Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65.
A) Are the first flight leaving on time and the luggage making the connection independent events? Explain.
B) What is the probability that her luggage arrives in Denver with her?

The value of given expression is 16

Solution:

Given expression is:

[tex]\sqrt{x^2} + \sqrt{x} \times \sqrt{x} + 6[/tex]

We have to find the value of expression when x = 5

Substitute x = 5

[tex]\sqrt{x^2} + \sqrt{x} \times \sqrt{x} + 6\\\\\sqrt{5^2} + (\sqrt{5} \times \sqrt{5}) + 6[/tex]

We know that,

[tex]\sqrt{a} \times \sqrt{a} = a[/tex]

Therefore, the above equation becomes,

[tex]\sqrt{5^2} + 5 + 6\\\\\sqrt{25} + 5 + 6\\\\5 + 5 + 6 = 10 + 6 = 16[/tex]

Thus the value of given expression is 16

Answer:

Superintendent of the region will select approximately 4 Science teachers in the board.

Step-by-step explanation:

Given:

Number of math teachers = 40

Number of English teachers = 45

Number of Science teachers = 27

Number Social Studies teachers = 32

Number of teachers to be selected in the board =20

We need to find the number Science teachers should be selected in the board.

Solution:

First we ill find the Total number of teachers.

Now we can say that;

Total number of teachers is equal to sum of Number of math teachers, Number of English teachers,Number of Science teachers and Number Social Studies teachers

framing in equation form we get;

Total number of teachers = [tex]40+45+27+32=144[/tex]

Probability of Science teacher can be calculated by Dividing Number of Science teacher by Total number of teachers.

[tex]P(S)=\frac{27}{144}=0.1875[/tex]

Now  the number of Science teachers should be selected in the board we need to multiply P(S) with Number of teachers to be selected in the board.

framing in equation form we get;

number of Science teachers should be selected in the board = [tex]0.1875\times 20=3.75\approx4[/tex]

Hence We can say that;

Superintendent of the region will select approximately 4 Science teachers in the board.

Calculate the proportion of science teachers out of the total and apply it to the board size to determine the number of science teachers to select.

To determine how many science teachers the superintendent should select for a board of 20 teachers:

Answer:

The answer to your question is below

Step-by-step explanation:

1.- Find the volume of the cylinder

Data

diameter = 9 cm

radius = 4.5 cm

height = 15 cm

Formula

   V = πr²h

   V = π(4.5)²(15)

  V = 303.75π         This is te answer for the volume in terms of π

       = 952.78 cm³                

2.- Find the volume of the cylinder

height = 40 yd

radius = 12 yd

Formula

   V = πr²h

   V = π(12)²(40)

   V = 5760π              This is te answer for the volume in terms of π

       = 18086.4 cm³

3.- What is the height .......

height = q

side length = r

4.- Volume of a pyramid

    Volume = Area of the base x height

Area of the base = 11 x 11 = 121 cm²

    Volume = 121 x 18

   Volume = 2178 cm³

Answer:

1. 953.775 cm³

2. 18,086.4 yd³

3. height: q ; side: r

4. 726 cm³

Step-by-step explanation:

1. Volume = pi × r² × h

= 3.14 × (9/2)² × 15

= 953.775 cm³

2. Volume = pi × r² × h

= 3.14 × 12² × 40

= 18086.4 yd³

3. height: q ; side: r

4. Volume = ⅓ base area × height

= ⅓ × 11² × 18

= 726 cm³

Answer:

The 98% confidence interval for population proportion of people who refuse evacuation is {0.30, 0.33].

Step-by-step explanation:

The sample drawn is of size, n = 5046.

As the sample size is large, i.e. n > 30, according to the Central limit theorem the sampling distribution of sample proportion will be normally distributed with mean [tex]\hat p[/tex] and standard deviation [tex]\sqrt{\frac{\hat p (1-\hat p)}{n} }[/tex].

The mean is: [tex]\hat p=0.31[/tex]

The confidence level (CL) = 98%

The confidence interval for single proportion is:

[tex]CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }][/tex]

Here [tex]z_{(\alpha /2)}[/tex] = critical value and α = significance level.

Compute the value of α as follows:

[tex]\alpha =1-CL\\=1-0.98\\=0.02[/tex]

For α = 0.02 the critical value can be computed from the z table.

Then the value of [tex]z_{(\alpha /2)}[/tex] is ± 2.33.

