The total area of the shaded regions is 72 unit sq.
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
Given that square has an area of 196.
The region contains two overlapping squares that is the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1.
We can come up with equations as;
Since the area of their overlap is 1 then the side length is 1 unit.
Let the length of the smaller square is x.
The length of the larger square is 2x.
Therefore,
x + 2x - 1 = 3x - 1
Thus, 3x - 1 = 14
x = 5
The area of larger square = 100
The smaller one is 25
The area of shaded region;
196 - 124 = 72.
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an airplane flying at an elevation of 3,500 ft., directly above a straight highway. two motorists are driving cars on the highway on opposite sides of the plane. the angle of depression to one car is 31 degrees and to the other is 53 degrees. how far apart are the cars?
The first and second cars are 7724 feet apart from each other.
The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:
tan = opposite/ adjacent
⇒ tan(31°) = 3500/x
⇒ 0.60086 = 3500/x
⇒ 0.67 x = 3500 [ rounding up 0.60086 = 0.67]
⇒ x = 5223.88
That means the first car is 5223.88 feet from the point on the highway below the plane.
We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:
tan(53°) = 3500/x
⇒ 1.327 = 3500/x
⇒ 1.4x = 3500 [ rounding 1.327 = 1.4]
⇒ x = 3500/1.4
⇒ x = 2500
That means the second car is 2500 feet from the point on the highway below the plane.
Add the two distances together to get the total distance from car to car:
5223.88 + 2500.00 = 7723.88
So, rounded to the nearest foot, the cars are 7724 feet apart.
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Write the equation of the line
that is perpendicular to y=-2x
and passes through (-2, -1)
A) y = 1/2x + 1
B) y = -3x - 7
C) y = -2x - 5
D) y = 1/2x
E) y = 1/2
there are 6 circles and 9 triangles what is the simplest ratio of circles to triangles?
Tiffany’s allowance is reduced $1. 25 every time she forgets to clean her room. If she forgets to clean her room 7 times this month, by how much money is tiffany’s allowance reduced?.
The amount of money that is reduced from Tiffany's allowance is $8.75
The amount of allowance reduced every time she forget to clean her room = $1.25
Number of times that she forgets to clean her room = 7 times this month
The amount of money is reduced from Tiffany's allowance = Number of times that she forgets to clean her room × The amount of allowance reduced every time she forget to clean her room
Here we have to use the multiplication to find the amount
Substitute the values in the equation
The amount of money is reduced from Tiffany's allowance = 7 × 1.25
Multiply the terms
= $8.75
Hence, the amount of money that is reduced from Tiffany's allowance is $8.75
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Which value of x solves the equation cos x° = sin (20° + x°), where 0 < x < 90?
sin x = cos (90 - x) or cos x = sin (90 - x)
This identity holds when the two angles are complementary
i.e. they sum up to 90 degrees.
The value of x is 35°
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cos x° = sin (20° + x°), where 0 < x < 90
We know that,
sin x = cos (90 - x) or cos x = sin (90 - x)
This identity holds when the two angles are complementary
i.e. they sum up to 90 degrees.
x + 90 - x = 90
Now,
cos x = sin (20 + x)
x + 20 + x = 90
2x + 20 = 90
2x = 70
x = 35
Thus,
The value of x is 35°
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I need help please!!!!!
Jess has to spend 12000 on expenses each year. If that amount of money is 30 percent of her salary, then how much much does jess make as an administrador per year? Round your answer to the nearest whole number if necessary
Jess makes $40000 per year as an administrator .
What is an administrator?
Administrators support the efficient operation of offices by carrying out clerical jobs and initiatives. You can be planning project meetings in the construction business as an administrator.
Main Body:
Expenses incurred by Jess = $12000
According to the question , 30% of his annual salary is his expenses
Let his annual salary be x.
so,
⇒30% of x = 12000
⇒ (30/100)*x = 12000
⇒x = 12000*100/30
⇒x= 40000
Hence the salary made by Jess in a year is $40000.
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for 50 points and brainliest! (Part 2)
Lesson: Linear Inequalities in Two Variables
Directions: Answer the following problem. And graph it.
Please I want a complete answer with a clear explanation. Thank you in advance :)
Answer:
4.a) Broken line.
4.b) True.
5.a) Solid line.
5.b) True.
Step-by-step explanation:
When graphing inequalities:
< or > : broken line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Question 4Given inequality:
[tex]y < -\dfrac{1}{2}x+2[/tex]
a) As the "<" sign has been used, the line will be a broken line.
b) Substitute (0, 0) into the inequality:
[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 0 & < -\dfrac{1}{2}(0)+2\\0 & < 0+2\\0 & < 2\end{aligned}[/tex]
As zero is less than 2, the solution at (0, 0) is true.
Graphing the inequality
Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:
[tex]\begin{aligned}x=-2: \quad y &=-\dfrac{1}{2}(-2)+2\\y &=1+2\\y&=3\end{aligned}[/tex]
[tex]\begin{aligned}x=4: \quad y &=-\dfrac{1}{2}(4)+2\\y &=-2+2\\y&=0\end{aligned}[/tex]
Plot the points (-2, 3) and (4, 0).
Draw a broken straight line through the points.
Shade below the line.
Question 5Given inequality:
[tex]2x+5y \leq 10[/tex]
a) As the "≤" sign has been used, the line will be a solid line.
b) Substitute (0, 0) into the inequality:
[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 2(0)+5(0) &\leq 10\\0+0 &\leq 10\\0 &\leq 10\end{aligned}[/tex]
As zero is less than 10, the solution at (0, 0) is true.
Graphing the inequality
Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:
[tex]\begin{aligned}x=-5: \quad 2(-5)+5y &=10\\-10+5y &=10\\5y &=20\\y&=4\end{aligned}[/tex]
[tex]\begin{aligned}x=5: \quad 2(5)+5y &=10\\10+5y &=10\\5y &=0\\y&=0\end{aligned}[/tex]
Plot the points (-5, 4) and (5, 0).
Draw a solid straight line through the points.
Shade below the line.
Find the value of 49^-1/2
Find the value of (27/125)^2/3
The value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.
According to the question,
We have the following expressions:
[tex]49^{-1/2}[/tex]
Now, we will convert the base of these expressions in exponential form in such a way the denominator of powers will get divided:
[tex]7^{2*(-1/2)}[/tex]
[tex]7^{-1}[/tex]
Or it can be 1/7 because we have positive exponents.
Now, we have another expression:
[tex](\frac{27}{125}) ^{2/3}[/tex]
We will follow the same steps to solve this expression:
[tex](\frac{3}{5}) ^{3*2/3}[/tex]
[tex]\frac{3}{5} ^{2}[/tex]
Now, expanding the numerator and denominator of the fraction by multiplying them two times, we have the following fraction:
9/25
Hence, the value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.
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Which graph represents a function with direct variation?
Graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
The graph is shown in the pictures
As we know,
The proportional relationship can be defined as:
y ∝ x
y = kx
k is the constant of proportionality:
y = kx is the equation of the line which passes through the origin.
Graph four passes through origin.
Thus, graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.
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Farmer joe separates his farm into 10 regions. He then randomly selected 5 trees from each region to estimate the number of apples produced on his apple tree farm. What type of sampling is this?.
it's a Stratified sampling
suppose that pulse rates among healthy adults are normally distributed with a mean of 80 beats/minute and a standard deviation of 10 beats/minute. what proportion of healthy adults have pulse rates that are more than 86 beats/minute? round your answer to at least four decimal places.
The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%
Z- Score gives an idea how far a data point is from mean .
z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .
Given , mean = 80beats/minute
standard deviation = 10 beats/minute
x = 86 beats/minute
Applying z score formula :
z-score = (x-mean)/standard deviation
P(x>86) = P(z > 86-80/10)
=P(z>6/10)
=P(z>0.6) = 1 - P(z<0.6)
= 1 -0.7257
= 0.2742
Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742
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fill in the table using this function rule y=-2x-5
For given equation y = -2x - 5,
x y
-4 3
-2 -1
0 -5
2 -9
In this question we have been given an equation y = -2x - 5
We need to complete the table using given function rule.
for x = -4,
y = -2(-4) - 5
y = 8 - 5
y = 3
for x = -2,
y = -2(-2) - 5
y = 4 - 5
y = -1
for x = 0,
y = -2(0) - 5
y = -5
for x = 2,
y = -2(2) - 5
y = -4 - 5
y = -9
Therefore, for given equation y = -2x - 5,
x y
-4 3
-2 -1
0 -5
2 -9
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Select the correct answer.
Solve the following equation by completing the square.
4z²-16z +8=0
O A z = 2 + √2 orz = 2-√2
OB.
z = 2 + √2 or z = − 2 + √2
z = −2+ √2 orz = -2-√2
z = 4 or z = 0
O C.
