According to the general equation for conditional probability, if P(A, B) =4/7

and P(B) =7/8 - what is P(AIB)?

Answer:

480 cubic feet

Step-by-step explanation:

The volume of any rectangular prism can be found by multiplying together the length, width and height. In this case, 8*6*10=48*10=480 cubic feet. Hope this helps!

Answer:

[tex]480 {ft}^{3} [/tex]

Step-by-step explanation:

[tex]area \\ = l \times b \times h \\ = 8 \times 6 \times 10 \\ = 48 \times 10 \\ = 480 {ft}^{3} [/tex]

hope this helps

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Answer:

C.

Step-by-step explanation:

the standard form of a QE is ax2+bx+c. This includes x squared, and when graphed, it forms the graph of a QE, a parabola.

Hope this helps!

The parent function of f(x) = x^2 is the quadratic parent function.

We have given that,

f(x) = x^2

We have to determine the parent function of the given function.

Here the highest power of the x is 2.

We remember that the quadratic equation has the highest power is 2.

The standard form of a quadratic equation is ax^2+bx+c.

This includes x squared and when graphed it forms the graph of a quadratic equation is a  parabola.

We have given function is  f(x) = x^2

Therefore the value of the a,b and  c  are,

a=1

b=0 and c=0

Therefore, option C is correct.

The parent function of f(x) = x^2 is the quadratic parent function.

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Answer:

Step-by-step explanation:

Using either the critical value rule or the p-value rule, a conclusion can be drawn at a level of significance (alpha)

The null hypothesis: u = hypothesized mean

Alternative hypothesis: u > u0 or u < u0 for a one tailed test

Alternative hypothesis for a two tailed test: u =/ u0

To draw a conclusion by failing to reject the null hypothesis as stated then: using critical value

Observed z score > critical z score for both the one and two tailed test.

Or using p value:

P-value > alpha for a one tailed test

P-value > alpha/2 for a two tailed test

Thus, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis will also not be rejected at the same significance level.

Answer:

A

Step-by-step explanation:

(f-g)(x) means that the 2 functions are being subtracted.

[tex]3^{x}[/tex] +10x -(5x-3) =[tex]3^{x}[/tex] +10x-5x+3

simplify!

[tex]3^{x}[/tex] +5x+3

the answer is A

Answer:

Probability that 32 or more from this sample used Internet Explorer as their browser is 0.9015.

Step-by-step explanation:

We are given that according to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market.

A random sample of 70 users was selected.

Let [tex]\hat p[/tex] = sample proportion of users who used Internet Explorer as their browser.

The z score probability distribution for sample proportion is given by;

                            Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, p = population proportion of users who use internet explorer = 53.4%

           [tex]\hat p[/tex] = sample proportion = [tex]\frac{32}{70}[/tex] = 0.457

           n = sample of users = 70

Now, probability that 32 or more from this sample used Internet Explorer as their browser is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.457)

      P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.457) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.457-0.534}{\sqrt{\frac{0.457(1-0.457)}{70} } }[/tex] ) = P(Z [tex]\geq[/tex] -1.29)

                            = P(Z [tex]\leq[/tex] 1.29) = 0.9015

The above probability is calculated by looking at the value of x = 1.29 in the z table which has an area of 0.9015.

Answer: C≈ 37.7cm

Step-by-step explanation: C=2πr=2·π·6≈37.69911cm

Hope this helps.

Answer:

C = 37.7 cm

Step-by-step explanation:

Circumference = 2πr

Where r = 6 cm, π = 3.14

C = 2(3.14)(6)

C = 37.69

C ≈ 37.7 cm

Answer:

3.25 h = 3 h 15 m

Step-by-step explanation:

156 mi * 1h/48 mi = 3.25 h = 3 h 15 m

Answer: 195 min or 3 hr and 15 min

Step-by-step explanation:

We can set up a proportion to solve this problem.

[tex]\frac{48mi}{60 min} =\frac{156 mi}{x}[/tex]

[tex]48x=156*60[/tex]

[tex]48x=9360[/tex]

[tex]x=195 min[/tex]

We can also write this in terms of hours and minutes.

