△EFG~△BCD. Find EG.
8
8
E
F
G
1
1
B
C
D
EG =

Answer:

Please check the explanation.

Step-by-step explanation:

Part a)

Given

It is clear that m∠ABD and m∠CBD lie on a straight line.

Thus, the sum of m∠ABD and m∠CBD will be 180°.

Hence,

m∠ABD and m∠CBD are supplementary angles.

Part b)

As m∠ABD and m∠CBD are supplementary angles, so the sum of m∠ABD and m∠CBD will be 180°.

Thus,

m∠ABD + m∠CBD = 180°

substitute m∠ABD = (7q-46)° and m∠CBD = (3q + 6)°

(7q-46)° + (3q + 6)° =  180°

Part c)

Given the equation

(7q-46)° + (3q + 6)° =  180°

Combining the like terms

7q + 3q - 46 + 6 = 180

10q - 40 = 180

10q = 180 + 40

10q = 220

divide both sides by 10

10q/10 = 220/10

q = 22

Therefore, the value of q = 22

Part d)

As

m∠ABD = (7q-46)°

substituting q = 22

m∠ABD = 7(22) - 46

             = 154 - 46

             = 108°

also

m∠CBD = (3q + 6)°

substituting q = 22

m∠CBD = 3(22) + 6

              = 66+6

              = 72°

Therefore,

Answer:

Here you go

Step-by-step explanation:

Answer:

Slope of green line:

\(m = \frac{ - 3 - 3}{4 - ( - 4))} = - \frac{6}{8} = - \frac{3}{4} \)

Slope of red line:

\(m = \frac{3 - ( - 5)}{3 - ( - 3)} = \frac{8}{6} = \frac{4}{3} \)

The slopes of these two lines are negative reciprocals of each other.

Therefore, the correct answer is True (A).

Answer:

Step-by-step explanation:

The second equation tells you ...

  ♧ = 21/3 = 7

The third equation tells you ...

  ♢ = 20 -2(7) = 6

Then the first equation tells you ...

  ♤ = 15 -7 -6 = 2

Finally, the last equation tells you ...

  ♡ = 13 -6 -2 = 5

Answer

Club = 7

Diamond = 6

Spade = 2

Heart = 5

Step-by-step explanation

Here it shows that 1 club + 1 diamond + 1 spade is equal to 15. Ok, let's get back to that one later.

In the next hint it shows that 3 clubs equals 21. So, in order to get the value of the club, divide 21 by 3, and you'll get 7. This means that 7 is the value of the club.

Now on to the third hint. Here it shows that 1 diamond plus 2 clubs are equal to 20. We already got the value of the club, which is 7, so add 7+7 and you'll get 14. Then, subtract 14 from 20 and you'll get the value of the diamond, which is 6.

Finally, the fourth hint. Here it shows that 1 diamond + 1 heart + 1 spade = 13. So, inorder to get the value of the heart, add the value of the diamond and the spade, which sums up to 8. Then subtract 8 from 13 and you'll get the value of the heart, which is 5.

After answering the provided question, we can conclude that t = 1.833 is standard deviation the critical value for a one-tailed t-test with 9 degrees of freedom and a significance level of 0.05.

A statistic that communicates the fluctuation or variance of a number set is the standard deviation. A high standard deviation indicates that the values seem to be more dispersed, whereas a low standard deviation indicates that the values are closer to the established mean. The standard deviation is a measure of how far the data varies from the mean (or ). So when standard deviation is small, the data tends to cluster around the mean; when it is huge, the data is more dispersed. The standard deviation represents the average variability of something like the data set. It displays the average deviation from the mean of each score.

To decide whether the new manufacturing technique should be used, we must first determine whether the standard deviation of the drug concentration in the new process is less than 4 g/l. A hypothesis test can be used with the following null and alternative hypotheses:

H0 (null hypothesis): In the new process, the standard deviation of drug concentration is 4 g/l.

Alternative hypothesis (Ha): In the new process, the standard deviation of drug concentration is less than 4 g/l.

For the standard deviation, we can use a one-tailed t-test with a

\(t = (n - 1) * s^2 / \sigma^2\\s = \sqrt(1/(n-1) * \sum(xi - x\bar)^2) = 0.004 g/l\\t = (n - 1) * s^2 / \sigma^2 = (10 - 1) * 0.004^2 / 4^2 = 0.0007\)

t = 1.833 is the critical value for a one-tailed t-test with 9 degrees of freedom and a significance level of 0.05.

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Answer:

the answer is 135

Step-by-step explanation:

........

