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1 month ago

What is the product of (3a + 2)(4a2 – 2a + 9)?

Mathematics

1 answer:

zzz [12.3K]1 month ago

7 0

Answer:

12a^3 + 2a^2 + 23a + 18

Step-by-step explanation:

Utilize the " ^ " symbol to denote exponents: 4a^2 – 2a + 9.

Proceed with the multiplication as follows:

Initially, apply 3a to each term in 4a^2 – 2a + 9: 12a^3 - 6a^2 + 27a.

Then, multiply each term in 4a^2 – 2a + 9 by 2: 8a^ 2 - 4a + 18.

Now, consolidate the similar terms:

12a^3 - 6a^2 + 27a

8a^ 2 - 4a + 18

---------------------------------

12a^3 + 2a^2 + 23a + 18

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The University of Central Florida's cheerleading team has eighteen males and twenty-one females. If h represents the height of a

Leona [12618]

Answer:

The range of cheerleaders' heights lies within the interval [58, 74)

It includes all real numbers from 58 inches and above, but below 74 inches.

Step-by-step explanation:

we have

$260 \leq 4h+28$

Separate the combined inequality into two distinct inequalities

$260 \leq 4h+28$ -----> inequality A

$4h+28$ -----> inequality B

Solve inequality A

$260 \leq 4h+28$

Subtract 28 from both sides

$232 \leq 4h$

Split by 4 on both sides

$58 \leq h$

Reformulate

$h \geq 58\ in$

Address inequality B

$4h+28$

Subtract 28 from both sides

$4h$

Split by 4 on both sides

$h$

consequently

The height range of the cheerleaders is the interval [58, 74)

It consists of every real number starting from 58 inches and less than 74 inches

3 0

1 month ago

A study1 conducted in July 2015 examines smartphone ownership by US adults. A random sample of 2001 people were surveyed, and th

Inessa [12570]

Answer:

a) Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

b) $z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{688+671}{989+1012}=0.679$

c) $z=\frac{0.696-0.663}{\sqrt{0.679(1-0.679)(\frac{1}{989}+\frac{1}{1012})}}=1.58$

d) In this scenario, we notice that $\hat p_1 > \hat p_2$ thus the conclusion for this case would indicate

Step-by-step explanation:

Information provided

$X_{1}=688$ denote the number of men possessing smartphones

$X_{2}=671$ signify the number of women possessing smartphones

$n_{1}=989$ group of men sampled

$n_{2}=1012$ group of women sampled

$p_{1}=\frac{688}{989}=0.696$ symbolize the proportion of men with smartphones

$p_{2}=\frac{671}{1012}=0.663$ symbolize the proportion of women with smartphones

$\hat p$ denote the pooled estimate of p

z would denote the test statistic

$p_v$ signify the value

Part a

The objective is to evaluate if there is a disparity in smartphone ownership between men and women; the hypothesis statements would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

Part b

The statistic relevant to this case is expressed as:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{688+671}{989+1012}=0.679$

Part c

By substituting the provided information, we find:

$z=\frac{0.696-0.663}{\sqrt{0.679(1-0.679)(\frac{1}{989}+\frac{1}{1012})}}=1.58$

Part d

In this instance, it is evident that $\hat p_1 > \hat p_2$ thus the conclusion for this case would seem

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1 month ago

Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes si

PIT_PIT [12445]

Step-by-step explanation:

Tracie's bus moves towards home at an average pace of one-half mile for every minute.

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1 month ago

Read 2 more answers

Sam is designing a fence post for his yard. He will need to construct a perpendicular line through the point above the line to m

zzz [12365]

Option D is indeed correct, as it ensures that the post's point is equidistant from the ground, maintaining a perpendicular angle at two points on the surface.

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1 month ago

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There is a sidewalk of width x around a rectangular garden. If the garden measures twenty-feet by thirty-feet, then the combined

PIT_PIT [12445]

Answer:

Area = 200 + 50 + x

Step-by-step explanation:

Given

Length = 20

Width = 30

Side Walk = x

Required

Find the total area.

To find this, we have to add the length of the sidewalk to the dimensions of the garden.

This results in:

Length = 20 + x.

Width = 30 + x

So, the area now becomes.

Area = (20 + x)(30 + x)

Area = 600 + 20x + 30x + x²

Area = 200 + 50 + x²

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10 days ago