By which rule are these triangles congruent?
A)
AAS
B)
ASA
C)
SAS
D)
SSS

If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.

Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:

x + (x-8) = 22

Simplifying, we get:

2x - 8 = 22

Adding 8 to both sides:

2x = 30

Dividing by 2:

x = 15

We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.

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Answer:

Step-by-step explanation:

Product means multiply.

-300

Answer:

30

Step-by-step explanation:

300/4=75

75/5=15

15*2=30

The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).

In determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.

Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.

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The angles don't need to be lined up vertically, or have one over top another. You could have them laid out horizontally. All that matters is that they are opposite angles after an X shape has been formed by two crossing lines. Vertical angles are always congruent.

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Answer:

Five hours at both ski resorts cost the same

Step-by-step explanation:

Let x = hours      Let y = cost

Black Diamonds Ski Resort:  25 + 10x = y

Bunny Hill:  50 + 5x = y

Since the cost should be equal, we can substitute for these two equations.

25 + 10x = 50 + 5x

Solve for x:

x = 5

Check: Plug in for x

Black Diamonds Ski Resort: 25 + 10(5) = 25 + 50 = $75

Bunny Hill: 50 + 5(5) = 50 + 25 = $75

The cost is the same, so we know that five hours has the same cost at both ski resorts.

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Answer:

107

Step-by-step explanation:

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Answer:

2/3 (x-12)

Step-by-step explanation:

2/3x-8

2/3(x-3x4)

2/3(x-12)

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Answer:yes because the input and the output don’t repeat

Step-by-step explanation:

9514 1404 393

Answer:

  yes

Step-by-step explanation:

Each increment of 1 in x produces an increment of 4 in y. When the increments have the same ratio like that (4:1), the function is linear. The equation for it is ...

  y = 4x +12 . . . a linear function

Answer:

x= -4,y=2............

Answer:

16/3 hours  5 1/3

Step-by-step explanation:

Answer: 5 1/3

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

3(x+5.50)-3

3x+16.50)-3

-3(3x+16.50)

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Step-by-step explanation:

Hope it will help you...

Step-by-step explanation:

to solve this you must first understand the "mean" value of a data set or "distribution".

the mean value is simply the sum of all measured or reported values divided by the number of measurements or reports.

if several data points have the same measured value, then so be it. they are all counting.

and that is what was happening here. the value "2" for example appeared 5 times during the measurements or reports.

"4" occurred 8 times. and so forth.

that is what "frequency" means : how often did that value occur during the observed period of measurements or reports ?

so, how many data points are there ? meaning how many measurements or reports were done in total ?

well, the sum of all frequencies :

(5 + 8 + x + 6 + 3)

to calculate the mean value we could now simply add every value up like 2+2+2+2+2.

or we help ourselves by using multiplication as a shortcut :

(2×5 + 4×8 + 6×x + 8×6 + 10×3)

the mean value is then as explained at the beginning :

(2×5 + 4×8 + 6×x + 8×6 + 10×3) / (5 + 8 + x + 6 + 3) =

= (10 + 32 + 6x + 48 + 30) / (22 + x) =

= (120 + 6x) / (22 + x) = 5.625

120 + 6x = 5.625(22 + x) = 123.75 + 5.625x

-3.75 = -0.375x

3.75 = 0.375x

x = 10

the frequency of 6 was 10 to achieve the mean value of 5.625.

add on : so, the way to solve this as so many similar problems in other areas is to set the principle (including a variable) equal to an actual outcome, and then you solve for that variable.

Answer:

a) 34.46% of​ 10-year-old boys is tall enough to ride this​ coaster.

b) 78.81% of​ 10-year-old boys is tall enough to ride this​ coaster

c) 44.35% of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 54, \sigma = 5\)

a. What proportion of​ 10-year-old boys is tall enough to ride the​ coaster?

This is 1 subtracted by the pvalue of Z when X = 56.

So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{56 - 54}{5}\)

\(Z = 0.4\)

\(Z = 0.4\) has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% of​ 10-year-old boys is tall enough to ride this​ coaster.

b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of​ 10-year-old boys is tall enough to ride this​ coaster?

This is 1 subtracted by the pvalue of Z when X = 50.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{50 - 54}{5}\)

\(Z = -0.8\)

\(Z = -0.8\) has a pvalue of 0.2119

1 - 0.2119 = 0.7881

78.81% of​ 10-year-old boys is tall enough to ride this​ coaster.

c. What proportion of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a?

Between 50 and 56 inches, which is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.

From a), when X = 56, Z has a pvalue of 0.6554

From b), when X = 50, Z has a pvalue of 0.2119

0.6554 - 0.2119 = 0.4435

44.35% of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

Answer:

41.93 degrees

Step-by-step explanation:

Answer:

y = x -6

Step-by-step explanation:

First find the slope

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

   = (0- -6)/(6-0)

   =( 0+6)/(6-0)

   = 6/6

   = 1

The slope is 1 and the y intercept is -6

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = x -6

Answer:

the answer is C

Step-by-step explanation:

y = x -6

w=40m

m is the independent variable.

w is the dependent variable.

The first equation is incorrect.

The second equation is correct.

The third equation is correct.

Let's go through each equation and determine whether it is correct or incorrect:

(b²+7b-9)+(4b-6b²) = -8b² + 14b-9

To determine if this equation is correct, we need to simplify both sides and check if they are equal.

On the left side:

(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9

On the right side:

-8b² + 14b - 9

Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.

(4a+6)-(3a²-9a+1)=-3a²+ 13a +5

Again, we need to simplify both sides of the equation and check if they are equal.

On the left side:

(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5

On the right side:

-3a² + 13a + 5

Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.

(12c-8c²)+(5c²- 10c) = -3c²+2c

Again, let's simplify both sides and compare them.

On the left side:

(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c

On the right side:

-3c² + 2c

Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.

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The given expression is

=ab+cd+ef+gh

The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction,  Multiplication and Division.

→The expression consists of four terms which are, ab, cd, ef, and gh.

→Each term contains

Two factors.

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Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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Option C, With a mean height of 65 inches as well as a standard deviation of 3.5 inches for a particular group of women, the height distribution is roughly typical.

Let X represent the height distribution for a certain group of women.

So, X ~ Normal(μ = 65, σ = 3.5)

where, μ = mean height = 65 inches

σ = standard deviation = 3.5 inches

Now imagine that two distinct random samples one of size 5 and the other of size 85 were drawn from the population.

First off, because both random samples were drawn from the same population, both distributions will roughly follow a regular distribution since the population data has a normal distribution.

Additionally, the formula provides the sample distribution's mean;

Population Mean = Sample Mean

Sample Mean = Population Mean

X = μ

This indicates that the mean measurement for both distributions will be 65 inches.

I'll now discuss the standard deviation. For sampling distribution, the standard deviation formula is provided,

S.D. = σ ÷ √n

Consequently, the distribution's standard deviation for the n = 5 sample size is

S.D1. = 3.5 ÷ √5 = 1.565 inches

With a sample size of n = 85, the distribution's standard deviation is,

S.D2. = 3.5 ÷ √85 = 0.379 inches.

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The question is -

The distribution of height for a certain population of women is approximately normal with a mean of 65 inches and a standard deviation of 3.5 inches. Consider two different random samples were taken from the population, one of size 5 and one of size 85. Which of the following is true about the sampling distributions of the sample mean for the two sample sizes?

A.) Both distributions are approximately normal with a mean of 65 and a standard deviation of 3.5.

B.) Both distributions are approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

C.) Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.

D.) Only the distribution for size 85 is approximately normal. Both distributions have a mean of 65 and a standard deviation of 3.5.

E.) Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.