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Anuta_ua [19.1K]
3 years ago
9

Bryan’s monthly electric bill is determined by adding a flat administration fee to the product of the number of kilowatt hours o

f electricity used and the cost per kilowatt hour. When he uses 1,100 kilowatt hours of electricity, his bill is $113. When he uses 1,500 kilowatt hours of electricity, his bill is $153. What is the monthly administration fee?
Mathematics
2 answers:
Sophie [7]3 years ago
6 0
We will form the equations for this problem:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
z = ? Monthly administration fee is notated with z, and that is the this problem's question.
Number of kilowatt hours of electricity used are numbers 1100 and 1500 respectively.
Cost per kilowatt hour is notated with y, but its value is not asked in this math problem, but we can calculate it anyway.
The problem becomes two equations with two unknowns, it is a system, and can be solved with method of replacement:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
----------------------------
(1) z = 113 - 1100*y [insert value of z (right side) into (2) equation instead of z]:
(2) 1500*y + (113 - 1100*y) = 153
-------------------------------------------------
(1) z = 113 - 1100*y
(2) 1500*y + 113 - 1100*y = 153
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y + 113 = 153
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y = 153 - 113
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y = 40
------------------------------------------------
(1) z = 113 - 1100*y
(2) y = 40/400
------------------------------------------------
(1) z = 113 - 1100*y
(2) y = 1/10
------------------------------------------------
if we insert the obtained value of y into (1) equation, we get the value of z:
(1) z = 113 - 1100*(1/10)
(1) z = 113 - 110
(1) z = 3 dollars is the monthly fee.
Anna007 [38]3 years ago
5 0

Answer:

3

Step-by-step explanation:

correct on ed (:

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You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 nigh
kirill [66]

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean GPA of night students and μ2 be the mean GPA of day students.

The random variable is μ1 - μ2 = difference in the mean GPA of night students and the mean GPA of day students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

μ1 = 2.35

μ2 = 2.58

s1 = 0.46

s2 = 0.47

n1 = 30

n2 = 25

t = (2.35 - 2.58)/√(0.46²/30 + 0.47²/25)

t = - 1.8246

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.46²/30 + 0.47²/25]²/[(1/30 - 1)(0.46²/30)² + (1/25 - 1)(0.47²/25)²] = 0.00025247091/0.00000496862

df = 51

We would determine the probability value from the t test calculator. It becomes

p value = 0.0746

Since alpha, 0.05 < than the p value, 0.0746, then we would fail to reject the null hypothesis.

3 0
3 years ago
10+8+7(-10)-(-1)
Elina [12.6K]

Answer:

-51

Step-by-step explanation:

Let's do order of operations.

10+8-70-(-1)     <- We did negative 7 times 10.

18-70-(-1)    <- We did 10 plus 18.

-52-(-1)     <- We did 18 minus 70

When you open the () we get:

-52--1

Negative minus a negative equals a positive.

-52+1=

-51

5 0
3 years ago
HELP PLEASE!!!!!!!!!!!
emmainna [20.7K]

Answer:

Part 1) y=-x^{2}  ---> Translated up by 1 units

Part 2) y=x^{2}+1  ---> Reflected across the x-axis

Part 3) y=-(x+1)^{2}-1  ---> Translated left by 1 unit

Part 4) y=-(x-1)^{2}-1 ----> Translated right by 1 unit

Part 5) y=-x^{2}-1  ----> Reflected across the y-axis

Part 6) y=-x^{2}-2  ----> Translated down by 1 unit

Step-by-step explanation:

we know that

The parent function is

y=-x^{2}-1 ----> this is a vertical parabola open downward with vertex at (0,-1)

<em>Calculate each case</em>

Part 1) Translated up by 1 unit

The rule of the translation is

(x,y) -----> (x,y+1)

so

(0,-1) ----> (0,-1+1)

(0,1) ----> (0,0) ----> the new vertex

The new function is equal to

y=-x^{2}

Part 2) Reflected across the x-axis

The rule of the reflection is

(x,y) -----> (x,-y)

so

(0,-1) ----> (0,1) ----> the new vertex

The new function is equal to

y=x^{2}+1

Part 3) Translated left by 1 unit

The rule of the translation is

(x,y) -----> (x-1,y)

so

(0,-1) ----> (0-1,-1)

(0,1) ----> (-1,-1) ----> the new vertex

The new function is equal to

y=-(x+1)^{2}-1

Part 4) Translated right by 1 unit

The rule of the translation is

(x,y) -----> (x+1,y)

so

(0,-1) ----> (0+1,-1)

(0,1) ----> (1,-1) ----> the new vertex

The new function is equal to

y=-(x-1)^{2}-1

Part 5) Reflected across the y-axis

The rule of the reflection is

(x,y) -----> (-x,y)

so

(0,-1) ----> (0,-1) ----> the new vertex

The new function is equal to

y=-x^{2}-1

Part 6) Translated down by 1 unit

The rule of the translation is

(x,y) -----> (x,y-1)

so

(0,-1) ----> (0,-1-1)

(0,1) ----> (0,-2) ----> the new vertex

The new function is equal to

y=-x^{2}-2

3 0
3 years ago
Suppose you add 10% of a number to the number, and then you subtract 10% of the total. Is the result greater than, less then, or
anyanavicka [17]
Let's say the number is 9. 10% of 9 is 0.9. Add that to 9 and you would get 9.9. 10% of 9.9 is 0.99. Subtract and you would get 8.91. Then you could do the rest.
5 0
3 years ago
What value of c makes the polynomial below a perfect square? x^2+10+c
Inessa05 [86]

Answer: Hi there

To find the last term in order to obtain the perfect square, take the middle term, divide it by 2, and take its square. 

10 ÷ 2 = 5

5^2 = 25

Thus, the equation would be x^2 + 10x + 25

The answer is 25

Maybe mark Brainliest

:D

4 0
2 years ago
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