Gunther's average on ten quizzes is 7.8. Each score is a positive whole number less than or equal to 10. He remembers that he scored at least one 5, at least three 7's, at least two 9's and at least one 10. What is the sum of all the distinct possible values for Gunther's median quiz score

The value of x that makes the photo area half of the entire area is: 1.12 in

The area of a rectangle is given by the formula:

A = L * w

where:

L is length

w is width

Thus:

Area of photo = 4 * 2 = 8 in²

We are told that this area is half of the entire ad. Thus:

¹/₂(4 + x)(2 + x) = 8

x² + 6x + 8 = 16

x² + 6x - 8 = 0

Solving using a quadratic calculator gives:

x = 1.12 in

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Answer: the answer is false

Step-by-step explanation:

i just took the test :)

Answer:

This is false

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hey there! I'm happy to help!

When dealing with picking things and finding the number of possibilities, we can be dealing with two different types of things: permutations or combinations. We use permutations when order is important to the groups and we use combinations if order is not important.

It appears here that order is not important here as the subcommittee doesn't have to be in a specific order, so we will be using combinations.

So, we have ten seventh graders to choose from. Then we will have 9, and then 8. So, we multiply these numbers of choices.

10×9×8=720

Now, we need to divide by 6. This is to show that order doesn't matter. Why? Because there are  6 possible ways to organize 3 seats on the committee (3×2×1), and we want to divide out all of the different orders so it is just the specific group of people and not their different organizations that are counted.

720/6=120

Now, we need to find this with the eighth graders.

8×7×6=336

And we divide by the number of seats factorial (3 seats for the eighth graders, so 3×2×1=6 again)

336/6=56

Now, we multiply our numbers for seventh and eighth graders to find all off the possibilities.

120×56=6720

So, there are 6720 subcommittees possible.

Have a wonderful day and keep on learning! :D

Annual Medical cost = 1269.86

monthly premium cost to Ronald for the Blue Shield plan = $48.48.

For all doctor office visits, prescriptions, and major medical charges, Ronald will be responsible for 35 percent and the insurance company will cover 65 percent of covered charges.

The annual deductible cost = $630.

Ronald decided to review his medical bills from the previous year to see what costs he had incurred and to help him evaluate his choices. He visited his general physician 6 times during the year at a cost = $105 for each visit.

He also spent $71 and $95 on two prescriptions during the year.

= (Monthly premium cost × 12) + Deductible cost + (Coinsurance percent × Coinsurance expenses)

= (48.48 x 12) + 630 + (0.35 x 166)

= 1269.86

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Answer: 360

Step-by-step explanation:

done

Answer:

"Certain" Maby I dont know

Step-by-step explanation:

\( {7}^{ - 3} \times {7}^{ - 5} \times 7 {}^{ - 1} \)

\( \frac{1}{7 {}^{3} } \times \frac{1}{ {7}^{5} } \times \frac{1}{7 } \\ \frac{1}{ {7}^{3 + 5 + 1 } } \\ \frac{1}{ {7}^{9} } \\ \)

Step-by-step explanation:

\( = {7}^{ - 3} \times {7}^{ - 5} \times {7}^{ - 1} \)

\( = {7}^{( - 3 - 5 - 1)} \)

\( = {7}^{ - 9} \)

\( = \frac{1}{ {7}^{9} } \)

Answer:

Step-by-step explanation:

The option that gives chart elements a realistic, three-dimensional look is D. Plot Area.

The option that gives chart elements a realistic, three-dimensional look is the plot area. The plot area is the portion of the chart that displays the data points and is typically the main focus of the chart. Adding shading and depth to the plot area, can give the chart a more lifelike appearance and make the data more visually engaging. Additionally, three-dimensional charts can also be created by using specialized charting software that allows for the creation of 3D visualizations. These types of charts can be useful for highlighting patterns and trends in the data, especially when dealing with large datasets.
In a chart, the plot area is the space where the actual data points, bars, lines, or pie slices are displayed. By applying three-dimensional effects to the plot area, you can make the chart elements appear more realistic and visually appealing. This can enhance the viewer's understanding of the data being represented and make the chart more engaging.
In summary, to give chart elements a realistic, three-dimensional look, you should focus on the plot area (Option D). The axis (Option A), chart area (Option B), and legend (Option C) do not directly contribute to creating a three-dimensional appearance for the chart elements.

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Answer:

1. 900

2. 350

Step-by-step explanation:

the formula,

A= P(1+rt)

A= final amount

P= starting amount

r= intrest rate

t= time

1. A=750(1+.05*4)

A=750(1.2)

A=900

2. A=1500(1+.1*2)

A=1500(1.1)

A=1650

But theyre

asking for how much intrest will they get back, so you subtract the new amount by the starting amount to find how much intrest was earned

1650-1500=350

Answer:

2x^2 +x-6

3x^2-6 answer

this is not equal to zero

Answer:

where is it

Step-by-step explanation:

The following is true about the study: e. It has one factor (medication) blocked by age.

In statistics, when a factor (independent variable) is blocked by another factor, it means that the effect of the first factor is controlled or eliminated by the second factor.

In this case, the factor that is blocked is the medication, which means that the effect of medication on the outcome variable is controlled by age.

Blocking a factor is often done in experimental design to remove the effects of extraneous variables or to control the influence of certain factors on the outcome variable.

In this case, age is considered a blocking variable because it is not of interest in the study, but it may have an effect on the outcome variable. By blocking the effect of medication by age, the study can better isolate the effect of medication on the outcome variable.

In summary, the statement e. "It has one factor (medication) blocked by age" is correct which means that the study controlled for the effect of age on the outcome variable by blocking the effect of medication by age.

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Answer:

The amount invested in the 5% account is $4,250

Step-by-step explanation:

Let the amount invested in the first be $x and the amount invested in the second be $y

Total of both is $11,000

Thus, we have

x + y = 11,000 •••••••••(i)

For the first account, the interest earned will be;

5/100 * x = 5x/100 = 0.05x

For the second account , the interest earned will be;

8/100 * x = 0.08x

Adding both gives the total amount of interest

That will be ;

0.05x + 0.08y = 752.50 •••••(ii)

From equation i above;

y = 11,000 - x

Substitute this into ii

0.05x + 0.08(11,000-x) = 752.5

0.05x + 880 - 0.08x = 752.5

0.08x-0.05x = 880-752.5

0.03x = 127.5

x = 127.5/0.03

x = $4,250

Answer:

y + (1/4)(x + 4)

Step-by-step explanation:

One point on the graph is (-4, 0); another is (4, 2).

The change in x from the first point to the second is 8; this is the 'run.'

The change in y is 2 (which is 2 - 0).  This is the 'rise.'

Thus, the slope of the line is m = rise / run = 2/8 = 1/4

Let's use the point-slope form of the equation of a straight line:

y  - k = m(x - h).  Substituting 0 for k and -4 for h, we get:

y - 0 = (1/4)(x + 4), or

y + (1/4)(x + 4)

Answer:

ITS D

Step-by-step explanation:

I JUST DID THIS LOL

We can start by placing the center at (-5,1).

The radius of the circle will be the distance between the center and the point (-2,-3).

If we graph this two points, we can use an angle protractor to draw the circle passing through point P(-2,-3) and centered at (C(-5,1):

Answer:

The midpoint is (-6,-4)

Step-by-step explanation:

The formula for the midpoint is

M = (x1+x2)/2, (y1+y2)/2

Substituting what we know

= (-8+-4)/2, (-1+-7)/2

= -12/2, -8/2

= -6, -4

The length of the shortest straight  is approximately 28.01 ft.

What is the right triangle?

A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".

To find the length of the shortest straight beam,we can use the Pythagorean theorem.

Let's denote the length of the beam as L and  a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.

Using the Pythagorean theorem,

\(L^2 = (28 ft)^2 + (1 ft)^2\)

Simplifying the equation:

\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)

\(L = \sqrt{785}ft\)

Calculating the value of L:

L ≈ 28.01 ft

Therefore, the length of the shortest straight beam  is approximately 28.01 ft.

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Whave established that the series l~=l an - z converges uniformly for Re(z) ≤ c

What is uniformly?

The keyword "uniformly" refers to the concept of uniform convergence. In the context of the given question, it is stated that the series l~=l an - z converges uniformly for Re(z) ≤ c. Uniform convergence means that the convergence of the series is independent of the value of z within a certain range (Re(z) ≤ c in this case).

To show that the series l~=l an - z converges uniformly for Re(z) ≤ c, where an is a bounded sequence of complex numbers and we choose the principal branch of n - z, we need to demonstrate that for any ε > 0, there exists an N such that for all n > N and for all z with Re(z) ≤ c, the inequality |l~=l an - z| < ε holds.

Given that an is a bounded sequence, there exists an M > 0 such that |an| ≤ M for all n.

Let's consider the series l~=l an - z. We can write it as:

l~=l an - l z.

Now, since |an| ≤ M for all n, we have:

|an - z| ≤ |an| + |z| ≤ M + c.

By choosing N such that M + c < ε, we can ensure that for all n > N and for all z with Re(z) ≤ c, the inequality |an - z| < ε holds.

Now, using the triangle inequality, we have:

|l~=l an - z| ≤ |an - z|.

Since we have shown that |an - z| < ε for n > N and Re(z) ≤ c, it follows that |l~=l an - z| < ε for n > N and Re(z) ≤ c.

Therefore, we have established that the series l~=l an - z converges uniformly for Re(z) ≤ c.

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The true statement regarding the comparison of t-distributions to the standard normal distribution is that t-distributions approach the standard normal distribution as the sample size increases.

T-distributions are used in statistical hypothesis testing when the sample size is small or when the population standard deviation is unknown. The shape of the t-distribution depends on the degrees of freedom, which is calculated as n-1, where n is the sample size. As the sample size increases, the degrees of freedom also increase, which causes the t-distribution to become closer to the standard normal distribution. Therefore, option D is the correct answer.

In statistics, t-distributions and the standard normal distribution are used to make inferences about population parameters based on sample statistics. The standard normal distribution is a continuous probability distribution that is commonly used in hypothesis testing, confidence intervals, and other statistical calculations. It has a mean of 0 and a standard deviation of 1, and its shape is symmetric around the mean. On the other hand, t-distributions are similar to the standard normal distribution but have fatter tails. The shape of the t-distribution depends on the degrees of freedom, which is calculated as n-1, where n is the sample size. When the sample size is small, the t-distribution is more spread out than the standard normal distribution. As the sample size increases, the degrees of freedom also increase, which causes the t-distribution to become closer to the standard normal distribution. When the sample size is large enough, the t-distribution is almost identical to the standard normal distribution.

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In the metric system, each millimeter increment is equal to 0.1 centimeters.

The metric system is a standardized system of measurements used in many countries around the world. It is based on a set of units that are multiples or fractions of the base unit. One of the key benefits of the metric system is that it is easy to convert from one unit to another, as the conversions are based on powers of 10.

In the metric system, the basic unit of length is the meter, which is abbreviated as "m". However, in many situations, it is more convenient to use smaller units, such as millimeters (mm), which are 1/1000 of a meter. To convert millimeters to centimeters, we multiply the number of millimeters by 10, since 1 centimeter is equal to 10 millimeters. Hence, every millimeter increment is equal to 0.1 centimeters in the metric system.

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An off-by-one error is a common type of error that occurs when programming or solving mathematical problems.

It refers to a situation where a programmer or mathematician makes an error by including or excluding an element that they should have not. This can lead to unexpected results and bugs in the code or calculation. The error is typically caused by a misunderstanding of the boundaries of an array, list or any other data structure. These types of errors can be difficult to spot and can cause serious problems, especially in situations where precision is important.

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Answer:

$450

Step-by-step explanation:

You want to calculate the interest on $3000 at 3% interest per year after 5 year(s).

The formula we'll use for this is the simple interest formula, or:

Where:

P is the principal amount, $3000.00.

r is the interest rate, 3% per year, or in decimal form, 3/100=0.03.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 3000 × 0.03 × 5 to get that:

The interest is: $450.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),

or 3000.00 + 450.00 = 3450.00.

Although part of your question is missing, you might be referring to this full question: What are the vertex and range of y = |2x + 6| + 2?

(0, 2); 2 < y < ∞

(0, 2); −∞ ≤ y < ∞

(−3, 2); 2 < y < ∞

(−3, 2); −∞ ≤ y < ∞

The vertex of the function is (–3, 2) and the range of the function is 2 < y < ∞.

The given modulus function:

y = |2x + 6| + 2

Now, we get two equations out of the absolute value function:

y = 2x + 6 + 2

y = 2x + 8

and

y = –2x – 6 + 2

y = –2x – 4

The vertex of the function will be at a point where these two equations are equal. So, we can calculate the vertex as follows:

2x + 8 = –2x – 4

2x + 2x = –4 – 8

4x = –12

x = –3

If x = –3, then y = 2(–3) + 8 = –6 + 8 = 2

Thus, the vertex of the function is (–3, 2).

Now, the values that y can take will range from 2 to infinity as y cannot take values below the vertex.

Thus, the range of the function is 2 < y < ∞.

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Answer:

The numbers are 4 and 3

Step-by-step explanation:

HOPE THIS HELPS

The first integer is 4 and the second integer is -3.

Given

The sum of two integers is 1.

Their difference is 7.

Let the first integer be x and the second integer is y.

The sum of two integers is 1.

\(\rm x+y =1\)

Their difference is 7.

\(\rm x-y=7\)

On solving both the equations

From equation 2;

\(\rm x-y=7\\\\x=7+y\)

Substitute the value of  x in equation 1

\(\rm x+y = 1\\ \\7+y+y=1\\\\2y = 1-7\\\\2y = -6\\\\y = \dfrac{-6}{2} \\\\y = -3\)

Substitute the value of y in equation 1

\(\rm x+y =1 \\\\ x-3=1\\\\x=1+3\\\\x=4\)

Hence, the first integer is 4 and the second integer is -3.

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