Use the diagram to the right to complete the statement. If m<MON=74 then m<KJR=

Jaime knows that 30² is 900. He wonders if knowing that 30² can help him finds 29x31. Raquel knows what 25² equals. How can she

iragen [17]

9514 1404 393

Answer:

Jaime: yes: 29·31 = 900 -1 = 899

Raquel: 24·26 = 25^2 -1 = 624

Step-by-step explanation:

The difference of squares factors as the product of the sum and difference of the roots:

a^2 -b^2 = (a -b)(a +b)

<u>Jaime</u>

29·31 = (30 -1)(30 +1) = 30^2 -1^2 = 900 -1 = 899

Jaime can subtract 1 from 30^2 to find 29·31

__

<u>Raquel</u>

24·26 = (25 -1)(25 +1) = 25^2 -1^2 = 625 -1 = 624

Raquel can subtract 1^2 from 25^2 to find 24·26.

3 0

3 years ago

At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical popul

dmitriy555 [2]

Answer:

The interval is [910.053; 959.946]

p-value 0.00596

Decision: Reject null hypothesis.

Step-by-step explanation:

Hello!

You need to make a 95% Confidence Interval for the population mean of scholarship examination scores for the freshman.

It is known to be μ= 900 and the assistant dean wants to test if it changed.

The study variable is:

X: -scholarship examination score of one applicant.

population variance is known as σ²= (180)²

Assuming that the variable has a normal distribution the formula for the interval is:

X[bar] ± $Z_{1-\alpha /2}$ * $\frac{S}{\sqrt{n} }$

935 ± 1.96* $\frac{180}{\sqrt{200} }$

The interval is [910.053; 959.946]

To test if the examination scores have changed the hypothesis is:

H₀: μ = 900

H₁: μ ≠ 900

α: 0.05

To use a Confidence Interval the following conditions should be met:

1) Both the test and the interval should be made for the same parameter.

2) The hypothesis has to be two_tailed

3) Confidence level 1 - α and significance level α should be complementary.

To make the decision you have to see if the value given to the population mean in the null hypothesis is contained or not by the interval.

If the value is contained by the interval, you do not reject the null hypothesis.

If the value is not contained by the interval, then the decision is to reject the null hypothesis.

Since 900 is not contained by the 95% Confidence interval [910.05; 959.95], the decision is to reject the null hypothesis. This means that the scholarship examination scores of freshman applications have changed.

To calculate the p-value you have to know the value of the statstic under the null hypothesis:

Z= $\frac{935-900}{\frac{180}{\sqrt{200} } }$ = 2.749 ≅ 2.75

p-value is

P(Z<2.75) + P(Z>2.75)= P(Z<2.75) + (1 - P(Z<2.75))= 0.00298+ (1 - 0.9702= 0.00596

I hope it helps!

4 0

3 years ago

What is the binary number for 24

Anika [276]

Answer:

Here im to lazy to solve so a pic

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The points plotted below are on the graph of a polynomial. In what range of

Irina-Kira [14]

Answer:

the answer is 0 to 1 and 3 to 4

7 0

3 years ago

Aunt Becky gave 5/6 of a cup of pudding to each of her 3 nephews. How many cups of pudding did she give out?

bulgar [2K]

Answer:

2 $\frac{1}{2}$ Cups

Step-by-step explanation:

First make 3 a fraction by throwing a one under it. Next multiple the two tops of the fractions together and then the two bottoms together:

$\frac{5}{6} X\frac{3}{1} = \frac{15}{6}$

Next we convert to a mixed number:

$2\frac{3}{6}$

Finally, we simplify the fraction:

2 $\frac{1}{2}$

7 0

3 years ago