Allan works at the DMV and has 9 appointments for the Driver’s
License. He estimates that the probability of the student passing
the test is 0.80.
What is the probability that no greater than 6 stud

Answer:

1.59 ft.. sort of

Step-by-step explanation:

4th and final attempt:

10 * 5 + 2(10x + 2x) + 2(5x) = 104

50 + 2(12x) + 10x = 104

50 + 24x + 10x = 104

50 + 34x = 104

34x = 104 - 50

34x = 54

x = 54 / 34

x ~= 1.59

Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:

We had 21 dollars and we spent 5x on the notebooks, this can be express as:

Finally we know that this is equal to the six dollars we had at the end, then we have the equations:

Solving for x we have:

Therefore each notebook cost $3

The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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If two independent events a and b have p(a) > 0, p(b) > 0. The statement that a and b are mutually exclusive events is false.

If two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event occurring. In other words, the probability of A and B both occurring is equal to the product of their individual probabilities: P(A and B) = P(A) x P(B).

Mutually exclusive events, on the other hand, are events that cannot occur at the same time. If one event occurs, then the other event cannot occur. The probability of both events occurring is zero: P(A and B) = 0.

So, two events A and B can be independent without being mutually exclusive, and they can be mutually exclusive without being independent. The only requirement for independence is that P(A and B) = P(A) x P(B), while the requirement for mutual exclusivity is that P(A and B) = 0.

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The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

What is the discriminant of a polynomial?

The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.

It is represented as ‘D’

D = b² - 4ac

Where,

a is the coefficient of x²

b is the coefficient of x

c is a constant term

x² + 5x + 4 = 0

We have given:

x² + 5x + 4 = 0

Comparing the equation with the standard form.

a = 1, b = 5 and c = 4

Substituting it in the formula

D = 5² - 4 × 1 + 4

By further calculation

D = 25 - 16

D = 9,

The quadratic roots are real and distinct

Therefore, the value of b² - 4ac is 9.

Hence, The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

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Answer:

17/20 or 0.85

Step-by-step explanation:

hope this helps

Answer:

2, 3, 4, 5

Step-by-step explanation:

Answer:

I believe 4 of these are correct,

answer choice, 2,3,4and

Step-by-step explanation:

2 and 3 are correct because of the inverse of the parallel theorem and answer choice 4 is just a straight line has an angle of 180. Since angle 3 corresponds to angle 7 also meaning they are congruent. We can say angle 1 and 7 add up to 180. As for answer 5, it is the same side interior thereom

Kaelyn wants to use yarn to make hats and scarves. Each hat requires 0.2 kg of yarn, while each scarf requires 0.1 kg. She plans to make 333 times more scarves than hats and use a total of 555 kg of yarn.

Let h be the number of hats and s be the number of scarves Kaelyn makes. The first equation represents the total yarn used, which is 0.2h (for hats) plus 0.1s (for scarves) equal to 555 kg. The second equation represents the ratio of scarves to hats, where s is 333 times greater than h, i.e., s = 333h. So the system of equations is:

0.2h + 0.1s = 555

s = 333h

Kaelyn plans to use her yarn to make hats and scarves, with hats requiring 0.2 kilograms of yarn and scarves needing 0.1 kilograms. She aims to make 333 times more scarves than hats using a total of 555 kilograms of yarn.

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Answer:

It took Pedro  3.81 hours to reach the lake.

Step-by-step explanation:

Time taken by Mike to hike a lake = 4.5 hours

Average rate of Mike while hiking the lake = \(2\frac{1}{5}\ miles/hr\)

Formula for distance can be seen as:

\(Distance = Speed\times Time\)

Distance traveled by Mike = \(4.5 \times 2\frac{1}{5} = 4.5\times \frac{11}{5} = 9.9\ miles\)

Rate of Pedro while hiking the same distance = \(2\frac{3}{5}\ miles/hr = \frac{13}{5}\ miles/hr\)

Given that, Pedro also travels the same distance.

And we have to find the Time.

\(Time = \dfrac{Distance}{Speed}\)

\(Time = \dfrac{9.9}{\frac{13}{5}}\\\Rightarrow Time = \dfrac{9.9\times 5}{13} = \bold{3.81\ hours}\)

It took Pedro  3.81 hours to reach the lake.

Given an angle that is positive, less than 360°, and coterminal with 395° is 35°.

Subtract 360° from 395°.

We know that 1 revolution is equal to 360°.

Therefore, a positive angle that is less than 360° and coterminal with 395° is 35°.

When an angle is less than 360° and shares the same terminal side with another angle that is less than 360°, then the angle is referred to as a coterminal angle.

In other words, the two angles have the same initial side and terminal side but can be either positive or negative.

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Answer:

If this is a parallelogram:

∠y = 112°

corners opposite the 112° corners = 68°      [(360° - 112° - 112°)/2 = 68°]

∠z = 68° - 40° = 28°

∠x = ∠z = 28°

Answer:

x = 28°, y = 112°, z = 28°

Step-by-step explanation:

suppose it's a parallelogram,

in a parallelogram, opposite angles are congruent: y = 112°

40 + 112 + x = 180

=> x = 28°

If 2 lines are cut by a transversal, then the alternate interior angles are congruent: x = z => 28° = z

Answer:

equation

Step-by-step explanation:

Equations have equals signs, expressions do not

15x-10 is an expression

9+5 = 32 is an equation  ( it is a wrong equation)

Answer:

24

Step-by-step explanation:

She visits 3 temples one by one

She offers 1/2 of what she has in the baske

She is left with 3 flowers

If she gave 1/2 of what she had left to the 3rd, and the other half was 3

Then it means she gave the 3rd 3 flowers

So 3 is 1/8th of what she had at the beginning

Multiply 3*8 and you get 24

Hope this helps ^_^

The deposit is given as follows:

$7,502.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for this problem are given as follows:

t = 4, A(t) = 10000, r = 0.0725, n = 4.

Hence the deposit is obtained as follows:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(10000 = P\left(1 + \frac{0.0725}{4}\right)^{4 \times 4}\)

1.33296156P = 10000

P = 10000/1.33296156

P = $7,502.

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The maximum possible daily profit is $19,050. In the synthetic division: -3 | 5 9 -4 -5 -15 18 -42 5 -6 14 -47

The dividend is the polynomial being divided, which is represented by the coefficients in the synthetic division. In this case, the dividend is:

5x^10 + 9x^9 - 4x^8 - 5x^7 - 15x^6 + 18x^5 - 42x^4 + 5x^3 - 6x^2 + 14x - 47

To find the maximum possible daily profit, we need to find the vertex of the parabola represented by the profit function P(x) = -30x^2 + 1560x - 1470.

The vertex of a parabola can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic term and linear term, respectively.

In this case, a = -30 and b = 1560. Plugging these values into the formula, we have:

x = -1560 / (2(-30))

x = -1560 / (-60)

x = 26

So, the maximum possible daily profit occurs when x = 26 cars produced per shift.

To find the maximum profit, we substitute this value back into the profit function:

P(26) = -30(26)^2 + 1560(26) - 1470

P(26) = -30(676) + 40,560 - 1470

P(26) = -20,280 + 40,560 - 1470

P(26) = 19,050

Therefore, the maximum possible daily profit is $19,050.

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The total value of the investment after 3 years given the amount invested is $12,774.

The total value of the investment is the sum of the amount invested and the interest earned.

The total value of the investment = amount invested + simple interest earned

$12,0000 + (principal x time x interest rate)

$12,000 + (12,000 x 0.0215 x 3) = $12,774

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Answer:

6 i think

Step-by-step explanation:

Answer:

24/4 or 6

Step-by-step explanation:

3/4 / 1/8

flip the 1/8 and the sign

3/4x8/1

3x8=24

4x1=4

We would need 3 milliliters of the sample to have 9 million yeast cells for making bread.

To find out how many milliliters of a sample you would need to obtain 9 million yeast cells, given a yeast concentration of 3 million yeast cells/ml, you can follow these steps,

1. Determine the number of yeast cells needed: 9 million yeast cells.
2. Identify the yeast concentration: 3 million yeast cells/ml.
3. Divide the total number of yeast cells needed by the yeast concentration to find the required sample volume.

In this case,

(9 million yeast cells) / (3 million yeast cells/ml) = 3 ml

So, you would need 3 milliliters of the sample to have 9 million yeast cells for making bread.

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We would need 3 milliliters of the sample to have 9 million yeast cells for making bread.

To find out how many milliliters of a sample you would need to obtain 9 million yeast cells, given a yeast concentration of 3 million yeast cells/ml, you can follow these steps,

1. Determine the number of yeast cells needed: 9 million yeast cells.
2. Identify the yeast concentration: 3 million yeast cells/ml.
3. Divide the total number of yeast cells needed by the yeast concentration to find the required sample volume.

In this case,

(9 million yeast cells) / (3 million yeast cells/ml) = 3 ml

So, you would need 3 milliliters of the sample to have 9 million yeast cells for making bread.

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For the given standard deviation the minimum value we would assign is 22.the maximum value we would assign is 88.

To calculate the minimum and maximum values based on the given information, we need to consider the standard deviation and the respective interest rates for the 3-year and 10-year periods.

Given:

S = 26.32 (Initial value)

E = 55 (Expected value)

t = 3 (Years)

Standard deviation = 60% (of the expected value)

3-year interest rate = 2.4%

10-year interest rate = 3.1%

To find the minimum value, we will calculate the value at the end of the 3-year period using the lowest possible growth rate.

Minimum value calculation:

Minimum value = E - (Standard deviation * E) = 55 - (0.6 * 55) = 55 - 33 = 22

Therefore, the minimum value we would assign is 22.

To find the maximum value, we will calculate the value at the end of the 10-year period using the highest possible growth rate.

Maximum value calculation:

Maximum value = E + (Standard deviation * E) = 55 + (0.6 * 55) = 55 + 33 = 88

Therefore, the maximum value we would assign is 88.

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The grocer's selection and weighing of the apples is the experiment, while the specific result of the experiment - an average weight of 165 grams - is the outcome.

An event is a combination of one or more outcomes, such as an average weight between 150 and 165 grams. Finally, the average weight of five apples is the numerical representation of an outcome, which is known as the random variable.
Hi! I'd be happy to help explain these terms in the context of your question:

1. Experiment: Selecting and weighing the apples. This is the activity undertaken to gather data.
2. Outcome: The 165 grams average weight. This is a specific result of the experiment.
3. Event: An average weight between 150 and 165 grams. An event is a combination of one or more outcomes.
4. Random variable: The average weight of five apples. This is a numerical representation of an outcome.

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Answer:

48.852

Step-by-step explanation:

\(5.31=\dfrac{p}{9.2}\)

Multiply both sides by 9.2:

\((5.31)\times9.2=(\dfrac{p}{9.2} )\times9.2\)

\(48.852=p\)

\(\boxed{p=48.852}\)

The lower limit of the 95% confidence interval for the proportion of all X-ray machines that malfunction is [lower_limit]. The upper limit of the 95% confidence interval for the proportion of all X-ray machines that malfunction is [upper_limit].

To calculate the confidence interval, we can use the formula for proportion confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

The sample proportion is the proportion of machines in the sample that malfunctioned. Let's denote this proportion as p.

The margin of error can be calculated using the formula:

Margin of Error = Z ×√[(p × (1 - p)) / n]

Where Z is the critical value corresponding to the desired confidence level, p is the sample proportion, and n is the sample size.

This is a 95% confidence interval, the critical value Z is approximately 1.96 (obtained from the standard normal distribution).

Once we have the sample proportion and the margin of error, we can calculate the lower and upper limits of the confidence interval as:

Lower Limit = p - Margin of Error

Upper Limit = p + Margin of Error

Please note that the exact values for p and the sample size (n) are not provided in the question, so it is not possible to calculate the confidence interval without that information.

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Answer:

Step-by-step explanation: We can begin by rewriting the equation. That would look like so:

3/9 = x/12

We need to solve for x. Our first step is to identify a common denominator. Let's list the multiples of each denominator.

9: 9, 18, 27, 36

12: 12, 24, 36

Our common denominator is 36.

Now, let's cross multiply:

3 x 12 = 36

9 x ? = 36

36 ÷ 9 = 4

x = 4

Final answer: 3/9 = 4/12, where x = 4.

Answer:

The set of numbers 3 in, 4 in, and 5 in can form a triangle. a) is correct

Explanation:

A triangle is possible to be drawn only if the sum of the lengths of any two sides is greater than the length of the third side.

a) Is correct.

Testing all the posible combinations: 3+4>5, 4+5>3, 3+5>4. True. Hence, Option a is the correct choice,

b) Is incorrect

Since 1+7>8 is false, this choice is not correct

c) Is incorrect

Since 3+5>9 is false, this choice is not correct

Answer:

- 4x³ - 2xy - 2y²

Step-by-step explanation:

3x³ + 5xy - 8y² - (7x³ + 7xy - 6y²) ← distribute parenthesis by - 1

= 3x³ + 5xy - 8y² - 7x³ - 7xy + 6y² ← collect like terms

= - 4x³ - 2xy - 2y²

Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

Given the equation:

8x + 7y = -50

We will check the options to find which order pair is the solution of the equation

Point (-6 , -1)

8 * -6 + 7 * -1 = -48 - 7 = -55 ≠ -50

Point ( 0 , -6)

8 * 0 + 7 * - 6 = -42 ≠ -50

Point (-6, 0 )

8 * - 6 + 7 * 0 = -48 ≠ -50

Point (-1 , -6)

8 * -1 + 7 * -6 = -8 - 42 = -50

so, the order pair which is a solution for the equation is (-1 , -6 )

Answer:

2/3 gallons

Step-by-step explanation:

0.67 gallons or 2/3 gallons is used on the fence.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

Amount of gallons = 2 gallons

The amount used on a fence.
= 1/3 of 2 gallons

Now,

1/3 x 2 gallons

= 2/3 gallons

= 0.67 gallons

Thus,

0.67 gallons or 2/3 gallons is used on the fence.

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