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Brilliant_brown [7]
3 years ago
6

One cell phone plan charges 20$ per month plus$0.15 per minute used.

Mathematics
2 answers:
maw [93]3 years ago
7 0
So for the first one... Let's just use x for months and m for minutes.

(20m)+(.15m)

20 times the number of months plus .15 times the number of minutes

Same for the next one

(35x)+ (.10m)

35 times the number of months +.10 times the minutes.
Zepler [3.9K]3 years ago
6 0

Answer:

300 minutes

Step-by-step explanation:

Equation: 20 + 0.15x = 35 + 0.10x

0.05x = 15

x = 300 minutes

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Will mark as Brainliest!
Sati [7]
I think the answer is A
6 0
3 years ago
You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as y
pochemuha

Answer:

I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.

Step-by-step explanation:

The number of total objects collected by me  = 20

The number of objects collected by my friend  = 20

Let us assume:

The number of rocks collected by me  = m

The number of fossils collected by me  = 2 k

⇒ m +  2 k =  20  .... (1)

So, according to the question:

The number of rocks collected by my friend = 3 x (rocks collected by me)  

= 3 x (m)  = 3 m

The number of fossils collected by my friend = 1/2 x (fossils collected by me)    = 1/2 x (2k )  = k

⇒ 3 m +   k =  20  .... (2)

Solving (1)and (2) for the value of m and k, we get:

m +  2 k =  20     ⇒ m = 20 - 2 k ... Put this in (2)

3 m +   k =  20  ⇒  3 (20 - 2 k) +  k = 20

⇒ 60 - 6 k +  k  = 20

or, - 5k = -40

or, k = 40/5  = 8

⇒ k= 8

m + 2(8)  = 20

or, m = 4

Hence, the number of rocks collected by me  = m = 4

The number of fossils collected by me  =  2 k = 2 (4)  = 16

Hence, the number of rocks collected by my friend   = 3 m  = 3 x 4 = 12

The number of fossils collected by my friend   =   k =  8

Hence, I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.

4 0
2 years ago
You are putting a rectangular hot tub on your back porch. It is 6 feet long, 5 feet wide, and 3 feet deep. How much will it cost
igor_vitrenko [27]

Answer:

Cost=\$3.66234\approx \$3.67

Step-by-step explanation:

Height\ of\ tub=3\ feet\\\\Length\ of\ tub=6\ feet\\\\width\ of\ tub=5\ feet\\\\Volume=Length\times Width\times Height\\\\Volume=6\times 5\times 3=90\ feet^3

1\ feet^3=7.48052\ gallons\\\\90\ feet^3=90\times 7.48052=673.2468\ gallons

cost\ of\ 1000\ gallons=\$5\\\\cost\ of\ 1\ gallons=\$ \frac{5}{1000}\\\\cost\ of\ 673.2468\ gallons=\$ \frac{5}{1000}\times 673.2468=\$3.366234

5 0
2 years ago
A researcher used a sample of n = 60 individuals to determine whether there are any preferences among six brands of pizza. Each
Blizzard [7]

Answer:

1) χ² ≥ 11.07

2) Goodness of fit test, df: χ²_{3}

Independence test, df: χ²_{1}

The goodness of fit test has more degrees of freedom than the independence test.

3) e_{females.} = 80

4) H₀: P_{ij}= P_{i.} * P_{.j} ∀ i= 1, 2, ..., r and j= 1, 2, ..., c

5) χ²_{6}

Step-by-step explanation:

Hello!

1)

The researcher took a sample of n=60 people and made them taste proof samples of six different brands of pizza and choose their favorite brand, their choose was recorded. So the study variable is the following:

X: favorite pizza brand, categorized in brand 1, brand 2, brand 3, brand 4, brand 5 and brand 6.

The Chi-square goodness of fit test is done with the following statistic:

χ²= ∑\frac{(O_i-E_i)^2}{E_i} ≈χ²_{k-1}

Where k represents the number of categories of the study variable. In this example k= 6.

Remember, the rejection region for the Chi-square tests of "goodnedd of fit", "independence", and "homogeneity" is allways one-tailed to the right. So you will only have one critical value.

χ²_{k-1; 1 - \alpha }

χ²_{6-1; 1 - 0.05 }

χ²_{5; 0.95 } = 11.070

This means thar the rejection region is χ² ≥ 11.07

If the Chi-Square statistic is equal or greather than 11.07, then you reject the null hypothesis.

2)

The statistic for the goodness of fit is:

χ²= ∑\frac{(O_i-E_i)^2}{E_i} ≈χ²_{k-1}

Degrees of freedom: χ²_{k-1}

In the example: k= 4 (the variable has 4 categories)

χ²_{4-1} = χ²_{3}

The statistic for the independence test is:

χ²= ∑∑\frac{(O_ij-E_ij)^2}{E_ij} ≈χ²_{(r-1)(c-1)} ∀ i= 1, 2, ..., r & j= 1, 2, ..., c

If the information is in a contingency table

r= represents the total of rows

c= represents the total of columns

In the example: c= 2 and r= 2

Degrees of freedom: χ²_{(r-1)(c-1)}

χ²_{(2-1)(2-1)} = χ²_{1}

The goodness of fit test has more degrees of freedom than the independence test.

3)

To calculate the expected frecuencies for the independence test you have to use the following formula.

e_{ij} = n * P_i. * P_.j = n * \frac{o_i.}{n} * \frac{o_.j}{n}

Where o_i. represents the total observations of the i-row, o_.j represents the total of observations of the j-column and n is the sample size.

Now, this is for the expected frequencies in the body of the contingency table, this means the observed and expected frequencies for each crossing of categories is not the same.

On the other hand, you would have the totals of each category and population in the margins of the table (subtotals), this is the same when looking at the observed frequencies and the expected frequencies. Wich means that the expected frequency for the total of a population is the same as the observed frequency of said population. A quick method to check if your calculations of the expected frequencies for one category/population are correct is to add them, if the sum results in the subtotal of that category/population, it means that you have calculated the expected frequencies correctly.

The expected frequency for the total of females is 80

Using the formula:

(If the females are in a row) e_{females.} = 100 * \frac{80}{100} * \frac{0}{100}

e_{females.} = 80

4)

There are two ways of writing down a null hypothesis for the independence test:

Way 1: using colloquial language

H₀: The variables X and Y are independent

Way 2: Symbolically

H₀: P_{ij}= P_{i.} * P_{.j} ∀ i= 1, 2, ..., r and j= 1, 2, ..., c

This type of hypothesis follows from the definition of independent events, where if we have events A and B independent of each other, the probability of A and B is equal to the product of the probability of A and the probability of B, symbolically: P(A∩B) = P(A) * P(B)

5)

In this example, you have an independence test for two variables.

Variable 1, has 3 categories

Variable 2, has 4 categories

To follow the notation, let's say that variable 1 is in the rows and variable 2 is in the columns of the contingency table.

The statistic for this test is:

χ²= ∑∑\frac{(O_ij-E_ij)^2}{E_ij} ≈χ²_{(r-1)(c-1)} ∀ i= 1, 2, ..., r & j= 1, 2, ..., c

In the example: c= 3 and r= 4

Degrees of freedom: χ²_{(r-1)(c-1)}

χ²_{(3-1)(4-1)} = χ²_{6}

I hope you have a SUPER day!

4 0
3 years ago
Find the surface area of a cylinder with a height of 8 yd and a base radius of 3 yd. Use 3.14 for π and dont do any rounding.
gulaghasi [49]
<span>Surface area</span> = 2πr(h+r) =  2 * 3.14 * 3(8+3) = 207.24 yd²
3 0
3 years ago
Read 2 more answers
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