O. D.
Reset
Next
Step-by-step explanation:
4z-16z+8=0
[4×8]=32
factors of 32
1,2,4,8,....
in a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. one car will be selected at random from the parking lot. if each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green?
If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .
In the question ,
it is given that ,
total numbers of car in the parking lot = 200 cars
number of white cars = 50
number of red cars = 30
number of silver cars = 20
let the number of green cars be "x" ,
So , the number of green cars possible = 200 - 100 = 100
that means x ≤ 100 .
So , P(green) = x/200
Option(a)
p = 0.2 ,
So , x/200 = 0.2
x = 40
Option(b)
p = 0.1 ,
So , x/200 = 0.1
x = 20
Option(c)
p = 0.6 ,
So , x/200 = 0.6
x = 120
Option(d)
p = 0.5 ,
So , x/200 = 0.5
x = 100 ,
We can see that only option(c) gives the number of green cars as 120 , which is not possible .
Therefore , If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .
The given question is incomplete , the complete question
In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. one car will be selected at random from the parking lot. if each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green ?
(a) 0.2
(b) 0.1
(c) 0.6
(d) 0.5
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Given the exponential growth function †(x) = 75(1.0025)*
What is the initial value of the function?
What is the growth factor, or growth rate of the function (as a percent)?
The initial value of the function is 75.
The growth factor or growth rate of the function as a percent is 0.25%
An exponential growth model is defined as :
F(x) = A( 1 + r)^x
Where;
A = Initial amount,
r = rate of increase
x = time
Comparing the exponential growth function with the exponential growth model given;
f(x)=75(1.0025)ˣ
A = 75 = Initial amount
The growth rate of the model expressed as a percentage :
Taking :
(1 + r) = 1.0025
1 + r = 1.0025
r = 1.0025 - 1
r = 0.0025
Expressing r as a percentage:
r = 0.0025×100
= 0.25%
Hence we get the required answers.
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[50 Points help!] A circle graph shows that an office supply store spends a total of $1200 per month on expenses. If the company spends $300 on paper, what would be the measure of the central angle for paper in the circle graph?
A. 75 degrees
B. 90 degrees
C. 120 degrees
D. 150 degrees
E. 175 degrees
Answer:
B. 90 degreesStep-by-step explanation:
The circle represents a 360° angle.
Total spending corresponds to full circle and part of it spent on paper.
The ratio of paper over total is:
300/1200 = 1/4This is the part of circle which is:
360°*1/4 = 90°Correct choice is B.
Answer:
b) 90 degrees
Step-by-step explanation:
Forming the expression,
→ 360° × (300/1200)
Let's solve given expression,
→ 360° × (300/1200)
→ 360° × (1/4)
→ (360°/4)
→ 90°
Hence, the answer is 90°.
what is the answer to 5=6h+5(h-5)
Answer: the answer is 30/11
Step-by-step explanation:
hope it helps:)
8. Emily predicted her car
payment to be
$250 each month. Her actual car
$275 each month.
payment is
Enrique predicted his car
payment to be $200 each month. His actual
car payment is $225 each month.
a. By what percent was Emily's prediction off?
b. By what percent was Enrique's prediction off?
Emily's prediction was off by 9.09%
Enrique's prediction was off by 11.11%
What is a percentage?The percentage is calculated by dividing the required value with the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Emily:
Each month payment = $250
Each month actual payment = $275
The percentage prediction is off by.
= (275 - 250) / 275 x 100
= 25/275 x 100
= 9.09%
Enrique:
Each month payment = $200
Each month actual payment = $225
The percentage prediction is off by.
= (225 - 200)/225 x 100
= 25/225 x 100
= 11.11%
Thus,
Emily's prediction was off by 9.09%
Enrique's prediction was off by 11.11%
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What’s the answer to this ?? Does anyone know it ??
Please explain the steps and how you got the answer ): i have a ton more of these to answer and i need to know how to do it.
ONLY ANSWER IF YOU KNOW IT ! WILL REPORT UR ANSWER IF U PUT ANYTHING ELSE.
The equilibrium quantity is 97 items and equilibrium price is $582
The equation of the price when quantity demanded
p = 873 - 3q
The equation of the price when quantity supplied
p = 6q
At equilibrium price and quantity
873 - 3q = 6q
Move the like terms to one side
6q + 3q = 873
Add the like terms
9q = 873
q = 873 / 9
Divide the terms
q = 97 items
Substitute the value of q in the equation 2
p = 6q
p = 6 × 97
Multiply the terms
p = $582
Hence, the equilibrium quantity is 97 items and equilibrium price is $582
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a college believes that 28% of applicants to that school have parents who have remarried. how large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 6 percentage points with 95% confidence?
The sample size required for the true proportion of students who have parents who have remarried is 607.
What is termed the Confidence Interval?
The confidence interval is indeed the range of values within which you expect your forecast to fall a certain proportion of the time if you repeat your experiment or re-sample a population in the same manner.
The alpha value determines the confidence level, which is the percentage of times you anticipate reproducing an approximate between both the upper and lower limits of the confidence interval.
The above problem is based on the use of determining sample size to estimate the true percentage of students given the constraints.
We may also need to consult the table to determine the Z value.
For the given question,
α = 0.5
Consider the Z-table,
Zα/2 = Z (0.1/2)
Z (0.025) = 1.96
Let 'n' be the sample size required for the true proportion of students who have parents who have remarried.
For calculating the margin error 'E' is given 3%.
n = Z² (α/2) / E² × (P°(1 - P°))
Put the given values.
n = (1.96)² / (0.03)² × (0.28(1 - 0.28))
On solving,
n = 4268.444(0.2016)
n = 860.51
n ≈ 860.51
Thus, the sample size required for the true proportion of students who have parents who have remarried is 860.
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2) Ahmad had 15 coins in nickels and quarters. He knows he has a $2.95 in change. How many
quarters and nickels does he have?
Answer:
11 quarters and 4 nickels
Hope this helps! :3
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The ratio of cats to dogs in a shelter is 3:8.
Check all statements that must be true based on the statement above.
If none of the statements is true, check "None of the above".
There are 8 cats to every 3 dogs in the shelter.
O For every 8 cats in the shelter, there are 3 dogs.
There are 3 dogs to every 8 cats in the shelter.
There are 8 dogs to every 3 cats in the shelter.
None of the above
Answer:
Step-by-step explanation:
no
A circle has a radius of 16 ft. What is the area of the circle in terms of π?
Responses
A. 256π ft2
B. 128π ft2
C. 64π ft2
D. 32π ft2
The area of the circle in terms of π if the circle has a radius of 16 ft is 256 π ft^2. Option A is correct.
First, let us understand the circle:
A circle is nothing more than a round form with no corners or line segments. In geometry, it is a closed curve shape.
Some formulas related to circle:
Area of the circle = πr^2
Circumference of the circle = 2πr
where, r = radius of the circle.
We are given;
A circle has a radius of 16 ft.
We need to find the area of the circle in terms of π.
Area of the circle = πr^2
Put the value of r in the above formula:
Area of the circle = π 16^2 * ft^2
Area of the circle = 256 ft^2
Thus, the area of the circle in terms of π if the circle has a radius of 16 ft is 256 π ft^2. Option A is correct.
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Answer:
option A
Step-by-step explanation:
Evaluate the expression if a = −2, b = −3, c = 2, x = 2.1, y = 3, and z = −4.2.
4a−|3b+2c|
The value of the expression when evaluated is: -18.
How to Evaluate an Expression?Evaluation of an expression involves plugging in the values of the given variables and then solving to determine the value of the expression in it's simplest form.
Given the expression, 4a - |3b + 2c|, to evaluate, substitute a = -2, b = -3, c = 2 into the expression and solve:
4(-3) - |3(-3) + 2(2)|
-13 - |-9 + 4|
-13 - |-5|
-13 - 5
= -18
The value of the expression is: -18.
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write the percent 144 as a decimal
HELP! I WILL NAME YOU THE BRAINLIEST. Solve the system by graphing.
y = x + 4
-x + y = -3
Distribute to create an equivalent expression with the fewest symbols possible.
4(x - 2 + y) =4(x−2+y)
The equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is 4(x - 2 + y). The equivalent expression will be solved as,
E = 4(x - 2 + y)
E = 4x - 8 + 4y
Therefore, the equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.
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20 units rotated to 90 cc reflected over the x axis and translated 6 units down is ?
Answer:
.
Step-by-step explanation:
Need help on algebra
The required value of the given equation when x = 5 is y = 585.5
What is an algebra ?The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.
Given : y = 114.50x + 13
To find ; The value of this equation when x = 5
Thus to find this value we have to simply substitute the value of x in the given equation
Hence, we will get ,
y = 114.50 × 5 + 13
this implies y = 572.5 + 13
which is equal to y = 585.5
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