A scale factor of a famous statue uses a scale factor of 210:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?

The number of years for the interest amount to reach $ 1,500 at 4 % is given by b = 10.35 years

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount invested be P = $ 1,000

Let the number of years be = b

Let the number of times the interest is applied n = 1

Let the rate of interest be r = 4 %

Now , the compound interest + amount = $ 1,500

A = P ( 1 + r/n )ⁿᵇ

And , the number of years b = ln ( A / P ) / n [ ln ( 1 + r / n ) ]

On simplifying , we get

b = ln ( 1,500.00 / 1,000.00 ) / ( 1 × [ ln ( 1 + 0.04 ) ] )

b = 10.338 years

Hence , the number of years is 10.35 years

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Answer:

Step-by-step explanation:

To determine how many yards of fabric Charles has left, we need to subtract the total amount of fabric used for the costume, pillows, and bag from the initial amount of fabric (m yards). The total amount of fabric used is:

Now, we can subtract the total used fabric from the initial amount of fabric:

The correct expressions that show how many yards of fabric Charles has left are:

So, the correct options are (A), (C), (E), (F), (G), and (H).

________________________________________________________

Answer:

D. [If D is saying "x = 4"]

Step-by-step explanation:

We can start solving the equation 216 = 62x - 1 by adding 1 to both sides to isolate the term with x:

216 + 1 = 62x

Simplifying the left side, we get:

217 = 62x

To solve for x, we can divide both sides by 62:

217/62 = x

Using a calculator, we can evaluate the quotient:

3.5 = x

Therefore, the solution to the equation 216 = 62x - 1 is x = 3.5.

Since none of the answer choices match this result exactly, we can round 3.5 to the nearest integer. Rounding 3.5 up to the nearest integer gives us x = 4.

The factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.

The breaking or breakdown of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.

The given polynomial is:

x² - x - 42 = 0

Expand the quadratic equation:

x² + 6x - 7x - 42 = 0

Take the common terms out from the equation:

x(x + 6) - 7(x + 6) = 0

(x - 7)(x + 6) = 0

Hence, the factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.

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The sequence of transformations that maps triangle ABC onto triangle A”B”C” is given as follows:

First we must look at one vertex of the original triangle, and I am going to choose vertex A, which has the coordinates given as follows:

A(-1,1).

From the change in the orientation of the triangle, we can see that it was reflected over the x-axis, transformation for which the rule is (x,y) -> (x, -y), hence:

A'(-1,-1).

The coordinates of vertex A'' are given as follows:

A(-4,-4).

This means that each coordinate of vertex A' was multiplied by 4, thus the second transformation is a dilation with a scale factor of 4.

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The value of the integral ∫(1+3x) dx is equal to 14.

Integration is a process of adding up small elemental volumes to find the larger volume.

Given is to find the integral -

∫(1+3x)

We can find the equivalent values as -

∫(1+3x) dx = ∫1 dx + ∫3x dx

∫(1+3x) dx = x + 3x²/2

For the limit x = 1 to x = 3, we can write -

∫(1+3x) dx = (3 + 27/2) - (1 + 3/2)

∫(1+3x) dx = 33/2 - 5/2 = 14

Therefore, the value of the integral ∫(1+3x) dx is equal to 14.

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Answer:

y= -6x+5

y= 2x+(-5)

Step-by-step explanation:

This is the equation of the line in point-slope form.
y - 5 = (-5/4)(x + 6)

The equation in slope-intercept form is y = (-5/4)x - 5/4.

And So the equation in standard form is 5x + 4y = -5.

Answer:

C revenue

Step-by-step explanation:

The values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

What is a linear factor?

A linear factor is a polynomial of degree one, which means it has one variable raised to the first power and a constant coefficient. In other words, it is an expression of the form ax + b, where a and b are constants and x is the variable.

We can factor the quadratic 2x² + kx - 5 into the product of two linear factors with integer coefficients if and only if its discriminant is a perfect square.

The discriminant of the quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, a = 2, b = k, and c = -5. Therefore, the discriminant is:

b² - 4ac = k² - 4(2)(-5) = k² + 40

For the quadratic to be factored into two linear factors with integer coefficients, k² + 40 must be a perfect square.

One way to proceed is to list the perfect squares that are 40 greater than a square, and see if k is one of the corresponding values. We can do this by solving the equation:

k² + 40 = m²

where m is an integer. Rearranging, we get:

k² - m² = -40

This is a difference of squares, so we can factor it:

(k + m)(k - m) = -40

We now need to find integer values of k and m that satisfy this equation. We can do this by considering all possible pairs of factors of -40 and solving for k and m.

The pairs of factors of -40 are:

(-1, 40), (-2, 20), (-4, 10), (-5, 8)

For each pair, we can solve the system of equations:

k + m = a

k - m = b

where a and b are the two factors in the pair. Adding these equations, we get:

2k = a + b

Subtracting them, we get:

2m = a - b

Solving for k and m, we obtain:

k = (a + b)/2

m = (a - b)/2

We can now check if the values of k and m are integers and if they satisfy the original equation.

For example, if we take the pair (-1, 40), we get:

k + m = -1

k - m = 40

Adding these equations, we get:

2k = 39

This implies that k = 39/2, which is not an integer, so this pair does not work.

Trying the other pairs, we find that:

(-2, 20) gives k = 9 and m = 11, which works

(-4, 10) gives k = 3 and m = 7, which works

(-5, 8) gives k = 1 and m = 3, which works

Therefore, the values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

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The sum of the given series is -

6 ∑{1/(2n + 1)² - 1}.

Integration is a process of adding up small elemental volumes to find the larger volume.

Given is the series as -

6/(3² - 1) + 6/(5² - 1) + 6/(7² - 1) + ....

The given series is -

S = 6/(3² - 1) + 6/(5² - 1) + 6/(7² - 1) + ....

S = 6{1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + ....}

S = 6 ∑ {1/(2n + 1)² - 1}

Therefore, the sum of the given series is -

6 ∑{1/(2n + 1)² - 1}.

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The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.

Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).

In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:

a + b + c = 180

Substituting the given values, we get:

(6x-1) + 20 + (x+14) = 180

Simplifying and solving for x, we get:

7x + 33 = 180

7x = 147

x = 21

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:

angle a = (6x-1) = (6*21-1) = 125 degrees

angle b = 20 degrees

angle c = (x+14) = (21+14) = 35 degrees

Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

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Answer:

347

Step-by-step explanation:

Im not sure if that helps but thats the answer I got.

By using the long division method, The value of expression  8328 ÷ 24 after divide is,

⇒ 8328 ÷ 24

   = 347

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, To dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The mathematical expression for divide is,

⇒ 8328 ÷ 24

Now, We can formulate;

We can use the long division method for the expression as;

⇒ 8328 ÷ 24

⇒ 8328 / 24

 24 ) 8328 ( 347

     -  72

       -----

        112

     -   96

        ------

             168

           -  168

            --------

                  0

Therefore, We get the correct answer,

By using the long division method,

The value of expression  8328 ÷ 24  after divide is,

⇒ 8328 ÷ 24

   = 347

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It takes the toy car 2.43 seconds to fall to the bottom floor,  answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

An equation is a mathematical statement that asserts that two expressions are equal. An equation consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=).

For example, 2x + 5 = 11 is an equation, where the left-hand side is 2x + 5 and the right-hand side is 11. This equation asserts that the expression 2x + 5 is equal to 11, and the value of x can be determined by solving for x.

Equations can be simple or complex, and they can involve one or more variables. They can also be linear or nonlinear, depending on the nature of the expressions involved.

Solving an equation involves finding the values of the variables that make the equation true. This may involve applying algebraic operations and simplification techniques to isolate the variable on one side of the equation.

Equations are used in many areas of mathematics, science, engineering, and economics, and they provide a powerful tool for modeling and analyzing real-world situations. They are also used extensively in computer programming and cryptography, where they play a critical role in the development of algorithms and data encryption methods.

We have the equation [tex]h = 94 - 16t^2[/tex], where h is the height of the toy car in feet and t is the time in seconds.

When the toy car reaches the bottom floor, its height will be h = 0. So we can set the equation equal to 0 and solve for t:

[tex]0 = 94 - 16t^216t^2 = 94t^2 = 94/16[/tex]

[tex]t = \sqrt{(94/16)} = \sqrt{(23.5/4)} = 2.43 seconds[/tex] (rounded to two decimal places)

Therefore, it takes the toy car 2.43 seconds to fall to the bottom floor.

The closest answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

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The runners can finish in 362880 possible results

What is Permutation?

Permutation is the different number of arrangements that can be formed by taking r things from the n available things.

The formula  n! = 1 × 2 × 3 × 4 × .......× n.

To get the order the runners could possibly finish,

= 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 326880

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The next step on solving completing square is: 5 (x² + 4x) = 7 and 5(x² + 4x + 4) = 7 + 20. So, these steps could he use to solve the quadratic equation by completing the square.

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a ≠ 0 is true is known as a quadratic equation.

Case 1:

Given equation becomes:

5x² + 20x - 7 = 0

Firstly, we will add of 7 in both sides:

5x² + 20x - 7 + 7 = 0 + 7

Now, same variable of opposite sign is cancelled:

5x² + 20x = 7

Now, taking 5 common from left side:

5 (x² + 4x) = 7

Case 2:

Given equation becomes:

5x² + 20x - 7 = 0

Firstly, we will add of 7 in both sides:

5x² + 20x - 7 + 7 = 0 + 7

Now, same variable of opposite sign is cancelled:

5x² + 20x = 7

Now, we will add of 20 in both sides

5x² + 20x + 20 = 7 + 20

Now, taking common of 5 from left side:

5(x² + 4x + 4) = 7 + 20

So, The next step on solving completing square is: 5 (x² + 4x) = 7 and 5(x² + 4x + 4) = 7 + 20

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Answer:

The answer is (A) 8.1%.

Step-by-step explanation:

The probability of flipping a coin and getting heads is 1/2 or 0.5. Assuming the coin is fair, the probability of getting heads 4 times in 11 flips is given by the binomial probability formula:

P(4 heads in 11 flips) = (11 choose 4) * (0.5)^4 * (0.5)^(11-4) = 330 * 0.5^11

Using a calculator, we get:

P(4 heads in 11 flips) ≈ 8.1%

Therefore, the answer is (A) 8.1%.

The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,

µ = 3. 5 and σ = 0. 5

and the random sample of 100 male students has a mean GPA 3.42 is considered.

The z-score value is,

Z=( 3.42-3.5)/ (0.5/√100)

Z= -0.08/0.05

Z=-1.6

The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:

The required probability is,

P(X>3.42)=P(z>-1.6)

= 1- P(Z≤-1.6)

From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.

P(X>3.42)= 1- P(Z≤-1.6)

=1-0.0548

=0.9452

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.

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y = 14/11 x is the required equation. Option Cis correct

If the variable y varies directly with x, this is expressed as:

y = kx

where

k is the constant of proportionality

Given that x = 11 and y = 14, hence;

k = y/x

k = 14/11

Substitute k into the original equation

y = kx

y = 14/11 x

Hence the required equation from the given information is y = 14/11 x

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Answer:

Step-by-step explanation:

a) The slope of the line passing through the points (5,6) and (-1,6) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (5,6) and (x2, y2) = (-1,6).

m = (6 - 6) / (-1 - 5) = 0 / -6 = 0

Therefore, the slope of the line is 0.

b) The slope of the line passing through the points (3,-2) and (3,-1) cannot be calculated using the previous formula since the points have the same x coordinate. This means that the line is vertical and therefore its slope is infinite (or undefined).

c) The slope of the line passing through the points (2,2) and (-5,2) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (2,2) and (x2, y2) = (-5,2).

m = (2 - 2) / (-5 - 2) = 0 / -7 = 0

Therefore, the slope of the line is 0.

d) The slope of the line passing through the points (9,-2) and (-7,-2) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (9,-2) and (x2, y2) = (-7,-2).

m = (-2 - (-2)) / (-7 - 9) = 0 / -16 = 0

Therefore, the slope of the line is 0.

e) The slope of the line passing through the points (-8,22) and (1,4) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-8,22) and (x2, y2) = (1,4).

m = (4 - 22) / (1 - (-8)) = -18 / 9 = -2

Therefore, the slope of the line is -2.

f) Since we know the slope m = 2 and one of the points is (3,6), we can use the formula:

y - y1 = m(x - x1)

where (x1, y1) = (3,6). Substituting m and (x1, y1) into the formula, we get:

y - 6 = 2(x - 3)

Expanding the formula and solving for y, we get:

y = 2x - 6 + 6

y = 2x

Therefore, the y-coordinate of the second point is y = 2(4) = 8. The second point is (4,8).

The probability that he will make both free throws is 0.84.

What exactly is the meaning of probability?

Probability expresses the possibility of an event. This branch of mathematics studies the occurrence of a random event. The value ranges between 0 and 1. Probability is used in mathematics to anticipate the possibility of events occurring.

Probability refers to the likelihood of something occurring. This fundamental premise of probability theory is used by the probability distribution. We must first know the entire number of possibilities before we can assess the possibility of an event occurring.

P(E) is the probability of an event occurring divided by the total number of outcomes.

Now,

Given that player makes 92% of freethrows

that means p(making free throws)=92/100

=23/25

so making two free throws probability will be =23*23/25*25

=529/625

=0.84

Hence,

           The probability that he will make both free throws is 0.84.

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Answer:

1st one

Step-by-step explanation:

Answer: A. (2/5,-3)

Step-by-step explanation:

in order to find the solution to the set of equations, you need to find one variable first, lets fing y first

10x+3y=-5

10x = -5 - 3y

x = (-5 -3y)/10

substitute this in for x in the other equation

-5((-5 - 3y)/10) -4y = 10

(25 + 15y)/10 -4y = 10

25/10 + 15y/10 -4y = 10

make all fractions on the left side

25/10 + 15y/10 - 40y/10 = 10

combine

25/10 -25y/10 = 10

multiply both sides by 10 to get rid of the denominator

25 - 25y = 100

combine like terms

-25y = 75

divide

y = -3

plug y into the first equation to find x

10x + 3(-3) = -5

10x -9 = -5

10x = 4

x = 4/10

simplify

x = 2/5

hope this helps!

Answer:

0.1369

Step-by-step explanation:

(37/100)^2=0.1369

from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar.

While from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.

Assuming that the slips of paper are randomly distributed and the student does not have any information about the distribution, let's analyze the probabilities for each choice:

Thus, from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar. On the other hand, from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.

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The cubic root of z = -27 is -3

A real cube and tree roots may be the first images that come to mind when we hear the terms "cube" and "root." Is it not? Well, the concept is the same. Root refers to the main source or starting point. So, all we need to do is consider "which number's cube should be taken to get the given number." The cube root definition in mathematics is expressed as The cube root is the quantity that must be three times multiplied to yield the initial quantity. Let's look at the cube root equation: ∛x = y, where y is the cube root of x. Every number with a little 3 inscribed on it can be represented by the radical sign as the cube root symbol.

In this problem, the cubic root of z = -27 can be calculated as;

z = -∛-27

z = -3

This is because 27 is a perfect cube

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The slope of the line segment is -1/2 . Option A is correct.

What is slope ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

The slope is the "rise over run" between any two points on the line.

Count out how much "up or down" vs "left or right" to find the slope:

   We go up 5 and right 5, giving us the fraction

Thus , slope is given by -5 /10 = -1 /2      

When counting, up and right are counted as positive; left and down are counted as negative.

Hence , the slope of the line segment is -1/2 . Option A is correct.

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Answer:

-27/64 or -0.4219

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve this, we can take the numerator and denominator, and cube them.

The new fraction is now [tex]-\frac{27}{64}[/tex].

Therefore, [tex]-\frac{3}{4}[/tex] cubed as a fraction is [tex]-\frac{27}{64}[/tex].

The expression as a fraction is -27/64.

We have,

Expression:

(-3/4)³

This can be written as,

-3³ / 4³

Now.

Simplifying each term.

-3³ = -3 x -3 x -3 = -27

4³ = 4 x 4 x 4  = 64

Now,

(-3/4)³ = -27/64

Thus,

The expression as a fraction is -27/64.

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Answer:

Step-by-step explanation:

To find the x-intercepts of the polynomial function f(x) = x^4 - x^2, we need to set f(x) = 0 and solve for x. That is, we need to find the values of x that make the function equal to zero.

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

Setting f(x) = 0, we get:

x^4 - x^2 = 0

Factoring out x^2, we get:

x^2(x^2 - 1) = 0

Using the zero product property, we get:

x^2 = 0 or x^2 - 1 = 0

Solving for x in each case, we get:

x = 0 or x = ±1

Therefore, the x-intercepts of the polynomial function f(x) = x^4 - x^2 are (0, 0), (1, 0), and (-1, 0).

Answer: One foot is equal to 12 inches, and since 1 inch is equal to 2.54 centimeters, we have:

1 foot = 12 inches = 12 x 2.54 cm = 30.48 cm

So the length of the flat bar is 30.48 cm. Multiplying this length by the price per cm, we get:

30.48 cm x 2 pesos/cm = 60.96 pesos

Therefore, we need 60.96 pesos to buy a flat bar of length 1 foot at a price of 2 pesos per cm.

Step-by-step explanation: