At a pep rally 14 out of 20 students who entered the gym were carrying a backpack. Based on this information, if 1,400 students were at the pep rally, how many students could be expected to be carrying a backpack

Based on the given information, we know that triangle LMN is congruent to triangle PQR, so the corresponding angles are congruent. The value of x in degrees is 56.

Therefore, the measure of angle N in triangle LMN is equal to the measure of angle R in triangle PQR, which can be found using the angle sum property of triangles:

angle R = 180 - angle P - angle Q

= 180 - 52 - 72 (since angle P is not given)

= 56 degrees

Since angle N in triangle LMN is congruent to angle R in triangle PQR, we have:

x = angle N = angle R = 56 degrees

Therefore, the value of x in degrees is 56.

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LMN≅PQR

What is the value of x in degrees? Enter your answer in the box. ​x​ = °

Coordinate graph showing triangle L M N and triangle P Q R. Triangle L M N has coordinates begin ordered pair negative 2 comma 3 end ordered pair, begin ordered pair negative 1 comma 6 end ordered pair, and begin ordered pair 1 comma 3 end ordered pair. Triangle P Q R has coordinates begin ordered pair 2 comma 1 end ordered pair, begin ordered pair 3 comma negative 4 end ordered pair, and begin ordered pair 5 comma negative 1 end ordered pair. The measure of angle L is labeled 72 degrees. The measure of angle N is labeled x degrees. The measure of angle Q is labeled 52 degrees.

There are 128 four-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7, with 7 appearing before 3).

To determine the number of 4-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7 with 7 appearing before 3), we can break down the problem step by step.

Step 1: Choose the positions of 3 and 7.

Since 7 must appear before 3, we have two possible cases:

Case 1: 7 is in the thousands place, and 3 is in the hundreds place.

Case 2: 7 is in the hundreds place, and 3 is in the thousands place.

Step 2: Determine the digits in the remaining two positions.

In the remaining two positions (tens and units place), we have eight possible digits to choose from (0, 1, 2, 4, 5, 6, 8, 9). This is because we have used the digits 3 and 7, leaving eight options for the remaining two positions.

Step 3: Calculate the total number of valid numbers.

For each case in Step 1, we multiply the number of choices from Step 2 to get the total count.

Case 1: 7 in thousands place, 3 in hundreds place.

In this case, we have 8 choices for the tens place and 8 choices for the units place. The total count for Case 1 is 8 * 8 = 64.

Case 2: 7 in hundreds place, 3 in thousands place.

Similarly, we have 8 choices for the tens place and 8 choices for the units place. The total count for Case 2 is also 8 * 8 = 64.

Step 4: Sum up the counts from both cases.

To get the final answer, we sum up the counts from both cases:

64 (Case 1) + 64 (Case 2) = 128.

Therefore, there are 128 four-digit numbers that satisfy the given conditions (exactly one digit 3 and exactly one digit 7, with 7 appearing before 3).

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Answer:

This question are you saying that Joe spends 4 dollars or do you mean saves 4 dollars

The length of each side of the sign will be 14.81-inch approx.

It is assumed that an Octagon sign is created by cutting out triangles from a square's corners, and that the stop sign's overall length is 36 inches. Since we are aware that squares have right angles on all four sides, we can use Pythagoras' theorem to solve for the side of the sign in the image below.

           \(s^{2} =x^{2} +x^{2} \\s^{2}=2x^{2} ...................Eq.1\)

Also, it is a square. So, the measurement of length from side to side

            \(2x+s=36....................Eq.2\)

solving Eq.1 we get,

\(s=\sqrt{2} x\)...putting this value in Eq.2,

            \(s=36-2x\\\\\sqrt{2} x=36-2x\\\\x=\frac{36}{2+\sqrt{2} }\)

Putting this value of x in Eq.1,

          s = 14.8

Hence, The length of each side of the sign will be 14.81-inch approx.

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1.5(4) = 6

jess used 6 cups of rice

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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T A can be seen as a linear transformation from R^2 to R^3.

To find the range and codomain of the matrix transformation T A, we need to first determine the matrix T A . The matrix T A is obtained by multiplying the input vector x by A:

T A (x) = A x

Therefore, T A can be seen as a linear transformation from R^2 to R^3.

To determine the range of T A , we need to find all possible outputs of T A (x) for all possible inputs x. Since T A is a linear transformation, its range is simply the span of the columns of A. Therefore, we can find the range by computing the reduced row echelon form of A and finding the pivot columns:

A =  (\left[\begin{array}{cc}1 & 2 \ 1 & -2 \ 0 & 1\end{array}\right]) ~ (\left[\begin{array}{cc}1 & 0 \ 0 & 1 \ 0 & 0\end{array}\right])

The pivot columns are the first two columns of the identity matrix, so the range of T A is spanned by the first two columns of A. Therefore, the range of T A is the plane in R^3 spanned by the vectors [1, 1, 0] and [2, -2, 1].

To find the codomain of T A , we need to determine the dimension of the space that T A maps to. Since T A is a linear transformation from R^2 to R^3, its codomain is R^3.

If the functions were not linear, it would not make sense to talk about their range or codomain in this way. The concepts of range and codomain are meaningful only for linear transformations.

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We cannot construct such an interval using the normal approximation.

Null Hypothesis: The heart transplant procedure did not alter the survival rates of the observed patients. Alternate Hypothesis, Ha: The claim was that the patients getting a heart transplant were more likely to survive than those who did not.

Normal distribution is the approximation for large distribution from binomial, poisson distribution etc. Moreover, the variables are discrete and few; and instead of the actual observations we are working on counts data. In the given situation it is preferred to use chi square distribution. As chi square test is used we can check whether the two groups are the same or different. Therefore, it is not possible to construct a confidence interval.

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The addition of the given algebraic expressions is; -7x² - 6x + 1

When adding algebra expressions, what we do is to find like terms and group them and then add and then we have the final expression.

The algebraic expressions given are;

-8x - 3 and -7x² + 2x + 4.

Thus, the addition is;

-8x - 3 + -7x² + 2x + 4.

Grouping like terms together gives;

-7x² + 2x - 8x + 4 - 3

= -7x² - 6x + 1

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The given system of equations do not have a solution since their related line equations have the same slope.

The given system of equations is:

-x + 5y = 3   .......... (1)

2x - 10y = 4   ........(2)

In Equation (1), add both sides by (-5y)

-x + 5y + (-5y) = 3 + (-5y)

-x = -3 - 5y

Multiply by (-1)

x = 3 + 5y

Substitute x = 3 + 5y into equation (2)

2x - 10y = 4

2.(3 + 5y) - 10y = 4

6 + 10y - 10y = 4

6 = 4 (False)

Since the last equation is false, we might suspect that the given system of solution does not have solutions.

We need to check the slope of both equations:

-x + 5y = 3

⇒ 5y = x + 3

⇒ y = 1/5 x + 3/5

2x - 10y = 4

⇒ -10 y = -2x + 4

⇒ y = (2/10) x - 4/10

⇒ y = 1/5 x - 2/5

We can see that both equations have the same slope, i.e. 1/5.

Hence, they do not have solutions since the lines are parallel to each other.

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Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

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Answer:

y = 2(x²+3x)

Step-by-step explanation:

The given statement "When creating a contact sheet digitally, it is possible to share your sheet digitally, but it is not possible to print a copy of it." is false. Because Digital contact sheets can be printed on paper using a printer, allowing for physical copies to be made.

When creating a contact sheet digitally, you have the flexibility to both share it digitally and print physical copies if desired. Digital contact sheets can be easily shared through various digital channels such as email, messaging apps, or file-sharing platforms.

Additionally, you can also choose to print a copy of the contact sheet using a printer. Printing a digital contact sheet allows you to have a tangible copy that can be used for reference or distribution.

So, while sharing the sheet digitally is possible, it is certainly not true that printing a copy of it is not possible. So, the given statement is False.

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Therefore, the total number of ways the lights can be arranged on the string is: 14! / (2! * 4! * 5! * 2!).

To find the number of ways the lights can be arranged on a string, we need to calculate the total number of permutations.

The total number of lights is 2 red lights + 4 yellow lights + 5 blue lights + 1 green light + 2 pink lights = 14 lights.

Since all the lights are distinct, we can arrange them in 14! (factorial) ways. However, since there are repetitions of certain colors, we need to account for that.

The red lights are identical, so we divide by 2! (the number of permutations of the red lights among themselves).

The yellow lights are identical, so we divide by 4! (the number of permutations of the yellow lights among themselves).

The blue lights are identical, so we divide by 5! (the number of permutations of the blue lights among themselves).

The pink lights are identical, so we divide by 2! (the number of permutations of the pink lights among themselves).

Therefore, the total number of ways the lights can be arranged on the string is:

14! / (2! * 4! * 5! * 2!)

You can calculate this expression to find the specific number of arrangements.

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Answer:

\(a_{1}=35\) degrees

\(a_{2} = 75\) degrees

\(a_{3}=70\) degrees

Step-by-step explanation:

I have a picture that explains it.

The histogram that correctly represents the set of data for the students in gymnastics class is Histogram B .

To find the histogram, first order the numbers in ascending order :

3, 4, 7, 8, 9, 10, 11, 12, 12 15, 16 , 18

Then look at the intervals and put the numbers into those intervals.

1 - 5 = 2 numbers

6 - 10 = 4 numbers

11 - 15 = 4 numbers

16 - 20 = 2 numbers

The histogram that shows this set of data is therefore Histogram B as shown attached.

