7x + 3 = 5 and y - 1= 6

Answer:

Step-by-step explanation:

Given that:

X(t) = be the number of customers that have arrived up to time t.

[tex]W_1,W_2[/tex]... = the successive arrival times of the customers.

(a)

Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;

[tex]E(W_!|X(t)=2) = \int\limits^t_0 {X} ( \dfrac{d}{dx}P(X(s) \geq 1 |X(t) =2))[/tex]

[tex]= 1- P (X(s) \leq 0|X(t) = 2) \\ \\ = 1 - \dfrac{P(X(s) \leq 0 , X(t) =2) }{P(X(t) =2)}[/tex]

[tex]= 1 - \dfrac{P(X(s) \leq 0 , 1 \leq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]

[tex]= 1 - \dfrac{P(X(s) \leq 0 ,P((3 \eq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}[/tex]

Now [tex]P(X(s) \leq 0) = P(X(s) = 0)[/tex]

(b)  We can Determine the conditional mean E[W3|X(t)=5] as follows;

[tex]E(W_1|X(t) =2 ) = \int\limits^t_0 X (\dfrac{d}{dx}P(X(s) \geq 3 |X(t) =5 )) \\ \\ = 1- P (X(s) \leq 2 | X (t) = 5 ) \\ \\ = 1 - \dfrac{P (X(s) \leq 2, X(t) = 5 }{P(X(t) = 5)} \\ \\ = 1 - \dfrac{P (X(s) \LEQ 2, 3 (t) - X(s) \leq 5 )}{P(X(t) = 2)}[/tex]

Now; [tex]P (X(s) \leq 2 ) = P(X(s) = 0 ) + P(X(s) = 1) + P(X(s) = 2)[/tex]

(c) Determine the conditional probability density function for W2, given that X(t)=5.

So ; the conditional probability density function of [tex]W_2[/tex] given that  X(t)=5 is:

[tex]f_{W_2|X(t)=5}}= (W_2|X(t) = 5) \\ \\ =\dfrac{d}{ds}P(W_2 \leq s | X(t) =5 ) \\ \\ = \dfrac{d}{ds}P(X(s) \geq 2 | X(t) = 5)[/tex]

Answer:

150 minutes (2.5 hours)

Step-by-step explanation:

We must consider that the total time that the radio program lasted  represents the 100%.

Of that 100% we are told that 20% is dedicated to commercials. So the 30 minutes of commercials correspond to 20% of the air time, which can be represented in the following table:

Percentage of time             time

        20%                       ⇒     30min

and we are looking for how long the show was on the air (the 100%).

So updating the table( I will call x the total time on the air):

Percentage of time             time

        20%                       ⇒     30min

        100%                       ⇒     x

This reationship between three values can be solve by the rule of three: multiply the cross quantities on the table (100 by 30) and divide by the remaining amount (20):

x = 100*30 / 20

x= 3000 / 20

x = 150 minutes

The radio show was 150 minutes (2.5 hours) long.

Answer:

Step-by-step explanation:

(x + 4)^2 - 2 = 7 simplifies to

(x + 4)^2 = 5

We must isolate x.  To do this, take the square root of both sides, obtaining:

x + 4 = ±√5

There are two roots/solutions.  They are:

x = -4 + √5 and x = -4 - √5            

You must include the square root operator (√).  Use "  ^  " to denote exponentiation.

The solutions to the given equation (x + 4)² - 2 = 7 when calculated are; 1 and 7

We are given the equation as;

(x + 4)² - 2 = 7

Add 2 to both sides to get;

(x + 4)² = 9

Find the square root of both sides to get;

x + 4 = ±3

Thus;

x = 3 + 4 and x = -3 + 4

x = 1 and 7

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Answer:

The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:

[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]

[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]

[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]

And the 90% confidence interval would be given (0.131;0.169).

