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2 years ago

Question :

Mathematics

1 answer:

Darya [45]2 years ago

6 0

Answer:

1156

Step-by-step explanation:

We know that,

( a + b ) ² = a² + 2ab + b²

We can follow the same method to find the value of this.

12² + 22²

( 12 + 22 ) ²

12² + 2 × 12 × 22 + 22²

144 + 24 × 22 + 484

144 + 528 + 484

672 + 484

1156

Let me know if you have any other questions. :)

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9. How many gallons of paint will you need to buy if you are painting a room that is 30 ft by

pentagon [3]

Answer:

To paint the room with dimension 30 ft by 50 ft by 50 ft is 26.67 gallon

Step-by-step explanation:

Given as :

The Length of wall = L = 50 ft

The width of wall = W = 30 ft

The height of wall = H = 50 ft

Each gallon of paints should cover 300 sq feet

Let the amount o gallon required to paint the room = x

SO, Area of four wall = 2 × ( L + W ) × H

Or, Area of four wall = 2 × ( 50 + 30 ) × 50

Or, Area of four wall = 2 × ( 80 ) × 50

SO, Area of four wall = 8000 ft²

∵ To paint 300 sq ft the amount of paint required = 1 gallon

∴ To paint 8000 sq ft the amount of paint required = 26.67 gallon

Hence ,to paint the room with dimension 30 ft by 50 ft by 50 ft is 26.67 gallon answer

6 0

3 years ago

The drama department needs to raise at least 575.00 for a trip to see a play they have already 163.00 if they sell candybars for

olga2289 [7]

Answer:

330

Step-by-step explanation:

575 - 163 = 412

412 / 1.25 = 329.6

Since we need to exceed the goal and we can only sell whole candy bars, we round 329.6 up to 330.

3 0

3 years ago

In AOPQ , the measure of angle Q=90^ , OQ = 33, PO = 65 , and QP = 56 What ratio represents the tangent of angle P ?

ladessa [460]

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4 0

2 years ago

What is the sum of the interior angles of a polygon that has eleven sides? Enter

OLEGan [10]

Answer:

1620

Step-by-step explanation:

180(n)-360=interior angle sum

180(11)-360=1620

n = number of sides

You also can divide it by 11 to know each interior angle.

1620/11=~147.27

6 0

3 years ago

The national mean annual salary for a school administrator is $90,00 a year (The Cincinnati Enquirer, April 7, 2012). A school o

timurjin [86]

Answer:

a) Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

b) $p_v =2*P(t_{(24)}$

c) If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

Step-by-step explanation:

1) Data given and notation

77600 ,76000 ,90700 ,97200 ,90700 ,101800 ,78700 ,81300 ,84200 ,97600 ,

77500 ,75700 ,89400 ,84300 ,78700 ,84600 ,87700 ,103400 ,83800 ,101300

94700 ,69200 ,95400 ,61500 ,68800

We can calculate the sample mean and deviation with the following formulas:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

The values obtained are:

$\bar X=85272$ represent the mean annual salary for the sample

$s=11039.23$ represent the sample standard deviation for the sample

$n=25$ sample size

$\mu_o =90000$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part a: State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean salary differs from 90000, the system of hypothesis would be:

Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part b: Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{85272-90000}{\frac{11039.23}{\sqrt{25}}}=-2.141$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=25-1=24$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(24)}$

Part c: Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

6 0

3 years ago