The 98% confidence interval for population proportion is:

[tex]CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]\\=[0.31-2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} },\ 0.31+2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} } ]\\=[0.31-0.0152,\ 0.31+0.0152]\\=[0.2948,0.3252]\\\approx[0.30,\ 0.33][/tex]

Thus, the 98% confidence interval [0.30, 0.33] implies that there is a 0.98 probability that the population proportion of people who refuse evacuation is between 0.30 and 0.33.  

Final answer:

The 98% confidence interval for the proportion of coastal residents who would evacuate is between approximately 67.49% and 70.51%. This reflects our confidence that the true proportion falls within this range, with only a 2% chance of being outside these bounds.

Explanation:

To estimate the proportion of coastal residents who would evacuate using a 98% confidence interval based on the available survey data, we look at the reported figure that 31% of the people will refuse to evacuate, which implies that 69% would evacuate. The sample size is 5046 adults. To calculate the 98% confidence interval for the true proportion, we use the formula for the confidence interval of a proportion:

Confidence interval = p ± Z*sqrt((p(1-p))/n)

where:

p is the sample proportion (0.69 in this case),

Z is the Z-score associated with the confidence level (2.326 for 98% confidence),

sqrt denotes the square root function,

n is the sample size.

Plugging the values into the formula, we get:

Confidence interval = 0.69 ± 2.326 * sqrt((0.69(1-0.69))/5046)

Performing these calculations:

Confidence interval = 0.69 ± 2.326 * sqrt(0.2141/5046)

Confidence interval = 0.69 ± 2.326 * sqrt(0.0000424451086)

Confidence interval = 0.69 ± 2.326 * 0.0065134

Confidence interval = 0.69 ± 0.015143

So the 98% confidence interval for the proportion of coastal residents who would evacuate is approximately 0.6749 to 0.7051, or 67.49% to 70.51%.

Interpreting this confidence interval at the 98% confidence level means that we can be 98% confident that the true proportion of all coastal residents in these high-risk areas who would evacuate falls between 67.49% and 70.51%. This does not mean that the true proportion is within this interval with 100% certainty, but rather that there's a 2% chance that the true proportion lies outside of this interval.

Answer:

The sample is a Simple Random sample.

explanation:

A simple random sample is the process where there is equal chance of selecting each member of a population to form a sample. in the example stated in the question there are equal chances of selecting every ticket among the five hundred ticket of the participant so as to form another set of ten tickets that win a prize.

Answer:

Step-by-step explanation:

Let n represent the number of nickels in the jar.

The jar contains only​ pennies, nickels,​ dimes, and quarters. There are 14 ​pennies, 28 ​dimes, and 16 quarters. This means that the total number if pennies, dimes and quarters would be

14 + 28 + 16 = 58

This means that the number of coins that are not nickel is 58

The total number of coins in the jar is 70. Therefore, the equation that can be used to find n is

n + 58 = 70

n = 70 - 58

n = 12 nickels

Answer: 343 in³

Explanation: In this problem, we're asked to find the volume of a cube.

It's important to understand that a cube is a type of rectangular prism and the formula for the volume of a rectangular prism is shown below.

Volume = length × width × height

In a cube however, the length, width, and height are all the same. So we can use the formula side × side × side instead.

So the formula for the volume of a cube is side × side × side or s³.

So to find the volume of the given cube, since each side has a length of 7 inches, we can plug this information into the formula to get (7 in.)³ or (7 in.)(7 in.)(7 in).

7 x 7 is 49 and 49 x 7 is 343.

So we have 343 in³.

So the volume of the given cube is 343 in³.

Answer:

343 in³

Step-by-step explanation:

Answer: An adult ticket cost $12

A child ticket cost $5

Step-by-step explanation:

Let x represent the price for one adult ticket.

Let y represent the price for one child ticket.

A movie theater sold 4 adult tickets and 7 children's tickets for $83 on Friday. It means that

4x + 7y = 83 - - - - - - - - - - - -1

The next day the theater sold 5 adult tickets and 6 children tickets for $90. It means that

5x + 6y = 90 - - - - - - - - - - - -2

Multiplying equation 1 by 5 and equation 2 by 4, it becomes

20x + 35y = 415

20x + 24y = 360

Subtracting, it becomes

11y = 55

y = 55/11 = 5

Substituting y = 5 into equation 1, it becomes

4x + 7 × 5 = 83

4x + 35 = 83

4x = 83 - 35 = 48

x = 48/4 = 12

Option D: [tex]20 \div 6-4[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]

Option E: [tex]\frac{1}{6} (20-24)[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]

Option F: [tex](20-24) \div 6[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]

Explanation:

The expression is [tex]6(x+4)=20[/tex]

Let us find the value of x.

