Write an expression that is equivalent to 3(7+).

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

It is an incorrect claim from the student that the measures of central tendency will change.

It is a correct claim from the student that the measures of spread will change but only range and standard deviation.

Step-by-step explanation:

The complete question is: Suppose a person in the club with 91 members transfers to the club with 71 members. A student claims that the measures of centers and the measures of spread will all change. Correct the student’s error.

Data set was: 80, 74, 77, 71, 75, and 91.

Firstly, we have to represent the original data set in ascending order;

Original data set = 71, 74, 75, 77, 80, and 91.

Now, it is stated that a person in the club with 91 members transfers to the club with 71 members, so the new data set is;

New data set = 72, 74, 75, 77, 80, and 90.

Now, first taking into account the measure of central tendency that is; Mean and Median.

Mean of both the data will remain the same because there is no change in the sum of all values in both the data set, i.e;

Mean of original data =  \(\frac{71+74+75+77+80+91}{6}\)

                                    =  \(\frac{468}{6}\)  = 78

Mean of new data =  \(\frac{72+74+75+77+80+90}{6}\)

                               =  \(\frac{468}{6}\)  = 78

Now, the median of both the data set will also remain the same because there is a change in the first and last term of the data, so there will be no effect on the middle value in both the data.

Hence, it is an incorrect claim from the student that the measures of central tendency will change.

Now, taking into account the measure of spread that is; Range, Inter-quartile range, and Standard deviation.

Range is given by = Highest value - Lowest value

So, the range of original data = 91 - 71 = 20

and the range of new data = 90 - 72 = 18

This means that the range of data has been changed.

Now, the inter-quartile range = Second last term - Second term of data

So, the inter-quartile range of original data = 80 - 74 = 6

and the inter-quartile range of new data = 80 - 74 = 6

This means that the inter-quartile range of data has not been changed.

Now, the standard deviation =  \(\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }\)

So, the standard deviation of the original data =  \(\sqrt{\frac{(71-78)^{2} +.......+ (91-78)^{2} }{6-1} }\)

                                                                             =  7.043

The standard deviation of the new data =  \(\sqrt{\frac{(72-78)^{2} +.......+ (90-78)^{2} }{6-1} }\)

                                                                   =  6.481

This means that the standard deviation has been decreased.

The calculated volume of the prism is 702 cubic cm

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

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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The third angles in the given cases are:a) 68°b) 79°c) 106°d) 120°e) 64°.

To calculate the third angle of a triangle in which two of the angles are given, we need to use the fact that the sum of all the angles of a triangle is always 180°. Let's use this fact to solve each case given:a) Two angles are given as 47° and 65°. To find the third angle, we subtract the sum of the given angles from 180°.

That is, third angle = 180° - (47° + 65°) = 68°.b) Two angles are given as 24° and 77°. Similar to the previous case, the third angle = 180° - (24° + 77°) = 79°.c) Two angles are given as 56° and 18°. The third angle = 180° - (56° + 18°) = 106°.

d) Two angles are given as 39° and 21°. The third angle = 180° - (39° + 21°) = 120°.e) Each of the two angles is given as 58°. To find the third angle, we subtract twice the value of one of the given angles from 180°. That is, third angle = 180° - (2 × 58°) = 64°.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

2 whole and 1/8

Step-by-step explanation:

Find out the total pounds of strawberries for the 4 containers.

4/8 + 2/8 + 5/8 + 6/8 = 17/8

17/8 = 2 whole and 1/8

Answer:

2 1/8

Step-by-step explanation:

4/8+2/8+5/8+6/8=17/8

17/8 as a mixed number is 2 1/8

The graph we need is \(y=-3^x\), which is shown in the attached image.

The correct answer is option C: \(\(k + 4 = 16\).\) This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

\(\[Tina = Kai + 4\]\)

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

\(\[16 = k + 4\]\)

This equation represents the fact that Tina has volunteered \(16\) times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

\(\[k + 4 = 16\]\)

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: \(\(k + 4 = 16\).\)

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Answer:

The ten packs

Step-by-step explanation:

If he buys the ten pack, he would spend $72

If he buys the 6 pack, he would spend $75

Therefore, he should buy the ten packs

There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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Infinite number of solutions

The given system of equation is:

21x + 6y = 42........................(1)

7x + 2y = 14............................(2)

From equation (1)

3 (7x + 2y) = 42

7x + 2y = 14..........................(3)

Since the two equations (2) and (3) are exactly similar, the system of equations has infinite number of solutions

On solving the linear equations we get the result  as

x1   + x2   − 2x3 + 3x4 + 2x5 = 6

3x1 + 3x2 − x3   + x4   + x5   = 12

2x1 + 2x2 − x3   + x4   − 2x5 = 5

4x1 + 4x2 + x3    +0x4 − 3x5 = 16

8x1 + 5x2 − 2x3 − x4   + 2x5 = 29

where ,

x1 =  5,x2 = -1, x3 =  3 ,x4 =  2 , x5 =  1

Finding the value of an equation's unknown variable can be done by solving the equation. If an equation contains a "equal to" sign, it is considered to be balanced. This equation so shows that the two quantities on both sides of it are equal. Left hand side and right hand side are the two sides of the equation (Right hand side).

One equation is x - 4 = 5, for instance. It illustrates that x - 4 (LHS) = 5. (RHS). Here, x is an unknowable quality or variable. Therefore, in order to determine the value of x, we must solve this equation.

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The simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

We can write the simplified form of the given expression using the exponent rule as -

{aˣ/aⁿ} = {aˣ a⁻ⁿ} = {aˣ ⁻ ⁿ}

Given is the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\)

We can simplify the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (27)^{\frac{1}{2} \times \frac{2}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 27^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (3)^{3}^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 3\)

Therefore, the simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

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The results are:

i. Range: Le 635,000

ii. Mean: Le 445,666.67

iii. Median: Le 420,000

iv. Mode: None

We have,

To compute the range, mean, median, and mode of the given data set, let's first arrange the rent amounts in ascending order:

Le 00,000, Le 335,000, Le 373,000, Le 385,000, Le 410,000, Le 410,000, Le 430,000, Le 462,000, Le 515,000, Le 535,000, Le 578,000, Le 635,000

i. Range:

The range is calculated by subtracting the minimum value from the maximum value in the data set:

Range = Maximum value - Minimum value

Range = Le 635,000 - Le 00,000

Range = Le 635,000

ii. Mean:

The mean is the average of the rent amounts. We sum up all the values and divide by the number of values in the data set:

Mean = (Sum of all rent amounts) / (Number of rent amounts)

Mean = (Le 00,000 + Le 335,000 + Le 373,000 + Le 385,000 + Le 410,000 + Le 410,000 + Le 430,000 + Le 462,000 + Le 515,000 + Le 535,000 + Le 578,000 + Le 635,000) / 12

Mean = Le 5,348,000 / 12

Mean = Le 445,666.67

iii. Median:

The median is the middle value in the sorted data set. In this case, since we have 12 rent amounts, the median will be the average of the 6th and 7th values:

Median = (Le 410,000 + Le 430,000) / 2

Median = Le 420,000

iv. Mode:

The mode is the value that appears most frequently in the data set. In this case, there is no rent amount that appears more than once, so there is no mode.

Therefore,

The results are:

i. Range: Le 635,000

ii. Mean: Le 445,666.67

iii. Median: Le 420,000

iv. Mode: None

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Answer:

it would be 11....................

Answer:

its 11

according to the BODMAS RULE

Answer:

56/100=0.56

Step-by-step explanation:

Total box=100

shaded=56

Answer:

Unit rate: 56.67 miles per hour

9 hours: 510 miles

plz mark brainliest :DD

Answer:

1. 56.66666667

2.504

Step-by-step explanation:

Answer:27

Step-by-step explanation:

Its pretty simple. Perimeter is the addition of all the sides. Add 4+9+8+6 to get 27.

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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The transformation in the picture is option c Reflection.

Given,

Reflection transformation:

A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.

According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.

Here,

In the picture the transformation is reflection.

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Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

Answer:

Yup

Step-by-step explanation:

91 - 22 = 69

The solution to the system of equations is given as follows:

(1,9).

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

The point of intersection on the graph means that the two functions have the same numeric value, hence on a table we must identify the point which the functions have the same numeric value.

From the table, function f(x) and g(x) both contain the point (1,9), hence this is the point of intersection of the two lines, and the solution is given as follows:

(1,9).

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The speed of the second pedestrian is 5 kilometers per hour.

Let's say that the speed of the second pedestrian is S.

We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:

(4km/h + S)*3h = 27km

It says that both pedestrians work, together, a total of 27km in 3 hours.

Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.

4km/h + S = 27km/3h = 9 km/h

S = 9km/h - 4km/h = 5km/h

The speed of the second pedestrian is 5 kilometers per hour.

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Answer: B

Step-by-step explanation:

Ms. Zentz would buy 17 protractors if she buys one quarter of the 65 items.

If you buy 65 items and one quarter of them are protractors, then the number of protractors you buy can be calculated as:

Number of protractors = 65 x 1/4

Number of protractors = 16.25

Since you cannot buy a fractional part of a protractor, you would need to round the answer to the nearest whole number. In this case, you would round up to 17 protractors.

Therefore, Ms. Zentz would buy 17 protractors if she buys one quarter of the 65 items.

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The answer is 369,072. This is the total number of copies sold to date.

An expression that uses symbols to represent the relationship between two or more values.

This is calculated by solving the equation 9.7% × x = 35,800, where x is the total number of copies sold to date.

To solve this equation, we first need to convert the percentage to a decimal.

To do this, we divide 9.7 by 100, giving us 0.097.

We can then multiply both sides of the equation by this decimal, giving us 0.097x = 35,800.

We can then solve for x by dividing both sides of the equation by 0.097. This gives us x = 369,072. This is the total number of copies sold to date.

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