A recent survey found that about 72.5% of all gasoline purchases at a certain service station chain are paid with a credit or debit card. If 300 gasoline purchases completed at this chain are randomly selected, find the probability that at most 210 of those purchases are paid with a credit or debit card.

The image is missing, so i have attached it.

Answer:

x = 56.44°

Step-by-step explanation:

From the attached image, we can see that this is a right angle triangle which has opposite, adjacent and hypotenuse as sides. Since we want to find the angle x, thus, we can make use of trigonometric ratios.

From the attached image, the side opposite to angle x is 10ft and the hypotenuse is 12 ft.

From trigonometric ratios, we know that, sin x = opposite/hypotenuse

So, sin x = 10/12

x = sin^(-1) (10/12)

x = sin^(-1) 0.8333

x = 56.44°

Answer:

7| 1 1 3 4 5 5 9

8| 5

hope it helps!

Step-by-step explanation:

In a stem leaf plot, the stem is the number in the tens place and all the numbers that follow in the ones place go in leaf

For 7:

The numbers are 71, 71, 73, 74, 75, 75, 79

The stem leaf plot is

7| 1 1 3 4 5 5 9

For 8:

The numbers are (85) only

So the plot is

8| 5

Answer:

We have the equation:

(14 N/mm)*X = Y N/cm

So we want to transform 1/mm to 1/cm.

We know that:

10mm = 1cm

1 = 10mm/1cm (we want to have mm on the numerator, so it cancelates with the mm in the denominator)

then the conversion is from 1/mm to 1/cm is:

X = 10mm/cm

then we have:

(14N/mm)*(10mm/cm) = 140 N/cm

Answer:

48

Step-by-step explanation:

You times 8 by 3 to get 24. Then you multiply 24 by 3 to get 48

Answer:

216

Step-by-step explanation:

8x³

Put x as 3.

8(3)³

Solve for the power first.

8(27)

Multiply both terms.

216

Answer:

[tex] \: \: \: \: \: \: \: \: \: \: \dfrac{x}{5} = 7 \\ \implies \: x = 7 \times 5 \\ \implies \: x = 35[/tex]

So,b. multiplication

Answer:

A. division

Step-by-step explanation:

[tex]x/5=7[/tex]

[tex]x[/tex] is being divided by an integer.

[tex]x=35[/tex]

[tex]35/5=7[/tex]

35 divided by 5 is equal to 7.

Answer:

the gram

Step-by-step explanation:

casegunnell is my gram, follow if your a real g

Following are the calculation to the given points:

When the ABCD is parallelogram:

The properties of parallelogram:

[tex]\to \angle CBD = \angle ADB \\\\[/tex]

[tex]\to \angle BCA = \angle DAC \\\\[/tex]

When the Two-lines are parallel and alternate interior angles are equal:

[tex]\to \Delta BEC \cong \Delta AED \ \ \ \ \ \ \ \{ASA\} \\\\\to \overline {AE} \cong \overline{CE}\\\\ \to \overline{BE} \cong \overline{ED} \\\\[/tex]

When the properties of congruent triangle.

Learn more:

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Answer:

3 - 3i

Step-by-step explanation:

The conjugate is the opposite sign i of the original. So you simply switch the sign of 3i to -3i to find your conjugate.

Answer:

3 - 3i

Step-by-step explanation:

Change the sign only of the imaginary part.

The conjugate of 3 + 3i is 3 - 3i.

Answer:

It would increase by 1

Step-by-step explanation:

Step 1: Find the mean of the original

(9+6+1+1+3)/5 = 4

Step 2: Find the mean of the new

(9+6+1+1+8)/5 = 5

Step 3: Find the difference

5 - 4 = 1

Answer:

The complete factored form of this equation is (d + 6)²

Step-by-step explanation:

The first step in factoring this equation is multiply the first term and the last term together. Out first term is d² and our last term is 36. Since d² does not have a coefficient, then we assume this number to be 1.

1 × 36 = 36

So, now we need to find two factors that multiply to 36 and add together to get 12. Two factors that best represents this is 6 and 6. So, we will plug these numbers into our equation. Replace 12d with 6d + 6d.

d² + 6d + 6d + 36

Group the first two terms together and the last two terms together.

(d² + 6d) + (6d + 36)

Now, find the greatest common factor of each parentheses and factor the terms.

d(d + 6) + 6(d + 6)

From looking at this, we can tell that this equation is a perfect squared equation. So, this means instead of writing both parentheses, we can just write one of the parentheses and square it.

So, the factored form of this equation is (d + 6)²

Answer:

[tex] SE =\sqrt{\frac{p(1-p)}{n}}[/tex]

And replacing we got:

[tex] SE=\sqrt{\frac{0.75*(1-0.75)}{900}}= 0.014[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] n=900[/tex] represent the sample size selected

[tex]p = 0.75[/tex] represent the population proportion

We want to find the standard error and we can use the distribution for the sample proportion and for this case since the sample size is large enough and we satisfy np>10 and n(1-p) >10 we have:

[tex] \hat p \sim N (p,\sqrt{\frac{p(1-p)}{n}})[/tex]

And the standard error is given;

[tex] SE =\sqrt{\frac{p(1-p)}{n}}[/tex]

And replacing we got:

[tex] SE= \sqrt{\frac{0.75* (1-0.75)}{900}}= 0.014[/tex]

Answer:

x = 100 units

Step-by-step explanation:

C = 2.5x^2 + 75x + 25000

To find average cost per unit, divide C by x:

C/x or Average cost (AC) per unit = [tex]\frac{2.5x^2 + 75x + 25000}{x}[/tex] = 2.5x + 75 + 25000/x ⇔ 2.5x + 75 + 25000x^-1 (equation 1)

To find cost minimising, we use differentiation (differentiate equation 1 in respect to x and set it equal to 0):

d(AC)/dx = 0

d(AC)/dx ⇔ 2.5 - 25000x^-2 = 0

2.5 = 25000x^-2

2.5 = [tex]\frac{25000}{x^2}[/tex]

2.5x^2 = 25000

x^2 = 10000

x = [tex]\sqrt{10000}[/tex]

x = 100 units

Cost functions are used to model the outputs from inputs.

The average cost per unit will be minimized at 100 units of production level.

The cost function is given as:

[tex]\mathbf{C(x) = 2.5x^2 + 75x + 25000}[/tex]

Calculate the average cost function using

[tex]\mathbf{A(x) = \frac{C(x)}{x}}[/tex]

So, we have:

[tex]\mathbf{A(x) = \frac{2.5x^2 + 75x + 25000}{x}}[/tex]

Simplify

[tex]\mathbf{A(x) = 2.5x + 75 + \frac{25000}{x}}[/tex]

Differentiate

[tex]\mathbf{A'(x) = 2.5 + 0 - \frac{25000}{x^2}}[/tex]

[tex]\mathbf{A'(x) = 2.5 - \frac{25000}{x^2}}[/tex]

Set to 0

[tex]\mathbf{2.5 - \frac{25000}{x^2} = 0}[/tex]

Collect like terms

[tex]\mathbf{-\frac{25000}{x^2} = -2.5}[/tex]

Cross multiply

[tex]\mathbf{-2.5x^2 = -25000 }[/tex]

Make x^2 the subject

[tex]\mathbf{x^2 = 10000 }[/tex]

Take square roots of both sides

[tex]\mathbf{x = 100 }[/tex]

Hence, the average cost per unit will be minimized at 100 units of production level.

Read more about cost functions at:

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Answer:

after the 1st year

Step-by-step explanation:

$2300 × 75% = $1725.00

$2300-$1725= $575

Answer:

[tex]\boxed{ \ dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t\ }[/tex]

Step-by-step explanation:

it is a long time I have not applied Ito's lemma

I would say the following

for [tex]f(x)=x^2[/tex]

f'(x)=2x

f''(x)=2

so using Ito's lemma we can write that

[tex]dY_t=2V_tdV_t+\phi^2dt[/tex]

[tex]dY_t=2(\theta+\psi V_t^2)dt+2\phi V_tdW_t+\phi^2dt[/tex]

[tex]dY_t=(2\theta+2\psi V_t^2+\phi^2)dt+2\phi V_tdW_t[/tex]

so it comes

[tex]dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t[/tex]

Answer:

(x-4) (x-4)

Step-by-step explanation:

x^2-8x+16

What 2 numbers multiply to 16 and add to -8

-4*-4 = 16

-4+-4 = -8

(x-4) (x-4)

Answer:

correct ^

Step-by-step explanation:

Answer:

Height of tomato plant is the dependent variable

Presence of walnut leaves in the soil is the independent variable

Tomato plants grown without walnut leaves is the control

Step-by-step explanation:

An independent variable is the variable in an experiment that can be altered to test for a certain result. It is independent, or does not change with change in other factors in the experiment. In this case, the presence or absence, or quantity of walnut available in the soil is the independent variable in the experiment.

A dependent variable varies, and depends on the independent variable. It is what is measured in the experiment. In this case, the height of the tomato plants is the dependent variable that depends on the presence, absence or quantity of walnut in the soil.

A control in an experiment, is a replicate experiment, that is manipulated in order to be able to test a single variable at a time. Controls are variables are held constant so as to minimize their effect on the system under study. In this case, some of the tomato plants are planted without walnut in the soil, to test the effect of the absence of the walnut in the soil.

Answer:

X= -3

Y= 7

a= -6

b = -28

C = 9

D= -7

Step-by-step explanation:

2x – 4y = -34

-3x - y = 2

2x – 4y = -34

-12x - 4y = 8

-14x = 42

X= 42/-14

X= -3

-3x - y = 2

-3(-3) -y = 2

9-y = 2

9-2= y

Y= 7

a = 2x

a= 2*-3

a= -6

b = -4y

b = -4*7

b = -28

C= -3x

C= -3*-3

C = 9

D= -y

D= -7

Answer:

A= 2 B=-4

C= -3 D= -1

Step-by-step explanation:

Took it on Edge

Answer:

Step-by-step explanation:

The question is incomplete. The missing information is the group of answer choices. The group of answer choices are

a) none of the above

b) Data provides sufficient evidence, at 1% significance level, to reject the expert's claim. In addition the p-value (or the observed significance level) is equal to P( T < -3.281).

c) Data provides insufficient evidence, at 1% significance level, to support the expert's claim. In addition the p-value (or the observed significance level) is equal to P( Z > 2.896).

d) Data provides sufficient evidence, at 1% significance level, to support the expert's claim. In addition the p-value (or the observed significance level) is equal to P( T >3.355).

e) Data provides insufficient evidence, at 1% significance level, to support the researcher's claim. In addition the p-value (or the observed significance level) is equal to P(Z > 2.896).

Solution:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ ≥ 10

For the alternative hypothesis,

µ < 10

This is a left tailed test.

Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.

Since n = 9,

Degrees of freedom, df = n - 1 = 9 - 1 = 8

t = (x - µ)/(s/√n)

Where

x = sample mean = 13.5

µ = population mean = 10

s = samples standard deviation = 3.2

t = (13.5 - 10)/(3.2/√9) = 3.28

Since α = 0.01, the critical value is determined from the t distribution table. Recall that this is a left tailed test. Therefore, we would find the critical value corresponding to 1 - α and reject the null hypothesis if the test statistic is less than the negative of the table value.

1 - α = 1 - 0.01 = 0.99

The negative critical value is - 2.896

Since - 3.28 is lesser than - 2.896, then we would reject the null hypothesis.

By using probability value,

We would determine the p value using the t test calculator. It becomes

p = 0.0056

Level of significance = 1%

Since alpha, 0.01 > than the p value, 0.0056, then we would reject the null hypothesis. Therefore, At a 1% level of significance, the sample data showed significant evidence that the average useful lifetime of a typical car transimssion which comes with ten years warranty is significantly less than 10 years

The correct option is

a) none of the above

Answer:

50.40% probability that it weighs more than 0.8544 g.

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

[tex]\mu = 0.8551, \sigma = 0.0518[/tex]

If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8544 g.

This is 1 subtracted by the pvalue of Z when X = 0.8544. So

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

[tex]Z = \frac{0.8544 - 0.8551}{0.0518}[/tex]

[tex]Z = -0.01[/tex]

[tex]Z = -0.01[/tex] has a pvalue of 0.4960

1 - 0.4960 = 0.5040

50.40% probability that it weighs more than 0.8544 g.

Answer:

  5.5 in

Step-by-step explanation:

The altitude is (√3)/2 times the length of a side, so the side length is the inverse of that times the length of the altitude:

  side length = (2/√3)(4.8 in) ≈ 5.5 in

Answer:

Step-by-step explanation:

[tex]H_0 : \texttt {null hypothesis}\\\\H_1 : \texttt {alternative hypothesis}[/tex]

The null hypothesis is the drink preferences are not changed at coffee shop.

The alternative hypothesis is the drink preferences are changed at coffee shop.

the level of significance = α = 0.05

We get the Test statistic

[tex]\texttt {Chi square}=\frac{\sum (F_o-F_e)}{F_e}[/tex]

Where, [tex]F_o[/tex] is observed frequencies and

[tex]F_e[/tex] is expected frequencies.

N = 6

Degrees of freedom = df = (N – 1)

= 6 – 1

= 5

the level of significance  α = 0.05

Critical value = 11.07049775

( using Chi square table or excel)

Tables for test statistic are given  below

                             F_o                F_e                 Chi square

Americanos           115                 153                9.4379

Capp.                     88                  94.5             0.447

Espresso               69                  63                 0.5714

Lattes                    59                  49.5               1.823

Macchiatos           44                   45                 0.022

Other                    75                   45                  20

Total                    450                 450                 32.30

[tex]\texttt {Chi square}=\frac{\sum (F_o-F_e)}{F_e}[/tex] = 32.30

P-value = 0.00000517

( using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

This is because their sufficient evidence to conclude that Drink preferences are changed at coffee shop.

Answer:

I answered this one for you already I think.

Answer:

  17

Step-by-step explanation:

Let x represent the smaller integer. Then we have ...

  (x +1)² +(x +2)² = 40x +5

  2x² +6x +5 = 40x +5

  x² -17x = 0 . . . . . subtract (40x+5), divide by 2

  x(x -17) = 0 . . . . . factor

The solution of interest is x = 17.

The smaller integer is 17.

Answer:

The probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% is 0.9946.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

 [tex]\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The information provided here is:

p = 0.27

n = 423

As n = 423 > 30, the sampling distribution of sample proportion can be approximated by the Normal distribution.

The mean and standard deviation of the sampling distribution of sample proportion are:

[tex]\mu_{\hat p}=p=0.27\\\\\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.27\times(1-0.27)}{423}}=0.0216[/tex]

Compute the probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% as follows:

[tex]P(|\hat p-p|<0.06)=P(p-0.06<\hat p<p+0.06)[/tex]

                           [tex]=P(0.27-0.06<\hat p<0.27+0.06)\\\\=P(0.21<\hat p<0.33)\\\\=P(\frac{0.21-0.27}{0.0216}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.33-0.27}{0.0216})\\\\=P(-2.78<Z<2.78)\\\\=P(Z<2.78)-P(Z<-2.78)\\\\=0.99728-0.00272\\\\=0.99456\\\\\approx 0.9946[/tex]

*Use a z-table.

Thus, the probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% is 0.9946.

Answer:

41 in.

Step-by-step explanation:

You have to use the Pythagorean Theorem.  You have the values for the two sides (length and width).  Now, you need to solve for the hypotenuse (diagonal).

a² + b² = c²

(35.7)² + (20.1)² = c²

1274.49 + 404.01 = c²

1678.5 = c²

√1678.5 = c

c = 40.97

c ≈ 41

The diagonal length is 41 in., to the nearest whole number.

Answer:

The parabolic shape of the door is represented by [tex]y - 32 = -\frac{2}{49}\cdot x^{2}[/tex]. (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

[tex]y - k = C \cdot (x-h)^{2}[/tex]

Where:

[tex]h[/tex] - Horizontal component of the vertix, measured in inches.

[tex]k[/tex] - Vertical component of the vertix, measured in inches.

[tex]C[/tex] - Parabola constant, dimensionless. (Where vertix is an absolute maximum when [tex]C < 0[/tex] or an absolute minimum when [tex]C > 0[/tex])

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

[tex]V (x,y) = (0, 32)[/tex] (Vertix)

[tex]A (x, y) = (-28, 0)[/tex] (x-Intercept)

[tex]B (x,y) = (28. 0)[/tex] (x-Intercept)

The following equation are constructed from the definition of a parabola:

[tex]0-32 = C \cdot (28 - 0)^{2}[/tex]

[tex]-32 = 784\cdot C[/tex]

[tex]C = -\frac{2}{49}[/tex]

The parabolic shape of the door is represented by [tex]y - 32 = -\frac{2}{49}\cdot x^{2}[/tex]. Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

[tex]y -32 = -\frac{2}{49} \cdot x^{2}[/tex]

[tex]x^{2} = -\frac{49}{2}\cdot (y-32)[/tex]

[tex]x = \sqrt{-\frac{49}{2}\cdot (y-32) }[/tex]

If y = 22 inches, then x is:

[tex]x = \sqrt{-\frac{49}{2}\cdot (22-32)}[/tex]

[tex]x = \pm 7\sqrt{5}\,in[/tex]

[tex]x \approx \pm 15.652\,in[/tex]

Head must 15.652 inches away from the edge of the door.

Answer:

domain = {-5, -3, -2, 4, 8, 12}

Step-by-step explanation:

The domain is the set containing the x-coordinates of all ordered pairs.

domain = {-2, -3, 12, 8, 4, -5}

If you'd like, you can put the numbers in ascending order:

domain = {-5, -3, -2, 4, 8, 12}

Answer:

It can travel 45 / 2 = 22.5 miles per gallon so the answer is 22.5 * 5.6 = 126 miles.

Answer:

5/33649= approx 0.00015

Step-by-step explanation:

Total number of outcomes are  C24 6= 24!/(24-6)!/6!=19*20*21*22*23*24/(2*3*4*5*6)= 19*14*22*23

Half of the Committee =3 persons. That mens that number of the women in Commettee=3.  3 women from 6 can be elected C6  3  ways ( outputs)=

6!/3!/3!=4*5*6*/2/3=20

So the probability that 3 members of the commettee are women  is

P(women=3)= 20/(19*14*22*23)=5/(77*19*23)=5/33649=approx 0.00015

The probability that precisely half of the members will be women is;

P(3 women) = 0.1213

This question will be solved by hypergeometric distribution which has the formula;

P(x) = [S_C_s × (N - S)_C_(n - s)]/(NC_n)

where;

S is success from population

s is success from sample

N is population size

n is sample size

We are give;

s = 3 women (which is precisely half of the members selected)

S = 6 women

N = 24 men and women

n = 6 people selected

Thus;

P(3 women) = (⁶C₃ * ⁽¹⁸⁾C₍₃₎)/(²⁴C₆)

P(3 women) = (20 * 816)/134596

P(3 women) = 0.1213

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Answer:

The longer diagonal has a length of 7.3 meters.

The angles are 31.65° and 18.35°

Step-by-step explanation:

If one angle of the parallelogram is 50°, another angle is also 50° and the other two angles are the supplement of this angle. so the other three angles are:

50°, 130° and 130°.

The longer diagonal will be the one opposite to the bigger angle (130°), and this diagonal divides the parallelogram in two triangles.

Using the law of cosines in one of these two triangles, we have:

[tex]diagonal^2 = a^2 + b^2 - 2ab*cos(130\°)[/tex]

[tex]diagonal^2 = 3^2 + 5^2 - 2*3*5*(-0.6428)[/tex]

[tex]diagonal^2 = 53.284[/tex]

[tex]diagonal = 7.3\ meters[/tex]

So the longer diagonal has a length of 7.3 meters.

To find the angles that this diagonal forms with the sides, we can use the law of sines:

[tex]a / sin(A) = b/sin(B)[/tex]

[tex]5 / sin(A) = diagonal / sin(130)[/tex]

[tex]sin(A) = 5 * sin(130) / 7.3[/tex]

[tex]sin(A) = 0.5247[/tex]

[tex]A = 31.65\°[/tex]

The other angle is B = 50 - 31.65 = 18.35°

Please check the image attached for better comprehension.