what is the property of (9x2)x6=9x(2x6)

The height of the tree is 13.2 m.

What is proportional ?

 The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.  

We can set up a proportion comparing the height of each object to the length of the shadow.

Then , \(\frac{h}{s}\).

=> \(\frac{3.8}{1.3} = \frac{h}{4.5}\)

=> h = \(\frac{3.8*4.5}{1.3}\)

=> 13.2 m.

Hence the height of the tree is 13.2 m.

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Answer:

uhm what? from how it looks its a multiplucation sign and 3 x 2 isnt 48 is 6 but 2 times 24 IS 48 and 3 times 16 IS 48

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

3 · x · 2 = 48

3 · 2 = 6

48 ÷ 6 = 8

3 · 8 · 6 = 48

Answer:

C)

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

5/5 - 1/5 = 4/5 is the probability that a person does not live in an industrialized country

The P( person does not lives in an industrialized country ) = 4/5

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

P( person lives in an industrialized country ) = 1/5

Now, using the Completement probability

P ( person lives in an industrialized country )  + P( person does not lives in an industrialized country ) = 1

P( person does not lives in an industrialized country )

= 1- P ( person lives in an industrialized country )

P( person does not lives in an industrialized country )

= 1- 1/5

= 4/5

Hence, P( person does not lives in an industrialized country ) = 4/5.

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The original dimensions of the garden are 12 ft by 16 ft.

Width: x + 4 (not 2 because the width has two ends)

Length: x + 8 (same reason; this is x + 4 + 4)

The area of the garden and the border combined is 320 sq. ft.

The dimensions of the garden with the border around it are (x + 4) and (x + 8).

A (rectangle) = lw

A (garden with border) = lw

320 sq. ft. = (x + 4) (x + 8)

320 sq. ft. = x2 + 12x + 32

Transpose 320 to the right side of the equation.

0 = x2 + 12x + 32 - 320

0 = x2 + 12x - 288

Factor out.

0 = (x + 24) (x - 12)

One or both of the amounts are equal to zero when the product of two values is zero.

Equate the factors to 0.

x + 24 = 0 x - 12 = 0

x = - 24 x = 12

Since we cannit have a negative measure of distance, x = 12.

Find the original dimensions of the garden.

The original dimensions of the garden (without the border) are x and x + 4.

Width = x = 12

Length = x + 4 = 12 + 4 = 16

The original dimensions of the garden are 12 ft by 16 ft.

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The value of f(1) is the y-value when x=1.

From the graph, we see that y=0 when x=1. Thus, the value of f(1) is 0, which is option A.

Let me know if you need any clarifications, thanks!

Answer: the answer is B

Step-by-step explanation: just took it

To find the probability of a person with "some college or an associate's degree" and in the labor force being employed, we need the following information: the number of people with that education level who are employed and the total number of people with that education level in the labor force.

Let's assume we have the following data (these are just example numbers, you can replace them with actual data if you have it):

1. Number of people with "some college or an associate's degree" who are employed: 400
2. Total number of people with "some college or an associate's degree" in the labor force: 500

Step 1: Divide the number of employed people (400) by the total number of people in the labor force (500).
Probability = (Number of employed people with some college or an associate's degree) / (Total number of people with some college or an associate's degree in the labor force)

Step 2: Calculate the probability
Probability = 400 / 500 = 0.8

Based on the given data, the probability that a person who has completed some college or an associate's degree and is in the labor force is employed is 0.8 or 80%. This means that 80% of individuals with that education level in the labor force are employed.

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The value of x for the given quadratic expression is x = 5 ± √11.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is 3(x-5)²=33. The value of x will be calculated as,

3(x-5)²=33

(x - 5 )² = 11

(x - 5 )  = ±√11

x = 5 ± √11

Therefore, the value of x for the given quadratic expression is x = 5 ± √11.

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Answer:

5/4

Step-by-step explanation:

Given :

Finding the missing side :

Taking the sec ratio :

Answer:

Top right: quadrant 1

Top left: quadrant 2

Bottom left: quadrant 3

Bottom right: quadrant 4

The first number of an ordered pair is the x axis, and the second is the y axis

A: 10,3 quadrant 4

B:8, 9 quadrant 2

c: 3,2 Q 3

D: 4,0 Q4

E:4,7 Q3

F: 8,7 Q1

G: 0,7 Q4

H: 1,5 Q1

From the information, the correct value that expresses the division will be 300 ÷ 75 = R

From the information given, the thing to do is simply to use the number in the box to divide the number beside it and get the information.

