PLEASE HELP MEE !!!!!!

The Z-score of $29,700 is approximately 2.71 (rounded to the nearest hundredth).

The percentage of time the company makes less than $29,700 is approximately 99.66% (rounded to two decimal places).

The probability that the company makes more than $29,700 is approximately 0.34% (rounded to two decimal places).

The probability that the company makes between $15,200 and $25,200 is approximately 85.83% (rounded to four decimal places).

To solve these questions, we will use the standard normal distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. We'll first standardize the values using the formula:

Z = (X - μ) / σ

Where:

Z is the standard score (Z-score)

X is the value

μ is the mean

σ is the standard deviation

Given:

Mean (μ) = $20,500

Standard Deviation (σ) = $3,400

To find the Z-score of $29,700:

Z = (29,700 - 20,500) / 3,400

Z = 9,200 / 3,400

Z ≈ 2.71 (rounded to the nearest hundredth)

To find the percentage of time the company makes less than $29,700:

We need to find the area under the normal distribution curve to the left of the Z-score -2.71. Referring to the standard normal distribution table or using a calculator, we find that the area to the left of -2.71 is approximately 0.0034.

Therefore, the percentage of time the company makes less than $29,700 is approximately 0.34% (rounded to two decimal places).

To find the probability that the company makes more than $29,700:

Since the total area under the normal distribution curve is 1, and we have already found the area to the left of -2.71 as 0.0034 in question 2, we can subtract this value from 1 to find the probability of making more than $29,700.

Probability = 1 - 0.0034

Probability ≈ 0.9966 (rounded to four decimal places)

Therefore, the probability that the company makes more than $29,700 is approximately 0.9966.

To find the probability that the company makes between $15,200 and $25,200:

We'll first find the Z-scores for the given values using the formula:

For $15,200:

Z1 = (15,200 - 20,500) / 3,400

Z1 = -1.56

For $25,200:

Z2 = (25,200 - 20,500) / 3,400

Z2 = 1.39

Next, we'll find the areas under the normal distribution curve to the left of each Z-score.

From the standard normal distribution table or calculator:

The area to the left of Z1 (-1.56) is approximately 0.0594.

The area to the left of Z2 (1.39) is approximately 0.9177.

To find the probability of the company making between $15,200 and $25,200, we subtract the area to the left of Z1 from the area to the left of Z2:

Probability = 0.9177 - 0.0594

Probability ≈ 0.8583 (rounded to four decimal places)

Therefore, the probability that the company makes between $15,200 and $25,200 is approximately 0.8583.

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The area of the shaded which is obtained using the composite figure formed the shaded region and the area under the curve of the specified function is; (2·π - 3·√3)/2 square units

A composite figure is one that is composed of two or more simpler figures.

The area can be considered of comprising of a composite figure of the area under the curve of the function and the area of the shaded region

The function representing the curve under the shaded region can be presented as follows;

y = 3·cos(x) + 1

The interval specified under the curve can be expressed as follows;

0 ≤ x ≤ π/3

Therefore, the area under the curve can be found as follows;

[tex]\int\limits^\frac{\pi}{3} _3 {3\cdot cos(x) + 1} \, dx = [3\cdot sin(x) + x]^{\frac{\pi}{3} }_0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3} - 0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3}[/tex]

sin(π/3) = (√3)/2

Therefore; 3·sin(π/3) + π/3 = 3·(√3)/2 + π/3 = (2·π + 9·√3)/6

The area of the rectangle = (4 - 0) × (π/3 - 0) = 4·π/3

The area of the shaded region = Area of the rectangle - Area under the curve of the specified function

Therefore, area of the shaded region = 4·π/3 - (2·π + 9·√3)/6 = (2·π - 3·√3)/2

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Answer:

they're pronounced different

Susan's gross capital loss on the sale of the stock was $127.62.

We have,

Susan's initial investment in the stock.

= 24.87 shares x $33.12/share

= $823.98

Four years later, she sold the shares.

