Answer:
$550+/-$20.79
= ( $529.21, $570.79)
Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $550
Standard deviation r = $75
Number of samples n = 50
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
$550+/-1.96($75/√50)
$550+/-1.96($10.60660171779)
$550+/-$20.7889393668
$550+/-$20.79
= ( $529.21, $570.79)
Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points? It takes Aaron about 1 hour to mow 2 acres. Aaron’s rate for mowing lawns is 0.5 acres per hour. The ratio of acres to time is 5 acres to 3 hours. The rate to mow a lawn is 0.6 hours per acre
Answer:
Slope of this line is given by:
Aaron’s rate for mowing lawns is 0.5 acres per hour
Step-by-step explanation:
It is given that time is tracked by Aaron related to x coordinate.
and the area of land mowed in acres is related to y coordinate.
Two of his points are given as:
(3, 1.5) and (5,2.5)
We know that the coordinates are represented in the form of (x,y)
i.e. first coordinate represents x coordinate and
second coordinate represents y coordinate.
So, it can be observed that:
[tex]x_1=3, y_1=1.5\\x_2=5, y_2=2.5[/tex]
Change in x coordinate = [tex]x_2-x_1=5-3 = 2[/tex]
i.e. total time taken is 2 hours.
Change in y coordinate = [tex]y_2-y_1=2.5-1.5 = 1[/tex]
i.e. total land mowed taken is 1 acre.
In other words, it takes 2 hours for Aaron to mow 1 acre of land.
So, "option 1) It takes Aaron about 1 hour to mow 2 acres." is incorrect.
Rate of mowing lawn is the land mowed by Aaron in 1 hour.
Land mowed in 2 hours = 1 acre
Land mowed in 1 hours = [tex]\frac{1}{2}[/tex] acre i.e. 0.5 acre
Also, slope of a line is given as:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here [tex]y_2 - y_1 = 1[/tex]
[tex]x_2 - x_1 = 2[/tex]
As per formula:
[tex]m = \dfrac{1}{2} = 0.5[/tex]
So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.
Using the slope concept, it is found that the correct option is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.
---------------------------
A linear function has the following format:
[tex]y = mx + b[/tex]
The slope is m, which is the rate of change, that is, by how much the output y changes when the input changes by 1.---------------------------
In this question, the input is the time in hours and the output is the area of land mowed, thus the slope represented the rate of area mowed per hour.Two points, (3, 1.5) and (5, 2.5). The slope is change in y divided by the change in x, thus:[tex]m = \frac{2.5 - 1.5}{5 - 3} = \frac{1}{2} = 0.5[/tex]
Thus, the correct option is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.
A similar problem is given at https://brainly.com/question/17460142
In a pile of playing cards, there are 6 hearts, 4 clubs, and 8 spades. What is the probability that you will draw a heart?
1. 1/2
2. 1/6
3. 1/3
4. 1/12
Answer:
1/3
Step-by-step explanation:
The probability that you will draw a heart is 1/3, the correct option is 3.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
Number of cards= 6 hearts, 4 clubs, and 8 spades
Now,
To find the probability of drawing a heart, we need to divide the number of hearts by the total number of cards in the pile. The number of hearts is 6 and the total number of cards is 6 + 4 + 8 = 18.
The probability of drawing a heart is 1/18=1/3
Therefore, by probability the answer will be 1/3.
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A 74-inch rake is leaning against a wall. The top of the rake hits the wall 70 inches above the ground. How far is the bottom of the rake from the base of the wall?
Answer:24
Step-by-step explanation:
By Pythagoras
a^2=b^2 +c^2
74^2-70^2=c^2
C=√576
C=24
(THIS IS 90 POINTS!!!)
Solve the following system of equations:
x − 2y = 5
2x − 4y = 10
A. Infinitely many solutions
B. No solutions
C. (0, 0)
D. (5, 10)
Answer:
A. Infinitely many solutions
Step-by-step explanation:
x − 2y = 5 | × (- 2)
2x − 4y = 10
- 2x + 4y = - 10
2x - 4y = 10
----------------------- +
- 2x + 2x + 4y - 4y = - 10 + 10
0 = 0
A. Infinitely many solutions
16+12x-5x+4y-7 Simply the expression
Answer:
Combing like terms we get 7x + 4y + 9.
A line that passes through the point (x,y), with a y intercept of band a slope of m, can be represented by the equation y = mx + b.
A line is drawn on the coordinate plane that passes through the point (3.-6) and has a slope of 4. The y intercept of the line is
Answer:
y = 4x - 18
Step-by-step explanation:
Write out y = mx + b.
The slope of the line in question is 4. Thus we have y = 4x + b.
Finally, substitute -6 for y, 3 for x and solve for b:
-6 = 4(3) + b, or -6 = 12 + b. Then b = -18, and the equation of this line is
y = 4x - 18
Answer:
18
Step-by-step explanation:
y=4x-18 is the solution and 18 is the y-intercept because the b (18) is the y-intercept.
When the point (3,k) lies on each of these lines, find the value of k.
a) y=3x+2
b) y=4x-2
c) y=3-2x
d) x+y=7
e) x-2y=1
If you answer you don't have to explain but please do
Here is a scale drawing of a swimming pool where 1 cm represents 1 m. The dimensions of the drawing are 6.5 cm by 13 cm.
How long and how wide is the actual swimming pool?
Answer:
1cm
Step-by-step explanation:
- 2.5f + 0.4f - 15 - 4
Answer:
Simplify the f's variables -2.1
Simplify the numbers -19
-2.1f -19 is the answer
-2.1f -19Answer-2.1f-24:
Step-by-step explanation:
I need A and B. Thanks
Answer:
A: its 13 cm
B:15cm
Step-by-step explanation:
A: its because its on a slight incline
B:again its on a big incline
Which function has a constant additive rate of change of -1/4?
4
1y
4
y
y
2
2
20
-1
-12
7
21
-1.5
-11
11
2
4
- 2
-2
-4-2
-2
22
-2
-10
14
23
-2.5
-9
17
Intro
Done
Answer:
4,20,11,2,1y
Step-by-step explanation:
The first graph has a constant additive rate of change of -1/4.
First of all, when we talk about a rate of change, that means a linear relation between variables, which is proper of a linear function represented by the first function showed in the image.
Also, if you observe the linear graph, you would see that the line represents a negative rate of change, because the line is going down (the function is decreasing). In other words, as x-variable increases, y-variable decreases.
Therefore, the first graph shows a ratio of change of -1/4.
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Enzo drew Triangle K L N. In Enzo's triangle, Measure of angle K is represented as x degrees. The measure of Angle L is 5 times Measure of angle K. The measure of Angle N is 16 degrees less than 8 times Measure of angle K. Which statements must be true about the angle measures of Enzo's triangle? Check all that apply. Measure of angle K = x degrees Measure of angle L = (5 x) degrees Measure of angle N = (16 minus 8 x) degrees Measure of angle K + measure of angle L = measure of angle N Measure of angle K + measure of angle L + measure of angle N = 180 degrees
Answer: (1) Measure of angle K = x degrees
(12) Measure of angle L = (5x) degrees
(3) Measure of angle k + Measure of angle L + Measure of angle N = 180 degrees
Step-by-step explanation: First of all, what we have is a triangle, and one of the properties of a triangle is all three angles add up to 180 degrees. This simply means that the addition of angles K and L and N would be equal to 180 degrees.
The question states that angle K is represented as x degrees, and angle L is 5 times the measure of angle K. Therefore, if K is x degrees, then L is 5 times x, which becomes 5x degrees. Also, angle N is given as 16 degrees less than 8 times the measure of angle K (x degrees). Eight times the measure of angle K is given as 8x. Sixteen degrees less than 8x would now become, 8x - 16 (degrees). Therefore, the angles have been derived as;
Angle K = x degrees
Angle L = 5x degrees
Angle N = 8x - 16 degrees
Having known that one of the properties of any triangle is all angles adding up to 180 degrees, we can now derive the following equation;
x + 5x + 8x - 16 = 180
14 x - 16 = 180
Add 16 to both sides of the equation
14x = 196
Divide both sides of the equation by 14
x = 14
Therefore, angle K = 14 degrees (x), angle L = 70 degrees (5x) and angle N = 96 degrees (8x - 16)
*14 + 70 + 96 = 180*
Answer:
145
Step-by-step explanation:
Find the volume of the pyramid. HELP
Answer:
187.5 in^3
Brainliest plzStep-by-step explanation:
V=(lwh )/3
7.5 x 5 x 5= 187.5
Answer:
62.5 inches squared
Step-by-step explanation:
To find the volume of a pyramid, you need to use the formula : (length x width x height)/3. It's simple once you plug the values in.
Length = 5
Width = 5
Height = 7.5
1. 5 times 5 times 7.5 = 187.5
2. 187.5/3 = 62.5
3. The answer is 62.5 inches squared
PLEASE HELP ASAP, BRAINLEST
Indicate the equation of the line, in standard form, that passes through (2, -4) and has a slope of 3/5.
Enter your answer into the blank equation box.
Answer:
equation in standard form is -3x + 5y = -26
Step-by-step explanation:
standard form of equation of line is
Ax + By = C
where A,B and C are integers.
such line has slope -A/B
Another form of line equation is slope intercept form, which can be written as
y = mx+ c
since in problem m = 3/5
thus, equation is
y = 3/5 x + c
Given that (2,-4) passes through this line, this point will satisfy the above equation
-4 = 3/5 *2 + c
=> - 4 = 6/5 + c
=> c = -4 -6/5 = (-4*5 - 6)/5
=> c = (-20 - 6)/5 = -26/5
Thus, equation in slope intercept form is
y = 3/5 x -26/5
lets rewrite this equation in Ax + By = C
Multiplying LHS and RHS by 5 we have
5y =( 3/5 x)* 5 - (26/5 * 5)
=> 5y = 3x - 26
we have to bring 3x on LHS for that
we subtract 3x from both side
5y -3x = 3x - 26 -3x
=> 5y -3x = - 26
rearranging the equation
-3x + 5y = -26
Thus, equation in standard form is -3x + 5y = -26
plz can someone help me with this plzz
Answer:
p: 42
a: 82.16
Step-by-step explanation:
For perimeter, add all the sides together
For area, multiple the longer side by the shorter side
Write in radical form and simplify if possible: (5x)⅓
Answer: [tex]\sqrt[3]{5x}[/tex]
Now your teacher is hosting a picnic for their family and discovers that 30 relatives are coming to the picnic and everyone wants to eat 2 hot dogs! What is the least number of packages of hot dogs and hot dog rolls that your teacher will have to buy to feed all her relatives?
Answer:
6 hot dogs package assuming she's buying a single package to contains 10 package or approximately 8 rolls if she buys the 8 package containing above 60 rolls of hot dogs.
In my opinion, she needs at least 8 package of hot dog rolls to make hot dogs for her guests.
Step-by-step explanation:
Hello,
There are typically 10 hot dogs in a single package. However some may contain 8 hot dogs rolls in a single pack so we'll solve for both in case which ever one she decides to buy.
My teacher is expecting 30 guests coming to the party and each 1 one them wants to eat 2 hot dogs.
To solve this question, we would first of all know the total number of hot dogs they'll probably eat at the party.
2 hot dogs = 1 person
y hot dogs = 30 people
y = (30 × 2) / 1
y = 60 hot dog.
Therefore, the guest would most likely consume at least 60 hot dogs at the party.
However, in a single hot dog package, it contains 10 hot dogs in it.
Now we'll have to find out the total number of hot dogs package my teacher needs to buy to prepare the hot dogs for her guests.
To do that, we'll have to divide the total number of hot dogs expected to be consumed by the total number of hot dogs in one package.
Number of package = total number of hot dogs expected to be consumed / total number of hot dogs in one package.
Number of package she needs = 60 / 10
Number of package she needs = 6
Therefore, my teacher requires 6 hot dog package.
