Covert 1/4 to seconds

the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.

There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.

The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:

Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)

Expected gain = 38/13 - 10/13 - 18/13

Expected gain = 10/13 ≈ 0.77

Therefore, the expected gain is $0.77, rounded to the nearest cent.

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To locate the stations and draw cirradius cles on the map of California, follow these steps:

1. Identify the city stations on the map: Find the city stations indicated on the map, such as San Francisco, Los Angeles, and San Diego.

2. Use a compass: Set your compass to the scale provided on the map.

For example, if the scale says 1 inch = 100 km, adjust your compass accordingly.

3. Determine the distance from the epicenter: Based on the information provided, determine the distance from each city station to the epicenter. If it is not provided, refer to additional resources or data.

4. Draw the circles: Place the compass point on each city station and draw a circle with a corresponding to the distance determined in

step 3. Ensure the radius is in scale with the map.

5. Identify the epicenter: The point where all the circles intersect is the approximate location of the epicenter.

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0.18x + 4 - 0.40x = 2

-0.22x = -2

x = 9.09

Therefore, the pharmacist should mix 9.09 liters of 18% alcohol solution and 0.91 liters of 40% alcohol solution to make 10 liters of 20% alcohol solution.

[tex]x=\textit{Liters of solution at 18\%}\\\\ ~~~~~~ 18\%~of~x\implies \cfrac{18}{100}(x)\implies 0.18 (x) \\\\\\ y=\textit{Liters of solution at 40\%}\\\\ ~~~~~~ 40\%~of~y\implies \cfrac{40}{100}(y)\implies 0.4 (y) \\\\\\ \textit{10 Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~10\implies \cfrac{20}{100}(10)\implies 2 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{alcohol only}}&\stackrel{\textit{Liters of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.18&0.18x\\ \textit{2nd Sol'n}&y&0.4&0.4y\\ \cline{2-4}&\\ mixture&10&0.2&2 \end{array}~\hfill \begin{cases} x + y = 10\\\\ 0.18x+0.4y=2 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=10\implies y=10-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{0.18x+0.4(10-x)=2}\implies 0.18x+4-0.40x=2 \\\\\\ -0.22x+4=2\implies -0.22x=-2\implies x=\cfrac{-2}{-0.22}\implies \boxed{x\approx 9.09} \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y\approx 10-9.09\implies \boxed{y\approx 0.91}[/tex]

Answer:

there

Step-by-step explanation:

The variance is 7.2.

We can use the binomial distribution formula to calculate the variance. The formula for the variance of a binomial distribution is

Variance = n × p × (1 - p)

where n is the number of trials, p is the probability of success on each trial, and (1 - p) is the probability of failure on each trial.

In this case, n = 30 (the number of homes on the route), p = 0.48 (the probability of a home having a dog), and (1 - p) = 0.52 (the probability of a home not having a dog).

The postal employee encountered 12 dogs, which means there were 18 homes without dogs. So, the actual probability of success in this case is

P(dogs) = 12/30 = 0.4

Using the formula above, we can calculate the variance

Variance = n × p × (1 - p)

= 30 × 0.4 × 0.6

= 7.2

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The point that partitions segment AB in a 1:4 ratio is (-1, -0.4).

In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 4.

In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:

Q(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have;

Q(x, y) = [(1(7) + 4(-3))/(1 + 4)],  [(1(-10) + 4(2))/(1 + 4)]

Q(x, y) = [(7 - 12)/(5)],  [(-10 + 8)/5]

Q(x, y) = [-5/5],  [(-2)/(5)]

Q(x, y) = [-1, -2/5]

Q(x, y) = [-1, -0.4]

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a. No, w is not in fv1; v2; v3g. There are three vectors in fv1; v2; v3g.

b. There are three vectors in the span of fv1; v2; v3g.

c. No, w is not in the subspace spanned by fv1; v2; v3g. This is because the subspace is the set of all linear combinations of the vectors in the span, and w does not have to be a linear combination of the vectors in the span.

To prove this, we first need to recall the definition of the span: it is the set of all linear combinations of a set of vectors. A linear combination is a sum of the vectors, multiplied by constants. For example, if we have a vector v1, and two constants a and b, then the linear combination of a*v1 and b*v1 is (a + b)*v1. If a vector w is not a linear combination of v1, then w is not in the span of v1.

The same logic applies to the vectors fv1; v2; v3g. If w is not a linear combination of these three vectors, then w is not in the subspace spanned by these three vectors. We can prove this by showing that w cannot be a linear combination of fv1; v2; v3g. This is because the only way to create a linear combination of these vectors is to multiply them by constants, and since w is not one of the vectors, it cannot be multiplied by a constant. Therefore, w is not in the subspace spanned by fv1; v2; v3g.