The height of the right triangle is 24 centimeters. This is determined by solving the equation for the area of the triangle, which is given as 96 cm², and considering that the height is 3 times the length of the base. By substituting the values and solving the equation, we find that the height is indeed 24 centimeters.

To determine the height of the right triangle, we can use the formula for the area of a triangle, which is given by the formula A = (1/2) * base * height. In this case, the area is known to be \(96 cm^2\).

Let's denote the length of the base as x. According to the problem statement, the height is 3 times the length of the base, so the height can be expressed as 3x.

Substituting these values into the area formula, we get:

\(96 = (1/2) * x * 3x\)

Simplifying the equation:

\(96 = (3/2) * x^2\)

To solve for x, we can divide both sides of the equation by (3/2):

\(64 = x^2\)

Taking the square root of both sides, we find:

x = 8

Since the height is 3 times the length of the base, the height is:

3 * 8 = 24 centimeters.

Therefore, the height of the right triangle is 24 centimeters.

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The acceptable conclusions of a hypothesis test depend on the test and significance level. If the test statistic falls outside the rejection region, there's insufficient evidence to reject the null hypothesis. If it falls within, there is sufficient evidence to support the alternative hypothesis. The statement is true.

However The acceptable conclusions to a hypothesis test depend on the specific test and the chosen significance level,  in general:

Therefore, the acceptable conclusions to a hypothesis test are:

The main point of the answer is that the acceptable conclusions to a hypothesis test depend on the specific test and chosen significance level, but generally, if the test statistic falls outside the rejection region, there is insufficient evidence to reject the null hypothesis, and if it falls within the rejection region, there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.

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One way to simplify variables with many levels (or decimal places) when creating a frequency distribution is to organize the data into class intervals (option B).

By grouping the data into intervals, the frequency distribution becomes more manageable and easier to interpret. This process involves dividing the range of values into distinct intervals or categories and then counting the number of observations falling within each interval. Class intervals provide a summary of the data by grouping similar values together, reducing the complexity of individual levels or decimal places.

This simplification technique is particularly useful when dealing with large datasets or continuous variables that have numerous levels or decimal values, allowing for a clearer representation and analysis of the data.

Option B holds true.

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Answer:

3 loaves

Step-by-step explanation:

See attachment for complete question.

Represent Loaves with L and Flour with F

Since L is proportional to F, the relationship can be defined as:

L = kF

Where k represent the constant of proportionality

When L = 4, F = 20

Substitute these values in the above formula.

4 = k * 20

Divide both sides by 20

4/20 = k

⅕ = k

k = ⅕

To solve for 15 cups of Flour, we have:

F = 15

Substitute 15 for F and ⅕ for k in L = kF

L = ⅕ * 15

L = 3

Hence, 3 loaves will be baked using 15 cups of flour

Answer:

6 trips

Step-by-step explanation:

12 divided by 4 equals 3

18 divided by 3 equal 6

she will have to take six trips to drive 18 kilometers.

Answer:

Your answer is (6x−1)(3x−2)

Step-by-step explanation:

A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

A function is a mathematical concept that assigns a unique output value for each input value.

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

To model the world population data, we can use a mathematical function to fit the data points. A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

To find the expected world population in 2017, we would need to estimate the polynomial regression model using the data points provided and then evaluate the model at the year 2017.

Research shows that the actual world population in 2017 was approximately 7.5 billion, which is higher than our estimated value based on the limited data points provided. This highlights the importance of considering additional factors and data when making predictions about the world population.

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The complete question is

Given: AQ ≅ RQ, it should be noted that AQY ≅ RQF based on SAS Congruence. Therefore, AQY ≅ RQF.

Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

1. AQ ≅ RQ (Given)

2. ∠YAF and ∠FRY are right angles (Given)

3. ∠AQY = ∠RQF (Vertical angles are congruent)

4. AQ = RQ (Given)

5. AY = RY (Side-Angle-Side Congruence)

6. ∠QYA = ∠RFQ (Angle-Side-Angle Congruence)

7. AQY ≅ RQF (SAS Congruence)

Therefore, AQY ≅ RQF.

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Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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Answer:

4 1/2 pounds of meat

Step-by-step explanation:

if you have 2 adding fractions with 3 quarters just add it like 1 1/2 + 2 1/2 and add half to your final answer

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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Answer:

Step-by-step explanation:

\(X_1 = 7X_2\\X_1 + X_2 \leq 60\\7X_2 + X_2 \leq 60\\8X_2 \leq 60\\\)

since the two numbers are integers,

the largest the smaller number can be is 7

so our numbers are

\((1, 7), (2, 14), (3, 21), (4, 28), (5, 35), (6, 42), (7, 49)\)

the two integers are 7, 49

The largest two numbers which make the statement true are 7 and 49.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.

Given that the larger of two integers is 7 times the smaller. The sum of the integers is at most 60.

The two equations will be,

x₁ = 7x₂

x₁ + x₂ ≤ 60

7x₂ + x₂≤ 60

8x₂ ≤ 60

The collection of the numbers are (1,7),(2,14),(3,21),(4,28),(5,35),(6,42),(7,49).

The largest number is 7 in the collection.

Therefore, the largest two numbers which make the statement true are 7 and 49.

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The surface can be described as a circular cylinder whose axis is parallel to the y-axis, whose cross-section is a circle, and whose radius is the square root of 7. Hence, the correct option is circular cylinder.

The surface is a circular cylinder whose axis is parallel to the y-axis, whose cross-section is a circle, and whose radius is the square root of 7. In more detail, this surface is a circular cylinder.

This implies that the graph of the surface would be an infinite number of lines (in one direction) that are parallel to the y-axis. Because the x and z coordinates in this equation are squared, the cylinder has a circular cross-section.

If the radius of the circle is equal to the square root of 7, the circle is positioned at a distance of the square root of 7 from the y-axis.

Therefore, the surface can be described as a circular cylinder whose axis is parallel to the y-axis, whose cross-section is a circle, and whose radius is the square root of 7. Hence, the correct option is circular cylinder.

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The work done pulling the bucket to the top of the well is 104,299.4 pound-force-feet (lb*ft).

To find the work done pulling the bucket to the top of the well, we need to consider the weight of the bucket, the weight of the water, and the work done against gravity.

First, let's calculate the weight of the bucket and water combined. The weight of the bucket is 4 pounds, and the weight of the water is 35 pounds. Therefore, the total weight is 4 + 35 = 39 pounds.

Next, let's calculate the distance the bucket is pulled up. The well is 83 feet deep, so the bucket is pulled up a distance of 83 feet.

Now, let's calculate the work done against gravity. Work is calculated by multiplying the force applied by the distance over which the force is applied. In this case, the force is equal to the weight of the bucket and water, which is 39 pounds. The distance is 83 feet.

Work = Force * Distance
Work = 39 pounds * 83 feet

To calculate the work, we need to convert the weight from pounds to a unit called pound-force (lbf). 1 pound force is equal to the force exerted by a mass of 1 pound under acceleration due to gravity.

To convert from pounds to pound-force, we need to multiply by the acceleration due to gravity. The acceleration due to gravity is approximately 32.2 feet per second squared.

39 pounds * 32.2 feet per second squared = 1255.8 pound-force

Finally, we can calculate the work done pulling the bucket to the top of the well.

Work = 1255.8 pound-force * 83 feet
Work = 104,299.4 pound-force-feet (or lb*ft)

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The solution to the given system of equations x₁ +5x₂ + 4x₂ + 3x4 +6x5 = 2 x₁ +6x₂ +6x₂ +6x₁ +7x₂5 = 6 x₁ +7x₂ +8x3 +10x4 +8x5 = 12 x₁ +6x₂ +6x3 +7x₁ +7x₂ = 8 in vector notation is x = [1, 0, 1, 1, 1].

The system of equations can be written in vector notation as: A*x = b,where x is the column vector [x₁, x₂, x₃, x₄, x₅], A is the coefficient matrix, and b is the column vector [2, 6, 12, 8].

To find the solution, we can solve the equation Ax = b by taking the inverse of matrix A and multiplying it with vector b: x = A⁻¹ * b.

To solve the system of equations, we rearrange the equations to match the vector notation. The coefficients of the variables form the coefficient matrix A, and the right-hand side values form the column vector b. By taking the inverse of A, we can solve for the vector x.

Note that for the given system of equations, it is important to verify if matrix A is invertible. If A is not invertible, it means that the system has either no solution or infinitely many solutions. Additionally, if A is a singular matrix, the inverse does not exist.

Please note that without the explicit values of the coefficients in the equations, it is not possible to provide the exact solution in vector notation.

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Answer:

he is correct bc the pattern correct

Step-by-step explanation:

The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

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Answer:

The lenght of AB is (4.45)

Step-by-step explanation:

Thanks and, Is that right??

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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Answer:

pi=3.14

Step-by-step explanation:

3.14

Answer:

You’ve studied and now you’re geared up for the ACT math section (whoo!). But are you ready to take on the most challenging math questions the ACT has to offer? Do you want to know exactly why these questions are so hard and how best to go about solving them? If you’ve got your heart set on that perfect score (or you’re just really curious to see what the most difficult questions will be), then this is the guide for you.

