Princeton Middle School is having a math competition. Four students are called to the stand to answer a question. The question is: 58.483 – 12.418 Based on the answer choices, which student was correct? Taylor: 46.565 John: 46.085 Kate: 46.135 Alex: 46.065

Answer:he should build them 25x10

Step-by-step explanation:

Encik Ahmad can build 10 square plots with three different sizes.

Rectangle is a polygon in two dimensional geometry which has four sides and four angles and each angle being right angles.

Length of the rectangular plot = 85 m

Width of the rectangular plot = 30 m

We have to find the number of square plots Encik Ahmad can built of three different sizes.

For that first we take a 45 m length of the plot.

Divide it to three equal lengths. We get three lengths with each 15 m length.

Along the width also, divide into two equal width, each having a width of 15 m.

Each 15 m length, we will get two square plots.

Along 45 m length, we get 3 × 2 = 6 square plots.

The remaining rectangle has length 40 m and width 30 m.

Divide this length as 30 m and 10 m.

So we get a square of dimension 30 m.

Remaining is a rectangle whose remaining length is 10 m and width 30 m.

Along the width, divide into three equal widths, each 10 m.

So there we get three square plots with side length 10 m.

So we have 10 square plots, 6 having the side length 15m, 1 having the side length 30 m and 3 having the side length 10 m.

Hence he get 10 square plots having three different sizes as 15 m, 30 m and 10 m.

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Answer:

\((x-8)^2+y^2=1\)

Step-by-step explanation:

Center of circle is (h,k)=(8,0) and radius is r=1, therefore, the equation is:

\((x-h)^2+(y-k)^2=r^2\\(x-8)^2+(y-0)^2=1^2\\(x-8)^2+y^2=1\)

Step-by-step explanation:

That means the 96 is  75% of your grade

   96 (.75) + 75 (.25) = 90.75  final grade

The number of people who bought £4 tickets are 139.

Let £4 tickets be x

Let £5 tickets be y.

Therefore based on the information given, this will be:

x + y = 223 ..... i

4x + 5y = 936 ..... ii

From equation i

x = 213 - y

Put this into equation ii

4x + 5y = 936

4(213 - y) + 5y = 936

852 - 4y + 5y = 936

Collect like terms

y = 84

This implies that the number of £5 tickets is 84.

Recall that x + y = 223

x + 84 = 223

x = 223 - 84

x = 139

The number of £4 tickets is 139

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Answer:

12

Step-by-step explanation:

25-13=x

x=12

Answer:

x=12

x is being isolated

Step-by-step explanation:

I'm assuming you mean to solve for x? if so

you have to first isolate x

x+13=25 subtract 13 from both sides

-13 -13

x= 12 there's ur answer

the child would take 11.5 days (working 24 hours per day) to fill the swimming pool

an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep.

filling rate =2*10*π*(0.1)^2

or 0.002 π cubic meters per minute

or 0.12 cubic meters per hour

or 2.88 cubic meters per day

volume to fill = 100 cubic meters

how many days to fill ? × days= 2.88π × x=100

this implies x= 100/2.88π

   x= 11.05

the complete question is

an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep. a child starts to fill the pool using a saucepan with a circular base having a diameter of 20cm and a depth of 10 cm. the child can fill the saucepan and empty it into the pool twice per minute. how many days would it take the child (working 24 hours per day) to fill the pool? don’t round to the nearest day.

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Answer:

Approximatley 5.8 units.

Step-by-step explanation:

We are given two angles, ∠S and ∠T, and the side opposite to ∠T. We need to find the unknown side opposite to ∠S. Therefore, we can use the Law of Sines. The Law of Sines states that:

\(\frac{\sin(A)}{a}=\frac{\sin(B)}{b} =\frac{\sin(C)}{c}\)

Replacing them with the respective variables, we have:

\(\frac{\sin(S)}{s} =\frac{\sin(T)}{t} =\frac{\sin(R)}{r}\)

Plug in what we know. 20° for ∠S, 17° for ∠T, and 5 for t. Ignore the third term:

\(\frac{\sin(20)}{s}=\frac{\\sin(17)}{5}\)

Solve for s, the unknown side. Cross multiply:

\(\frac{\sin(20)}{s}=\frac{\sin(17)}{5}\\5\sin(20)=s\sin(17)\\s=\frac{5\sin(20)}{\sin(17)} \\s\approx5.8491\approx5.8\)

Answer:

for a rectangle to be called a square with 4 sides must be equal

for rectangle to be called a square its four angles must be equal.

Answer:

all parallel sides are the same lengths

all angles are 90°

Step-by-step explanation:

We know that the square has the definition of an object or plane that has all the four sides of equal length,

And all the angles related to the sides are also same. (all angles are 90°)

Whereas, a rectangle gets defined as the plane figure with four straight sides and the same number of right angles where the two parallel sides become of equal length.

To complete the table of values for the rational function f(x) = 8x/(x-4), we need to plug in different values of x and evaluate the function.

x | f(x)
--|----
-3| 24
-2| -16
0 | 0
2 | 16
4 | undefined
6 | -24
Let me explain how I arrived at each value. When x=-3, we get f(-3) = 8(-3)/(-3-4) = 24. Similarly, when x=-2, we get f(-2) = 8(-2)/(-2-4) = -16. When x=0, we get f(0) = 8(0)/(0-4) = 0. When x=2, we get f(2) = 8(2)/(2-4) = 16. However, when x=4, we get f(4) = 8(4)/(4-4) = undefined, since we cannot divide by zero. Finally, when x=6, we get f(6) = 8(6)/(6-4) = -24.I hope this helps you understand how to evaluate a rational function for different values of x. Let me know if you have any other questions!

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

2  171717/100000

Answer:

(0,-8)

x=0

y=-8

Step-by-step explanation:

There are a couple of ways you can solve this I used what I think is called the elimination method

We first start by writing the equations in linear form (y=mx+b)

For the first one we have -12x-5y=40

we add 5y to both sides and subtract 40 to get

-12x-40=5y

divide by 5 to get

-12/5x-8=y

Then the second one we have

12x-11y=88

same deal here, add 11y and subtract 88 to get

12x-88=11y

divide by 11 and get

12/11x-8=y

We then set the two equations equal to each other and get

-12/5x-8=12/11x-8

We can add 8 to both sides and get

-12/5x=12/11x

Just by looking at it you can see that the only solution for x is 0

Plug in 0 to the first equation and get -12*0-5y=40

This means that -5y=40

Solve for y and get -8

Answer:

x=0 , y= -8

Step-by-step explanation:

Answer:

x = 90 degrees, right triangle

Step-by-step explanation:

48 + 42 + x = 180

90 + x = 180

180 - 90 = x

x = 90 degrees

Answer:

Step-by-step explanation:

Since there are 985 square feet to cover, and it costs 12.50 per square foot, you multiply 12.50 by 985 to get 12,312.50, the total cost and answer.

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

9

Answer:

C) g(x)=2(x+4)(x-7)

Step-by-step explanation:

g(x)=2x²-6x-56

g(x)=(2x+8)(x-7)

g(x)=2(x+4)(x-7)

Therefore, C is correct. You can expand to check your answer.

The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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The name of the segment inside the large triangle is called the: 3. angle bisector.

The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.

The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.

A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.

Therefore, we can state that the name of the segment is: 3. angle bisector.

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The Shapley-Shubik power index is a measure of the power of individuals in a voting structure. The measure calculates the number of times an individual is pivotal, where "pivotal" is defined as causing the formation of a winning coalition.

1. Player 1 can be added to a coalition in 3 ways. If player 1 is not included in a coalition, the other members have a total voting weight of 19, which is greater than the quota needed to pass a motion. Therefore, player 1 is never pivotal when he is excluded. If player 1 is included in a coalition, the other members have a total voting weight of 9, 8, or 2. To form a winning coalition, another member must be included. In each case, there are two possibilities. Therefore, player 1 is pivotal 6 times. His power is 30 percent.

2. Player 2 can be added to a coalition in 3 ways. If player 2 is not included in a coalition, the other members have a total voting weight of 10, which is less than the quota needed to pass a motion. Therefore, player 2 is never pivotal when he is excluded. If player 2 is included in a coalition, the other members have a total voting weight of 10, 8, or 2. To form a winning coalition, another member must be included. In each case, there are two possibilities. Therefore, player 2 is pivotal 6 times. His power is 30 percent.

