Find the length of the third side. If necessary. Write in simplest radical form

The area of the circle is approximately 55.39 square inches.

The circumference of the circle is approximately 26.38 inches.

The area of a circle = πr²

The circumference of the circle = 2πr

Where, r is the radius of the circle, which is half of the diameter of the circle.

Therefore, we have:

radius (r) = 8.4/2 = 4.2 inches

π = 3.14

Thus:

The area of the circle = πr² = 3.14 * 4.2²

Area ≈ 55.39 square inches [nearest hundredth]

The circumference of the circle = 2πr = 2 * 3.14 * 4.2

Circumference ≈ 26.38 inches.

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Ivory needs to make an additional 17 successful free throws without a miss to attain a success rate of 75%.

Let's start by finding Ivory's current free-throw success rate:

\(success rate = \frac{number of successful free throws}{total numbers of free throw} =\frac{7}{15}\)

We want to find the number of additional successful free throws Ivory must make to attain a success rate of $75%$, which can be written as:

\(success rate = \frac{numbers of successful free throws}{total numbers of free throws} = \frac{3}{4}\)

Let's call the number of additional successful free throws that Ivory needs to make "x". Then, we can write an equation based on the above expressions for success rate:

\(\frac{7 + x}{15 + x } =\frac{3}{4}\)

To solve for x, we can cross-multiply:

4( 7 + x) = 3 (15 + x)

28 + 4x = 45 + 3x

x= 17

Therefore, Ivory needs to make an additional 17 successful free throws without a miss to attain a success rate of 75%.

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The approximate volume of the remaining solid is 77.43 cubic inches

The volume of the rectangular prism is given by

V_rectangular_prism = base_area x height

where the base area is the area of a square with side length 4 inches

base_area = 4 x 4 = 16 square inches

So, the volume of the rectangular prism is

V_rectangular_prism = 16 x 6 = 96 cubic inches

The volume of the cylinder is given by

V_cylinder = π x r^2 x h

where r is the radius of the cylinder (1 inch) and h is the height of the rectangular prism (6 inches). So, the volume of the cylinder is

V_cylinder = π x 1^2 x 6 = 6π cubic inches

To find the volume of the remaining solid, we need to subtract the volume of the cylinder from the volume of the rectangular prism

V_remaining = V_rectangular_prism - V_cylinder

V_remaining = 96 - 6π ≈ 77.43 cubic inches

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The given question is incomplete, the complete question is:

A solid metal prism has a square base with sides of 4 inches, and a height of 6 inches. A hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism. What is the approximate volume of the remaining solid, in cubic inches?

The symbol ≤ could be written in both circles to represent this system algebraically.

Based on the given information, we have two dashed lines on the coordinate plane. The first line has a positive slope and goes through the points (-2, -2) and (0, 0). This line represents the inequality y ≥ x.

The second line has a negative slope and goes through the points (-2, 2) and (0, 0). This line represents the inequality y ≤ -x.

In order to represent this system of inequalities algebraically, we need to find a symbol that satisfies both inequalities. The symbol that can represent this is ≤ (less than or equal to). By using ≤, we can express the system of inequalities as follows:

y ≥ x

y ≤ -x

It's important to note that the choice of the symbol may vary depending on the conventions or context of the problem. In this case, ≤ is a suitable choice based on the given information.

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The equation of the problem is \(5(n+7)\)

The sentence is asking 5 times the sum of n+7, so you are multiplying (n+7) by 5.

Answer:

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Answer:

option D is correct

x=O and x=-8

Answer:

Step-by-step explanation:

Given parabola:

Complete the square to convert the equation into vertex form:

(C) Regression analysis is the statistical method commonly used to estimate the level and trend in a time series by modeling the relationship between the data and independent variables.

Regression analysis is the statistical method used to estimate the level and trend in a time series. Time series data represents observations taken at different points in time and is commonly used to analyze trends and patterns over time.

Regression analysis allows us to model the relationship between a dependent variable (in this case, the time series data) and one or more independent variables (such as time or other relevant factors). By using regression analysis, we can identify the underlying trend in the time series and estimate its level.

The regression model captures the relationship between the dependent variable (the time series) and the independent variable(s) by fitting a line or curve that best represents the data. This line or curve helps to identify the overall trend and level of the time series.

While moving average, simulation method, covariance analysis, and correlation analysis are useful techniques in analyzing time series data, they are not specifically designed to estimate the level and trend in a time series. Therefore, (C) regression analysis is the most appropriate method for estimating the level and trend in a time series.

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The function is continuous   in D where

\($D \mathcal{D}\left\{(x, y): x > -y^6\right\}$\)

Generally, A continuous and bounded function is a function that is continuous over a finite interval, and whose range of values are within finite bounds. For example, the function f(x)=x^2 is continuous and bounded over the interval [-2,2], since it is continuous over the whole interval and the range of values is between 0 and 4.

Given that

\($F(n y)=e^{x^2 y}+\sqrt{n+y^6}$where \\\\ $e^{x^2 y}$ is cortinous everywhereAnd. \\\\\$\sqrt{n+y^6}$ is continoas if $n+y^6 > $ ?\\\\\$\Rightarrow y^6 > -n$\\\\\)

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If both parents are carriers of a recessive trait, the probability that all three children will have the normal phenotype is around 42.19%.

If both parents are carriers of a recessive trait, the probability that their children will have the normal phenotype can be determined using a Punnett square. Since both parents are carriers, their genotypes are heterozygous (Aa).

When we create a Punnett square, we see the following outcomes for their children's genotypes:
- AA (25%)
- Aa (50%)
- aa (25%)

To have a normal phenotype, the child must have either AA or Aa genotype. Therefore, the probability of one child having a normal phenotype is 75% (25% + 50%).

Now, to calculate the probability of all three children having a normal phenotype, we multiply the probabilities of each child:

0.75 × 0.75 × 0.75 = 0.421875, or approximately 42.19%.

So, the probability that all three children will have the normal phenotype is around 42.19%.

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Answer:

3/2 or 1.5

Step-by-step explanation:

Finding the gradient

Answer:

gradient = \(\frac{3}{2}\)

Step-by-step explanation:

calculate the gradient (slope) m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, - 1 ) and (x₂, y₂ ) = (4, 5 )

m = \(\frac{5-(-1)}{4-0}\) = \(\frac{5+1}{4}\) = \(\frac{6}{4}\) = \(\frac{3}{2}\)

To determine whether the series ∑(n=1 to infinity) 7n/n is convergent or divergent, we can apply the ratio test. The ratio test helps us determine the convergence or divergence of a series by examining the limit of the ratio of consecutive terms.

In this case, let's calculate the ratio of consecutive terms using the formula for the ratio test:

lim(n→∞) |(7(n+1)/(n+1))/((7n/n)|

Simplifying the expression, we get:

lim(n→∞) |7(n+1)/n|

As n approaches infinity, the limit evaluates to:

lim(n→∞) |7(n+1)/n| = 7

Since the limit is a finite positive value (7), which is less than 1, the ratio test tells us that the series is convergent.

However, you mentioned identifying an (term) in the series, and it seems there may be an incomplete part of the question. Please provide additional information or clarification about identifying an term in the series so that I can provide a more specific answer.

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Answer:

Leave em alone or go be noisy?

Step-by-step explanation:

Answer:

D. y + y + y + y

Step-by-step explanation:

By applying Pythagoras theorem,we get

(hypotenuse)^2=(base)^2+(perpendicular)^2

=>(h)^2=(7)^2+(4)^2

=>(h)^2=49+16

=>(h)^2=65

=>h=√65

Therefore, option B is correct,i.e.,√65

Answer:

Square root of 65 units

Step-by-step explanation:

This is the correct answer

The equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).

To find the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1), first, determine the slope of the given line. The slope is -8. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the new line will be 1/8.

Now, use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point (-4, 1). Plug in the values: y - 1 = (1/8)(x - (-4)).

Simplify the equation: y - 1 = (1/8)(x + 4). Distribute the 1/8: y - 1 = (1/8)x + (1/2). Finally, add 1 to both sides: y = (1/8)x + (1/2) + 1.

So, the equation of the line that is perpendicular to y = -8x + 2 and contains the point (-4, 1) is y = (1/8)x + (3/2).

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ANSWER :

A. 15

EXPLANATION :

Recall the secant-secant formula :

That will be :

Solving for x :

the base of the triangular window is 24 feet and the height is 10 feet.

Let's denote the height of the triangular window as h feet. According to the given information, the area of the window is 120 square feet.

The formula to calculate the area of a triangle is:

Area = (1/2) × base × height

In this case, we can write the equation as:

120 = (1/2) × base × h

Now, we are also given that the base of the window is 4 feet more than twice the height. So we can express the base as:

base = 2h + 4

Substituting this expression for the base into the area equation, we have:

120 = (1/2) × (2h + 4) × h

Now we can solve this equation for the height.

Multiplying both sides of the equation by 2 to remove the fraction:

240 = (2h + 4) × h

Expanding the right-hand side:

240 = 2h² + 4h

Rearranging the equation and setting it equal to zero:

2h² + 4h - 240 = 0

Now we can solve this quadratic equation. Factoring out a 2:

2(h² + 2h - 120) = 0

Factoring the quadratic expression inside the parentheses:

2(h + 12)(h - 10) = 0

Setting each factor equal to zero:

h + 12 = 0   or   h - 10 = 0

Solving these equations, we get:

h = -12   or   h = 10

Since height cannot be negative in this context, we discard the negative value. Therefore, the height of the triangular window is h = 10 feet.

Substituting the height value back into the expression for the base:

base = 2h + 4

    = 2(10) + 4

    = 20 + 4

    = 24

Therefore, the base of the triangular window is 24 feet and the height is 10 feet.

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Answer:

86

Step-by-step explanation:

y + 28 + 58 = 180

y + 86 = 180

y = 180 - 86

y = 94

x + y = 180

x + 94 = 180

x = 180 - 94

x = 86

For conservative forces, force can be fouind as being the negative of the deriviation of potential energy.

It should be noted that a conservative force simply means the force in moving a particle from a particular point to another. In this case, the force is independent of the path that's taken by the particle.

It should be noted that F = du/dr as u is the potential energy. Therefore, force is the negative derivative of the potential energy.

Therefore, for conservative forces, force can be fouind as being the negative of the deriviation of potential energy.

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Complete question

For conservative forces, force can be fouind as being the negative of the deriviation of?

momentum

kinetic energy

impulse

work

potential energy

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

Reflection

Step-by-step explanation:

Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

Answer:

Step-by-step explanation:

43

Answer:

if i am sure it is one i could be wrong bc 9 over 9 is 1 and then it to the third power is 1

Step-by-step explanation:

Answer:

The correct answer to (9/9)^3 = 1

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For a standard normal random variable, what z-score has a) Probability 0.200 to the right z = 0.841. (3 decimal places) b) probability 0.900 to the left z = 1.282. (3 decimal places)

We are looking for the z-score that has a probability of 0.200 to the right. Since the normal distribution is symmetric, we can use a standard normal table to find the z-score that has a probability of 0.800 to the left, which is 0.800 = P(Z ≤ z). From the table, we find that the z-score for a probability of 0.800 to the left is approximately 0.84. Therefore, the z-score for a probability of 0.200 to the right is simply the negative of 0.84, which is -0.84.

We are looking for the z-score that has a probability of 0.900 to the left. Using a standard normal table, we find that the z-score for a probability of 0.900 to the left is approximately 1.28. Therefore, the z-score for a probability of 0.900 to the right is simply the negative of 1.28, which is -1.28.

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Answer:

A: cos(-pi/3)

Step-by-step explanation:

just did the unit test review on EDGE

The trigonometric expression cos(π/12) cos(5π/12) + sin(π/12) sin(5π/12) is equivalent to cos(- π/3). Then the correct option is A.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ cos(π/12) cos(5π/12) + sin(π/12) sin(5π/12)

We know that the formula of cosine.

cos (a - b) = cos a · cos b + sin a · sin b

Then the expression will be

⇒ cos(π/12) cos(5π/12) + sin(π/12) sin(5π/12)

⇒ cos(π/12 - 5π/12)

⇒ cos(π - 5π/12)

⇒ cos(-4π/12)

⇒ cos(- π/3)

The trigonometric expression cos(π/12) cos(5π/12) + sin(π/12) sin(5π/12) is equivalent to cos(- π/3).

Then the correct option is A.

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