Identify the reciprocal of each number. Type it in the blank, using a slash (/) to show a fraction.

32

The complete question is:

In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have no more than $30 to spend.  You expect to purchase at least 3 pounds of hamburgers.  

Justify your answers

Answer:

A) System of inequalities:

B) Graph: see the picture attached

C) Three possible combinations:

Explanation:

A) Write the system of inequalities to represent this situaction.

1. Variables:

2. Costs:

3. First constraint:

4. Second constraint:

5. Additional constraints:

6. System of equations:

B) Graph

You have to graph all the constraints in a x-y coordinate system.

1. To graph 2x + 3y ≤ 30 graph the line 2x + 3y = 30

2. To graph x ≥ 3 just draw the vertical line x = 3 and shade the region to the right of it. The points of the line are included (solid line).

3. The constraints x ≥ 0 and y ≥ 0 mean that the region is restricted to the first quadrant (including the positive axis).

4. The feasible solutions are the set of points inside the common regions (intersection).

With all that information the graph is the one attached. The feasible solutions is the region defined by the triangle with vertices (3,8), (3,0), and (15,0).

C) Give 3 possible combinations.

You can pick any three points inside the region, as long as the coordinates are integer numbers. For instance the 3 vertices are solutions:

You could also prove that (5,4), 5 pounds of hamburgers and 4 pounds of chicken meet, the inequalities.

This is how you prove it:

And you can do the same for any pairs to verify whether they are solution or not.

Final answer:

The point estimate for the proportion of homeowners in the given sample is 75%, calculated by dividing the number of homeowners (24) by the total number surveyed (32).

Explanation:

To obtain a point estimate of the proportion of homeowners from the given sample, we would calculate the proportion of those who did not rent, since owning and renting are the only two options provided. Out of 32 people, 8 said they rented, which means 32 - 8 = 24 owned their home. The point estimate for the proportion of homeowners is then given by the number of homeowners divided by the total number of people surveyed:

Point estimate for homeowners = (Number of homeowners) / (Total number surveyed) = 24 / 32 = 0.75 or 75%

This mean 75% of the surveyed individuals are estimated to be homeowners.

Answer:

Step-by-step explanation:

From the given diagram we notice that

1. Line AB is equal to Line DE.

2. Line AC is equal to line DF.

3. Angle A is equal to angle D

Then, it shows that 2 sides of the triangle are similar and 1 of it's angle is also similar. Then, it is SAS

Where, S- represent sides and A- represents angle

NOTE : we have SSS, ASA, AAS and SAS, we don't have SSA

To write the similar triangle equation

∆ABC ≈ ∆DEF

Since AB is equal to DE, the we replace It with DE and also Angle A is equal to angle D. Also AC is equal to DF, then we replace C with F.

So the answer is C

∆ABC ≈ ∆DEF SAS

Answer:

a = - 17

Step-by-step explanation:

Given

- 2(a + 16) = 2 ( divide both sides by - 2 )

a + 16 = - 1 ( subtract 16 from both sides )

a = - 17

Answer:

a=-17

Step-by-step explanation:

-2(a+16) =2

-2a-32=2

+32 +32

-2a=34

divided in both sides by -2

a=-17

Final answer:

Three half squared is (3/2)², which equals 9/4 when you square the numerator (3² = 9) and the denominator (2² = 4) separately.

Explanation:

The expression 'three half squared' refers to the quantity (3/2) squared. To square a fraction, you square the numerator and the denominator separately. Therefore, (3/2) squared is (3 squared) over (2 squared), which is 9 over 4. Since there are no further simplifications to make, 9/4 is the final answer as a fraction.

To understand this conceptually, think about the process of squaring as finding the area of a square with side lengths of the original number. So, if the side length of a square is 3/2, the area (which represents the square of the number) will be 9/4 square units.

Final answer:

To determine what three-half squared is as a fraction, you simply square the numerator and denominator separately, arriving at the fraction 9/4.

Explanation:

Calculating Three-Half Squared as a Fraction

To find what three half squared is as a fraction, you square both the numerator and the denominator of the fraction 3/2. When you square the numerator (3), you get 9, and when you square the denominator (2), you get 4. Therefore, the answer to three half squared is 9/4, as we have calculated (3/2)² = (3²)/(2²) = 9/4.

This calculation is similar to understanding that if you start with half of a pie and you multiply this amount by itself, you are essentially getting a fraction of the original whole. In our example, by squaring half, we get a quarter, thereby following the intuitive sense of fractions.

Answer:

$87.76

Step-by-step explanation:

108.25/100 = 95/x

95×100=9500

9500÷108.25=87.76

To find the total price including tax after a meal at a restaurant, convert the tax rate to a decimal, then multiply it by the total cost and add the result to the original total cost.

First, find the amount of sales tax. To do this, convert the percent to a decimal by dividing by 100: 8.25% = 0.0825.

Then multiply the total cost by the decimal tax rate to get the tax amount. In this case, $95 * 0.0825 = $7.8375.

Next, add the tax amount to the original total cost to find the total price: $95 (original cost) + $7.8375 (tax) = $102.8375.

Therefore, the total price, including tax, for Shirley and her family's meal last night was $102.84.

Answer:

500 miles per hour

Step-by-step explanation:

6000 miles/12 hours = 500 miles per hour

Answer:

The company's profit be in the year 2008 is $8.3 million.

Step-by-step explanation:

Given:

In the year 2006, a company made $7 million in profit, their profit increased by 9%.

So, we need to calculate the company's profit be in the year 2008.

Now, by putting the formula to find the profit(P) after the two year:

Difference between the year = 2008 - 2006 = 2 year.

So, number of years(n) = 2 year

Rate of profit increasing(r) = 9%

Amount company made in 2006 (A) = $7 million.

[tex]P=A(1+\frac{r}{100})^{n}[/tex]

[tex]P=7(1+\frac{9}{100})^{2}[/tex]

[tex]P=7(1+0.09)^{2}[/tex]

[tex]P=7(1.09)^{2}[/tex]

[tex]P=7\times 1.188[/tex]

[tex]P=8.316[/tex]

Profit in the year 2008 would be 8.316 million, and nearest to the tenth of a million dollars is $8.3 as 3 is in the tenth place of the decimal and 1 in the hundredth so rounding will change $8.316 to $8.3.

Therefore, the company's profit be in the year 2008 is $8.3 million.

Final answer:

To find the company's profit in 2008 after a 9% increase each year from 2006, we calculate compound growth over two years. The profit in 2008 would be $8,316,700, which rounds to $8.3 million.

Explanation:

To calculate the company's profit in the year 2008 after it increased by 9% each year following 2006, we can use the formula for compound interest which is similar to calculating compounded profit growth. The formula is:

[tex]P = P_0 \times (1 + r)^t[/tex]

Where:

P is the future profit

P₀ is the initial profit ($7 million)

r is the annual growth rate (9% or 0.09)

t is the number of years since 2006 (2008 - 2006 = 2 years)

Let's calculate the profit for 2008:

P = $7,000,000 × (1 + 0.09)²

First, calculate the growth factor for one year:

1 + 0.09 = 1.09

Now, apply the growth factor for two years:

1.09² = 1.1881

Multiply the initial profit by the growth factor:

P = $7,000,000 × 1.1881 = $8,316,700

To the nearest tenth of a million dollars, the company's profit in 2008 would be $8.3 million.

Final answer:

To find the alcohol percentage in the 4:1 ratio, we use the information from the 3:2 ratio. For every 3 parts alcohol, there are 2 parts water. When mixed at a ratio of 4:1, the alcohol percentage is 24%.

Explanation:

To determine the alcohol percentage of the solution when mixed at a ratio of 4:1, we can use the information given in the question. When mixed at a ratio of 3:2, the solution contains 18% alcohol. This means that for every 3 parts alcohol, there are 2 parts water. We can use this information to find the alcohol percentage for the 4:1 ratio.

Let's say we have 4 mL of alcohol and 1 mL of water. The total volume is 4+1 = 5 mL. In the 3:2 ratio, the alcohol percentage is 18%. So, for 3 mL of alcohol, the total volume is 3+2 = 5 mL. Therefore, the alcohol percentage for the 4:1 ratio is (18/3) * 4 = 24%.

Answer:

x=3, y=22. (3, 22).

Step-by-step explanation:

-5x+3y=51

y=10x-8

----------------

-5x+3(10x-8)=51

-5x+30x-24=51

25x-24=51

25x=51+24

25x=75

x=75/25

x=3

y=10(3)-8

y=30-8

y=22

The value of x is 3 and y is 22.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

-5x+3y=51 ..........(1)

y=10x-8 .............(2)

Put the value of y from equation (2) in equation (1) we get

-5x+ 3(10x - 8)= 51

-5x + 30x - 24 = 51

25x = 51+ 24

25x = 75

x= 3

and, y= 10(3)- 8= 30 -8 = 22

Hence, the value of x is 3 and y is 22.

Learn more about Equation here:

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Answer:

First number is 1379.63% of the second number.

Step-by-step explanation:

Consider the provided information.

1192 people per square mile in New Jersey.

The national average is 86.4.

We need to 1192 people per square mile in New Jersey is how much % of a national average of 86.4 Americans per square mile in 2012.

Let 1192 is x percent of 86.4.

[tex]1192=\frac{x}{100}\times 86.4[/tex]

[tex]x=\frac{1192\times 100}{86.4}[/tex]

[tex]x=\frac{119200}{86.4}[/tex]

[tex]x\approx 1379.63\%[/tex]

Hence, first number is 1379.63% of the second number.

Answer:

c = 36

Step-by-step explanation:

Given

a² + 12a + c

To complete the square

add ( half the coefficient of the a- term )² to a² + 12a

a² + 2(6)a + 6²

= (a + 6)² + 36

Hence the value of c = 36

Answer:

$12.09

Step-by-step explanation:

formula; Y= kx

where;    y = $24.18

               x = 2 books

               k = constant of proportionality

Step 1. Do the equation based on the data given

Y = kx

$24.18 = k2

Step 2. Compute the mathematical equation. Divide both sides by 2 to eliminate coefficient in the variable.

24.18 =k2

       2

k = $ 12.09 is the constant of proportionality cost in dlooars per book

Answer:

0.3

Step-by-step explanation:

To find p we require the cube root of 0.027, that is

p³ = 0.027, then

p = [tex]\sqrt[3]{0.027}[/tex] = [tex]\sqrt[3]{\frac{27}{1000} }[/tex] = [tex]\frac{3}{10}[/tex] = 0.3

Answer:

Step-by-step explanation:

Re-write the equation, for convinience, as

y = 1/4(x) + 4

set x = 0 to get y = 1 and set y = 0 to get x = -4.

You have the coordinates of 2 points, (0 , 1) and ( -4 , 0).

Join the two points which obviously cuts the y-axis at y = 1,

Answer:

2.5%

Step-by-step explanation:

The price increased from 2 to 2.05. So the increase was:

2.05 - 2 = 0.05 dollars

Now, to find percentage increase, we use the formula below:

[tex]\frac{New-Old}{Old}*100[/tex]

Where

New is the latest price (here it is the increased price of 2.05)

Old is the previous price (here it is the less price of 2.00)

Now, we substitute and find:

[tex]\frac{2.05-2.00}{2.00}*100=2.5[/tex]

So the price increase was 2.5%

Each increase of 1 in x decreases y by 7, i.e. increases y by -7.  That's a slope of

Answer: -7

Answer:

[tex] -7[/tex]

Step-by-step explanation:

Use the rise over run equation

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

Answer:

62,000 grams as there are 1000 grams in a kilogram

Answer:

$2 per ride

Step-by-step explanation:

$32-$20=$12

McKenna rode 6 rides so $12 divided by 6 rides is $2 for every ride

Final answer:

The equation to find the price for each ride McKenna paid at the carnival is $32 - 6P = $20. Solving for P gives us P = $2, so each ride costs $2.

Explanation:

To find the price for each ride that McKenna paid at the carnival, we need to set up an equation based on the information given. McKenna started with $32 and ended with $20 after riding 6 rides. The amount spent on rides is the difference between the starting amount and the remaining amount.

The equation will be:

Initial amount - (Price per ride × Number of rides) = Remaining amount

$32 - (Price per ride × 6) = $20

Let's denote the price for each ride as P. So the equation becomes:

$32 - 6P = $20

To solve for P, we rearrange the equation:

6P = $32 - $20

6P = $12

P = $12 / 6

P = $2

Hence, the price for each ride is $2.

Final answer:

Vertex-edge graphs can model real-world problems, not all graphs can be solved, Euler paths and Hamilton paths are different, and in a Hamilton circuit, all vertices must be used exactly once.

Explanation:

Vertex-edge graphs, also known as graphs or networks, are mathematical structures that consist of vertices (also called nodes) connected by edges. They are widely used to model real-world problems across various fields such as computer science, transportation planning, and social networks, among others (1). While some vertex-edge graphs can be solved, it is not true that all graphs can be solved. Solvability depends on the specific problem being represented by the graph and the algorithms or methods used to solve it (2). Euler paths and Hamilton paths are not the same. An Euler path is a path in a graph that visits every edge exactly once, while a Hamilton path visits every vertex exactly once (3). In a Hamilton circuit, all vertices must be used exactly once, but not in a Hamilton path. There can be more than one Hamilton path in a graph, depending on its structure (4).

Answer:

1,440 feet

Step-by-step explanation:

there are 12 feet in one yard

you have 120 yards so you need to multiply 120*12

you would get 1,440

Answer:

360 feet

Step-by-step explanation:

1 yard = 3 feet

120 yard x 3 = 360 feet

Answer:

the answer should be 1:38 pm, but if not, 1:33 pm is correct

Answer:

1:33 PM

Step-by-step explanation

When the plane arrives in Salt Lake City, the time in eastern time period should be 15:33 or 3:33 PM. From eastern time period to the mountains, the time should decrease by 2 hours. 3:33 - 2 hours is 1:33. 1:33 is still in the afternoon so the answer is 1:33 PM.

Answer: radius=8, circumference=16π

Step-by-step explanation:

diameter is 16 centimeters

the radius of a circle is half its diameter

so, radius = 16/2 = 8

circumference of a circle = 2πr

so, circumference = 2π(8cm) = (16π) cm

Answer:

30

Step-by-step explanation:

1 foot=3 in

10*3=30 there,easy

Answer:

Should be 120 inches

Step-by-step explanation:

1 feet = 12 inches

10 feet = 12( inches) × 10 (feet)

Therefore, the formula should be:

12×10

=120 ( inches)

Hope it helps!

Answer:

-12x^3+17x^2+x+2

Step-by-step explanation:

3x^2+x+2-4x^2(3x-4)

3x^2+x+2-12x^3+14x^2

3x^2+14x^2-12x^3+x+2

17x^2-12x^3+x+2

-12x^3+17x^2+x+2

Answer:

30 yellow straws and 45 red straws

30:45

Step-by-step explanation:

Make a ratio:

2:3, 2 being the yellow straw and 3 being the red straws

They are now asking how many red if there are 30 yellow straws

2:3 = 30:x

You could either cross multiply or simply do 30 ÷ 2 = 15 then 15 × 3 = 45. Your answer is 45

Cross multiplying

2x = 90

90 ÷ 2 = 45

Answer:

5x + y - 4 = 0

Step-by-step explanation:

When we are given two points and are asked to find the equation of the line we use the two - point form.

Two - point form: [tex]$ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} $[/tex].

where: [tex]$ (x_1,y_1) $[/tex] and [tex]$ (x_2,y_2) $[/tex] are the two points on the line.

Given the two points are: (5,21) and (-5,-29).

Substituting in the two point form:

⇒  [tex]$ \frac{y - 21}{-29 - 21} = \frac{x - 5}{-5 -5} $[/tex]

[tex]$ \implies \frac{y - 21}{-50} = \frac{x - 5}{-10} $[/tex]

[tex]$ \implies y - 21 = 5x - 25 $[/tex]

⇒                              5x + y - 4 = 0

Hello.

Answer: -55. When adding two negatives, you add like you would any positive number.

Answer:

m = 0 or 5

Step-by-step explanation:

m² − 5m = 0

Factor out m:

m (m − 5) = 0

Set each term to 0:

m = 0

m − 5 = 0

Solve for m:

m = 0

m = 5