This will be:

= 3000 ÷ 75 = 40

= 300 ÷ 75 = 4

Therefore, the expression is 300 ÷ 75 = R.

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The amount of wrapping paper for the gift is A = 279 inches²

Given data ,

To calculate the amount of wrapping paper Laura will need to wrap the gift, we need to find the total surface area of the gift.

The surface area of a rectangular box is given by the formula:

Surface Area = 2 x (length x width + length x height + width x height)

Given that the length of the gift is 6 inches, the width is 13.5 inches, and the height is 3 inches, we can substitute these values into the formula:

Surface Area = 2 x (6 x 13.5 + 6 x 3 + 13.5 x 3)

Surface Area = 2 x (81 + 18 + 40.5)

Surface Area = 2 x 139.5

The surface area of a rectangular box = 279 inches²

Hence , Laura will need 279 inches² of wrapping paper to wrap the gift

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I think it's D.

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The mixture would contain approximately 0.849 cups of caramel popcorn and 1.698 cups of cheese popcorn.

Let's define the variables:

Let x be the number of cups of caramel popcorn in the mixture

Let y be the number of cups of cheese popcorn in the mixture

We are given that the mixture has two times as much cheese popcorn as caramel popcorn, so y = 2x.

We are also given that the total number of calories in the mixture is 254. To find an equation that relates x and y, we can use the calorie information for each type of popcorn:

Calories from caramel popcorn = 183x

Calories from cheese popcorn = 58y = 58(2x) = 116x

Total calories in the mixture = 183x + 116x = 299x

Setting the total calories equal to 254 and solving for x:

299x = 254

x = 0.849

So we would need 0.849 cups of caramel popcorn in the mixture.

To find the number of cups of cheese popcorn, we can use the equation y = 2x:

y = 2(0.849) = 1.698

So we would need 1.698 cups of cheese popcorn in the mixture.

Therefore, the mixture would contain approximately 0.849 cups of caramel popcorn and 1.698 cups of cheese popcorn.

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when X = 3, Ŷ equals 4,601. The correct answer is (c) 4,601.

If the least squares regression equation is Ŷ = 1,202 + 1,133X, we can find the value of Ŷ when X = 3 by substituting X = 3 into the equation and solving for Ŷ:

Ŷ = 1,202 + 1,133(3)

Ŷ = 1,202 + 3,399

Ŷ = 4,601

what is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equals sign (=). The expressions on either side of the equals sign can be numbers, variables, or combinations of both, connected by arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, logarithms, and trigonometric functions.

An equation can be either true or false, depending on the values of the variables and constants involved. Equations are used in a wide variety of mathematical contexts, from basic arithmetic to advanced calculus, physics, and engineering.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The most common method for solving a risk analysis problem is to select the alternative with the B) greatest expected value. The expected value is the weighted average of all possible outcomes, where the weight of each outcome is its probability of occurrence.

It represents the long-term average of a random variable and is a useful tool in decision-making under uncertainty.
In risk analysis, the expected value is used to compare different alternatives and assess their potential outcomes. By selecting the alternative with the greatest expected value, decision-makers aim to maximize their chances of achieving the best possible outcome.
However, it is important to note that expected value is not the only criterion for decision-making in risk analysis. Other factors, such as the variability of outcomes, the level of risk aversion, and the potential impact of different outcomes, may also need to be considered.
Therefore, while selecting the alternative with the greatest expected value is a common method for solving risk analysis problems, it should be used in conjunction with other decision-making criteria to ensure a comprehensive and effective risk management strategy.

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The ratio of the height of shape A to the height of shape C is \(\frac{3}{10}\)

Recall that similar figures have the same scale factor squared due to the ratio of its surface area.

