Acellus
Find the probability that a randomly
selected point within the circle falls
in the red shaded area (square).
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r = 4 cm
4 √2 cm
[?]%
Round to the nearest tenth of a percent.
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The most accurate statement about the mean absolute deviation (MAD) is:

The MAD is a measure of the variability or spread of a set of data that is calculated by finding the average of the absolute deviations from the mean of the data.

Explanation:

The mean absolute deviation is a statistical measure that is used to calculate the average distance between each data point and the mean of the data set. It provides a measure of the variability or spread of the data set and is often used to compare the dispersion of different data sets.

To calculate the MAD, we first find the mean of the data set. Then, we find the absolute deviation of each data point from the mean, which is the distance between the data point and the mean, ignoring the sign. Finally, we calculate the average of the absolute deviations to get the MAD.

The MAD is a useful measure of variability because it is not affected by extreme values or outliers in the data set, unlike other measures of dispersion such as the variance or standard deviation.

Therefore, the most accurate statement about the MAD is that it is a measure of the variability or spread of a set of data that is calculated by finding the average of the absolute deviations from the mean of the data.

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A corporate bond has a face value of p dollars. The interest each year is 6% of the face value.  the total interest /, in dollars, as a function of the age f, in years, of the bond is

a)I(f) = 0.06 * f * p

b) P(f) = I(f) + p

Generally, (a) The total interest, in dollars, as a function of the age f, in years, of the bond can be expressed as:

I(f) = 0.06 * f * p

This represents the total interest paid over f years, which is calculated by multiplying the annual interest rate (0.06), the number of years (f), and the face value of the bond (p).

(b) The payout P, in dollars, as a function of f can be expressed as:

P(f) = I(f) + p

This represents the total payout over f years, which is calculated by adding the total interest paid (I(f)) and the face value of the bond (p).

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Answer:

6x+6 or 4x+10

Step-by-step explanation:

hope u like it

Answer:

a) 196cm^2

b) 225cm^2

c) 180 cm^2

Step-by-step explanation:

a) The figure is a square, so you can use the formula: a = l^2, or area equals length of one side squared.

a = (14cm)^2

a = 196cm^2

b) a = (15cm)^2

   a = 225cm^2

c) This one is a parallelogram, so it's trickier. However, we can imagine the figure as a rectangle by taking the small triangle that sticks out on the right and putting it into the gap in the left. Now, we can solve this using the formula for a rectangle: a = l x w.

a = l x w

a = 18cm x 10 cm = 180 cm^2

:)

At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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Answer:

$44.44444444

Step-by-step explanation:

So as per question employees get 10% discount of the discounted price. So our equation would be considering discounted price = x

=> x- 10x/100 = 40 => 100x-10x/100 = 40 => 90x = 4000 => x= $44.4444

Answer:

x = -2

Step-by-step explanation:

I hope this helps!

The domain of the function f(h) = 7.5h is all real numbers or (-∞, ∞).

The given equation is f(h) = 7.5h. Here, "h" is the input variable and "f(h)" is the output variable. In order to determine the domain of the function, we need to identify all the possible values of "h" for which the function will produce a valid output.The given function is a linear function where the variable h is multiplied by a constant (7.5) and therefore has a domain of all real numbers. This means that any value of h can be plugged into the equation and a valid output will be produced. Therefore, the domain of the function is (-∞, ∞) or all real numbers.In summary, the domain of the function f(h) = 7.5h is all real numbers or (-∞, ∞).

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The positive value of sin x/2 is \(\frac{\sqrt{30} }{10}\)

Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.

