The radius of the area the sprinkler has watered is 8.06 yards.
What is Rotation ?Rotation is spinning around a fixed point with a fixed radius in circular motions.
It is given that a sprinkler rotates 360 degree
The area watered is 204 sq. yards
Radius = ?
A sprinkler rotates in circle
Therefore the area of the circle = π r²
204 = π r²
204 * 7 /22 = r²
r² = 64.91
r = 8.06 yards
Therefore the radius of the area the sprinkler has watered is 8.06 yards.
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3. Determine if the following triangle is a right triangle or not using the Pythagorean Theorem Converse. Triangle with side lengths of: 37 ft, 35 ft, and 12 ft
False, these measures do not form a right triangle.
True, these measures do form a right triangle.
Answer:
false
Step-by-step explanation:
these measure do not form a right triangle
56. Kelly found that the length of the hypotenuse of a triangle was equal to the square root of 125. The length of the hypotenuse was between which two consecutive integers?
A. 10 and 11
C. 30 and 31
B. 11 and 12
D. 62 and 63
Answer: B: 11 and 12
Step-by-step explanation:
- An integer is simply a whole number
- So consecutive integers are simply whole numbers that follow each other (ex: 1, 2, 3)
- The square root of 125 (in decimals) is 11.1803398875, meaning it is higher than 11 but less than 12
- So 11.1803398875 falls between 11 and 12, making the answer B
hope this helps :)
What is the solution to the equation 3 +6=2
Answer: no solution
Step-by-step explanation:
if we simplify this equation, we derive that 9=2.
this is a false statement, which means this equation has no real solutions.
HELP PLEASE
factor completely.
25d^8−80d^4+64=
Answer:
(5d⁴ − 8)²
Step-by-step explanation:
I hope this is helpful!
3. What is the distance from (0,0) to (24,10) on the
coordinate plane?
[tex]\sqrt{(24-0)^{2}+(10-0)^{2}}=\boxed{26}[/tex]
Answer:
26
Step-by-step explanation:
√(24 - 0)2 + (10 - 0)2
= √(24)2 + (10)2
= √676 and that would equal
26
need help with these graphs really quickplease
Answer:
Concave up: (0, infinity)Concave down: (-infinity, 0)a. The graph is concave up in the interval 0 ≤ x ≤ +∞
b. The graph is concave down in the interval -∞ ≤ x ≤ 0
To answer the question, we need to know what intervals are
What are intervals?Intervals are range of values in which a function is valid. It can either be the range of values of input or output of the function.
a. Interval where the graph is concave upFrom the graph, we see that the function is concave up in the interval 0 ≤ x ≤ +∞
So, the graph is concave up in the interval 0 ≤ x ≤ +∞
b. Interval where the graph is concave down
From the graph, we see that the function is concave down in the interval -∞ ≤ x ≤ 0
So, the graph is concave down in the interval -∞ ≤ x ≤ 0
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how to convert 798 in the base of 2
Subtract the largest power of 2 from 798 such that the difference is not negative.
2⁹ = 512 and 2¹⁰ = 1024, so the largest power of 2 smaller than 798 is 2⁹, and
798 = 512 + 286 = 2⁹ + 286
Repeat this process with the remainder, 286.
2⁸ = 256, so
286 = 256 + 30 = 2⁸ + 30
⇒ 798 = 2⁹ + 2⁸ + 30
2⁴ = 16 and 2⁵ = 32, so
30 = 16 + 14 = 2⁴ + 14
⇒ 798 = 2⁹ + 2⁸ + 2⁴ + 14
2³ = 8, so
14 = 8 + 6 = 2³ + 6
⇒ 798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 6
2² = 4, so
6 = 4 + 2 = 2² + 2¹
⇒ 798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 2² + 2¹
or more completely,
798 = 1×2⁹ + 1×2⁸ + 0×2⁷ + 0×2⁶ + 0×2⁵ + 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 0×2⁰
Then the base-2 representation of 798 is
11 0001 1110₂
f CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
Segment AC was dilated by a scale factor of 2 to form A'C' measuring 16 units
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
Let us assume that segment AC was dilated by a scale factor of 2 to form C'A', hence:
A'C' = 2 * AC = 2 * 8 = 16 units
Segment AC was dilated by a scale factor of 2 to form A'C' measuring 16 units
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Suppose water was being drained at from a conical tank. The radius is decreasing at a rate of 2 inch per minute and the height is decreasing at 4 inches per minute. Find the change in the volume when the height is 5 inches and the radius is 6 inches.
The change in volume is -88π
Volume?The volume is nothing but the amount of space occupied by a three-dimensional figure as measured in cubic units.
What is volume change?Volume Change is defined as the variation in the existing volume of the service type which is provided by the Supplier under the Agreement
Given:The radius is decreasing at 2 inches per minute
The height is given as decreasing at 4 inches per minute
So let [tex]\frac{dr}{dt}=-2[/tex] and
[tex]\frac{dh}{dt}=-4[/tex]
and we have radius r=6,
height h=5
The volume of the cone is represented by V as V=[tex]\frac{1}{3}\pi r^{2}h[/tex]
Then
[tex]\frac{dv}{dt}=\frac{\pi }{3}[r^{2}\frac{dh}{dt} +h*2r\frac{dr}{dt}][/tex]
[tex]=\frac{\pi }{3}[6^{2}(-4)+5*2(6)(-2)][/tex]
[tex]=\frac{\pi }{3}[36(-4)+5(12)(-2)]\\ =\frac{\pi }{3}[-144+(-120)]\\ =\frac{-264}{3}\pi \\ =-88\pi[/tex]
So the volume change is [tex]-88\pi[/tex]
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Do anyone know thissss
Answer: False
Step-by-step explanation:
This is not a function because the single input [x] of 6 has outputs [y] of 2 and 4, and the single input [x] of 12 has outputs [y] of 2 and 4.
A function must have only one output [y-value] for every input [x-value].
What will be the answer for 25 out of 100?
Hello !
[tex]\frac{25}{100}=0.25[/tex]
Have a nice day ;)
Answer:
25
Step-by-step explanation:
25
Answer: 25% of 100 is 25.
61. The true proportion p of people who give a favorable
rating to Congress is 8% with a margin of error of
1.5%. Describe this statement using an absolute
value equation.
Answer:
The expression for the statement using absolute value notation is [tex]$|p-0.08| \leq 0.015$[/tex].
Step-by-step explanation:
It is given in the question that the true proportion p of people who give a favourable rating to Congress is 8% with a margin of error of 1.5%. It is required to express the statement using absolute value notation.
To express the statement using absolute value notation, deduce the statement in the form of an equation.
The error margin for the hypothesis is 1.5% which implies the absolute difference between p and 8% should be less than or equal to 1.5%.[tex]$$|p-0.08| \leq 0.015$$[/tex]
Hi I don't know how to do this question
Answer:
7 (option B)
Step-by-step explanation:
the area of a trapezoid can be found using the formula:
[tex]A = \frac{a+b}{2}h[/tex]
where
A: area
a: base
b: other base
h: height
here, we can plug in our known variables to solve for h (height)
A: 119
a: 10
b: 24
h: ??
[tex]A = \frac{a+b}{2}h[/tex]
[tex]119 = \frac{10+24}{2}h[/tex]
{now, simplify!}
[tex]119 = \frac{10+24}{2}h[/tex] {add 10 + 24}
[tex]119 = \frac{34}{2}h[/tex] {divide 34 by 2}
119 = 17 · h
119 = 17 · h
÷ 17 ÷17 {divide both sides by 17to isolate h}
7 = h
So, the height (h) of this trapezoid is 7
hope this helps! have a lovely day :)
However, in the anonymous follow-up survey that re-interviewed the respondents, only 80 percent responded that they would be open to supporting a woman candidate. What could be generating these different results
Social-desirability biases is the sort of response bias that is the tendency of the survey respondent to answer the question in a manner that is favorable to others.
As Maria found that most respondents 98% of the voters were open to support women candidates. The social desirably bias poses a serious problem during the self-reporting as the bias interferes with the interpretations of the average tendencies.
As however during the anonymous survey of the voters or respondents showed only 80% of them would support the women candidate.
Hence the social desirability bias is the main culprit for such a response.
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A graph titled Cost of a Lunch in a School's Cafeteria has Days since school started on the x-axis and cost of lunch (dollars) on the y-axis. A horizontal line is at y = 2.5.
Which is correct about the graph’s slope?
Its slope is positive.
Its slope is negative.
Its slope is zero.
It has no slope.
The true statement about the graph's slope is (c) Its slope is zero.
How to determine the true statement?From the question, we have:
A horizontal line is at y = 2.5.
The horizontal line implies that the cost of lunch do not change
Horizontal lines have a slope of 0
Hence, the true statement about the graph's slope is (c) Its slope is zero.
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What can be concluded about the line represented in the table? Select 3 options.. x y –6 –7 2 –3 8 0 The slope is 2. The slope is One-half. The y-intercept is –4. The y-intercept is 8. The points (–2, –5) and (8, 0) are also on the line. The points (–5, –2) and (1, 10) are also on the line.
The correct statements regarding the linear function are given as follows:
The slope is 1/2.The y-intercept is -4.The points (–2, –5) and (8, 0) are also on the line.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the line goes through points (-6,-7) and (8,0), hence the slope is given by:
[tex]m = \frac{0 - (-7)}{8 - (-6)} = \frac{7}{14} = \frac{1}{2} = 0.5[/tex]
Hence:
y = 0.5x + b
When x = 8, y = 0, hence the y-intercept is given as follows:
0 = 0.5(8) + b
b = -4.
When x = -2, we have that:
y = 0.5(-2) - 4 = -1 - 4 = -5.
The points (–2, –5) and (8, 0) are also on the line.
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Answer:
B,C,E
Step-by-step explanation:
took the test on edge and got 100
Jack and Susie want to save to buy a trampoline for their children. They each open a savings account that earns 1.5% a year. Jack opens his account with $1,000, and Susie opens her account with $800.
x = number of years
The following functions represent the value of the savings accounts in x years:
Jack’s savings account: f(x) = 1000(1.015)x
Susie’s savings account: g(x) = 800(1.015)x
Which function represents the total amount Jack and Susie will save in x years?
200(1.015)x
1800(1.015)x
1800(1.015)2x
1800(1.030)x
The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let f(x) and g(x) represent the value in the savings account of Jack and Susie respectively after x years. Hence:
f(x) = 1000(1.015)ˣ, g(x) = 800(1.015ˣ
Hence:
Total savings = 1000(1.015)ˣ + 800(1.015)ˣ = (1.015)ˣ[1000 + 800] = 1800(1.015)ˣ
The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ
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The diagram shows AKLM. Which term describes point N?
K
L
A. Orthocenter
N
B. Circumcenter
C. Centroid
D. Incenter
The term that describes point N is centroid. The correct option is C. Centroid
Centroid of a triangleThe centroid of a triangle is the point in which the three medians of the triangle intersect.
The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.
In the given diagram, we can observe that the lines join the midpoints of each side to the corresponding opposite vertex.
Point N is the point where the lines intersect.
Hence, the term that describes point N is centroid. The correct option is C. Centroid
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Answer:
B. Circumcenter
Have an Amazing day/night!!
if Ben has 10.4L of deride and Madison has 940 cal of diesel how much does the pair have altogether
Based on the calculations, the total volume which the pair have altogether is equal to 19.8 Liters.
How to calculate the total volume?In Science, volume is a unit of measurement which indicates the capacity of a container and it has the following units:
Liters (L)Centiliter (cL)Cubic meter (m³)Next, we would convert the volume of Madison's diesel in centiliter to liter as follows:
1 centiliter = 0.01 liter
940 centiliter = X liter
Cross-multiplying, we have:
X = 940 × 0.01
X = 9.4 L.
Total volume = 9.4 + 10.4
Total volume = 19.8 Liters.
