Peyton is taking a multįple choice test with a total of 20 points available. Each
question is worth exactly 2 points. What would be Peyton's test score (out of 20) if
she got 4 questions wrong? What would be her score if she got x questions wrong?

Answer:

sum of all angles of a triangle= 180°

Let angle A be x,

then 63°+90°+x=180°

x=17°

the probability of drawing 3 or more white marbles when 5 marbles are drawn from the bag without replacement.

To calculate this probability, we can use the formula for the hypergeometric distribution, which is:

P(X ≥ 3) = [C(10,3) * C(10,2)] / C(30,5) + [C(10,4) * C(10,1)] / C(30,5) + [C(10,5)] / C(30,5)

Where C(n,r) is the number of ways to choose r items from a set of n items.

formula is that we need to consider three different cases: drawing exactly 3 white marbles, drawing exactly 4 white marbles, and drawing all 5 white marbles. For each case, we calculate the probability of drawing the required number of white marbles and the probability of drawing the remaining marbles (non-white marbles), and then multiply them together. Finally, we add up the probabilities for all three cases to get the total probability of drawing 3 or more white marbles.

Using the formula, we get:

P(X ≥ 3) = [(C(10,3) * C(20,2)) + (C(10,4) * C(20,1)) + C(10,5)] / C(30,5)

= [(120 * 190) + (210 * 20) + 252] / 142506

= 0.209

Therefore, the probability of drawing 3 or more white marbles when 5 marbles are drawn from the bag without replacement is 0.209.

using the hypergeometric distribution formula, we can calculate the probability of drawing 3 or more white marbles from a bag containing 5 red marbles, 6 blue marbles, 10 white marbles, and 9 yellow marbles when 5 marbles are drawn without replacement. The probability is 0.209.

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Answer:

25151/100000

Step-by-step explanation:

To solve this problem, we need to use the same process described in the question. We start by placing three different one-digit positive integers in the bottom row of cells. Let's call these integers A, B, and C.

We add the numbers in adjacent cells to get the sums and place them in the cell above them. In the first row, we get A+B, B+C, and C+A.

We continue the same process in the second row by adding the numbers in adjacent cells in the first row. We get (A+B)+(B+C), (B+C)+(C+A), and (C+A)+(A+B).

Simplifying these expressions, we get 2A+2B+2C, 2A+2B+2C, and 2A+2B+2C.

So the top cell will always have the same value of 2A+2B+2C, regardless of the values of A, B, and C.

To find the largest and smallest possible values of the top cell, we need to consider the largest and smallest possible values of A, B, and C.

The smallest possible value for A, B, and C is 1, so the smallest possible value for the top cell is 2(1+1+1) = 6.

The largest possible value for A, B, and C is 9, so the largest possible value for the top cell is 2(9+9+9) = 54.

Therefore, the difference between the largest and smallest numbers possible in the top cell is 54-6 = 48.

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If all other factors are held constant, decreasing the significance level results in an increase in the probability of a type II error. This is true. we can say that the probability of making a type II error increases when the significance level is lowered.

What is a type II error? In hypothesis testing, a type II error occurs when a false null hypothesis is not rejected. When there is a real effect and the null hypothesis is false, this happens. It's a mistake that occurs when a researcher fails to reject a false null hypothesis.

A false negative is another term for a type II error. The power of the test, the size of the sample, the confidence level, and the effect size are all factors that influence the probability of making a type II error. Only if we decrease the significance level can the probability of a type II error be increased.

What is the significance level? The significance level is also known as alpha. It is the probability of rejecting a null hypothesis when it is true. It is represented by α. It is usually set at 0.05 or 0.01 in most studies. When the significance level is lowered, the probability of making a type I error decreases, but the probability of making a type II error increases. Therefore, we can say that the probability of making a type II error increases when the significance level is lowered.

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Answer:, Volume of triangular prism = (1/2) bh × L.

The amount that Leila needs to pay after the tax is applied is:

P(x) = 1.07*x

We know that Leila buys a dinosaur model with a price of x dollars, and then we need to add a 7% tax.

Remember that an increase (like a tax) of X (a percentage) is written as:

A*(1 + X/100%)

Where A is the initial value.

Here the initial price is x, so the amount that Leila needs to pay is:

P(x) = x*(1 + 7%/100%)

P(x) = x*(1 + 0.07)

P(x) = 1.07*x

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Answer: 56

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

The day that Angelique and Bentley will be at the gym on the same day is; the 42nd day.

Angelique's days:
6, 12, 18, 24, 30, 36, 42

Bentley's days:
7, 14, 21, 28, 35, 42

In conclusion, the earliest day that Angelique and Bentley will be at the gym on the same day will be, the 42nd day.

Step-by-step explanation:

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The functions have been arranged in ascending order from the least to the highest value below

This is used in mathematics as well as other disciplines to explain the order by which values are arranged. This arrangement is usually done in such a way that the smallest value would come first and continue to climb till we get to the value that is the highest.

The values here have been arranged in this order in such a way that the smallest values came first while the bigger values are at the end.

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Answer:

y = 3x - 6

Step-by-step explanation:

The line here is parallel

Equation of line

The relation that is an inverse variation is the one in the first table:

x 2 4 6 8

f(x) 12 6 4 3

An inverse variation between two variables x and y can be written as follows:

y = k/x

Where k is a constant.

Notice that x is on the denominator, so, as x increases, the value of y decreases.

Now, for example if we use the values of the first table:

x 2 4 6 8

f(x) 12 6 4 3

The first pair is (2, 12)

Replacing that in the inverse variation formula we get:

12 = k/2

12*2 = k

24 = k

For the second pair (4, 6) we will get:

6 = k/4

6*4 = k

24 = k

And so on for all the pairs. If the variation is inverse, you should always get the same value of k (like in this case).

So this is the correct answer.

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Answer:

by multiplying the variable k by 11

Step-by-step explanation:

\(\frac{k}{11}\) × 11, this cancels out the 11 in the denominator, which isolates the variable

Answer:

Step-by-step explanation:

Divide both sides by 11

The remainder when 2019 is divided by 5 is 4.

What is the division?

A division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each, and so on.

To find the remainder when 2019 is divided by 5, we can use the modulo operator (%), which gives the remainder of the division. In Python, we can write:

2019 % 5

The output will be the remainder of the division of 2019 by 5, which is:

4

Therefore, the remainder when 2019 is divided by 5 is 4.

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Answer:

15² + 4(1/2)(15)(8) = 225 + 240 = 465 cm²

Answer:

B

Step-by-step explanation:

You have to match up the corresponding sides in the 2 triangles

The sides you have to find are AB/BC

The side that corresponds to AB in triangle DEF is DE

The side that corresponds to BC is EF

Answer:

D. Hamish earns $20 per hour, and Harry earns $26 per hour.

Step-by-step explanation:

Hamish and Harry work as plumbers. Harry earns a dollar more than 5/4 the amount Hamish earns per hour. The amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour. How much does each of them earn per hour?

Hamish earnings per hour = x

Harry earnings = 1 + 5/4x

The amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour

Harry also earns = 7/5x - 2

Equate both Harry's earnings

1 + 5/4x = 7/5x - 2

Collect like terms

1 + 2 = 7/5x - 5/4x

3 = 28x-25x/20

3 = 3/20x

Divide both sides by 3/20

x = 3 ÷ 3/20

= 3 × 20/3

x = 20

Hamish earnings per hour = x

= $20

Substitute Harry's earnings into 7/5x - 2

= 7/5 × 20 - 2

= 28 - 2

= 26

Harry's earnings = $26

D. Hamish earns $20 per hour, and Harry earns $26 per hour.

MEDIAN is the middle value of a data.

In general, the best measure of the central location for a data set that

contains outliers is the median. Median is the number that is halfway into

the set. The median is less affected by outliers than the mean, as it

represents the middle value when the data is sorted in ascending order.

To find the median, follow these steps:

1. Arrange the data in ascending order.

2. If there is an odd number of data points, the median is the middle value.

3. If there is an even number of data points, the median is the average of the two middle values.

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The horizontal distance between the base of the ladder and the wall is 6.51 ft.

Given that; Amira leans a 16-foot ladder against a wall so that it forms an angle of 66 with the ground.

This forms a right tiangle.

To solve for the horizontal distance between the base of the ladder and the wall, we use rigonometric ratio.

Cosine = Adjacent / Hypotensue

cos( 66° ) = x / 16ft

Solve for x

x = cos( 66° ) × 16ft

Using a calculator, we can find that cos(66) is approximately 0.4067. Hence:

x = 0.4067 × 16ft

x = 6.51 ft

Therefore, the value of x is 6.51 ft.

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Answer: \(184,724.153\)

Step-by-step explanation:

Given

In 1990, there were 1200 cell phone subscriber in small town of stephenville

It is increasing by 75% per year after 1990

In year 1991 it is

\(\Rightarrow 1200+1200\times 0.75\\\Rightarrow 122(1.75)\)

In year 1992 it is

\(\Rightarrow 1200(1.75)+1200(1.75)\times 0.75\\\Rightarrow 1200(1.75)(1+0.75)\\\Rightarrow 1200(1.75)^2\)

So, it is increasing as \(1200(1.75)^x\)

where \(x=\)no of years spent

After 9 years, it is

\(\Rightarrow 1200(1.75)^9=184,724.153\)

The positive difference between the two probabilities is 11/35.

To calculate the probability that three distinct numbers chosen at random without replacement from the set would have an even sum, Jan would consider the number of ways to choose three even numbers (4 choose 3) and divide that by the total number of combinations of three numbers (7 choose 3).

To calculate the probability that three distinct numbers chosen at random without replacement from the set would have an even product, Judy would consider the number of ways to choose three numbers such that the product is even (3 choose 2) and divide that by the total number of combinations of three numbers (7 choose 3).

The positive difference between the two probabilities would be the difference between these two calculations. In this case, 11/35 is a positive difference, meaning that the probability of having an even product is 11/35 higher than the probability of having an even sum.

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Answer:

D.

(DNE)

Step-by-step explanation:

when you plug in 1 to the denominator, 1 minus 1 becomes 0. a fraction with 0 as the denominator does not exist.

The limit of the function f(x)=\(x^{3}-1\)/x-1 as x approaches 1 is 3.

Limit is the value that a function approaches as the value of variable approaches some value. They are essential to calculas and mathematical analysis and are use to define continuity , derivatives and integrals. It can change value of function at different values of x.

We have been given a function f(x)=\(x^{3}-1\)/x-1 and we have to find the limit of function.

F(x)=\(x^{3} -1\) /(x-1) [\(x^{3} -y^{3} =x^{2} +y^{2} +xy\)]

\(\lim_{x \to \0}x^{3}-1/x-1\)

\(\lim_{x \to \0} (x-1)(x^{2} +1+x)\)/x-1

\(\lim_{x \to \0} x^{2} +x+1\)

change limit by putting x=1-h

\(\lim_{h \to \0} (1-h)^{2} +1+1-h\)

Put the value of h=0.

=1+1+1

=3

Hence the limit of the function \(x^{3}-1/x-1\) is 3.

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The expression "x - y + z" can be simplified and rearranged using the associative property and commutative property of addition. Let's break it down step by step:

1. x - y + z

According to the associative property of addition, the grouping of terms does not affect the result when only addition and subtraction are involved. Therefore, we can choose to group "y" and "z" together:

2. x + (-y + z)

Next, using the commutative property of addition, we can rearrange the terms "-y + z" as "z + (-y)":

3. x + (z + (-y))

Now, we have the expression "x + (z + (-y))". According to the associative property of addition, we can group "x" and "z + (-y)" together:

4. (x + z) + (-y)

Finally, we can rewrite the expression as "(x + z) - y", which is equivalent to "(x - y) + z":

5. (x + z) + (-y) = (x - y) + z

Therefore, "x - y + z" is indeed the same as both "x - (y + z)" and "(x - y) + z" due to the associative and commutative properties of addition.

Answer:

The rate of change in the table is 78 students per year

Step-by-step explanation:

Here, we want to get the rate of change of the function

Mathematically, we can get this by using the formula;

m = (y2-y1)/(x2-x1)

(x1,y1) and (x2,y2) are points we are to select from the table

Let us select the point (4,704) and (17,1718) from the table

The slope is thus;

m = (1718-704)/(17-4) = 78 students per year

the lines are parallel.

To determine whether the lines are parallel or identical, we can compare the direction vectors of the lines.

For the first line, we have the direction vector:

d₁ = (6, -3, 5)

For the second line, we have the direction vector:

d₂ = (12, 6, -10)

If the direction vectors are proportional, then the lines are parallel. If the direction vectors are equal, then the lines are identical.

To check for proportionality, we can compare the components of the direction vectors:

d₁ = (6, -3, 5)

d₂ = (12, 6, -10)

To check if d₁ and d₂ are proportional, we can see if the ratios of their corresponding components are equal:

6/12 = -3/6 = 5/-10

Simplifying, we get:

1/2 = -1/2 = -1/2

Since the ratios are equal, the direction vectors are proportional, which means the lines are parallel.

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Answer:

sorry

Step-by-step explanation:i need points

There are a total of three numbers in a combination lock, and no digit can be repeated. To open the lock,

The correct answer is B. 720.

The first number can be any of the 10 digits, and the second number can be any of the 9 remaining digits because no digit can be repeated.

Finally, since there are 8 digits left, the third digit can be any of these.

The combination can be created in the following manner:

The total number of possible combinations = (Number of ways to select the first number) x (Number of ways to select the second number) x (Number of ways to select the third number).

= 10 x 9 x 8 ⇒ 720.

Therefore, the sequence of the combination is 720, and option (B) is correct.

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To solve for x at an angle, you must first understand what type of angle you are working with. If the angle is a right angle, you can use the Pythagorean theorem to solve for x. If the angle is an obtuse angle, you can use the law of cosines to solve for x. If the angle is an acute angle, you can use the law of sines to solve for x.

To solve for x at a right angle using the Pythagorean theorem, you must have the lengths of the two neighboring sides of the triangle. The sum of the squares of the two sides is equal to the square of the hypotenuse, according to the Pythagorean theorem. By rearranging the components and solving for x, this equation may be used to find x.

To use the law of cosines to solve for x at an obtuse angle, you must know the lengths of all three sides of the triangle. According to the law of cosines, the square of one side's length equals the sum of the squares of the other 2 sides minus twice the product of the other 2 sides multiplied by the cosine of the obtuse angle. You can use this equation to solve for x by rearranging the terms and solving for x.

To apply the law of sines to solve for x in an acute angle, you should first know the lengths of the triangle's two sides as well as the acute angle's measurement. According to the law of sines, the ratio of one side's length to the sine of the opposite angle equals the ratio of the other side's length to the sine of the acute angle. By rearranging the terms and solving for x, you may use this equation to solve for x.

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