[tex]\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}[/tex]

Now, we shall find the expression that is equivalent to the value [tex]x=-\frac{2}{3}[/tex]

Option A: [tex](20-4) \div 6[/tex]

Simplifying the expression, we have,

[tex]\frac{16}{6}=\frac{8}{3}[/tex]

Since, [tex]\frac{8}{3}[/tex] is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-4) \div 6[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option A is not the correct answer.

Option B: [tex]16(20-4)[/tex]

Simplifying the expression, we have,

[tex]16(16)=256[/tex]

Since, 256 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]16(20-4)[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option B is not the correct answer.

Option C: [tex]20-6-4[/tex]

Simplifying the expression, we have,

[tex]20-10=10[/tex]

Since, 10 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20-6-4[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option C is not the correct answer.

Option D: [tex]20 \div 6-4[/tex]

Using PEMDAS and simplifying the expression, we have,

[tex]$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$[/tex]

Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20 \div 6-4[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option D is the correct answer.

Option E: [tex]\frac{1}{6} (20-24)[/tex]

Simplifying the expression, we have,

[tex]$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]

Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]\frac{1}{6} (20-24)[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option E is the correct answer.

Option F: [tex](20-24) \div 6[/tex]

Simplifying the expression, we have,

[tex]$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]

Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-24) \div 6[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option F is the correct answer.

To solve 6(x + 4) = 20, we isolate x to get x = -2/3. The correct expressions representing the solution are E. 1/6(20 - 24) and F. (20 - 24) / 6.

To solve the equation 6(x + 4) = 20, we need to isolate x.

First, distribute the 6 on the left-hand side:

6x + 24 = 20

Next, subtract 24 from both sides:

6x = -4

Finally, divide by 6:

x = -4/6 = -2/3

Now, let's analyze the given choices:

Therefore, the correct choices are E and F.

Answer:

The people forming the line form a well ordered set, this means, every non empty subset has a minimum. In other words, in any smaller (but non empty) set of people there will always be one that is last in the line.

Lets take the subset formed of all the Women in the line. This subset in non empty because there is a women in the line (the first person in the line is a women), therefore, there is a women that is behind every other women in the line; this women can only have men behind, if any. If she had no men behind her, then she should be last in the line, bacause the doesnt have any men or women behind her. This is a contradiction because there is a man at the end of the line, not a woman. This shows that this woman that is behind every other woman has men behind, in particularly immediately behind, her.

Using well - ordering property in mathematical induction, we have been able to prove that; if n people stand in a line, where n is a positive integer, then somewhere in the line there is a woman directly in front of a man.

Now, we want to prove that  If n people stand in a line, where  n is a positive integer, and if the first person in the line is a woman and the last person in line is a man, then somewhere in the line, there is a woman directly in front of a man.

Now, let us deduce as follows;

Thus;

When n = k + 1, what we will get is that;

- A new person is before a woman that is directly in front of a man.

- The new person is after the man directly after the woman.

- A new person is added between the woman and the man.

In conclusion;

For every positive integer n(n > 2), there is always a woman directly in front of a man.

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Answer:

y = -5x + 6

Step-by-step explanation:

y = 1/5 x + 4/5

so that two lines are perpendicular, its slope must be opposite and reciprocal

y = m x + b

m: slope           perpendicular  -1/m

if our formula is     y = 1/5 x + 4/5

m = 1/5

so the slope of our new formula will be

m' = -5/1

m' = -5

now if you tell us that you have to go through a certain point  (1/1)

we just have to replace the values ​​in the following formula and solve

y - y1 = m ( x - x1)

y - 1 = -5 ( x - 1)

y = -5x + 5 + 1

y = -5x + 6

Answer:

[tex]x_1=3.55[/tex]

[tex]x_2=-1.55[/tex]

Step-by-step explanation:

we know that

If the vertex is  (1,-13) and the y-intercept is  (0.-11) (y-intercept above the vertex), we have a vertical parabola open upward

The equation of a vertical parabola written in vertex form is equal to

[tex]y=a(x-h)^2+k[/tex]

where

a is a coefficient

(h,k) is the vertex

substitute the given value of the vertex

[tex]y=a(x-1)^2-13[/tex]

Find the value of a

Remember that we have the y-intercept

For x=0, y=-11

substitute

[tex]-11=a(0-1)^2-13[/tex]

[tex]a=13-11\\a=2[/tex]

so

[tex]y=2(x-1)^2-13[/tex]

Find the x-intercepts

For y=0

[tex]2(x-1)^2-13=0[/tex]

[tex]2(x-1)^2=13[/tex]

[tex](x-1)^2=6.5[/tex]

[tex]x-1=\pm\sqrt{6.5}[/tex]

[tex]x=1\pm\sqrt{6.5}[/tex]

[tex]x_1=1+\sqrt{6.5}=3.55[/tex]

[tex]x_2=1-\sqrt{6.5}=-1.55[/tex]

Answer: Danny had 65 coins altogether in his collection.