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Assume that they all agree on the sample size and the sample mean use the pairs below to select the team that has the smallest sample standard deviation?
Step-by-step explanation:
A.Confidence Level: 99.7%; Confidence Interval: 42 to 48
B.Confidence Level: 95%; Confidence Interval: 43 to 47
C.Confidence Level: 68%; Confidence Interval: 44 to 46
D.Confidence Level: 95%; Confidence Interval: 44 to 46
According to the partial construction shown, what is the next step in constructing a line perpendicular to a point on the line?
O Place compass at point D, and draw an arc that intersects the arc above DF.
1
O Place compass at point F, and draw an arc that intersects the arc above DF-
O Place compass at point P, and draw an arc above DF
O Place compass at point P, and draw an arc below DF
The next step in constructing a line perpendicular to a point on the line is A. Place a compass at point D, and draw an arc that intersects the arc above line DF.
To make a perpendicular line:
Draw a line segment like DFKeep the point on D and make an arc by increasing the length of the compassKeep the point on F and make an arc like same as beforeName the point as any meeting on the drawn arcConnect it to the point with PTherefore, the next step would be to Place a compass at point D, and draw an arc that intersects the arc above line DF.
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Which of the following is equivalent to (8 – 5) ÷ 23 ?
A 3/8
B 19/8
C 27/8
D 1/125
Answer:
none
Step-by-step explanation:
(8-5)=3
8-5÷23
=179/23
Using the function p(t)=5*2^t, estimate the boa constrictor population in 2 years, 3 years, and 4 years. Show your work.
Answer:
2 years: 203 years: 404 years: 80Step-by-step explanation:
There are several ways you can find the values of an exponential function for different values of the independent variable. You can read them from its graph, evaluate the formula, or recognize the relationship between the values.
P(t) for different tThe graph shows you the population is 10 in year 1, up by a factor of 2 from the population of 5 in year 0. The exponential nature of the function means the population will double in each of the next few years:
2 years: 2 × 10 = 20
3 years: 2 × 20 = 40
4 years: 2 × 40 = 80
__
Additional comment
You can always use a calculator to evaluate the function for different values of t.
2 divided by 9 = 5/2 divided by 5/4
The given equality 2 divided by 9 = 5/2 divided by 5/4 is seen to be; False because LHS ≠ RHS
How to solve equalities?We are given the equality;
2 divided by 9 = 5/2 divided by 5/4
We want to check whether the left hand side of the equality is equal to the right hand side. Thus;
Left hand side can be expressed as;
2 divided by 9 = 2/9
Now, right hand side can be expressed as;
5/2 ÷ 5/4
⇒ (5/2) * (4/5)
⇒ 2
Therefore we can see that LHS is not equal to RHS and so the equality is false.
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5. Please answer the question on exponential growth or decay. Round to
the nearest whole number or penny if the question is concerning money if
necessary
For tax purposes, a car rental company
assumes each car in their fleet depreciates
by 7% per year. If the initial value of a
car is $32,200.00, what will the value be
when the car is 9 years old?
The value of this car when it is 9 years old is equal to $16,757.00.
How to calculate the value?In order to determine the value of this car when it is 9 years old, we would use an exponential function which also relates to compound interest as follows:
A = P(1 - r)^t
Substituting the given parameters into the formula, we have;
A = 32,200(1 - 0.07)^9
A = 32,200(0.93)^9
A = 32,200 × 0.5204
A = $16,757.00.
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If f(x) = 5x - 7, what is {3)?
O A. 22
O B. 2
O c. 1
• D. 8
Work Shown:
f(x) = 5x - 7
f(3) = 5(3) - 7 .... every x replaced with 3
f(3) = 15 - 7
f(3) = 8
[tex] \: [/tex]
Given :
f(x) = 5x - 7x = 3To Find :
What is the value of x ?Calculating the value of x :
[tex]\sf : \implies \: 5x - 7[/tex]
[tex]\sf : \implies \: 5(3) - 7[/tex]
[tex]\sf : \implies \: 15 - 7[/tex]
[tex]\bf : \implies \: 8[/tex]
Hence,
[tex] \implies \boxed{ \bf \: \therefore \: The \: value \: of \: x \: is \: 8 \: } \\ \\ [/tex]
10. What is the perimeter of the triangle with sides 15 in, 20 in, and 25 in?
O 72 in
60 in
300 in
O 150 in
k
Answer:
P = 60 inches
Step-by-step explanation:
Perimeter is the distance around the outside of a shape. So, to find perimeter, add up all the sides.
The side lengths were given, add them:
15 + 20 + 25
= 60
The perimeter is 60 inches.
Time Remaining
59:49
Triangle E G F is cut by line H J. Line H J goes from side E G through side G F. Lines E F and H J are parallel.
Using the side-splitter theorem, which segment length would complete the proportion?
StartFraction G H Over H E EndFraction = StartFraction question mark Over J F EndFraction
GF
JH
GJ
EF
Using the side-splitter theorem, the segment length that would complete the proportion is GJ.
How to illustrate the information?It should be noted that the side splitter theorem states that when a line intersects two sides of a triangle and is also parallel to the third side, then it'll divide the sides proportionally.
From the information given, it can be deduced that EF and HJ are parallel while H is on the side EG and J is on GF. Therefore, according to the theorem, GH/HE = GJ/JF
Therefore, the correct option is GJ.
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Answer: C.
Step-by-step explanation: Trust Me! It was correct on the Edge quiz! :)
a+a+b=14 b+b+c=08 a+b+c=18 b=
The value of b in the expression is -2.
How to find the variable in an expression?a + a + b = 14
b + b + c = 8
a + b + c = 18
Therefore,
2a + b = 14
2b + c = 8
c = 8 - 2b
Hence,
a + b + 8 - 2b = 18
a - b = 18 - 8
a - b = 10
2a + b = 14
a - b = 10
3a = 24
a = 8
8 - b = 10
b = 8 - 10
b = -2
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Answer:
a = 8
b = -2
c = 12
Step-by-step explanation:
a + a + b = 14
2a + b = 14 ⇒ ( 1 )
b + b + c = 8
2b + c = 8 ⇒ ( 2 )
a + b + c = 18 ⇒ ( 3 )
First, let us make a as the subject in equation 1.
2a + b = 14
2a = 14 - b
[tex]a=\frac{14-b}{2} \\a = 7-\frac{b}{2}[/tex] ⇒ ( 4 )
Let us make c as the subject in equation 2.
2b + c = 8
c = 8 - 2b ⇒ ( 5 )
Now it is clear for us that, we can replace a & c with ( 7 - b / 2 ) & ( 8 - 2b ) respectively.
And now let us solve the equation 3 to find the value of b.
[tex]a+b+c=18\\\\7-\frac{b}{2} +b+8-2b=18\\\\Combine\: \:like\:\: terms.\\\\[/tex]
[tex]15-\frac{b}{2} -b=18\\\\\frac{15*2}{1*2} -\frac{b}{2}-\frac{b*2}{1*2}=18\\\\\frac{30}{2} -\frac{b}{2}-\frac{2b}{2}=18\\\\\frac{30-3b}{2} =\frac{18}{1} \\\\Use\:\: cross\;\: multiplication[/tex]
[tex]30-3b=18*2\\\\30-3b=36\\\\30-36=3b\\\\-6=3b\\\\-2 = b[/tex]
And now let us find the value of a
For that, let us use the equation 1. There, we can replace b with ( -2 ) to find the value of a.
[tex]2a+b=14\\\\2a-2=14\\\\2a = 14+2\\\\2a=16\\\\a=8[/tex]
Now, let us find the value of c.
For that, let us take the equation 2. There also, we can replace b with -2 to find the value of c.
[tex]2b+c=8\\\\2*-2+c=8\\\\-4+c=8\\\\c=8+4\\\\c=12[/tex]
What is the first quartile of the data set: 11, 24, 13, 18, 16, 21, 23, and 29?
Answer: 15, 15, 16, 21, 23, 29
Step-by-step explanation: