I need help with this question.

Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.

To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.

The formula for finding the number of permutations is:

n! / (n-r)!

where n is the total number of objects and r is the number of objects we choose.

Using this formula, we can calculate the number of permutations as follows:

4! / (4-3)!

= 4! / 1!

= 4 x 3 x 2 x 1 / 1

= 24

Therefore, we can arrange the chosen 3 letters in 24 different ways.

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Step-by-step explanation:

remember the trigonometric triangle inside a circle.

sine is the up/down leg, cosine is the left/right leg.

the Hypotenuse (baseline) of the right-angled triangle is the angle-defining radius of the circle.

this is the basic definition inside the norm-circle with radius = 1.

for any other size sine and cosine need to be multiplied by the actual radius for the actual triangle side lengths.

I think you need the answer in simplified fraction and square root notification (you cut that off), but I give you also the decimal result, just in case.

so,

78 = cos(30)×y

78 = (sqrt(3)/2) × y

y = 78 / (sqrt(3)/2) = 2×78/sqrt(3) = 156/sqrt(3) =

= 90.06664199...

x = sin(30) × y = 0.5 × 156/sqrt(3) = 78/sqrt(3) =

= 45.033321...

The result of the formula  [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is  [tex]-29/2[/tex]  .

When [tex]y = 3[/tex] is used, the value of the expression [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex]  has a value of  [tex]-29/2[/tex] .

To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.

If  [tex]y = 3[/tex] , we can insert it into the expression & simplify as follows to evaluate   [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for  [tex]y = 3[/tex]  .

[tex]12 - 3(3)^2 + (√4) / (2(3) - 2)[/tex] (y = 3 replacement)

[tex]12 - 27 + 2 / 4\s-15 + 1/2\s-29/2[/tex]

Therefore, The result of the formula  [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is  [tex]-29/2[/tex]  .

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Once we have this data, we can substitute the values into the formula to find the empirical probability that a person prefers apple pie given that they prefer whipped cream. Therefore, the missing probability is 1/12, and we know this because it is the value that makes the sum of all probabilities equal to 1.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. For example, if the probability of winning a coin toss is 1/2, this means that there is an equal chance of the coin landing heads or tails. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability approach. Another approach is empirical probability, where probabilities are calculated based on observed data or experiments. Lastly, subjective probability involves making an informed guess or estimate about the likelihood of an event occurring based on subjective factors such as experience, intuition, or expert opinion. Probability is a fundamental concept in statistics and is used in many application

Here,

1. The formula needed to calculate the empirical probability that a person prefers apple pie given that they prefer whipped cream is:

P(Apple Pie | Whipped Cream) = P(Apple Pie and Whipped Cream) / P(Whipped Cream)

where P(Apple Pie and Whipped Cream) is the probability that a person prefers both apple pie and whipped cream, and P(Whipped Cream) is the probability that a person prefers whipped cream.

This formula is used because it is a conditional probability, which is a measure of the probability of an event occurring given that another event has occurred. In this case, we want to find the probability that a person prefers apple pie given that they already prefer whipped cream.

To calculate P(Apple Pie and Whipped Cream), we would need to gather data on the number of people who prefer both apple pie and whipped cream. Similarly, to calculate P(Whipped Cream), we would need to gather data on the number of people who prefer whipped cream.

2. To find the missing probability, we need to use the fact that the sum of all probabilities in a probability distribution must be equal to 1. Therefore, we can set up an equation to solve for the missing probability:

1/6 + 1/3 + x + 5/12 = 1

Simplifying the equation by finding a common denominator gives:

2/12 + 4/12 + x + 5/12 = 1

Combining like terms gives:

11/12 + x = 1

Subtracting 11/12 from both sides gives:

x = 1 - 11/12

x = 1/12

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Answer:

7x² - 2x + 4

Explanation:

(5x² + 2x + 11) − (7 + 4x - 2x²) ​

= 5x² + 2x + 11 - 7 - 4x + 2x²

= 7x² + 2x + 11 - 7 - 4x

= 7x² - 2x + 11 - 7

= 7x² - 2x + 4

So, the answer is 7x² - 2x + 4

The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a given a right angle triangle in the picture

It is required to find the measure of angle A

Applying cos ratio to find the measure of the angle A:

cosA = 9/14

cosA = 0.642

A = 49.99 ≈ 50 degree

Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

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So,

120% is the same as 1.2 or 6/5.  80% is the same as 0.8 or 4/5.

