At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 10% fill their tanks (event B). Of those customers using plus, 20% fill their tanks, whereas of those using premium, 30% fill their tanks.

Required:
a. What is the probability that the next customer will request plus gas and fill their tank ?
b. What is the probability that the next customer fills the tank ?
c. If the next customer fills the tank, what is the probability that the regular gas is requested?

Answer:

54% ...

Step-by-step explanation:

this is the answer I guess

The confidence level that produces the widest interval is the one with the highest percentage, which is 54%.

Option B is the correct answer.

A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.

It measures the unusual or extreme a particular data point is compared to the rest of the distribution

We have,

The width of a confidence interval is proportional to the critical value of the corresponding confidence level.

The critical value is determined by the standard normal distribution or t-distribution, depending on the sample size and whether the population standard deviation is known.

In general,

The wider the confidence interval, the less precise the estimate of the population means.

Therefore, we want to choose the confidence level that produces the widest interval, which corresponds to the largest critical value.

For a given sample size,

The critical value increases as the confidence level increases.

For example, the critical value for a 95% confidence level is larger than the critical value for a 90% confidence level.

Therefore,

The confidence level that produces the widest interval is the one with the highest percentage, which is 54%.

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Answer:

[tex]x = \frac{4 \sqrt{3} }{3} [/tex]

Step-by-step explanation:

The explanation is in the picture!❤

Answer:

Hello,

Step-by-step explanation:

Let say t the time the hose is left running

235 ≤ t < 245 (in min)

Let say d the amount of water coming out of the hose each minute

2.05 ≤ d < 2.15 (why d : débit in french)

235*2.05 ≤ t*d < 245*2.15

481.75 ≤ t*d < 526.75    (litres)

Answer:

Lower bound: [tex]495\; \rm L[/tex] (inclusive.)

Upper bound: [tex]505\; \rm L[/tex] (exclusive.)

Step-by-step explanation:

The amount of water from the hose is the product of time and the rate at which water comes out.

When multiplying two numbers, the product would have as many significant figures as the less accurate factor.

In this example, both factors are accurate to two significant figures. Hence, the product would also be accurate to two significant figures. That is:

[tex]240 \times 2.1 = 5.0 \times 10^{2}\; \rm L[/tex] ([tex]500\; \rm L[/tex] with only two significant figures.)

Let [tex]x[/tex] denote the amount of water in liters. For [tex]x\![/tex] to round to [tex]5.0 \times 10^{2}\; \rm L[/tex] only two significant figures are kept, [tex]495 \le x < 505[/tex]. That gives a bound on the quantity of water from the hose.

Answer:

c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.

Step-by-step explanation:

Given :

Groups:

x1 = 69 ; s1 = 19 ; n1 = 38

x2 = 32 ; s2 = 14 ; n2 = 37

1 - α = 1 - 0.95 = 0.05

Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :

The confidence interval obtained is :

(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between

(24.32 ; 39.68) .

Answer:

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Apartment:

38 out of 78, so:

[tex]p_A = \frac{38}{78} = 0.4872[/tex]

[tex]s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566[/tex]

Home:

46 out of 84, so:

[tex]p_H = \frac{46}{84} = 0.5476[/tex]

[tex]s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543[/tex]

Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:

At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:

[tex]H_0: p_A - p_H = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:

[tex]H_1: p_A - p_H \neq 0[/tex]

The test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_A - p_H = 0.4872 - 0.5476 = -0.0604[/tex]

[tex]s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784[/tex]

Value of the test statistic:

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

[tex]z = \frac{-0.0604 - 0}{0.0784}[/tex]

[tex]z = -0.77[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.

Looking at the z-table, z = -0.77 has a p-value of 0.2207.

2*0.2207 = 0.4414

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Answer:

[tex]C=1.15cents[/tex]

Step-by-step explanation:

Generally the equation for is mathematically given by

Charge Power P=4watts

Rate r=12cents/hour

Time consumed T=24

Generally

Power consumed by smartphone in 24 hours

[tex]P_t=P*T\\\\P_t=24*4[/tex]

[tex]P_t=0.096kwh[/tex]

Therefore the Cost will be

[tex]C=12*0.096kwh[/tex]

[tex]C=1.15cents[/tex]

Answer:

y = -3x/2 - 1/2

Step-by-step explanation:

slope m = -3/2

-5 = (-3/2)×3+b

or, b = -1/2

putting it into y = mx + b

y = -3x/2 - 1/2

Answered by GAUTHMATH

Answer:

f'(1) = 7/2

Step-by-step explanation:

We are given the function: [tex]f'(x)=\frac{7}{2\sqrt{x} }[/tex]

To find f'(1), substitute the value for x and evaluate it.

[tex]f'(1)=\frac{7}{2\sqrt{1} }\\\\f'(1)=\frac{7}{2(1)}\\\\f'(1)=\frac{7}{2}[/tex]

Therefore, f'(1) = 7/2.

opposite angles are equal

[tex]\\ \sf\longmapsto 13x+19=84[/tex]

[tex]\\ \sf\longmapsto 13x=84-19[/tex]

[tex]\\ \sf\longmapsto 13x=65[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{65}{13}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Answer:

[tex]\boxed {\boxed {\sf x=5}}[/tex]

Step-by-step explanation:

We are asked to solve for x.

We are given a pair of intersecting lines and 2 angles measuring (13x+19)° and 84°. The angles are opposite each other, so they are vertical angles. This means they are congruent or have the same angle measure.

Since the 2 angles are congruent, we can set them equal to each other.

[tex](13x+19)=84[/tex]

Solve for x by isolating the variable. This is done by performing inverse operations.

19 is being added to 13x. The inverse operation of addition is subtraction. Subtract 19 from both sides of the equation.

[tex]13x+19-19= 84 -19[/tex]

[tex]13x= 84 -19[/tex]

[tex]13x=65[/tex]

x is being multiplied by 13. The inverse operation of multiplication is division. Divide both sides by 13.

[tex]\frac {13x}{13}= \frac{65}{13}[/tex]

[tex]x= \frac{65}{13}[/tex]

[tex]x= 5[/tex]

For this pair of vertical angles, x is equal to 5.

Step-by-step explanation:

A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.

h=-16t^2+16t+32

Answer:

M = (1,3) - 1 right, 3 up

A = (4,0) - 4 right, 0 up

T = (3,6) - 3 right, 6 up

H = (6,2) - 6 right, 2 up

Step-by-step explanation:

Remember, to write the ordered pair using the correct order (x,y) x means it moves either left or right and y moves up or down.

First identify the x-coordinate of a point on a graph. Start at (0,0) which is where the x and y axis meet. (Basically the center of the coordinate plane.)

Then move either left or right and count the number of spaces you move until you are under or over the coordinate. The number of spaces you counted it the x value.

Next, identify the y-coordinate of a point. Now move up or down and count the number of spaces until you meet the coordinate. The number of spaces you counted is the y value.

I tried my best to explain. Let me know if you are still confused.

Answer:

B

Step-by-step explanation:

Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:

[tex]\displaystyle \tan 54^\circ = \frac{16}{BC}[/tex]

Solve for BC. We can take the reciprocal of both sides:

[tex]\displaystyle \frac{1}{\tan 54^\circ} = \frac{BC}{16}[/tex]

Multiply:

[tex]\displaystyle BC = \frac{16}{\tan 54^\circ}[/tex]

Use a calculator. Hence:

[tex]\displaystyle BC \approx 11 .62\text{ units}[/tex]

BC measures approximately 11.62 units.

Our answer is B.

Answer:

9

Step-by-step explanation:

it's as simple as that 9 is 9 away from 0

Answer:

for the first one, simply add g(x) and h(x) :

x+3 + 4x+1 = 5x + 4

the second one, you would multiply them :

(x+3)(4x+1) = 4x^2 + 13x + 3

the last one, you would subtract :

(x+3)-(4x+1) = -3x + 2

and then substitute 2 for 'x' :

-3*2 + 2 = -6 + 2 = -4

Answer:

1. 5x+4

2. [tex]4x^2+13x+3[/tex]

3. -4

Step-by-step explanation:

1. (x+3)+(4x+1)

Take off the parentheses and Add.

5x+4

2. (x+3)(4x+1)

Use the FOIL method to multiply.

