A radio is giving away tickets to a play. They plan to give away tickets for seats that cost $10 and $20. They want to give away at least 20 tickets. The total cost of all the tickets they give away can be no more then $280

Answer:

Line segment is part of a line bounded by two endpoints

Step-by-step explanation:

Line segment is part of a line bounded by two endpoints

Answer:

  40 mph

Step-by-step explanation:

We assume "outbound" refers to the trip to the lake. The ratio of speeds is inversely proportional to the ratio of times, so ...

  outbound speed : inbound speed = 4 : 3

These differ by one ratio unit, so that one ratio unit corresponds to the speed difference of 10 mph. Then the 4 ratio units of outbound speed will correspond to ...

  4×10 mph = 40 mph

Paul's average speed on the outbound trip was 40 mph.

___

The distance to the lake was 120 mi.

Answer:Paul's average speed on the outbound trip is 40mph

Step-by-step explanation:

Let x represent Paul's outbound trip which is the trip to the lake.

The trip to the lake took 3 hours.

Distance travelled = speed × time

It means that

Distance covered on the trip to the lake would be

3 × x = 3x

the trip back took 4 hours. He averaged 10 mph faster on the trip there than on the return trip. It means that his speed would be

x - 10

Therefore, distance travelled on return trip would be

4(x - 10) = 4x - 40

Since the distance travelled is the same, it means that

3x = 4x - 40

4x - 3x = 40

x = 40

Answer:

C. Stratified Sampling

Step-by-step explanation:

Stratified sampling is a sampling method in which the overall population is divided into a number of smaller sub groups.

These smaller sub-groups are called as strata.

These sub-groups are formed on the basis of similar characteristics and attributes shared by the population.

It is also known as proportional random sampling.

Answer:the equation relating E to H is

E = 20H

Step-by-step explanation:

Let E represent her earnings (in dollars) after tutoring for H hours.

For each hour that she tutors, she earns 20 dollars. This means that in H hours, her total earnings would be

E = 20H

To find Mai's earnings after tutoring for 17 hours, we would substitute H = 17 into the equation. It becomes

E = 20 × 17

E = $340

Mai's earnings [tex](\(E\))[/tex] after tutoring for 17 hours would be $340, calculated as [tex]\(E = 20 \times 17\).[/tex]

To relate Mai's earnings [tex](\(E\))[/tex] to the number of hours she tutors [tex](\(H\))[/tex], we can use the following equation:

[tex]\[E = 20H\][/tex]

This equation represents that Mai earns $20 for each hour she tutors. By multiplying the number of hours [tex](\(H\))[/tex] by the rate of $20 per hour, we get her total earnings [tex](\(E\))[/tex].

Now, to find Mai's earnings after tutoring for 17 hours, we can plug in [tex]\(H = 17\)[/tex] into the equation:

[tex]\[E = 20 \times 17\][/tex]

[tex]\[E = 340\][/tex]

So, Mai's earnings after tutoring for 17 hours would be $340.

Answer: b) y = negative one fifthx + seven fifths

Step-by-step explanation:

Equation of a line in Slope intercept form : [tex]y=mx+c[/tex]   (1)

, where m is slope and c is constant.

Given : The equation of line LM is [tex]5x - y = -4.[/tex]

Convert it into slope- intercept form, we get

[tex]y=5x+4[/tex]

Comparing it to (1) , we get

[tex]m= 5[/tex]

Let [tex]m_1[/tex] be the slope pf the line perpendicular to LM.

Since the product of slopes of two perpendicular lines is -1.

Therefore , [tex]m_1\cdot m=-1\Rightarrow m_1=\dfrac{-1}{m}=\dfrac{-1}{5}[/tex]

Equation of line passing through (-3,2) and having slope [tex]m_1=\dfrac{-1}{5}[/tex] will be :-

[tex](y-2)=\dfrac{-1}{5}(x-(-3))\\\\ y-2=(-\dfrac{1}{5})(x+3)=\dfrac{-1}{5}x-\dfrac{3}{5}\\\\\ y=\dfrac{-1}{5}x-\dfrac{3}{5}+2=\dfrac{-1}{5}x-\dfrac{10-3}{5}\\\\\Rightarrow\ y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex]

Hence, the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2) is [tex]y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex].

Hence, the correct answer is b) y = negative one fifthx + seven fifths.

We want to find a line perpendicular to 5x - y = -4 that passes through the point (-3, 2). We will find that the line is: y = (-1/5)*x + 7/5

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Such that a line is perpendicular to the above one if and only the slope of this other line is the inverse of the opposite of the above slope, so the perpendicular line will be something like:

y = (-1/a)*x + c

Now we start with the line that we know, we need to find its slope:

5x - y = -4

We need to isolate y

y = 5x + 4

Then the slope of this line is a = 5, so the perpendicular line will be:

y = (-1/5)*x + c

Now we need to find the value of c such that the line passes through (-3, 2), this means that x = -3 and y = 2, then we have:

2 = (-1/5)*-3 + c

2 = (3/5) + c

2 - 3/5 = c

10/5 - 3/5 = c

7/5 = c

Then the equation is:

y = (-1/5)*x + 7/5

So the correct option is b.

If you want to learn more about linear equations, you can read:

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Answer:

[tex]66\dfrac{2}{3}\%[/tex]

Step-by-step explanation:

Given,

The number of cartons = k,

Time taken by machine a = 8 hours,

So, the number of cartons made by machine a in one hour

= [tex]\frac{\text{Cartons in 8 hours}}{8}[/tex]

= [tex]\frac{k}{8}[/tex]

Time taken by machine b = 4 hours ,

So, the number of cartons made by machine b in one hour

= [tex]\frac{k}{4}[/tex]

Total cartons made in 1 hour = [tex]\frac{k}{8}+\frac{k}{4}[/tex]

[tex]=\frac{k+2k}{8}[/tex]

[tex]=\frac{3k}{8}[/tex]

∵ for the whole number value of k,

[tex]\frac{k}{4}>\frac{k}{8}[/tex]

i.e.  machine b is faster,

Also, the percent of the cartons were sealed by the machine b

[tex]=\frac{\text{Cartons made in 1 hour by machine b}}{\text{Total cartons}}\times 100[/tex]

[tex]=\frac{\frac{k}{4}}{\frac{3k}{8}}\times 100[/tex]

[tex]=\frac{2}{3}\times 100[/tex]

[tex]=\frac{200}{3}[/tex]

[tex]=66\dfrac{2}{3}\%[/tex]

Hence, OPTION D is correct.

This means 339 calories burned while combining diet with 1 hour of exercise

Step-by-step explanation:

Given the functions as:

f(x)=2x+210  

g(x)=2x+125 then

(f+g)(x) = 2x+210 +2x+125 = 4x +335

(f+g)(1) = 4(1)+335

           =339

This means 339 calories burned while combining diet with 1 hour of exercise

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Step-by-step explanation:

f(1) = 2+210 = 212

g(1) = 2+125 = 127

127+212= 339

The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising.

The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the number of hours spent exercising.

Answer:

meaning it is 339 calories burned while combining diet with 1 hour of exercise.

Answer:

[tex]a=29000 -1.28*2400=25928[/tex]

Tires that wear out by 25928 miles will be replaces free of charge

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(29000,2400)[/tex]  

Where [tex]\mu=29000[/tex] and [tex]\sigma=2400[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

He wants to give a guarantee for free replacement of tires that don't wear weel so then we need to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.90[/tex]   (a)

[tex]P(X<a)=0.10[/tex]   (b)

Because we are interested in the lower tail.

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.10 and P(z>-1.28)=0.90

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.1[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.1[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=-1.28=<\frac{a-29000}{2400}[/tex]

And if we solve for a we got

[tex]a=29000 -1.28*2400=25928[/tex]

So the value of height that separates the bottom 10% of data from the top 90% is 25928 mi.  

Tires that wear out by 25928 miles will be replaces free of charge

Answer:

  C.  1 3/4 - (a fraction less than 3/4)

Step-by-step explanation:

Your number sense should be able to help you with this one.

A. 5 × 1/10 = 1/2, not a number greater than 1

B. 4/9 + 1/3 = 7/9, not a number greater than 1

C. 1 3/4 -1/2 = 1 1/4, a number greater than 1 (see below for more explanation)

D. 7/8 × 1/2 = 7/16, not a number greater than 1.

__

More explanation

Let x represent a number less than 3/4. Then we want to make sure that ...

  y = 1 3/4 - x

will be greater than 1.

Solving for x, we get ...

  x = 1 3/4 - y

Applying the requirement that x < 3/4, we have ...

  x < 3/4

  (1 3/4 -y) < 3/4

  1 3/4 < y + 3/4 . . . . . . add y

  1 < y . . . . . . . . . . . . . . .subtract 3/4

We see that the condition on x makes sure that y is always greater than 1.

The equations that are true according to the exponent rules for powers of 10 include: [tex]10^5 / 10^3 = 10^5-3, 10^5 * 10^3 = 10^5+3,[/tex] and [tex]10^5 / 10^3 = 10^5-3.[/tex]

The subject in question deals with exponent rules for powers of 10. Here, we'll identify which equations are true based on these rules:

a. (10^5)^3 = 10^5×3. This is not correct. According to the power of a power rule, we should multiply the exponents, so the answer should be 10^15.

b. [tex]10^5 / 10^3 = 10^5-3.[/tex] This is correct. When dividing bases that are the same, we subtract the exponent of the denominator from the exponent of the numerator, hence 10^(5-3) = 10^2.

c. 10^5 × 10^3 = 10^5+3. This is correct. When multiplying bases that are the same, we add the exponents, hence 10^(5+3) = 10^8.

d. [tex]10^5 / 10^3 = 10^5-3[/tex]. This is correct, as explained in point b. The answer is 10^2.

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Final answer:

Equation c [tex](10^5*10^3 = 10^{(5+3)})[/tex] and equations b and d [tex](10^5/10^3 = 10^{(5-3)})[/tex] are correct. To multiply or divide numbers in scientific notation, multiply or divide the coefficients and add or subtract the exponents, respectively. This method can be used to calculate without converting to standard form.

Explanation:

The equations that are true out of the ones provided are as follows:

To evaluate (8.552 × 10^6) ÷ (3.129 × 10^3) without entering scientific notation into your calculator, first divide the coefficients (8.552 ÷ 3.129) and then subtract the exponents for the powers of 10 (10^6 ÷ 10^3 = 10^(6-3) or 10^3). The result is approximately 2.73189 × 10^3.

Answer:

Step-by-step explanation:

If the relationship between cost and the number of chairs produced is linear, we would write an equation that expresses this relationship in the slope intercept form. It is expressed as

y = mx + c

Where

m represents the slope

c = intercept.

Slope = (y2 - y1)/(x2 - 1)

y2 = final value of y = 4800

y1 = initial value of y = 2200

x2 = final value of x = 300

x1 = initial value of x = 100

Slope, m = (4800 - 2200)/(300 - 100) = 2600/200 = $13 per chair.

To determine the intercept, we will substitute y = 4800, x = 300 and m = 13 into y = mx + c. It becomes

4800 = 13×300 + c = 3900

c = 4800 - 3900 = 900

The equation becomes

y = 13x + 900

To write an equation that expresses the relationship between cost and the number of chairs produced, we need to find the slope and y-intercept of the linear equation. The equation that expresses this relationship is Cost = $26(Number of Chairs) - $400.

We must determine the slope and y-intercept of the linear equation in order to build an equation that describes the link between the price and the quantity of chairs produced.

Slope = Change in Cost / Change in Number of Chairs
Using the given values, the slope is (4800 - 2200) / (300 - 100) = $26 per chair.

Now, let's find the y-intercept. We can use either of the given data points. Substituting the values of one data point, we have:
$2200 = $26(100) + b
b = $2200 - $2600 = -$400.

Therefore, the equation that expresses this relationship is:
Cost = $26(Number of Chairs) - $400.

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Answer:

The difference between the circumference of the tires is 12.56 inches.

Step-by-step explanation:

Given:

Diameter of old bicycle tires = 12 inch

Diameter of new bicycle tires = 16 inch

We need to find the difference in circumference of the tires.

Solution:

First we will find the circumference of Old bicycle tires.

Circumference can be calculated by π times diameter.

Circumference of Old bicycle tire = [tex]\pi \times 12 = 37.68\ in[/tex]

Now we will find the circumference of new bicycle tire.

Circumference of New bicycle tire = [tex]\pi \times 16 = 50.24\ in[/tex]

Now to find the difference between the circumference of the tires we will subtract Circumference of New bicycle tire from Circumference of Old bicycle tire we get;

framing in equation form we get;

difference between the circumference of the tires = [tex]50.24-37.68 =12.56\ in[/tex]

Hence The difference between the circumference of the tires is 12.56 inches.

Answer:

Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2

(i) Monday

(ii) Tuesday

(iii) Wednesday

(iv) Thursday

Ans

(iv)Thursday

Step-by-step explanation:

Forecast for

Monday +4 Abs |+4| = 4

Tuesday –6 Abs |-6| = 6

Wednesday +7 Abs |+7| = 7

Thursday –2 Abs |-2| = 2

The most accurate is the day closest the temperature forecast is closest to observed temperature, which is

Thursday (-2)

Answer:

it is thursday

Step-by-step explanation:

hope it helps

Answer:

[tex]\sqrt{29}[/tex]

Step-by-step explanation:

The complex number x + yi can be expressed in coordinate form as

x + yi → (x, y ), thus

4 + 3i → (4, 3 )

6 - 2i → (6, - 2 )

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (6, - 2)

d = [tex]\sqrt{(6-4)^2+(-2-3)^2}[/tex]

   = [tex]\sqrt{2^2+(-5)^2}[/tex]

   = [tex]\sqrt{4+25}[/tex]

   = [tex]\sqrt{29}[/tex]

Answer:

Smallville is growing at a greater rate

Step-by-step explanation:

use the formula for percentage increase to find what percentage the population of Bigville increased.

(Increase ÷ original number) * 100 = % of increase

increase = 571,533 - 387,480 = 184,053

(184,053 ÷ 387,480) * 100 = 47.5

Bigville percent of increase is 47.5%

Smallville percent of increase is 53.67%

since, smallville has a bigger percentage, it is growing at the greater rate  

The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]

Step-by-step explanation:

We have to add the fractional weight of both boxes to find the combined weight of both boxes.

Given

Weight of Box 1: [tex]8\frac{2}{9}[/tex] kilograms

Weight of Box 2: [tex]3\frac{2}{10}[/tex] kilograms

So the total weight will be:

[tex]= 8\frac{2}{9} + 3\frac{2}{10}[/tex]

Simplifying the fractions

[tex]=\frac{74}{9} + \frac{32}{10}\\\\= \frac{74(10)+32(9)}{90}\\\\=\frac{740+288}{90}\\\\=\frac{1028}{90}\\\\=11\frac{38}{90}\\\\=11\frac{19}{45}\\[/tex]

Hence,

The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]

Keywords: Fractions, addition

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Answer: 38

Step-by-step explanation:

14 - 2xy

(substitute x and y)

14 - 2 (-6) (2)

14 + 24

38

Answer:

its 38

Step-by-step explanation:

Do xy first and you get -24 and 14-(-28) would be a double negative so you add them together.

Answer:

Amy's car tank capacity is 16 gallons.

Step-by-step explanation:

Let the capacity of the tank be 'x'

Given:

Amount of gas in the car till it is refilled = [tex]\frac{1}{8}\times x = \frac{1}{8}x \ gallons[/tex]

Amount of gas added = 14 gallons.

We need to find the capacity of the tank.

Solution:

Now we can say that

Total Capacity of the tank is equal to sum of Amount of gas in the car till it is refilled and Amount of gas added.

framing in equation form we get;

[tex]x=\frac{x}{8}+14[/tex]

Combining the like terms we get;

[tex]x-\frac{x}{8}=14[/tex]

Now making the denominators common we will use L.C.M.

[tex]\frac{8x}{8}-\frac{x\times1}{8\times1}=14\\\\\frac{8x}{8}-\frac{x}{8}=14\\\\\frac{8x-x}{8}=14\\\\\frac{7x}{8}=14[/tex]

Now multiplying both side by 8 we get;

[tex]\frac{7x}{8}\times 8=14\times8\\\\7x = 112[/tex]

Now dividing both side by 7 we get;

[tex]\frac{7x}{7}=\frac{112}{7}\\\\x=16\ gallons[/tex]

Hence Amy's car tank capacity is 16 gallons.

Answer: False

Step-by-step explanation:

The phenol would not evaporate or boil and would not reduce in quantity as it has a higher boiling point. So mixing it in different containers would not change the mass of phenol.

Answer:

The answer to your question is A coordinate plane with a line passing through (0, -3) and (2,0)

Step-by-step explanation:

Line

                             3x - 2y = 6

Solve for y

                              -2y = -3x + 6

                                 y = 3/2 x - 3

Find "y" when x = 0

                                 y = 3/2(0) - 3

                                 y = -3                      Point (0, -3)

Find "x" when y = 0

                                0 = 3/2x - 3

                                 3 = 3/2 x

                                x = 6/3

                                x = 2                       Point (2, 0)

The graph of the equation 3x - 2y = 6 passes through the points (0, -3) and (2, 0). This conclusion is reached after rearranging the equation into the slope-intercept form and comparing the slope and the y-intercept with coordinates of the given lines.

To find the correct graph for the equation 3x - 2y = 6, we first need to rearrange the equation in the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.

We rearrange our equation as follows: 3x - 6 = 2y. Simplifying, we get y = 1.5x - 3.

This equation tells us that the y-intercept (where the line crosses y-axis) is -3, and the slope is 1.5, in other words, for each step in positive x-direction, y increases by 1.5 steps.

Now looking at our coordinate plane options, the graph that fits this description is the one with a line passing through the points (0, -3) and (2, 0). Hence, this is the graph of the given equation.

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Answer:

The answer is 118.

Step-by-step explanation:

First we need to subtract the meal cost from average unit cost for each meal:

[tex]7-5.75=1.25[/tex]

A restaurant profits 1.25$ for each meal. If we divide fixed cost to profit for each meal:

[tex]147.5/1.25=118[/tex]

The restaurant have to sell 118 meals at least each day for the owner to break even

Answer:

a) (n²-n+m²-m)÷((n+m)×(n+m-1))

b)(n²+m²)÷(n+m)

c) part b is larger ,check below.

Step-by-step explanation:

a)If there are n white and m black balls ,total will be n+m balls. Let's find the probability of choosing two balls white.

First ball as white n÷(n+m)  second ball to be white again is n-1÷(n+m-1) the reason why we take away 1 is because we already chose one white ball in the beginning .So the probability will be product of these to get the both balls white.

Let's find the the probability of choosing both black.Same strategy ,first ball black  is m÷(n+m),second ball black is m-1÷(n+m-1).So the probability will be product of these to get the both balls black. We should add the final products and simplify

b)Because this time they are replacing the ball ,we will not take away 1.So to get both white probability is n÷(n+m) times n÷(n+m) .The probability of both black is m÷(n+m) times m÷(n+m).Add the products .

c) b will be always larger,We should compare the final products.

In b  (n²+m²) is divided by (n+m)

In a (n²-n+m²-m)÷((n+m)×(n+m-1))  less amount divided by a bigger value ,so it will result always with a smaller quotient

Answer:

Area of each tile = 19.5 inches^2

Step-by-step explanation:

Rhombus:-

A rhombus is a type of quadrilateral whose opposite sides are parallel and equal.Also, the opposite angles of a rhombus are equal and the diagonal intersect each other perpendicularly.

To find the area of a rhombus when the measures of its height and side length are given, use the formula

A = Base X height

Area of a rhombus = 6.5 X  3

                          A      = 19.5 inches^2

The area of each rhombus-shaped tile is 19.5 square inches for the given dimensions. Thus, each tile has an area of 19.5 square inches.

To find the area of a rhombus, you can use the formula

⇒ Area = base × height

In this case, the height is given as 3 inches and the length of each side is 6.5 inches, but the length of the sides is not needed, as we are working with the base and height directly.

So, the area can be calculated as follows:

⇒ Base = 6.5 inches

⇒ Height = 3 inches.

⇒ Area = base × height.

⇒ Area = 6.5 inches × 3 inches

= 19.5 square inches.

Therefore, the area of each rhombus-shaped tile is 19.5 square inches.

Answer:

The number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]

Step-by-step explanation:

Given the initially 30 bacteria present in the culture.

Also, the number of bacteria got doubled every hour.

So, using the equation

[tex]A=A_0r^{n-1}[/tex]

Where [tex]A[/tex] is number of bacteria after [tex]n[/tex] hours.

[tex]A_0[/tex] is bacteria present initially.

[tex]r[/tex] is the common ration, in our problem it is given that bacteria doubles every hour. So, [tex]r=2[/tex]

And [tex]n[/tex] is the number of hours. In our problem we need amount of bacteria at the end of [tex]8th[/tex] hours. So, [tex]n=8[/tex]

Plugging values in the formula we get,

[tex]A=30(2)^{8-1}\\A=30\times 2^7\\A=30\times 128\\A=3840[/tex]

So, number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]

Answer:the angles are 12 degrees, 48 degrees and 120 degrees.

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees.

The measures of the angles of XYZ are in the ratio 1:4:10. The total ratio is the sum of the proportion of each angle. It becomes

1 + 4 + 10 = 15

Therefore, the measure of the first angle would be

1/15 × 180 = 12 degrees

Therefore, the measure of the second angle would be

4/15 × 180 = 48 degrees

Therefore, the measure of the third angle would be

10/15 × 180 = 120 degrees

Answer: the number of hotdogs that were sold is 35

the number of orders of fries is 52

Step-by-step explanation:

Let x represent the number of hotdogs that were sold.

Let y represent the number of orders of fries.

You sold a total of 87 hotdogs and orders of fried combined. This means that

x + y = 87

Each hot dog costs 1.50 and each order of fries costs 0.50. At the end of the night you made a whopping $78.50! This means that

1.5x + 0.5y = 78.5 - - - - - - - - - - -1

Substituting x = 87 - y into equation 1, it becomes

1.5(87 - y) + 0.5y = 78.5

130.5 - 1.5y + 0.5y = 78.5

- 1.5y + 0.5y = 78.5 - 130.5

- y = - 52

y = 52

Substituting y = 52 into x = 87 - y, it becomes

x = 87 - 52

x = 35

Answer:

slope is 5

Step-by-step explanation:

the slope represents the cost of the kayak for as many hours as the person rents it for. the y intersect is 20 because that is the cost just to rent the boat before using it.

Answer:

the cylinder with height 6 has a volume of 60/π in³ greater than the volume of the cylinder with height 10 (option B , if 60π is changed for 60/π)

Step-by-step explanation:

The volume of a cylinder is

V= π*R²*H  (H=height)

since the length L of the piece of paper is L=2*π*R  →R=L/(2*π) (since is rolled to form the cylinder), then:

V= π*R²*H  = π*L²/(2*π)²*H  = L²*H/(4*π)

with L=10 in and H= 6 in we have

V₂= L²*H/(4*π)

the other way around is changing H for L

V₁= H²*L/(4*π)

the difference between the volumes will be

V₂- V₁ = L²*H/(4*π)  - H²*L/(4*π) = L*H *(L-H)/(4*π)  

replacing values

V₂- V₁ = L*H *(L-H)/(4*π)  = 10*6*(10-6)/(4*π) = 60/π in³  

then the cylinder with height 6 has a volume of 60/π in³ greater than the volume of the cylinder with height 10

Answer: B

Step-by-step explanation:

Mathematical statements are those that can be objectively proven true or false. Among the options provided, statements B and F qualify as mathematical statements. Therefore, the correct answer choice is A.

The student asks which of the following statements are mathematical statements:

A: All the ladies love me.
B: 5 = 7
C: Contemporary Math is the best class ever.
D: Bye, Felicia!
E: The square root of 64 is 8 something, right?
F: If the storm is coming, then the sky is blue.

Mathematical statements are statements that can be objectively proven true or false.

Thus, the correct answer is A. B, F

Answer: Both Technicians

Step-by-step explanation: A drive shaft which is also called the propeller shaft,is a major part of a the drive train/ unit of a vehicle with the role of Transmitting TORQUE POWER TO THE WHEELS,it is usually made up of STEEL.

Drive shaft is elongated,it is round and it requires needle bearing for friction reduction and taping to prevent it from falling off when the shafts are removed during servicing. Both Technicians are correct as both options are needed.

Both technicians are correct. Technician A's suggestion to tape the U-joint caps is a preventative measure to prevent loss of needle bearings. Technician B is correct that needle bearings are used with U-joints.

Both Technician A and Technician B are correct in their assertions. Technician A's suggestion to tape the U-joint caps when servicing a drive shaft is a basic preventative measure to ensure they do not come loose and cause a problem. This is because losing a cap can lead to a loss of the needle bearings, which are crucial to U-joint function.

Technician B's statement is also correct that needle bearings are indeed used with these type of U-joints. Needle bearings allow the U-joints to rotate smoothly under the high pressure of the drive shaft. If the needle bearings were to fail or come out, it can cause the U-joint to fail.

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