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3 years ago

Solve each system by substitution.

Mathematics

1 answer:

jek_recluse [69]3 years ago

4 0

-8x + 4y = 20
-8x = 20 - 4y

Subtitute -8x with 20-4y
-8x + 7y = 5
(20-4y) + 7y = 5
20 + 3y = 5
3y = 5 - 20
3y = -15
y = -15/3
y = -5

Find x
-8x = 20 - 4y
-8x = 20 - 4(-5)
-8x = 20 + 20
-8x = 40
x = 40/-8
x = -5

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The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar

Serggg [28]

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

$\bar x$ represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical values.

The excel commands would be: "=CHISQ.INV(0.025,9)" "=CHISQ.INV(0.975,9)". so for this case the critical values are:

$\chi^2_{\alpha/2}=19.022$

$\chi^2_{1- \alpha/2}=2.700$

And replacing into the formula for the interval we got:

$\frac{(9)(4.798)^2}{19.022} \leq \sigma \frac{(9)(4.798)^2}{2.700}$

$10.892 \leq \sigma^2 \leq 76.736$

Now we just take square root on both sides of the interval and we got:

$3.30 \leq \sigma \leq 8.76$

So the best option would be:

3.30<σ<8.76

7 0

3 years ago

Solve for the variable c in this equation a(c + b) = d

noname [10]

Multiply everything in the parenthesis by a.

ac + ab = d

Subtract ab from both sides.

ac = d - ab

Divide a on both sides.

c = d - ab / a

Hope this helps!

3 0

4 years ago

Solve the equation. Round the solution to the tenths place.<br> 6.35t = 56.515<br> t =

Westkost [7]

Answer:

t = 8.9

Step-by-step explanation:

6.35t = 56.515

56.515 / 6.35 = t

t = 8.9

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4 years ago

Complete the blank with either ∈ or ∉ so that the resulting statement is true. −2__{−6,−3,−5,−1}

Misha Larkins [42]

Answer:

−2 ∉ {−6,−3,−5,−1}

Step-by-step explanation:

Given

Set = {−6,−3,−5,−1}

Element = -2

Required

The interpretation of the question is to state if -2 is an element of the given set or not

The first thing to do is to check through the set to count the number of occurrence of -2

Looking through Set = {−6,−3,−5,−1}, we have that the occurrence of -2 is 0

This implies that -2 is not an element of the given set and this is represented by the symbol ∉

Hence:

−2 ∉ {−6,−3,−5,−1}

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3 years ago

Redo! one geo question thank youu

svetlana [45]

Answer is in the pic above. Theorems used:

Exterior angle theorem

Inscribed angle theorem.

$\angle EBF=32.5°$

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3 years ago