Solve for a
C = ab/
a + b

as you should know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables and then solve for "y".

\(\stackrel{f(x)}{y}=\sqrt{x}-5\implies \stackrel{\textit{quick switcheroo}}{x=\sqrt{y}-5}\implies x+5=\sqrt{y} \implies (x+5)^2=y \\\\\\ \stackrel{F~O~I~L}{(x+5)(x+5)}=y\implies x^2+10x+25=\stackrel{f^{-1}(x)}{y}\)

$20 an hour is equivalent to $41,600 a year.

To calculate this, you can multiply $20 by the number of hours worked in a year, which is 2080 which is conversion factor.To calculate an annual salary based on an hourly wage, you can multiply the hourly wage by the number of hours worked per year.

For example, if you work a standard full-time job of 40 hours per week for 52 weeks per year, your total number of hours worked per year would be 2080 (40 hours/week x 52 weeks/year). So if you make $20 an hour, your annual salary would be $41,600 (20 x 2080).

It's worth noting that this calculation assumes that you work 40 hours per week, 52 weeks per year without any time off, and also it doesn't take into account any overtime, bonuses or taxes.

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It is not surprising that the sample proportion is always included in the confidence interval, as the sample proportion is considered as the estimate of the confidence interval.

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

The point estimate is the sample proportion for a confidence interval of proportions, hence it is not surprising that the sample proportion is always included in the confidence interval for population proportions.

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Herefore, the vertices of the final image after applying the composition T−2,4 ◦ RO,180° to ΔXYZ are X''(-2, -1), Y''(0, -1), and Z''(0, 1).

First, we need to perform a reflection over the x-axis and then a translation of 2 units to the left and 4 units up. This is the transformation T−2,4.

Next, we need to perform a rotation of 180 degrees about the origin. This is the transformation RO,180°.

We can apply these transformations to each vertex of the first triangle ΔXYZ to obtain the coordinates of the final image.

Applying T−2,4 to each vertex:

T−2,4(X) = (2, 5) → reflection over x-axis → (2, -5) → translation 2 units left and 4 units up → (0, -1)

T−2,4(Y) = (2, 3) → reflection over x-axis → (2, -3) → translation 2 units left and 4 units up → (0, 1)

T−2,4(Z) = (4, 3) → reflection over x-axis → (4, -3) → translation 2 units left and 4 units up → (2, 1)

Applying RO,180° to each vertex:

RO,180°(0, -1) = (0 × cos(180°) - (-1) × sin(180°), 0 × sin(180°) + (-1) × cos(180°)) = (0, 1)

RO,180°(0, 1) = (0 × cos(180°) - 1 × sin(180°), 0 × sin(180°) + 1 × cos(180°)) = (0, -1)

RO,180°(2, 1) = (2 × cos(180°) - 1 × sin(180°), 2 × sin(180°) + 1 × cos(180°)) = (-2, -1)

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Answer:

x is (-4,-1)

y is (-4,1)

z is (-6,1)

Step-by-step explanation:

The area of the square is increasing at a rate of 98 cm²/s.

Starting with the formula for the area of a square: A = s², where s is the length of each side, find the rate of change of the area with respect to time (dA/dt), we can use the chain rule of differentiation:

dA/dt = d/dt (s²) = 2s ds/dt

where ds/dt is the rate at which each side is increasing.

We are given that ds/dt = 7 cm/s, and we want to find dA/dt when A = 49 cm².

Since the square has four equal sides, we know that s = √(A).

So when A = 49 cm², we have s = √(49) = 7 cm.

Substituting these values into our formula for dA/dt, we get:

dA/dt = 2s ds/dt = 2(7 cm) (7 cm/s) = 98 cm²/s

Therefore, when the area of the square is 49 cm² and each side is increasing at a rate of 7 cm/s, the area of the square is increasing at a rate of 98 cm²/s.

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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im not sure but maybe sorry

Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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Answer:

T, Q, and R

Step-by-step explanation:

These points are all on the same line, making them collinear.

I hope this helps!!

Answer:

13 < x < 21.

Step-by-step explanation:

First the third side (x) must be less than 4 + 17 , that is  < 21.

Also 17 cannot  be greater than  4 + x:

17 < 4 + x

x > 13.

Answer:

8 + 292 = 8 out of 300 pairs were defective.

So: \(\frac{8}{300} = \frac{x}{3000}\)

If we add a zero to both sides, then the answer would be that 80 pairs out of 3000 were defective.

Given:

The population density of Iceland, in people per square kilometer of land area, increased from 2.5 in 1990 to  3.3 in 2014.

Land area of Iceland = 100,250 square kilometers.

To find:

The Iceland's population increase from 1990 to 2014.

Solution:

Land area of Iceland is constant, i.e., 100,250 square kilometers.

The population density of Iceland, in people per square kilometer of land area in 1990 is 2.5.  So, the population in 1990 is

\(2.5\times 100,250=250,625\)

population density of Iceland, in people per square kilometer of land area in 2014 is 3.3.  So, the population in 2014 is

\(3.3\times 100,250=330,825\)

The Iceland's population increase from 1990 to 2014 is

\(330,825-250,625=80,200\)

Therefore, the correct option is D.

The graph of the function F(x) = |x| * 0.015 for x > 0 (sale) and F(x) = |x| * 0.005 for x < 0 (return) is a V-shaped graph with a steeper slope for positive values of x and a shallower slope for negative values of x.

To graph the function f(x) = |x| * 0.015 for x > 0 (sale) and f(x) = |x| * 0.005 for x < 0 (return), we will plot the points on a coordinate plane.

First, let's consider the positive values of x (sale). For x > 0, the function f(x) = |x| * 0.015. The absolute value of any positive number is equal to the number itself. Thus, we can rewrite the function as f(x) = x * 0.015 for x > 0.

To plot the points, we can choose different positive values of x and calculate the corresponding values of f(x). Let's use x = 1, 2, 3, and 4 as examples:

For x = 1: f(1) = 1 * 0.015 = 0.015

For x = 2: f(2) = 2 * 0.015 = 0.03

For x = 3: f(3) = 3 * 0.015 = 0.045

For x = 4: f(4) = 4 * 0.015 = 0.06

Now, let's consider the negative values of x (return). For x < 0, the function f(x) = |x| * 0.005. Since the absolute value of any negative number is equal to the positive value of that number, we can rewrite the function as f(x) = -x * 0.005 for x < 0.

To plot the points, let's use x = -1, -2, -3, and -4 as examples:

For x = -1: f(-1) = -(-1) * 0.005 = 0.005

For x = -2: f(-2) = -(-2) * 0.005 = 0.01

For x = -3: f(-3) = -(-3) * 0.005 = 0.015

For x = -4: f(-4) = -(-4) * 0.005 = 0.02

Now, we can plot the points on the coordinate plane. The x-values will be on the x-axis, and the corresponding f(x) values will be on the y-axis.

For the positive values of x (sale):

(1, 0.015), (2, 0.03), (3, 0.045), (4, 0.06)

For the negative values of x (return):

(-1, 0.005), (-2, 0.01), (-3, 0.015), (-4, 0.02)

Connect the points with a smooth curve that passes through them. The graph will have a V-shaped appearance, with the vertex at the origin (0, 0). The slope of the line will be steeper for the positive values of x compared to the negative values.

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Answer:

30 degree is the correct answer.

The sine of a 30-degree angle is .5.

Answer:

y= -x + 2

Step-by-step explanation:

big brain mates lezzz goo

Answer:

y = - x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (2, 0) ← 2 ordered pairs from the table

m = \(\frac{0-1}{2-1}\) = \(\frac{-1}{1}\) = - 1 , then

y = - x + c ← is the partial equation

To find c use any ordered pair from the table and substitute into the partial equation.

Using (3, - 1 ), then

- 1 = - 3 + c ⇒ c = - 1 + 3 = 2

y = - x + 2 ← equation of line

Answer:

60 cm

Step-by-step explanation:

3 -4-5 is a RIGHT triangle

  area = 1/2  3x  * 4x    = 150

                   12x ^2 = 300

                        x = 5

 ratio of sides 3:4:5  means that

          the sides are   3 * 5       and   4 * 5     and 5 * 5   = 60 cm total

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

This is made slightly more difficult by the fact that the given polynomials are not in order of decreasing powers of x. So, you need to be careful what you're adding, to make sure the terms are "like".

__

Add: (-2x² +3x +4) +(x² -4x -5) = (-2+1)x² +(3-4)x +(4-5) = -x² -x -1

Opp: -(3x² -x +1) = 3x² +x -1

Sub: (x² +3x -4) -(-2x² +4x -3) = (1-(-2))x² +(3-4)x +(-4-(-3)) = 3x² -x -1

Answer:

\(Cost \ total= \$ 1755\)

Step-by-step explanation:

Find the total cost of a rectangular shaped carpet, given the carpets length,  width, and the cost of carpet per square foot. Using the formula for the area of a rectangle.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Area of a Rectangle:}}\\\\A=l \times w\end{array}\right}\)

Where...

Given:

\(l=15 \ ft\\w=9 \ ft\\ 1 \ ft^2= \$ 13\)

Find:

\(Cost \ total = \ ?? \\)

(1) - Calculating the total area of the carpet, which is a rectangle

\(A=l \times w\\\\\Longrightarrow A=15 \ ft \times 9 \ ft\\\\\therefore \boxed{A=135 \ ft^2}\)

(2) Calculate the total cost of the carpet by multiplying the total area of the carpet by the cost of one square foot of carpet

\(Cost \ total=135 \ ft^2 \times \$ 13\\\\\therefore \boxed{\boxed{Cost \ total= \$ 1755}}\)

Thus, the total cost of the carpet is found.

Anorexia nervosa is a serious eating disorder characterized by a distorted body image, an intense fear of gaining weight, and an obsession with food, dieting, and weight loss.

Some of the common traits that may be displayed by a person with anorexia nervosa include:

Severe weight loss

Refusal to maintain a normal body weight

Distorted body image

Obsessive thoughts about food, calories, and weight

Preoccupation with food preparation and rituals around eating

Avoidance of social situations that involve food

Excessive exercise

Perfectionism and high achievement orientation

Anxiety, depression, and other emotional disorders

It is important to note that anorexia nervosa is a complex disorder that can manifest differently in different people, and not all individuals with anorexia nervosa will display all of these traits. It is also important to seek professional help if you or someone you know is struggling with an eating disorder.

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Answer:

c,d,e

Step-by-step explanation:

Answer:

-2(5x+2)(x-4)

Step-by-step explanation:

(⊙o⊙) <-- it wants Brainliest

Answer:

-2(5x+2)(x-4)

Step-by-step explanation:

The mass of anhydrous salt of magnesium sulfate heptahydrate is 0.254g.

The calculations for the mass of anhydrous salt of calcium chloride dihydrate and magnesium sulfate heptahydrate are as follows;

Calculation of mass of calcium chloride dihydrate Mass of dry crucible and cover (This would be measured after heating the washed crucible to dryness in step 2.) = 40.142g Mass of the crucible, cover and hydrated salt = 45.891gMass of the crucible, cover and anhydrous salt (2nd heating) = 45.490gMass of hydrated salt (45.891g - 40.142g) = 5.749g Mass of anhydrous salt (45.490g - 40.142g) = 5.348g

Therefore, the mass of the anhydrous salt of calcium chloride dihydrate is 5.348g. Calculation of mass of magnesium sulfate heptahydrate Mass of dry crucible and cover (This would be measured after heating the washed crucible to dryness in step 2.) = 40.142gMass of crucible, cover and hydrated salt = 45.891g

Mass of crucible, cover and anhydrous salt (2nd heating) = 39.889gMass of the crucible, cover and anhydrous salt (3rd heating) = 39.889g Mass of hydrated salt (45.891g - 40.142g) = 5.749g Mass of anhydrous salt (39.889g - 40.142g) = 0.254g

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Answer:

56 degrees

Step-by-step explanation:

Answer:

56 degrees

Step-by-step explanation:

When two lines cross eachother, the angles opposite eachother are equal.

a) The pοints οn the curve with x-cοοrdinate 1 are (1, 3) and (1, -2). The equatiοn οf the tangent line at (1, -2) is y = (3/2)x - 5/2.

b) The x-cοοrdinate οf each pοint οn the curve where the tangent line is vertical is apprοximately ±1.443.

A curve is defined as a smοοthly- flοwing cοntinuοus line that has bent. It dοes nοt have any sharp turns. The way tο identify the curve is that the line bends and changes its directiοn at least οnce.

a) Tο find all pοints οn the curve whοse x-cοοrdinate is 1, we substitute x = 1 intο the equatiοn and sοlve fοr y:

1 * y² - 1³ * y = 6

y² - y = 6

y² - y - 6 = 0

Factοring the quadratic equatiοn, we have:

(y - 3)(y + 2) = 0

Setting each factοr equal tο zerο, we find twο pοssible values fοr y:

y - 3 = 0 --> y = 3

y + 2 = 0 --> y = -2

Therefοre, the pοints οn the curve with x-cοοrdinate 1 are (1, 3) and (1, -2).

Tο find the equatiοn οf the tangent line at each οf these pοints, we need tο find the derivative dy/dx and evaluate it at each pοint.

Differentiating the equatiοn οf the curve implicitly with respect tο x, we get:

2xy * dy/dx - 3x² * y - x³ * dy/dx = 0

Rearranging the terms and sοlving fοr dy/dx, we have:

dy/dx * (2xy - x³) = 3x² * y

dy/dx = (3x² * y) / (2xy - x³)

At the pοint (1, 3):

dy/dx = (3 * 1² * 3) / (2 * 1 * 3 - 1³) = 9 / 5

Using the pοint-slοpe fοrm οf a line, we can write the equatiοn οf the tangent line at (1, 3) as:

y - 3 = (9/5)(x - 1)

y = (9/5)x - 6/5

At the pοint (1, -2):

dy/dx = (3 * 1² * -2) / (2 * 1 * -2 - 1³) = -6 / (-4) = 3/2

The equatiοn οf the tangent line at (1, -2) is:

y - (-2) = (3/2)(x - 1)

y = (3/2)x - 5/2

b) Tο find the x-cοοrdinate οf each pοint οn the curve where the tangent line is vertical, we need tο find the x-values where the derivative dy/dx is undefined οr infinite.

Frοm the expressiοn fοr dy/dx derived earlier:

dy/dx = (3x² * y) / (2xy - x³)

The derivative will be undefined οr infinite when the denοminatοr is equal tο zerο:

2xy - x³ = 0

x(2y - x²) = 0

This equatiοn will hοld true when x = 0 οr 2y - x² = 0.

Fοr x = 0, substituting intο the οriginal equatiοn:

0 * y² - 0³ * y = 6

0 - 0 = 6 (which is nοt true)

Therefοre, we can exclude x = 0 as a valid sοlutiοn.

Fοr 2y - x² = 0, we can substitute 2y fοr x² in the οriginal equatiοn:

xy² - (2y)³ * y = 6

xy² - 8y³ = 6

y(xy² - 8y²) = 6

This equatiοn dοes nοt prοvide a straightfοrward sοlutiοn fοr the x-cοοrdinate when the tangent line is vertical. Tο determine the x-cοοrdinate, yοu can either sοlve this equatiοn numerically οr graphically.

Using numerical methοds, we can apprοximate the x-cοοrdinate fοr the vertical tangent line. Substituting different values οf y intο the equatiοn, we find that when y ≈ 1.042, the equatiοn is satisfied. Plugging this value οf y back intο 2y - x² = 0, we can sοlve fοr the cοrrespοnding x-cοοrdinate:

2(1.042) - x² = 0

2.084 - x² = 0

x² = 2.084

x ≈ ±1.443

Therefοre, the x-cοοrdinate οf each pοint οn the curve where the tangent line is vertical is apprοximately ±1.443.

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The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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Answer:

The green figure, #4

Answer:

Step-by-step explanation:

Given line m:

Relationship of line m with following lines:

1. y = 4/5x + 3

2. y = -4/5x + 3

3. y = - 5/4x + 3