"Children under the age of 13 are not allowed to operate a boat." Part A: Write an inequality to show the age of children who are allowed to operate a boat. (5 points) Part B: Describe in words how you can show the solution to this inequality on a number line. (5 points)

Answer:

y-1 = 3(x-2)

Step-by-step explanation:

The point slope form of a line is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-1 = 3(x-2)

Answer:

Step-by-step explanation:

Confidence interval for the difference in the two proportions is written as

Difference in sample proportions ± margin of error

Sample proportion, p= x/n

Where x = number of success

n = number of samples

For district C,

x = 22

n1 = 100

p1 = 22/100 = 0.22

For district M,

x = 26

n2 = 100

p2 = 26/100 = 0.26

Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, the z score for the confidence level of 95% is 1.96

Margin of error = 1.96 × √[0.22(1 - 0.22)/100 + 0.26(1 - 0.26)/100]

= 1.96 × √0.00364

= 0.12

Confidence interval = (0.22 - 0.26) ± 0.12

= - 0.04 ± 0.12

The required  95 percent confidence interval for the difference is ( 0.8, 0.16).

Given that,

A random sample of 100 voters in District C, 22 percent responded yes to The question "Are you in favor of an increase in state spending on the arts?"

An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question.

We have to determine,

A 95 percent confidence interval for the difference.

According to the question,

A random sample of 100 voters in District C, 22 percent responded yes to The question "Are you in favor of an increase in state spending on the arts?"

An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question.

Confidence interval for the difference in the two proportions is written as,

Difference in sample proportions ± margin of error

Sample proportion, p= x/n

Where x = number of success

n = number of samples

From a random sample of 100 voters in District C,

[tex]x = 22\\\\n_1= 100\\\\p_1 = \dfrac{22}{100} = 0.22[/tex]

From a random sample of 100 voters in District M,

[tex]x = 26\\\\n_1= 100\\\\p_1 = \dfrac{26}{100} = 0.26[/tex]

Therefore,

[tex]Margin \ of \ error = \sqrt{\dfrac{p_1(1-p_1}{n_1} + \dfrac{p_2(1-p_2)}{n_2}}[/tex]

To determine the z score, subtract the confidence level from 100% to get b

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since,  the area in the middle, it becomes

1 - 0.025 = 0.975

The z-score corresponding to the area on the z table is 1.96. Thus, the z score for the confidence level of 95% is 1.96,

[tex]Margin \ of \ error = \sqrt{\dfrac{0.22(1-0.22)}{100} + \dfrac{0.26(1-0.26)}{100}}[/tex]

                           [tex]= \sqrt{\dfrac{0.22(0.78)}{100} +\dfrac{0.26(0.76)}{100}}\\\\= \sqrt{\dfrac{0.17}{100}+ \dfrac{0.19}{100}}\\\\= \sqrt{\dfrac{0.36}{100}}\\\\= \sqrt{0.0036}\\\\= 0.06[/tex]

Then, Confidence interval is given as;

[tex](0.22 - 0.26) \pm 0.12\\\\(-0.4) \pm 0.12\\\\(-0.4+0.12 , -0.4-0.12)\\\\(0.8, 0.16)[/tex]

Hence, The required  95 percent confidence interval for the difference is( 0.8, 0.16)

To know more about Confidence interval click the link given below.

https://brainly.com/question/15349022

Answer: 20

Step-by-step explanation: 5 times 4 is 20 times 2 is 40, but when you divide by 1/2 you drop down to 20.

Answer:

y=7

Step-by-step explanation:

Slope: 7-7/4-0=0

Point: (0,7)

pt/slope form:

y-7=(0)(x-0)

y=7

Answer:

38 Units

Step-by-step explanation:

7 each down each side

10 each across top and bottom

2 more for each indent on bottom

7+7+10+10+2+2

14+20+4

38

Answer:

19.82 units

Step-by-step explanation:

The number of units of tile simply refers to the perimeter.

So, we need to find all the sides of the rectangle.

Now, we have AB = 4.24 units and BD = 7.07 units.

