Circle A has been dissected into 16 congruent sectors. The base of one sector is 1.95 units, and its height is 4.9 units. What is the approximate area of circle A?

a) 27.52 units^2
b) 48.92 units^2
c) 78.39 units^2
d) 76.44 units^2

Answer: The Answer Is 9

Step-by-step explanation:

If 4x - 12 = 24, add 12 to 24, and divide 36 by 4.

Answer: B.9

Step-by-step explanation:

You know that [tex]\angle A[/tex]≅[tex]\angle B[/tex], this means that the measure of the angle A and the measure of the angle B are equal. Then:

[tex]m\angle A=m\angle B[/tex]

You know that:

[tex]m\angle A=4x-12[/tex] and [tex]m\angle B=24[/tex]

Therefore, you can substitute them into [tex]m\angle A=m\angle B[/tex] :

[tex]4x-12=24[/tex]

Now you can solve for the variable "x":

[tex]4x=24+12\\\\4x=36\\\\x=\frac{36}{4}\\\\x=9[/tex]

You can observe that this value of "x" matches with the option B.

Answer:

Square with side length 25/4 m

Step-by-step explanation:

The area is always going to be largest for a rectangle when the two dimensions are equal.  You are looking for a square. What square has perimeter 25? 4s=25 so the side length of this rectangle (Square) is 25/4 m.

Answer:

It's a square  6.25 * 6.25 m.

Step-by-step explanation:

We can do this using calculus.

Let the  length of the  rectangle be x m.

2x + 2w = 25   where w = the width.

2w = 25 - 2x

w = 12.5 - x

So the area A = x(12.5 - x) = 12.5x - x^2.

Finding the derivative:

dA /dx = 12.5 - 2x

For a maximum area this = zero

12.5 - 2x = 0

x = 6.25m.

and w = 25 - 12.5  = 6.25m.

(For any rectangle the  maximum area is always a square).

Answer:

yes

Step-by-step explanation:

connect dc to <abc and you have a triangle

connect bc to <ebc and you have the same triangle just reflected over the y axis

Congruent triangles are the exact same triangles, but they might be placed at different positions. The correct option is B.

Congruent triangles are the exact same triangles, but they might be placed at different positions.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

In the two of the given triangle, therefore, ΔADC and ΔEBC,

∠CAD = ∠CEB {Already given in the triangle}

∠ACD = ∠ ECB {It is the common angle between two triangles}

CD = CB {Already given in the triangle}

Since in the two triangles, two angles are equal and a side is equal as well, therefore, the two triangles are congruent using the AAS (Angle-Angle-Side) postulate.

Hence, the correct option is B.

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Answer:

The mixed number, can be written as the improper fraction, . The reciprocal of is found by interchanging (“flipping”) the numerator and denominator. When you divide by a whole number, you multiply by the reciprocal of the divisor.

Step-by-step explanation:

To get the reciprocal of a fraction, swap the numerator and denominator; if the original fraction's numerator is divisible by the denominator, the reciprocal will be a whole number. Multiplying by a fraction is the same as dividing by its reciprocal.

To find the reciprocal of a fraction, you simply swap the numerator and the denominator.

For example, the reciprocal of ⅔ (which is 2/8) is 8/2.

However, if you have a fraction and you want to get a reciprocal that is a whole number, you must ensure that the numerator of the original fraction is divisible by the denominator.

If we consider the fraction ⅕ (which is 1/5), its reciprocal is 5/1, or simply 5, which is a whole number.

In essence, finding a reciprocal involves flipping the fraction: turning the top number (numerator) into the bottom number (denominator), and the bottom number into the top number.

This process is akin to multiplying or dividing by the fraction.

For instance, when you multiply a value by a fraction, you are effectively dividing by its reciprocal, and vice versa.

Multiplying fractions involves multiplying the numerators together and the denominators together, and simplifying where possible.

Answer:

A

Step-by-step explanation:

2y=3x-4

4=3x-2y

3x-2y=4

Answer:

The variance of the data is 49.

The median is 64.

The data point 50 is tow standard deviations away for the mean.

The correct statements are true about the curve are as follows;

The variance of the data set is 49.

The median is 64.

The data point 50 is two standard deviations away from the mean.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The correct statements are true about the curve are as follows;

1. The variance of the data set is;

[tex]\rm \sigma ^2=7^2\\ \\ \sigma ^2=49[/tex]

The variance of the data set is 49.

2. The median is the middle value of the data set.

The median is 64.

3. The data point 50 is two standard deviations away from the mean.

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Answer:

No, because it does not have a constant rate of change.