[tex]\frac{60 min}{1 hr} =\frac{195 min}{x}[/tex]

[tex]60x=195[/tex]

[tex]x=3.25[/tex]

3 hr and 15 min

Answer:

4/5

Step-by-step explanation:

[tex]y=\dfrac{1}{3}x+\dfrac{11}{15} \\\\1=\dfrac{1}{3}x+\dfrac{11}{15}\\\\\dfrac{4}{15}=\dfrac{1}{3}x\\\\\dfrac{4}{5}=x[/tex]

Hope this helps!

Answer:

x=4/5

Step-by-step explanation:

y=1/3x+11/15

1=1/3x+11/15

4/15=1/3x

multiply both sides by 3

4/5=x

Answer:

$2

Step-by-step explanation:

Because 3/12 is 0.25 and then you multiply it by 8 to get 2.

Answer:

Dimensions: 165 feet by 110 feet.

Maximum Area =18,150 Square feet

Step-by-step explanation:

Let the dimension of the playground be x and y.

The rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground.

Let the side parallel to one side of the playground =x

Therefore, the total length of fencing =2x+x+2y

P=3x+2y

Six hundred and sixty feet of fencing is used.

We have: 3x+2y=660

3x=660-2y

[tex]x=\dfrac{660-2y}{3}[/tex]

Area of the Playground A=xy

We write the area in terms of y by substitution of x derived above.

[tex]A(y)=y\left(\dfrac{660-2y}{3}\right )\\A(y)=\dfrac{660y-2y^2}{3}[/tex]

We want to maximize the total enclosed area.

To do this, we first find the derivative of A(y).

[tex]A'(y)=\dfrac{660-4y}{3}[/tex]

Next, we solve A'(y) for its critical point.

[tex]A'(y)=\dfrac{660-4y}{3}=0\\660-4y=0\\660=4y\\y=660 \div 4\\y=165$ feet\\[/tex]

Recall that: [tex]x=\dfrac{660-2y}{3}[/tex]

Therefore:

[tex]x=\dfrac{660-2(165)}{3}=\dfrac{660-330}{3}=\dfrac{330}{3}\\x=110$ feet[/tex]

Therefore, the dimensions of the playground that maximize the total enclosed area is 165 feet by 110 feet.

Maximum Area =165 X 110

=18,150 Square feet

Answer:

Dimensions: 165 feet by 110 feet.

Maximum Area =18,150 Square feet

Maximum Area =165 X 110

=18,150 Square feet

Complete Question

The complete qustion is shown on the first uploaded image

Answer:

The correct option is B

Step-by-step explanation:

From the question we are told that

      The sample size  is  [tex]n = 49[/tex]

       The mean is  [tex]\mu = 17ppb[/tex]

       The standard deviation is [tex]\sigma = 14 ppb[/tex]

Generally the standard error of this measurement is mathematically represented as

       [tex]\sigma_z = \frac{\sigma}{\sqrt{n} }[/tex]      

substituting values

      [tex]\sigma_{\= x} = \frac{14}{\sqrt{49} }[/tex]  

     [tex]\sigma_{\= x} = 2[/tex]ppb

Now the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb represented as P(X < 15 )

Next is to find the z value

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

     [tex]z = \frac{15-17}{2}[/tex]

      [tex]z = -1[/tex]

Now checking the z-table for the z-score of  -1 we have  

      [tex]P(X<15) = P(Z < -1 )= 0.16[/tex]

Using the normal distribution and the central limit theorem, it is found that there is a 0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

In this problem:

The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb is the p-value of Z when X = 15, hence:

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{15 - 17}{2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.16

0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.

For more on the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213

Answer:

She would use 136 yards in 4 skirts, 238 yards in 7 skirts, and 306 yards in 9 skirts. Hope this helps

Step-by-step explanation:

Answer:

For the domain since we have a quadratic function then the domain would be all the real numbers:

[tex] D =[x | x \in R][/tex]

And if we want to find the range we can find the vertex:

[tex] v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}[/tex]

And now we can find th coordinate of y of the vertex like this:

[tex] f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875[/tex]

And then the range would be:

[tex] R=[x \geq 2.875][/tex]

Step-by-step explanation:

We have the following function given:

[tex] y = 2x^2 -x +3[/tex]

For this case we can plot the function with a calculator and we got the plot in the figure attached.

For the domain since we have a quadratic function then the domain would be all the real numbers:

[tex] D =[x | x \in R][/tex]

And if we want to find the range we can find the vertex:

[tex] v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}[/tex]

And now we can find th coordinate of y of the vertex like this:

[tex] f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875[/tex]

And then the range would be:

[tex] R=[x \geq 2.875][/tex]

Answer:

Race covers 1911 meters.

Step-by-step explanation:

Triangle ABC represents a race path.

Total distance covered by the race = Perimeter of the triangle ABC

We will apply Sine rule in the given triangle to find the unknown sides.

By Sine rule,

[tex]\frac{SinB}{AC}=\frac{SinA}{BC}=\frac{SinC}{AB}[/tex]

[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}=\frac{Sin60}{AB}[/tex]      [Since m∠A = 180° - (85 + 60)° = 35°]

[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}[/tex]

AC = [tex]\frac{450\times \text{Sin85}}{\text{Sin35}}[/tex]

     = 781.57 meters

[tex]\frac{Sin35}{450}=\frac{Sin60}{AB}[/tex]

AB = [tex]\frac{450\times \text{Sin60}}{\text{Sin35}}[/tex]

     = 679.44 meters

Perimeter of the triangle = AB + BC + AC

                                         = 679.44 + 450 + 781.57

                                         = 1911.01

                                         ≈ 1911 meters

Therefore, the race covers 1911 meters.

Answer:

1911

Step-by-step explanation:

yes

Answer:

-2x/yz

Step-by-step explanation:

You can cancel out terms using division and properties of exponents. x^a/x^b = x^a-b

Answer:

H = 49.56 m

Step-by-step explanation:

We have,

A kite is flying in the air has a 91 ft string attached to it.

The angle of elevation of the kite is 57 degrees.

It is required to find the height of the kite. If we consider a right angled triangle, 91 ft is the hypotenuse. Let H is the height of the kite.

[tex]\cos\theta=\dfrac{H}{91}\\\\H=91\times \cos(57)\\\\H=49.56\ m[/tex]

Hence, the height of the kite is 49.56 m.

Answer:

[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]

And if we solve for a we got

[tex]a=104.5 -1.282*23.62=74.22[/tex]

And the best answer for this case would be:

b) $74.23

Step-by-step explanation:

Let X the random variable that represent the stocks price of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(104.5,23.62)[/tex]  

Where [tex]\mu=104.5[/tex] and [tex]\sigma=23.62[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.90[/tex]   (a)

[tex]P(X<a)=0.10[/tex]   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.282. On this case P(Z<-1.282)=0.10 and P(z>-1.282)=0.90

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]

And if we solve for a we got

[tex]a=104.5 -1.282*23.62=74.22[/tex]

And the best answer for this case would be:

b) $74.23

Answer:

Step-by-step explanation:

What is P(D), the probability that a student in the class has a dog?

D=66%

What is P(C), the probability that a student in the class has a cat?

C=60%

What is P(D and C), the probability that a student in the class has a dog and a cat?

DC=50%

Answer:

A: Ben has been a member longer because 1 year, 2 weeks, 3 days is longer than 372 days.

B: 10 days longer

Step-by-step explanation:

1 year, 2 weeks, 3 days is 382 days -> 365 + 14 + 3 = 382

Answer:

so she saved 82 cents in the interest the month after

Step-by-step explanation:

case 1: payment is $75

interest on 2000 = 0.125/12×2000 = $20.83

so the actual repayment on the balance = (75-20.83) = $54.17

therefore,balance =$(2000-54.7)=$1945.83

interest in the next month = $20.27

case 2: payment is $100

interest on 2000 is still $20.83

repayment = $79.73

balance = $1920.27

interest in the next month = 20.01

so she saved 82 cents in the interest the month after

Answer:

$101

Step-by-step explanation:

Check link explanation.

Answer:

A trinomial

Step-by-step explanation:

Since there are three terms, x^2, 3x, and 8, it is a trinomial

Answer:

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If [tex]Z \leq 2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered to be unusual.

In this question:

[tex]\mu = 8.21, \sigma = 1.9[/tex]

Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

This is the pvalue of Z when X = 5. So

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

[tex]Z = \frac{5 - 8.21}{1.9}[/tex]

[tex]Z = -1.69[/tex]

[tex]Z = -1.69[/tex] has a pvalue of 0.0455.

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

Answer:

B (2.5, 0)

Step-by-step explanation:

2x - y = 5 (multiply all by 4)

8x- 4y = 20

-8x - 4y = - 20

eliminate the 4y

8x- 4y = 20

-8x - 4y = - 20

-------------------- –

16x = 40

x = 40/16 = 2.5

now we substitute x with 2.5

2x - y = 5

2(2.5) - y = 5

y = 0

Answer:

its B

Step-by-step explanation:

took the test

Answer:

Option (E)

Step-by-step explanation:

In the figure attached,

Given a isosceles right triangle with two equal legs measuring [tex]3\sqrt{2}[/tex] units

By Pythagoras theorem,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

Since, hypotenuse = h

Leg 1 = Leg 2 = 3√2

Now we substitute the values,

h² = (3√2)² + (3√2)²

h² = 18 + 18

h = √36

h = 6 units

Therefore, length of the hypotenuse is 6 units.

Option (E) will be the answer.

Using the Pythagorean Theorem, the length of the hypotenuse is: E. 6.

Given that the hypotenuse length of a right triangle is c, and the other legs are a and b, the Pythagorean Theorem states that: c = √(a² + b²).

Thus:

h = √((3√2)² + (3√2)²)

h = √(18 + 18)

h = √36

h = 6

Therefore, using the Pythagorean Theorem, the length of the hypotenuse is: E. 6.

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Answer:

1

Step-by-step explanation:

Answer:

graph of exponential rising up to the right, through the point 0, negative 2

Step-by-step explanation:

I graphed the function on the graph below so you can see that it rises to the right and goes through the point (0,-2).

Answer:

graph of exponential rising up to the right, through the point 0, negative 2

Step-by-step explanation:

f(x)=3x-2

f(0)=3*0-2= -2

(0, -2) is the last given option

Answer:

-37

Step-by-step explanation:

Answer:

I think it is 310 plus 300 and

320 plus 390

Step-by-step explanation:

Answer:

Translated 3 units down 2 units left.

Step-by-step explanation:

It looks like the functions are the same, so if you see, it was translated 3 units down and 2 units left.

Answer:

The probability that the three drivers would wear seat belts is 0.5

Step-by-step explanation:

Given

Percentage of drivers using seat belt = 80%

Number of drivers pulled over = 3

Required

Probability that all three drivers wore seat belt

First, the probability that a driver would wear seat belt has to be calculated.

Let's represent that with P(D)

P(D) is equivalent to the percentage of drivers using seat belt

[tex]P(D) = 80%[/tex]%

[tex]P(D) = \frac{80}{100}[/tex]

[tex]P(D) = 0.8[/tex]

Let the probability that the three drivers would wear seat belts be represented as P(All).

P(All) is calculated as thus;

(Probability that the first driver would wear seat belt) and (Probability that the second driver would wear seat belt) and (Probability that the first driver would wear seat belt).

Mathematically, this means

[tex]P(All) = P(D) * P(D) * P(D)[/tex]

Substitute [tex]P(D) = 0.8[/tex]

[tex]P(All) = 0.8 * 0.8 * 0.8[/tex]

[tex]P(All) = 0.512[/tex]

[tex]P(All) = 0.5[/tex] --- Approximated

Hence, the probability that the three drivers would wear seat belts is 0.5