Hence,

We would make:

\(z^2 = x/y\\z= 2/5\)

Therefore, the ratio of the height of shape A to the height of shape B is = \(\frac{hA}{hB} = \frac{2}{5}\)

To find the ratio of the height of shape B to the height of shape C, we would perform a similar operation which is:

\(z^3 = 27/64\\z= 3/4\)

The ratio is:

\(\frac{hB}{hC} = \frac{3}{4}\)

To find the ratio of the height of shape A to the height of shape C would be:

\((\frac{hA}{hB}) (\frac{hB}{hC} )= \frac{hA}{hC}\)

= 6/20

= 3/10

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The value that separates the bottom 81% from the top 19% is approximately 79.108

What is Standard Deviation?

The standard deviation is a number that tells how the measurements for a group are spread out from the mean (mean or expected value). A low standard deviation means that most of the numbers are close to the mean, while a high standard deviation means that the numbers are more spread out Advertisement Smart User What is Standard Deviation?

To find the value that separates the bottom 81% from the top 19% in a normally distributed set of scores with a mean of 68.9 and a standard deviation of 11.6, we can use the Z-score formula.

The Z-score represents the number of standard deviations a particular value is from the mean. By finding the Z-score corresponding to the desired percentile, we can then convert it back to the original scale using the formula:

Z = (X - μ) / σ

Where:

Z is the Z-score,

X is the desired value,

μ is the mean, and

σ is the standard deviation.

To find the value that separates the bottom 81% from the top 19%, we need to find the Z-score that corresponds to the 81st percentile.

Since the normal distribution is symmetric, the Z-score that separates the bottom 81% from the top 19% is the same as the Z-score that separates the top 19% from the bottom 81%.

Using a Z-table or statistical software, we can find that the Z-score corresponding to the 81st percentile is approximately 0.88.

Now we can solve for X using the Z-score formula:

0.88 = (X - 68.9) / 11.6

Simplifying the equation:

0.88 * 11.6 = X - 68.9

10.208 = X - 68.9

X = 10.208 + 68.9

X ≈ 79.108

Therefore, the value that separates the bottom 81% from the top 19% is approximately 79.108.

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a) The sine function represents the y-coordinate of a point on the unit circle, given the angle in radians. Starting at the positive x-axis, 3π/2 radians takes us three-quarters of the way around the circle in the clockwise direction, ending at the negative y-axis. Therefore, sin(3π/2) = -1.
b) Similarly, -π radians takes us halfway around the circle in the clockwise direction, ending at the negative x-axis. Therefore, sin(-π) = 0.
c) The cosine function represents the x-coordinate of a point on the unit circle, given the angle in radians. 3π/2 radians takes us three-quarters of the way around the circle in the clockwise direction, ending at the negative y-axis. Therefore, cos(3π/2) = 0.
d) -π/2 radians takes us a quarter of the way around the circle in the clockwise direction, ending at the negative y-axis. Therefore, cos(-π/2) = 0.
e) The tangent function represents the ratio of the sine to the cosine of an angle. 4π radians takes us twice around the circle, ending at the positive x-axis. At this point, the cosine is 1 and the sine is 0, so tan(4π) = 0/1 = 0.
f) -π radians takes us halfway around the circle in the clockwise direction, ending at the negative x-axis. At this point, the cosine is -1 and the sine is 0, so tan(-π) = 0/-1 = 0.

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Answer:

Divide the price by the number of months to find the monthly rate.

$237.36 ÷ 24 = $9.89 per month

$184.50 ÷ 18 = $10.25 per month

The two year club, Aqua Plus is cheaper

Step-by-step explanation:

Answer:

C).  Aqua Plus has the lower cost of $9.89 per month.

Step-by-step explanation:

Hope this helps! :D

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

Simplify

Step-by-step explanation:

I'm not sure what the question is referring to but if it's an improper fraction you Simplify.

Let's take 9/3 you divide 9 and 3 and the fraction will be a whole number.

but if it's like 14/3 were counting in 3's like 3, 6, 9, 12, 15... 14 does not line up.

How many 3's fit into 14?

4 threes. So the fraction will now be 4 2/3.

To get the improper fraction again multiply the whole number and the bottom number of the fraction.

4 x 3 = 12.

Add the remaining number which is 2.

12 + 2 = 14.

Sorry if this isn't what you meant.

Answer:

The market equilibrium price is approximately $36.43 per barrel.

Step-by-step explanation:

To find the market equilibrium price, we need to set the quantity supplied (QS) equal to the quantity demanded (QD) and solve for the price (P).

Given:

QS = -250 + 7P

QD = 260 - 7P

Setting QS equal to QD:

-250 + 7P = 260 - 7P

Now, let's solve for P:

Add 7P to both sides:

-250 + 7P + 7P = 260 - 7P + 7P

Combine like terms:

14P - 250 = 260

Add 250 to both sides:

14P - 250 + 250 = 260 + 250

Simplify:

14P = 510

Divide both sides by 14:

14P/14 = 510/14

Simplify:

P = 36.43

The market equilibrium price can be found by setting the quantity supplied (QS) equal to the quantity demanded (QD) and solving for the price (P) that satisfies this condition.

In the given scenario, the supply function is QS = -250 + 7P, and the demand function is QD = 260 - 7P. To find the equilibrium price, we set QS equal to QD:

-250 + 7P = 260 - 7P

Simplifying the equation, we get:

14P = 510

Dividing both sides by 14, we find:

P = 36.43

Therefore, the market equilibrium price is approximately $36.43 per barrel. At this price, the quantity supplied and quantity demanded will be equal, resulting in a state of equilibrium in the perfectly competitive domestic crude oil market.

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Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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Answer:

she is wrong, offer 2 results in lower interests

Step-by-step explanation:

total amount paid if offer 1 is accepted:

$6,000 x (1 + 3%)² = $6,000 x 1.0609 = $6,365.40

she will pay $365.40 in interests

total amount paid if offer 2 is accepted:

($6,000 x 1.01) x 1.05 = $6,060 x 1.05 = $6,363

she will pay $363 in interests

Compounding interest refers to interest that earns more interest itself, e.g. in the first offer, the $180 of interests charged for the first year will earn $5.40 in extra interests. While offer 2 only charges $60 in interests during the first year which will in turn earn $3 of interests. The difference between both offers is that interest charges in offer 1 earn more interests than the interest in offer 2 = $5.40 - $3 = $2.40

The answer is , Yes, you can use the principle of mathematical induction to find a formula for the sum of the first n terms of a sequence.

Yes, you can use the principle of mathematical induction to find a formula for the sum of the first n terms of a sequence. To do this, you would need to first establish a base case, typically when n = 1, and show that the formula holds for this case. Next, you would assume that the formula holds for some arbitrary value of n, and use this assumption to prove that the formula also holds for n+1. This process of induction can be used to derive a general formula for the sum of the first n terms of the sequence, which can be used to find the sum for any value of n.

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Answer:

  -1 ≤ x ≤ 2

Step-by-step explanation:

You want the solution to |x +1| +|x -2| = 3.

We find it convenient to solve these absolute value equations using a graphing calculator. When we subtract 3 from both sides, we have ...

  |x +1| +|x -2| -3 = 0

The solutions will show on the graph as places where the expression has a value of 0, that is, the x-intercepts.

The left-side expression has a value of 0 for all values of x between -1 and +2, inclusive. That is, the solution is ...

  -1 ≤ x ≤ 2

The absolute value function is piecewise defined:

  |x| = x . . . . for x ≥ 0

  |x| = -x . . . . for x < 0

That is, the behavior of the function changes at x=0.

In the given equation the absolute value function arguments are zero at ...

  x +1 = 0   ⇒   x = -1

  x -2 = 0   ⇒   x = 2

These x-values divide the domain of the equation into three parts.

In this domain, both arguments are negative, so the equation is actually ...

  -(x +1) -(x -2) = 3

  -2x +1 = 3

  -2x = 2

  x = -1 . . . . . . not in the domain

In this domain, the argument (x+1) is positive, but the argument (x-2) is negative. That means the equation is ...

  (x +1) -(x -2) = 3

  1 +2 = 3

True for all x in this domain.

In this domain, both arguments are positive, so the equation is ...

  (x +1) +(x -2) = 3

  2x -1 = 3

  2x = 4

  x = 2 . . . . in the domain (this point was excluded from x < 2).

The solution is -1 ≤ x ≤ 2.