3. Player 3 can be added to a coalition in 3 ways. If player 3 is not included in a coalition, the other members have a total voting weight of 18, which is greater than the quota needed to pass a motion. Therefore, player 3 is never pivotal when he is excluded. If player 3 is included in a coalition, the other members have a total voting weight of 10, 9, or 8. To form a winning coalition, another member must be included. In each case, there are two possibilities. Therefore, player 3 is pivotal 6 times. His power is 30 percent. Therefore, the Shapley-Shubik power distribution for this weighted voting system is [30:30,30]. Each player has a power of 30 percent.

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We have here a case of a linear situation. We have that:

1. We have a fixed cost of $4.99.

2. And we need to add $0.30 for every ounce the package weighs.

The equation that represents the total cost of the shipping is:

We can see that per every ounce, we need to multiply it by $0.30 to obtain the total cost (plus the fixed cost of $4.99).

We expressed the equation in the slope-intercept form (y = mx +b).

He will break even on the 25th month.

The cost to start the business is $20,000 and the monthly costs are $8,000.

He has been earning $8,800 every month in revenue.

Profit = Selling Price - Cost Price

Therefore,

let

x = number of month

Hence,

selling price = 8800x

cost price = 20000 + 8000(x) = 20,000 + 8000x

Therefore,

profit =  8800x - (20,000 + 8000x)

profit = 8800x - 20000 - 8000x

profit = 8800x - 8000x - 20000

profit = 800x - 20000

Hence,

The month when they will break even is as follows:

8800x = 20,000 + 8000x

20000 = 8800x - 8000x

20000 = 800x

x = 20000 / 800

x = 25

Therefore, he will break even on the 25th month.

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you will have 8 hours in each part.

24/3 = 8

0am to 8 am

8am to 4pm

4pm to 0am

Answer:

If we'll divide 3 to get equally in to a day.

We'll get 8hr. in each time

\( \frac{24 \: hr}{3} = 8 \: h\)

We can imagine this as

1am - 9am

9am - 5pm

5pm - 1am

Or as u want !!

Answer:

dimensional figure are

Answer:

The answer is 9 miles.

Step-by-step explanation:

14-5=9.

Answer:

9 miles

Step-by-step explanation:

So if you pay $5 for the cab ride then 1$ for every mile driven and you have to pay a total of $14 you go 14-5=9

Answer:

Simplifying the expression \((3\:.\:2)^5\div (3^2\:.\:2^3)\) so, there is only one power of each base we get \(\mathbf{3^3\:.\:2^2}\)

Option D is correct answer.

Step-by-step explanation:

We need to simply the expression \((3\:.\:2)^5\div (3^2\:.\:2^3)\) so, there is only one power of each base.

Solving:

\((3\:.\:2)^5\div (3^2\:.\:2^3)\)

We can write it as:

\(\frac{(3\:.\:2)^5}{3^2.2^3}\)

Now using exponent rule: \((a\:.\:b)^m=a^m\:.\:b^n\)

\(\frac{3^5\:.\:2^5}{3^2.2^3}\)

Now using the exponent rule: \(\frac{a^m}{a^n}=a^{m-n}\) the bases should be same

\(3^{5-2}\:.\:2^{5-3}\\=3^3\:.\:2^2\)

So, simplifying the expression \((3\:.\:2)^5\div (3^2\:.\:2^3)\) so, there is only one power of each base we get \(\mathbf{3^3\:.\:2^2}\)

Option D is correct answer.

Answer:

The distance between campsite and checkpoint is: 4.47 miles

Step-by-step explanation:

Given that the coordinates :

Campsite at (-8,-6) and

Next checkpoint at (-4,-4).

To find:

Distance between campsite and checkpoint = ?

Solution:

Let point A be the campsite i.e. A(-8, -6)

Let point B be the next checkpoint i.e. B(-4, -4)

We have to find the distance AB.

We can use Distance formula  to find the distance between two points on xy coordinate plane:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(x_1 = -8\\y_1 = -6\\x_2 = -4\\y_2 = -4\)

\(AB = \sqrt{(-4-(-8))^2+(-4-(-6))^2}\\\Rightarrow AB = \sqrt{4^2+2^2}\\\Rightarrow AB = \sqrt{16+4}\\\Rightarrow AB = \sqrt{20}\\\Rightarrow \bold{AB=4.47}\)

So, the distance between campsite and checkpoint is: 4.47 miles

Answer:

Step-by-step explanation:

180-120=60 by the properties of parallel lines