Step-by-step explanation:

Let x represent the number of coins that Danny has in his collection.

20% of his collection are quarters. This means that the number of quarters that Danny has in his collection is

20/100 × x = 0.2 × x = 0.2x

If Danny has 13 quarters, it means that

0.2x = 13

Dividing the left hand side and the right hand side of the equation by 0.2, it becomes

0.2x/0.2 = 13/0.2

x = 65

Answer:

Option 5) 23.5% is a parameter and 28% is a statistic

Step-by-step explanation:

We are given the following in the question:

"According to the U.S. Census bureau, 23.5% of people in the United States are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18."

Population of interest:

People in the United States

Parameter:

23.5% of people in the United States are under the age of 18

Sample:

Random sample of 250 residents of a small town in Ohio

Statistic:

28% of the sample was under 18

Thus, the correct answer is

Option 5) 23.5% is a parameter and 28% is a statistic

Answer:

The estimate is less than the actual length of the CD.

Step-by-step explanation:

Consider the provided information.

Maurice's new CD has 12 songs. Each song lasts between 3 and 4 minutes.

That means the minimum length of the CD should be: 12×3=36 minutes.

The maximum length of the CD should be: 12×4=48 minutes

He estimates that the whole CD is about 30 minutes long.

30 minutes is less than 36 minutes.

That means, the estimate is less than the actual length of the CD.

Hence, the correct statement is: The estimate is less than the actual length of the CD.

Answer:

  see below

Step-by-step explanation:

The formula is the same whether the rate of change is positive or negative. Here, it is negative.

  A = Pe^(rt)

for P = 4000, r = -0.10. Then you have ...

  A = 4000e^(-0.10t)

Answer:

y=-5x+55

Step-by-step explanation:

i had a quiz and i got the correct answer on the test corrections your welcome

The total number of people surveyed is 134. The number of people who listened to either rap or alternative rock is 76. The number of people who listened to heavy metal only is 1.

To solve this problem, we can use a Venn diagram to organize the given information. Let's start by filling in the total number of people surveyed, which is the sum of those who listened to rap, heavy metal, alternative rock, and none of the three channels. From the given information, we have:

To find the total number of people surveyed, we add these numbers:

37 + 30 + 49 + 18 = 134.

Therefore, 134 people were surveyed.

b. To find the number of people who listened to either rap or alternative rock, we need to add the number of people who listened to rap and the number of people who listened to alternative rock, while making sure we don't double count those who listened to both:

37 + 49 - 10 = 76.

Therefore, 76 people listened to either rap or alternative rock.

c. To find the number of people who listened to heavy metal only, we need to subtract those who listened to heavy metal and either rap or alternative rock from the total number of people who listened to heavy metal:

30 - 13 - 16 = 1.

Therefore, 1 person listened to heavy metal only.

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Answer:

[tex]cos \frac{\theta}{2}= 0.894[/tex].

Step-by-step explanation:

Given:

[tex]cos\ \theta= \frac35[/tex]

We need to find [tex]cos \ \frac{\theta}{2}[/tex]

Solution:

[tex]cos\ \theta= \frac35[/tex]

First we will find the value of [tex]\theta[/tex].

Now taking [tex]cos^{-1}[/tex] on both side we get;

[tex]\theta= cos^{-1} \ \frac{3}{5}\\\\\theta = 53.13[/tex]

Now we will find the [tex]\frac{\theta}{2}[/tex].

[tex]\frac{\theta}{2}[/tex] = [tex]\frac{53.13}{2} = 26.565[/tex]

Now we will find [tex]cos \ \frac{\theta}{2}[/tex] we get;

[tex]cos \frac{\theta}{2}=cos\ 26.565 = 0.894[/tex]

Hence [tex]cos \frac{\theta}{2}= 0.894[/tex].

Answer:

+/- (2\sqrt(5))/(5)

Step-by-step explanation:

Answer: The total amount that he paid for the suit is $170

Step-by-step explanation:

The original price of the suit was $260.

