What is the measure of APD? (6x - 10) (4x + 8)

Answer:

32,768

Step-by-step explanation:

8^5=8×8×8×8×8=32,768

Answer:

Hi

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Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

To determine the service fee as a percentage of the deposited amount, we can use the following formula:

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Service fee percentage = (Service fee / Deposited amount) x 100

In this case:

Service fee percentage = (31.74 / 2239.10) x 100 = 1.41%

So, the service fee for depositing the amount of R2239.10 was 1.41% of the deposited amount.

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Answer: -4x +7y=26

4x +7y=2

=. 0+ 14x=28

X= 2. Plug x in. Y =. 4(2) +7y= 2. = 8+7y=2. 7y=2-8 7y=-6 y=-6/7

Step-by-step explanation:

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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Answer:

38

Step-by-step explanation:

In the standard direct variation equation, y = kx, k is the constant of proportionality.

Since the equation is y = 38x, it is in the direct variation form.

Using this, 38 is the k value, since it is the coefficient of x.

So, the constant of proportionality (k) is 38.

Answer:

38

Step-by-step explanation:

Answer:

A)  Mr. Simpson's class; it has a larger median value 14.5 pencils.

Step-by-step explanation:

A box plot is a visual display of the five-number summary:

From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:

Mr Johnson's class:

Mr Simpson's class:

In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.

The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.

The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).

As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.

In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.

Answer:

456

Step-by-step explanation:

Product means an answer derived from multiplication.  Therefore, if the product is 155952, and one value is 342, then the following equation is true:

342x = 155952, or 342 * x = 155952

Divide 155952 by 342 to get: 456.

Check the work in the equation:

342(456) = 155952

155952 = 155952, which is true, so the answer is 456.

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The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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Given

initial velocity = 60 feet per second

initial height = 95 feet

Find

Maximum height attained by the ball

Explanation

we have given

put h'(t) = 0

to find the maximum height find the value of h(1.875)

Final Answer

Therefore , the maximum height attained by the ball is 151.25 feet

Answer:

17.9

Step-by-step explanation:

Use the Pythagorean theorem, c²= a² + b². We can rewrite it as c = √(a² + b²),  a=16 and b=8. Plug it in as c = √(16² + 8²) then simplify.

c = √(16² + 8²)

c = √(256 + 64)

c = √320

c≈17.9 (rounded to the nearest tenth)

The probability of obtaining a value less than or equal to 10 is given as follows:

P(X ≤ 10) = 0.7.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For this problem, we are already given the distribution, as follows:

Then, considering the desired outcomes, the probability is obtained as follows:

P(X ≤ 10) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.7.

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In every 10 minutes an average of 3 customers will arrive to the pizza station

Given,

The number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour.

We have to find the average number of customers arrives in each 10 minutes.

Here,

The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:

P (X = x) = (e^-μ × μ^x) / x!

Where,

The number of successes is x.

The Euler number is e = 2.71828.

μ is the average over the specified range.

Now,

Rate of 18 customers per hour;

μ = 18 n

n is the number of hours.

Number of customers arrive in each 10 minutes

10 minutes = 10/60 = 1/6

Then,

μ = 18 x 1/6 = 3

That is,

In every 10 minutes an average of 3 customers will arrive to the pizza station.

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Answer:

March through August

Step-by-step explanation:

Ok, in order to solve this problem, we must start by building an equation to solve. The original equation was:

\(S=56.9-40.7cos (\frac{\pi}{6}t)\)

and we need to figure out the months when the sales exceed 7700 units. Since the equation is given in hundreds of units, we need to divide those 7700 units into one hundred to get 77 hundred units. So we can go ahead and substitute that value in the equation:

\(77=56.9-40.7cos (\frac{\pi}{6}t)\)

if you wish you can rewrite the equation so the variable is on the left side of it but it's up to you. So you get:

\(56.9-40.7cos (\frac{\pi}{6}t)=77\)

and now we solve for t

\(-40.7cos (\frac{\pi}{6}t)=77-56.9\)

\(-40.7cos (\frac{\pi}{6}t)=20.1\)

\(cos (\frac{\pi}{6}t)=\frac{20.1}{-40.7}\)

\(cos (\frac{\pi}{6}t)=-0.4938\)

\(\frac{\pi}{6}t=cos^{-1}(-0.4938)\)

\(\frac{\pi}{6}t=2.087\)

\(t=\frac{2.087(6)}{\pi}\)

\(t=3.98 months\)

but there is a second answer to this problem. Notice that the function cos can be 2.87 at \(2\pi-2.087=4.1962 rad\) as well, so we repeat the process:

\(\frac{\pi}{6}t=4.1962\)

\(t=\frac{4.1962(6)}{\pi}\)

\(t=8.014 months\)

So now we need to determine on which period of times the number of items sold exceed 77 hundred units so we build different intervals for us to test:

(1,3.98)  (3.98,8.014) and (8,014, 13)

and find a test value for each of the intervals and test it.

(1,3.98) t=2

\(S=56.9-40.7cos (\frac{\pi}{6}(2))\)

S=36.55

this is less than 77 so this is not our answer.

(3.98,8.014) t=5

\(S=56.9-40.7cos (\frac{\pi}{6}(5))\)

S=92.15

this is more than 77 so this is our answer.

(8.014,13) t=10

\(S=56.9-40.7cos (\frac{\pi}{6}(10))\)

S=36.55

this is less than 77 so this is not our answer.

so, since our answer is the interval (3.98,8.014)

this means that between the months of march and august we will be sellin more than 7700 units.

Answer:

8.1

Step-by-step explanation:

2x^2 -9 = 121

        +9    +9

2x^2 = 130

/2         /2

x^2   = 65

x= sqrt (65)

x= 8.06225...

x = 8.1

Answer:

30-3p and 3(10-p)

Step-by-step explanation:

We know that he starts with 30 candy bars.

Now, we know that he has p friends, and that each friend received 3 candy bars.

Therefore, the answer is 30-3p

However, if you divide 30-3p by 10, you get the expression 3(10-p)

Thus, either answer is acceptable.

Answer:

\(\frac{18}{45}\) and  \(\frac{14}{35}\)

Step-by-step explanation:

One way you can tell is to divide the fractions.

Put in your calculator 18÷45 = 0.4

Put in your calculator 14÷35 = 0.4

The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.

To find the probability that a randomly selected student will like pizza but not chicken nuggets.

Let P = the number of students who like pizza but not chicken nuggets

Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets

P = 28n - 8

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students)

We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:

Total number of students = 28n + 15 - 8 = 28n + 7

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)

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The smaller number is 6 .

The larger number is 22

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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Answer:

g(x) = f(x + 2)

Step-by-step explanation:

The x value has been translated by 2

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Looking at the asymptotes  graph, it crosses the y-axis at y = h(x) = -1

Thus, the y-intercept is -1. The graph also crossed x-axis at..

How do you find the asymptotes on a graph?

Set the denominator to 0 and solve for x to discover the vertical asymptotes. Given that this has already been factored, solve by setting each component to zero. They are expressed as equations of lines because the asymptotes are lines.

Consequently, -1 is the y-intercept. The graph also veers off the x-axis here.

Consequently, -1 is the y-intercept. The graph also veers off the x-axis here.

As soon as the denominator equals 0, the vertical asymptotes appear. Accordingly, (2x)(x-4)=0. Vertical asymptotes are thus defined as x=0 and x=4.

Given that the degrees are identical, the horizontal asymptote in this situation corresponds to the ratio of a leading coefficients. y = [(1)(1)/(2)(1)] = 1/2.

Simply changing x = 0 makes finding the y-intercept simpler. On the other hand, because x = 0 is indeed a vertical asymptote,

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for a ratonal, the expression only makes sense if the denominator is not 0, since if that occurs then the expression becomes undefined, a division by 0 is always undefined, for this case, when does that occur?  Let's set the denominator to 0 and solve for "x".

\(\cfrac{\sqrt{2}}{\sqrt{x-1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{setting the denominator to 0}}{\sqrt{x-1}=0\implies (\sqrt{x-1})^2=0^2}\implies x-1=0\implies x=1\)

well then, let's see what happens when x = 1

\(\cfrac{\sqrt{2}}{\sqrt{x-1}}\implies \cfrac{\sqrt{2(1)}}{\sqrt{1-1}}\implies \cfrac{\sqrt{2}}{\sqrt{0}}\implies \cfrac{\sqrt{2}}{0}\leftarrow und efined\)

so the only values that makes sense is anything but x < 1, because a smaller value of 1 will give us an imaginary value from the root, so the only values that makes sense are namely { x | x ∈ ℝ; x > 1 }

Answer:

25/9

Step-by-step explanation:

3 1/3 ÷ 1 1/5

3 1/3 = 10/3

1 1/5 = 6/5

10/3 ÷ 6/5 = 10/3 x 5/6 = 50/18 = 25/9

So, the answer is 25/9

Answer:

1. x = {1.5, 0.2}  

2. x = 1

Step-by-step explanation: