Divya is solving the following equation for w. 3w -√20-5w = 2 Her first few steps are given below. 3w = √20-5w+2 3w-2= √/20 - 5w (3w - 2)² =(√20 – 5w) 9w² - 12w + 4 = 20 - 5w Is it necessary for Divya to check her answers for extraneous solutions?​

Answer:

f^-1(x)=8x/5

Step-by-step explanation:

The inverse of f(x)=5x/3+5 is 8x/5

The inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15

We have:

f(x)=5x/3+5

Rewrite as:

y=5x/3+5

Swap x and y

x = 5y/3 + 5

Subtract 5 from both sides

5y/3 = x - 5

Multiply through by 3

5y = 3x - 15

Divide through by 5

y = 3x/5 - 15

Rewrite as:

f-1(x) = 3x/5 - 15

Hence, the inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15

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Answer:

(f-g)(x) = 7x+5

Step-by-step explanation:

Given that,

f(x)=2x+2 and g(x) =-5x-3

To Find:

Solution:

[tex](f - g)(x)[/tex]

Re-write as:

Now substitute the values on the polynomial/function:

Simplify using this order:BPEMDAS

Hence,(f-g)(x) = 7x+5.

Answer:

The ratio of decay rates is 3:4. So, option D is correct.

Step-by-step explanation:

Concept: The Decay rate for any  function can be calculated by the formula Decay rate = Difference in y values / Difference in x values in given interval

Decay Rate for the exponential function in the interval -2 ≤ x ≤ 0 is (4-1) / (-2-0) = 3/2.

Decay rate for quadratic function in same interval = [(4-0) ÷ -(-2-0)] = 2.

Ratio of decay rates = (3/2) : (2) = 3:4

Option D, the exponential function decays at three-fourths the rate of the quadratic function is the correct answer.

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The rules of the calculation are:

The complete question is added as an attachment

The equation is given as:

0.738 × 0.28 = 0.20664

When approximated, we have:

0.738 × 0.28 ≈ 0.21

The above approximation can mean any of the following:

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By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.

Let x and y the number of weeks and the height of the plant, respectively. Given the consideration of direct proportionality, the height of the plant inasmuch as the number of weeks increases. Then, the constant of proportionality (in inches per week) is found by dividing the height of the plant by the number of the respective week:

k = 18 inches /6 weeks = 15 inches /5 weeks = 12 inches/4 weeks = 3 inches/week

By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.

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Answer:

The mean will increase more than the median, but both will increase.

[third option listed]

Step-by-step explanation:

the median of a data set is the number in the middle [when listed from lowest to highest in value]

1 2 3 4 5 6 7 8 9 10 11 12 13

is the current median

let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)

1 2 3 4 5 6 7 8 9 10 11 12 12 13

[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]

so, 7.5 is the current median

(this is an increase of 0.5)

--

the mean of a data set is what we commonly refer to as the "average"

[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]

1 2 3 4 5 6 7 8 9 10 11 12 13

mean of original data set:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]

_______________________________________

                                    13

[91 ÷ 13 = 7]

because our number is greater than our original mean [12 > 7], we know that the mean must increase:

[91 + 12 = 103]

[103 ÷ 14 ≈ 9.36]

[we had an increase of 2.36]

so, median increased by 0.5, mean increased by 2.36

so, both values increased, whilst the mean increased by more than the median [as to be expected]

you could also express this as "The mean will increase more than the median, but both will increase." [third option listed]

hope this helps!! :)

Answer:

C

Step-by-step explanation:

The horizontal line, y=2, is solid and shaded above, so it represents

[tex]y \geqslant 2[/tex]

The slanted line, y=x is dashed and shaded below, so it represents y<x.

Answer

Answer is A

Step-by-step explanation:

Answer: [tex]x=65^{\circ}, y=65^{\circ}, z=65^{\circ}[/tex]

Step-by-step explanation:

All radii of a circle are congruent, so by the base angles theorem

Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.

Answer:

12.5 meters

Step-by-step explanation:

1 hour manually = 25/6 meters

1 hour using machine = 25/6 × 3 meters

1 hour using machine = 12.5 meters

Hope this helped and have a good day

The variance of the probability distribution is 400

The Variables of X and their Probability Distribution.

To find Variance, first we should find out Mean and then Variance

The expected value of a discrete random variable X, symbolized as E(X), is often referred to as the long-term average or mean (symbolized as μ)

The variance of a probability distribution is symbolized as σ2. To find the variance σ2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products.