But some hot dogs comes in 8 rolls per package
Using the same method above,
Number of rolls she needs = 60 / 8
Number of rolls she needs = 7.5 approximately 8 rolls
Triangle GHJ has the exterior angles shown below. Triangle G H J. The exterior angles are (9 x + 6) degrees, (10 x + 7) degrees, (10 x minus 1) degrees. For Triangle G H J, what is the value of x? 2.7 5.8 12 29
Answer:
b) 5.8
Step-by-step explanation:
Explanation
Given diagram the angles are (9 x + 6)°, (10 x + 7)°, (10 x - 1)°
we know that the sum of the angles of the triangle is equal to 180°
∠A +∠B +∠C = 180°
(9 x + 6)°+(10 x + 7)°+ (10 x - 1)° = 180°
On simplification , we get
29 x + 12 = 180
29 x = 180 -12
29 x = 168
x = 5.79 ≅ 5.8
Answer:
b
Step-by-step explanation:
If f(x) = x^2 - 2x and g(x) = 6x + 4, for what value of x does (f + g)(x) = 0?
Answer:
x = -2
Step-by-step explanation:
[tex]f(x) =x^2 -2x\:\: and \:\: g(x) = 6x + 4\\(f+g)(x) = f(x) + g(x) \\(f+g)(x) = x^2 -2x+ 6x + 4\\(f+g)(x) = x^2+4x + 4\\(f+g)(x) = (x+2)^2\\ 0 = (x+2)^2...[\because (f+g)(x) =0]\\0 = x+2\\\therefore x = -2[/tex]
Answer:
x = -3 + √5 and x = -3 - √5
Step-by-step explanation:
Combine f and g:
f = x^2 -2x
+g = 6x + 4
-------------------------
(f + g)(x) = x^2 + 6x + 4
Set this result = to 0 and solve for x:
By completing the square, we get:
y = x^2 + 6x + 9 - 9 + 4, or
y = (x + 3)^2 - 5 = 0
Thus, (x + 3)^2 = 5, and:
x + 3 = ±√5, or
x = -3 + √5 and x = -3 - √5
Point A lies on the circle and has an x-coordinate of 1.
Which is the correct calculation of the y-coordinate of point A?
Answer:
y=0
correct way to solve it is y= xtan(theta)
Step-by-step explanation:
You did not mention if it is trigonometry but we assume that it is.
In trigonometry, a point with x-coordinate = 1 at a circle is horizontal line. the angle at this point is 0.
The correct way to solve it is to say tan = opposite/adjacent
since the angle is zero, and adjacent side x=0, tan 0=opposite/1
opposite (y) = 1 tan 0
y = 1*0 =0
Answer:
d
Step-by-step explanation:
u do the thing and u do it right and somehow it equals 2 (edge 2022)
match the expressions 21/25 60% 13/20 84% 2/5 75% 65% 3/4 3/5
Answer:
21/25 ---> 84%
13/20 ---> 65%
3/5 ---> 60%
3/4 --->75%
2/5 ---> 40%
Direct Variation: If y = 12, when x = 4, find y when x = 20. a.40 b.48 c.12 d.60
Answer:
d
Step-by-step explanation:
Given the x and y are in direct variation then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 12 when x = 4, that is
12 = 4k ( divide both sides by 4 )
3 = k
y = 3k ← equation of variation
When x = 20 , then
y = 3 × 20 = 60 → d
Which terms are like terms in the following expression? 3x + 3xy – 2x + 5y + 5x2
In this problem, we have a pair of like terms in our x terms.
3x and -2x are like terms because they are exactly alike except for the coefficients or the numbers in front of the variables.
______________________________
Hey!!
3x and -2x are the like terms.
Explanation:
To add and subtract the algebraic expression, there should be the like and unlike terms.Unlike terms are those which do not have the same base and like terms are those which have the same base.
Hope it helps
Good luck on your assignment
_____________________________
what is the radius of circle O
Answer:
8.5 units
Step-by-step explanation:
first we gotta find the length of the diameter. they made it into a triangle, so we can use pythagorean theorem.
15² + 8² = c²
225 + 64 = c²
289 = c²
17 = c
so now we know that the length of the diameter is 17 units, so the radius would be half of that.
17 ÷ 2 = 8.5
so the radius is 8.5
The radius of the given circle, it can be calculate by using theorem of circle and it will come out, 13/2
What is Pythagoras theorem?It is the most important theorem of mathematics, which tells us the relationship between sides of the right angle triangle, which are known as Base(A), Height(B), Hypotenuse(H).
Pythagoras theorem,
H² = A² + B²
Given that,
A circle which has diameter AOB,
Two chords are, AC & BC their lengths are respectively, 15 and 8 units
According to theorem of circle,
Angle made by end-points of diameter at any point on a circle is 90
Pythagoras theorem can be used here,
AB² = AC² + BC²
AB² = 12² + 5²
AB² = 169
AB = 13
Radius = AB/2
= 13/2
Hence, the radius is 13/2 units
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People pay to visit a stately home [tickets age 16 and over : £18.60 ..under 16:£12.80] 155 people pay and 49 of these people are under 16. How much money is collected
Answer: £2598.80
Step-by-step explanation:
Let those under 16 be x
Those over 16 be y
49 + y = 155
y = 155-49
y = 106 = over 16
for over 16, y * 18.60
= 106 * 18.60 = 1971.60
For under 16, x * 12.80
= 49 * 12.80 = 627.20
What is the numerical solution to the equation five less than three times a number equals four more than eight times rhetorical number?
Answer:
3n-5=8n+4
Step-by-step explanation:
SUBJECT: Mathematic
ASSIGNMENT
The diagram below shows a cylindrical moulding tool of diameter 16cm with a cylindrical hole of diameter 10cm. The height of the cylinder is 18cm and the hole is 6cm deep. Calculate the volume of the tool.
The height of a right circular cone is 6cm and its radius is 8cm.
Calculate its curved surface area.
Calculate the volume of the cone.
Answer:
Section A
Volume of the cylindrical tool = 1413.72cm³
Section B
1) Curved Surface Area of the right circular cone = 251.33cm²
2) Volume of the right circular cone = 402.12cm³
Step-by-step explanation:
Section A
We are asked to find the volume of the cylindrical moulding tool.
Volume of a cylinder = πr²h
From the question, the cylindrical tool had a diameter of 10cm. This means the radius of the tool = Diameter ÷ 2 = 10cm ÷ 2 = 5cm
The height of the cylindrical tool = 18cm
Volume of the cylindrical tool = π × (5cm)² × 18cm
1413.7166941cm³
Approximately = 1413.72cm³
Section B
The height of a right circular cone is 6cm and its radius is 8cm.
1) Calculate its curved surface area.
The formula for the curved surface area of a right circular cone =
πrl
r = radius = 8cm
h = height = 6cm
l = √(r² +h²) = √(8² + 6²) = √100
l = 10cm
The curved surface area = πrl
= π × 8cm × 10cm
= 251.33cm²
2) Calculate the volume of the cone.
The formula for the volume of a cone=
1/3πr²h
radius (r) = 8cm
height (h) = 6cm
1/3πr²h
1/3 × π × 8² × 6
= 402.12cm³
Find the volume of the sphere. Round to the nearest tenth, if necessary. (Use π = 3.14)
113.0 in^3
339.1 in^3
28.3 in^3
113.0 in^2
Steps:
Shape: Sphere
Solved for volume
Radius: 3
Formula: V=4 /3πr3
1: know the height. We don't have to round to the nearest tenth. The correct answer for this question is 113.0.
Answer: 113.0
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Hope this helps.
Express 0.96 as an percent
Answer:
96%
Step-by-step explanation:
0.96 × 100/100
(0.96 × 100)× 1/100 = 96/100
percentage = 96%
Answer:
96%
Step-by-step explanation:
What is the smallest number that can be added to 2018·2019·2020 so that the result of the addition is a perfect cube? Please answer soon!
Answer:
[tex]802[/tex]
Step-by-step explanation:
[tex]18^3=5832[/tex]
[tex]19^3=6859[/tex]
[tex]2018+2019+2020=6057[/tex]
[tex]6859-6057=802[/tex]
Check.
[tex]6057+802=6859[/tex]
[tex]\sqrt[3]{6859} =19[/tex]
Answer:
2019.
Step-by-step explanation:
Let x = 2018, then x + 1 = 2019 and x + 2 = 2020.
x(x + 1)(x + 2)
= x(x^2 + 3x + 2)
= x^3 + 3x^2 + 2x ................(A)
Now the perfect cube of x + 1 is:
(x + 1)^3 = x^3 + 3x^2 + 3x + 1
If we add x + 1 to (A) we get this expression so the answer is x + 1
= 2019.