So, we can find AD using pythagoras theorem.

So,

(AD)² + 4.24² = 7.07²

(AD)² + 17.978 = 49.985

(AD)² = 49.985 - 17.978

AD = √32.007

AD = 5.66 units

AD = BC = 5.66 units

Likewise, AB = DC = 4.24 units

Thus,

perimeter = 2(5.66) + 2(4.24) = 19.8 units

Closest answer among the options is approximately 19.82

Answer:

19.82 units

Step-by-step explanation:

just took test and got it right

Answer:

105.12 ft^2

Step-by-step explanation:

Area of a rectangle: bh

In this case 8*10.... so area of the rectangle is 80

Area of a circle: pir^2

Half it for a semicircle.

so 1/2 pi r^2

radius is 4 cuz its half of 8.

so 1/2(3.14)(4^2)=(0.5)(3.14)(16)=25.12

Now add up 80+25.12

Total is 105.12

Hope I helped :)

Answer:

The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 394.3 ms

Standard deviation = 84.6 ms

Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.

140.5 = 394.3 - 3*84.6

So 140.5 is 3 standard deviations below the mean.

648.1 = 394.3 + 3*84.6

So 648.1 is 3 standard deviations above the mean.

By the Empirical Rule,

The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.

Answer:

(1,-7/2)

Step-by-step explanation:

The midpoint of (9,2)(-7,-9) is (1,-7/2)

Answer:

1

Step-by-step explanation:

g(-4) means what is the y value when x is -4.

Find x=-4, and when x=-4. y=1

Answer:

1

Step-by-step explanation:

Answer:

C. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale

Step-by-step explanation:

Th Coefficient of Variance is a measure of dispersion that can be calculated using the formula:

[tex]CV = \frac{\sigma_{x} }{\mu_{x} } * 100%[/tex]

Where [tex]\sigma{x}[/tex] is the Standard Deviation

and [tex]\mu_{x}[/tex] is the sample mean

From the formula written above, it is shown that the Coefficient of Variation expresses the Standard Deviation as a percentage of the mean.

Coefficient of variation can be used to compare positive as well as negative data on the ratio and interval scale, it is not only used for positive data.

The Interquartile Range is not a measure of central tendency, it is a measure of dispersion.

Answer:

Ratio of Able's score to Ben=6:1

Ratio of Ben's score to Cal's=1:2

Ratio of able's score to ben;s score to cal's score=6:1:2

Step-by-step explanation:

Let Ben's score =x

Able scored six times Ben's score

Able=6*x

=6x

Cal scored a third of Able's score

Cal=1/3 of 6x

=1/3(6x)

Ratio of Able's score to Ben

6x:x

=6:1

Ratio of Ben's score to Cal's score

x:1/3(6x)

=x:6x/3

=x:2x

=1:2

Ratio of able's score to ben;s score to cal's score=6:1:2

Answer:

18.66 ft/s

Step-by-step explanation:

The distance between you and the elevator is given by:

[tex]h=\sqrt{x^2+y^2}[/tex]

The rate of change for the distance between you and the elevator is given by:

[tex]\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}[/tex]

[tex]-16=\frac{dh}{dy}*\frac{dy}{dt}[/tex]

[tex]\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\[/tex]

Applying the chain rule:

[tex]u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}[/tex]

Therefore, at x=300 and y = 500, dy/dt is:

[tex]-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s[/tex]

The elevator is descending at 18.66 ft/s.

Answer:

nickels- 5, quarters- 11

Step-by-step explanation:

nickel= 5 p,  quarter= 25 p

5x+25(x+6)= 300

30x+150=300

30x=150

x=150/30

x=5 nickels

x+6= 11 quarters

Answer:

Please see steps below

Step-by-step explanation:

In order to factor by grouping, we divide the four terms given into two groups, and extract on each group any common factor  we can.

In our example, we can select the terms: [tex]w^2[/tex]  and [tex]w[/tex] as one of our groups, and [tex]3w[/tex] and 3 in the other group. Then we re-organize the expression as:

[tex](w^2+w)+(3x+3)[/tex]

Now we extract from the first binomial group, the factor [tex]w[/tex] as a common factor of both terms, and from the second group we extract the factor "3" as common factor of those two terms:

[tex](w^2+w)+(3x+3)\\w(w+1)+3(w+1)[/tex]

We notice now that after the extraction, we are left with two exactly equal binomial factors [tex](w+1)[/tex] that appeared in the first group and in the second group. We proceed then to extract it as common factor for the two groups:

[tex]w(w+1)+3(w+1)\\(w+1)(w+3)[/tex]

this last product of two binomials ([tex](w+1)\,(w+3)[/tex] is the result of factoring the original expression.

Answer:

range 11

Step-by-step explanation:

The range is the largest number minus the smallest number

The largest number is 12 and the smallest number is 1

12 - 1 = 11

Answer:

Dear dandrexbox

Answer to your query is provided below

She will burn 351.6 calories if she run 3 miles.

She needs to run 4 miles (approx) per day for a week to burn one pound calories.

Step-by-step explanation:

Explanation for the same is attached in image

Answer:

The area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.

Step-by-step explanation:

To solve this question, we need to find the corresponding probabilities for the standardized values (or z-scores) z = 1.23 and z = 0.86, and then subtract both to obtain the area of the shaded region between these two z-scores.

We need to having into account that a z-score is given by the following formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

Where

A z-score indicates the distance of x from the mean in standard deviations units, where a positive value "tell us" that x is above [tex] \\ \mu[/tex], and conversely, a negative that x is below [tex] \\ \mu[/tex].

The standard normal distribution is a normal distribution with [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex], and has probabilities for standardized values obtained using [1]. All these probabilities are tabulated in the standard normal table (available in any Statistical book or on the Internet).

Using the cumulative standard normal table, for [tex] \\ z = 1.23[/tex], the corresponding cumulative probability is:

[tex] \\ P(z<1.23) = 0.89065[/tex]

The steps are as follows:

Following the same procedure, the cumulative probability for [tex] \\ z = 0.86[/tex] is:

[tex] \\ P(z<0.86) = 0.80511[/tex]

Subtracting both probabilities (because we need to know the area between these two values) we finally obtain the corresponding area between them (two z-scores):

[tex] \\ P(0.86 < z < 1.23) = 0.89065 - 0.80511[/tex]

[tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex]

Therefore, the area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.

We can see this resulting area (red shaded area) in the graph below for a standard normal distribution, [tex] \\ N(0, 1)[/tex], and  [tex] \\ z = 0.86[/tex] and [tex] \\ z = 1.23[/tex].

Answer19/40=x/3.6

By cross multiplication

19*3.6=40*x

68.4 =40x

x=68.4/40

x=1.71

x=

Answer: C

Step-by-step explanation:

[tex]\frac{19}{40} = \frac{x}{3.6}[/tex]     solve by cross product

40x = 68.4   Divide both sides by 40

x =  1.71

Answer:

- Trinomials that can be factored into two binomials are:

1. x² + 5x + 6

Factored to: (x + 3)(x + 2)

2. x² + x - 2

Factored to: (x - 1)(x + 2)

Example of a Trinomial that cannot be factored into two binomials:

x² + 5x + 1

Step-by-step explanation:

- A trinomial is a polynomial that consist of three terms. It is in the form:

ax² + bx + c.

- A binomial is a polynomial that consists of two terms. It is of the form:

bx + c.

A trinomial is said to be factorable if the can be written as a product of two binomials.

Example 1:

The expression: x² + 5x + 6

Can be rewritten as:

x² + 2x + 3x + 6

Grouping this, we have

(x² + 2x) + (3x + 6)

Which becomes

x(x + 2) + 3(x + 2)

Factoring (x + 2), we have

(x + 3)(x + 2)

Which is a product of two binomials as required.

Therefore, the expression is factorable.

