MATHEMATICS COLLEGE

The test statistic of zequalsnegative 2.40 is obtained when testing the claim that less than 0.32. a. Using a significance level of alphaequals0.10, find the critical value(s). b. Should we reject Upper H 0 or should we fail to reject Upper H 0

Answers

Answer 1

Answer:

Answer:

a) Critical value = -1.285

b) We should reject null hypothesis that the mean equals 0.32

Step-by-step explanation:

Given that the statistic of z equals negative 2.40 is obtained when testing the claim that less than 0.32

i.e. for hypotheses

$H_0: \bar = 0.32\nH_a: \bar x <0.32\n$

(one tailed test at 10% significance level)

Z critical value for 90% one tailed = -1.285

Since our test statistic is less than -1.285 we reject null hypothesis

a) Critical value = -1.285

b) We should reject null hypothesis that the mean equals 0.32

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HELP ME PLEASE I DO NOT UNDERSTAND PLEASE THANK YOU HAVE A GOOD DAYa.) Draw a rectangular prism with these dimensions: 3 units x 9 units x 27 units.

b.) Draw a net of the rectangular prism and label each face with its surface area.

c.) Use the net of the rectangular prism to find the surface area of the solid.

Answers

You can draw a rectangular prison not to scale and just label these on the prism length= 3 width= 9 and height =27
Then you would draw a net the rectangular prism like if you were to unfold it then use the calculation from a and solve for the surface area
Then you add the surface areas together I believe sorry if I get this wrong and it should be the surface area of everything

Simplify the expression 4^4/4^6

Answers

Answer:

$1/16$

Step-by-step explanation:

$(4^(4) )/(4^(6) )$

$4^(4-6)$

$4^(-2)$

$(1)/(4^(2) )$

$(1)/(16)$

Final answer:

By using the rules of exponents, we find that $4^4/4^6$ simplifies to $1/4^2$ , which equals 1/16.

Explanation:

The expression you're looking to simplify is $4^4/4^6$ . In mathematics, when you divide two numbers with the same base, you subtract the exponents. To simplify this expression, subtract the exponent 6 from the exponent 4. This gives us $4^(-2)$ , and any number raised to a negative exponent is 1 divided by the number raised to that exponent. Thus, the simplified form of the expression is $1/4^2$ or 1/16.

Learn more about exponents here:

brainly.com/question/33831961

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If two systems of linear equations have the same solution set (in other words, the two systems are equivalent), then they must have the same number of equations. a. True
b. False

Answers

Answer:

False.

Step-by-step explanation:

Equivalent systems of equations are those that have the same solutions or roots, although they have different numbers of equations. Equivalent systems of equations must have the same number of unknowns.

In other words, two systems of equations are said to be equivalent when they have the same solutions. Equivalent systems of equations do not have to have the same number of equations, although they do have to have the same number of unknowns.

So, the sentence is false.

265000 in standard form

Answers

Answer:

2.65×10^5

Step-by-step explanation:

Answer:

$2.65 \cdot 10^5$

Step-by-step explanation:

265000 can be rewritten as $2.65 \cdot 10^5$ , since the decimal place moved 5 to the left. Hope this helps!

In Exercise, expand the logarithmic expression.
ln(x + 1)2

Answers

Answer:

In(x^2+2x+1)

Step-by-step explanation:

In(x+1)^2 = In(x+1)(x+1) = In(x^2+x+x+1) = In(x^2+2x+1)

At a given time, the length, L, of the shadow of an object varies directlyas the height of the object, H. If the shadow is 27 ft when the height of
the object is 12 ft, what is the height of the object if the shadow is 18 ft?

Answers

Answer:

8 ft

Step-by-step explanation:

Use the direct variation equation, y = kx, where k is a constant.

Change the equation to fit the variables: L = kH

Plug in the given length of the shadow and the height of the object, then solve for k:

L = kH

27 = k(12)

2.25 = k

So, the equation is L = 2.25H

Then, plug in 18 as L, and solve for H:

L = 2.25H

18 = 2.25H

8 = H

So, when the shadow is 18 feet, the height of the object is 8 ft

Final answer:

Using the concept of direct variation, we find that the constant of variation is 2.25. Subsequent substitution in the equation reveals that the object's height when the shadow is 18ft is 8ft.

Explanation:

The question involves the concept of direct variation in mathematics. In direct variation, two quantities increase or decrease together to keep their ratio constant. This concept is given by the equation Y = kX, where Y and X are the quantities and k is a constant.

In our situation, the length of the shadow (L) varies directly with the object's height (H), i.e., L = kt. We are given that L=27ft when H=12ft, we can find the constant k by solving the equation 27ft = k * 12ft. This will get us k = 27ft/12ft = 2.25.

Now, we can determine the object's height if the shadow is 18ft. By substituting the values into the equation, we get 18ft = k * H. Substituting the value of k (2.25) will yield H = 18ft /2.25 = 8ft. Hence, the object's height when the shadow is 18ft is 8ft.