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2 years ago

2. The seniors at our high school decided to play a prank on the principal by completely filling his office with

Mathematics

2 answers:

Kobotan [32]2 years ago

7 0

Answer:

C. 12,600

Step-by-step explanation:

You can try a rough approximation by finding the volume of the room, finding the volume of one basketball, an dividing the first volume by the second one. This method will give a large estimate since there will be empty space between the balls.

volume of room:

V = L * W * H = 15 * 20 * 10 ft^3 = 3,000 ft^3

volume of one ball:

circumference = 29 in.

From the circumference we find the radius.

circumference = 2(pi)r

2(pi)r = 29 in.

r = (29 in.)/(2pi) = 4.61549 in.

Now we convert inches to feet.

4.61549 in. = 4.61549/12 ft = 0.384624 ft

Now we use the radius of a ball in ft to find the volume of a ball in cubic feet.

V = (4/3)(pi)r^3 = (4/3)(3.14159)(0.384624 ft)^3 = 0.23834 ft^3

Now we divide the volume of the room by the volume of a ball.

number of balls = (3,000 ft^3)/(0.23834 ft^3) = 12,587

The closest answer is C. 12,600

melisa1 [442]2 years ago

3 0

Answer:

idk

Step-by-step explanation:

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Triangles E F G and E prime F prime G prime are shown. Angles F E G and F prime E prime G prime are 72 degrees. Angles E F G and

Karolina [17]

Answer:

We need a non-included side of one triangle

Step-by-step explanation:

By means of the AAS postulate.

The Angle-Angle-Side postulate (AAS) tells us that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

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2 years ago

Simplify this expression: 3(x + 4.5) + 2(2.6x – 3) 1. Distribute the 3 and 4 through the parentheses: 3(x) + 3(4.5) + 2(2.6x) -

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In order to combine like terms, they have to first be organized. First combine the terms with the variable x, then the terms with no variables.

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2 years ago

Read 2 more answers

A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored

pickupchik [31]

Answer:

We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.

Step-by-step explanation:

The complete question is: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:

Number sampled: 1,000 (republican) , 800 (democrats)

Number in favor: 200 (republican) , 168 (democrats)

At the 0.02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.

Let $p_1$ = proportion of Republicans in favor of lowering the standards.

$p_2$ = proportion of Democrats in favor of lowering the standards.

SO, Null Hypothesis, $H_0$ : $p_1 \geq p_2$ {means that there is an equal or larger proportion of Republicans in favor of lowering the standards}

Alternate Hypothesis, $H_A$ : $p_1 < p_2$ {means that there is a larger proportion of Democrats in favor of lowering the standards}

The test statistics that would be used here Two-sample z-test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of Republicans in favor of lowering the standards = $\frac{200}{1000}$ = 0.20

$\hat p_2$ = sample proportion of Democrats in favor of lowering the standards = $\frac{168}{800}$ = 0.21

$n_1$ = sample of Republicans = 1000

$n_2$ = sample of Democrats = 800

So, the test statistics = $\frac{(0.20-0.21)-(0)}{\sqrt{\frac{0.20(1-0.20)}{1000}+\frac{0.21(1-0.21)}{800} } }$

= -0.52

The value of z test statistics is -0.52.

Now, P-value of the test statistics is given by the following formula;

P-value = P(Z < -0.52) = 1 - P(Z $\leq$ 0.52)

= 1 - 0.6985 = 0.3015

Now, at 0.02 significance level, the z table gives a critical value of -2.054 for left-tailed test.

Since our test statistic is more than the critical value of z as -0.52 > -2.054, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.

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2 years ago

Rosa says she can break this array(6 rows,8 in each row) into 3 different sets of two smaller arrays.Is Rosa correct.Explain

snow_tiger [21]

Answer:

Rosa is correct

Step-by-step explanation:

Rosa has array $6 \times 8$ (6 rows and 8 columns). She can break this array into two smaller arrays in such ways:

1st array $5\times 8$ (5 rows and 8 columns) and 2nd array $1\times 8$ (1 row and 8 columns);
1st array $4\times 8$ (4 rows and 8 columns) and 2nd array $2\times 8$ (2 rows and 8 columns);
1st array $3\times 8$ (3 rows and 8 columns) and 2nd array $3\times 8$ (3 rows and 8 columns);
1st array $6\times 1$ (6 rows and 1 column) and 2nd array $6\times 7$ (6 rows and 7 columns);
1st array $6\times 2$ (6 rows and 2 columns) and 2nd array $6\times 6$ (6 rows and 6 columns);
1st array $6\times 3$ (6 rows and 3 columns) and 2nd array $6\times 5$ (6 rows and 5 columns);
1st array $6\times 4$ (6 rows and 4 columns) and 2nd array $6\times 4$ (6 rows and 4 columns).