ASAP!!! Question 7 (Essay Worth 5 points)
(02.03)
Part A: Use ratio language to describe the relationship of any two things you can think of.

Example: For every 5 minutes of jogging, I ran 500 yards.

Be creative and come up with your own idea.

Part B: Determine the unit rate in your example.

this is what i have for part a: For every 1 student out of school, there are 10 students going to school

help me with part B pls I need to find the unit rate for my part a.

Considering the given table, we have that:

A function has a relative maximum when it changes from increasing to decreasing.

Looking at the given table, it happens when x is near 3.

Also, looking at the table, for x > 3 the function is decreasing, hence as x approaches positive infinity, the value of the function approaches negative infinity.

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Answer:

The 3rd graph from the top.

Step-by-step explanation:

Just Like the story, the third graph goes up slowly and plateaus for the duration of a school day, then goes back down quicker than it went up.

The thing that best describes the values of x and y is option B; they will be real numbers greater than or equal to 0.

The real number refers to the union of both rational and irrational numbers that can have negative or positive values.

From the given information:

Peaches are being bought and sold for $2 per pound.

There is no negative value used here if x represents the number of pounds of peaches bought and y represents the total cost of the peaches.

Thus, a conclusion that can be reached as to the values of x and y is that they contain real numbers greater than or equal to 0.

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Answer:

im pretty sure its d

Step-by-step explanation:

----- ______------

Answer:

$30

Step-by-step explanation:

Let,

  x - fiction book

  x + $6 - novel

EQUATION:

  4(x) + 2(x + $6) = $84

  6x + $12 = $84

  6x = $84 - $12

  6x = $72

  x = $12

SUBSTITUTE:

    novel = $12

    fiction = $18

TOTAL COST OF NOVEL AND FICTION

$18 + $12 = $30

Answer: 1344

Step-by-step explanation:

Using the Pythagorean theorem, if we consider the unknown leg of the base, we get that it has a length of 12.

So, the area of the base is 96.

Multiplying this by the height, we get the volume is 1344 cubic inches.

The area of the trapezoid is 87.5 square cm if the parallel side lengths are 10 and 15 cm, the height is 7 cm.

It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a trapezoid ABCD shown in the picture.

As we know the area of the trapezoid is given by:

= (a+b)h/2

= (10+15)(7/2)

= 87.5 square cm

Thus, the area of the trapezoid is 87.5 square cm if the parallel side lengths are 10 and 15 cm, the height is 7 cm.

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Answer:

28 should do it

Step-by-step explanation:

35+35+82= 152

180-152=28

Answer:

373 feet

Step-by-step explanation:

Since the rate of the machine producing ribbon is proportional to time, we can determine the number of inches of ribbon in 8 hours by some quick operations.

There are 16 1/2 hours in 8 hours, so we can multiply 280 by 16.

[tex]280 *16=4480[/tex]

Now, we have the number of inches it can produce in an 8-hour work day. However, we must convert to feet since that is the form of measurement the question is asking for. We can do so by dividing by 12.

[tex]4480/12=373.33[/tex]

Therefore, the number of feet the machine can produce in an 8-hour work day is 373.

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Step-by-step explanation:

the other answer is correct.

a few add-ons :

1 ft = 12 in

30 minutes = 1/2 hour (as every hour has 60 minutes)

every hour has therefore 2 half hours.

1 hour = 2 × 1/2 hour

8 hours = 8 × 2 × 1/2 hours = 16 × 1/2 hour

so, in 16 times the amount of time (8 hours) the machine can produce 16 times the amount of ribbon (16 × 280 in).

16 × 280 = 4480 in

and because every 12 in is 1 ft, this is then

4480/12 = 373.3333333... ft

therefore, 373 is the right answer (rounded).

The linear model for the data is expressed as: R = 20p - 160.

Using two pairs of values from the table values, say, (32, 480) and (33, 500), find the unit rate (m).

Unit rate (m) = (500 - 480)/(33 - 32) = 20/1

Unit rate (m) = 20.

Substitute (p, R) = (32, 480) and m = 20 into R = mp + b to find b

480 = 20(32) + b

480 = 640 + b

480 - 640 = b

b = -160

To write the linear model, substitute m = 20 and b = -160 into R = mp + b:

R = 20p - 160

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The table that has a constant average rate of change represents a linear function.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input.

When this rate is constant, the function is said to be linear, hence the table that has a constant average rate of change represents a linear function.

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Answer:

C

Step-by-step explanation:

Answer:

36 pieces of ribbon

Step-by-step explanation:

When Audrey cuts the ribbon into pieces that are each 1/3 yards long, she has 18 pieces (1/3 * 18 is 6, or the other way to think about it would be, 6 / (1/3) = 18). If she were to cut each of the pieces in half one more time, she would have 18 * 2 or 36 pieces of ribbon

Answer:

The relation {(2,1),(3,2),(-1,1),(0,-2)} is a function because the domain {2,3,-1,0} and range {1,2,1,-2} of the relation is paired exactly only once.

Step-by-step explanation:

The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.

It is required to determine the relation is a function.

Step 1 of 1

The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.

This relation shows that the domain of the relation {2,3,-1,0} is paired with one element of the range {1,2,1,-2}.

Hence, the relation is a function.

a = 3, b = 4, and c = 2

a + b = c

3 + 4 = 2

3a + 4b = 2c
       -4     -4
     3a = -6c
      3       3
       a = -2

3a + 4b = 2c
-3             -3
      4b = -1c
        4     4

The confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).

Given sample mean coefficient of restitution 0.835,population standard deviation of 0.019 and the confidence level of 0.835.

We have to find the confidence interval for the true mean coefficient of restitution.

We can easily find the confidence interval through the formula of margin of error.

Margin of error is the difference between the calculated values and the real values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the z value of p value,

σ is population mean or sample mean,

n is the sample size.

In our problem the sample size is 30.

z value for the p value of 0.99 is 2.576.

Margin of error=2.576*0.019/[tex]\sqrt{30}[/tex]

=0.048944/5.4772

=0.0089

Upper level=mean +margin of error

=30+0.0089

=30.0089

Lower level=Mean-margin of error

=30-0.0089

=29.9911.

Hence the confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).

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Answer:

x = 4

Step-by-step explanation:

3(-3x -3) + 2x + 4 = -33

(3*-3x + 3*-3) + 2x + 4 = -33

(-9x - 9) - 2x + 4 = -33

-9x + 2x - 9 + 4 = -33

-7x -5 = -33

-7x = -33 + 5

-7x = -28

x = -28/-7

x = 4

Check:

3((-3*4)-3) + 2*4 + 4 = -33

3(-12-3) + 8 + 4 = -33

3(-15) + 12 = -33

-45 + 12 = -33

Answer:

Step-by-step explanation:

5x-9 = 2(x+23) or 5x-9 = 2x+46

Let' x be the "number."

"Five times a number decreased by nine" means: 5x - 9

"equal to twice the number increased by 23" means:  = 2(x+23)

Put them together:  5x-9 = 2(x+23)

5x-9 = 2(x+23)

5x-9 = 2x+46

[The formatting of the possible answers does not include parentheses nor algebraic symbols, making selection of a correct answer difficult. ]

The probability that a student takes art, given that the student takes music is 10.8%

In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.

For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."

Two events, A and B, are independent if

P(A ∣ B)=P(A)

P(A).P(B) = P(A ∩ B)

In the given question there are independent events.

Given:-

P(A) = Student takes both art and music = 0.9

P(B) = Student takes music = 0.12

P(A ∩ B) = student takes art, given that the student takes music

Thus by using the formula we get,

P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%

The probability that a student takes art, given that the student takes music is 10.8%

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A)√500 is the correct answer.

It is an expression that has the same value but does not look the same. If you simplify an expression, you're  trying to write it in the simplest way possible.

According to the question,

The given expression is 10√5.

By computing the number out of the square root,

So,

[tex]=10 \sqrt{5} \\=\sqrt{10^2(5)} \\=\sqrt{100 (5)} \\=\sqrt{500}[/tex]

Therefore,

The equivalent expression for 10√5 is √500.

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Answer:

(2, - 2 )

Step-by-step explanation:

4x - y = 10 → (1)

x - 4 = y → (2)

substitute x - 4 = y into (1)

4x - (x - 4) = 10 ← distribute parenthesis on left side by - 1

4x - x + 4 = 10

3x + 4 = 10 ( subtract 4 from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2 - 4 = y

- 2 = y

solution is (2, - 2 )

Answer:

x = 2 , y = -2

Step-by-step explanation:

I will use the elimination method :

4x-y = 10 - Equation Number 1

x-4 = y  - Equation Number 2

For the second equation we add 4 to both sides and subtract y from both sides :

x = y + 4

x - y = 4 - Let's call this equation number 3 :

Now we can subtract the equation 1 with 3 to eliminate y :

3x = 6

x = 2

Now we substitute this value into equation 2 to solve for y :

(2)-4 = y

y = -2

Substitute these values into equation 1 to verify :

4(2) - (-2) = 10

8 + 2 = 10

10 = 10

So these values must be correct

Hope this helped and have a good day

The range of the step function is all negative integers, thus, the correct option is A.

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

For the given function h(x)=-2|x|, any value of x will return a negative value, therefore, the range of the function is all negative numbers. This can be observed in the graph given below.

Hence, the range of the step function is all negative integers, thus, the correct option is A.

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Two triangles are said to be congruent if they have similar properties. Thus the required options to complete the paragraph proof are:

a. angle 1 is congruent to angle 2.

b. alternate angles are congruent if two parallel lines are cut by a transversal.

c. [tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]

The similarity property of two or more shapes implies that the shapes are congruent. Thus they have the same properties.

From the given diagram in the question, it can be deduced that

ΔABC ≅ ΔABE (substitution property of equality)

Given that EA is parallel to BD, then:

i. <2 ≅ <3 (corresponding angle property)

ii. <1 ≅ < 4 (alternate angle property)

Thus, the required options to complete the paragraph proof are:

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The reason why people sometimes assume that the calculation 9 + 10 = 21 is as explained below.

We want to find out the reason why people say that; 9 + 10 = 21

Now, the way you have explained it is one way to look at it by utilizing number bases to play around with the figures to arrive at 21.

However, another way is to use algebra trick pattern which is;

9 can be expressed as 3 * 3

Also, 10 can be expressed as 5 * 2. Thus, we now have;

(3 * 3) + (5 * 2)

The applying properties of algebra to cross multiply gives;

(3 * 2) + (5 * 3)

= 6 + 15

= 21

Now, though your explanation arrived at 21 and mine also 21, but those are not correct mathematical methods as 9 + 10 must be equal to 19 and not 21.

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The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

The function is given as:

f(x) = (x + 3)^3 - 1

Rewrite as:

y = (x + 3)^3 - 1

Swap x and y

x = (y + 3)^3 - 1

Add 1 to both sides

(y + 3)^3 = x +  1

Take the cube root of both sides

[tex]y + 3 = \sqrt[3]{x + 1}[/tex]

Subtract 3 from both sides

[tex]y = \sqrt[3]{x + 1} - 3[/tex]

Rewrite as:

[tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]

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Answer:

f(5)=17

Step-by-step explanation:

if,f(x)=3x+2

Then,f(5)=3*5+2

f(5)=17

Answer:

84 mm (C)

Step-by-step explanation:

We are given the centimeter/millimeter side of the ruler. It is probably easier to first look at the centimeters since the lines are much bigger. We can see that the line goes from 0cm to around 8.4cm. Now, we can convert centimeters to millimeters because we know that there are 10 millimeters in one centimeter. 8.4cm * 10 gives us 84 millimeters (C)

(a) Fermat's little theorem states that for any prime [tex]p[/tex], we have

[tex]a^{p-1} \equiv 1 \pmod p[/tex]

for any integer [tex]a[/tex]. Then

[tex]999,999 \equiv 1,000,000 - 1 \equiv 10^6 - 1 \equiv 1 - 1 \equiv 0 \pmod 7[/tex]

so 7 does indeed divide 999,999.

(b) Generalizing, we have

[tex]10^{12n} - 1 \equiv \underbrace{999\ldots999}_{12n \text{ nines}} \equiv (10^n)^{12} - 1 \equiv 0 \pmod {13}[/tex]

for positive integer [tex]n[/tex]. Now, since 1 = 1001 - 1000 and [tex]-1\equiv1000\pmod{1001}[/tex], it follows that [tex]10^3[/tex] is its own inverse modulo 1001, i.e.

[tex]10^3 x \equiv 1\pmod{1001} \implies x = 10^3[/tex]

This means

[tex]10^{12n} \equiv (10^3\times10^3)^{2n} \equiv 1^{2n} \equiv 1\pmod{1001} \\\\ \implies 10^{12n} - 1 \equiv 0 \pmod{1001}[/tex]

which is what we wanted to show.

Answer:

B

Step-by-step explanation:

It has both point and line symmetry