[tex]4x^2+x+12x+3[/tex]

[tex]4x^2+13x+3[/tex]

3. First, set up the equation as (g-h)(x)

(x+3)-(4x+1)

x+3-4x-1

Solve.

-3x+2

Substitute in 2 for x.

-3(2)+2

-6+2

-4

Answer:

-2pi/3

Step-by-step explanation:

y = 2 cos 3(x + 2π∕3) +1

y = A sin(B(x + C)) + D  

amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

We have a shift to the left of 2 pi /3

Answer:

A

Step-by-step explanation:

The standard cosine function has the form:

[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]

Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.

We have the function:

[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]

We can rewrite this as:

[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]

Therefore, a = 2, b = 3, c = -2π/3, and d = 1.

Our phase shift is represented by c. Thus, the phase shift is -2π/3.

Our answer is A.

a) The slope of the line MU is [tex]\frac{4}{5}[/tex]

b) The distance between the coordinates of the line MU is √41

c) There are differences and similarities between (a) and (b).

The slope of a line is used to describe how steep the line is. This is expressed mathematically as;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where:

(x1, y1) and (x2, y2 are the coordinate points)

From the graph shown, we are given the coordinates M(-1, 1) and U(4, 5)

a) The slope of the line MU will be expressed as;

[tex]m=\frac{5-1}{4-(-1)}\\m=\frac{4}{5}[/tex]

The slope of the line MU is [tex]\frac{4}{5}[/tex]

The formula for calculating the equation of a line is expressed as y = mx + b

b is the y-intercept.

Substitute m = 4/5 and (-1, 1) into the expression y = mx + b

[tex]1 = -(4/5) + b\\1 = -4/5 + b\\b = 1 +4/5\\b = \frac{5+4}{5} \\b = \frac{9}{5}[/tex]

Get the required equation.

Substitute m = 4/5 and b = 9/5 into y = mx + b

[tex]y=\frac{4}{5}x+\frac{9}{5}\\5y=4x+9\\5y-4x=9[/tex]

The required equation of the line is 5y - 4x = 9

b) The formula for calculating the distance between two points is expressed as;

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the given coordinates in (a) to get the distance MU

[tex]MU=\sqrt{(4-(-1))^2+(5-1)^2}\\MU=\sqrt{(4+1)^2+(5-1)^2}\\MU=\sqrt{(5)^2+(4)^2}\\MU=\sqrt{25+16}\\MU=\sqrt{41}[/tex]

Hence the distance MU is √41

c) There are similarities and differences in the calculations in (a) and (b). The similarities lie in the usage of the change in the coordinates for the calculation of the slope and the distance.

The difference is that we do not need the slope of the line to calculate the distance MU but the slope y-intercept is required to calculate the equation of the line.

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Find the intersection of the two planes. Do this by solving for z in terms of x and y ; then solve for y in terms of x ; then again for z but only in terms of x.

-4x + 2y - z = 1   ==>   z = -4x + 2y - 1

3x - 2y + 2z = 1   ==>   z = (1 - 3x + 2y)/2

==>   -4x + 2y - 1 = (1 - 3x + 2y)/2

==>   -8x + 4y - 2 = 1 - 3x + 2y

==>   -5x + 2y = 3

==>   y = (3 + 5x)/2

==>   z = -4x + 2 (3 + 5x)/2 - 1 = x + 2

So if we take x = t, the line of intersection is parameterized by

r(t) = ⟨t, (3 + 5t )/2, 2 + t⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

(a) The tangent vector to r(t) is parallel to this line, so you can use

v = dr/dt = d/dt ⟨2t, 3 + 5t, 4 + 2t⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in x = -1, y = 1, and z = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

A factor is a natural number that can be multiplied by another natural number to get a value. The greatest common factor refers to when one compares the factors of two numbers, the largest natural number that both numbers have in common is the number's greatest common factor.

In the case of ([tex]m^2[/tex]) and ([tex]m^4[/tex]), the greatest common factor is ([tex]m^2[/tex]) because there are no factors of ([tex]m^2[/tex]) that are larger than it. No number can have a factor larger than itself. Since ([tex]m^2[/tex]) is also a factor of ([tex]m^4[/tex]) it is the greatest common factor of the two numbers.

Using the hypergeometric distribution, it is found that there is a 0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.

The containers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that exactly one of the containers is from the Florida supplier is P(X = 1), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,18,3,11) = \frac{C_{11,1}C_{7,2}}{C_{18,3}} = 0.2831[/tex]

0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.

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The 15 percent-off $123 or 15 percent discount for a item in which the original price is $123 is: $18.45

Using this formula

Amount = Original Price x Discount

Let plug in the formula

Amount= 123 x 15 / 100

Amount = 1845 / 100

Amount = $18.45

Inconclusion the 15 percent-off $123 is $18.45.

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Step-by-step explanation:

[tex](2 - 1 \frac{3 {3}^{2} }{?} [/tex]

Answer:

[tex]y=2[/tex]

Step-by-step explanation:

To solve this question, we can use the point-slope formula as we are given points on the line. This is the format:

[tex]y-y_{1} =m(x-x_{1} )[/tex]

The first step is to find the slope by substituting in two of the points. Let's try using (7,2) and (3,2):

[tex]2-2=m(7-3)\\0=4m\\m=0[/tex]

So now we have found that our slope is 0 meaning it is a flat line (shown by the unchanging y values through all three points).

The form for line equations is:

[tex]y=mx+c[/tex]

However, since our m=0, it is simplified to this:

[tex]y=c[/tex]

The y-value for all the points is 2, meaning c=2 (as it is also the y-intercept)

Therefore our final equation is:

[tex]y=2[/tex]

Hope this helped!

Answer:

12.6 ft

Step-by-step explanation:

I believe the question is:

What is the solution to 5x + 1 +9 - 3

In this case, we solve for X.

5x + 1 + 9 - 3

5x + 10 - 3

5x + 7

5x = -7

x = -7/5

Unfortunately, It is not one of the answer choices it looks like.

Maybe you should reword your question but hopefully this is correct.

If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5

The value of x in a given expression is -7/5.

We have given that,

5x + 1 + 9 - 3

We have to determine the value of x.

A variable is any factor, trait, or condition that can exist in differing amounts or types. Scientists try to figure out how the natural world works

In this case, we solve for X.

5x + 1 + 9 - 3

5x + 10 - 3

5x + 7

5x = -7

x = -7/5

If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5.

Therefore we get the value of x is -7/5.

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Answer:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Now we know that point D, which we can write as (x, y), is at a distance of 8 units from the origin.

Where the origin is written as (0, 0)

We also know that point D is 6 units away along the y-axis.

Then point D could be:

(x, 6)

or

(x, -6)

Now, let's find the x-value for each case, we need to solve:

[tex]8 = \sqrt{(x - 0)^2 + (\pm6 - 0)^2}[/tex]

notice that because we have an even power, we will get the same value of x, regardless of which y value we choose.

[tex]8 = \sqrt{x^2 + 36} \\\\8^2 = x^2 + 36\\64 - 36 = x^2\\28 = x^2\\\pm\sqrt{28} = x\\\pm 5.29 = x[/tex]

So we have two possible values of x.

x = 5.29

and

x = -5.29

Then the points that are at a distance of 8 units from the origin, and that are 6 units away along the y-axis are:

(5.29, 6)

(5.29, -6)

(-5.29, 6)

(-5.29, -6)

Answer:

y=-1/2x+-1

Step-by-step explanation:

try desmos with this equation.

y=mx+b

m=the slope which is -1/2. It goes down 1 it is negative because it is going down, and to the right 2.

b=y-intercept meaning the point which the line crosses the line y .-1

Answer:

C. rotation 180º about the origin

Step-by-step explanation:

Given

Quadrilaterals GWVY and G'W'V'Y'

Required

Describe the transformation rule

Pick points Y and Y'

[tex]Y = (5,-4)[/tex]

[tex]Y' = (-5,4)[/tex]

The above obeys the following rule:

[tex](x,y) \to (-x,-y)[/tex]

When a point is rotated by 180 degrees, the rule is:

[tex](x,y) \to (-x,-y)[/tex]

Hence, (c) is correct

You end up at the point (5, 5).