We are given the value of a, which is 12.

6/5 of a, or 1.2 times a, is equal to 4/5 of b, or 4/5 times b.

[tex]\dfrac{6}{5} (12)=\dfrac{4}{5} b[/tex]

Simplify.

[tex]\dfrac{72}{5} =\dfrac{4}{5} b[/tex]

Multiply both sides by 5/4.

[tex]\dfrac{72}{4} \ \text{or} \ 18=b[/tex]

Therefore, the sum of a and b is 12 + 18 = 30.

Answer:

Step-by-step explanation:

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

That is what Slope is.

Answer:

Step-by-step explanation:

Slope :( 1,1)

You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)

Answer:

Step-by-step explanation:

Using a standard normal table, we can find the area under the curve between -2.11 and -0.85.

P(-2.11 < z < -0.85) = P(z < -0.85) - P(z < -2.11)

Using the table, we find:

P(z < -0.85) = 0.1977

P(z < -2.11) = 0.0174

Therefore,

P(-2.11 < z < -0.85) = 0.1977 - 0.0174 = 0.1803

So the probability that a standard normal random variable falls between -2.11 and -0.85 is 0.1803.

The cost to rent one shed of the rectangular prism shaped shed is $2772.

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent sides. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the extent of its cross-section.

Volume of prism= BH

where B= area of base and H= height

B= 11*7 = 77 feet²

H= 12 feet

Volume= 77*12=924 cubic feet

Cost =$3 per cubic foot

Total cost= 3*924= $2772

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The displacement of the block at any time t is then x= 0.05cos5tm. (option b).

Now, when the block is released, it starts oscillating back and forth about its equilibrium position due to the force exerted by the spring. This motion is described by the equation of motion for a simple harmonic oscillator:

x = Acos(ωt + φ)

The angular frequency ω of the oscillation is given by:

ω = √(k/m)

where k is the spring constant and m is the mass of the block.

Substituting the given values of k and m, we get:

ω = √(50/2) = 5 rad/s

The phase angle φ depends on the initial conditions of the system, i.e., the initial displacement and velocity of the block. Since the block is initially at rest, its initial velocity is zero and the phase angle is zero as well.

Therefore, the equation of motion for the displacement of the block is:

x = 0.05cos(5t)

Hence, option B, x = 0.05cos(5t), is the correct answer.

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The rate at which the water level is rising in the pyramid is 5 cm/s when the water level is 3 cm.

A pyramid is a three-dimensional object with triangle faces that meet at a shared vertex and a base that is a polygon. The perpendicular distance between a pyramid's base and apex determines the structure's height. The base form of a pyramid can be used to categorise them. A square pyramid, for instance, has a square base, a triangle-shaped pyramid, a triangle-shaped base, and so on. From the ancient Egyptian pyramids to the contemporary pyramids found in cities all over the world, pyramids have been employed in architecture and art for thousands of years.

Given that, sides of length 3 cm and the height is 5cm.

The volume of a pyramid is given by:

V = (1/3) * A * h

where A is the area of the base.

The base of the pyramid is a square thus,

Area = (3)(3) = 9 sq. cm.

Substitute the value of A and h in volume:

V = (1/3) * 9 * 5 = 15

Now, water is being filled at a constant rate of 45 cubic cm per second.

The rising level can thus be calculated as:

r - 45/9 = 5 cm/s

Hence, the rate at which the water level is rising is 5 cm/s when the water level is 3 cm.

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f(x) = (x+4)^2(x-3) has polynomial function with the following zeros: double zero at -4 simple zero at 3.

If a polynomial has a double zero at -4, it means that it can be factored as (x+4)^2.

If it also has a simple zero at 3, then the factorization must include (x-3).

Therefore, the polynomial function with these zeros is :-

f(x) = (x+4)^2(x-3)

This polynomial has a double zero at -4, because $(x+4)^2$ has a zero of order 2 at -4, and a simple zero at 3, because $(x-3)$ has a zero of order 1 at 3.

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The given statement " when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests. " is false. Because in distribution of sample means, population variance is unknown.

When the population variance is not known and must be estimated from the data, we use a t-statistic instead of a z-statistic for our hypothesis tests.

This is because the distribution of the sample means follows a t-distribution when the population variance is unknown, whereas it follows a standard normal distribution (z-distribution) when the population variance is known.

The t-distribution has fatter tails than the z-distribution to account for the extra uncertainty introduced by estimating the population variance from the sample.

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Answer:

resultant force

Step-by-step explanation:

the body will move to the direction where greater force is applied

Therefore , the solution of the given problem of unitary method comes out to be  the attraction sold 943 child tickets and 736 adult tickets on that particular day.

It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.

Here,

Assume the attraction sold x tickets for adults and y tickets for kids.

Based on the supplied data, we can construct the following two equations:

=>  x + y = 1679 (equation 1, representing the total number of tickets sold)

=>  35x + 20y = 44620 (equation 2, representing the total revenue generated)

Using the elimination technique, we can find the values of x and y.

When we divide equation 1 by 20, we obtain:

=>  20x + 20y = 33580 (equation 3)

Equation 3 is obtained by subtracting equation 2 to yield:

=>  15x = 11040

=>  x = 736

When we enter x = 736 into equation 1, we obtain:

=>  736 + y = 1679

=> y = 943

As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.

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In response to the stated question, we may state that The equivalent trigonometry expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

tan(A + B) = (tan A + tan B)/(1 - tan A tan B)

Set A = 90 degrees and B = b degrees:

tan(90 + b) = (tan 90 + tan b)/(1 - tan 90 tan b)

tan(90 + b) = (undefined + tan b)/(1 - undefined tan b)

tan(90 + b) = -cot b

7/tan b + 7tan b

= 7/(tan b) + 7(tan(90 + b) - 1)

= 7/(tan b) + 7(-cot b - 1)

= (7 - 7tan b cot b)/sin b

The equivalent expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.

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Answer: D) Angle R is 65 degrees

Step-by-step explanation:

In the given figure, we have a right-angled triangle PQR.

Using the property of angles in a triangle, we know that the sum of angles in a triangle is 180 degrees. Therefore,

∠QRP + ∠QPR + ∠PRQ = 180 degrees

Since ∠PRQ is a right angle (90 degrees), we have:

∠QRP + ∠QPR = 90 degrees

Now, we are given that ∠QPR is 25 degrees. Substituting this in the above equation, we get:

∠QRP + 25 = 90 degrees

Solving for ∠QRP, we get:

∠QRP = 90 - 25 = 65 degrees

Therefore, the measure of angle R is 65 degrees, which is option (D).

Answer:

Answer is D

Step-by-step explanation:

SPiDerMom is so hot bTw

The given statement 'to calculate the average of the numeric values in a list  the first step is to get the sum of all the given values ' is a true.

Average of the numeric values in a list,

First step is to get the sum of values in the list.

It is not the total number of values.

Once we have the sum, we can divide it by the number of values to get the average.

Here is an example,

Suppose we have a list of numeric values are as follow,

[2, 4, 6, 8, 10].

To calculate the average of these values, we first find their sum,

2 + 4 + 6 + 8 + 10 = 30

Next,

divide the sum by the number of values in the list

Number of values = 5

30 / 5 = 6

This implies,

The average of the values in the list is 6.

Therefore, to get the average first step is to get the total of all values is true statement.

