60% of all the students passed an exam. if a random sample of 10 students is selected, what is the mean and standard deviation ? write every rule you are going to use.

Answer:

1:2

Step-by-step explanation:

The total number of marbles is

3+5+8 = 16

blue : total

8 : 16

Divide each side by 8

8/8 : 16/8

1:2

Answer:

1:2

Step-by-step explanation:

There are 16 marbles in total. 3+5+8=16

8 of them are blue so it is 8:16 simplify 1:2

Answer:

3

Step-by-step explanation:

Using PEMDAS:

We can evaluate 7 + 2 × 4 - 8 - 4.

Start with multiplication:

Now we can add and subtract from left to right.

The answer to this problem is 3.

Answer:

Step-by-step explanation:

here because its an expression you use bodmas then you take 7+2= 9 take  9 times 4 = 36 take 36 minus 8 = 28 take 28 minus 4 = 24 this is the answer

Tom's preferences, the value of b in the function W(x, y) = 160xᵇ y⁶⁸ should be greater than 1.

A utility function is a mathematical representation used in economics to quantify the preferences or satisfaction a consumer derives from consuming different goods or bundles of goods. It assigns a numerical value, known as utility, to each possible combination of goods or services, reflecting the consumer's preferences.

The utility function is typically denoted as U(x1, x2, ..., xn), where x1, x2, ..., xn represent the quantities of different goods or services consumed. The utility function maps the combination of goods to a real number, indicating the level of satisfaction or utility the consumer derives from that combination.

Utility functions can take different functional forms, depending on the assumptions and models used. Common types include linear utility functions, Cobb-Douglas utility functions, and logarithmic utility functions. These functions capture different patterns of preferences and allow economists to analyze various economic phenomena, such as consumer demand, welfare analysis, and decision-making under uncertainty.

To represent Tom's preferences, the utility function U(x, y) = 24xy is given.

We need to find the value of b in the function W(x, y) = 160x^b y^68 such that it also represents Tom's preferences.

To match Tom's preferences, the two utility functions, U(x, y) and W(x, y), should have the same ranking of preferences. In other words, if U(x1, y1) > U(x2, y2), then W(x1, y1) should also be greater than W(x2, y2).

Let's compare the utility values for two sets of goods (x1, y1) and (x2, y2) using the given utility function U(x, y) = 24xy:

U(x1, y1) = 24x1y1

U(x2, y2) = 24x2y2

For the function W(x, y) = 160xᵇ y⁶⁸, we need to determine the value of b such that W(x1, y1) > W(x2, y2) whenever U(x1, y1) > U(x2, y2).

Comparing the utility values, we have:

24x1y1 > 24x2y2

To maintain the same ranking of preferences, we can equate the corresponding W values:

160x1 y1⁶⁸ > 160x2 y2⁶⁸

Now, canceling out the common factors, we get:

x1ᵇ y1⁶⁸ > x2ᵇ y2ᵇ^68

Since this should hold for any x1, y1, x2, y2, we can compare the exponents of x and y separately:

b > 1

To represent Tom's preferences, the value of b in the function W(x, y) = 160x^b y^68 should be greater than 1.

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The point (0, 4) is on the graph of the function y = 8x + 4.

What is the graph of a function?

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function is a special case of the graph of an equation.

The point on the graph of the function y = 8x + 4 depends on the values of x that you plug into the equation.

For any value of x, you can find the corresponding y-value using the equation.

For example:

x = 0, y = 8 * 0 + 4 = 4

So the point (0, 4) is on the graph of the function y = 8x + 4.

Similarly, for any other value of x, you can plug it into the equation and find the corresponding y-value to determine the point on the graph of the function.

Hence, the point (0, 4) is on the graph of the function y = 8x + 4.

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in the y = kx + b graph, k equals to tan(θ), where θ is the angle between the graph and Ox. In this case, k = 0.5.

This graph is the graph y = 0,5x shifted by 1 to the left, so its formula is 0.5(x + 1) = 0.5x + 0.5.

The answer is y = 0.5x + 0.5.

You can also get the equation from the system of equations.

we will take two points from the graph: (-1; 0); (1; 1)

First equation is 0 = k * -1 + b;

the second is 1 = k * 1 + b.

From the 1st, k = b; from the second, k = 1 - b. b = 1 - b; 2b = 1; b = 0.5; k = b = 0.5.

y = 0.5x + 0.5.

60 ml and 20 ml of each drug is required to make 80 ml of the solution.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

As two drugs are to be combined in a 3:1 ratio to produce a needed solution.

The ratio is 3:1 so the needed solution are 60 ml/ 20 ml.

Hence, 60 ml and 20 ml of each drug is required to make 80 ml of the solution.

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The process capability index Cpk for the provided process ≈ 0.7687.

To calculate the process capability index Cpk, we need to use the following formula:

Cpk = min((USL - μ) / (3 * σ), (μ - LSL) / (3 * σ))

where USL is the upper specification limit, LSL is the lower specification limit, μ is the process mean, and σ is the process standard deviation.

