Please help me I've been stumped on this problem

By simplifying the given square root , we get Simplified Root : 6 xz • [tex]\sqrt{(2xz) }[/tex]

Factor 72 into its prime factors

          72 = 23 • 32

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          36 = 22 • 32

Factors which will remain inside the root are :

          2 = 2

To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          6 = 2 • 3

At the end of this step the partly simplified square root looks like this:

        6 • [tex]\sqrt{ (2x3z3) }[/tex]

Simplify the Variable part of the square root

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

   [tex]\sqrt{(x8)}[/tex]=x4

 [tex]\sqrt{ (x^6)}[/tex]=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

   [tex]\sqrt{ (x5)}[/tex]=x2•[tex]\sqrt{x}[/tex]

  [tex]\sqrt{ (x^7)}[/tex]=x-3•[tex]\sqrt{x}[/tex]

Applying these rules to our case we find out that

[tex]\sqrt{ (x3z3)}[/tex] = xz • [tex]\sqrt{(xz) }[/tex]

Combine both simplifications

      [tex]\sqrt{ (72x3z3)}[/tex] = 6 xz •[tex]\sqrt{(2xz) }[/tex]

Simplified Root :

6 xz • [tex]\sqrt{(2xz) }[/tex]

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Yes, it is possible for the range of a data set of positive data values to be less than the mean of that data set.

The range of a data set is the difference between the maximum and minimum values in the data set, while the mean (also known as the average) of a data set is the sum of all the values divided by the total number of values.

For example, consider the following data set of positive values: {2, 3, 5, 7, 9}. The range of this data set is 9 - 2 = 7, while the mean is (2 + 3 + 5 + 7 + 9)/5 = 26/5 = 5.2. In this case, the range (7) is less than the mean (5.2).

This can occur when the data set has a relatively small range, meaning that the difference between the maximum and minimum values is not very large compared to the mean.

the distribution of the data set and the specific values within it can affect the relationship between the range and the mean.

It's important to note that range and mean are just two measures of central tendency and variability, and other measures such as median, mode, and standard deviation can provide additional insights into the characteristics of a data set.

therefore, Yes, it is possible for the range of a data set of positive data values to be less than the mean of that data set.

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Answer:

It'd be 4300 mililiters

Step-by-step explanation:

3.8× 100= 3800

3800+500=4300

Answer: the population density is approximately 121.75 people/km^2.

Step-by-step explanation: Assuming a scenario whereby the island in question is entirely populated and encompasses a total expanse of 100 square kilometers, it follows that the resulting population density would be as follows:

The formula for population density can be expressed as the ratio of total population to a given geographic area. Mathematically, it is written as Population density = Population / Area.

The metric for measuring population density yields a value of 121.75 individuals per hectare.

The metric expressing the number of individuals residing in a given geographic area is referred to as population density. In this specific instance, the population density is calculated to be 121.75 persons per square kilometer.

Assuming a complete occupancy of the island and a cumulative surface area of 100 square kilometers, it can be posited that...

Answer:

The number series 2, 4, 6, 8, 10, 12, . . . . , 80. Therefore, 1640 is the sum of first 40 even numbers.......Sep 23, 2018

PLS MARK BRAINLIEST

Step-by-step explanation:

The probability of rolling an even number on a dice is 1/2, since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes (1, 2, 3, 4, 5, and 6).

The probability of landing on tails when flipping a coin is also 1/2, since there are only two possible outcomes (heads or tails) and they are equally likely.

To find the probability of both events happening together, we need to multiply their probabilities:

1/2 (probability of rolling an even number) x 1/2 (probability of landing on tails) = 1/4

Therefore, the probability of rolling an even number on a dice and landing on tails when flipping a coin is 1/4 or 0.25 (25%).

~~~Harsha~~~

If on Tuesday, Friday,  Saturday, and Sunday, she collected 43 cans each day. Tina got $14.15 for her cans last week.

Tina collected 37 cans on Monday, Wednesday, and Thursday, which is a total of 37 x 3 = 111 cans. She collected 43 cans on Tuesday, Friday, Saturday, and Sunday, which is a total of 43 x 4 = 172 cans. The total number of cans she collected last week is 111 + 172 = 283 cans.

Since Tina gets 5 cents for every can she recycles, she made 5 x 283 = $14.15 for recycling all of the cans she collected last week.

Therefore, Tina got $14.15 for her cans last week.

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Complete question is:

Tina collects cans to recycle at the supermarket. Last week, on Monday, Wednesday and Tursday, she collected 37 cans each day. On Tuesday, Friday,  Saturday, and Sunday, she collected 43 cans each day. Tina gets 5 cents for every can she recycles.  How much money did Tina get for her cans last week?

Step-by-step explanation:

to vary inversely means that

y = k/x

the opposite would be to vary directly :

y = kx

so, in our case

5 = k/1

k = 5

y = 5/x

therefore, for x = -3

y = 5/-3 = -5/3 = -1.666666666...

The axis of symmetry for y = (x - 1)² - 4 is x = 1.

Given the equation in the question;

y = (x - 1)² - 4

The axis of symmetry for a parabola in standard form is expressed as:

y = a(x - h)² + k is the vertical line passing through the vertex (h, k).

Comparing y = (x - 1)² - 4 to the standard form

We can see that h = 1 and k = -4.

Therefore, the vertex is (1, -4).

Since the axis of symmetry is the vertical line passing through the vertex, the equation of the axis of symmetry is

x = 1.

Therefore, the axis of symmetry is x = 1.

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Answer:

562496

Step-by-step explanation:

i think

Answer:189504

Step-by-step explanation:

To get the 1.4% of population you need to multiply it like this: 752000 × 1.4% = 10528.

10528 is the population decrease every year, to find the population decrease after 18 years you need to multiply it again like this: 10528 × 18 = 189504.

189504 is the population decrease after 18 years.

The mass of the watermelons is 24 kg and the mass of the mangoes is 8 kg.

A physical quantity is mass. The unit of mass measurement is the body's weight. Normal mass units like grammes, kilogrammes, and pounds can be used to measure it.

We are informed of the following:

T + W = 27 (total mass of trolley and watermelons is 27 kg)

T + M = 11 (total mass of trolley and mangoes is 11 kg)

W = 3M (mass of watermelons is three times the mass of mangoes)

Elimination or substitution can be used to solve this set of equations. Substitutions made

We can enter W = 3M into the first equation in place of the third equation to obtain:

T + 3M = 27

From the second equation, we can substitute T = 11 - M into this equation to get:

(11 - M) + 3M = 27

Simplifying this equation, we get:

2M = 16

So, M = 8 kg. This means that the mass of the mangoes is 8 kg.

We can substitute this value of M back into the second equation to get:

T + 8 = 11

So, T = 3 kg. This means that the mass of the trolley is 3 kg.

Finally, we can substitute these values of T and M into the first equation to get:

3 + W = 27

So, W = 24 kg. This means that the mass of the watermelons is 24 kg.

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The remaining amount that Jackson has is $5.

The cost of 5 books at $7 each is:

5 books * $7/book = $35

To find the amount of change Jackson got from $40, we need to subtract the cost of the books from $40:

$40 - $35 = $5

Therefore, Jackson got $5 in change.

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only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

How to solve the question?

The mathematical term "indirectly proportional" refers to a relationship in which two variables are related in such a way that when one increases, the other decreases, and vice versa. In other words, the two variables vary in opposite directions.

Out of the four equations given, only one shows an indirect proportional relationship. This equation is:

y=1/x

In this equation, y and x are indirectly proportional. As x increases, the value of 1/x decreases, and therefore, the value of y decreases as well. Similarly, as x decreases, the value of 1/x increases, and the value of y increases as well. This relationship is commonly known as an inverse relationship, where the two variables vary in opposite directions.

On the other hand, the other three equations do not show an indirect proportional relationship. The equation y=5x shows a direct proportional relationship, where y increases as x increases and vice versa. The equation y=-2x+1 is a linear equation with a negative slope, where y decreases as x increases, and y increases as x decreases. Lastly, the equation y=3x+5 is also a linear equation with a positive slope, where y increases as x increases, and y decreases as x decreases.

In summary, only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

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A graph which is that of the inequality shown include the following: D. Graph D.

In order to to graph the solution to the given linear inequality on a coordinate plane, we would use an online graphing calculator to plot the given linear inequality and then take note of the points that lie on its line;

y ≥ -3x + 1

Next, we would use an online graphing calculator to plot the given linear inequality as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that a possible solution for the linear equation is the ordered pairs (0, 1) and (1, -2), with a solid line that is shaded above to indicate the solution, and this must be represented with the greater than or equal to (>) inequality symbol.

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If the perimeter of a rectangular living room is 38 meters, the length of the living room is 105 meters.

The perimeter of a rectangle is the sum of the lengths of all its sides. Let's denote the length of the living room as "L". The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

We know that the width of the living room is 9 meters, and the perimeter is 38 meters. Substituting these values in the formula, we get:

38 = 2(L + 9)

Dividing both sides by 2, we get:

19 = L + 9

Subtracting 9 from both sides, we get:

L = 105

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The cosine function that could model the height of the Ferris wheel is given as follows:

y = cos(4π).

The cosine function is defined as follows:

y = cos(Bx).

In which the period of the function is given by 2π/B.

The car completes 4 whole rotations in a time period of 2 minutes, hence it completes 2 rotations per minute, thus the period of the function is of 0.5 minutes.

Considering the period of 0.5 minutes, the coefficient B is given as follows:

2π/B = 0.5

0.5B = 2π

B = 2π/0.5

B = 4π.

Hence the function is given as follows:

y = cos(4π).

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The heights that people had a foot size smaller than 24 centimetres would be = 162cm, 152cm, 162cm, 161cm,162cm.

The total number of people whose foot sizes and heights where obtained for the study = 15

The heights that had foot sizes less than 24cm= 162cm, 152cm,162cm,161cm,162cm.

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The simplified form of the expression (⅓m - 2/x) ÷ (9-y²) ÷ (2x²m-12x) ÷ (9x+3xy) is (x-3m)/(4mx (mx-6) (3-y)).

Mathematical expression is a mathematical statement involving numerical values, mathematical operations, variables, power of variables and combination of that.

The expression is = (⅓m-2/x)÷(9-y²) ÷(2x²m-12x)÷(9x+3xy)

We have to simplify the expression.

Simplifying the expression we get,

(1/3m - 2/x) ÷ (9 -y²) ÷ (2x²m -12x) ÷ (9x +3xy)

= ((x-3m) / 6mx)*(1 / (3²-y²)) ÷ ((2x (mx-6)) / (3x (3+y)))

= ((x-3m) / 6mx (3+y) (3-y)) * (3x (3+y) /2x (mx-6)) [Since, a²- b² = (a+b)(a-b)]

= (x-3m)/(4mx (mx-6) (3-y))

Hence the simplified expression is = (x-3m)/(4mx(mx-6)(3-y)).

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The number 369.964 in expanded form as 369.964 = 300 + 60 + 9 + 0.9 + 0.06 + 0.004

To express 369.964 in expanded form, we must break down the number by its place value. The digits to the left of the decimal point represent whole numbers, while the digits to the right represent fractions or decimals.

So let's start with the whole number part, 369. We can express this in expanded form by breaking it down into its component parts according to its place value. The digit 3 is in the hundreds place, which means it has a value of 300. The digit 6 is in the tens place, which means it has a value of 60. The digit 9 is in the ones place, which means it has a value of 9. Therefore, we can write 369 in expanded form as:

369 = 300 + 60 + 9

Now let's move on to the decimal part, 0.964. The digit 9 is in the tenths place, which means it has a value of 0.9. The digit 6 is in the hundredths place, which means it has a value of 0.06. The digit 4 is in the thousandths place, which means it has a value of 0.004. Therefore, we can write 0.964 in expanded form as:

0.964 = 0.9 + 0.06 + 0.004

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Therefore, the solution to the system of equations is: x = 13/12, y = -3/4 that is option C.

In mathematics, an equation is a statement that asserts the equality of two expressions, separated by an equals sign (=). The expressions on either side of the equals sign are referred to as the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between variables and to solve problems.

Here,

To solve the system of equations:

4y + 12x = 10 ...(1)

2y - 6x = -8 ...(2)

We can use the method of elimination or substitution.

Method of elimination:

We can eliminate x by multiplying equation (2) by 2 and adding it to equation (1) to obtain:

4y + 12x = 10

(4y - 12x = -16)

8y = -6

Dividing both sides by 8, we get:

y = -6/8

y = -3/4

Substituting this value of y in equation (1), we get:

4(-3/4) + 12x = 10

Simplifying and solving for x, we get:

-3 + 12x = 10

12x = 13

x = 13/12

So the answer is C. x = 13/12, y = -3/4.

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The Monthly Budget for fast food is Option A. $136.

To determine how much money you should budget for fast food, we need to calculate the total amount of money you spend on fast food each week. To do this, we simply multiply the cost of one fast food meal by the number of meals you buy in a week, which is four in this case.

$850 x 4 = $3400 per week

Next, we need to figure out how much money you spend on fast food per month. To do this, we need to multiply the weekly amount by the number of weeks in a month. Most months have around four weeks, so we will use that as an estimate.

$3400 x 4 = $13600 per month

Therefore, the answer is Option A. $136. You should budget around $136 per month for fast food if you buy it four times a week and it costs you about $850 each time.

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The probability that a congressman selected at random supports Bill A or Bill B is 0.83.

The probability that a congressman selected at random supports Bill A but not Bill B is 0.21.

The probability that a congressman selected at random supports neither Bill A nor Bill B is 0.17.

P(Bill A or Bill B) = P(Bill A) + P(Bill B) - P(Bill A and Bill B) = 0.35 + 0.62 - 0.14 = 0.83

ii. The probability that a congressman selected at random supports Bill A but not Bill B is the probability in the Bill A circle that is not in the overlap:

P(Bill A but not Bill B) = P(Bill A) - P(Bill A and Bill B) = 0.35 - 0.14 = 0.21

iii. P(neither Bill A nor Bill B) = P(not Bill A and not Bill B) = 0.17

Therefore, the probability that a congressman selected at random supports neither Bill A nor Bill B is 0.17.

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Answer:

Step-by-step explanation:

i wish i knew so i dont really know but i have heard that its 2 inches

In circle L in which secant lines TQ and SQ intersect at point Q outside the circle value of x = 54°, m ST = 143°, m PR = 79°

∠PQR = 1/2( ST - PR)

∠PQR = 32°

m ST = (3x - 19)°

m PR = (x + 25)°

Putting the value in the equation we get

32 = 1/2( 3x - 19 - (x + 25) )

32 × 2 = 3x -19 -x -25

64 = 2x - 44

64 + 44 = 2x

108 = 2x

x = 54°

m ST = (3x - 19)°

m ST = 3(54) -19

m ST = 162 - 19

m ST = 143°

m PR = (x + 25)°

m PR = 54 + 25

m PR = 79°

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The actual distance from Marcus's house to the peak is 0.328 miles and the Skye's distance is 0.330 miles

Given that

The actual distance between Marcus and Skye's houses is 1 1/2 miles.

So, we have

Ratio = 0.246 : 1 1/2

Scale : Actual = 0.246 : 1 1/2

For Marcus, we have

2 : Actual = 0.246 : 1 1/2

So, we have

Actual = 0.246/(1 1/2) * 2

Evaluate

Actual = 0.328

For Skye, we have

2.015 : Actual = 0.246 : 1 1/2

So, we have

Actual = 0.246/(1 1/2) * 2.015

Evaluate

Actual = 0.330

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What percentage of 1.23 is 2.17?  The amount over 100% will be the increase:

[tex]2.17 = \huge \text(\dfrac{x}{100}\huge \text )(1.23)[/tex]

[tex]x =\dfrac{ 2.17(100)}{1.23}[/tex]

[tex]x = 176.4\%[/tex]

The increase is 76.4%

The scale factor in scale drawing from figutre A to figure B is 4

In a scale drawing, the scale factor represents the ratio of the size of an object in the drawing to the size of the corresponding object in real life.

In the given scale drawing, the object is scaled up from 7 cm to 28 cm.

Therefore, the scale factor can be calculated as follows:

scale factor = size of object in drawing / size of corresponding object in real life

scale factor = 28 cm / 7 cm

scale factor = 4

So, the scale factor in this scale drawing is 4.

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