The formula written in symbols as T =UN. Solve the formula for U.

We have the monthly cost is fixed: $29.95.

The cost varies directly as the number of minutes since the total cost per month will be:

If we make a call and spend 30 minutes. We need to add this cost to the payment:

Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.

5)

Transformation 2: the function is shifted 2 units up

Explanation

Step 1

the first transformation is the function multiplied by a constant ( 1/2)

If the function is multiplied by a value less than one, all the values of the equation will decrease, leading to a “shrunken” appearance in the vertical direction

so

Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.

5)

Step 2

the second transformation is add 5

If a positive number is added, the function shifts up the y-axis by the amount added.

so,

Transformation 2: the function is shifted 2 units up

I hope this helps you

Answer:

x= -6

Step-by-step explanation:

1

Distribute

2

Distribute

3

Distribute

4

Multiply by 1

5

Combine like terms

6

Subtract the numbers

7

Move terms to the left side

8

Distribute

9

Add the numbers

10

Combine like terms

11

Multiply by 1

12

Combine like terms

13

Use the quadratic formula

14

Evaluate the exponent

15

Multiply the numbers

16

Subtract the numbers

17

Evaluate the square root

18

Add zero

19

Multiply the numbers

20

Cancel terms that are in both the numerator and denominator

In the line, the point B represents the integer -3, because it is 3 units left from 0.

Its opposite is the number 3, that is 3 units right from 0.

Angle 2 and angle of 34° are vertical angles, then they are congruent, that is,

Angle 6 and angle of 34° are corresponding angles, then they are congruent, that is,

Angle 4 and angle of 34° are alternate interior angles, then they are congruent, that is,

Angle 7 and angle of 34° are same-side interior angles, then they are supplementary, that is,

Angles 4 and 3 are same-side interior angles, then they are supplementary, that is,

Angles 7 and 5 are vertical angles, then they are congruent, that is,

Angles 1 and 3 are vertical angles, then they are congruent, that is,

25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. The probability is it that the shipment will be accepted is 0.7323.

Given that,

An organization utilizes the following acceptance sampling strategy for ordering shipments of 600 machine parts: 25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. This specific component is known to have a 4% fault rate.

We have to find how probability is it that the shipment will be accepted.

By binomial we get,

Binomial Problem:

n = 25 ; p = 0.04

P(0<= p <= 2)

= 0.7323

Therefore, The probability is it that the shipment will be accepted is 0.7323.

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The largest number when the sum of 4 consecutive integers is 170 will be 44.

According to the question,

We have the following information:

Sum of four consecutive integers = 170

Now, let's take the first integer to be x.

So, the next 3 integers will be (x+1), (x+2) and (x+3) respectively.

Now, the largest number will be (x+3).

Adding 4 consecutive integers:

x+ (x+1) + (x+2) + (x+3) = 170

4x+6 = 170

4x = 170-6 (Moving 6 from the left hand side to the right hand will result in  the change of the sign from plus to minus.)

4x = 164

x = 164/4

x = 41

So, the next three consecutive integers will be 42, 43 and 44.

Hence, the largest of the four consecutive integers is 44.

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Answer:

The three correct corresponding pairs that gives the same area are;

The areas are the same in each case because the product of each pair is the same.

Explanation:

Given the base and height pairs in the question.

Let us use the corresponding pairs that gives the same area.

Firstly, for the first pair;

Secondly, the second pair is;

Thirdly, the third pair;

Therefore, the three correct corresponding pairs that gives the same area are;

The areas are the same in each case because the product of each pair is the same.

Answer:

I cannot include a picture, but the slope is -2/3, and the y-intercept is (0, 3).

Step-by-step explanation:

When given an equation like this, remember the formula y=mx+b that you should have learned. This formula is the slope-intercept formula that you can use. The m is the slope and the b is the intercept. In the equation, the x is what we are trying to find.

y=-2/3x+3

y=mx+b

m=-2/3

b= (0,3)

So, graph the slope as -2/3 and the y-intercept as (0,3).

Hope this helps!

We need to find the greatest common factor of

We will find the greatest common factor of 64 and 56, first

Since the factors of 64 are

Since the factors of 56 are

Then the common factors are 1, 2, 4, 8

The greatest is 8, then

The GCF of 64 and 56 is 8

The greatest common factor of the same variables is the least power

Then the GCF of a^8 and a^5 is a^5

The GCF of b^4 and b^8 is b^4

Then the greatest common factor of the given terms is

The binomials  5x-2yz are a factor of this expression

25x^2-4y^2z^2

This is further explained below.

Generally, A binomial is a kind of polynomial that is used in algebra and is defined as the sum of two terms, each of which is a monomial.

After monomials, this is the sort of sparse polynomial that is the easiest to understand.

The word "binomial" refers to an algebraic expression that consists of just two different terms. This is a polynomial with two terms.

25 x^2-4 y^2 z^2

Rewrite 25 x^2 as (5 x)^2.

(5 x)^2-4 y^2 z^2

Rewrite 4 y^2 z^2 as (2 y z)^2.

(5 x)^2-(2 y z)^2

Since both terms are perfect squares, factor using the difference of squares formula, a^2-b^2=(a+b)(a-b) where a=5 x and b=2 y z.

(5 x+2 y z)(5 x-(2 y z))

Simplify.

(5 x+2 y z)(5 x-2 y z)

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Answer:We have 70 dogs

Step-by-step explanation:

dogs: cats: total5          2      7We want 98 animals98/7 =14We need to multiply each number by 14dogs: cats: total…

hope this helps

Answer:

Step-by-step explanation:

B - 6 million

b. 6 Million

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Answer:

=====================

Total number of marbles:

Probability of selecting a blue marble:

Probability of  selecting a black marble after replacing the blue:

Probability of selecting blue and black marbles in same order with replacement:

C) x= -1/10

1) Evaluating the following expression

23x+2= 15x + 48x + 6 Add the like terms

23x +2 = 63x +6 Subtract 63x and 2 from both sides

23x -63x = 6 -2

-40x =4 Divide both sides by -40

x = -4/40 Simplify it by 4

x= -1/10

2) Hence, the answer is x= -1/10

For a random day with the standard deviation, the probability that there are less than 200 shoppers on a random day, is 0.0039.

The average total number of shoppers on a  grocery store in 1 day is 506; the standard deviation is 115.

The number of shoppers is normally distributed.

Let, X be the random variable denoting the number of shoppers on a random day.

Then, X follows normal with mean 506 and standard deviation of 115.

Then, we can say that,

Z=(X-506)/115 follows standard normal with mean 0 and standard deviation of 1.

We have to find

P(X<200)

[tex]=P(Z < \frac{200-506}{115})[/tex]

=P(Z<-2.66)

Where, Z is the standard normal variate.

ρ = -0.266

Where, ρ is the distribution function of the standard normal variate.

From the standard normal table, this becomes

=0.0039

For a random day, the probability that there are less than 200 shoppers on a random day, is 0.0039.

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In a equation as above:

a is the leading coefficient

n is the degree

For the given equation:

In order to determine the farthest integer related to the origin ona a number line, apply the absolute value of the given numbers, this gives you the distance of the specific number to the origin.

The absolute value of a number, negative or positive, is always equal to the same positive number.

Then,for the given asnwer choices you have:

|-11| = 11 where the bars |-11| expresses absolute

Answer:

The system of equations is:

• C(x)=2400+60x

• R(x)=120x

The number of bicycles to break even = 40

Explanation:

Let the number of bikes sold = x

• The operating cost of the store per month = $2400

• Cost Price Per bike = $60

Thus, the total monthly cost for the store:

Next, the average selling price of each bicycle is $120, therefore, the monthly revenue of the store:

The store breaks even when the cost equals its revenue.

We then solve for x:

The store must sell 40 bicycles in order to break even.

A graph which represents the reflection of this figure across the x-axis is: graph 5.

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:

(x, y) → (x, -y) = (3, 1) → (3, -1).

(x, y) → (x, -y) = (4, 0) → (4, 0).

(x, y) → (x, -y) = (3, -1) → (3, 1).

(x, y) → (x, -y) = (4, -2) → (4, 2).

(x, y) → (x, -y) = (2, -4) → (2, 4).

(x, y) → (x, -y) = (0, -2) → (0, 2).

In conclusion, a reflection across the x-axis would transform the geometric figure to that shown in the graph attached in the image below.

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h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .

Translation is the process of reworking text from one language into another to maintain the original message and communication.

The parent function is: g(x)=|x|

we stretch the parent function y = |x| by a factor of 3.

h= |x/3|

If the constant is between 0 and 1, we get a horizontal stretch

if the constant is greater than 1, we get a horizontal compression of the function.

Hence h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .

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Based on the fact that the line passes through (-2, 7) and the slope, the value of a can be found to be  -1

To find the value of a, you first need to find the y-intercept to complete the linear equation which takes the form:

y = slope (x) + y-intercept

7 = -5(-2) + y-intercept

7 = 10 + y-intercept

y-intercept = 7 - 10

y-intercept = -3

The line equation is:

y = -5x - 3

The line y = -5x - 3 is passing through the point (a,2) is:

2 = -5(a) - 3

3 + 2 = -5a

a = 5 / -5

a = -1

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Answer:

the answer is  -1

Step-by-step explanation:

The speed of the faster cyclist is 14\ miles/hr.

What is speed?

It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.

Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,

[tex]2s+s=42\\3s=42\\s=14[/tex]

Now, distance coverd by the first cyclist is [tex]2s=2\times 14\\=28 \ $miles[/tex].

Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.

[tex]Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr[/tex]

Hence, the speed of the faster cyclist is 14\ miles/hr.

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The absolute change in the population was 59 million. The relative change in the population was 23.69%

The absolute population change is the magnitude of the increase or decrease in population for a defined period.

Absolute change describes the straightforward difference between the indicator over two time periods. The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage.

Small numbers can make relative changes appear more significant than they actually are. This is true because a minor change in the number's absolute value can generate a significant change in the percentage.

Big numbers may make relative changes appear less significant. This is so that any change in the number that represents a substantial relative change may be seen.

The relative change can be minor even when the absolute change is significant if it is a change on a larger number.

Absolute change = Final value – Initial value

                            = 308m- 249m = 59m

The absolute change in the population was 59 million

Relative change Formula = (Final value – Initial value) / Initial value * 100%

                                         =  308m- 249m/ 249*100 = 23.69%

The relative change in the population was 23.69%

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Answer:

t = 192

Step-by-step explanation:

1/4t = 1/3t + (-16)

  1            1

-------t = -------t - 16

  4           3

  1(3)        1(4)

-------t = -------t - 16

  4(3)      3(4)

  3           4

-------t = -------t - 16

  12         12

  3           4

-------t = -------t - 16(12)

(   12         12 ) 12

3t = 4t - 192

-4t   -4t

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

-t = -192

÷-1  ÷-1

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

t = 192

I hope this helps!

Answer:

12

Step-by-step explanation:

Total number of questions = 30 questions.

Each correct answer gets = 10 marks.

Marks deducted for each wrong answer = 5 marks.

Total marks scored by Kareem = 180 marks.

If Kareem had attended all the questions, then

Let 'α' be the number of questions he answered wrong, then the number of questions answered correctly by him, will be = (30 - α)

Then we have,

Total marks obtained = (correct answers x 10 marks ) - (wrong answers x 5 marks )

that is.,

180 = [(30 - α) x 10] - [α  x  5] = 300 - 10α - 5α

180 - 300 = -15α

α =  120/15  = 8 questions.

Therefore, 8 questions were answered wrong by Kareem.

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Answer: the y = -2/5x - 1

Step-by-step explanation: hoped this help you two