Mr.Nguyen bought a suit that was on sale for 40% off the original price. This means that the amount of discount in the suit is

40/100 × 260 = 0.4 × 260 = $104

The sale price would be

260 - 104 = $156

He paid 9% sales tax on the sale price. This means that the amount of sales tax that he paid is

9/100 × 156 = 0.09 × 156 = $14.04

The total amount that he paid for the suit, including tax is

156 + 14.04 = $170 to the nearest dollar

Answer:

d.  His own

Step-by-step explanation:

John is the leader of the particular project team. He is in charge of delegating different tasks to his team members and also endure that everything is in order. He will also develop the necessary agenda and formulate the final report of the project. Therefore, the name that will be attached on the final tasks is his own.

Tom, the representative from top management, should be responsible for explaining the project's necessity, as his role allows him to address strategic concerns and ensure buy-in across the team.

In the context of the Joint Application Development (JAD) group, explaining the reason for the project, especially given the internal skepticism about its necessity, is a pivotal responsibility that typically falls onto someone influential and with comprehensive knowledge of the project's goals and business impact. In this scenario, Tom, as the representative from top management, is the most suitable member to address this point on the agenda. Tom's position allows him to articulate the strategic importance of the project to the organization, reassuring the rest of the team and potentially quelling any concerns about its necessity. It is critical that this explanation is conveyed convincingly to ensure buy-in from all members of the team.

It is advantageous for team members to take on tasks that align with their strengths, as suggested in the reference material, but also to challenge themselves and learn by undertaking tasks outside their usual domain, with the support of their colleagues. This approach fosters a collaborative environment and harnesses the diverse skill sets of the team members, leading to a more efficient and innovative project outcome. To help manage this process, tools like the Honeycomb Map encourage the distribution of responsibilities and help with project visualization and tracking.

Answer: 7

Step-by-step explanation:

Given : The list shows the number of viewers of an online music video each day for 5 consecutive days.

5;  35;  245;  1,715;  12,005;

In exponential growth equation : [tex]y=Ab^x[/tex] , A = initial value , b= growth factor and x = time period.

In the given table A = 5  , at x = 0

Growth factor is the common ratio between the consecutive terms.

So [tex]b=\dfrac{35}{5}=7[/tex]

and we can check that it is common between each consecutive terms is 7.

Hence, the factor by which the number of viewers change each day to the first day to the fifth day = 7

The number of viewers changed by a factor of 2401 from the first day to the fifth day.

The number of viewers of an online music video changed each day by multiplying the previous day's viewers by a constant factor. To find this factor, we divide the viewers on the fifth day by the viewers on the first day. By doing this, we get a factor of 12005/5 = 2401.

So, the number of viewers changed by a factor of 2401 from the first day to the fifth day.

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Answer:

We conclude that the statement B is true. The solution is also attached below.

Step-by-step Explanation:

As the inequality graphed on the number line showing that solution must be   < x    (-∞, 3] U [5, ∞)

So, lets check the statements to know which statement has this solution.

Analyzing statement A)

[tex]x^2-3x+5>\:0[/tex]

[tex]\mathrm{Write}\:x^2-3x+5\:\mathrm{in\:the\:form:\:\:}x^2+2ax+a^2[/tex]

[tex]2a=-3\quad :\quad a=-\frac{3}{2}[/tex]

[tex]\mathrm{Add\:and\:subtract}\:\left(-\frac{3}{2}\right)^2\:[/tex]

[tex]x^2-3x+5+\left(-\frac{3}{2}\right)^2-\left(-\frac{3}{2}\right)^2[/tex]

[tex]\mathrm{Complete\:the\:square}[/tex]

[tex]\left(x-\frac{3}{2}\right)^2+5-\left(-\frac{3}{2}\right)^2[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\left(x-\frac{3}{2}\right)^2+\frac{11}{4}[/tex]

So,

[tex]\left(x-\frac{3}{2}\right)^2>-\frac{11}{4}[/tex]

Thus,

[tex]x^2-3x+5>0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

Therefore, option A) is FALSE.

Analyzing statement B)

(x + 3) (x - 5) ≥ 0

[tex]x^2-2x-15\ge 0[/tex]

[tex]\left(x+3\right)\left(x-5\right)=0[/tex]       [tex]\left(Factor\:left\:side\:of\:equation\right)[/tex]

[tex]x+3=0\:or\:x-5=0[/tex]

[tex]x=-3\:or\:x=5[/tex]

So

[tex]x\le \:-3\quad \mathrm{or}\quad \:x\ge \:5[/tex]

Thus,

[tex]\left(x+3\right)\left(x-5\right)\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-3\quad \mathrm{or}\quad \:x\ge \:5\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-3]\cup \:[5,\:\infty \:)\end{bmatrix}[/tex]

Therefore, the statement B is true.

