what types of problems can be solved using the greatest common factor?what type of problems can be solved using the least common multiple

Answer:

50π feet^2

Step-by-step explanation:

area of the circle = 10^2 π = 100π feet^2

A of the sector = 100π/2 = 50π feet^2

Answer: I = -13

Step-by-step explanation:

We just need to take the -11 -2 = -13.  A negative -11 subtracts negative 2 = -13

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Answer: -13

Step-by-step explanation:

The answer is negative 13 because a negative added by a negative equals a negative

Slope is "change in y over change in x".

    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using those two points, you'd have

    [tex]m=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{0-6}{3-0}=\dfrac{-6}{3}=-2[/tex]

Notice that doesn't match any of the listed answers.  The reason is that two of those answers aren't reduced.

If you reduce the first answer of [tex]\dfrac{6}{-3}[/tex], you have  [tex]\dfrac{6}{-3}=-2[/tex].  So that first answer is equivalent to the calculation above.

The answer from your list is the first one.

Answer:

7/8

Step-by-step explanation:42/48 divide both by 6 since that's the greatest common number that divides both

The given expression of trigonometry is equivalent to cos(2θ).

trigonometry capability, in math, one of six capabilities (sine [sin], cosine [cos], digression [tan], cotangent [cot], secant [sec], and co-secant [csc]) that address proportions of sides of right triangles. These six geometrical capabilities comparable to a right triangle.

We have,

1 - tan^2(θ)/1 +  tan^2(θ)

Use 1 + tan^2(θ) = sec^2(θ)

1 - tan^2(θ)/ sec^2(θ)

1/ sec^2(θ) - tan^2(θ)/sec^2(θ)

Use tan(θ) = sin(θ)/cos(θ)

cos^2(θ) - sin^2(θ)×cos^2(θ)/cos^2(θ)

cos^2(θ) - sin^2(θ)

Using sin^(θ) + cos^2(θ) = 1

cos^2(θ) - (1 - cos^2(θ))

2cos^2(θ) - 1

Here we have 2cos^2(θ) - 1 = cos(2θ)

Then, simplification of given expression is cos(2θ).

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Correct question:

which expression is equivalent to 1 - tan^2(θ)/1 +  tan^2(θ) for all values of θ for which 1 - tan^2(θ)/1 +  tan^2(θ) is defined?

Explained the quotient property "one of the properties of logarithms, the division becomes subtraction" has been explained with an example

In one of the properties of logarithms, the division becomes subtraction. That is the quotient property of the logarithm

Consider the two positive numbers x and y and a ≠ 0

Then,

[tex]log_a[/tex] (m /n) = [tex]log_a[/tex] m -  [tex]log_a[/tex] n

Here division became the subtraction

For example

To find the value of  [tex]log_2[/tex] (15/ 7) we will use the quotient property of logarithm, here the division of the numbers will be subtraction

[tex]log_2[/tex] (15 / 7) =  [tex]log_2[/tex] 15 -  [tex]log_2[/tex] 7

Therefore, the quotient property of the logarithm has been explained with example

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The value of k is -3.

What is a tangent line?

The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are endlessly close to one another.

Here, we have

Given

x + y = k

y = x² + 3x

slope of tangent line = dy/dx = 2x+3

k is y-intercept of the tangent line

2x+3 = -1

x = -2

y = (-2)^2+3(-2)+1 = -1

The tangent line passes through the point (-2,-1)

k = x+y

k = -2 -1

k = -3

Hence, the value of k is -3.

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The required simple interest of 10% of four year on principle amount is $857.

Simple interest depends on the chief measure of a credit or the first store in quite a while account. Straightforward interest doesn't build, and that implies a loan boss will just compensation interest on the chief sum and a borrower couldn't have ever to pay more interest on the recently gathered interest.

We have,

Amount of four year = $1200

simple interest = 10%

Let loaned amount is x

Then,

interest of four year =×4 x×10/100 = 4x/10

According,

x + 4x/10 = $1200

14x/10 = $1200

x = $12000/14

X = $857 (appox)

Thus, the required loaned amount is $857.

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Answer:

3 is in the ones place

0 is in the tens place

9 is in the thousandths place

Step-by-step explanation:

thousands, hundreds, tens, ones (DECIMAL) tenths, hundredths, thousandths

Answer:

he would have a 50% chance of getting one of the 10 prizes

Answer:

30.

Step-by-step explanation:

First, we have to split up the equation:

(7 x 4) + (10 ÷ 5)

Now, we simplify:

(7 x 4) + (10 ÷ 5)

28 + 2

28 + 2 = 30.

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Surface area of the box measuring 5 inches by 3 inches by 7 inches is 142 square inches.

The surface area of the object that refers to the overall space that is filled by its surfaces. Different 3D shapes in the geometry have various surface areas, which can be quickly estimated using the formulas. Two categories are used to classify the surface area:

Curved surface area or Lateral surface area

Surface area in total

Surface area of rectangle = 2 ( lb + bh + hl )

Dimensions of box = 5 inches by 3 inches by 7 inches

Hence,

Length = 5 inches

Breadth = 3 inches

Height = 7 inches

By putting it in formula of surface area of rectangle

= 2 ( lb + bh + hl )

= 2 ( 5*3 + 3*7 + 7*5 )

= 2 ( 15 + 21 + 35 )

= 2 * 71

 = 142 square inches

Hence, the total surface area of the box is 142 square inches.

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Answer:

Perimeter is 12+2√26

Step-by-step explanation:

Question:

The perimeter of quadrilateral PQRS with the vertices

P(-2, -2), Q(-1, 3), R(5, 3), and S(4, -2)​

Find distances PS and QR:

Notice the y-coordinates are the same for 2 pairs of points

P(-2, -2), S(4, -2)​ and Q(-1, 3), R(5, 3)

So the distance PS = |-2|+4= 6 and QR = |-1|+5 = 6

Find the distances PQ and SR:

Use the distance formula:

[tex]d= \sqrt{(x_{2}-x_{1} ) ^{2} + (y_{2}-y_{1} ) ^{2} }[/tex]

P([tex]x_{1}[/tex] = -2, [tex]y_{1}[/tex] = -2), Q( [tex]x_{2}[/tex] = -1, [tex]y_{2}[/tex] = 3)

PQ = [tex]\sqrt{(-1--2)^{2} +(3- -2)^{2} } = \sqrt{1^{2} +5^{2} } = \sqrt{26}[/tex]

SR = [tex]\sqrt{26}[/tex], because of PQ and SR are equal.

Find the perimeter of quadrilateral PQRS:

The perimeter is equal to the sum of all sides of the quadrilateral.

P= PS + QR + PQ + SR = 6+6+ √26 +√26 = 12+2√26

The horse was worth it for $1800.

What is proportion?

A mathematical comparison of two numbers is called a proportion. Ratios and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers.

Based on the given question condition, where, 'h' denotes the amount for the horse in dollars,  the proportion can be defined as:

or,  [tex]\frac{19200 + h}{12} = \frac{10450+h}{7}[/tex]

or, (19200 + h)7 = (10450 + h)12

or, 134400 + 7h = 125400 + 12h

or, 12h - 7h = 134400 - 125400

or, 5h = 9000

or, h = 9000/5 = 1800

Hence, the horse was worth $1800.

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Answer:

Figure B.

Step-by-step explanation:

Figure A uses what is visually similar in size cylinders to give a detailed image of the amount of money (assumingly as profit). Each given cylinder that is in similar size represents $200, and so it is easy to figure out how the amount of money per store.

In the case of Figure A,

Save Store = $400

Leff's Store = $800

Low Pricer = $1200

In the case of Figure B, however, while it gives a legend for price per cylinder of that proportion, it does not make use of the legend, and does not give a adequate legend to decipher the Figure. In essence, the data given in Figure B is useless as it makes no use of its legend.

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4. a. The graph of the system is attached below.

b. The solution is: (-1, 3).

5. a. (2, 40) is the solution as shown by the graph.

b. (2, 40) means that both will complete 40 cranes after 2 days

On a graph, when two lines are plotted for different equations, the solution is the coordinates of the point where both lines intersect.

4. a. The graph of y = -3x is the red line in the image attached below, while that of y = x + 4 is the blue line. They both intersect each other at (-1. 3).

b. The solution of the system is therefore, (-1, 3).

5. a. Using the graph given that shows the lines of the equations of DeAndre and Leah, both lines intersect at (2, 40).

We can therefore state that the solution to the system as shown in the graph is: (2, 40).

b. In the context of the scenario given, the solution (2, 40) means that both will have completed equal amounts of 40 cranes after 2 days.

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The equation that will be used to solve the given question is [2.75x+3.10=27.85] and with the help of this equation we know that Aaden took a ride of 9 miles.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, we know that:
The pick-up fee that the company charges is: #3.10

Ride charges per mile: $2.75

Total fare price: $27.85

So, let x be the number of miles ridden, the equation that will be used to solve the given question will be:

2.75x + 3.10 = 27.85

Now, solve as follows:

2.75x + 3.10 = 27.85

2.75x = 27.85 - 3.10

2.75x = 24.75

x = 24.75/2.75

x = 9

Therefore, the equation that will be used to solve the given question is [2.75x+3.10=27.85] and with the help of this equation we know that Aaden took a ride of 9 miles.

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Answer: 256

Step-by-step explanation:

8^8/3 is the same as an 8 square root! We have to factor out and I get 2^8 after finish factor the smallest number and get 256!

Answer:

∠BEC is supplementary to ∠AEB

∠AED and ∠BEC are a pair of vertical angles

Testing the hypothesis "Americans express executives hypothesize that 40% of college students own an Americans express credit card." is an example of generalizing.

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge. A straightforward hypothesis only hypothesizes the relationship between two independent and dependent variables.

An example of testing a generalization is "American Express executives' hypothesis that 40% of college students own an American Express credit card."

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The probability that the sample mean diameter surpasses 71 when n = 30 is 0.5 if the distribution is normal (the quoted article makes this assumption and even gives the related normal density curve).

The likelihood that the sample mean diameter exceeds 71 when n = 30 is 0.5, since the normal distribution is symmetric around the mean. This means that there is a 50% probability of the sample mean diameter being above the mean, and a 50% probability that it is below the mean.

The correct question is : suppose the distribution is normal (the cited article makes that assumption and even includes the corresponding normal density curve). a. how likely is it that the sample mean diameter exceeds 71 when n = 30

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Answer: 20 cards.

Step-by-step explanation: If Sarah can make 4 cards in 60 minutes, then she can make 1 card in 60/4 = 15 minutes.

Therefore, in 300 minutes, she can make 300/15 = <<300/15=20>>20 cards.

The probability is 0.25.

What is probability?

Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To determine how likely an event is to occur, mathematics has created the concept of probability.

Given there are 2 coins flipped 4 times, we get the following sample space

S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

Now, A = event of having at least 3 heads.

A= {HHHH, HHHT, HHTH, HTHH, THHH}

The number of events having the first flip heads is 4.

Therefore, the probability is:

P(A) =

[tex]=\frac{successful \space\ events}{total\space\ sample\space\ events}\\=\frac{4}{16}\\=0.25[/tex]

Therefore, the probability of flipping at least 3 heads in 4 flips of 2 fair coins given that the first flip is heads is 0.25.

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answer:

f(g(x))=4x^2-2

step-by-step explanation:

plug g(x) into f(x) to get f(g(x))=2(x^2-1). when this is simplified, you get the answer presented above. the correct answer would be the green option. hope that helps!

In 2.63  hours the prices of the two stocks be the​ same

Two or more expressions with an Equal sign is called as Equation.

Given,

The price of Stock A at 9 A.M. was $12.71.

Price has been increasing at the rate of $0.08 each hour

Price of Stock B was $13.21

The price has been decrease at the rate of $0.11 each hour.

We can write in the form of equation , to find how many hours will the prices of the two stocks be the​ same

12.71+0.08h=13.21-0.11h

0.11h+0.08h=13.21-12.71

0.19h=0.5

Divide both sides by 0.19

h=0.5/0.19

h=2.63

Hence, in 2.63  hours the prices of the two stocks be the​ same

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The percentage of increase in the population is  17 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the percentage increase in the population be = A

Now , the equation will be

The initial population of the city = 117,000

The increase in population of the city = 136,890

Now , the percentage increase in population is given by the formula

initial population of the city + ( A / 100 ) x  initial population of the city = increase in population of the city

So , on substituting the values in the equation , we get

Percentage increase in population = 117000 + ( A/100 ) x 117000 = 136890

117000 + ( A/100 ) x 117000 = 136890

Subtracting 117000 on both sides of the equation , we get

( A/100 ) x 117000 = 19890

Divide by 117000 on both sides of the equation , we get

A / 100 = 0.17

Multiply by 100 on both sides of the equation , we get

A = 17 %

Therefore , the value of A is 17 %

Hence , The percentage of increase in the population is 17 %

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The new sale price of the product after the deduction of discount is $60

In order to solve the given task, use the concept of percentage.

New price of the product = Regular price of the product - (Percentage discount × Regular price of the product)

= 150 - (60% × 150)

= 150 - (0.6 × 150)

= 150 - 90

= $60

Consequently, the new selling price of the product is $60

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Answer:  The correct answer is 83

Step-by-step explanation:

Complete the equations within each set of brackets

(71+9+3)-(9-11+2)

71+9+3 = 83

9-11+2 = 0

Subtract the results

83 - 0 = 83