Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $8 monthly fee and charges an additional $0.12 for each minute of calls. The second plan has a $18 monthly fee and charges an additional $0.7 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer:

∆EDA~∆ECB (AAA)

3÷ (15+3) = AB ÷ (12+AB)

AB = 2.4

Answer:

(7.5 x 10-10 kg) / (9.1 x 10-31 kg) ≅ 8.24 x 1020

Step-by-step explanation:

Divide the mass of one dust particle by the mass of one electron, and that will be your answer.

(7.5 x 10-10 kg) / (9.1 x 10-31 kg) ≅ 8.24 x 1020

Answer:

one solution

the solution is x=0

Answer:

1

Step-by-step explanation:

You can figure this out using a simple trick. The highest number to the power that a variable goes to is the number of answers for that question. Meaning if There was an x cubed in that problem, there would be 3 answers.

Answer:

positive 8 i think

Step-by-step explanation:

-8=8

Answer:

the third option

Step-by-step explanation:

Answer:

0.23

Step-by-step explanation:

Answer:

you are right

Step-by-step explanation:

Use the law of law of cos

c^2=a^2+b^2﹣2abcos√angle

(2√13)^2=52=4+36-24cos(a)

cos(a) = -12/24 =  -1/2

a = 120 degrees

so yes, you are right

Answer:

Step-by-step explanation:

I think its B, (30)

Answer:

yes, yes, no, no

Step-by-step explanation:

Answer:

Roberto makes 7 shots

Step-by-step explanation:

35% is 0.35 as a decimal. Multiply the decimal by the total amount of attempted shots.

20(0.35)=7

Roberto makes 7 shots.

Area of shaded region = area of circle - area of segment

(where "segment" refers to the unshaded region)

Area of circle = π (11.1 m)² ≈ 387.08 m²

The area of the segment is equal to the area of the sector that contains it, less the area of an isosceles triangle:

Area of segment = area of sector - area of triangle

130° is 13/36 of a full revolution of 360°.  This is to say, the area of the sector with the central angle of 130° has a total area equal to 13/36 of the total area of the circle, so

Area of sector = 13/36 π (11.1 m)² ≈ 139.78 m²

Use the law of cosines to find the length of the chord (the unknown side of the triangle, call it x) :

x ² = (11.1 m)² + (11.1 m)² - 2 (11.1 m)² cos(130°)

x ² ≈ 404.82 m²

x = 20.12 m

Call this length the base of the triangle. Use a trigonometric relation to determine the corresponding altitude/height, call it y. With a vertex angle of 130°, the two congruent base angles of the triangle each measure (180° - 130°)/2 = 25°, so

sin(25°) = y / (11.1 m)

y = (11.1 m) sin(25°)

y ≈ 4.69 m

Then

Area of triangle = xy/2 ≈ 1/2 (20.12 m) (4.69 m) ≈ 47.19 m²

so that

Area of segment ≈ 139.78 m² - 47.19 m² ≈ 92.59 m²

Finally,

Area of shaded region ≈ 387.08 m² - 92.59 m² ≈ 294.49 m²

Answer:

4(3) - 7 = 4(3 - 1) - 3

12 - 7 = 4(2) - 3

5 = 8 - 3

= 5

They are equivalent because when they are both simplified they have the same answer 5

This is how you do it.

Use the distance formula to find the distance from A to B, B to C, C to D and D to A. Then add up all 4 distances to find the perimeter.

Answer:The answer is c

Step-by-step explanation:

The best estimate of the number of boxes Graphic DesignWorks is able to store is 1440000 boxes.

Volume is the three-dimensional space enclosed by a three-dimensional object.

We have to find the volume of the box and the volume of the storage space.

Volume = length × breadth × height

= 24 × 18× 16 in³

=6912 in³

Volume = length × breadth × height

= 400 × 240 × 60 ft³

= 5760000 ft³

Therefore, 5760000 ft³ = 5760000 × (12)³ in³

Number of boxes that can fit inside the storage space = (5760000 × (12)³ in³)/6912 in³

= 1440000 boxes.

Thus, the best estimate of the number of boxes Graphic DesignWorks is able to store is 1440000 boxes. The correct answer is option B.

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Answer:

a) 0.1587 = 15.87% probability that a battery will last more than 20 hours.

b) 15.44 hours.

c) Approximately the 16th percentile.

d) 0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.

e) 0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this question, we have that:

[tex]\mu = 18, \sigma = 2[/tex]

(a) What is the probability that a battery will last more than 20 hours?

This is 1 subtracted by the pvalue of Z when X = 20. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20 - 18}{2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that a battery will last more than 20 hours.

(b) Find the 10th percentile of the lifetimes.

This is X when Z has a pvalue of 0.1. So X when Z = -1.28

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 18}{2}[/tex]

[tex]X - 18 = -1.28*2[/tex]

[tex]X = 15.44[/tex]

So 15.44 hours.

(c) A particular battery lasts 16 hours. What percentile is its lifetime on?

We have to find the pvalue of Z when X = 16. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{16 - 18}{2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

Approximately the 16th percentile.

(d) What is the probability that the lifetime of a battery is between 17.5 and 18.5?

This is the pvalue of Z when X = 18.5 subtracted by the pvalue of Z when X = 17.5. So

X = 18.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{18.5 - 18}{2}[/tex]

[tex]Z = 0.25[/tex]

[tex]Z = 0.25[/tex] has a pvalue of 0.5987

X = 17.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{17.5 - 18}{2}[/tex]

[tex]Z = -0.25[/tex]

[tex]Z = -0.25[/tex] has a pvalue of 0.4013

0.5987 - 0.4013 = 0.1974

0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.

(e) Ten batteries are chosen at random, what is the probability that the mean lifetime is between 17.5 and 18.5?

Sample of 10 means that, by the Central Limit Theorem, [tex]n = 10, s = \frac{2}{\sqrt{10}} = 0.6325[/tex]

X = 18.5

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{18.5 - 18}{0.6325}[/tex]

[tex]Z = 0.79[/tex]

[tex]Z = 0.79[/tex] has a pvalue of 0.7852

X = 17.5

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{17.5 - 18}{0.6325}[/tex]

[tex]Z = -0.79[/tex]

[tex]Z = -0.79[/tex] has a pvalue of 0.2148

0.7852 - 0.2148 = 0.5704

0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5

Answer:

1, 2, 3, 6, 9, 18, 27, 54.

Step-by-step explanation:

factors:

1, 2, 3, 6, 9, 18, 27, 54.

Therefore, all the factor pairs for 54 is 1, 2, 3, 6, 9, 18, 27, 54..

Answer: (1,54) (2,27) (3,18) (6,9)

Step-by-step explanation: 54 x 1 = 54    27 x 2 = 54    3 x 18 = 54   6 x 9 = 54

Answer: 30u

Step-by-step explanation:

If GY is 6u long, x=6. (4x-2) is 4x6 which is 32, 32 - 2 = 30u long

(U = units)

Answer:

In algebra, we often study relationships where a change to one variable causes change in another variable. Describe a situation you’re familiar with where one quantity changes constantly in relation to another quantity. How are the two quantities in the situation related? If you represent the two quantities on a graph, what will it look like?

Step-by-step explanation:

Answer:

Well if it is 1 to 9 and you press it 4 times you will have 9 possible outcomes

Step-by-step explanation:

The number of possible outcomes when the button is pressed 4 times is; 81 outcomes

This is because the sample space includes odd numbers between 1 and 9 excluding 1 and 9.

Since number of possible choices for one press is 3,then for four presses, we will have;

3⁴ = 81 possible outcomes

Read more on probability outcomes at; https://brainly.com/question/25376712

Answer:

0

Step-by-step explanation:

Answer:

C.9

Step-by-step explanation:

2 doz =3eggs

4 doz = 6 eggs

6 doz = 9 eggs

Answer: it triples by 3 so 15,45, 135

Step-by-step explanation: this is by 3 because it goes on by 15,45,135

Answer:

5n+5-15=0

5n-10=0

5n=10

therefore n = 10/5 = 2

therefore n=2

Complete question :

Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Usin these values for the mean and standard deviation for the U.S. population, find the probability that a randonm sample of size 50 will have a mean: (mg). They found a) Greater than 800 mg b) Less than 700 mg. c) Between 700 and 850 mg.

Answer:

0.10935

0.3718

0.9778

0.606

Step-by-step explanation:

μ = 721 ; σ = 454 ; n = 50

P(x > 800)

Zscore = (x - μ) / σ/sqrt(n)

P(x > 800) = (800 - 721) ÷ 454/sqrt(50)

P(x > 800) = 79 / 64.205295

P(x > 800) = 1.23

P(Z > 1.23) = 0.10935

2.)

Less than 700

P(x < 700) = (700 - 721) ÷ 454/sqrt(50)

P(x < 700) = - 21/ 64.205295

P(x < 700) = - 0.327

P(Z < - 0.327) = 0.3718

Between 700 and 850

P(x < 850) = (850 - 721) ÷ 454/sqrt(50)

P(x < 850) = 129/ 64.205295

P(x < 700) = 2.01

P(Z < 2.01) = 0.9778

P(x < 850) - P(x < 700) =

P(Z < 2.01) - P(Z < - 0.327)

0.9778 - 0.3718

= 0.606

Answer:

Option E, two-proportion z test  should be used to determine whether these data provide sufficient evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same as the proportion of shoppers in the large downtown shopping area who had been to a movie in the past month

Step-by-step explanation:

The complete question is

In a random sample of 60 shoppers chosen from the shoppers at a large suburban mall, 36 indicated that they had been to a movie in the past

month. In an independent random sample of 50 shoppers chosen from the shoppers in a large downtown shopping area, 31 indicated that

they had been to a movie in the past month. What significance test should be used to determine whether these data provide sufficient

evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same

as the proportion of shoppers in a large downtown shopping area who had been to a movie in the past month?

A one-proportion z interval B two-proportion z interval

B two-proportion z interval

C two-sample t test D one-proportion z test

D one-proportion z test

E two-proportion z test

Solution

Two proportion z test is used to compare two proportions. In this test the null hypothesis is that the two proportions are equal and the alternate hypothesis is that the proportions are not the same. The random sample of populations serve as two proportions.

Hence, option E is the best choice of answer

Answer:

Volume ≈ 0.5236

Step-by-step explanation:

V=4/3πr3=4/3·π·0.53≈0.5236