The relationship between cos x and sin x/2 is

sin x/2 = \(\sqrt{\frac{1 - cosx}{2} }\)

cos x = 2/5

sin x/2 = \(\sqrt{\frac{1-\frac{2}{5} }{2} }\)

1 - 2/5 = 3/5

simplifying 3/5 ÷ 2

removing division sign and taking the reciprocal of 2, we have

3/5 x 1/2 = 3/10

so that

sin x/2 = \(\sqrt{\frac{3}{10} }\)

which can be written as

sin x/2 = \(\frac{\sqrt{3} }{\sqrt{10} }\)

By rationalizing   \(\frac{\sqrt{3} }{\sqrt{10} }\) we multiply it with \(\frac{\sqrt{10} }{\sqrt{10} }\)

so that we have  \(\frac{\sqrt{3} }{\sqrt{10} }\) x  \(\frac{\sqrt{10} }{\sqrt{10} }\) = \(\frac{\sqrt{30} }{10}\)

In conclusion, the radical form of sin x/2 is  \(\frac{\sqrt{30} }{10}\)

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Answer:

A. {x | x = -4, -1, 3, 5, 6}

Step-by-step explanation:

Domain refers to x, so based on that you can eliminate both answers B and D. Because we know domain refers to x, you can look at the x coordinate in each point on the graph, and record all those as your domain. Therefore, the answer is A.

Answer:

Yes

Step-by-step explanation:

The Elephant Building is 335 feet high. A real Asian elephant is 12 feet tall. If 29 real elephants could stand on top of each other, would they reach the top of the building?

They are asking if 29 12' elephants are as tall as as a 335' building:

29 × 12' = 348' elephant stack

because 348' is taller than 335' building then yes, 29 staked elephant would reach and pass the top of a 335' building.  

Answer:

35 hours

Step-by-step explanation:

We Know

Her pay rate is $8.75

Penny was paid 306.25 this week

How many hours did she work?

We Take

306.25 / 8.75 = 35 hours

So, she works 35 hours.

Answer:

slope:  3; vertex:  (5, -8)

Step-by-step explanation:

Compare the given y+8=3(x−5) to the slope-vertex form y - k = m(x - h).  We see that the slope, m, must be 3 and the vertex must be (h, k):  (5, -8).

Answer:

p = 43

Step-by-step explanation:

(x²²)(x⁷)³

first, multiply the power of 7 times the power of 3

(x⁷)³ = x⁷ ° ³ = x²¹

second, add the power of (x²²) with (x²¹)

x²² ⁺ ²¹ = x⁴³

therefore, the value of p = 43

I hope this helps!

Answer:

2 hours

Step-by-step explanation:

2 times 35 = 70

70 + 75 = 145

Answer:

He worked 2 hours

Step-by-step explanation:

75 + 35*2 = 145

The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

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

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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2/63 as a percentage round to the nearest tenth of a percent can be written as 31.7%

Fractions refer to a part of a whole. The word fraction comes from Latin word Fractus meaning broken. A percentage is a number that can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol %.

Fractions can be converted into percentages by the following steps:

1. Convert the fraction into decimals.

Therefore, on converting 2/63 to decimal we get 0.317

2. Multiply the given decimal by 100 to get a percentage

Hence, the percentage we get after multiplication is 31.7%.

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People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

Pi, which is represented by the Greek letter π, is an irrational number that starts with 3.14 and continues for an infinite amount of digits. The numerical value of pi is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.1415926535897932384626433832795. The date and time of March 14th, 1:59 is a way to represent the first four digits of pi (3.14). People celebrate Pi Day by eating pie, making pi-related crafts, and sharing facts about pi. People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

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Answer:

5 weeks

Step-by-step explanation:

Substract 319.5 (the amount he has to save) to the amount he has already saved, which is 21.95. Now the constant amount of change is 63 dollars each week so divided it by that. So the equation should be (319.5-21.95) and divide all that by 63 to get 4.72 or rounded to the nearest number, is 5.

It would take approximately 15.7 hours for the jet to fly 1.25 times around the Earth at a fixed distance of 3,966 miles from the Earth's center at a constant speed of 2,000 miles per hour.

To determine the number of hours it would take for the jet aircraft to fly 1.25 times around the Earth at a fixed distance of 3,966 miles from the Earth's center at a constant speed of 2,000 miles per hour,

we can use the formula for circumference as follows:

Circumference of the circle = 2πr

where r = 3,966 miles

Since the jet is flying around the Earth 1.25 times,

the distance it will cover would be 1.25 times the circumference of the Earth.

Distance covered by the jet = 1.25 × 2π × 3,966 miles

                                               = 31,332.5 miles

Now, we can find the time it would take the jet to fly this distance by using the formula for speed as follows:

Speed = Distance / Time

we get:Time = Distance / Speed

Time = 31,332.5 miles / 2,000 miles per hour

= 15.67 hours (rounded to the nearest tenth)

Therefore, it would take approximately 15.7 hours.

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Answer:

the second one 35x greater than or equal to 140 also she would need to work at least 4 hours since 35x4 is 140

Step-by-step explanation:

Answer:

7/8 * 3/9 = 7/24 ≅ 0.2916667

Step-by-step explanation:

7/8 * 3/9 = 7 · 3/8 · 9 = 21/72 = 7 · 3/24 · 3 = 7

have a nice Day and you are welcome

Answer:

3/6 or 1/2

Step-by-step explanation: 3 odd numbers on a dice with six sides

Step-by-step explanation:

1: Variable term

2: constant term

3: Variable term

Answer:

y = x + 3

Step-by-step explanation:

In point slope form, the equation of line is,

\(y - b = m(x - a)\)

where a and b correspond to the x and y coordinates of the given point and m is the slope

Since the line is parallel to y = x+4, it has the same slope so m = 1 since the slope of y = x+4 is 1

and putting the values of the point (-1,2), we get,

y - 2 = x - (-1)

y-2 = x + 1

y = x + 3

The required distance of Cori from where he started is 35km.

Distance is a quantitative or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimation based on other criteria in physics or everyday usage. Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is also used metaphorically to mean a measurement of the amount of difference between two similar objects or a degree of separation. The concept of a metric space is used to codify most such conceptions of distance, both physical and metaphorical.

Given,

Cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers.

The distance of Cori from starting point=9+20+6

=15+20

=35

Hence, the required distance of Cori from where he started is 35km.

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Answer:

(here i assume that the daily record is another rectangle)

For a rectangle with width W and length L, the perimeter is:

P = 2*W + 2*L

in this case we know that:

P = 125

W = 15

Replacing these in the perimeter equation we get:

125 = 2*15 + 2*L

125 = 30 + 2*L

125 - 30 = 2*L

95 = 2*L

95/2 = L = 47.5

Now we know that the daily record has a scale factor of 60%.

This means that each measure of this rectangle is (60%/100%) times the equivalent measure of the rectangle garden.

Then if the width of the daily record is W' and the length of the daily record is L'

This means that:

L' = (60%/100%)*L = 0.6*L = 0.6*47.5

W' = (60%/100%)*W = 0.6*W = 0.6*15

Then the perimeter is:

P' = 2*0.6*47.5 + 2*0.6*15 = 75

(notice that is exactly the same than multiplying the original perimeter by (60%/100%) = 0.6)

For the options C, D, and E, (where the 3 sides are given) result in the construction of unique triangles.

We will have unique triangles only if the length of the 3 sides are completely determined, so we need to know the 3 sides, or two sides and one angle.

With that in mind, for options C, D, and E (in the 3 cases the 3 sides of the triangles are given). Then for these 3 options, we can make a unique triangle.

While for the first two options, where we only know the angles, we can make infinite triangles.

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Answer:

what do you need help with

Step-by-step explanation:

Answer:

The result is a right cone

Step-by-step explanation:

The solution to the system of equations is x = 4 and y = 1.

So, the ordered pair solution is (4, 1).

To solve the system of equations by elimination method:

Multiply the first equation by 2, and the second equation by -1 to eliminate y.

Simplify and add the two equations together to solve for x.

Substitute the value of x into one of the equations and solve for y.

The steps are:

2*(-4x - 2y = -12) -> -8x - 4y = -24

-1*(4x + 8y = -24) -> -4x - 8y = 24

Add the two equations: -8x - 4y = -24 + (-4x - 8y) -> -12x = -48 -> x = 4

Substitute x=4 into the first equation: -4*4 + 8y = -24 -> 8y = 8 -> y = 1

Therefore, the solution to the system of equations is x = 4 and y = 1.

So, the ordered pair solution is (4, 1).

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