which situation could be modeled by using a linear function

Answers

Answer 1

if the ice-cream is cheaper, I buy more pints... say the initial price of the ice-cream gallon(8 pints) is hmmm $10, then I'd buy 1 pint

[tex]\bf \begin{array}{ccllll} \begin{array}{llll} price\ of\\ gallon \end{array}& \begin{array}{llll} pints\\ bought \end{array}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 10&1\\ 9&2\\ 7&3\\ 6&4 \end{array}\impliedby \begin{array}{llll} \textit{now if you graph that}\\ \textit{will give you a \underline{line}}\\ \textit{thus a \underline{line}ar function} \end{array}[/tex]

Related Questions

three tables are placed side by side. one table is 6 feet 9 inches, another is 5 feet 11 inches wide, and the third is 2 feet 10 inches wide. how wide are they combined

Answers

15 feet 6 inches.
6+5+2=13 feet
10+9+11=30 inches
30 inches in feet is 2 and 6 inches.

Which is equivalent to “12 chairs for every 3 tables”?

Answers

Answer:

A 12 chairs per 3 table

Step-by-step explanation:

4/1 is equivalent to 12 chairs for every 3 tables.

What is fraction?

Fractions are used to represent smaller pieces (or parts) of a whole.

Given a statement, 12 chairs for every 3 tables.

The statement represents 12 chairs per 3 tables, which means 12/3 = 4/1

Therefore, there are 4 chairs for every table.

Hence, 4/1 is equivalent to 12 chairs for every 3 tables.

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a mechanic charges 50 am hour plus parts if a bill is 450 including 150 in parts how many hours did it take

Answers

total = 450

parts = 150

450-150 = 300

50 per hour

300/50 = 6

it took 6 hours

Simplify x^2-4x-32/x^2+7x+12

Answers

It equals to:

(x - 8)(x + 4) / (x+3)(x+4)

If x ≠ -4

Then it equals to:

(x-8) / (x+3)

Simplify x^2-4x-32/x^2+7x+12
Answer see form:

A group of ladies meet for an afternoon tea party. They bring all their cats. In all, there are 26 heads and 84 feet. How many ladies and how many cats are in the room

Answers

X= ladies y = number of cats

Each lady has 2 feet and each cat has 4 feet

<=>

x + y = 26 (1) => number of characters
2x + 4y = 84 (2) => number of feet

<=> operation : (1) * 2

2x + 2y = 52 (1')
2x + 4y = 88 (2')

<=> operation : (2') - (1')

2y = 26

<=>

y = 20 and x = 32- 16 = 16

10 ladies and 16 cats

h=p+c (heads equals the sum of people and cats) since there are 26 heads:

p+c=26, solve for c, subtract p from both sides

c=26-p, now for feet...

2p+4c=f, using c found above gives you:

2p+4(26-p)=f and we are told that there are 84 feet so:

2p+4(26-p)=84 perform indicated multiplication on left side

2p+104-4p=84, combine like terms on left side

-2p+104=84 subtract 104 from both sides

-2p=-20 divide both sides by -2

p=10, and since c=26-p

c=26-10

c=16

So there are 10 people and 16 cats in the room.

A businessman has 10 employees. His salary is equal to 6 times the average of employees salaries. If the 11 of them receive a total of $64,000 in one year, what was the business mans salary that year ??

Answers

x = business man's salary
y = employee's salary

x + 10y = 64000
x = 6y

6y + 10y = 64000
16y = 64000
y = 64000/16 = 4000

x = 6*4000
x = 24000

business man's salary was $24,000

"apply quickselect to find the median of the list of numbers 9, 12, 5, 17, 20, 30, 8."

Answers

Final answer:

To find the median using quickselect, choose a pivot value, partition the list, and repeat the process with the appropriate partition until the pivot index matches the desired median index.

Explanation:

The median of a list of numbers is the middle value when the numbers are arranged in ascending order. To apply quickselect to find the median, start by choosing a pivot value from the list. Partition the list and move all values smaller than the pivot to the left and all values larger than the pivot to the right. If the pivot index is equal to the desired median index, then the pivot value is the median. Otherwise, if the pivot index is smaller, repeat the process with the right partition; if the pivot index is larger, repeat with the left partition.

In the given example, let's apply quickselect to find the median:

Choose a pivot value, let's say 17.

Partition the list: 5, 8, 9, 12, 17, 20, 30

The pivot index is 4, which is less than the desired median index.

Repeat the process with the right partition: 17, 20, 30

Choose a new pivot value, let's say 20.

Partition the list: 17, 20, 30

The pivot index is 1, which is equal to the desired median index.

Therefore, the median of the list of numbers 9, 12, 5, 17, 20, 30, 8 is 17.

Product A is an 8 oz bottle of cough medication that sells for $1.36. Product B is a 16oz bottle of cough medication that cost $3.20. Which product has the lower unit price

Answers

product a
^^^^^^^^^^^^^^^^

What is the next number in the series? 83 79 75 71 67 ?

Answers

Answer:

Given the series : 83 , 79 , 75 , 71 , 67, ?

Difference of two consecutive terms;

79 -83 = -4

75 -79 = -4

71-75 = -4

67-71= -4

Since, you can see that the number is decreases by 4 every time.

Let unknown term be x

then;

x - 67 = -4

x = 67-4

x = 63.

Therefore, the next term in the series is 63.

The next number in the series is 63.

In the given series, each number is decreasing by 4.

We can observe that the first number, 83, is decreased by 4 to get the next number, 79.

Similarly, each subsequent number is obtained by subtracting 4 from the previous number.

Following this pattern, the next number would be obtained by subtracting 4 from the last number in the series, which is 67.

67 - 4 = 63

Therefore, the next number in the series is 63.

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how do you make a equivalent ratio?

Answers

[tex]\bf Rowley\quad 16:14\implies \cfrac{16}{14}\qquad Rivera\quad 64:60\implies \cfrac{64}{60} \\\\\\ \textit{so, simplifying both fractions } \begin{cases} \cfrac{16}{14}\implies \cfrac{8}{7}\\\\ \cfrac{64}{60}\implies \cfrac{16}{15} \end{cases}\qquad \cfrac{8}{7}\ne \cfrac{16}{15}[/tex]

what is the square root of -1?

Answers

the square root of 1 is 1

The websites I looked at all said "i" and my calculator decided that it has no idea.

What type of graph would have the title, "Monthly Company Profit for the Year?"

bar graph
line plot
line graph
pictograph

Answers

A line graph would suit this situation the best.

Answer:

line graph

Step-by-step explanation:

You deposit $70 in a savings account that pays an annual interest rate of 30%. How much simple interest would you earn in 2.5 years?

Answers

The formula is
I=prt
I interest earned?
P principle 70
R interest rate 0.3
T time 2.5 years
I=70×0.3×2.5
I=52.5

What is the probability of rolling a number less than or equal to 8 with the sum of two dice, given that at least one of the dice must show a 6?

Answers

Given that one die is a 6. So for the sum of the dice to be less than or equal to 8, the other die must be equal to or less than 2.

And the probability of roll a two or less is:

P(≤2)=2/6=1/3

[tex]|\Omega|=6^2=36\\ |A|=4\\\\ P(A)=\dfrac{4}{36}=\dfrac{1}{9}\approx11\%[/tex]

95 is described as what

Answers

0.95 is rational number

answer is option 2

a rational number is any number that can be expressed as the quotient or fraction

so 0.95 = 95/100

hope that helps

Find the area of the shaded region when r = 4 feet and the area of the triangle is: 123√ square feet
Use 1.73 for 3√ and 3.14 for π. Round your answer to two decimal places.

Answers

Area of the shaded region :
A ( shaded ) = A ( circle ) - A ( triangle ) =
= r² π - 12 √ 3 =
= 4² π - 12 √ 3 =
= 16 π - 12 √ 3 =
= 16 · 3.14 - 12 · 1.73 =
= 50.24 - 20.76 = 29.48
Answer: Area of the shaded region is 29.48 ft².

The volume of a rectangular prism is b3 + 8b2 + 19b + 12 cubic units, and its height is b + 3 units. The area of the base of the rectangular prism is square units.

Answers

Given:

The volume of the rectangular prism is

[tex] b^{3}+8 b^{2} +19b+12 [/tex],

the height is h=(b+3)

1. The volume of a rectangular prism is (base area)*height

also, notice that the volume is a third degree polynomial, the height is a 1st degree polynomial, so the base area must be a 2nd degree polynomial, whose coefficients we don't know yet.
Let this quadratic polynomial be [tex](mb^{2}+nb+k)[/tex]

2

[tex]b^{3}+8 b^{2} +19b+12=(mb^{2}+nb+k)*(b+3)[/tex]

notice that [tex]b^{3}[/tex] is the product of the largest 2 terms: [tex]mb^{2}[/tex] and b, so m must be 1

also, notice that 12 is the product of the constants, k and 3

so k*3=12, this means k=4

3
we write the above equality again:

[tex] b^{3}+8 b^{2} +19b+12=(b^{2}+nb+4)*(b+3)[/tex]

[tex](b^{2}+nb+4)(b+3)= b^{3}+3 b^{2} +nb^{2}+3nb+4b+12[/tex]

=[tex]= b^{3}+(n+3)b^{2}+(3n+4)b+12[/tex]

4
now compare the coefficient with the left side:

[tex]8 b^{2}=(n+3)b^{2}[/tex]

8=n+3

n=5

substituting n=5:

the base area is [tex]b^{2}+5b+4 [/tex]

Answer: [tex]b^{2}+5b+4 [/tex]

Answer:

b^2 + 5b +4

Step-by-step explanation:

The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?

Answers

We are given the following variables:

Normal distribution

u = sample mean = 74

s = standard deviation of the samples = 7

x = sample value = 81

Since we are asked to find percent of the scores less than 81, this means we have to find the proportion using the z-score. The formula for z score is:

z = (x – u) / s

Substituting the given values:

z = (81 – 74) / 7

z = 1

Using the standard normal distribution tables for z, we find that:

P = 0.8413 at z = 1

Therefore this means that 84.13% of scores are less than 81.

The Answer is the two small boxes just got it right For Plato

FAR LEFT FAR RIGHT

If the total price paid for an item is $20.25 and the cost of the item before sales tax is $18.90, what is the rate of sales tax?

Answers

20.25 -18.90 = 1.35

1.35 / 18.90 = 0.071428571

= 7.14%

check:

18.90 x 1.34946 Round to 1.35

18.90 + 1.35 = 20.25

Sales tax = 7.14%

In △ABC, m∠A=72°, c=61, and m∠B=16°. Find a to the nearest tenth.

Answers

check the picture below

make sure your calculator is in Degree mode.

Using the law of sines, the length of side a to the nearest tenth is 58.1 units.

What is law of sines?

Law of sines states that When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.

In ΔABC,

∠A=72°

∠B=16°

∠A + ∠B + ∠C = 180° (angle sum property)

72° + 16° + ∠C = 180°

∠C = 180° - (72° + 16°) = 92°

Using sine law, (refer to the figure attached)

[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} =\frac{sin\ C}{c} \\\\\frac{sin72}{a} = \frac{sin16}{b} = \frac{sin92}{61} \\\\\frac{sin72}{a} =\frac{sin92}{61} \\\\a = sin72 * \frac{61}{sin92} \\\\= 0.9511 * \frac{61}{0.9994} \\\\=58.05193116\\\\= 58.1[/tex]

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On a resent business trip it took 7 hours 30 minutes to drive 375 miles how many miles per hour was the average

Answers

divide 375 by 7.5 to get the answer

Answer:

50 miles / hours.

Step-by-step explanation:

Speed may be defined as the distance covered by the object per unit time.

Speed = [tex]\frac{distance}{time}[/tex]

the distance of the business trip = 375 miles.

the time taken by the business trip = 7 hours 30 minutes = 7.5 hrs.

Speed = [tex]\frac{375}{7.5}[/tex]

Speed = 50 miles / hours.

Here, the average of miler per hour is 50 miles / hours.

Cos (pi/11)+cos (3pi/11)+cos (5pi/11)+cos (7pi/11)+cos(9pi/11)

Answers

Answer:

1/2

Step-by-step explanation:

is a kiloliter greater than one liter

Answers

Hello Mikaila

Kiloliters is a metric unit of volume equivalent to 1000 liters or 1 cube meter.

-------------------------------------------------------------------------------------------
Yes, a kiloliter is greater than one liter.

------------------------------------
1 kiloliter = 1000 liters

I hope that helps!

Tessa had $110 in her checking account. She paid her cable/internet bill for $75. She deposited $50 from her part-time job before writing a check for $85 to pay her credit card bill. What is Tessa's account balance?

Answers

110-75+50-85 =

110+50=160

75+85 = 160

160-160=0

her balance is 0

Cylindrical soup radius 4 centimeters height 12 centimeters what is the volume of the soup to the nearest tenth?

Answers

Volume of a cylinder=(pi)(radius^2)(height)
V=(pi)(4^2)(12)
V=(pi)(16)(12)
V=(pi)(192)
V=603.2 centimeters^3

The volume of a cylinder is:
V = π × r² × h

r = 4
h = 12

V = π × 4² × 12
V = π × 16 × 12
V = π × 192
V = 603.19

The volume of the soup to the nearest tenth is 603.2 cm³.

((81x^3 y^(-1/3))^1/4)/(x^2 y)^1/4 simplify

Answers

[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}} \\\\\\ \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{\left( 81x^3y^{-\frac{1}{3}} \right)^{\frac{1}{4}}}{(x^2y)^{\frac{1}{4}}}\implies \cfrac{81^{\frac{1}{4}}x^{3\cdot {\frac{1}{4}}}y^{-\frac{1}{3}\cdot {\frac{1}{4}}}}{x^{2\cdot {\frac{1}{4}}}y^{\frac{1}{4}}}\implies \cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}y^{-\frac{1}{12}}}{x^{\frac{2}{4}} y^{\frac{1}{4}}}[/tex]

[tex]\bf \cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}x^{-\frac{2}{4}}}{ y^{\frac{1}{4}}y^{\frac{1}{12}}}\implies \cfrac{(3^4)^{\frac{1}{4}}x^{\frac{3}{4}-\frac{2}{4}}}{y^{\frac{1}{4}+\frac{1}{12}}}\implies \cfrac{3^{4\cdot \frac{1}{4}}x^{\frac{1}{4}}}{y^{\frac{4}{12}}}\implies \cfrac{3^{\frac{4}{4}}x^{\frac{1}{4}}}{y^{\frac{1}{3}}} \\\\\\ \cfrac{3\sqrt[4]{x}}{\sqrt[3]{y}}[/tex]

If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.

Answers

2n-4= n-10
-n. -n
n-4=-10
+4. +4
n=-6

Final answer: -6

Find the value of 4 + (27 - 12·2) ÷ 2.
Answer's are 3.5,5.5 and 19
Which one is it

Answers

You follow the rule PEMDAS parenthesis, exponent, multipy, divide, add, substart. So you would start off by doing 27-12x2, you would do 12x2=24 first then 27-24=3. So then it would be 4+3/2, do 3/2=1.5, then add it 4+1.5=5.5. So the correct answer is 5.5

The value of 4 + (27 - 12·2) ÷ 2 would be 5.5.

What is simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

A Simplification usually involves making the expression simple and easy to use later.

WE follow the rule PEMDAS parenthesis, exponent, multipy, divide, add, substart.

4 + (27 - 12·2) ÷ 2

4 + (27 - 24 ) ÷ 2

4 + (3) ÷ 2

4+3/2, do 3/2=1.5

then add it

4+1.5 = 5.5.

Therefore, the correct answer is 5.5

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Compare the 3 in 536 to the 3 in 1,36 7.
Draw number 536 using base ten block?

Answers

For the number 536, the order of the numbers from left to right is "hundreds tens units", this means that the 3 is occupying the tens place.

For the number 1367. the order of the numbers from left to right is "thousands hundreds tens units", this means that the 3 is occupying the hundreds place.

As per the representation of 536 using base 10 blocks, it is shown in the attached picture:

The third term of an arithmetic sequence is 21, and the eighth term is 56. The first term is _____.

Answers

The first term is 7. This is because the sequence has a pattern of increasing by 7. If the first term was 7, the second would be 14, the third would be 21. The 4th would be 28, continue to the 8th term 56.

Final answer:

The first term of the given arithmetic sequence is 7. This can be determined by finding the common difference and moving backwards from the third term using this value.

Explanation:

The subject of this question is Arithmetic Sequence which is a topic in mathematics. An arithmetic sequence is defined by a common difference (d) between consecutive terms.

To solve this problem, we have to find the common difference first. The difference between the 8th term (56) and the 3rd term (21) is 35. But since there are 5 steps from the 3rd term to the 8th term, each step (or the common difference) must be 35 ÷ 5 = 7.

Now that we have the common difference (7), we can reverse it from the 3rd term (21) back to the 1st term which gives us: 21 - 2(7) = 7. So, the first term is 7.

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