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3 years ago

What is the y intrercept and what is the slope of -7y= 7x+21

Mathematics

1 answer:

k0ka [10]3 years ago

6 0

Answer:

The slope is -1 and y-intercept is at y = -3.

Step-by-step explanation:

-7y= 7x+21

Divide through by -7:

y = -x - 3

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Find the product of 4/5 and 5/12 put in simplest form

kotegsom [21]

Hello!

The answer is 20/60 simplest form is 1/3

To get 20/60 you must multiply the Numerator by Numerator (4*5) and Denominator by Denominator (5*12). Your answer will be 20/60.

To get 1/3 you must simplify a number that can go into 20 and 60 (which is 10). Divide 20/10 and 60/10 and get 2/6. Simplify 2/6 by 2 and get 1/3.

3 0

3 years ago

Please sketch graph of the function f(x) = |x+2|.

Burka [1]

Answer:

The absolute value can be graphed using the points around the vertex (-2, 0), (-4, 2), (-3, 1), (-1, 1), (0, 2).

Step-by-step explanation:

The find the x coordinate of the vertex, set the inside of the absolute value x + 2 equal to 0. In this case, x + 2 = 0.

x + 2 = 0

Subtract 2 from both sides of the equation.

x = -2

Replace the variable x with -2 in the expression.

y = |(-2) + 2|

The absolute value vertex is (-2, 0).

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

For each x value, there is on y value. Select few z values from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.

Substitute the x value -4 into f(x) = |x+2|. In this case, the point is (-4,2).

y=2

Substitute the x value -3 into f(x) = |x+2|. In this case, the point is (-3,1).

y=1

Substitute the x value 0 into f(x) = |x+2|. In this case, the point is (0,2).

y=2

You can find the graph in the attachment.

6 0

3 years ago

Fizzy Waters has been involved in multiple lawsuits regarding the alkaline substance concentration in their product and getting

ser-zykov [4K]

Answer:

Step-by-step explanation:

For the sample, n = 12

Mean, x = (158.2 + 162.8 + 161.5 + 161.2 + 166.5 + 160.1 + 158.4 + 175.6 + 159.9 + 168.8 + 161.9 + 163.7)/12 = 163.22

Variance, s² = (summation(x - mean)²/n

Summation(x - mean)² = (158.2 - 163.22)^2 + (162.8 - 163.22)^2 + (161.5 - 163.22)^2 + (161.2 - 163.22)^2+ (166.5 - 163.22)^2 + (160.1 - 163.22)^2 + (158.4 - 163.22)^2 + (175.6 - 163.22)^2 + (159.9 - 163.22)^2 + (168.8 - 163.22)^2 + (161.9 - 163.22)^2 + (163.7 - 163.22)^2 = 273.5368

Variance, s² = 273.5368/12 = 22.79

This is a test for a single variance. We would set up the test hypothesis.

For the null hypothesis,

H0: σ² ≥ 25

For the alternative hypothesis,

H1: σ² < 25

The formula for determining the test statistic,x² is

x² = (n - 1)s²/σ²

Where n - 1 is the degree of freedom, df.

df = 12 - 1 = 11

x² = (11 × 22.79)/25 = 10.0276

For a test of 90% reliability, Confidence level = 0.9

Cl = 1 - alpha(level of significance)

alpha = 1 - 0.9 = 0.1

The critical value from the chi-square distribution table is 17.28. Since 17.28 > 10.0276, we would reject the null hypothesis. Therefore, the filling machine does not need repair because the variance of the process is not more than 25 oz.

8 0

3 years ago

What is the Square root of 81

Alexeev081 [22]

The answer is 9, hope this helps

6 0

4 years ago

Read 2 more answers

A large electronic office product contains 2000 electronic components. Assume that the probability that each component operates

KIM [24]

Answer:

The probability is 0.971032

Step-by-step explanation:

The variable that says the number of components that fail during the useful life of the product follows a binomial distribution.

The Binomial distribution apply when we have n identical and independent events with a probability p of success and a probability 1-p of not success. Then, the probability that x of the n events are success is given by:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}$

In this case, we have 2000 electronics components with a probability 0.005 of fail during the useful life of the product and a probability 0.995 that each component operates without failure during the useful life of the product. Then, the probability that x components of the 2000 fail is:

$P(x)=\frac{2000!}{x!(2000-x)!}*0.005^{x}*(0.995)^{2000-x}$ (eq. 1)

So, the probability that 5 or more of the original 2000 components fail during the useful life of the product is:

P(x ≥ 5) = P(5) + P(6) + ... + P(1999) + P(2000)

We can also calculated that as:

P(x ≥ 5) = 1 - P(x ≤ 4)

Where P(x ≤ 4) = P(0) + P(1) + P(2) + P(3) + P(4)

Then, if we calculate every probability using eq. 1, we get:

P(x ≤ 4) = 0.000044 + 0.000445 + 0.002235 + 0.007479 + 0.018765

P(x ≤ 4) = 0.028968

Finally, P(x ≥ 5) is:

P(x ≥ 5) = 1 - 0.028968

P(x ≥ 5) = 0.971032

3 0

3 years ago