15 inches and 8 feet in the simplest form

Answer:

-4, 3

Step-by-step explanation:

you got's it :)

Answer:

F. 48.98 m

Step-by-step explanation:

What is circumference?

How does it apply here?

Solving

Step 1: Plug in your values.

Step 2: Simplify.

Therefore, the correct answer is F. 48.98 meters.

Answer:

it's a line

option (b)

Step-by-step explanation:

please mark me as

Answer:

p = -10

Step-by-step explanation:

-2(6p+5) = -6(p+5) - 8p

-12p-10 = -6p-30-8p

reduce

-12p-10 = -14p-30

add 10 to each side

-12p = -14p-20

add 14p to each side

2p = -20

p = -10

Answer:

2p+20

Step-by-step explanation:

-12p-10=-6p-30-8p

-12p-10=-14p-30

The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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y² + 2y - 15 = 0

y² + 5y - 3y - 15 = 0

y(y + 5) - 3(y + 5) = 0

(y + 5) (y - 3) = 0

taking (y + 5) = 0 => y = -5

now taking (y - 3) = 0 => y = 3

So, the required factors of the given equation are -5 and 3

In this exercise we have to factor the equation given in the statement, so we have to:

The factors of the given equation are -5 and 3.

So from the given equation we have that:

\(y^2 + 2y - 15 = 0\\y^2 + 5y - 3y - 15 = 0\\y(y + 5) - 3(y + 5) = 0\\(y + 5) (y - 3) = 0\)

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The solution to the given system of equations in vector notation is x = [1, -1, 2, 1, 0].

To solve the system of equations, we can represent the equations in matrix form, as A * x = b, where A is the coefficient matrix, x is the vector of variables, and b is the vector on the right-hand side.

The coefficient matrix A can be constructed by taking the coefficients of the variables from the left-hand side of the equations. The vector b contains the constant terms.

In this case, the coefficient matrix A and the vector b are:

A = [[1, 5, 4, 3, 6],

[1, 6, 6, 6, 7],

[6, 7, 8, 10, 8],

[1, 6, 6, 7, 7]]

b = [2, 6, 12, 8]

To find the solution, we can use matrix algebra to solve the equation A * x = b. We can multiply both sides by the inverse of A to isolate x:

x = A^(-1)  b

Calculating the inverse of A and multiplying it by b, we find that the solution is x = [1, -1, 2, 1, 0].

Therefore, the solution to the given system of equations in vector notation is x = [1, -1, 2, 1, 0].

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If a quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (4, 6), the vertex of the function defined as g(x) = f(x +2) - 2 is (2, 4).

In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Geometry, the function g(x) = f(x + 2) - 2 simply means shifting a graph of the parent function by 2 units to the left and 2 units down.

In this context, we can reasonably infer and logically deduce that the vertex of the image g(x) is given by;

Vertex = (4 - 2, 6 - 2)

Vertex = (2, 4).

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The surface area  of the given volume of the rectangular prism is equal to 13.86 square centimeters.

Volume of the rectangular prism is 6 cubic centimeters.

Let the dimensions of the rectangular prism be length (l), width (w), and height (h).

Volume of the rectangular prism = l x w x h

⇒ l x w x h = 6

Use the given volume to find one of the dimensions .

Then use that information to find the surface area.

To calculate the surface area at least two of the dimensions known.

Let us assume that the height (h) is 1 centimeter.

⇒l x w x 1 = 6

⇒ l x w = 6

Use this equation to solve for one of the dimensions.

⇒ l = 6/w

Substituting this value of l into the surface area formula, we get,

Surface area = 2lw + 2wh + 2lh

⇒Surface area = 2(6/w)w + 2w(1) + 2(6/w)(1)

⇒Surface area = 12/w + 2w + 12/w

⇒Surface area = 2w + 24/w

Value of w that gives the minimum surface area,

Take the derivative of the surface area formula with respect to w and set it equal to 0,

d/dw (2w + 24/w) = 0

⇒ 2 - 24/w^2 = 0

Solving for w, we get,

⇒w = √(12)

Substituting this value of w back into the surface area formula, we get,

⇒ Surface area = 2(√(12)) + 24/√(12)

⇒Surface area = 4√3 + 4√3

⇒Surface area = 8√3

⇒ Surface area = 13.86 square centimeters

Therefore, the surface area of the rectangular prism is approximately 13.86 square centimeters.

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Let

x = Trey's savings

x + 27 = Tyler's savings

The sum of their savings is $85, which can be translated to

(x) + (x+27) = 85

Simplify the equation

x + x + 27 = 85

2x + 27 = 85

The length of the radius AB is 6 units.

The angle ∠BAC is 90 degrees. The length of arc BC is 3π. The length of  

radius AB can be found as follows:

Hence,

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 90 / 360 × 2πr

3π = 1 / 4 × 2πr

cross multiply

12π = 2πr

divide both sides by 2π

r = 6 units

Therefore,

radius AB = 6 units

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Answer:

!

Step-by-step explanation:

Subtract 210 by the total number of students which you didn't give

The linear equation that represents this situation will be y = 4x + 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

To ride go-carts at Rick's Play Zone costs $4 per ride plus $3 to rent a helmet.

Let 'y' be the total cost in dollars and 'x' be the number of times you ride the go-carts. Then the equation is given as,

y = 4x + 3

The equation that represents this situation will be y = 4x + 3.

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Answer: 0.24 (4 repeating) repeating as a fraction  = 11/45

or, 0.24 (24 repeating) repeating as a fraction  = 8/33

Hope this helps! :)

Answer:

number is 8

Step-by-step explanation:

let n be the number then 4 times the number is 4n and increased by 30 means adding 30 to it , that is 4n + 30

70 decreased by the number means subtracting n fro 70 , 70 - n

then

4n + 30 = 70 - n ( add n to both sides )

5n + 30 = 70 ( subtract 30 from both sides )

5n = 40 ( divide both sides by 5 )

n = 8

Answer:

12 divide by 2+1

2+1=3 so

12/3

4

RNA's capability to self-replicate and catalyze chemical reactions make it the best candidate for the first life-form.

According to the scientists, RNA is considered the best candidate for the first life-form due to the fact that RNA is capable of self-replication and catalysis. This is possible because RNA can act both as a template to produce copies of itself and also as an enzyme to accelerate chemical reactions. These abilities suggest that RNA could have played a role in the emergence of the first living organisms on Earth.

An RNA molecule has the ability to catalyze reactions, which means that it can speed up chemical reactions without itself being altered. Thus, it is capable of serving as an enzyme. Scientists believe that the first life-form must have been capable of self-replication and catalysis, and RNA is capable of both functions.

This capability is significant because it is fundamental for the origin of life. Hence, RNA is believed to have played a significant role in the emergence of the first living organisms on Earth.

To conclude, RNA's capability to self-replicate and catalyze chemical reactions make it the best candidate for the first life-form.

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RNA is considered the best candidate for the first life-form by scientists because RNA is capable of self-replication and catalysis.

The correct option is the first one due to following reasons:

As a result, scientists believe that RNA may have played a crucial role in the origins of life on Earth.

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The appropriate x-axis and y-axis unit scales for the coordinates (6, 40) are 1 unit for the x-axis and 5 units for the y-axis, Hence, (1,5)

The x-axis represents the horizontal distance from the origin, and the y-axis represents the vertical distance from the origin. The coordinates (6, 40) means that the point is 6 units to the right of the origin and 40 units above the origin.

If we use a unit scale of 1 for the x-axis, then the point will be represented by a dot that is 6 units to the right of the origin. If we use a unit scale of 5 for the y-axis, then the point will be represented by a dot that is 40 units above the origin.

Hence, the most appropriate units scale is (1,5)

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The first six terms of the sequence are -7, -14, -28, -56, -112, -224.

To find the first six terms of the sequence, we need to determine the pattern or rule that generates the terms.

The given information suggests that the sequence is defined recursively, with the first term given as a₁ = -7, and the subsequent terms defined as an = -20n - 1.

Using this recursive formula, we can calculate the values of the sequence:

a₂ = -20(2) - 1 = -40 - 1 = -41

a₃ = -20(3) - 1 = -60 - 1 = -61

a₄ = -20(4) - 1 = -80 - 1 = -81

a₅ = -20(5) - 1 = -100 - 1 = -101

a₆ = -20(6) - 1 = -120 - 1 = -121

Therefore, the first six terms of the sequence are -7, -14, -28, -56, -112, and -224, matching the option A: -7, -14, -28, -56, -112, -224.

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The arithmetic sum of the given sequence 4, 9, ..., 219, 224 is 5130.

First, we need to find the common difference (d) between the consecutive terms in this arithmetic sequence. We can do this by subtracting the first term from the second term: 9 - 4 = 5.

Now that we know the common difference, we can determine the number of terms (n) in the sequence using the formula for the last term (L) in an arithmetic sequence: L = a + (n - 1)d, where a is the first term. In this case, the last term (L) is 224, and we have:

224 = 4 + (n - 1)5

Solving for n, we get:

220 = (n - 1)5

n - 1 = 44

n = 45

Now that we have the number of terms, we can compute the sum (S) of the arithmetic sequence using the formula: S = n/2(a + L). Plugging in the values, we get:

S = 45/2(4 + 224)

S = 45/2(228)

S = 45 × 114

S = 5130

So, the arithmetic sum of the given sequence is 5130.

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step 1

so so s ososoosososososososososososososoosososososzosoosossoosososo

Step-by-step explanation:

The most important thing to remember is: SOH CAH TOA

sin(x) = opposite/hypotenuse

cos(x) = adjacent/hypotenuse

tan(x) = opposite/adjacent

So in #1:

We have the angle and hypotenuse and need to solve for the side opposite of the angle. This smells like a sine question.

sin(42)=x/25

this means that x=25sin(42). Plug that into the calculator and get: 16.73.

(Make sure you are in degrees mode)

For #2:

We are given the angle, the opposite side, and have to solve for the adjacent side. Looks like we need the tangent.

tan(75)=12/x

This means that x=12/tan(75). Calculator says: 3.22

For #3:

We have the angle, adjacent, and have to solve for the hypotenuse. This would be a cosine.

cos(36)=19/x

Solve for x: x=19/cos(36). Calculator says: 23.49

For #4:

We have the angle, adjacent side, and need the opposite side. This is another tangent problem.

tan(53)= x/7

Solving for x: x=7tan(53). Calculator says: 9.29

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

Finding the square root of a number involves determining the value that, when multiplied by itself, gives the original number. Here are a few methods to find the square root:

Prime Factorization: This method involves breaking down the number into its prime factors. Pair the factors in groups of two, and take one factor from each pair. Multiply these selected factors to find the square root. For example, to find the square root of 36, the prime factors are 2 * 2 * 3 * 3. Taking one factor from each pair (2 * 3), we get 6, which is the square root of 36.

Estimation: Approximate the square root using estimation techniques. Find the perfect square closest to the number you want to find the square root of and estimate the value in between. Refine the estimate using successive approximations if needed. For example, to find the square root of 23, we know that the square root of 25 is 5. Therefore, the square root of 23 will be slightly less than 5.

Using a Calculator: Most calculators have a square root function. Simply input the number and use the square root function to obtain the result.

It's important to note that finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

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There are many more people awaiting such a transplant than there are available organs, leading to a large backlog of patients who are not able to receive an organ transplant.

In 2008, the United States Department of Health and Human Services reported that there were approximately 113,000 patients in the United States awaiting organ transplants. Of those, only 28,535 received an organ transplant that year. This is a ratio of approximately 1 in 4. This can be expressed mathematically as 28,535/113,000 = 0.25, or one fourth. This means that for every 4 people awaiting an organ transplant in the United States in 2008, only 1 actually received one. While organ transplants are a life-saving procedure for many, the reality is that there are many more people awaiting such a transplant than there are available organs, leading to a large backlog of patients who are not able to receive an organ transplant.

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Complete question:What were the numbers of patients waiting for and receiving an organ transplant/donation in the United States in 2008, according to Mark Cherry?

Imagine that a survey of randomly selected people finds that people who used sunscreen were more likely to have been sunburned in the past year.

There are several possible explanations for the finding that people who used sunscreen were more likely to have been sunburned in the past year.

However, without additional context or data, it is difficult to determine the most likely explanation definitively. Here are a few possible explanations to consider:

1. Ineffective or improper use of sunscreen: It is possible that the individuals who reported using sunscreen did not apply it correctly or did not reapply it as recommended.

Inadequate application or failure to follow proper sunscreen usage guidelines could result in insufficient protection from the sun's harmful rays, leading to sunburn.

2. Self-selection bias: It is possible that individuals who have previously experienced sunburns may be more likely to use sunscreen. They may be more aware of the potential risks and take precautions, including using sunscreen.

This could create an association between sunscreen use and sunburn, even though sunscreen itself is intended to prevent sunburn.

3. Recall bias: The survey responses may be subject to recall bias, where individuals may inaccurately remember or report their sunscreen use and sunburn experiences.

Memory limitations or subjective perceptions of sunburn severity could influence the reported data and the observed association between sunscreen use and sunburn.

4. Confounding factors: There may be other factors or variables at play that are related to both sunscreen use and sunburn. For example, individuals who engage in activities that increase sun exposure or who have certain skin types may be more likely to both use sunscreen and experience sunburn.

It is important to note that further investigation, including more detailed surveys, data collection and statistical analysis, would be necessary to determine the most likely explanation for the observed association between sunscreen use and sunburn.

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The correct answer is 14 because distance from center of dilation to point on pre-image is 14 times the distance from center of dilation to corresponding point on image

We can solve this problem using the formula of the scale factor of dilation which is given below:

Scale factor of dilation = (image distance)/(pre-image distance)

In the above formula, the image and pre-image distances are measured from the center of dilation.

Let us assume that the scale factor is x.

The vertices of the two triangles are labeled as follows:

Pre-image triangle vertices: A(-2,2), B(-1,3), and C(-3,3)

Image triangle vertices: A′(10,-14), B′(6,-10), and C′(14,-10)

Now, we can calculate the image and pre-image distances using the distance formula and the Pythagorean theorem.

Pre-image distance between A(-2,2) and B(-1,3) is

AB = √[(3 - 2)^2 + (-1 + 2)^2]

= √2

Pre-image distance between A(-2,2) and C(-3,3) is

AC = √[(3 - 2)^2 + (-3 + 2)^2]

= √2

Pre-image distance between B(-1,3) and C(-3,3) is

BC = √[(3 - 3)^2 + (-1 + 3)^2]

= 2

Pre-image perimeter of the triangle ABC is

P₁ = AB + AC + BC

= √2 + √2 + 2

= 2√2 + 2

The image distances are measured between the center of dilation (1,-1) and the vertices of the image triangle.

We can calculate the image distance between two points (x1,y1) and (x2,y2) using the formula below:

Image distance between (x1,y1) and (x2,y2) = x2 - x1 or y2 - y1

Let us calculate the image distances between the center of dilation and the vertices of the image triangle.Image distance between (1,-1) and A′(10,-14) is

10 - 1 = 9

Image distance between (1,-1) and B′(6,-10) is

6 - 1 = 5

Image distance between (1,-1) and C′(14,-10) is

14 - 1 = 13

Image perimeter of the triangle A′B′C′ is

P₂ = A′B′ + B′C′ + C′A′

=  √(9² + 13²) + √(5² + 9²) + √(13² + 5²)

= 39.25 + 10.3 + 14.42

≈ 64.97

Scale factor of dilation = (image distance)/(pre-image distance)

= P₂/P₁

= 64.97/(2√2 + 2)

≈ 14.

Hence, the correct option is 14.

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Answer:

120°

Step-by-step explanation:

We can see that b=a by opposite exteriors.

So a+1/2a=180

1.5a=180

a=180/1.5=120

And since b and a are equal, b also equals 120°

Rounding to the nearest whole number, we get that the score a student would need to have a 30th percentile score on the SAT is 1345.  Correct option is B.

To find the score corresponding to the 30th percentile, we need to use the standard normal distribution with a mean of 0 and a standard deviation of 1. We can convert the SAT score to a standard normal score using the formula:

z = (x - μ) / σ

where x is the SAT score, μ is the mean score (1509), and σ is the standard deviation (312).

To find the score corresponding to the 30th percentile, we need to find the z-score that has an area of 0.30 to its left. Using a standard normal table or calculator, we can find that the z-score corresponding to a 30th percentile is approximately -0.52.

Now we can use the formula to find the corresponding SAT score:

-0.52 = (x - 1509) / 312

Solving for x, we get:

x = -0.52 * 312 + 1509 = 1345.36

Therefore, the answer is (b) 1345.

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Complete question is:

What score would a student need to have a 30th percentile score on the SAT? Recall that the mean score was 1509, and the standard deviation of the scores is 312.

Group of answer choices

a. 1244

b. 1345

c. 1456

d. 1673

Answer:

i) 90

ii) 180

iii) supplementary

iv) linear pair

v) equal

vi) obtuse