                   = 0.1

                                                  = 10%

Answer:

To save 6 months' worth in a fund would be $2858.59.

Step-by-step explanation:

At a wage of $13.70 per hour for a 40 hour work week, your gross pay (not including any taxes or deductions) is $548 per week, or $2192 per month.  Deductions and taxes are 7.65% + 11.55% + 8.35%, for a total of 27.55% that comes out of your gross pay.  $2192 multiplied by 27.55%, or .2755, is $603.90, therefore, in order to find your realized income per month, you must subtract your gross pay by the amount of deductions and tax withholdings:  $2192 - $603.90 = 1588.10.  Another 30% of your realized income is for housing and fixed expenses, or $1588.10 multiplied by 30%, or 0.30, which comes to $476.43.  If you want to save 6 months' of expenses in an emergency fund, simply take your monthly expenses, $476.43, and multiply by 6 = $2,858.59.  

The correct answer is option d. $2,858.59

1. Monthly gross income should be calculated using the exact number of days in the month, which can vary. However, since we are given 4 weeks per month, we will continue with that assumption.

2. The tax rates are percentages, so we need to convert them to decimals for calculation:

Total tax rate = 0.0765 + 0.1155 + 0.0835 = 0.2755.

3. The realized income after taxes should be calculated as follows:

Realized income after taxes = [tex]\$2,192 \times (1 - 0.2755) = \$2,192 \times 0.7245 = \$1,588.53.[/tex]

4. The monthly housing and fixed expenses are correct at $476.56.

5. The emergency fund calculation is also correct:

Emergency fund = [tex]6 \times \$476.56 = \$2,859.36.[/tex]

Upon re-evaluation, the correct calculation for the emergency fund is $2,859.36, which should be rounded down to $2,858. However, the options provided suggest that the correct answer is $3,277.17. This indicates that there may be an error in the provided options or in the interpretation of the question.

Given the calculations above, none of the provided options match the calculated emergency fund. The closest option is d) $2,858.59.

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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[tex]100-2^3\times3+8^2\div4\\\\=100-8\times3+64\div4\\\\=100-24+16\\\\=76+16\\\\=\boxed{92}[/tex]