The height of the parallelogram is equal to the diameter of the circle. The base of the parallelogram is equal to half of the circumference of the circle. Therefore, the area of the circle (πr2) is equal to bh and the circumference of the circle is equal to 2b.
The height of the parallelogram is equal to the diameter of the circle. This can be seen because each of the eight sectors has the same area, so they are all the same size. If we place them next to each other in the shape of a parallelogram, we can see that the height of the parallelogram is equal to the diameter of the circle.
The base of the parallelogram is equal to half of the circumference of the circle. This is because the circumference of the circle is divided equally into eight sectors, and the base of the parallelogram is formed by placing two adjacent sectors together. Therefore, the base of the parallelogram is equal to the arc length of one sector plus the arc length of its adjacent sector. Each sector is 1/8th of the circle, so the arc length of one sector is 1/8th of the circumference. Adding the arc lengths of two adjacent sectors gives 1/4th of the circumference, which is half of the base of the parallelogram.
Therefore, the area of the circle (πr2) is equal to the area of the parallelogram (bh), where h is the diameter of the circle and b is half of the circumference of the circle. Additionally, the circumference of the circle is equal to the base of the parallelogram multiplied by 2.
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An above ground pool drains at a rate of 20
gallons every 3 minutes. The swimming pool
holds 5,000 gallons of water. How many hours
will it take to completely drain the swimming
pool?
The amount of time it would take to drain the swimming pool is equal to 75 minutes..
How to determine time it would take to drain the swimming pool?Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:
[tex]P(t) = I(1 - r)^t[/tex]
Where:
P(t ) represents the volume of water in gallons.t represents the time or number of years.I represents the initial volume of water.r represents the decay rate.Next, we would determine the amount of time it would take to have 0 gallons in the swimming pool:
20 gallons = 3 minutes
5,000 gallons = x minutes
20x = 1500
x = 1500/20
x = 75 minutes.
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Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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A fence 706 m long and is cut into three parts. Two parts are the same length, and the third part is 25 m longer than either of the other two parts. find the length of each part
Step-by-step explanation:
706 -25 = 681 ====> which is three pieces of 681/3 = 227 m
but one is 25 m longer so 227, 227 , and 227 + 25 =252 m
Urgent!!
Find the value of y in the figure above. Leave your answer in simplest radical form.
The value of y in the triangle is 20.
What is the triangle?
A triangle is a polygon with three sides and three angles. It is the simplest and most basic polygon in Euclidean geometry.
According to the given information:
From the figure, we can say that ΔABC and ΔABI are similar.
we can write proportions as
[tex]\frac{y}{30} =\frac{30}{y+25}[/tex]
y(y+25) = 30*30
[tex]y^{2}[/tex]+25y=900
[tex]y^{2}[/tex]+25y-900 = 0
On solving we can use quadratic formula y = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation y^2 + 25y - 900 = 0, we can identify a = 1, b = 25, and c = -900.
Plugging these values into the quadratic formula, we get:
y = (-25 ± √(25^2 - 4 * 1 * -900)) / (2 * 1)
Simplifying further:
y = (-25 ± √(625 + 3600)) / 2
y = (-25 ± √(4225)) / 2
y = (-25 ± 65) / 2
Now we can solve for two possible values of y:
y = (-25 + 65) / 2 = 40 / 2 = 20
y = (-25 - 65) / 2 = -90 / 2 = -45
So the two possible values of y that satisfy the given equation are y = 20 and y = -45.
distance cannnot be negative, so the value of y is 20.
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Jake and his friends
are bowling. The area of
the rectangular lane is 14x2-x-3
square feet. If the width of the lane is
2x -1 feet, write an expression to
represent the length of the lane.
SOLUTION:
Answer:
L = (14x^2 - x - 3) / (2x - 1)
Step-by-step explanation:
The area of the rectangular lane is given as 14x^2 - x - 3 square feet.
Let's assume that the length of the lane is L feet. Then the formula for the area of a rectangle is:
Area = Length x Width
Substituting the values given in the question, we have:
14x^2 - x - 3 = L x (2x - 1)
To find an expression for the length of the lane, we can rearrange the equation to solve for L:
L = (14x^2 - x - 3) / (2x - 1)
Therefore, the expression that represents the length of the lane is:
L = (14x^2 - x - 3) / (2x - 1)
The equity sections for Atticus Group at the beginning of the year (January 1) and end of the year (December 31) follow.
2. The total dollar amount for each cash dividend is $23,700.
Outstanding common shares, dividend and capitalization1. Calculation of outstanding common shares on each cash dividend date:
January 5: No change in outstanding shares since the date of record is January 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400 (47,400 issued - 3,000 treasury shares = 44,400 outstanding).April 5: No change in outstanding shares since the date of record is April 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.July 5: No change in outstanding shares since the date of record is July 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.October 5: No change in outstanding shares since the date of record is October 10, which is after December 31, 2017. Therefore, the outstanding shares are 47,400.2.
Calculation of total dollar amount for each cash dividend:
January 5: $0.50 per share x 47,400 outstanding shares = $23,700April 5: $0.50 per share x 47,400 outstanding shares = $23,700July 5: $0.50 per share x 47,400 outstanding shares = $23,700October 5: $0.50 per share x 47,400 outstanding shares = $23,700Therefore, the total dollar amount for each cash dividend is $23,700.
3.
Calculation of the capitalization of retained earnings for the stock dividend:
Market value per share on July 31: $12Number of outstanding shares before stock dividend: 47,400Number of shares to be issued for the stock dividend: 20% x 47,400 = 9,480Total value of shares to be issued for the stock dividend: 9,480 shares x $12 per share = $113,760The capitalization of retained earnings for the stock dividend is equal to the total value of shares issued, which is $113,760.Learn more on dividends here https://brainly.com/question/2960815
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The equity sections from Atticus Group’s 2016 and 2017 year-end balance sheets follow Stockholders’ Equity (December 31, 2016)
Common stock—$4 par value, 100,000 shares
authorized, 40,000 shares issued and outstanding . .. . . . . . . . . . $160,000
Paid-in capital in excess of par value, common stock .. . . . . . . . . . . . . . . . 120,000
Retained earnings .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320,000
Total stockholders’ equity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $600,000
Stockholders’ Equity (December 31, 2017)
Common stock—$4 par value, 100,000 shares
authorized, 47,400 shares issued, 3,000 shares in treasury . .. . . . . . . $189,600
Paid-in capital in excess of par value, common stock . . . . . .. . . . . . . . . . . . 179,200
Retained earnings ($30,000 restricted by treasury stock) .. . . . . . . . . . . . . 400,000
768,800
Less cost of treasury stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30,000)
Total stockholders’ equity . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . $738,800
The following transactions and events affected its equity during year 2017.
Jan. 5 Declared a $0.50 per share cash dividend, date of record January 10.
Mar. 20 Purchased treasury stock for cash.
Apr. 5 Declared a $0.50 per share cash dividend, date of record April 10.
July 5 Declared a $0.50 per share cash dividend, date of record July 10.
July 31 Declared a 20% stock dividend when the stock’s market value was $12 per share.
Aug. 14 Issued the stock dividend that was declared on July 31.
Oct. 5 Declared a $0.50 per share cash dividend, date of record October 10.
Required
1. How many common shares are outstanding on each cash dividend date?
2. What is the total dollar amount for each of the four cash dividends?
3. What is the amount of the capitalization of retained earnings for the stock dividend?
The number of people applying for financial aid has gone up in the past 10 years by 6.74%. If the number of people that used to apply was 9,720,000, then how many people are applying now (10 years later)?
There are currently about 10,361,248 people requesting financial aid, which is an increase of 6.74% from ten years ago.
How are financial aid amounts determined?By reducing the financial barrier, it supports the advancement of your academic and professional ambitions.
Its current number of applications can be determined by multiplying 9,720,000 with 1.0674 (which equals a 6.74% increase)
If there were 9,720,000 people asking for financial help 10 years ago and there have been 6.74 times as many applicants since then. As a result, there are currently 10,361,248 applicants for financial aid, or 9,720,000 x 1.0674.
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Hourly Wage Your wage is $8.00 per hour plus $0.75 for
each unit produced per hour. So, your hourly wage y in terms of the number of units produced is
y = 8 +0.75x.
(a) Find the inverse function.
(b) What does each variable represent in the inverse function?
(c) Determine the number of units produced when your hourly wage is $22.25.
(1) The inverse function is: [tex]f^-1 (y)[/tex] = (y - 8)/0.75 (2) In the inverse function, y represents the number of units produced and x is the hourly wage.(3) an hourly wage of $22.25 is approximately 14.93.
How do you know if a graph is a function?If a vertical line drawn anywhere on the graph of a relation only intersect at one point on the graph, then this graph represents a function. If a vertical line can intersect the graph at two or more points, the graph does not represent a function.
(a) To find the inverse function, we must solve for x in terms of y.
y = 8 + 0.75x
y - 8 = 0.75x
x = (y - 8)/0.75
So the inverse function is:
[tex]f^-1 (y)[/tex] = (y - 8)/0.75
(b) In the inverse function, y represents the number of units produced and x is the hourly wage.
(c) To determine the number of units produced when the hourly wage is $22.25, we need to plug y = 22.25 into the inverse function we found in part (a):
[tex]f^{-1}[/tex](22.25) = (22.25 - 8)/0.75
[tex]f^{-1}[/tex](22.25) = 14.93
Therefore, the number of units produced at an hourly wage of $22.25 is approximately 14.93.
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. How much you have to deposit in an account earning 8 percent compound monthly to pay a retired officer $1000 monthly for 12 years.
What is the lateral surface area
Answer:
A- 304.8 cm²
Step-by-step explanation:
Find the area for the 4 sides (excluding both the top and base).
(2(12×7.5))+(2(12×5.2)) = 302.8
Answer:
A. 304.8 cm²
Step-by-step explanation:
The rectangular prism has a total of 6 rectangular sides
~ two at the bottom and top both of equal dimensions 5.2 x 7.5
~ two at the front and back both of equal dimensions 12 x 7.5
~ two one on the left side and the other on the right side both of equal dimensions 12 x 5.2
The question is asking only for the lateral surface area. This means we ignore the top and bottom surfaces
For each of the other two pairs of rectangles, the surface area is nothing but the product of the dimensions for each rectangle
Therefore area of all the 4 rectangles is
2(5.2 x 7.5 + 12 x 5.2)
We multiply by 2 since there are 2 of each rectangular surface
2(5.2 x 7.5 + 12 x 5.2) = 304.8 cm² ANSWER
Mr. Hernandez has a high-speed printer that can produce 32 pages per minute.
Write an equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y.
y =
An equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y is y = 32x
The equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y, can be obtained using the following formula:
y = r * x
where r represents the rate of printing in pages per minute, which in this case is 32 pages per minute.
Therefore, the equation becomes:
y = 32x
This equation states that the number of pages printed, y, is directly proportional to the print time in minutes, x, at a rate of 32 pages per minute.
For example, if Mr. Hernandez wants to print 128 pages, we can use the equation to find out how long it will take him:
128 = 32x
x = 128/32
x = 4
Therefore, it will take Mr. Hernandez 4 minutes to print 128 pages on his high-speed printer.
In summary, the equation y = 32x represents the relationship between the print time in minutes, x, and the number of pages printed, y, when using a high-speed printer that can produce 32 pages per minute.
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The following is a list of student TGA scores from Unit 3:
73, 83, 72, 71, 65, 70, 76, 73, 83, 73
(a) What is the mean score? Show your work.
(b) What is the median score? Show your work.
Which is true about the relationship between 1 inch and 1 foot? A. 1 inch is 12 times as long as 1 foot. B. 1 foot is 12 times as long as 1 inch. C. 1 foot is 6 times as long as 1 inch. D. 1 inch is 6 times as long as 1 foot.
The true-relationship between 1 inch and 1 foot is (b) 1 foot is 12 times as long as 1 inch.
An "inch" is a unit to measure length and is equal to 1/12th of a foot. It is denoted by symbol "in"
A "foot" is a unit which measures the length and is equal to 12 inches. It is denoted as "ft" .
In the imperial system, the unit of length is the foot, and it is divided into 12 smaller units called inches,
So, 1 foot is equal to 12 inches, and we can write this as : 1 foot = 12 inches,
We rearrange this equation to get the relationship between 1 inch and 1 foot,
⇒ 1 inch = 1/12 foot,
This means that 1 inch is equal to one-twelfth of a foot. In other words, it takes 12 inches to make 1 foot.
Therefore, the correct option is (b).
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the table shows the favirote film of 20 people complete the pie chart
The complete table for the pie chart is;
Type of Film Frequency Angle in °
Action 4 72°
Horror 11 198
Comedy 5 90
How to interpret Pie chart?From the given table used to form the pie chart, we see that;
Type of Film Frequency Angle in °
Action 4 72°
Horror 11
Comedy 5
We know that the angles in a circle is equal to 360 degrees. Thus;
Angle composed of horror and comedy = 360 - 72 = 288°
Thus;
Angle for horror film = (11/(4 + 11 + 5)) * 360°
= (11/20) * 360°
= 198°
Thus;
Angle for comedy = 288° - 198° = 90°
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Jacob took out a loan from a bank today (now). The original agreement stated that to pay off the loan he had to make two equal payments: The first payment of $3000 was due 6 months from now, and the second payment of $3000 was due 12 months from now.
Suppose he renegotiated with the bank so that instead of the original agreement he will make a single payment 24 months from now to pay off the two original obligations.
What single payment 24 months from now will he have to make if the simple interest rate is 10%? The agreed focal date is 24 months from now.
The single payment Jacob would make in 24 months from now, to pay off the two obligations under the new agreement is $7,620.
We shall be solving this using the formula for Simple Interest,
What is the formula for Simple Interest?The interest accrued on each payment can be calculated using the formula for Simple Interest:
Interest = Principal × Rate × Time
where:
Principal = amount borrowed,
Rate = simple interest rate,
Time = time period in years.
Under the original agreement, Jacob shall make two payments of $3000 each, one 6 months from now and the other 12 months from now.
For payment1, the interest accrued would be:
Interest1 = $3000 × 0.10 × (6/12) = $150
For payment2, the interest accrued would be:
Interest2 = $3000 × 0.10 × (12/12) = $300
So the total amount Jacob was to pay under the original agreement is:
Total1 = $3000 + $150 + $3000 + $300 = $6,450
Now let's calculate the amount Jacob would have to pay under the new agreement.
Original principal for each payment is $3000.
The interest accrued on the sum of both payments can be calculated using the same formula for simple interest:
Interest3 = ($3000 + $150 + $3000 + $300) × 0.10 × (24/12) = $720
So the total amount Jacob would pay under the new agreement is:
Total2 = $3000 + $150 + $3000 + $300 + $720 = $7,620
So, Jacob would make a single payment of $7,620, 24 months from now,
to pay off both loans under the new agreement.
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Martin made a stick pattern such that each successive stick is twice as long as the one before it. If the shortest stick in the pattern is long, and there are sticks in total, which is closest to the combined length of the sticks in Martin's pattern?
I NEED HELP ON THIS!! 100 POINTS!!
When we solve the radical equation, we can see that the value of x is -113.
What is a radical equation?A radical equation is an equation in which one or more variables are under a radical sign, such as a square root, cube root, or higher-order root. These equations involve expressions with radicals that contain the variable, and the goal is usually to isolate the variable on one side of the equation.
Given that;
10 + √2x + 1 = -5
√2x + 1 = - 5 - 10
√2x + 1 = - 15
Square both sides;
2x + 1 = -225
2x = -225 - 1
2x = -226
x = -113
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643 N
5
2
T
-5-4-3-2-1₁-
-2
-3
-4
-5
y
-
2 3 4 5
X
What is the range of the function on the graph?
O all real numbers
Oall real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
The range of the function is all real numbers.
What is Function?In mathematics, a function is an expression, rule, or law that specifies a relationship between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
We know,
The x-values (Input values) on the graph define the domain of the function.
and, The y-values (output values) on the graph determine the range of a function.
From the graph attached,
Here the x value start from +1 to ∞.
Thus, the range of the function is all real numbers.
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7. Which line segments in circle A are the
radii in this circle?
M
R
B
Answer:
AM and AR
Step-by-step explanation:
A is the center, AR is a radius and so is AM
Try These questions out and I’ll give you brainliest
Answer:
1) -8m
2) -x
3) -4y
4)
[tex] - 17x {y}^{3} [/tex]
5) p
6) 0
7) 15m + 10
8) r - 7
9) 5x - 22
10)
[tex]3 {m}^{2} [/tex]
11)
[tex]7 {x}^{2} - x[/tex]
12) 22pq - 8p
13)
[tex] - 13 {r}^{2} - 6r[/tex]
14) -19
15) 0
16) 3.07y
17)
[tex] - 4 {m}^{2} - 35m[/tex]
18)
[tex]x {y}^{2} - 3 {x}^{2} y[/tex]
19) .3mn + 4.7m
20) 3r + 2j + m + 3
21)
[tex] - 4 {x}^{2} - 16x + 11[/tex]
22)
[tex]3 {y}^{4} - {y}^{2} + 11[/tex]
jenny earned a 77 on her most resent test. jennys score is no less than 5 points greater than 4/5 of terrance score if t represents terrances score which is the inequality represents the sisuation.
Answer: Jenny's score is no less than 5 points greater than 4/5 of Terrance's score.
Step-by-step explanation:
The inequality that represents the situation described is:
Jenny's score (denoted as "J") is no less than 5 points greater than 4/5 of Terrance's score (denoted as "T"):
J ≥ (4/5)T + 5
In this inequality, we are saying that Jenny's score "J" must be greater than or equal to 4/5 of Terrance's score "T", plus an additional 5 points. This reflects the condition that Jenny's score should be at least 5 points higher than 4/5 of Terrance's score.
For example, if Terrance's score "T" is 80, then 4/5 of Terrance's score is (4/5) * 80 = 64. Adding 5 points to this gives us 69. Therefore, Jenny's score "J" must be greater than or equal to 69 in this case, since it should be no less than 5 points greater than 4/5 of Terrance's score.
If 2-1=3 3-4=7 4-9=13 5-16=21 3-81=0 6-25=?
The result of (6 - 25) = (6² - √25) = (36 - 5) = 31
What is a sequence of series?A sequence is a list of numbers arranged in a specific order, while a series is the sum of the terms of a sequence. In other words, a sequence is a collection of numbers that follow a particular pattern or rule, and a series is the result obtained by adding these numbers together.
The sequence of equations, it appears that each result is obtained by subtracting the square of first number to the square root of second number:
2 - 1 = 2² - √1 = 4 - 1 = 3
3 - 4 = 3² - √4 = 9 - 2 = 7
4 - 9 = 4² - √9 = 16 - 3 = 13
5 - 16 = 5² - √16 = 25 - 4 = 21
3 - 81 = 3² - √81 = 9 - 9 = 0
Similarly,
6 - 25 = 6² - √25 = 36 - 5 = 31
Therefore, the result of 6 - 25 = 6² - √25 = 36 - 5 = 31
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In circle S with m/RUT = 17°, find the m/RST.
S
U
Q
R
T
The value of measure of ∠ RST is,
⇒ ∠ RST = 34°
We have to given that;
In circle S with m ∠RUT = 17°
Hence, We get;
⇒ ∠ RST = 2 × ∠ RUT
⇒ ∠ RST = 2 × 17°
⇒ ∠ RST = 34°
Thus, The value of measure of ∠ RST is,
⇒ ∠ RST = 34°
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Write the system first as a vector equation and then as a matrix equation.
7 x 1
plus
x 2
minus
3 x 3
equals
7
3 x 2
plus
2 x 3
equals
0
Question content area bottom
Part 1
Write the system as a vector equation where the first equation of the system corresponds to the first row. Select the correct choice below and fill in any answer boxes to complete your choice.
The given system of equations can be written as a vector equation [tex]7x^1+x^2-3x^3[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It usually consists of two expressions separated by an equals sign (=). The expressions may contain numbers, variables, and operations, such as addition, subtraction, multiplication, and division. The solution of an equation is the value of the variable that makes the equation true.
Vector equation:
[tex](7x^1+x^2-3x^3)=7[/tex]
Part 2
Write the system as a matrix equation. Select the correct choice below and fill in any answer boxes to complete your choice.
Matrix equation:
=
A =
[7 1 -3
3 2 2]
B =
[7
0]
Conclusion:
The given system of equations can be written as a vector equation [tex](7x^1+x^2-3x^3)[/tex] = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].
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help me and thank you
Answer:
Option A, is 8x^6.
Step-by-step explanation:
4x³ × 2x³ = (4 × 2) x^(3+3) = 8x^6
Therefore, 4x³ × 2x³ simplifies to 8x^6.
You're welcome. :)
A) 8x⁶
Step-by-step explanation:Exponents have different rules for operations such as multiplication.
Multiplying Coefficients
When multiplying different terms with exponents, the first thing we should do is multiply the coefficients. Even though there are variables with different exponents, we still multiply the coefficients like normal. This means that the coefficient of the answer should be 8 because 4 * 2 =8. However, you should note that you can only multiply the coefficients and simply the expression if the terms have the same variable.
Multiplying Exponents
To multiply 2 terms with exponents, you should add the exponents together. For example, x⁴ * x⁶ = x¹⁰. No matter what the coefficients are, if the variables are the same, then this method will work. This means that x³ * x³ = x⁶. Then, combine this with the coefficient from before and 4x³ * 2x³ = 8x⁶.
A. Using the given variables, translate the following to mathematical
expressions.
1. the sum of n and 8
2. M reduced by x
3. 12 subtracted from z
4. cincreased by d
5. 20 more than twice f
6. the square of the sum of x and y
7. twice the product of m and n
8. six less than twice b
9. the sum of the squares of u and v
10.the product of x and y divided by 2
Answer:
n + 8
M - x
z - 12
c + d
2f + 20 or 20 + 2f
(x + y)^2 or (x + y) × (x + y)
2mn or 2 × m × n
2b - 6 or 6 - 2b
u^2 + v^2 or v^2 + u^2
(xy)/2 or xy/2
What is 625x25 what is the answer to this problem
Answer
15,625
Step-by-step explanation:
Solution of expression 625 x 25 is, 15,625
We have to given that,
An expression to solve,
625 x 25
Since,To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We can multiply is,
625 x 25
= 15,625
Therefore, Solution of expression 625 x 25 is, 15,625
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Find the perimeter of the following shape,
given its curves are made from parts of
circles.
Give your answer in terms of TT.
6cm
30cm
14cm
The diagram is not drawn to scale.
The perimeter of the given shape in terms of pi is 22 cm + 25 pi cm.
How do you figure out perimeter?The circumference of the rectangle is equal to the sum of the lengths of its four sides. It is simple to do this because there are two of each side length; all that is needed is to sum the length and width and multiply the result by two.
By multiplying half of the semicircle's circumference by the diameter's length, one can determine the semicircle's perimeter. Thus, the semicircle's perimeter is as follows:
Perimeter of semicircle = 6 cm + (1/2) x pi x 6 cm
Perimeter of semicircle = 6 cm + 3 pi cm
Each quarter circle has a perimeter that is just one-fourth of its circumference. Consequently, the 14 cm quarter circle's perimeter is as follows:
Perimeter of quarter circle with radius 14 cm = (1/4) x 2 pi x 14 cm
Perimeter of quarter circle with radius 14 cm = 7 pi cm
And, the perimeter of the quarter circle with radius 30 cm is:
Perimeter of quarter circle with radius 30 cm = (1/4) x 2pi x 30 cm
Perimeter of quarter circle with radius 30 cm = 15 pi cm
Therefore, the total perimeter of the given shape is:
Perimeter = Perimeter of semicircle + Perimeter of quarter circle with radius 14 cm + Perimeter of quarter circle with radius 30 cm
Perimeter = (6 cm + 3 pi cm) + (7 pi cm) + (15 pi cm)
Perimeter = 22 cm + 25 pi cm.
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Find the prime factorization of 234.
Answer:2^1 × 3^2 × 13^1
Step-by-step explanation:
Let A and B be two events such that P(A) = 1⁄5 While P(A or B) = 1⁄2. Let P(B) = P. For what values of P are A and B independent?
The value of P for A and B to be independent is 3/8.
What is probability of something?Probability is a mathematical concept used to determine the likelihood or chance of an event occurring. It's a measure of how likely it is that a specific outcome will happen in a given situation. Probability values are expressed as numbers between 0 and 1, where 0 means the event is impossible, and 1 means it is certain to occur.
The probability of an event is calculated by dividing the number of outcomes that favor the event by the total number of possible outcomes. The total number of outcomes is the number of ways the event could happen, while the number of favorable outcomes is the number of outcomes that satisfy the event's conditions.
Probability theory has many applications in various fields, including finance, economics, science, engineering, and statistics. It is an essential tool for analyzing data, predicting outcomes, and making decisions.
Two events A and B are independent if and only if P(A and B) = P(A) * P(B).
Using the formula for the probability of the union of two events, we have:
P(A or B) = P(A) + P(B) - P(A and B)
Substituting the given values, we get:
1/2 = 1/5 + P - P(A and B)
Simplifying, we get:
3/10 = P - P(A and B)
We also know that P(A) = 1/5. Using the formula for the probability of the intersection of two events, we have:
P(A and B) = P(A) * P(B | A)
Substituting the given values, we get:
P(A and B) = (1/5) * P
Since we want to find the values of P for which A and B are independent, we can substitute this expression for P(A and B) in the earlier equation:
3/10 = P - (1/5) * P
Simplifying and solving for P, we get:
P = 3/8
Therefore, A and B are independent if and only if P = 3/8.
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