Step-by-step explanation:

We have the following info given:

[tex]n= 955[/tex] represent the sampel size slected

[tex] x = 812[/tex] number of students who read above the eighth grade level

The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:

[tex] \hat p =\frac{955-812}{955}= 0.150[/tex]

The confidence interval for the proportion  would be given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For the 90% confidence interval the significance is [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex], with that value we can find the quantile required for the interval in the normal standard distribution and we got.

[tex]z_{\alpha/2}=1.64[/tex]

And replacing into the confidence interval formula we got:

[tex]0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131[/tex]

[tex]0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169[/tex]

And the 90% confidence interval would be given (0.131;0.169).

Answer:

hope this helps you

Answer:

1 = 130° , 2 =50° , 3 = 85°, 4=45°

Step-by-step explanation:

1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}

2 = 180 - 1 { angles on a straight line equals 180}

= 180 -130 = 50°

4 = 180 - 135 = 45° { angles on a straight line equals 180}

3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}

3 = 135-50 = 85°

Note : sum of opposite interior angles equals external exterior angle, let's prove it:

If we look at the triangle at the bottom left, we have :

85, 45 and r { let's denote r as the missing angle}

So 85 + 45 + r = 180° { sum of angles of a triangle}

By simple arithmetic

r = 180 - ( 85+45) = 180 - 130 = 50°

but r + 4 = 180° { sum of angles in a straight line equals 180°}

4 = 180 - 50 = 130°

So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}

Answer:

If the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.

Step-by-step explanation:

When we performed a two-sided test and the null hypothesis failed to be rejected, when we perform a one-sided test we may reject or not the null hypothesis.

For instance, we have a 5% significance level test, where the test statistic is z=1.8.

For a two-sided test the critical values for α=5% are zc=±1.960. In this situation, the null hypothesis failed to be rejected.

But if we perform a one-sided test with the same significance level, we have a critical value z=1.645 and the conclusion is that the null hypothesis is rejected.

Then, if the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.

We are only sure that if a two-sided test rejects the null hypothesis, a one-side test with same significance level will always reject the null hypothesis.

Answer:

Richard works for $9 per hour

Step-by-step explanation:

Answer:

The answer is proportional. He makes 9$ an hour

Step-by-step explanation:

Your welcome

Answer:

Length = [tex]\frac{189}{4}\ m[/tex]

Width = 21 m

Area of garden = 992.25 [tex]m^{2}[/tex]

Step-by-step explanation:

Side of square = 1 cm

As per the given question figure, we can see that there are 11 square across the length of rectangular garden.

But the garden includes only 9 squares, the corner squares are not in the garden.

So, length of garden = 9 [tex]\times[/tex] 1 = 9 cm

Using the scaling given in the question,

[tex]\dfrac{2}{3}\ cm = 3\dfrac{1}{2}\ m\\[/tex][tex]\Rightarrow \dfrac{2}{3}\ cm = \dfrac{7}{2}\ m[/tex]

[tex]1 cm = \dfrac{\dfrac{7}{2}}{\dfrac{2}{3}} \ m \Rightarrow \dfrac{21}{4}\ m[/tex]

So, length of garden = [tex]\dfrac{21}{4} \times 9 \Rightarrow \dfrac{189}{4}\ m[/tex]

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

And, similarly width contains 4 squares, (Corner squares are excluded)

Width of garden = [tex]\dfrac{21}{4} \times 4 \Rightarrow 21\ m[/tex]

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

Area of garden = Length [tex]\times[/tex] Width

[tex]\Rightarrow \dfrac{189}{4} \times 21\\\Rightarrow \dfrac{3969}{4}\\\Rightarrow 992.25\ m^{2}[/tex]

Answer:

Plot f(x)=x^4+x^3-8x^2-12x

Step-by-step explanation:

Answer:

Step-by-step explanation:

The volume of a cone of height h and circular base of radius r, is [tex] V = \frac{\pi r^2 h}{3}[/tex]. In this case we have that [tex]V=72\pi[/tex].Then, we have that

[tex]72\pi = \frac{\pi r^2 h}{3}[/tex]

multiplying by 3 on both sides and dividing by [tex]\pi[/tex] we have that

[tex]216 = r^2\cdot h[/tex]

Suppose that we know the value of r, then we can find the value of h by solving h, that is

[tex] h = \frac{216}{r^2}[/tex].

So, by choosing any positive value of r, we can find the value for h. Note that if r=6, then [tex]h= \frac{216}{6^2} = 6[/tex]. This means that the amount of credit is infinite :)

Answer:

  2,856,271

Step-by-step explanation:

We presume your equation is intended to be ...

  P = 1,030,000(1.12)^t

To find the prediction in 9 years, put 9 where t is and do the arithmetic.

  P = 1030000(1.12^9) ≈ 2,856,271

In 9 years, the population is predicted to be about 2,856,271.

Answer:

To predict the population in nine years, substitute 9 for t in the equation and simplify:

P = 1,030,000(1.12)9

  = 1,030,000 ∙ 2.77

  = 2,853,100.

Step-by-step explanation:

Answer:

[tex]\frac{6}{40}=\frac{3}{20}[/tex]

Step-by-step explanation:

The experimental probability is the number of times the desired result was obtained over the total number of times the experiment was carried out:

[tex]P=\frac{TimesTheEventOccurs}{TotalNumberOfTrials}[/tex]

In this case the Event we are looking for is rolling a 3 on the number cube.

The total number of trials is:

40

because the student rolls the cube 40 times.

and the times that he got the number 3 (the times the desired event occurs) is:

6

because he rolls a 3 on the number cube 6 times.

Thus our experimental probability to roll a 3 is:

[tex]P=\frac{6}{40}[/tex]

Answer:

[tex]37[/tex]

[tex]77[/tex]

Step-by-step explanation:

[tex]17 \times 2 +3=37\\37 \times 2 +3=77[/tex]

Answer:

37   77

Step-by-step explanation:

2(17) + 3 = 37

2(37) + 3 = 77

Answer:

a. 0.1024

b. 0.8976

Step-by-step explanation:

The probability that x generators don't fail when they are needed follows a binomial distribution, because we have n identical and independent events (2 backup generators) with a probability p of success (1-0.32=0.68) and a probability q of failure (0.32).

So, the probability that x generator success are calculated as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*q^{n-x}\\P(x)=\frac{2!}{x!(2-x)!}*0.68^{x}*0.32^{2-x}[/tex]

Then, the probability that both generators fail during a power outage is equal to the probability that 0 generators success. It is calculated as:

[tex]P(0)=\frac{2!}{0!(2-0)!}*0.68^{0}*0.32^{2-0}=0.1024[/tex]

At the same way, the probability of having a working generator in the event of a power outage is equal to the probability that at least 1 generator success. It is calculated as:

[tex]P(x\geq1)=P(1)+P(2) \\P(1)=\frac{2!}{1!(2-1)!}*0.68^{1}*0.32^{2-1}=0.4352\\P(2)=\frac{2!}{2!(2-2)!}*0.68^{2}*0.32^{2-2}=0.4624\\P(x\geq1)=0.4352+0.4624=0.8976[/tex]

This probability is not high enough for the hospital, both generators fail approximately the 10% of the time when needed.

The probability that the women's team experiences 2 or more concussions is 0.0013.

We are given that;

The concussion rate = 0.63 per 1,000 participation hours

Now,

The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space when these events occur with a known average rate and independently of the time since the last event.

The probability mass function of the Poisson distribution is given by:

[tex]$P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$[/tex]

where X is the number of events occurring in the interval, k is a non-negative integer, and λ is the average rate of events per interval.

a. For collegiate men soccer players, the concussion rate is .41 per 1,000 participation hours.

Therefore, the average number of concussions per hour is λ = 0.41/1000 = 0.00041.

Let X be the number of concussions experienced by the men's team in an hour. Then X follows a Poisson distribution with parameter λ = 0.00041. We want to find P(X ≥ 2). Using the Poisson distribution formula,

[tex]$P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)$$= 1 - \frac{0.00041^0 e^{-0.00041}}{0!} - \frac{0.00041^1 e^{-0.00041}}{1!}$$= 1 - e^{-0.00041}(1 + 0.00041)$$\approx \boxed{0.0002}$[/tex]

b. For collegiate women soccer players, the concussion rate is .63 per 1,000 participation hours.

Therefore, the average number of concussions per hour is λ = 0.63/1000 = 0.00063.

Let Y be the number of concussions experienced by the women's team in an hour. Then Y follows a Poisson distribution with parameter λ = 0.00063. We want to find P(Y ≥ 2). Using the Poisson distribution formula,

[tex]$P(Y \geq 2) = 1 - P(Y < 2) = 1 - P(Y = 0) - P(Y = 1)$$= 1 - \frac{0.00063^0 e^{-0.00063}}{0!} - \frac{0.00063^1 e^{-0.00063}}{1!}$[/tex]

[tex]$= 1 - e^{-0.00063}(1 + 0.00063)$[/tex]

[tex]$\approx \boxed{0.0013}$[/tex]

Therefore, by poisson distribution formula answer will be 0.0013.

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Answer:

F(1) = 0

F(2) = -6 = 0 - 6 x 1 = F(1) - 6 x 1

F(3) = -12 = 0 - 6 x 2 = F(1) - 6 x 2

F(4) = -18 = 0 - 6 x 3 = F(1) - 6 x 3

...

F(n) = F(1) - 6 x (n - 1)

Hope this help!

:)

Answer:

Yes the explanation satisfy the questions stated.

See below for explanation

Step-by-step explanation:

From the question, distance is said to be a function of time and the constant rate of change is 64.

y = 64x + 22

The above is in the form of a Linear equation:

y = mx + c

Where y = dependent variable (distance)

x = independent variable (time)

m = slope = distance/time

c = constant = 22

m = constant rate of change = 64

If x (time) = 4

y (distance) = 278 miles

y = 64(4) + 22

y = 256 + 22

y = 256 + 22

y = 278 miles

Answer:

nclude that distance is a function of time?

include that the constant rate of change, or slope, is 64?

include the equation y = 64x + 22?

say to substitute 4 in for x to get 278 miles?

Step-by-step explanation:

Answer:

A. A larger sample size gives a narrower confidence interval.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

As the sample size increases(n increases), the margin of error decreases, given a narrower, more precise confidence interval.

So the correct answer is:

A. A larger sample size gives a narrower confidence interval.

Answer:

a. The positive difference between Nelson's height and the population mean is: [tex] \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in[/tex].

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: [tex] \\ z = -1.1739 \approx -1.174[/tex] (Nelson's height is below the population's mean 1.174 standard deviations units).

d. Nelson's height is usual since [tex] \\ -2 < -1.174 < 2[/tex].

Step-by-step explanation:

The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where

[tex] \\ z[/tex] is the z-score.

[tex] \\ \mu[/tex] is the population mean.

[tex] \\ \sigma[/tex] is the population standard deviation.

From the question, we have that:

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson​'s height and the​ mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

[tex] \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in[/tex].

That is, the positive difference is 2.7 in.

b. How many standard deviations is that​ [the difference found in part​ (a)]?

To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:

[tex] \\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174[/tex]

In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.

c. Convert Nelson​'s height to a z score.

Using formula [1], we have

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

[tex] \\ z = \frac{68\;in - 70.7\;in}{2.3\;in}[/tex]

[tex] \\ z = \frac{-2.7\;in}{2.3\;in}[/tex]

[tex] \\ z = -1.1739 \approx -1.174[/tex]

This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider​ "usual" heights to be those that convert to z scores between minus2 and​ 2, is Nelson​'s height usual or​ unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

[tex] \\ -2 < z_{Nelson} < 2[/tex]

[tex] \\ -2 < -1.174 < 2[/tex]

Then, Nelson's height is usual according to that statement.  

Answer:

A

Step-by-step explanation:

You can substitute 40 into c, work out the equation and you'll get $75 as the profit. Each candy bar is $2.5 so c would be the number of candy bars she sold.

Answer:68

Step-by-step explanation:

angle sum property

56+y+y-12=180

44+2y=180

2y=180-44=136

y=136/2

=68

VERIFICATION :56+68+56

                         =180

Y =112°

remember the sum of angles in a triangle equals 180°

EDIT : previous answer is right, i messed up with the sign

Step-by-step explanation:

Y= x - 2. Y = 3x + 5

Putting value of y

x - 2 = 3x + 5

-2 - 5 = 3x - x

-7 = 2x

-7/2 = x

Putting value of x

Y = 3(-7/2) + 5

Y = - 10.5 + 5

Y = - 5.5

Answer:

x=-10

Step-by-step explanation:

x+8=-2

x=-10 (Subtract 8)

Answer:

-10

Step-by-step explanation:

1. Write it out.

x+8=-2

2. Get x by itself.

To do this, we have to move the 8, but to do that that we have to move it to the other side of the equation. Because the opposite of addition is subtraction, we have to subtract 8 by both sides.  x+8=-2

                                                                                        -8  -8

                                                                                      x=-10

And that's the answer! Hope this helped :)

Answer:

m = 1/4

Step-by-step explanation:

We want to get the equation in slope intercept form

y = mx+b where m is the slope and b is the y intercept

x  -4y +3 =0

Add 4y to each side

x -4y+3 +4y = 0+4y

x-3 = 4y

Divide each side by 4

1/4x -3/4 =y

the slope is 1/4 and the y intercept is -3/4

Answer:

Step-by-step explanation:

If you draw a horizontal line through the shaded triangle such that it intersects the left vertex, you see that it bisects the 60° angle at that vertex. The measure of x is the same as the measure of either half of that bisected angle, so is 30°.

The pitch associated in the table with an angle of 30° is 7.

Answer:

The total amount of water needed is 540 cubic inches.

Step-by-step explanation:

A cubic prism has three dimension. Lenght l, width w and height h.

It's volume is:

[tex]V = l*w*h[/tex]

In this question:

[tex]l = 12.5, w = 6, h = 8[/tex]

Dimensions in inches, so the volume will be in cubic inches.

[tex]V = 12.5*6*8 = 600[/tex]

The volume is 600 cubic inches.

What is the total amount of water needed, to the nearest cubic inch, to fill 90% of the aquarium with water?

This is 90% of 600. So

0.9*600 = 540

The total amount of water needed is 540 cubic inches.

Answer:

Roughly 15% hourly rate.

Step-by-step explanation:

This is an exponential function that relates to natural growth.

Use the formula A = P*e^(rt)

I have attached the work to your problem.

Please see the attachment below.

I hope this helps!

Answer:

3600

Step-by-step explanation:

It consumes 3600 watt hours per day. Steps are included below.

We know that there is 24 hours in a day so we times 24 by the consumes watt hours that is 15300. So 24 times 15300. After that we need to time 4 times 24+6 = the answer that is 3600. That how you get the answer.

Steps:

1: 24*15300/(4*24+6)=3600

Answer: 3600 watt hours per day

Hope this helps.

Answer:

3,600

Step-by-step explanation:

In the question, there is energy consumption and a rate but not in an easy way.

In order to find out how much watt-hours the light bulb consumes per day, the easiest way is to multiply by the hour to find out how much it uses in a day.

In 4 days and 6 hours there are 102 hours.

[tex]4 \times 24 = 96[/tex]

[tex]96 + 6 = 102[/tex]The hours for 4 days...

[tex]96 + 6 = 102[/tex]

4 days plus 6 hours. The total time...

Now make the watt-hours usage an hourly rate...

[tex]15300 + 102 = 150[/tex]

150 watts/hour...

Take the hourly rate and multiply it by 24 (number of hours in a day) to find out how many watt-hours the lightbulb uses in a day...

[tex]150 \times 24 = 3600[/tex]