Step – 1: Calculation of Mean                               Step – 2: Calculation of Standard Deviation= σ2=∑(x−μ)²P(x)

Mean = X * P(X)     Variance = Sum of (X – Mean)²*P(X)

X P(X) X*P(X)

-50 0.029 -1.45

-30 0.121 -3.63

-10 0.210 -2.1

10 0.485 4.85

30 0.145 4.35

50 0.010 0.5

Mean  2.52

X  P(X) X - Mean  (X – Mean)² (X – Mean)²*P(X)

-50 0.029 -52.52 2758.35                 79.99216

-30 0.121 -32.52 1057.55                 127.9636

-10 0.210 -12.52 156.7504         32.91758

10 0.485 7.48          55.950                  27.13594

30 0.145 27.48 755.1504         109.4968

50 0.019 47.48 2254.35                 22.5435

Variance=400.00

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[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathsf{ASSUMING: }\\\mathsf{22\times90}\\\mathsf{= 90 \times 22}\\\mathsf{= 1,980}[/tex]

[tex]\mathsf{ASSUMING: }\\\mathsf{2 + 2 + 3 + 3 + 3 + 3}\\\mathsf{= 2\times 2 + 3\times4}\\\mathsf{= 4 + 12}\\\mathsf{= 16}[/tex]

[tex]\huge\textsf{Answer \#1. 1,980 }\huge\checkmark\\\\\\\huge\textsf{Answer \#2. 16 }\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The arc length of the semicircle is 5π units

From the question, we are to calculate the arc length of the semicircle

Arc length of a semicircle = 1/2 the circumference of the circle

∴ Arc length of a semicircle = 1/2 × 2πr

Arc length of a semicircle = πr

Where r is the radius

From the given information,

r = 5

∴ Arc length of the semicircle = 5 × π

Arc length of the semicircle = 5π units

Hence, the arc length of the semicircle is 5π units

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The average number of packages the led to be selected in order to find a package that was not delivered on time is 2.2 option first is correct.

With simple random sampling, each component of the population has an equal chance of being selected for the sample.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

A shipping company claims that 95% of packages are delivered on time.

From the table:

00- 04 is the package not delivered on time.

05-99 - package delivered on time.

The first simulation's third number, 31, 64, 04, is where you can locate an item that wasn't delivered on time.

The second simulation's second number, 34, 02, is the location of a late-delivered delivery.

The third simulation is equal to 96,00 - the second number, which is the location of a late package.

The second number where to find a shipment not delivered on time in the fourth simulation is 31,04

Where to find a box that wasn't delivered on time in the fifth simulation: 98, 01, second number

The average number = (3 + 2 + 2 + 2 + 2)/5

= 11/5

= 2.2

Thus, the average number of packages the led to be selected in order to find a package that was not delivered on time is 2.2 option first is correct.

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Answer:

y = 5z

Step-by-step explanation:

added in the picture

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[ let the point at which line segments SV and RT intersects be O ]

[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]

[ linear pair ]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]

[ Exterior angle = sum of opposite interior angles ]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]

( let it be equation 1 )

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]

[ Sum of angles of Triangle ]

[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]

( let it be equation 2 )

____________________________________

By comparing both equations :

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]

[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]

( Add 180° on both sides )

[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]

[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]

[tex]\qquad \tt \rightarrow \: y = 5z[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

7/4 * pi

Step-by-step explanation:

Area of circle = pi * r^2

Find radius:

pi * 49/64 = pi * r^2

49/64 = r^2

7/8= r

Circumference of circle = 2pi * r

2 * pi * (7/8) = 7/4 * pi

Assuming that the answer is in terms of pi as the question is in terms of pi

The quadratic inequality represented by the graph is:

y ≤ 2x² - 8x + 3

First, we can see that the shaded region is below the parabola, and the line of the parabola is solid, which means that the points on the parabola are solutions, then the inequality is:

y ≤ quadratic equation.

Now we need to get the quadratic equation.

Now, if you look at the y-intercept, you can see that it happens at y = 3. Then the constant term of the quadratic equation is 3.

The only one that has that (and the  ≤  symbol)  y-intercept is the first option:

y ≤ 2x² - 8x + 3

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Answer:

C is the answers for the question

Step-by-step explanation:

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The compound inequality can be expressed as "x > -4 or x ≤ 4."

The correct graph of the solution is:

OC. Solution: x > -4 and x ≤ 4

Let's solve the compound inequality step by step:

x + 7 > 3

Subtract 7 from both sides to isolate x:

x > 3 - 7

x > -4

and, we have,

x - 5 ≤ -1

Add 5 to both sides to isolate x:

x ≤ -1 + 5

x ≤ 4

Now, we have two inequalities for x:

x > -4

x ≤ 4

The compound inequality can be expressed as "x > -4 or x ≤ 4."

The correct graph of the solution is:

OC. Solution: x > -4 and x ≤ 4

The graph will include all values greater than -4 (open circle) and all values less than or equal to 4 (closed circle) on the number line.

The correct representation is:

OC. Solution: x > -4 and x ≤ 4

Graph:

-5 -4 -3 -2 -1 0 1 2 3 4 5

+---|---|---|---|---|---|---|---|---|---+

-4 0 4

The open circle at -4 indicates that x is greater than -4, and the closed circle at 4 indicates that x is less than or equal to 4.

The shaded area between -4 and 4 represents the solution to the compound inequality.

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Answer: No it could not be ACB.

Step-by-step explanation:

Angles are named based on the vertex of the angle so this could be referred to as ∠B. The other way to name an angle is by saying the three points, However, when you say the three points the vertex must be in the middle. Hence, the answer is ∠CBA as the middle point of the angle is in the middle of the name.

-5≥

so 8 x -5 = -40 - 16 = -56 and that's the smallest number you can get that will be greater than -64 hope this helps! :)

Answer:

x> -6

Step-by-step explanation:

Drag the -16 to -64. This will change the -16 to a positive 16. Add -64 and 16. The answer is -48. All that should be left is 8x>-48. Now we need to divide -48 and 8 so we can leave x. The answer should be -6 on one side, and x on the other side. x> -6

The equation of the line of best fit is y = -0.03x + 69.94

The column headers are given as:

Year    Time(s)

To enter the data values in a graphing calculator, we use the following representations:

x ⇒ Year

y ⇒ Time (s)

Using the above representations, we have the following calculation summary from a graphing calculator:

The equation of the line of best fit is:

y = bx + a

Where

b = SP/SSX = -514.6/17242.92 = -0.02984 ≈ -0.03

a = MY - bMX = 11.7 - (-0.03*1951.59) = 69.94497 ≈ 69.94

So, we have:

y = -0.03x + 69.94

A linear equation is represented as:

y = Slope * x + y intercept

So, we have:

Slope = -0.03

y intercept = 69.94

The y-intercept implies that the initial time is 69.94 seconds, while the slope implies that the time decreases by 0.03 seconds each year

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Answer:

A. 84x - 16y - 10.6

Explanation:

[tex]\sf \rightarrow 2(14x-3y+28x+12.2-5y-17.5)[/tex]

[tex]\sf \rightarrow 2 (42x-8y-5.3)[/tex]

apply distributive method: a(b + c) = ab + ac

[tex]\sf \rightarrow 2 (42x) -2(8y)-2(5.3)[/tex]

[tex]\sf \rightarrow 84x -16y-10.6[/tex]

The equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)

A line is the distance between two points. The equation of a line in point-slope form is expressed as:

y - y0 = m(x-x0)

Given the coordinates (-2, -4) and (2, 2) on the line, the slope is expressed as:

Slope = 2-(-4)/2-(-2)

Slope = (6)/4

Slope = 3/2

Find the equation of the line

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

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

Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)

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Answer:

d

Step-by-step explanation:

Answer:

w≈7.6in

Step-by-step explanation:

L= 7.25

D= 10.5

Answer:-

The width of this rectangle is = 7.59

Given:-

In this question, it is given that -

The diagonal of this rectangle is = 10.5

the length of this rectangle is = 7.25

To find:-

We have to find the width of this rectangle.

Solution:-

We can easily solve this problem using the Pythagorean theorem.

In this problem, it is given that the length of this rectangle is = 7.25 and the diagonal is =10.5

so by the Pythagorean theorem, we can get-

(length)² + (width)² = (diagonal)²

or, (7.25)² + (width)² = (10.5)²

or, (width)² = (10.5)² - (7.25)²

= 17.75 × 3.25

= 57.6875

or, width = 7.59

So, the width of the rectangle is 7.59.

The given radical root 84, the simplification is option B; [tex]2\sqrt{21}[/tex].

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given radical;

[tex]\sqrt{84} \\\\\sqrt{42 \times 2} \\\\\sqrt{7\times3\times 2 \times 2} \\\\2\sqrt{21} \\[/tex]

Thus, the correct option is B; [tex]2\sqrt{21}[/tex].

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Step-by-step explanation:

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Answer:

Scale factor is 3

It should be noted that a reflection is known as a flip and it's a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

Reflecting around x = 1 never touches the y coordinate, and the x coordinate transforms.

In other words, if a point were at x=π, it's distance to x=1 was π−1 so the new location is π−1 to the left of x=1.

The reflection is attached.

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The more appropriate measure of center is mean.

The more appropriate measure of spread is standard deviation.

Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.

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