We’ve put together what we believe to be the most 21 most difficult questions the ACT has given to students in the past 10 years, with strategies and answer explanations for each. These are all real ACT math questions, so understanding and studying them is one of the best ways to improve your current ACT score and knock it out of the park on test day.

Brief Overview of the ACT Math Section

Like all topic sections on the ACT, the ACT math section is one complete section that you will take all at once. It will always be the second section on the test and you will have 60 minutes to completed 60 questions.

The ACT arranges its questions in order of ascending difficulty. As a general rule of thumb, questions 1-20 will be considered “easy,” questions 21-40 will be considered “medium-difficulty,” and questions 41-60 will be considered “difficult.”

The way the ACT classifies “easy” and “difficult” is by how long it takes the average student to solve a problem as well as the percentage of students who answer the question correctly. The faster and more accurately the average student solves a problem, the “easier” it is. The longer it takes to solve a problem and the fewer people who answer it correctly, the more “difficult” the problem.

(Note: we put the words “easy” and “difficult” in quotes for a reason—everyone has different areas of math strength and weakness, so not everyone will consider an “easy” question easy or a “difficult” question difficult. These categories are averaged across many students for a reason and not every student will fit into this exact mold.)

All that being said, with very few exceptions, the most difficult ACT math problems will be clustered in the far end of the test. Besides just their placement on the test, these questions share a few other commonalities. We'll take a look at example questions and how to solve them and at what these types of questions have in common, in just a moment.

But First: Should You Be Focusing on the Hardest Math Questions Right Now?

If you’re just getting started in your study prep, definitely stop and make some time to take a full practice test to gauge your current score level and percentile. The absolute best way to assess your current level is to simply take the ACT as if it were real, keeping strict timing and working straight through (we know—not the most thrilling way to spend four hours, but it will help tremendously in the long run). So print off one of the free ACT practice tests available online and then sit down to take it all at once.

Once you’ve got a good idea of your current level and percentile ranking, you can set milestones and goals for your ultimate ACT score. If you’re currently scoring in the 0-16 or 17-24 range, your best best is to first check out our guides on using the key math strategies of plugging in numbers and plugging in answers to help get your score up to where you want it to. Only once you've practiced and successfully improved your scores on questions 1-40 should you start in trying to tackle the most difficult math problems on the test.

If, however, you are already scoring a 25 or above and want to test your mettle for the real ACT, then definitely proceed to the rest of this guide. If you’re aiming for perfect (or close to), then you’ll need to know what the most difficult ACT math questions look like and how to solve them. And luckily, that’s exactly what we’re here for.

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Ready, set...

21 Hardest ACT Math Questions

Now that you're positive that you should be trying out these difficult math questions, let’s get right to it! The answers to these questions are in a separate section below, so you can go through them all at once without getting spoiled.

#1:

body_ACT_0506_-_56

#2:

body_ACT_0506_-_59

#3:

body_ACT_0809_-_38_J

#4:

body_ACT_0809_-_54

#5:

body_ACT_0809_-_55-1

#6:

body_ACT_0809_-_56

#7:

body_ACT_0809_-_57-1

#8:

body_ACT_0809_-_60

#9:

body_ACT_1112_-__48-1

#10:

body_ACT_1112_-_45

#11:

body_ACT_1112_-_51-1

#12:

body_ACT_1112_-_52

#13:

body_ACT_1112_-_53

#14:

body_ACT_1112_-_58

#15:

body_ACT_1314_-_55-1

#16:

body_ACT_1314_-_59

#17:

body_ACT_1516_-_43

#18:

body_ACT_1516_-_44

#19:

body_ACT_1516_-_52

#20:

body_ACT_1516_-_57-1

#21:

body_ACT_1516_-_58-1

Step-by-step explanation:

Answer:

f(12) = 90

Step-by-step explanation:

This is more of a notation problem than anything else.

The x on the left means that the variable is x. That sounds weird I know, but it starts out this way.

f(variable) =  8*variable - 6

Where you see the word variable, you put the letter x and that gives you the question.

f(x) = 8*x - 6

That is math shorthand for whatever you see on the left, like an x or in this case 12, you put the value 12 in for x on the right. It will look like this.

f(12) = 8*12 - 6   Now it just becomes a calculator problem.

f(12) = 96 - 6

f(12) = 90

Step-by-step explanation:

We know that, triangle area is L = 1/2bh

L = 1/2(76)(45)

L = (38)(45)

L = 1710 cm²

Subject : Mathematics

Level : ES

Chapter : 2D Geometry

Answer:

It should be 72 degrees

Step-by-step explanation:

angle j and h are the same so you just add 63 to 45 and once you get 108, just subtract that from 180 degrees which is the full measure of the triangle.