Mr. Johnson placed three desks together in his classroom. Each desk measures at 1.5 meters.
How many centimeters are all three desks?

By using the fact that the measures ∠BAE and ∠EAC are equal, we will see that x = 20

Here we know that AE is an angle bisector of ∠BAC, this means that the measures of the two formed angles are the same ones.

Then we can write:

∠BAE = ∠EAC

Now we know that the measures of these angles are:

∠BAE = x + 30

∠EAC = 3x - 10

Replacing that in the equation above we willget:

x + 30 = 3x - 10

solving that for x, we will get:

30 + 10 = 3x - x

40 = 2x

40/2 = x

20 = x

That is the value of x.

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The correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The y-intercept of a line of fit is the value of y when x equals 0. In the context of this problem, the y-intercept represents the amount of diet soda that the machine starts with when it is filled.

Since the y-intercept of the line of fit is −5.1, this means that the machine starts with 5.1 ounces of diet soda.

This is a reasonable value, as it is unlikely that the machine would be completely empty when it is filled.

It's important to note that the slope of the line of fit is also relevant in this context.

The slope represents the rate at which the amount of diet soda in the machine decreases over time. However, the question only asked for the y-intercept.

Hence, the correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.

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Answer:

First, we can factor out 5x²y²z from each term:

15x²y³z+25x³y²z+35x²y²z² = 5x²y²z(3y+5xz+7z)

So the fully factorized expression is:

5x²y²z(3y+5xz+7z)

Tyler has run 10.4 miles, which is 65% of the total distance he plans to run this week. Tyler plans to run a total of 16 miles this week.

Let's use "x" to represent the total distance that Tyler plans to run this week. According to the problem, Tyler has already run 10.4 miles, which is 65% of the total distance he plans to run. We can set up an equation to represent this information:

10.4 = 0.65x

To solve for x, we can divide both sides of the equation by 0.65:

x = 10.4 ÷ 0.65

x = 16

Therefore, the total distance that Tyler plans to run this week is 16 miles.

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Answer:

no the didn't hear the question

Answer:

I am pretty sure the answer is that the question can't be heard

Step-by-step explanation:

we can, now  if we look at 0 = x² + 5, that's when the parabola y-value is 0, that is, what's "x" when y = 0? well, if we look at the graph, the graph never touches the x-axis, so that means the graph never has any "real roots", only complex ones or imaginary ones.  We can tell because the graph never touches the x-axis.

Answer:

Step-by-step explanation:

The total revenue from ticket sales is:

300 x £5 = £1500

The profit is the revenue minus the cost of the prize:

Profit = £1500 - £400 = £1100

Charity A receives 55% of the profit:

55% of £1100 = £605

Charity B receives 45% of the profit:

45% of £1100 = £495

Therefore, Charity A receives £605 and Charity B receives £495.

In conclusion 39 science fiction books were sold on Thursday.

How to solve and what does algebra mean?

Let's use algebra to solve this problem. Let x be the number of science fiction books sold on Thursday. Then we know that:

86 = 8 + 2x

We can solve for x by first subtracting 8 from both sides:

78 = 2x

Then dividing both sides by 2:

x = 39

Therefore, 39 science fiction books were sold on Thursday.

Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating those symbols. It involves using letters and other symbols to represent variables and quantities in equations and formulas.

Algebra is used in a wide range of fields, including mathematics, science, engineering, and economics, and it is an essential tool for solving many real-world problems.

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No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69

A newsletter publisher believes that under 69% of their readers own a Rolls Royce.

No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.

Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.

Null Hypothesis (H0): p ≤ 0.69

Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.

