Gregg’s phone plan charges $.50 per text message plus $.70 a day. Howard’s plan charges $.30 a text plus $2.50 a day. For what number of texts, a day are the cost of the phone plans the same? Show work.

Answer:

X = 27

2x = 54

5x = 135

7x = 189

Step-by-step explanation:

let 1:2:5:5:7 be 1x,2x,5x,5x,7x

Part A

Explanation:

A histogram is best because it helps show how the scores breakdown for the various bins or intervals or classes. It's effectively a visual summary of a grouped frequency table.

A dot plot would not work because we don't know the specific scores, but rather just the general region of where they fall.

A box plot doesn't work well either because we lose information on how the distribution is broken down. Sure we get the five number summary out of it, but we don't see how the bins are set up.

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Part B

We have the categories or bins of 0-4, 5-9, 10-14, 15-19, 20-24. Each bin will correspond to a bar that tells us how frequently the values show up. It tells us how frequent or how many scores we got in that sub-interval.

And so on. This all leads to the histogram shown below.

Answer:

Part A is a histogram.

Part B draw a histogram

Step-by-step explanation:

This is because a dot plot and a box plot are too specific for how the data was given. We don't know the exact number for each student.

Part B The x axis would be labeled by the groups, 0-4, 5-9, 10-14, 15-19, 20-24. The y axis would be labeled number of students. Then you could color in the area matching the correct number of students for each category.

Answer:

[tex]x^3-3x^2-12x+19[/tex] is divisible by [tex]x^2+x-6[/tex]  when [tex]2x+5[/tex] is added to it.

Step-by-step explanation:

Let [tex]p(x)=x^3-3x^2-12+19[/tex]  &  [tex]q(x)=x^2+x-6[/tex]

By division algorithm, when p(x) is divided by q(x), the remainder is a linear expression in x

So, let [tex]r(x)=ax+b[/tex] is added to [tex]p(x)[/tex] so that [tex]p(x)+r(x)[/tex] is divisible by [tex]q(x)[/tex]

Let, [tex]f(x)=p(x)+r(x)[/tex]

⇒ [tex]f(x)=x^3-3x^2-12x+19+ax+b[/tex]

⇒ [tex]f(x)=x^3-3x^2+x(a-12)+b+19[/tex]

We have,

[tex]q(x)=x^2+x-6=(x+3)(x-3)[/tex]

Clearly, [tex]q(x)[/tex] is divisible by [tex](x-2)[/tex] and [tex](x+3)[/tex]

{ [tex](x-2)[/tex] and [tex](x+3)[/tex] are factors of [tex]q(x)[/tex] }

We have,

[tex]f(x)[/tex] is divisible by [tex]q(x)[/tex]

⇒ [tex](x-2)[/tex] and [tex](x+3)[/tex] are factors of [tex]f(x)[/tex]

From factors theorem,

If [tex](x-2)[/tex] and [tex](x+3)[/tex] are factors of [tex]f(x)[/tex]

then [tex]f(2)=0[/tex] and [tex]f(-3)=0[/tex] respectively,

⇒ [tex]f(2)=0[/tex] ⇒ [tex]2^3-3(2)^2+2(a-12)+b+19=0[/tex]

⇒ [tex]8-12+2a-24+b+19=0[/tex]

⇒ [tex]2a+b-9=0[/tex]

Similarly,

[tex]f(-3)=0[/tex] ⇒ [tex](-3)^3-3(-3)^2+(-3)(a-12)+b+19=0[/tex]

⇒ [tex]-27-27-3a+36+b+19=0[/tex]

⇒ [tex]b-3a+1=0[/tex]

Subtract (1) from (2)

[tex]b-3a+1-(2a+b-9)=0-0[/tex]

⇒ [tex]b-3a+1-2a-6+9=0[/tex]

⇒ [tex]-5a+10=0[/tex] ⇒ [tex]5a=10[/tex] ⇒ [tex]a=2[/tex]

Put [tex]a=2[/tex] in equation 2

⇒ [tex]b-3[/tex] × [tex]2+1=0[/tex] ⇒ [tex]b-6+1=0[/tex] ⇒ [tex]b-5=0[/tex] ⇒ [tex]b=5[/tex]

∴ [tex]r(x)=ax+b[/tex] ⇒ [tex]r(x)=2x+5[/tex]

Hence, [tex]x^3-3x^2-12x+19[/tex] is divisible by [tex]x^2+x-6[/tex] when [tex]2x+5[/tex] is added to it.

Hope this helps...

Answer:

90.2

Step-by-step explanation:

Assuming that you can use a calculator, you would need to type in the square root symbol and type in the value 8136.04.

The square root of 8136.04 is 90.2.

In this question, two houses have an initial value of $179,000, and the projected values are given in the tables for houses 1 and 2.

Part a:

If the absolute value of the change is always the same, it is linear.

If the rate is the same, it is exponential.

House 1:

We have that:

193,606.4 - 186,160 = 7446.4

201,350.66 - 193,606.40 = 7744.26

Let's try exponential:

[tex]\frac{193,606.4}{186,160} = 1.04[/tex]

[tex]\frac{201,350.66}{193,606.40} = 1.04[/tex]

For house 1, the rate of change is the same, and thus, it is exponential.

House 2:

212,000  - 201,000 = 201,000 - 190,000 = 11,000.

Absolute value of change is the same, so linear.

Thus, for house 1, an exponential function is used, as the rate of change is the same, and for house 2, as the absolute value of change is always the same, it is linear.

Part B

House a:

Exponential function, with initial value of $179,000, and exponential growth rate of 1.04 - 1 = 0.04. Thus:

[tex]f_a(x) = 179000(1+0.04)^x[/tex]

[tex]f_a(x) = 179000(1.04)^x[/tex]

House b:

Linear function, with initial value of $179,000, increasing by $11,000 each year. So

[tex]f_b(x) = 179000 + 11000x[/tex]

Part c:

House a after 30 years:

[tex]f_a(30) = 179000(1.04)^30 = 580,568[/tex]

House b after 30 years:

[tex]f_b(30) = 179000 + 110000(30) = 509,000[/tex]

In 30 years, house a will have a value of $580,568, while house b will have a value of $580,568. House a will have a higher value, due to exponential growth.

For more about linear/exponential growth, you can check https://brainly.com/question/14983998

Answer:

one side should be given.

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

hope it helps...

have a great day!!

Answer:

uwuwhwhwnwjwjwiwieiwiwjwjjejeejjwje

Step-by-step explanation:

euwwuwjw

Answer:

10 x 15

Step-by-step explanation:

beam

The total work done is 1800 ft- lbs.

It should be converted to energy in order to move an object. Energy can be transferred by the use of force. Work done refers to the amount of energy used by a force to move an object.

Work is accomplished when we push a block with some force; the body moves more quickly. Work completed is noted as.

We have,

2 carts weigh 50 lbs. each.

4 carts weigh 20 lbs. each.

So, 2 carts weigh = 50 x 2 = 100 lbs

and, 4 carts weigh = 20 x 4 = 80

Then, work done = (100 + 80) x 10

                             = 1800 ft- lbs

Learn more about Work Done here:

https://brainly.com/question/13662169

#SPJ3

Answer:

The inequality is 0.6x < 12.5

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Step-by-step explanation:

14 gallons-1.5 gallons=12.5 gallons    

we know that  

If the remaining fuel is greater than  1.5 gallons Diego's father can drive the car without the warning light coming on    

so  

Let  

x ----> the number of days

0.6x < 12.5 inequality that represent the situation  

Solve for x

x < 12.5/0.6

x < 20.8 days

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Answer:

10000000

Step-by-step explanation:

gitcy is good for your spleen

Answer:

A.

Step-by-step explanation:

Basically.. when you draw a line from the vertex of a right triangle's 90 degree angle to its hypotenuse, it'll make two triangles with the same angles. Then you can use ratios to discern the size of said rectangles. I hope that helps.