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In linear equation, The actual height of the statue is 300 feet.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.  

                                  Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

A scale factor of a famous statue uses a scale factor of 250:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?

= 1.2 x 250

The actual height of the statue is 300 feet.

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Answer:(D) 300

Step-by-step explanation: the scale factor is 250:1 and the Hight of the drawing is 1.2 feet you need to multiply 1.2 by 250

1.2 x 250 = 300

Answer:

3

Step-by-step explanation:

Number of people in the choir = 80

Number of women = half of 80 = 40

Number of men in the choir is ¼ of the women = 40/4 = 10

Number of men plus women = 10 +40 = 50

Number of children = 80 - 50 = 30

Ratio of children to men = n:1 = 30:10

Divide both sides by 10

30:10 = 3:1

n = 3

Answer:33

Step-by-step explanation:45-12=33

The probability of finding 10 defective cores in a sample of 10 power cores is approximately 0.0000161, or about 0.0016%.

Assuming that each fuel rod is independent of each other and that the probability of finding a defective fuel rod is constant at 0.1%, we can model the number of defective fuel rods in a power core with a binomial distribution. Let X be the number of defective fuel rods in one power core, then X follows a binomial distribution with parameters n = 50000 and p = 0.1/100 = 0.001.

To find the probability of finding 10 defective cores, we can use the binomial distribution again, but with a different set of parameters. Let Y be the number of defective cores in a sample of 10 power cores, then Y follows a binomial distribution with parameters n = 10 and p = P(X ≥ 1), where P(X ≥ 1) is the probability of finding at least one defective fuel rod in one power core. We can find P(X ≥ 1) using the complement rule:

P(X ≥ 1) = 1 - P(X = 0)

= 1 - (1 - 0.001)^50000

≈ 0.3935

So, the probability of finding 10 defective cores in a sample of 10 power cores is:

P(Y = 10) = (10 choose 10) * (0.3935)^10 * (1 - 0.3935)^(10 - 10)

≈ 0.0000161

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Complete Question:

a power core contains about 50000 fuel rods. if the probability to find one defective fuel rod is 0.1%, what is the probability to find 10 defective cores.

The length of each arc intercepted by each slice is 2.09 inches.

The area of each slice 18.85 square inches .

To find the length of each arc intercepted by each slice and the area of each slice of a pizza that is 12 inches in diameter, follow the steps below. Length of each arc intercepted by each slice

The formula to find the length of each arc is given by:

L = θ/360 * 2πr

WhereL = length of arc

θ = angle of arc in degrees

r = radius of circle (diameter/2)

Given, diameter of pizza = 12 inches

So, radius of pizza = 12/2 = 6 inches

Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.

Now, substituting the given values in the formula:

L = 60/360 * 2π* 6L = 1/6 * 12πL = 2π/3 ≈ 2.09 inches

The formula to find the area of each slice is given by:

A = θ/360 * πr²

Given, diameter of pizza = 12 inches

So, radius of pizza = 12/2 = 6 inches

Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.

Now, substituting the given values in the formula:

A = 60/360 * π* 6²A = 1/6 * 36π

A = 6π ≈ 18.85 square inches

Thus, the length of each arc intercepted by each slice is approximately 2.09 inches and the area of each slice is approximately 18.85 square inches.

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Each student should receive 1/2 kg of soil.

To find out how much soil each student will have, we need to first add up the total amount of soil collected and then divide it equally among the 10 students.

Let's start by converting all the amounts of soil to a common unit, such as kilograms:

3 students brought 1/4 kg each, so they brought a total of 3/4 kg.

4 students brought 1/2 kg each, so they brought a total of 2 kg.

3 students brought 3/4 kg each, so they brought a total of 2 1/4 kg.

Adding up these amounts, we get:

3/4 + 2 + 2 1/4 = 5 kg

So the total amount of soil collected is 5 kg.

To redistribute this soil equally among the 10 students, we need to divide it by 10:

5 kg ÷ 10 = 1/2 kg per student

Therefore, each student should receive 1/2 kg of soil.

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Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.

Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.

the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:

m∠MGS = 90°

Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.

m∠SGM = 1/2 (mSE - mGE)

where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.

Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.

mSE = 2mGS

mSE = 2(84°) = 168°

m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°

Therefοre, m∠SGM = 84°.

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The standard deviation for the number of people with the genetic mutation in a group of 1000 individuals is approximately 4.89.

To find the standard deviation for the number of people with a particular genetic mutation in a group of 1000 individuals, we first need to understand the concept of binomial distribution.

Binomial distribution is a statistical probability distribution that represents the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).

In this case, the probability of success (having the genetic mutation) is 0.04, and the probability of failure (not having the mutation) is 0.96. Thus, we can model the number of people with the mutation in a group of 1000 individuals using a binomial distribution with n = 1000 and p = 0.04.

The formula for the standard deviation of a binomial distribution is:

σ = √(np(1-p))

Where σ is the standard deviation, n is the number of trials, and p is the probability of success. Plugging in the values, we get:

σ = √(1000 x 0.04 x 0.96) = 4.89

In other words, we can expect that the number of people with the genetic mutation in a group of 1000 individuals will vary around the mean of 40 (1000 x 0.04) by about 4.89, with about 68% of the observations falling within one standard deviation of the mean.

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The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%

The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values are between 5.8 and 10.6, and the total number of values is 95.4%.

To calculate the mean, we must first calculate the sum of all the values. To do this, we will use the following formula:

sum of values = (lowest value + highest value) / 2

In this case, the lowest value is 5.8 and the highest value is 10.6, so the sum of values is 8.2.

We now have the sum of all the values, so we can calculate the mean by dividing the sum by the total number of values. The total number of values is 95.4%, so the mean is 8.2 / 0.954 = 8.57.

Therefore, the mean of the normal distribution is 8.57.

In conclusion, the mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%. When the sum of all the values (8.2) was divided by the total number of values (0.954), the mean was calculated to be 8.57.

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Answer:

Step-by-step explanation:

It is possible if your friend has a bigger glass than you.

Answer:

Let's assume that the subset contains as many numbers as possible. We start by including all the numbers from 1 to 100 that are not divisible by 5. These are the numbers 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94, 96, 97, 98, 99.

This gives us a subset of 81 numbers. However, we need to remove any numbers that are multiples of other numbers in the subset. For example, if we include the number 6, we must remove 12, 18, 24, etc. Similarly, if we include the number 9, we must remove 18, 27, 36, etc. We can see that the only numbers that have multiples in the subset are 2, 3, 7, 8, 13, 17, 18, 19, 27, 28, 37, 38, 39, 52, 53, 54, 57, 58, 59, 68, 69, 73, 74, 78, 79, 83, 84, 87, 88, 89, 92, 93, 94, and 98.

Therefore, we need to remove these 34 numbers from the subset. This leaves us with a subset of 81 - 34 = 47 numbers.

However, we can still include the number 5, since it is not a multiple of any other number in the subset. This adds one more number to the subset, giving us a total of 48 numbers.

Therefore, the largest number of members that such a subset can have is 48, which corresponds to answer choice (e).

Therefore , the solution of the given problem of unitary method comes out to be hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.

This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.

Here,

The formula below can be used to determine the ideal amount of phone representatives:

=>  MR = MC

Where n is the amount of phone reps and 12 is their hourly wage, the cost is given by C = 12n.

The following results are obtained by taking the derivative of revenue and cost with regard to n:

=> MR=dR/dn = k

=>  dC/dn = 12 for MC.

When we set MR equal to MC, we obtain:

=> k = 12

Accordingly, Vi should hire as many phone representatives as are required to produce an hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.

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Answer:

33

Step-by-step explanation:

43-10=33 sarah has 33 bananas ledt

The two numbers are 6 and 2.

Let's assume the first number is x and the second number is y.

From the first statement, we can write the equation x = y + 4.

From the second statement, we can write the equation 2x = 4y + 2.

Now, we can substitute x in terms of y from the first equation into the second equation:

2(y + 4) = 4y + 2

Simplifying this equation, we get:

2y + 8 = 4y + 2

2y = 6

y = 3

Substituting y = 3 in the first equation, we get:

x = y + 4 = 3 + 4 = 7

Therefore, 6 and 2 are the two numbers,


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8. Spread = SD = sqrt(2*df)

9. The difference between the observed and expected frequencies of the outcomes of a set of events or variables.

10. Degrees of 1 freedom does the chi-square distribution.

11.  The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.

8. Describe the center and spread of the chi-square distributions.

Shape - skewed right because can't be zero

µ = df = tipping point

mode = df - 2 = peak

spread = SD = sqrt(2*df)

9. Chi-square test is a non-parametric test (a non-parametric statistical test is a test whose model does not specify conditions about the parameter of the population from which the sample is drawn.). It is used for identifying the relationship between a categorical variable and denoted by χ2.

10. A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom. Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution.

11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.

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First, note that the degree of the polynomial is the highest power of x that appears in the expression. In this case, the degree is max(n, 5, m, 2).

Next, consider the leading coefficient of the polynomial, which is the coefficient of the term with the highest power of x. In this case, the leading coefficient is a.

Based on this information, here are some possible general shapes of the graph of y=f(x):

If n is even and a > 0, the graph of y=f(x) looks like a "U" shape, with both ends pointing upwards.

If n is even and a < 0, the graph of y=f(x) looks like an upside-down "U", with both ends pointing downwards.

If n is odd and a > 0, the graph of y=f(x) looks like a "v" shape, with the vertex pointing upwards.

If n is odd and a < 0, the graph of y=f(x) looks like an upside-down "v", with the vertex pointing downwards.

Note that these are just general shapes, and the actual graph could be modified by the other terms in the polynomial. Additionally, the values of b, c, d, and the constants could also affect the shape and behavior of the graph.

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Complete Question is : let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. what is the possible graph of the function?

The angle of x in the given circle is 51 degrees.

In the case when a tangent line and a secant line originate from the same external point, the mean of the exterior angle is equal to half the difference between the major arc and the minor arc that are created by the tangent and secant lines.

From the given figure we observe that the secant line and tangent line start from the same exterior angle.

Thus, according to the theorem of secant and tangent line of circle we have:

angle x = (DA - DB) /2

angle x = (178 - 76) / 2

angle x = 102 /2

angle x = 51 degrees.

Hence, the angle of x in the given circle is 51 degrees.

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The conditions does the function f(x) to meet in order to be able to use the integral test to verify convergence or divergence is

1) f(x) must be continuous, positive, and decreasing for all x greater than some fixed value N.

2) The series to be tested must have non-negative terms.

3) The integral of f(x) from N to infinity must converge or diverge.

To use the integral test to verify the convergence or divergence of an infinite series, the following conditions must be met for the function f(x)

1) f(x) must be continuous, positive, and decreasing for all x greater than some fixed value N.

2) The series to be tested must have non-negative terms.

3) The integral of f(x) from N to infinity must converge or diverge.

If these conditions are met, then the integral test can be used to determine whether the series converges or diverges. Specifically, if the integral of f(x) converges, then the series converges. On the other hand, if the integral of f(x) diverges, then the series also diverges.

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The characteristics of each function has been explored based on the table below.

The graph of each function is shown in the image attached below.

In order to use the given functions to complete the table, we would have to substitute each of the values of x (x-values) into the function and then evaluate as follows;

A. f(x) = 2x

x                      process             f(x)

-2                  f(-2) = 2(-2)            -4

-1                   f(-1) = 2(-1)              -2

0                   f(0) = 2(0)               0

1                    f(1) = 2(1)                 2

2                   f(2) = 2(2)                4

B. G(x) = x²

x                      process             f(x)

-2                  f(-2) = (-2)²            4

-1                   f(-1) = (-1)²              1

0                   f(0) = (0)²               0

1                    f(1) = (1)²                 1

2                   f(2) = (2)²               4

B. H(x) = 2ˣ

x                      process             f(x)

-2                  f(-2) = (2)⁻²            1/4

-1                   f(-1) = (2)⁻¹              1/2

0                   f(0) = (2)⁰                1

1                    f(1) = (2)¹                 2

2                   f(2) = (2)²               4

In this scenario and exercise, we would use an online graphing calculator to plot each of the given functions as shown in the graph attached below.

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Answer: 14x + 10

Step-by-step explanation: The perimeter of the room without the door can be found by adding up the lengths of all four sides:

Perimeter = 2(4x-1) + 2(3x+6)

Simplifying and combining like terms, we get:

Perimeter = 14x + 10

Therefore, the perimeter of the room without the door in simplest form is 14x + 10.

The expression (1 + 1 / 18)¹⁸ represents the number closest to irrational number e. (Correct choice: A)

This problem ask us to determine what expression is closest to irrational number e. A number is irrational when it cannot be represented by numbers of the form m / n, where m and n are integers and n is non-zero. The number e can be defined by the following limit:

[tex]e = \lim_{x \to \infty} \left(1 + \frac{1}x}\right)^{x}[/tex], where x is a natural number.

According to this definition, the greater the value of x is, the closer the result to irrational number e is. Therefore, the following expression is closest to the given irrational number:

x = 18

e = (1 + 1 / 18)¹⁸

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