Alternative Hypothesis (H1): p > 0.69

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the correct answer is: none of these, as only binomial distribution is applicable to this scenario.

a) This scenario follows the binomial distribution, as we are drawing marbles with replacement and interested in the number of successes (getting a blue marble) in a fixed number of trials.

b) The Poisson distribution is used to model the number of events occurring in a fixed time interval, given a certain rate of occurrence. It is not applicable in this scenario.

c) The hypergeometric distribution is used to model the probability of obtaining a certain number of successes in a sample without replacement, given a finite population of items that can be classified into successes and failures. In this scenario, we are drawing with replacement, so the hypergeometric distribution is not applicable.

d) Therefore, the correct answer is: none of these, as only binomial distribution is applicable to this scenario.

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The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).

In geometry, dilation is a transformation that changes the size of a figure but not its shape. It is a type of similarity transformation.

When a figure is dilated, each point of the figure moves away or towards the center of dilation by a certain scale factor.

Here we have

Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one-eighth to create polygon A′B′C′D′.

To dilate polygon ABCD using a scale factor of one-eighth i.e 1/8 multiply the coordinates of each vertex by the scale factor of 1/8.

The coordinates of A are (-4, 6), multiply each coordinate by 1/8

A' = (-4/8, 6/8) = (-1/2, 3/4) = (-0.5, 0.75)

The coordinates of B are (-2, 2), multiplying each coordinate by 1/8

B' = (-2/8, 2/8) = (-1/4, 1/4) = (-0.25, 0.25)

The coordinates of C are (4, -2), multiplying each coordinate by 1/8

C' = (4/8, -2/8) = (1/2, -1/4) = (0.5, - 0.25)

The coordinates of D are (4, 4). Multiplying each coordinate by 1/8

D' = (4/8, 4/8) = (1/2, 1/2) = (0.5, 0.5)

Therefore,

The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).

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Answer: 17.888543819998

Step-by-step explanation:

Answer:

17.8885

Step-by-step explanation:

find the geometric mean between 16 and 20, we need to multiply the numbers and take the square root of the result. That is:

Geometric Mean = √(16 × 20)

Geometric Mean = √320

Geometric Mean ≈ 17.8885

Therefore, the geometric mean between 16 and 20 is approximately 17.8885.

the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.

There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.

The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:

Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)

Expected gain = 38/13 - 10/13 - 18/13

Expected gain = 10/13 ≈ 0.77

Therefore, the expected gain is $0.77, rounded to the nearest cent.

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Answer:

24% increase

Step-by-step explanation:

percent change = (new value - old value)/(old value) × 100%

A positive percent change is a percent increase.

A negative percent change is a percent decrease.

In this problem:

new value = 31

old value = 25

percent change = (31 - 25)/(25) × 100%

percent change = 24%

Since the percent change is positive, the percent change is a

24% increase

The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the an 24% increase in the puppy's weight in 1 month.

The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.

To explain this further, let's look at an example. If a puppy weighed 25 pounds at 4 months, and it gained 6 pounds over the course of the following month, it would weigh 31 pounds at 5 months. To calculate the percentage increase, take the difference in weight (6 pounds) and divide it by the starting weight (25 pounds). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight.

To calculate the percentage decrease, use the same steps as above, but subtract the starting weight from the final weight instead. For example, if a puppy weighed 25 pounds at 4 months and lost 6 pounds over the course of the following month, it would weigh 19 pounds at 5 months. The percentage decrease would be calculated as (25 - 19)/25 = 0.24, or a 24% decrease in the puppy's weight.

In summary, the percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.

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Generally, the water table in a swamp is located 2 miles below the surface.

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Therefore , the solution of the given problem of equation comes out to be  y=(x-12)³ and y=(x+8)³.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a distinct algorithm that divides 12 into two parts and can be used to assess data received from y + 7, normalization in this case yields b + 7.

Here,

The following two equations show a rightward translation of the parent equation's coordinate plane graph:

=> y=(x-12)³

=> y=(x+8)³

Therefore , the solution of the given problem of equation comes out to be  y=(x-12)³ and y=(x+8)³.

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The line of reflection for the given angle is  corresponding vertices.

1. Identify the original angle and its reflected angle in the diagram.
2. Find the midpoint between the corresponding vertices of the original and reflected angles.
3. Draw a line through the midpoint that is perpendicular to the line connecting the corresponding vertices.

In general, to reflect an angle across a line, you would draw a perpendicular line from the vertex of the angle to the line of reflection, and then extend the sides of the angle to intersect the line of reflection at the same angle. The line of reflection would be the perpendicular bisector of the segment connecting the vertex of the original angle to the corresponding vertex of the reflected angle.

This line is the line of reflection, and the angles are reflected across it. The justification for this method is that the line of reflection is equidistant from the corresponding points of the original and reflected angles

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The percentile rank of age 30 is 27.586%.

The percentile rank of age 30 can be calculated using the following equation:

Percentile rank = (number of scores below 30 / total number of scores) x 100

In this case, the total number of scores is 29, and there are 8 scores below 30 (18, 21, 22, 25, 26, 27, 29, and 30). Therefore, the percentile rank of age 30 is:

(8/29) x 100 = 27.586%

The percentile rank of age 30 is 27.586%.

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Answer: 9 miles

Step-by-step explanation: The speed of 12 miles per hour means that for every hour, Clare is 12 miles further from the starting point. 1 hour = 12 miles Since an hour is equivalent to 60 minutes, 60 mins = 12 miles We can divide both sides by 60 to find the distance travelled per minute. 1 min = 12 ÷60= 0.2 miles Multiply both sides by 45 to find the distance travelled in 45 minutes: 45 mins = 0.2(45)= 9 miles Given that the starting position is at zero, Clare's position is at 9 miles after 45 minutes.

The central limit theorem is a statistical theory that specifies the probability distribution of a sum or average of several random variables whose distribution is not known.

It is an important theorem since it is utilized to help forecast or estimate the behavior of a specific set of data.

This theorem holds that when you take repeated samples of the same size from a population with a finite standard deviation, the means of those samples will be normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Further more, the theorem indicates that the larger the sample size, the more closely the sample mean distribution will approximate a normal distribution.

This is why it is vital in the development and use of statistical quality control techniques, since they rely on correct assumptions about the population’s normality.

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Answer:

The equation y = -3x - 5 represents a linear function with a slope of -3 and a y-intercept of -5.

To understand what would happen to the graph if the slope was changed to 1, we need to compare the graphs of y = -3x - 5 and y = x - b, where b is some constant.

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. So, when we change the slope of the equation y = -3x - 5 to 1, we get:

y = x - b

To find the value of b, we can substitute the coordinates of any point on the line. Let's use the y-intercept, which is -5:

-5 = 1(0) - b

b = -(-5)

b = 5

Therefore, the equation y = x - 5 represents the line with a slope of 1 and a y-intercept of 5.

To compare the graphs of y = -3x - 5 and y = x - 5, we can graph both equations on the same coordinate plane. Here's what the two graphs look like:

Graph of y = -3x - 5 (slope = -3, y-intercept = -5):

|

-5| x

| x

| x

| x

| x

| x

x---------------

-3 -2 -1 0 1 2 3

Graph of y = x - 5 (slope = 1, y-intercept = 5):

|

5| x

| x

| x

| x

| x

| x

x---------------

-5 -4 -3 -2 -1 0 1 2 3

As we can see, changing the slope of the equation from -3 to 1 rotates the line counterclockwise and makes it steeper. The y-intercept remains the same at -5.

Answer: a=7.6

Step-by-step explanation:

solve for angle C:

[tex]\frac{sinc}{5} =\frac{sin120}{11}[/tex]

[tex]11sinc=5sin120[/tex]

[tex]C=23.2[/tex]

solve for A:

=180-(120+23.2)

=36.8

solve for a:

Using the law of sines

[tex]\frac{sin120}{11} =\frac{sin36.8}{a}[/tex]

[tex]asin120=11sin36.8[/tex]

[tex]a=7.6[/tex]