Solution is also attached below.

Analyzing statement C)

[tex]x^2+2x-15\ge 0[/tex]

[tex]\mathrm{Factor}\:x^2+2x-15:\quad \left(x-3\right)\left(x+5\right)[/tex]

So,

[tex]x\le \:-5\quad \mathrm{or}\quad \:x\ge \:3[/tex]

[tex]x^2+2x-15\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-5\quad \mathrm{or}\quad \:x\ge \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-5]\cup \:[3,\:\infty \:)\end{bmatrix}[/tex]

Therefore, option C) is FALSE.

Analyzing statement D)

- 3 < x < 5

[tex]-3<x<5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-3<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-3,\:5\right)\end{bmatrix}[/tex]

Therefore, option D) is FALSE.

Analyzing statement E)

None of the above

The statement E) is False also as the statement B represents the correct solution.

Therefore, from the discussion above, we conclude that the statement B is true. The solution is also attached below.

Find the number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].

Answer:

Therefore, [tex]\frac{37}{36}[/tex] is the number that is  [tex]\frac{1}{3}[/tex] of the way from  [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].

Step-by-step Explanation:

[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]

So,

[tex]2\frac{1}{6}=\frac{13}{6}[/tex]

[tex]5\frac{1}{4}=\frac{21}{4}[/tex]

As the length from [tex]\frac{21}{4}[/tex] to [tex]\frac{13}{6}[/tex] is

[tex]\frac{21}{4}-\frac{13}{6}=\frac{37}{12}[/tex]

Now Divide [tex]\frac{37}{12}[/tex] into 3 equal parts. So,

[tex]\frac{37}{12}\div \:3=\frac{37}{36}[/tex]

As we have to find number that is [tex]\frac{1}{3}[/tex] of the way from  [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex], it means it must have covered 2/3 of the way. As we have divided  [tex]\frac{37}{12}[/tex] into 3 equal parts, which is [tex]\frac{37}{36}[/tex]

Therefore, [tex]\frac{37}{36}[/tex] is the number that is  [tex]\frac{1}{3}[/tex] of the way from  [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].

Answer:

[tex]\left(2x+3\right)[/tex] is in the form [tex]dx+\:e[/tex].

Step-by-step Explanation:

Considering the expression

[tex]2x^2+11x+12[/tex]

Factor

[tex]2x^2+11x+12[/tex]

[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]

[tex]\left(2x^2+3x\right)+\left(8x+12\right)[/tex]

[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2+3x\mathrm{:\quad }x\left(2x+3\right)[/tex]

[tex]\mathrm{Factor\:out\:}4\mathrm{\:from\:}8x+12\mathrm{:\quad }4\left(2x+3\right)[/tex]

[tex]x\left(2x+3\right)+4\left(2x+3\right)[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}2x+3[/tex]

[tex]\left(2x+3\right)\left(x+4\right)[/tex]

Therefore, [tex]\left(2x+3\right)[/tex] is in the form [tex]dx+\:e[/tex].

Keywords: factor, ratio, solution

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Answer:

600 minutes = 10 hours

Step-by-step explanation:

Egan has to drain 21 000 ga of water out of the pool. Let the number of minutes it takes him to drain the pool be x minutes. The equation for determining x can be set up and solved as follows:

[tex]\frac{15 ga}{min}*xmin+\frac{20ga}{min}*xmin = 21000ga\\\\15x+20x=21000\\\\35x= 21000\\\\x = 600[/tex]

600 minutes = 10 hours

Answer:

Step-by-step explanation:

∆ ABE is similar to angle ACD. This means that the ratio of the length of each side of ∆ABE to the length of the corresponding side of ∆ ACD is constant. Therefore,

AB/AC = BE/CD = AE/AD

Therefore,

5/3 = (y + 3)/y

Cross multiplying, it becomes

5 × y = 3(y + 3)

5y = 3y + 9

5y - 3y = 9

2y = 9

Dividing the left hand side and the right hand side of the equation by 2, it becomes

2y/2 = 9/2

y = 4.5

Answer:

y = 4.5.

Step-by-step explanation:

Triangles ABE and ACD are similar, so their corresponding sides are in the same ratio.

AB/AC = AE / AD

Now AD = y + ED = y + 3, so:

3/5 = y / (y + 3)

5y = 3y + 9

2y = 9

y = 4.5.

Answer:

A) [tex]d_{I}=2.5t[/tex]

B)[tex]d_{C}=4.5t[/tex]

C) d=200-7t

D) t=28.57s

Step-by-step explanation:

A) in order to solve this part of the problem, we must remember that velocity is the ratio between a displacement and the time it takes for a body to go from one point to the other. So we can write it like this:

[tex]v=\frac{x}{t}[/tex]

when solvin for the distance x, we get the formula to be:

[tex]x=vt[/tex]

We can use this to write the expression they are asking us for, so we get:

[tex]d_{I}=2.5t[/tex]

B) the procedure for part b is the same as the procedure for par A with the difference that Carolyn's speed is different. So by using the same formula with Carolyn's speed we get:

[tex]d_{C}=4.5t[/tex]

C)

In order to find the distance between Ian and Carolyn, we subtract the distances found on the previous two questions from the 200ft, so we get:

[tex]d=200-d_{I}-d_{c}[/tex]

we can further substitute the d's with the equations we found on the previos two parts of the problem, so we get:

[tex]d=200-2.5t-4.5t[/tex]

which simplififfes to the following:

d=200-7t

D) we can figure the seconds out by substituing the distance for 0 and solving for t, so we get:

0=200-7t

which can be solved for t, lke this:

-7t=-200

[tex]t=\frac{-200}{-7}=28.57[/tex]

The probability of A = 1/4 = 0.25

The probability of B = 4/5 = 0.80

P(A ∩ B) = P(A) * P (B) = (0.25) * (0.80) = 0.20

P(A ∩ B') = P(A) * P (B') = (0.25) * (1-0.80) = 0.05

P(A' ∩ B') = P(A') * P (B') = (1-0.25) * (1-0.80) = 0.15

Answer:

A. P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.25 + 0.80 - 0.20 = 0.85

B. P(A U B') = P(A) + (1 - P(B)) - P(A ∩ B') = 0.25 + (1-0.80) - 0.05 = 0.40

C. P(A' U B') = (1 - P(A)) + (1 - P(B)) - P(A' ∩ B') = (1-0.25) + (1-0.80) - 0.15 = 0.80

The probabilities using the addition rule of probabilities are P(A ∪ B) = 17/20, P(A ∪ B') = 2/5, and P(A' ∪ B') = 4/5.

In solving this problem, we will use the addition rule for probabilities to find the likelihood of different combinations of randomly generated web ad designs based on given design elements.

A. P(A ∪ B)

We'll start by finding the probability of event A (the design color is red) and B (the font size is not the smallest one) occurring independently. Since there are four different colors, the probability of A is 1/4. When it comes to event B, since there are five different font sizes and the event is that the font size is not the smallest one, there are four font sizes that meet the criteria.

Therefore, the probability of B is 4/5. We can now calculate P(A ∪ B) using the formula P(A) + P(B) - P(A AND B). Assuming that the color choice and font size are independent of each other (the choice of one does not affect the choice of the other), the probability of both A and B occurring (A AND B) is simply the product of their separate probabilities: P(A) x P(B) = (1/4) x (4/5) = 1/5.

So, P(A ∪ B) = P(A) + P(B) - P(A AND B) = (1/4) + (4/5) - (1/5) = 1/4 + 16/20 - 4/20 = 1/4 + 12/20 = 5/20 + 12/20 = 17/20.

B. P(A ∪ B')

To find P(A ∪ B'), we first need to calculate P(B'). Since the probability of B is 4/5, the probability of B' (the font size is the smallest one) is the remaining fraction of 1, which is 1/5. We then apply the addition rule, which becomes P(A \∪\ B') = P(A) + P(B') - P(A AND B'), with P(A AND B') being the probability of choosing the red color and the smallest font size. Because A and B' are independent, P(A AND B') = P(A) x P(B') = (1/4) x (1/5) = 1/20.

Therefore, P(A ∪ B') = P(A) + P(B') - P(A AND B') = 1/4 + 1/5 - 1/20 = 5/20 + 4/20 - 1/20 = 8/20 or 2/5.

C. P(A' ∪ B')

To find P(A' ∪ B'), we need to determine the probabilities of A' and B' occurring separately. P(A') is the probability of not choosing the red color, which is the complement of P(A), meaning P(A') = 1 - P(A) = 3/4. P(B') as we calculated before, is 1/5. As these events are independent, P(A' AND B') = P(A') x P(B') = (3/4) x (1/5) = 3/20.