Step-by-step explanation:

On the x side of the table, there is a constant rate of change (+1). However, on the y side, it is not. The first change is +7, the next +5, and the last +6. The rate of change has to be constant on both sides for the table to be considered linear.

Answer:

3x = 6

Step-by-step explanation:

Combine:

6x + 5y =16

- (6x + 2y=10)

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

     3y = 6, so that y = 2 (We weren't actually asked to find the solution.)

Answer:

3y-6

Step-by-step explanation:

Answer:

5/9(F-32) = C

Step-by-step explanation:

F= 9/5C+32

Subtract 32 from each side

F-32= 9/5C+32-32

F-32 = 9/5 C

Multiply each side by 5/9 to isolate C

5/9(F-32) = 5/9*9/5 C

5/9(F-32) = C

Final answer:

To convert Celsius to Fahrenheit, multiply the Celsius temperature by 9/5 (or 1.8) and then add 32. For example, to convert 20 degrees Celsius to Fahrenheit: (9/5) * 20 = 36, and then add 32 to get 68 degrees Fahrenheit.

Explanation:

To solve the formula for converting temperature from degrees Celsius (C) to degrees Fahrenheit (F), you start with the given equation:

F = [tex]\frac{9}{5}[/tex]+ 32

This equation allows you to convert a temperature from Celsius to Fahrenheit by multiplying the Celsius temperature by 9/5 (or 1.8) and then adding 32. The formula reflects the fact that the Fahrenheit scale has a freezing point at 32 degrees higher than the Celsius scale's freezing point, and that each degree Celsius is equivalent to 1.8 degrees Fahrenheit. Here's a step-by-step explanation to convert Celsius to Fahrenheit:

Multiply the Celsius temperature by 9/5.

Add 32 to the result of this multiplication to get the temperature in Fahrenheit.

For instance, to convert 20 degrees Celsius to Fahrenheit:

(9/5) * 20 = 36

36 + 32 = 68 degrees Fahrenheit.

Hence, 20 degrees Celsius is equal to 68 degrees Fahrenheit when you apply the temperature conversion formula.

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, 9)

m = [tex]\frac{9-2}{3+4}[/tex] = [tex]\frac{7}{7}[/tex] = 1 → A

Answer:

0.03

Step-by-step explanation:

First you should find what is 20% of 2

This can be written as ;

[tex]=\frac{20}{100} *2=\frac{40}{100}\\ \\\\=\frac{40}{100} =0.4[/tex]

Let now find 3/7

[tex]\frac{3}{7} =0.4285\\\\\\=0.43[/tex]

Get the difference in the values

[tex]0.43-0.40=0.03\\\\\\[/tex]

You can see 3/7 is 0.03 larger than 20% of 2.

Answer:

Im pretty sure its answer d hope that helped

Step-by-step explanation:

D. f(x) = 5*.

The derivative of a function may be used to determine whether the function is increasing or decreasing at any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

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Answer:

The correct answer is last option (6x)² - (5)²

Step-by-step explanation:

It is given an expression in variable x,

36x² - 25

To find the equivalent expression of  36x² - 25

We have, 36 = (±6)²  and 25 = (±5)²

36x² - 25 can be written as,

36x² - 25 = (±6x)² - (±5)²

From the given options we get the correct answer is last option

(6x)² - (5)²

Answer:

D

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

If the triangle is translated ANY amount of units ANYWHERE, the length of each segment AND the angles will ALL be the same.

Why?

Because if you translate something, you are only moving it somewhere else. You aren't stretching the shape or making any modifications. You are simply moving it, and that will only change the coordinates the points will be at.

The length of A1B1 is 10.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

Given

If the triangle is translated ANY amount of units ANYWHERE, the length of each segment AND the angles will ALL be the same.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}-5x=y-5&\text{subtract y from both sides}\\-2y=-x-21&\text{add x to both sides}\end{array}\right\\\left\{\begin{array}{ccc}-5x-y=-5&\text{multiply both sides by (-2)}\\x-2y=-21\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x+2y=10\\x-2y=-21\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad11x=-11\qquad\text{divide both sides by 11}\\.\qquad x=-1\\\\\text{put the value of x to the first equation:}\\\\10(-1)+2y=10\\-10+2y=10\qquad\text{add 10 to both sides}\\2y=20\qquad\text{divide both sides by 2}\\y=10[/tex]

Answer:The person above is right

Step-by-step explanation:

Answer:

the answer is 181 2/4 OR 181 1/2 hours a month.

Step-by-step explanation:

you multiply the days per month=22

by the hours they work per day=8 1/4

(optional) You turn 1/4 into .25

then: 22 × 8.25= 181.5/181 1/2

Based on the number of days worked per month and the hours worked, the number of hours worked per month is 181.5 hours.

First convert the mixed fraction to a decimal:

1/4 = 0.25

8¹/₄ = 8.25

If they work 8.25 hours a day and work for 22 days, the number of hours worked per month is:

= 8.25 x 22 days

= 181.5 hours

In conclusion, they would work for 181.5 hours.

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inal answer:

To calculate the reimbursement rate per gallon, multiply the total miles traveled by all employees by the average gas mileage and divide the total reimbursement amount by the total gallons used, resulting in a rate of $1.40 per gallon.

Explanation:

To find the rate in dollars per gallon that the company uses to reimburse employees, we need to calculate the total gallons of gas consumed and then divide the total amount paid out by the total gallons used.

The average employee traveled 12,250 miles, and the average gas mileage was 22.5 miles per gallon:

Total miles for all employees: 126 employees × 12,250 miles/employee = 1,543,500 miles.

Total gallons consumed: 1,543,500 miles ÷ 22.5 miles/gallon = 68,600 gallons.

Rate of reimbursement per gallon: $96,040.00 ÷ 68,600 gallons ≈ $1.40 per gallon.

Therefore, the reimbursement rate is $1.40 per gallon.

Final answer:

The reimbursement rate in dollars per gallon is calculated by determining the total gallons of gas used by all employees and then dividing the total reimbursement amount by this figure. The computation shows a reimbursement rate of $1.40 per gallon.

Explanation:

To determine the rate in dollars per gallon that the company uses to reimburse employees, we need to calculate the total gallons of gas used by the average employee and then find out how much the company paid per gallon.

Thus, the correct answer is C) $1.40 per gallon.

Step-by-step explanation:

0.89 = 1 - 1/(k²)

Start by subtracting 1 from both sides:

0.89 - 1 = -1/(k²)

-0.11 = -1/(k²)

Multiply both sides by -1:

0.11 = 1/(k²)

Multiply both sides by k²:

0.11 k² = 1

Divide both sides by 0.11:

k² = 1 / 0.11

Take the square root:

k = √(1 / 0.11)

Answer:

+/- 3.015 to the nearest thousandth.

Step-by-step explanation:

0.89 = 1 - 1 / k^2

Multiply through by k^2

0.89k^2 = k^2 - 1

k^2 - 0.89k^2 = 1

0.11 k^2 = 1

k^2 = 1/0.11 = 9.091

k = +/- √0.091

= +/-3.015.

Answer:

try the third table

Step-by-step explanation:

try the third table because the others would end up nonlinear

Check the picture below.

let's recall Cavalieri's principle, that solids with equal altitudes and identitical cross-sectional areas at each part all the way up, have the same volume.

so, for a prism like this that is not oblique, with rhombic bases of area 600 and a height/altitude of 24, the volume will simply be the base * height, 600 * 24 = 14400.

well, based on Cavalieri's principle, an oblique one will also have the same volume.

Answer:

The volume of the prism is 14400 units³.

Step-by-step explanation:

It is given that an oblique prism is created using rhombuses with edge lengths of 25 units.

The volume of a prism is

[tex]V=B\times h[/tex]                   ..... (1)

Where, B is base area and h is height of the prism.

It is given that the area of one rhombus is 600 sq units. The perpendicular distance between the bases is 24 units.

Substitute B=600 and h=24 in equation (1) to find the volume of the prism.

[tex]V=600\times 24[/tex]

[tex]V=14400[/tex]

Therefore the volume of the prism is 14400 units³.

Step-by-step explanation:

if f = c/lambda

then c = f × lambda

Answer:

B. c = fλ

Step-by-step explanation:

Given formula,

f equals c over lambda,

[tex]\implies f=\frac{c}{ \lambda}[/tex]

Where, f = frequency,

c = wave speed,

λ = wavelength,

By the above formula,

[tex]f\times \lambda = c[/tex]   ( By cross multiplication ),

Hence, the required formula for c,

[tex]c=f\lambda[/tex]

Option 'B' is correct.

Answer:

[tex]\large\boxed{\dfrac{13}{20}=0.65}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\\\\dfrac{13}{20}=\dfrac{13\cdot5}{20\cdot5}=\dfrac{65}{100}=0.65\\\\\bold{METHOD\ 2}\\\\\dfrac{13}{20}=13:20\qquad\text{use the calculator or long division}\\\\=0.65[/tex]

Hello There!

[tex]\frac{13}{20}=0.65[/tex]

13÷20≈0.65

[tex]\frac{4}{7}/\frac{-3}{8}[/tex]

With division when using fraction the first fraction stays the same, but you will switch the division sign to multiplication and you will take the reciprocale (flip the numerator and denominator) of the second fraction like so...

[tex]\frac{4}{7}*\frac{-8}{3}[/tex]

Now you can multiply normally:

[tex]\frac{4*(-8)}{7*3}[/tex]

[tex]\frac{-32}{21}[/tex] <<<This is your answer

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

D

Step-by-step explanation:

The ratios of corresponding sides are equal, that is

[tex]\frac{BD}{CD}[/tex] = [tex]\frac{AD}{BD}[/tex]

Substitute values

[tex]\frac{h}{16}[/tex] = [tex]\frac{9}{h}[/tex] ( cross- multiply )

h² = 16 × 9 = 144 ( take the square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12 → D

Answer:

x=-16/3 (-5.33)

Step-by-step explanation:

3(x-2)+4x=10(x+1)

3x-6+4x=10x+10

7x-6=10x+10

-6-10=10x-7x

-16=3x

x=-16/3

Answer: [tex]x=-\frac{16}{3}[/tex]

Step-by-step explanation:

Given the equation [tex]3(x - 2) + 4x = 10(x+ 1)[/tex], you need to solve for the variable "x":

Apply Distributive property:

[tex]3x - 6 + 4x = 10x +10[/tex]

Add the like terms:

[tex]7x - 6= 10x+10[/tex]

Subtract 10 to both sides of the equation:

[tex]7x - 6-10= 10x +10-10\\\\7x-16=10x[/tex]

Subtract [tex]7x[/tex] from both sides:

[tex]7x-16-7x=10x-7x\\\\-16=3x[/tex]

And finally divide both sides by 3:

[tex]\frac{-16}{3}=\frac{3x}{3}\\\\x=-\frac{16}{3}[/tex]

Let's say that the coordinates of the squirrel are: (x, y)

Since the coordinates of the acorn is halfway, between the tree and the squirrel, that means the acorn is the midpoint.

To work out the midpoint you do:

(sum of x-coordinates) divided by 2,  (sum of y coordinates) divided by 2.

We can use this to form an equation .

So the sum of the x coordinates of the tree and the squirrel = -1   :

x-coordinates of the squirrel:

[tex]\frac{-3+x}{2}=-1[/tex]                   (now solve for x)

[tex]-3+x = -2[/tex]

[tex]x=1[/tex]

y-coordinates:

[tex]\frac{8+y}{2}=5[/tex]                   (now solve for y)

[tex]8+y=10[/tex]

[tex]y = 2[/tex]

So the coordinates of the squirrel are: (1, 2)

____________________

Answer:

(1, 2)

Answer:

(1,2)

Step-by-step explanation:

By the information given in the problem, we know that the midpoint of the squirrel's coordinates and the tree's coordinates are the coordinates of the acorn on the tree.

Let the squirrel's coordinates be $(x,y)$ so we have $$\left(\frac{-3+x}{2},\frac{8+y}{2}\right)=(-1,5).$$Solving $\frac{-3+x}{2}=-1$ and $\frac{8+y}{2} = 5$, we find that the squirrel's coordinates are $\boxed{(1,2)}$.

The mode is the number that appears most often in a data set.

For number two you have the numbers 100, 83, 97, 63, 83

The number 83 is listed two times and the other numbers are only listed once.

The mode would be 83

Answer:

simple random

In a simple random sample, individuals all have an equal chance of being selected, ensuring unbiased and representative data. Thus, option a. is correct.

In a simple random sample, individuals all have an equal chance of being selected, and all samples have an equal chance of being selected. This method ensures that each member of the population is equally likely to be chosen, resulting in unbiased and representative data.

Other sampling methods like cluster sampling and stratified sampling do involve randomness but in different ways. For instance, cluster sampling involves selecting entire clusters, such as departments or geographical areas, at random and including all members from those clusters in the sample.

In contrast, stratified sampling involves dividing the population into strata based on characteristics and then randomly sampling from each stratum.

Thus, option a. simple random sample is correct.

the angles are supplementary meaning they equal 180 degrees so 100-x=180

x=80

ANSWER

[tex]m \angle ACE = 80 \degree[/tex]

EXPLANATION

Recall that adjacent angles on a straight line will add up to 180°

From the diagram, m<ACD and m<ACE are adjacent angles on a straight line because they have a common vertex at C.

We sum the two angles and equate them to 180°

[tex] m \angle \: ACD + m \angle ACE = 180 \degree[/tex]

From the diagram

[tex]m\angle ACD= 100 \degree[/tex]

We substitute the known angle to obtain:

[tex]100 \degree + m \angle ACE = 180 \degree[/tex]

[tex]m \angle ACE = 180 \degree - 100 \degree[/tex]

[tex] \therefore \: m \angle ACE = 80 \degree[/tex]