Answer:
perimeter = 70 yards
Step-by-step explanation:
⭐What is the area of a rectangle?
area = length * width⭐What is the perimeter of a rectangle?
perimeter = 2(length) + 2(width)Strategy1. Make the equation for the area of the given rectangle and solve for x
2. Substitute x into the expressions of the length and width and solve for the perimeter
Working1. Define the expressions of the length and width of the rectangle
width: x
length: 4x
2. Make the equation for the area of the rectangle
[tex]196yd^2 = 4x * x\\196yd^2 = 4x^2[/tex]
3. Solve for x
[tex]\frac{196}{4} = x^2[/tex] . . . . . . . . . . divide both sides by 4
[tex]49 = x^2[/tex]
[tex]\sqrt{49} = \sqrt{x^2}[/tex] . . . . . . . . square root both sides to isolate x
∴ [tex]7 = x[/tex]
4. Substitute x into the expressions of the length and the width
width: x
width = 7
height: 4x
height = 4(7) = 28
5. Solve for the perimeter
[tex]perimeter = 2(length) + 2(width)[/tex]
[tex]perimeter = 2(28) + 2(7)\\perimeter = 56 + 14\\perimeter = 70[/tex]
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Answer:
110 in.²
Step-by-step explanation:
The figure is composed of a parallelogram and a rectangle
Therefore, the area of the figure = area of rectangle + area of parallelogram
= Length*Width + base*height
Length = 10 in.
Width = 6 in.
base = 10 in.
height = 5 in.
Area of the figure = 10*6 + 10*5
= 60 + 50
= 110 in.²
What is 1/4 : 3/4 :: 75 : =
Answer:
75 : 225
Step-by-step explanation:
[tex]\frac{\frac{1}{4} }{\frac{3}{4} } :\frac{75}{y}[/tex]
0.25 × y = 0.75 × 75
0.25y = 56.25
0.25y ÷ 0.25 = 56.25 ÷ 0.25
y = 225
Suppose that $20,000 is invested at 9% interest, compounded annually. After time t, in years, it grows to the amount A given by the function A(t) = $20,000(1.09)
a) Find the amount of time after which there will be $200,000 in the account.
b) Find the doubling time.
After what amount of time will there be $200,000 in the account?
Answer:
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = [log (200,000) -log (20,000)] / log (1.09)
Years = [5.3010299957 -4.3010299957] / 0.037426497941
Years = 1 / 0.037426497941
Years = 26.7190374471
*************************************************
Finding Doubling Time : (We'll calculate $100 becoming $200)
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = log (200) -log (100) / log(1.09)
Years = (2.3010299957 -2) / 0.037426497941
Years = .3010299957 / 0.037426497941
Years 8.0432317278
It takes 8.0432317278 years for money to double at 9% per year.
Source:
http://www.1728.org/compint2.htm
Step-by-step explanation:
Given the example below, determine the property displayed.
7+3=3+7
Answer:
commutative property of addition
Step-by-step explanation:
commutative property of addition
The commutative property of addition allows you to change the order of the numbers in an addition.
For example, 1 + 2 = 2 + 1
When is it best to solve a system of equations using substitution?
Answer:
It is best to solve a system of equations using substitution when one of the equations isolates one of the variables, or when the coefficient of one of the variables is 1 or -1.
Step-by-step explanation:
This makes it easier to substitute one variable for the other, allowing you to solve for the remaining variable. It is also a good idea to check the solution back in the original equations just to make sure it is a valid solution
Answer:
Answer Below
Step-by-step explanation:
It is best to use substitution if one of the variables is isolated or has a coefficient of 1 or -1.
The population growth of a certain city is given by the function P(t) = 0.9(1.5)^t, where t is time in years. Estimate lim P(t), if it exists.
Answer:
Infinity (∞)
Step-by-step explanation:
Graph the function and observe that the function P(t) increases without bound as x increases.
Which of the following equations show the relationship between x and y in the table?
1. y= x+3
2. Y= 3x+1
3. Y=2x+2
4.y=4x
Answer:
y=2x+2
Step-by-step explanation:
you have to substitute x and y in the given equations and which one works
for y=x+3 , 4=1+3 true , 6=2+3 false
for y=3x+1, 4=3*1+3 false
for y=2x+2, 4= 2*1+2 true, 6= 2*2+2 true, 8= 2*3+2 true, 10=2*4+2 true
for y=4x, 4=4*1 true, 6= 4*2 false
The equation below represents the amount of work required to complete a project, where x represents the number of hours each group member must contribute to the project. How many hours does each group member work on the project? x+45/4=4x 2 hours 4 hours 16 hours 3 hours
The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is x+45/4=4x.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
4x-x=45/4
3x=45/4
x=15/4
x=3.75
x≈4 hours
Therefore, option B is the correct answer.
