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Monica [59]
3 years ago
15

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $27 monthly fee

and charges an additional $0.12 for each minute of calls. The second plan has no monthly fee but charges $0.16 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Mathematics
1 answer:
NikAS [45]3 years ago
4 0
The first plan : y = 27 + 0.12x
Second plan : y = 0.16x

27 + 0.12x= 0.16x
27 = 0.04x

x = 67.5 minutes
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Check My Work According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Data
Salsk061 [2.6K]

Complete question :

According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Suppose data for the sale of 39 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017. Useα = 0.05for the level of significance, and state your conclusion

Answer:

H0 : μ = 3

H1 : μ ≠ 3

Test statistic = 1.897

Pvalue = 0.0653

fail to reject the Null ; Hence, we conclude that their is no significant to accept the claim that number I weeks taken to sell a house differs.

Step-by-step explanation:

Given :

Sample size, n = 40

Sample mean, x = 3.6

Population mean, μ = 3

Standard deviation, s = 2

The hypothesis :

H0 : μ = 3

H1 : μ ≠ 3

The test statistic :

(xbar - μ) ÷ (s/√n)

(3.6 - 3) / (2/√40)

0.6 / 0.3162277

Test statistic = 1.897

Using T test, we can obtain the Pvalue from the Test statistic value obtained :

df = n - 1; 40 - 1 = 39

Pvalue(1.897, 39) = 0.0653

Decison region :

If Pvalue ≤ α ; Reject the null, if otherwise fail to reject the Null.

α = 0.05

Pvalue > α ; We fail to reject the Null ; Hence, we conclude that their is no significant to accept the claim that number I weeks taken to sell a house differs.

7 0
3 years ago
You are asked to draw a triangle with the side lengths of 10 inches, 7 inches, and 2 inches. How many triangles like this can yo
podryga [215]

Answer:

B

Step-by-step explanation:

I am not sure . I am thinking it is . I maybe the answer

3 0
3 years ago
Square MATH is shown at the right. Assume its vertices have integer coordinates. What are the coordinates of the midpoint of the
Mariana [72]

Answer: F(-0.5,-0.5)

Step-by-step explanation:

A(3,3)      H(-4,-4)

The coordinates of the midpoint of the diagonal AH F(x,y):

\displaystyle\\F(x,y)=(\frac{3+(-4)}{2} ,\frac{3+(-4)}{2} )\\\\F(x,y)=(\frac{3-4}{2} ,\frac{3-4}{2})\\\\F(x,y)=(\frac{-1}{2},\frac{-1}{2})\\\\F (x,y) =(-0.5,-0.5)

8 0
1 year ago
Please give the correct answer and explain im really trying to learn this so I need the explanation not just an answer. Thankyou
Maksim231197 [3]

Answer:

x = tan⁻¹(⅘)

Step-by-step explanation:

We can solve for x by using trigonometric ratios (sin, cos, and tan)

We need to apply the appropriate ratio that uses the two sides 8 and 10 from the perspective of x. See attached image for information about ratios. (Source: Math is Fun)

The tangent ratio is opposite divided by adjacent. It will relate x to the two sides. So we would write

tan(x) = ⁸⁄₁₀

Then we simplify and move the tan to the other side by multiplying both sides by the inverse of tan (since you cannot divide by tan)

tan(x) = ⅘

x = tan⁻¹(⅘)

Then we can use a calculator to evaluate x

If you want to find y, now that you have two angles of the triangle, you can find the sum of 90 + x and subtract that from 180 (since all angles of a triangle add up to 180) to find y.

6 0
3 years ago
HELP WITH ANY OR ALL THESE PROBLEMS ASAP PLEASE LIKE NOW PLEASE<br>CAN SOMEONE PLEASE HELP 
LiRa [457]

Ques 8:

The Volume(V) in cubic feet of an aquarium id modeled by the polynomial function V(x)= x^{3}+2x^{2}-13x+10

a) We have to explain that why x =4 is not a possible rational zero.

By Factor theorem, which states that a polynomial f(x) has a factor (x - k) if and only if f(k)=0.

For this , we will substitute the value of x in the given function.

V(x)=x^{3}+2x^{2}-13x+10

V(4)=4^{3}+2(4)^{2}-13(4)+10

V(4)=4^{3}+2(4)^{2}-13(4)+10

V(4)=54 which is not equal to zero.

Therefore, x=4 is not a possible rational zero.

(b) To show that (x-1) is a factor of V(x).

By Factor theorem, which states that a polynomial f(x) has a factor (x - k) if and only if f(k)=0.

Let (x-1)=0

So, x=1.

Substituting x=1 in the given function.

V(1)=1^{3}+2(1)^{2}-13(1)+10

V(1)= -10+10

V(1) = 0

Therefore, (x-1) is a factor of V(x).

Now we will factorize the given function.

Dividing the given function by (x-1).

On dividing, we get quotient as x^{2}+3x-10

So, factored form is = (x-1)(x^{2}+3x-10)

= (x-1)(x^{2}+5x-2x-10)

= (x-1)(x(x+5)-2(x+5))

=(x-1)(x+5)(x-2)

(c) So, the dimensions are 1,2 and -5.

5 0
3 years ago
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