Answer:

A.) 6.4 units

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of AB.

If we find the horizontal and vertical distance of A and B, we form a triangle, with leg lengths of 5 and 4.

Now, we just solve using the Pythagorean theorem.

5^2 = 25

4^2 = 16

25 + 16 = 41

sqrt 41 ≈ 6.4 units.

Hope this helps!

If there is something wrong, just let me know.

Answer:

18.52%

Step-by-step explanation:

Relative error can be described as the ratio of the measured absolute value to the actual value

relative error = (stated age - actual age) / actual age x 100

(32 - 27) / 27 x 100

5 / 27 x 100 = 18.52%

Answer:

B could be (4,8), (6,11), (8,14), (10,17), (12,20), etc.

Step-by-step explanation:

quick mafhs

Answer:

11

Step-by-step explanation:

because line AD divided the triangle ABC into two equal halves

Given Statement:- The Number Must Exceed 10

Therefore, it means that the numbers are greater than 10

So Correct Option Will Be

B x > 10

Answer:

57.5

Step-by-step explanation:

20x - (10 x 110) = 50

=> 20x - 1100 = 50

=> 20x = 1150

=> x = 1150/20

=> x = 115/2

=> x = 57.5

Answer:

A = 0.1m

A = $6.5

Step-by-step explanation:

We are told that each minute of use costs $0.10.

If the minutes spent is represented by "m" and amount spent is "A', then the relation for amount spent is;

A = 0.1m

If he talked for 65 minutes, then we have;

A = 0.1 × 65

A = $6.5

Answer:

1/2

Step-by-step explanation:

Complete Question

The reading speed of second grade students in a large city is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.

What is the probability that a random sample of 12 second grade students from the city in a mean reading rate of more than 96 words per minute?

Answer:

[tex]P(\=x >96 )=0.01884[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=12[/tex]

Sample mean [tex]\=x =90[/tex]

Standard Deviation [tex]\sigma=10[/tex]

Generally

[tex]\sigma_x=\frac{\sigma}{\sqrt{10}}[/tex]

[tex]\sigma_x=\frac{10}{\sqrt{12}}[/tex]

[tex]\sigma_x=2.887[/tex]

Generally the equation for P(\=x >96 ) is mathematically given by

[tex]P(\=x >96 )=P(Z>\frac{\=x-\mu_x}{\sigma_x})[/tex]

[tex]P(\=x >96 )=P*(Z>\frac{90-96}{2.887})[/tex]

[tex]P(\=x >96 )=1-P(Z<2.08)[/tex]

[tex]P(\=x >96 )=1-0.98116[/tex]

[tex]P(\=x >96 )=0.01884[/tex]

Answer:

$368,640

Step-by-step explanation:

288,000 * .28 = 80640

288,000 + 80640 = 368640

Answer:

B. domain is all integers 0 through 9

Step-by-step explanation:

Domain values area usually plotted along the horizontal axis. In this case, the number of days is the domain of the of the function.

The domain of the function that is plotted on the graph ranges from 0, 1, 2 to 9.

1, 2, 3 to 9 are all integers. Therefore, we can conclude that the "domain is all integers 0 through 9."

Answer:

C

Step-by-step explanation:

Answer:

a) 10:10:10

b)[tex]A_s=600m^2[/tex]

Step-by-step explanation:

From the question we are told that:

Volume [tex]V=1000cm^3[/tex]

a) .

Generally for optimal dimensions

[tex]A=L*B*H[/tex]

Where

[tex]L=B=H[/tex]

Therefore

[tex]L=^3\sqrt{1000}\\L=10[/tex]

Therefore the optimal dimensions will be

10:10:10

b)

Generally the equation for surface area of a cube is mathematically given by

[tex]A_s=6l^2[/tex]

[tex]A_s=6*10^2[/tex]

[tex]A_s=600m^2[/tex]

Answer:

Quadrant 2 and 3

Approximately, 113 and 247 degrees.

Step-by-step explanation:

I just used Desmos and graphed the equation. The values of theta are 113 and 247.