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I just need help appreciate it and have a great day
On solving the provided question, we can say that - by doing the fraction we have 3/12 = 1/4
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
balloons is 12
blew up is 1/3
friend blew up is 5
1/3*12 = 4
4+5 = 9
3/12 = 1/4
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The dimensions of a rectangular Pyramid are shown in the diagram below what is the volume of the rectangular pyramid in cubic
Answer:
160 in³
Step-by-step explanation:
Volume of rectangular pyramid, V = (Length * width * height) / 3
Length = 10 in ; width = 8 in ; height = 6 in
V = (10 * 8 * 6) / 3
V = 160 in³
Kim is thinking of a prime number.
It is in between a multiple of 11 and a factor of 48
What number is Kim thinking of?
Answer:
35
Step-by-step explanation:
Solve algebraically the simultaneous equations 2x^2-y^2=17 x+2y=1
Here we go...
= 2x² - y² = 17
= 2x² = 17 + y²
= x² = 17 + y²/2
= x = √17+y²/2
= x + 2y = 1
= x = 1 - 2y
___________________
Sry,if i misunderstood the question.. do let me know in the comment section
Find the area of the shaded
NO DOCS,LINKS, FILES ETC
LOTS OF POINTS
WILL MARK BRAINLYEST
Answer:
40.5 m²
Step-by-step explanation:
Area of the shaded = area of the square - area of the triangle
Area of square = s²
s = 9 m
Area of square = 9² = 81 m²
Area of triangle = ½*b*h
b = 9 m
h = 9 m
Area of triangle = ½*9*9 = 40.5 m²
Area of the shaded = 81 - 40.5 = 40.5 m²
-69=7v-6
Please show your work, thank you.
What is the length of the longest diagonal
Answer:
pi 3.1415926535897932384626433832795
What IS the approximate length of arc s on the circle below? Use 3.14 for T Round your answer to the nearest
tenth.
Answer:
14.1 inches
Step-by-step explanation:
The formula to be used to find the arc length is Ф = s(arc length) / r(radius)
First we rearrange the formula to find the arc length which would be s = Ф * r
This formula only works in radians so the first step is converting 135° to radians so we would do 135° * π radians/180° which would give us 3π/4
We would then multiply 3π/4 * 6 and get 18π/4, plugging that value into a calculator returns us a value of ≈ 14.137
We then round to the nearest tenth and get an answer of 14.1 inches for the arc length of the circle below
Please help meeeeeee!!!!!!!!
Answer:
A
Step-by-step explanation:
Hi I don't usually upload pictures but I was too lazy to type so I did it on paper. I had to get the numbers in the parenthesis out so I multiplied the + by everything in the parenthesis following the negative and positive multiplication rules. Then, I combined and subtracted like terms.
Hope this helps !!
-Ketifa
How many 25 cents are there in $10?
Answer:
40 quarters are in $10
Step-by-step explanation:
Answer:
40 quarters i think cause there's 4 quarters in a dollar and then 10 x 4 equals 40...
Step-by-step explanation:
If a family has 7 children, in how many ways could the parents have 4 boys and 3 girls as children?
Answer:
add the 3 and 4
Step-by-step explanation:
Given that X≈2 is an approximate solution to x^2+2x-2=5, use the graph to find another approximate solution round your answer to the nearest integer. X≈ ___
The nearest integer that is a solution, gotten through graphing of the quadratic function x² + 2x - 2 = 5, is x = -4
How to find the graphical solution of the functionQuadratic equations when plotted on a graph follows a parabolic path.
To plot the functions there will be table of values that is used in making the graph. The table of values is solved as follows
x² + 2x - 2 = 5 rearranging the equation will result to x² + 2x - 7 = 0
For x = -20, y = (-20)² + 2 * -20 - 7 = 353
For x = 0, y = (0)² + 2 * 0 - 7 = -7
For x = 20, y = (20)² + 2 * 20 - 7 = 433
x y
-20 353
0 -7
20 433
The graph is plotted and attached. From the graph the solution is
x = -3.828, to the nearest integer = -4
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2. What number is a common multiple of
5 and 9?
The table at the right shows data representing a polynomial function. Answer A, B, and C.
a) The degree of the polynomial is 5.
b) The second difference is -726 -126 -6 114 714
c) The difference when they are constant is 480.
What is a polynomial?
A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
y values: -999 -140 -7 0 1 116 945
1st difference 859 133 7 1 115 829
2nd difference -726 -126 -6 114 714
3rd difference 600 120 120 600
4th difference -480 0 480
5th difference 480 480
The degree of a polynomial is the number of difference where it is constant.
The degree of the polynomial function is 5.
The constant is the 5th difference which is 480.
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A hospital near a ski resort records the type of injuries treated during ski season and other seasons and other seasons over a year. the results shown in the table will help determine the medical staff that is required at different times of the year. according to the data in the table, what is the probability that a patient will need to be treated with a broken bone during ski season.
Answer:
The answer is C
Step-by-step explanation:
You have to divide both numerators then the denominater.
So, it would look like: 160 over 90 x 100 over 290
160x100=16 90x290=25 16/25
PLEASE HELP!!!!! PLEASE GIVE A EXPLANATION AND SHOW WORK!!!! THANK YOU!!!!
In 2018, the population will grow to over 700,000. The population of a city in 2010 was 450,000 and was growing at a rate of 5% per year. In what year will the population be over 700,000? Show all work.
Answer:
2019
Step-by-step explanation:
2010: 450,000
2011: (5% of 450,000) + 450,000 = 472,500
2012: (5% of 472,500) + 472,500 = 496,125
2013: (5% of 496,125) + 496,125 = 520,931.25
2014: (5% of 520,931.25) + 520,931.25 = 546,977.8125
2015: (5% of 546,977.8125) + 546,977.8125 = 574,326.703125
2015: (5% of 574,326.703125) + 574,326.703125 = 603,043.038281
2016: (5% of 603,043.038281) + 603,043.038281 = 633,195.190195
2017: (5% of 633,195.190195) + 633,195.190195 = 664,854.949705
2018: (5% of 664,854.949705) + 664,854.949705 = 698,097.69719
2019: (5% of 698,097.69719) + 698,097.69719 = 733,002.582049
Basically, take five percent of the population of the year and add it to the population of the previous year. This is the long way of doing it, but you get the population count for each year.
Find the volume of this square
based pyramid.
10 in
12 in
[? ]in3
Answer:
[tex]v=480 ~in^3[/tex]
Step-by-step explanation:
[tex]v=1/3 Bh[/tex]
[tex]1/3(12)^210=[/tex]
[tex]480 ~in^3[/tex]
------------------------
hope it helps...
have a great day!!!
Can someone help fast please!!!!
Answer:
yes it is
Step-by-step explanation:
Consider the following. 12, 7, 18, 23, 24, 27 Compute the population standard deviation of the numbers. (Round your answer to two decimal place.) (a) Double each of your original numbers and compute the standard deviation of this new population. (Round your answer to two decimal place.) (b) Use the results of part (a) and inductive reasoning to state what happens to the standard deviation of a population when each data item is multiplied by a positive constant k.
Answer:
(a) [tex]\sigma = 7.04[/tex]
(b) [tex]\sigma = 14.1[/tex]
(c) The population standard deviation is multiplied by k
Step-by-step explanation:
Given
[tex]Dataset: 12, 7, 18, 23, 24, 27[/tex]
Solving (a): The population standard deviation
Start by calculating the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{12+7+18+23+24+27}{6}[/tex]
[tex]\mu = \frac{111}{6}[/tex]
[tex]\mu = 18.5[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
This gives:
[tex]\sigma = \sqrt{\frac{(12-18.5)^2 + (7 - 18.5)^2 + (18-18.5)^2 + (23-18.5)^2 + (24 - 18.5)^2 + (27 - 18.5)^2}{6}}[/tex]
[tex]\sigma = \sqrt{\frac{297.5}{6}}[/tex]
[tex]\sigma = \sqrt{49.5833}[/tex]
[tex]\sigma = 7.04[/tex]
Solving (b): Double the dataset and calculate the new population standard deviation
The new dataset is:
[tex]Dataset: 24, 14, 36, 46, 48, 54[/tex]
Start by calculating the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{24+ 14+ 36+ 46+ 48+ 54}{6}[/tex]
[tex]\mu = \frac{222}{6}[/tex]
[tex]\mu = 37[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
This gives:
[tex]\sigma = \sqrt{\frac{(24-37)^2 +(14-37)^2 +(36-37)^2 +(46-37)^2 +(48-37)^2 +(54-37)^2}{6}}[/tex]
[tex]\sigma = \sqrt{\frac{1190}{6}}[/tex]
[tex]\sigma = \sqrt{198.33}[/tex]
[tex]\sigma = 14.1[/tex]
Solving (c): What happens when the dataset is multiplied by k
In (a), we have:
[tex]\sigma = 7.04[/tex]
In (b), when the dataset is doubled,
[tex]\sigma = 14.1[/tex]
This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:
i.e.
[tex]New \sigma = k * \sigma[/tex]
Employee A gets paid $150 weekly, plus $0.50 for each latte they sell. If he was paid $275,
how many lattes did he sell this week?
Answer:
550 lattes he sold this week
Step-by-step explanation:
$275÷$0.50= 550
Irregular polygons has sides that are not equal lenght and angles that are not equal?
TRUE OR FALSE?
Answer:
yeah it's true
Step-by-step explanation:
regular polygon have all equal side and all equal angleIRREGULAR polygon have atleast one unequal side and one unequal angle............THANKS.........
A group of friends went to lunch. The bill before sales tax and tip was $37.50. A sales tax of 8% was added. The group then tipped 18% on the amount after the sales tax was added. What was the amount, in dollars, of the sales tax?
What was the total amount the group paid, including tax and tip?
Sales Tax = $3.00
The total amount paid by the group was $48.15
The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:
Sales tax = $37.50 * 8% = $3.00
The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:
Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15
So the total amount paid by the group was $48.15.