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TEA [102]
3 years ago
8

Solve the system of equations using elimination 3c - 8d =7 and c + 2d = -7

Mathematics
2 answers:
Bezzdna [24]3 years ago
6 0

Given.

(3c-8d=7)=(c+2d=-7)

Multiply 4 to the second equation.

4(c+2d=-7)

3c+8d=-28

Compare the like terms.

4c+3c-8d+8d=7-28

Solve.

7c=-21

Divide 7 to both sides

\frac{7c}{7}=\frac{-21}{7}

c=-3

Substitute (-3) for c into the original second equation.

c+2d=-7

-3+2d=-7

Add (3) to both sides.

(-3+2d=-7)+3

2d=-4

Divide (2) to both sides.

\frac{2d}{2}=\frac{-4}{2}

d=-2

Check your work.

3(-3)-8(-2)=7

-9+16=7

7=7

c+2d=-7

-3+2(-2)=-7

-3-4=-7

-7=-7

Therefore your answer is.

c=-3\\d=-2

mario62 [17]3 years ago
3 0

Answer:

d=-2 c=-3

Step-by-step explanation:

3c-8d=7

4(c+2d=-7)

3c-8d=7

4c+8d=-28

4c+3c-8d+8d=7-28

7c=-21

c=-3

c+2d=-7

-3+2d=-7

2d=-4

d=-2

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If the odds against a student receiving an A grade in a mathematics class are 7 to 3, what is the
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Answer:

70%

Step-by-step explanation:

Since it can't go over 100%, and our numbers are 7 and 3, they are 70% and 30%, which add up to 100%.

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2 years ago
Please help!! Which of the following is equal to the rational expression when x ≠ 2 or -4? 5(x-2)/(x-2)(x+4)
Stels [109]

Answer:

5 / (x+4)      x ≠2 x≠-4

Step-by-step explanation:

5(x-2)/(x-2)(x+4)

The denominator cannot be zero so x ≠2 x≠-4

Cancel like terms in the numerator and denominator

5 / (x+4)      x ≠2 x≠-4

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3 years ago
If Nathan scoops 8.5 cups of ice cream in 2 minutes, how many scoops of ice cream can he do in 8 minutes?
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Answer:

34

Step-by-step explanation:

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8 0
3 years ago
Read 2 more answers
The mean consumption of water per household in a city was 1425 cubic feet per month. Due to a water shortage because of a drough
liberstina [14]

Answer:

a)t=\frac{1175-1425}{\frac{250}{\sqrt{100}}}=-10    

The degrees of freedom are given by:

df=n-1=100-1=99  

The p value for this case would be given by:

p_v =P(t_{99}  

Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425

b) For this case we need to find a critical value in the t distribution with  99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:

t_{\alpha/2}=1.984

Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425

Step-by-step explanation:

Information given

\bar X=1175 represent the sample mean for the cubic feets of households

\sigma=250 represent the population standard deviation

n=100 sample size  

\mu_o =1425 represent the value to verify

\alpha=0.025 represent the significance level

t would represent the statistic

p_v represent the p value

Part a

We want to test that the mean consumption of water per household has decreased due to the campaign by the city council, the system of hypothesis would be:  

Null hypothesis:\mu \geq 1425  

Alternative hypothesis:\mu < 1425  

Since we don't know the deviation the statistic is given by:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

The statistic is given by:

t=\frac{1175-1425}{\frac{250}{\sqrt{100}}}=-10    

The degrees of freedom are given by:

df=n-1=100-1=99  

The p value for this case would be given by:

p_v =P(t_{99}  

Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425

Part b

For this case we need to find a critical value in the t distribution with  99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:

t_{\alpha/2}=1.984

Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425

6 0
3 years ago
Simplify completely. (w^15/w^5)^4 <br> HELP PLEASE
Umnica [9.8K]

Answer:

w^{40}

Step-by-step explanation:

To simplify recall exponent rules:

1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.

2. When we multiply terms with the same bases, we add exponents.

3. When we divide terms with the same bases, we subtract exponents.

4. When we have a base to the exponent of 0, it is 1.

5. A negative exponent creates a fraction.

6. When we raise an exponent to an exponent, we multiply exponents.

7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.

We will use these rules to simplify.

Use rule #3 to simplify inside the parenthesis first.

\frac{w^{15}}{w^5}  = w^{10}

Now simplify the exponent of 4 using rule 6.

(w^{10})^4 = w^{40}


8 0
3 years ago
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