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Answer and Step-by-step explanation: Power Functions are of the form:

\(f(x)=ax^{b}\)

where a is scaling factor, which means, it moves the values of \(x^{b}\) up or down;

and b is exponent or power, which determines the rate of growth or decay of the function.

The difference between exponential and power functions, is that in power functions, a variable base is elevated to a fixed exponent.

For that reason, Equations:

A. \(f(x)=2^{4\sqrt{x} }\)

B. \(f(x)=\frac{\pi}{x}\)

C. \(f(x)=2.3^{x}\)

D. \(f(x)=2^{3\sqrt{x} }\)

are NOT power functions.

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 2, - 4 )

m = \(\frac{-4-2}{-2-0}\) = \(\frac{-6}{-2}\) = 3

Since slopes of parallel lines are equal then every line parallel will have a slope of 3

Answer:

A solar eclipse is possible during a new moon.

Answer:

52, if I understand the question correctly.

Step-by-step explanation:

Is this:

3ab + 2b

and we want to know the value when a = -5 and b = 4?

If so:

3ab + 2b

3(-5)(4) + 2(4)

-60 + 8 = -52

-52, if I understand the question correctly.

3ab + 2b

and we want to know the value when a = -5 and b = 4

If so:

3ab + 2b

3(-5)(4) + 2(4)

-60 + 8 = -52

Values 3ab + 2b ​​are fundamental and fundamental beliefs that guide and motivate attitudes and actions. They help us determine what is important to us. Value is the goods, services or monetary value of a thing or person. An example of value is the amount an appraiser declares after appraising a home. An example of value is the value of a consultant's contribution to a committee. noun.

Values ​​reflect our sense of right and wrong. They help us grow and develop. They help shape the future we want. The choices we make every day reflect our values.

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Answer:

Step-by-step explanation:here is a example:Recall that the volume of a regular prism is given by the area of the base times the height.

Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.

The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.

Recall that the are of a triangle is given by 1/2 base times height.

Thus the area of of the pentagon base of the prism is given by

Therefore, the volume of the prism is given by volume=7x(2x+1)=14x2+7x

There are 120 different ways to award the gold, silver, and bronze medals to the 10 women in the 100 meters race.

The number of ways that the gold, silver, and bronze medals can be awarded to 10 women is a combination problem.

We can use the formula for combinations to determine the number of ways to choose 3 women out of 10 for the medals:

\(nCr = n! / (r! * (n - r)!)\)

Where n is the total number of women (10) and r is the number of medals (3).

So, the number of ways to award the gold, silver, and bronze medals to the 10 women is:

\(10C3 = 10! / (3! * (10 - 3)!) = 120\)

Therefore, there are 120 different ways to award the gold, silver, and bronze medals to the 10 women in the 100 meters race.

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Answer:

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Step-by-step explanation:

The study that found only 23% of social workers use the internet to provide services, compared to 48% of professional counselors is an example of Descriptive social research.What is descriptive social research?

Descriptive social research is a method that involves observing and describing behavior and social realities. Descriptive research aids in understanding, explaining, and describing the phenomena that are under study. This type of research is most often used to define characteristics, patterns, or relationships between variables by providing an accurate picture of reality and an in-depth understanding of the social world.

The study that found only 23% of social workers use the internet to provide services, compared to 48% of professional counselors is an example of Descriptive social research. Explanation:Descriptive research is the most common type of social research. This type of research is often used to describe characteristics, patterns, or relationships between variables by providing an accurate picture of reality and an in-depth understanding of the social world.

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Answer:

Step-by-step explanation:

I think not 100% sure

Hope this helps :)

Pls mark brainliest :3

And have an amazing day <3

The balance of the PLUS loan at the time of graduation is approximately $5,043.66.

The correct option is c. $5,043.66.

To calculate the balance of the PLUS loan at the time of graduation, we can use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)\)

Where:

A = Final amount (balance) of the loan

P = Principal amount (initial loan amount) = $4,590

r = Annual interest rate (6.3% or 0.063)

n = Number of times the interest is compounded per year (monthly compounding, so n = 12)

t = Time in years (18 months, so t = 18/12 = 1.5 years)

Plugging in the values into the formula:

\(A = 4590(1 + 0.063/12)^{(12 \times 1.5)]\)

\(A = 4590(1 + 0.00525)^{(18)\)

\(A = 4590(1.00525)^{ (18)\)

A ≈ 4590(1.09941)

A ≈ 5043.66.

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The angle 1 can be named as follows:

∠RST

∠TSR

∠S

There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

Therefore, let's name the angle 1 indicated on the diagram as follows:

Hence, the different ways to name the angle 1 is as follows:

∠RST or ∠TSR

Or

∠S

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