USL = 11.61 cm (upper specification limit)

LSL = 9.87 cm (lower specification limit)

μ = 10.85 cm (process mean)

σ = 0.33 cm (process standard deviation)

Substituting these values into the formula, we can calculate Cpk:

Cpk = min((11.61 - 10.85) / (3 * 0.33), (10.85 - 9.87) / (3 * 0.33))

Cpk = min(0.76 / 0.99, 0.98 / 0.99)

Cpk = min(0.7687, 0.9899)

Cpk = 0.7687 (rounded to four decimal places)

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Answer:

B

Step-by-step explanation:

The minimum number of homes the Northeast Home Builders Association should sample is approximately 6,487,904 to estimate the true mean number of days to within 10 days with 95% confidence.

To determine the minimum number of homes the Northeast Home Builders Association should sample, we need to use the formula for sample size in estimating a population mean with a specified margin of error and confidence level.

The formula is:

n = (Z * σ / E)^2

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (95% confidence corresponds to a Z-score of approximately 1.96)

σ = standard deviation of the population (unknown in this case)

E = desired margin of error (10 days)

Since the standard deviation of the population is unknown, we can use the worst-case scenario to estimate it. The worst-case scenario occurs when the standard deviation is at its maximum, which is half the range of the population. In this case, the range is 350 - 90 = 260, so the maximum standard deviation is 260 / 2 = 130.

Substituting the values into the formula:

n = (1.96 * 130 / 10)^2

n = (196 * 13)^2

n = 196^2 * 13^2

n = 38416 * 169

n = 6,487,904

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Answer:

B) 3x - 4y = -28

Step-by-step explanation:

Perpendicular = 90 degree angle

Answer:

B) 3x - 4y = -28

Elena plans on running a total of 5 miles.

Mile, any of several distance measurements, such as the statutory mile (5,280 ft) (1.609 km). It comes from of the Romans lire passus, also referred as the "1000 steps," which was equal to 5,000 Romans feet. Unit of length is a related topic. See all relevant material The "old London" mile was eight furlongs when it was first established in 1500.

The term mille passus, which translates to "a hundred paces" in Latin and meant a length of 1,000 rates of speed or 5,000 Rome feet, was originally used by the Romans. It is equivalent to around 1,480 metres, or 1,618 contemporary yards.

We are aware that she has covered 2 miles, or 40% of a total distance, in her run thus far:

\(2=0.4x\)

To find x,

\(2=0.4x\)

\(x=\frac{2}{0.4}\)

\(x=5\)

Therefore, Elena plans to run a total distance of 5 miles.

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Answer:

y = 133°

x = 47°

Step-by-step explanation:

y and 47 are straight angles, therefore:

y + 47 = 180

y = 133

x and 47 are vertically opposite angles, therefore:

x = 47

Answer:

18.2°, 161.8° and 378.2°

Step-by-step explanation:

Given the expression:

8 sin x = 2.5

Divide both sides by 8

sinx = 2.5/8

Sinx = 0.3125

x = arcsin(0.3125)

x1 = 18.2

Since sin theta is positive in the second quadrant, x2 = 180 - 18.2 = 161.8°

Since our angle must lie in between  0° and 720°,then;

x3 = 360 + 18.2 = 378.2°

Hence the required angles are 18.2°, 161.8° and 378.2°

Answer:

\( \sqrt{30} \)

Use the rate as a ratio and use proportions to find how long it takes to run each distance.

5 miles.

8 miles.

11 miles.

16 miles.

It takes 45, 72, 99 and 144 minutes to run 5, 8, 11 and 16 miles, respectively.

The domain of the function y = 2 - √(-3x+2) is (-∞ , 2/3] and the range of the function is (-∞ , 2]  .

In the question ,

it is given that , the function is ⇒ y = 2- √(-3x+2) .

For Domain ,

we know that the square root function is defined only when the number inside the root is non negative .

that means ,

-3x \(+\) 2 ≥ 0

Subtracting 2 from both the sides ,

we get ,

-3x ≥ -2

x ≤ 2/3

the Domain is (-∞ , 2/3] .

For range , we know that the root function value in always non negative .

√(-3x + 2) ≥ 0

Multiply by -1 on both sides

we get ,

-√(-3x + 2) ≤ 0

Adding 2 to both the sides

2 - √(-3x + 2) ≤ 2

y ≤ 2

the range is (-∞ , 2] .

Therefore , the domain is (-∞ , 2/3]   and the range is (-∞ , 2] .

How do we find the domain and range of the function y = 2- √(-3x+2) ?

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Answer:

20 scoops

Step-by-step explanation:

Zack fills two bird feeders with birdseed. Each bird feeder holds 2 1/2​ ​ cups of birdseed.

Hence, the two bird feeders would require:

2 × 2 1/2 cups of bird seed.

= 5 cups of bird seed

Zack's scoop holds 1/4 cup. Write an expression for the number of scoops Zack needs to fill both feeders.

The number of scoops zack needs to fill both feeders is:

= 5 ÷ 1/4

= 5 × 4/1

= 20 scoops

Zack would need 20 scoops to fill both feeders.

The answer is simply 20 cups

Step-by-step explanation: