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frosja888 [35]
2 years ago
10

How many times does 1/2 fit into 30

Mathematics
1 answer:
Leni [432]2 years ago
4 0
It fits in the 30, 60 times.

30 ÷ \frac{1}{2}

To divide by a fraction, multiply by its reciprocal (find reciprocal by flipping the fraction)

Ex. 30 * 2

Multiply 30 by 2 to get 60.
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In a representative sample of 1000 adult Americans, only 400 could name at least one justice who is currently serving on the U.S
lys-0071 [83]

Answer:

1) z = -6.32

2) p-value = 0.001 × 10^(-2)

3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

Step-by-step explanation:

We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.

Thus:

Sample proportion; p^ = 400/1000 = 0.4

Sample size: n = 1000

We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.

Thus, the hypothesis is defined as;

Null hypothesis:H0: p ≥ 0.5

Alternative hypothesis: Ha < 0.5

Formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values;

z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)

z = -6.32

From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;

We have:

p-value = 0.00001 = 0.001 × 10^(-2)

The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

8 0
2 years ago
A tree that is 14 feet tall casts a shadow that is 30 feet long. Find the angle of the elevation from the top of the shadow to t
Umnica [9.8K]

Let x = angle we must find

tan x = 14/30

arctan(tan x) = arctan(14/30)

x = 25.0168934781

Answer: 25 degrees

8 0
3 years ago
A scientist has two solutions, which she has labeled Solution A and Solution Each contains salt. She knows that Solution A is 40
Alexxandr [17]

Answer:

Step-by-step explanation:

Let the number of ounces of

A = x

B = y

A scientist has two solutions, which she has labeled Solution A and Solution Each contains salt. She knows that Solution A is 40% salt and Solution B is 55% salt. She wants to obtain 90 ounces of a mixture that is 45% salt. How many ounces of each solution should she use?

Our system of equations is given as

x + y = 90.... Equation 1

x = 90 - y

40% × x + 55% × y = 45% × 90 ounces

0.4x + 0.55y = 40.5....Equation 2

We substitute 90 - y for x in Equation 2

6 0
3 years ago
tank a has 100 gallons of water and is being filled at a rate of 2 gallons per hour. tank b has 140 gallons and is being drained
Artist 52 [7]

Answer:

5 hours must pass

Step-by-step explanation:

Graph the equations y = 2x + 100 and y = -6x + 140

Then find the x intercept of their intersection, in this case, that is 5

5 0
2 years ago
Josh is trying to factor the expression
mrs_skeptik [129]

Answer:

a) Josh likely made the negative and positive multiplication error.

b) -20a-8+12b

= -4(5a+2-3b)

Step-by-step explanation:

To check if you are correct, you can always simplify it again:

-4(5a+2-3b)

=-20a-8+12b

Remember:

Negative times negative equals to positive, negative times positive equals to negative!

I hope this is helpful! :)

4 0
2 years ago
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