= 24.87 shares x $28/share

= $696.36

To calculate the capital loss, we need to subtract the sale price from the purchase price:

= $823.98 - $696.36

= $127.62

Therefore,

Susan's gross capital loss on the sale of the stock was $127.62.

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To solve the equation [tex]2\cos(\theta) - \sqrt{2} = 0\\[/tex] and express the answer in radians in terms of π, we can follow these steps:

Step 1: Add [tex]\sqrt{2}\\[/tex] to both sides of the equation:

[tex]2\cos(\theta) = \sqrt{2}\\[/tex]

Step 2: Divide both sides of the equation by 2:

[tex]\cos(\theta) = \frac{\sqrt{2}}{2}\\[/tex]

Step 3: Recall the special values of cosine in the first quadrant:

[tex]\cos(\theta) = \frac{\sqrt{2}}{2}\\[/tex]¥ corresponds to [tex]\\ \theta = \frac{\pi}{4}\\[/tex] in radians.

Therefore, the solution to the equation in radians in terms of π is [tex]\theta = \frac{\pi}{4}\\[/tex].

Answer:

x²+9

Step-by-step explanation:

F(x)=x+3

G(x)=x²

now

gof(x)=g.(x+3)

=(x+3)²

=x²+9

Space is used in art Area around an object​. Therefore, the correct option is option D.

The term "art" refers to a wide range of human endeavours and the resulting works that reflect technical mastery, aesthetic beauty, emotional heft, or mental concepts. No single definition of what makes art exists, and different cultures and historical periods have interpreted it very differently. Space is used in art Area around an object​.

Therefore, the correct option is option D.

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Null hypothesis: µ = 162 lbs (mean weight of male nurses is equal to 162 lbs)

Alternative hypothesis: µ ≠ 162 lbs (mean weight of male nurses is not equal to 162 lbs)

Hypothesis testing is a method of making decisions about a population based on sample data.

The null hypothesis (H₀) represents the default position that there is no significant difference between specified populations, or that there is no effect of a particular treatment.

On the other hand, the alternative hypothesis (H₁) represents the opposite of the null hypothesis, which is that there is a significant difference between the populations or that there is an effect of the treatment being tested.

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Answer:

  A.  no triangle

Step-by-step explanation:

You want to know if the Triangle Inequality Theorem allows a triangle from side lengths 33.7, 62.9, and 96.6.

The theorem requires for any side lengths a, b, c, this inequality must hold:

  a + b > c

Using the given side lengths, we have ...

  33.7 +62.9 > 96.6

  96.6 > 96.6 . . . . . . . . False

The three sides do not form a triangle.

__

Additional comment

These side lengths will join ends to ends to form a "triangle" that looks like a line segment of length 96.6 with a point on it at 33.7 from one end. Most authors do not recognize this figure as a triangle. For those authors who write the theorem as a +b ≥ c, these segments will form a triangle.

You should check your curriculum materials to see whether your Triangle Inequality Theorem uses the > or the ≥ relation.

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The equivalent value of the expression is xy² = 18

Given data ,

Let the equation be represented as A

Now , the value of A is

A = xy²

where the value of the first variable x = 2

And , the value of the second variable y = -3

Now , the expression is solved as

A = xy²

On simplifying the equation , we get

A = ( 2 ) ( -3 )²

A = 2 ( 9 )

On further simplification , we get

A = 18

Therefore , the value of A is 18

Hence , the expression is A = 18

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Answer:

25

Step-by-step explanation:

Given from the question,

125 cubed = [tex]125^3[/tex]

Therefore square root of 125 cubed is:

[tex]\sqrt{125^3} \\ =125^\frac{2}{3} \\ \\=25[/tex]

43.33 lbs of water must be drained from the melon so that the melon is 25% water.

First, we find out how much water is in the melon when it is 90% water.

The melon weighs = 50 lbs, and

so the weight of the water in the melon is:

0.9 x 50 lbs = 45 lbs

This means there are 45 lbs of water in the melon, and the remaining 5 lbs is the weight of the melon's solid components.

Now, we want to drain some of the water so that the melon is 25% water. Let's call the water weight we need to drain "x" (in lbs).