Thus, P(A' ∪ B') = P(A') + P(B') - P(A' AND B') = 3/4 + 1/5 - 3/20 = 15/20 + 4/20 - 3/20 = 16/20 or 4/5.

Answer:

The volume of cube is increasing at a rate 7.5 cubic meter per hour.  

Step-by-step explanation:

We are given the following in the question:

Surface area of cube = 24 square meters.

Let l be the edge of cube.

Surface area of cube =

[tex]6l^2 = 24\\l^2 = 4\\l = 2[/tex]

Thus, at that instant the edge of cube is 2 meters.

[tex]\dfrac{dS}{dt} = 15\text{ square meters per hour}\\\\\dfrac{d(6l^2)}{dt} = 15\\\\12l\dfrac{dl}{dt} = 15\\\\\dfrac{dl}{dt} = \dfrac{15}{12\times 2} = \dfrac{15}{24}[/tex]

We have to find the rate of change in volume.

Volume of cube =

[tex]l^3[/tex]

Rate of change of volume =

[tex]\dfrac{dV}{dt} = \dfrac{d(l^3)}{dt} = 3l^2\dfrac{dl}{dt}\\\\\dfrac{dV}{dt} = 3(2)^2\times \dfrac{15}{24} \\\\\dfrac{dV}{dt} = 7.5\text{ cubic meter per hour}[/tex]

Thus, the volume of cube is increasing at a rate 7.5 cubic meter per hour.

The rate of change of the volume of the cube at the given instant is; dV/dt = 7.5 m³/h

Surface area is increasing at a rate of 15 m²/h

Thus, dS/dt = 15 m²/h

Now, at a certain instant the surface area of the cube is 24 m².

Formula for cube surface area is; S = 6l²

Thus;

6l² = 24

l² = 24/6

l² = 4

l = √4

l = 2 m

From S = 6l², differentiating both sides with respect to t gives;

dS/dt = 12l(dl/dt)

We know that dS/dt = 15

Thus;

12l(dl/dt) = 15

dl/dt = 15/(12l)

putting 2 for l gives;

dl/dt = 15/(12 * 2)

dl/dt = 0.625 m/h

Now formula for volume of a cube is; V = l³

Differentiating both sides with respect to t gives;

dV/dt = 3l²(dl/dt)

plugging in then relevant values gives;

dV/dt = 3 × 2² × (0.625)

dV/dt = 7.5 m³/h

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Answer:

Part A) see the explanation

Part B) see the explanation

Step-by-step explanation:

Let

x ----> the distance from one side of the tunnel in feet:

f(x) ---> the height of a tunnel in feet

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?

1)

we know that

The x-intercepts are the values of x when the value of the function is equal to zero

In the context of the problem, the x-intercepts are the distances from one side of the tunnel when the height of the tunnel is equal to zero

2)

The maximum value of the graph is the vertex

The x-coordinate of the vertex represent the distance from one side of the tunnel when the height is a maximum value

The y-coordinate of the vertex represent the maximum height of the tunnel

In this problem

the vertex is (18,32)

That means

The maximum height of the tunnel is 32 feet and occurs when the distance from one side of the tunnel is 18 feet

3)

we know that

The function is increasing at the interval [0,18)

That means

As the distance from one side of tunnel increases the height of the tunnel increases too

The function is decreasing at the interval (18,36]

That means

As the distance from one side of tunnel increases the height of the tunnel decreases

Part B: What is an approximate average rate of change of the graph from x = 5 to x = 15, and what does this rate represent?

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change using the graph is equal to

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

In this problem we have

[tex]a=5[/tex]

[tex]b=15[/tex]

[tex]f(a)=f(5)=15[/tex]  ----> see the attached figure

[tex]f(b)=f(15)=31[/tex]  ----> see the attached figure

Substitute

[tex]\frac{31-15}{15-5}=1.6[/tex]

That means

The height of the tunnel increases 1.6 feet as the distance from one side of tunnel increases 1 foot in the interval from x=5 to x=15

Answer:

9 yards

Step-by-step explanation:

Given data:

Needed fabric = 58feet

Available fabric = 10 1/3 yards

To convert yard to feet, the yards are multiplied by 3

10 1/3 yards = 31/3 * 3 = 31 feet.

More fabric needed = 58 - 31

More fabric needed = 27 feet

More fabric needed in yards = 27/3

More fabric needed in yards = 9

Answer:

9

Step-by-step explanation:

it's nine because 1 yard has three feet and um well like yeah