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Your question is incomplete. The complete question is: Consider the following algebraic statements and determine the values of x for which each statement is true. On a number line, show the set of all points corresponding to the values of x.

|x| = 7

4=|-2x|

The values of x for which each statement is true are:

|x| = 7: x = -7 or x = 7

4 = |-2x|: x = -2    or x = 2

a) |x| = 7

-x = 7 or x = 7

x = -7 or x = 7

This statement is true for two values of x:

x = -7 and x = 7.

b) 4 = |-2x|

4 = -2x or 4 = 2x

x = -2    or x = 2

This statement is true for two values of x:

x = -2 and x = 2.

The number line is shown in the image attached.

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The equation connecting z and p is:

z = x + (1/p)

To find z when p = 6, we can use the values of x and y when p = 2 and p = 4 to calculate the corresponding value of z when p = 6.

When p = 2, x = 4 and y = 1, so z = 5

When p = 4, x = 16 and y = 0.25, so z = 16.25

Therefore, when p = 6, x = 36 and y = 0.167, so z = 36.167

Answer:

x = [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }{6}[/tex]  or x = 210°, 330°

Step-by-step explanation:

4sin(x) + 2 = 0

4sin(x) = -2

sin(x) = -1/2

x = [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }{6}[/tex]

Consider the line segment AB shown the locations for point C makes ABC a right triangle with hypotenuse AB

In a coordinate pair the points are as represented as (x, y).

The point that forms the right triangle is located by tracing the point on the x axis of of the point A and the point on the y axis of the point B.  This is done below

therefore we can say that the point C that forms the right triangle is

C (2, 3)

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Answer:

Answer: B. Symmetric.

Explanation:

In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.

Answer:

[-1,inf) and [-2,inf)

Step-by-step explanation:

Domain is all the X coordinates that the function will pass through. it starts at -1 and goes to inf so [-1,inf) is the domain. The range is all the Y coordinates the function will pass through. It starts at -2 and goes up to inf so [-2,inf) and that is your answer

the correct options are A), B), and E).

why it is and what is Gallon?

A) 2 quarts = 8 cups

B) 8 cm = 80mm

E) 96 inches = 8 feet

The number 8 cannot correctly fill in the blank for statements C and D.

C) 1 gallon = 16 cups, so 4 gallons = 64 cups, not 8 cups.

D) 1 hour = 60 minutes, so 96 minutes = 1 hour and 36 minutes, not 8 hours.

Therefore, the correct answers are A), B), and E).

A gallon is a unit of measurement for volume commonly used in the United States and some other countries. There are two different sizes of gallons: the US gallon and the imperial gallon.

The US gallon is defined as exactly 3.785411784 liters, and is used for measuring liquids such as gasoline, milk, and other beverages.

The imperial gallon, which is used in the United Kingdom and some other countries, is defined as exactly 4.54609 liters.

In both cases, a gallon is typically divided into smaller units such as quarts, pints, and fluid ounces for measuring smaller amounts of liquid.

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Answer:

C) ∠1 ≅ ∠7

Step-by-step explanation:

If ∠1 = ∠3, then ∠3 = ∠7, behind there is written ∠1 = ∠3, so it's A) ∠1 = ∠7.

The value of the probability is 0.3125 and this is proved by the calulations below

The probability of getting exactly 3 heads in 5 coin tosses can be calculated by multiplying the probability of one specific combination of 3 heads and 2 tails by the number of possible combinations.

The probability of one specific combination, for example HHTTT, is (1/2)^5 = 1/32, because each toss has a 1/2 chance of being a head or a tail.

There are 5C3 = 10 possible combinations of 3 heads and 2 tails in 5 tosses.

For example: HHTTT, HTHTT, HTTHT, HTHHT, TTHHH, etc.

Therefore, the probability of getting exactly 3 heads is:

Probability = 10 * (1/32)

Probability = 10/32

Probability = 0.3125.

Hence, the value of the probability is 0.3125.

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