After draining x lbs of water, the weight of the remaining solid components of the melon will still be 5 lbs, but the total weight of the melon will be:

= (50  - x) lbs

The weight of the water that remains in the melon after draining x lbs is:

(45 - x) lbs

According to the problem, this remaining water must be 25% of the total weight of the melon:

(45 - x) lbs = 0.25 x (50 - x) lbs

Now we solve for x:

45 - x = 0.25 x (50 - x)

45 - x = 12.5 - 0.25x

0.75x = 32.5

x = 43.33 lbs

Therefore, we must drain 43.33 pounds of water from the melon for 25%.

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Answer:

Jelly beans are $2.50 per pound

Almonds are $1.75 per pound

Step-by-step explanation:

3j + 2a = $11

5j + 6a = $23

Multiply equation 1 by 3

9j + 6a = $33

Subtract

9j + 6a = $33

-(5j + 6a = $23)

=(4j + 0a = $10)

4j = $10

j = $2.50

Plug j into any equation.

3(2.5) + 2a = $11

7.5 + 2a = $11

2a = 3.5

a = $1.75

Jelly beans are $2.50 per pound

Almonds are $1.75 per pound

Answer:

3 and 4 both SAS (Side-Angle-Side) axiom.

Step-by-step explanation:

Note:

There are four basic conditions for two triangles to be congruent. These are:

One of the conditions should be needed to fulfill to determine whether the two triangles are congruent.

Over here:

3.

In ΔOMT and ΔOGE

MT=GE Given Side

∡MOT=∡GOE Vertically Opposite angle Angle

MO=OE Given Side

It fulfills the condition of the SAS (Side-Angle-Side) axiom.

ΔOMT ≅  ΔOGE by SAS (Side-Angle-Side) axiom.

4.

In ΔKJL and ΔIJH

JL=JH Given Side

∡KJL=∡HJI Vertically Opposite angle Angle

IJ=JK Given Side

It fulfills the condition of the SAS (Side-Angle-Side) axiom.

ΔKJL≅ ΔIJH by the SAS (Side-Angle-Side) axiom.

Answer:

the amount of soup that I can make in my crockpot

Step-by-step explanation:

A) is an area. the foil would be cut into a square or circle, making it an area.

B) is the soup in the pot. the amount is given by the cross-sectional area of the pot (if circular Area of circle = π r ²) multiplied by the depth of the pot. since we have r ² (which is r X r) multiplied by a length (depth of pot) , it is a volume.

C) like A) this would be a two-dimensional item. so it is an area.

D) this will just be a number

The pair of possible coordinates of point D are (0, 8), (0, -8), (8, 0) and (-8, 0)

From the question, we have the following parameters that can be used in our computation:

D = 8 units away from the origin.

using the above as a guide, we have the following:

The possible coordinates of point D are

(0, ±8), (±8, 0)

When expanded, we have

(0, 8), (0, -8), (8, 0) and (-8, 0)

Hence, the pair of possible coordinates of point D are (0, 8), (0, -8), (8, 0) and (-8, 0)

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The number of cubes in the 5th term is 125

From the question, we have the following parameters that can be used in our computation:

The sequence of cubes

In the above sequence, we can see that the term is raised to the power of 3 to get the new term

This means that

The nth term is then represented as

f(n) = n³

For the 5th cube, we have

n = 5

Substitute the known values in the above equation, so, we have the following representation

f(5) = 5³ = 125

Hence, the number of cubes in the 5th term is 125

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Area of small sector is,

⇒ A = 3.28π cm²

And,. Area of large sector is,

⇒ A = 5.73π  cm²

We have to given that;

Angle ACB = 131°

And, radius = 3 cm

Since, We know that;

⇒ Area of sector = θ/360 × πr²

Hence, For θ = 131°

So, Area of small sector is,

⇒ A = 131/360 × π × 3²

⇒ A = 1179/360π

⇒ A = 3.28π cm²

For large sector,

Angle = 360 - 131

          = 229°

Hence, Area of large sector is,

⇒ A = 229/360 × π × 3²

⇒ A = 2061/360π

⇒ A = 5.73π  cm²

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We can use the property of Multiplication  5x8=40 to determine the product of 5x800, which is 4000.

To find the product of 5x800 using the basic fact 5x8=40, we can use the property of multiplication that states that multiplying a number by 10 increases its value by one place value. Therefore, we can rewrite 800 as 80x10 and multiply it by 5 as shown below:

5x800 = 5x(80x10)   (replacing 800 with 80x10)

     = (5x80)x10   (associative property of multiplication)

     = 400x10      (using the basic fact 5x8=40)

     = 4000

Thus, we can use the basic fact 5x8=40 to determine the product of 5x800, which is 4000.

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A non-example of mean, mode, median and range are as follows;

1. A non example of a mode in the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is other numbers except 7.  7 is the mode because it is repeated more frequently.

2. Non-example of median is 9 because it is not the middle value of the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 when arranged orderly.

The mean is the average of all the values in a dataset. And therefore a non-example of mean in the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is 70. Which is gotten by adding all the numbers together.

The mean can be found by saying 7 + 8 + 9 + 7 + 5 + 9 + 7 + 4 + 3 + 7 divided by 10. this should be 7.

The non-example of range in the dataset 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is choosing the lowest value of the set 3.

The range is the difference between the highest and lowest values in a dataset. which is 9-3 = 6

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Hello!

4.9 × 10⁻¹

= 4.9 × 0.1

= 0.49

Johnny stopped running for the first time after 15 minutes.

From the graph, we can see that Johnny ran for the first 15 minutes without stopping. During this time, he covered a distance of around 1.5 miles. After 15 minutes, he stopped running for a short time, and then continued running. Therefore, Johnny stopped running for the first time after 15 minutes.

The cost of each chair is $6.2 and  the cost of each table is $1.34.

Let's solve this problem by assuming the cost of each chair as ‘c’ and the cost of each table as ‘t.’ We can create two equations from the information given we can obtain the values of ‘c’ and ‘t.’

From the given information, the first equation is ‘c + 4t = 53’ because the cost to rent one chair and four tables is $53. The second equation is ‘3c + 2t = 25’ because the cost to rent three chairs and two tables is $25.

We can solve this by either substitution or elimination, but the method we used earlier works - multiplying the first equation by 3 and subtracting the second equation from it, to obtain:

3c + 12t = 159

- (3c + 2t =25)

------------------

10t = 134

Therefore, the cost of each table is $13.4.

We can plug this value back into equation 1 and solve for c

c + 4(13.4) = 53

c + 53.6 = 53

c = -0.6

This isn't a possible solution as the cost of the chair cannot be negative.

Thus, we need to check if an error was made earlier. We can plug the value of t in the second equation:

3c + 2t = 25

3c + 2(13.4) = 25

3c + 26.8 = 25

This equation is contradictory, indicating that there is no solution. We need to revise the problem statement, a possible typo can be a misplaced decimal point for example, if the cost of each table is instead $1.34, all equations will hold, and the final answer will be:$6.2 and $1.34 respectively according to the question.

This is a possible solution and makes sense.

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Answer:

Step-by-step explanation:

Sure! Here’s how you can solve the equation 3²⁽ˣ⁺¹⁾-8.3ˣ⁺¹=9 for x:

First, let’s rewrite the equation in terms of a common base. Since 9 can be written as 3², we can rewrite the equation as 3²⁽ˣ⁺¹⁾-8.3ˣ⁺¹=3².

Now, let’s isolate the exponential terms on one side of the equation by adding 8.3ˣ⁺¹ to both sides: 3²⁽ˣ⁺¹⁾=3²+8.3ˣ⁺¹.

Next, let’s take the logarithm of both sides with base 3: log₃(3²⁽ˣ⁺¹⁾)=log₃(3²+8.3ˣ⁺¹).

Using the properties of logarithms, we can simplify the left side of the equation: 2(x+1)=log₃(3²+8.3ˣ⁺¹).

Now, let’s solve for x by isolating it on one side of the equation: x=log₃(3²+8.3ˣ⁺¹)/2-1.

This is an approximate solution for x. To find a more precise value for x, you can use a numerical method such as Newton’s method or a calculator.

I hope this helps!

0.0007% of students in Class 7 spent less than 15 minutes on homework.

Total students = 100

Number of students spent less than 7 minutes are: 0.7

Now, the percentage of students less than 15 minute

= 0.7/100 x 100

= 7/1000 x 100

= 0.0007 x 100

= 0.0007%

Thus, 0.0007% of students in Class 7 spent less than 15 minutes on homework.

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-2x≤6 and 2x≥-6 is the inequalities represented by the number line

The visual representation of the real numbers on a straight lineis known as number line

On a number line each  point of  is assumed to correspond to a real number, and every real number to a point.

As we observe the graph the red line is directed towards left side which means the values are decreasing and line has solid point  at 6 so it is included

Hence, the number line shows that -2x≤6 and 2x≥-6

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what you mean but heres the points on the map u were talking about

Answer: The slope m = 3/5

Step-by-step explanation:

The slope can be found by using the formula: m = y2 - y1 / x2-x1

Where m is the slope and (x1, y1) and (x2, y2) are the two points on the line.

x1 = 2  , y1 = 1

x2 = -3 , y2 = -2

Substituting the values from the points in the problem gives :

m = -2-1 / -3-2

m = 3/5

Hence, the slope that passes through (2, 1) and (-3, -2) is 3/5.

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a) The area of the shaded region is equal to S'' = 0.25 · sin 2θ + 0.5 · θ.

b) The angle associated with the shaded region is equal to θ ≈ 20.189°.

In this problem we need to determine the measure of an angle associated with a geometric system formed by a circular arc and a right triangle. a) The area of a triangle is defined by this formula:

S = 0.5 · OA · AB

Where:

The base and the height of the triangle are equal to:

OA = sin θ, AB = cos θ

Then, the area of the triangle is:

S = 0.5 · sin θ · cos θ

S = 0.25 · sin 2θ

And the rest of the shaded area is:

S' = 0.5 · θ

The shaded area is described by the following formula:

S'' = S + S'

S'' = 0.25 · sin 2θ + 0.5 · θ

b) If we know that S = 0.5, then the measure of the angle is:

0.5 = 0.25 · sin 2θ + 0.5 · θ

1 = 0.5 · sin 2θ + θ (Please notice that θ is in radians, π radians = 180°)

Then, by numerical methods:

θ ≈ 20.189°

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The graph of y = 3(3/5)^x is an exponential growth curve that starts at the point (0, 3) and approaches the x-axis and y = 3 asymptotically.

We have,

The graph of the exponential function y = 3(3/5)^x is an upward curve that approaches but never touches the x-axis, as the base of the exponential term (3/5) is between 0 and 1.

As x approaches negative infinity, the function rapidly approaches the y-axis, which is the vertical asymptote.

As x increases, the value of the function increases rapidly, but at a decreasing rate, as the base of the exponential term is less than 1.

As x approaches infinity, the function approaches but never touches the horizontal line y = 3, which is the horizontal asymptote.

Therefore,

The graph of y = 3(3/5)^x is an exponential growth curve that starts at the point (0, 3) and approaches the x-axis and y = 3 asymptotically.

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Based on the calculations, the measure of angle M is -15°.

The given diagram, it appears that we have a triangle MNL with an angle measure of 88° at point L and an angle measure of 107° at point K.

We are asked to find the measure of angle M, denoted by m∠MLK.

The measure of angle M, we can use the fact that the sum of the angles in a triangle is always 180°.

We can subtract the measures of angles L and K from 180° to find the measure of angle M.

m∠M = 180° - m∠L - m∠K

Substituting the given values:

m∠M = 180° - 88° - 107°

m∠M = 180° - 195°

m∠M = -15°

This result is not physically possible since angles cannot have negative measures.

It is likely that there was an error in the given information or in the calculations.

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