Example 2:

The trinomial expression:

x² + x - 2

Can be written as:

x² + 2x - x - 2

= (x² + 2x) - (x + 2)

= x(x + 2) - (x + 2)

Factoring (x + 2), we have

(x - 1)(x + 2)

This a product of two binomials, hence, the tutorial is factorable.

Example 3:

Consider the trinomial:

x² + 5x + 1

This is not factorable, because the term 5x cannot be split into a sum or difference, in such a way that it has a common factor with x² and with 1.

Unlike in the case of Example 1.

x² + 5x + 6

5x was split into the sum of 2x and 3x

That is, x² + 5x + 6 = x² + 2x + 3x + 6

So that, 2x has a common factor, x with x², and 3x has a common factor, 3 with 6.

Answer:

[tex] - 45[/tex]

[tex]2.25( - 2) = - 45 \\ - 45[/tex]

Answer:

a) [tex]V(t) = 24 - 2t[/tex]

b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Step-by-step explanation:

The volume of the tank in terms of the time can be described by the following equation:

[tex]V(t) = V(0) - at[/tex]

In which V(0) is the initial volume and a is the hourly decrease rate.

a. Write a formula that expresses v in terms of t.

The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]

Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]

Then

[tex]V(t) = V(0) - at[/tex]

[tex]V(t) = 24 - 2t[/tex]

b. As t increases from 3 to 6, v varies from _________ to _________

[tex]V(t) = 24 - 2t[/tex]

[tex]V(3) = 24 - 2*3 = 18[/tex]

[tex]V(6) = 24 - 2*6 = 12[/tex]

So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Answer:

The system of inequalities is:

[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]

Step-by-step explanation:

We will write each of the conditions stated in this problem

Patricia wants to buy at least 30 individual songs.

[tex]x\geq30[/tex]

She wants to buy 4 albums at most.

[tex]y\leq4[/tex]

The total expenditure has to be equal or less than $80, when each album cost $10 and each individual song cost $1.

[tex]10x+1y\leq80[/tex]

The system of inequalities is:

[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]

Answer:

a) [tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]

And from the empirical rule we know that this probability is 0.997 or 99.7%

b)[tex] P(195.2 <X<322.2)[/tex]

Using the z score we have:

[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]

[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]

And within one deviation from the mean we have 68% of the values

Step-by-step explanation:

For this case we defien the random variable of interest X as "blood platelet counts" and we know the following parameters:

[tex] \mu = 258.7, \sigma =63.5[/tex]

Part a

We can use the z score formula given by:

[tex] z =\frac{\bar X -\mu}{\sigma}[/tex]

And we want this probability:

[tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]

And from the empirical rule we know that this probability is 0.997 or 99.7%

Part b

For this case we want this probability:

[tex] P(195.2 <X<322.2)[/tex]

Using the z score we have:

[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]

[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]

And within one deviation from the mean we have 68% of the values

Answer:

Step-by-step explanation:

Twelve years ago Jane was five times as old as Anne.  

 J-12=5(A-12)

In three years time, Anne will be half of Jane's age.  

A+3=1/2(J+3)

Simplify and solve this system of equations:

 J-12=5(A-12)

A+3=1/2(J+3)

Answer:

D.

Step-by-step explanation:

So you know you have to have $62 as the base fee.

If you exceed 2 gigabytes, you subtract that by 2 because you want to find how many gigabytes you're going over. You then multiply it by 30 to find the cost.

You get C = 62 + 30(g - 2)

Answer:

anwser is d because it is write.

Step-by-step explanation:

Answer:

P(greater than 1.25 minutes) = 0.8611 (Approx)

Step-by-step explanation:

Given:

Waiting time = 0 - 9 minutes

Find:

Probability that selected passenger has a waiting time greater than 1.25 minutes.

Computation:

⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =

⇒  P(greater than 1.25 minutes) = [9-1.25] / 9

⇒ P(greater than 1.25 minutes) = [7.75] / 9

⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)

Answer:

A

Step-by-step explanation:

Volume of cone = (1/3) πr²h

Answer:

So the diagram couldn't come due to coronavirus?

Answer:

there is no diagram

Step-by-step explanation: