The interval of the data if, The mean of 73.5 years and the standard deviation of 6.5 years, is (67,80) so, option D is correct.
What is mean?Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Given:
The mean of 73.5 years and the standard deviation of 6.5 years,
the middle 99.7% of ages of residents living at the facility,
Calculate the interval as shown below,
The coordinates of x in the interval = Mean - Standard deviation
The coordinates of x in the interval = 73.5 - 6.5
The coordinates of x in the interval = 67
The coordinates of y in the interval = Mean + Standard deviation
The coordinates of y in the interval = 73.5 + 6.5
The coordinates of y in the interval = 80
Thus, the interval will be (67, 80).
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What is the inverse of the function f(x) = 2x + 1? h(x) = one-halfx – one-half h(x) = one-halfx + one-half h(x) = one-halfx – 2 h(x) = one-halfx + 2
Step-by-step explanation:
To find the inverse we just switch f(x) and x so we get :
x = 2f(x) + 1
2f(x) = x - 1
h(x) = 1/2x - 1/2
Hope this helps!
Answer:
x = 2f(x) + 1
2f(x) = x - 1
h(x) = 1/2x - 1/2
Step-by-step explanation:
What is the y-intercept of the line?
x 16 24 32
y 44 64 84
Answer:
The y-intercept of the line is 2
Step-by-step explanation:
You could try to find the slope of the line and then find the intercept with y axis by sloving b = y - ax
But here it seems easy enough once you see that the x values in the table increase by a factor of 8 and the y values in the table increase by a factor of 20.
(By the way, this is enough to give you the slope, because it is 8/20 ). But why bother?
Just extrapolate the table to the left, and you will find the y value where x = 0
x 0 8 16 24 32
y 2 22 44 64 84
So the y-intercept of the line is 2.
Extra:
The full equation of the line is:
y = 8/20x + 2
Answer:
(0,4)
Step-by-step explanation:
A rectangle measures 9 feet by 6 feet. What is the measure of the diagonal? Round your answer to the nearest tenth.
Answer:
~10.8 (ft)
Step-by-step explanation:
Apply the Pythagorean theorem, you can work out the measure of diagonal.
[tex]Diagonal = \sqrt{9^{2}+6^{2} } =\sqrt{81 + 36} =\sqrt{117} =~10.8(ft)[/tex]
The measure of the diagonal of a rectangle is 10.8 feet.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, a rectangle measures 9 feet by 6 feet.
Let the length of diagonal be x.
x²=9²+6²
x²=81+36
x²=117
x=√117
x=10.8 feet
Therefore, the measure of the diagonal of a rectangle is 10.8 feet.
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Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t, y = e−4t, z = 5t − t5; (0, 1, 0) x(t), y(t), z(t) = t,1−4t,5t Illustrate by graphing both the curve and the tangent line on a common screen.
Answer:
Step-by-step explanation:
At the point (0, 1,0) t = 0
Find the tangent vector:
[tex]\frac{dx}{dt}= 1[/tex]
[tex]\frac{dy}{dt}= -4e^{-4t}[/tex]
[tex]\frac{dz}{dt}=5-5t^4[/tex]
The tangent vector for all points [tex]\vec v(t)[/tex] is
[tex]\vec v(t) = \hat {i}-4e^{-4t}\hat{j}+(5-5t^4)\hat{k}[/tex]
[tex]\rightarrow \vec v (0)= \hat{i}-4\hat{j}[/tex]
The vector equation of the tangent line is
[tex](x,y,z) = (0,1,0)+s(\hat{i}-4\hat{j})[/tex]
The parametric equation for this line are
[tex]x= s[/tex]
[tex]y=1-4s[/tex]
[tex]z=0[/tex]
Parametric equations for the tangent line to the curve with the given parametric equations at the specified point are
x=s
y=1-4s
z=0
What is the parametric equation?In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
At the point (0, 1,0) t = 0
Find the tangent vector:
[tex]\dfrac{dx}{dt}=1[/tex]
[tex]\dfrac{dy}{dt}=-4e^{-4t}[/tex]
[tex]\dfrac{dz}{dt}=5-5t^4[/tex]
The tangent vector for all points is
[tex]v(t)=i-4e^{-4t}j+(5-5t^4)k[/tex]
[tex]v(0)=i-4j[/tex]
The vector equation of the tangent line is
[tex](x,y,z)=(0,1,0)+s(i-4j)[/tex]
The parametric equation for this line is
[tex]x=s\\\\y=1-4s\\\\z=0[/tex]
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6+7=73.5
7+8=84
11+12=126
12+24=390.6
24+28=?
Answer:
52
Step-by-step explanation:
24+28 = 52
52 - 24 = 28
Myra wants to save at least $500 by the end of her summer vacation. She currently has $350 saved. She can earn $25 cutting a lawn in her neighborhood. Myra solves an inequality to determine the least number of lawns, n, she must cut to reach her goal.
What number is the minimum number of lawns Myra needs to mow to meet her goal?
Answer:
6 ≤ b.
(6).
Step-by-step explanation:
So, we are given in the question that the amount that Myra wants to say is $500 at the end of her summer vacation and she has saved up to $350. Thus, it remain ($500 - $350 = $150) for completion.
Also, "She can earn $25 cutting a lawn in her neighborhood."
Therefore, the total amount of money she wants to save = a = 500. Then,
Total amount of money, a = 350 + 25b.
500 = 350 + 25b.
=> 500 ≤ 350 + 25b.
Note that the ' =' sign has changed to '≤' sign since she wants that amount(at least). Also, the question specified that she used inequality.
Hence, the amount remaining for it to complete is $150. Therefore;
150 ≤ 25b.
6 ≤ b.
Thus, Myra will have to mow at least 6 lawns
Answer:
6
Step-by-step explanation:
Took the quiz on edge!
The cost of 12 pairs of shoes is $960. what is the cost of 1 pair of shoes?
Answer:
$80 for 1 pair of shoes
divide $960 by 12
what is 42 + 7x + 12x – 8 i really need help
Solution,
42+7x+12x-8
Combine like terms,
= 7x+12x+42-8
Simplify
=19x+34
hope it helps
Good luck on your assignment
Answer:
36+19x
Step-by-step explanation:
Ok, first, combine like terms, so the two values with X.
42 + 7x + 12x – 8
42 +19x – 8
Now, we combine the two values that have no X
42+19x– 8 Imagine there is a plus sign in front of the 42 because it's positive.
So 42-8=36
36+19x
That's your solution, that's the most this can be simplified.
Answer if you can and help other people out
Solution,
radius=21 cm
Circumference of circle=2 pi r
=2*3.142*21
=131.964 cm
hope it helps
Good luck on your assignment
In a study in Scotland (as reported by Devlin 2009), researchers left a total of 320 wallets around Edinburgh, as though the wallerts were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them. With the following steps, use the data to estimate the proportion of lost wallets that are returned, and give a 95% confidence interval for this estimate.
Required:
a. What is the observed proportion of wallets that were returned (rounded to the nearest thousandths)?
b. Calculate p to use in the Agresti-Coull method of calculating a 95% confidence interval for the population proportion rounded to the nearest thousandths).
c. Calculate the lower bound of the 95% confidence interval (rounded to the nearest thousandths)
d. Calculate the upper bound of the 95% confidence interval (rounded to the nearest thousandths)
Answer:
a) The observed proportion of wallets that were returned
p = 0.45625
b) 95% of confidence intervals for Population proportion
0.40168 , 0.51082)
c) The lower bound of the 95% confidence interval = 0.40168
d) The upper bound of the 95% confidence interval = 0.51082
Step-by-step explanation:
Step(i):-
a)
Given data the researchers left a total of 320 wallets around Edinburgh, as though the wallets were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them
Given sample size 'n' = 320
Given data 'x ' = 146
Sample proportion
[tex]p = \frac{x}{n}[/tex]
[tex]p = \frac{x}{n} = \frac{146}{320} = 0.45625[/tex]
Step(ii):-
b) 95% of confidence intervals for Population proportion
Level of significance = 95% or 0.05%
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
95% of confidence intervals for Population proportion are determined by
[tex](p - Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} })[/tex]
[tex](0.45625 - 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} } , 0.45625 + 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} })[/tex]
(0.45625 - 0.05457 , 0.45625 + 0.05457)
( 0.40168 , 0.51082)
c) The lower bound of the 95% confidence interval = 0.40168
d) The upper bound of the 95% confidence interval = 0.51082
Can I please get some help on this...I have tried to many times...
Answer: A
Step-by-step explanation:
First, the problem is g(f(x)). You would plug in f(x) wherever you see an x in g(x). To find the domain, you take the bottom function, and set it equal to 0.
[tex]\sqrt{x-2} =0[/tex]
When you solve that, you get x=2. You know your domain is x≥2, but there is as asymptote at x=11. That means the graph never reaches x=11, but gets very close. You find that by setting the entire equation equal to 0 and solve from there.
Abigail had a fish tank that was in the shape of a box. The dimensions were 1 foot deep by 24 inches wide, by 18 inches tall. How many cubic inches of water will it take to completely fill the tank?
Answer:
volume= 5,184 cubic inches
Step-by-step explanation:
The sum of two numbers is 15. One of the
numbers is 12 times the other. Find the
bigger number.
Answer:
The Sum of two number is 15: x + y = 15
One of the numbers is 12 times the other: x = 12y:
System of equations:
x + y = 15
x = 12y
Plug x = 12y into equation one(x + y = 15)
12y + y = 15
13y = 15
y = 15/3
y ≈ 1.15
Now we know x = 12y
x = 12(15/13) = 180/13
x = 180/13
x ≈ 13.85
The biggest number is x = 180/13.
Explain how you could calculate the surface area of a square pyramid
Answer:
calculate the area of a square using the length * width formula, and then add the areas of the other triangles, of which you can calculate by using the base * height formula
Step-by-step explanation:
Answer:
Multiply the side length of the base by the slant height and divide by two. Then, multiply by 4. This will give you the lateral surface area of the pyramid.Step-by-step explanation:
If the frame of a Ferris wheel is a circle with a 10 meter diameter, what is the circumference of this circle?
Answer:
C = 10π
Step-by-step explanation:
C = Dπ
D = 10
C = 10π
Answer:
see below
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
C = 10 pi m
We can approximate pi by 3.14
C = 3.14 * 10
C =31.4m
or we can approximate pi by using the pi button
C =31.41592654m
(03.04) What is the vertex of the graph of y = −4(x + 2)2 + 5? (1 point) (2, 5) (−2, 5) (5, −2) (5, 2)
Answer:
(-2, 5)
Step-by-step explanation:
The form you're trying to match is the vertex form of the equation of a parabola:
y = a(x -h)^2 +k . . . . . . . vertex (h, k)
You have ...
y = -4(x +2)^2 +5
Comparing forms, you see that a=-4, h=-2, k=5.
Then the vertex (h, k) is (-2, 5).
Which graph is the solution to Ixl > 10?
Answer: D with the open circles at -10 and 10 with a line in between them.
Step-by-step explanation:
Since x has an absolute value sign around it this means that all the values will be positive which includes negative numbers.
Since the solution must be less than 10 we need all values under 10 which is 1-9.9 repeating. we can show the 9.9 repeating with an open circle on the value of 10. This also goes for the negative values for x as we can go up to -9.9 repeating because it will become positive.
The only graph that shows these values is D with the open circles at -10 and 10 with a line in between them.
Answer:
D
Step-by-step explanation:
Hope this helps
2. The perimeter of a rectangular pool is 98 feet.
The ratio of the width to the length is 3:4.
What are the dimensions of the pool?
Answer:
56 and 42
Step-by-step explanation:
3:4
3 + 4 = 7
98 / 7 = 14
14 x 3 = 42
14 x 4 = 56
56 + 42 = 98
The dimensions of the pool can be categorized as below:
Length equals 28 feet
Width equals 21 feet
What is the perimeter?The perimeter of a rectangle is the outside length of the rectangle. To find the perimeter we add all the 4 sides of the rectangle.
Perimeter = 2(length) + 2 (width )
The ratio of the width to the length is 3:4. The width of the rectangle is 3x
We know,
Length of the rectangle is 4xWidth =3x
Length = 4x
Substitute it in the perimeter formula and solve for x.
Given that,
Perimeter of a rectangle = 98 feet
Perimeter = 2(length )+2(width)
98 = 2(4x)+2(3x)
98 = 8x+6x
98 = 14x
∵ x = 7
Now, we will find out the length and width of the pool.
Length = 4x
= 4(7)
= 28 ft.
and,
Width = 3x
= 3(7)
= 21 ft.
Thus, the length of the pool is 28 feet and the width of the pool is 21 feet
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How to solve 3/7+3/14
Answer:
About 0.642
Step-by-step explanation:
Solve the system of equations.
y=x2-5
y=-2x+3
A. (2-1) and (4.-5)
B. -2.7) and (4-5)
C. (-411) and (2-1)
O D. (-4, 11) and (-27)
Find the volume of a cone with the radius of radius of 80 and height of 21
Answer:
140672
Step-by-step explanation:
formula for cone volume=pi*r^2*h*1/3
80^2*3.14*21=422016
422016*1/3
=140672
Among 6 electrical components exactly one is known not to function properly. If 2 components are randomly selected, find the probability that all selected components function properly?
Answer:
66.67% probability that all selected components function properly
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the components are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Desired outcomes:
2 components which function properly, from a set of 5. So
[tex]D = C_{5,2} = \frac{5!}{2!(5-2)!} = 10[/tex]
Total outcomes:
2 components, from a set of 6. So
[tex]T = C_{6,2} = \frac{6!}{2!(6-2)!} = 15[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{10}{15} = 0.6667[/tex]
66.67% probability that all selected components function properly
What’s the correct answer for this?
Answer:
x = 5
Step-by-step explanation:
Since TV bisects (equally divides) EF hence <EKT = 90°
Also <EKT = 5x+65
So
5x+65 = 90
5x = 90-65
5x = 25
Dividing both sides by 5
x = 5
Solve for the value of x
What is the range of g?
Answer:
[-4, 9]
Step-by-step explanation:
The range is the vertical extent of the relation.
__
The minimum value of g is marked by the solid dot at (x, y) = (4, -4). That minimum is -4.
The maximum value of g is the peak at (x, y) = (-2, 9). That maximum is 9.
The function is continuous between these values, so the range includes all values between -4 and +9, inclusive.
range: [-4, 9]
Answer:
Step-by-step explanation:
range: [-4, 9]
Set up each situation and simplify if possible. Then, choose all situations that are best modeled by a rational inequality.
Answer:
Problem: 3x/5x + 5 ≤ 8 + 2x
Solution: x ≥ -15/7
Step-by-step explanation:
Example of this inequality is:
3x/5x + 5 ≤ 8 + 2x
3x/5x - 2x ≤ 8 - 5
(3x - 10x)/5 ≤ 3
-7x ≤ 15
x ≥ -15/7
25. If the area of a circle is 144cmthen find
a. lts diameter
b. Its circumference
Answer:
a. lts diameter = 13.540550005146 cm
b. Its circumference = 42.538892421732 cm
Step-by-step explanation:
suppose A the area ; d the Diameter ; P the circumference and r the radius
A = πr²
P = d×r = 2πr
then
r² = A/π = 144÷π = 45.836623610466
then
→ r = √(45.836623610466) = 6.770275002573
d = 6.770275002573×2 = 13.540550005146
→ P = 13,.540550005146×π = 42.538892421732
1. Michel buys a leash for his dog. The leash is 6 ft 3 inches. How long, in inches, is the leash?(1 ft = 12 inches)
A) 48 inches
B) 51 inches
C) 72 inches
D) 75 inches
2. What is the area of a triangular garden with base of 6 ft and a height of 9 ft? (A = 1/2BH)
A) 27 square feet
B) 48 square feet
C) 54 square feet
D) 24 square feet
Answer:
1. D) 75 inches
2. A) 27 square feet
Step-by-step explanation:
1. You need to convert 6 feet to inches. In one foot, there are 12 inches. Multiply 6 by 12 to find the number of inches in 6 feet. Add 3 inches to the product to find the total number of inches.
6 × 12 = 72
72 + 3 = 75
You will have 75 inches in total.
2. Use the formula to solve. You are given the base and the height already. Simply plug in and solve.
A = 1/2BH
A = 1/2(6)(9)
A = 3(9)
A = 27 ft²
The area is 27 ft².
Answer:
Step-by-step explanation:
The graph of F(x), shown below, has the same shape as the graph of
G(X) = x2, but it is shifted up 3 units and to the right 1 unit. What is its
equation?
Answer:
The answer is A.
Step-by-step explanation:
First, recall the vertex form of a quadratic equation: [tex]f(x)=a(x-h)^2+k[/tex], where [tex]h[/tex] represents the horizontal change and [tex]k[/tex] represents the vertical change.
The original equation is [tex]g(x)=x^2[/tex], or, in other words, [tex]g(x)=1(x-0)^2+0[/tex].
We are told that the graph is shifted up 3 and right 1. Thus, both values are positive (right and up). Note that up 3 corresponds to a positive vertical change of 3 while right 1 represents a positive horizontal change of 1.
Thus, put these back into the equation in place of [tex]h[/tex] and [tex]k[/tex].
We have:
[tex]f(x)=1(x-(+1))^2+(+3)[/tex]
Or, simplified:
[tex]f(x)=(x-1)^2+3[/tex]
The answer is A.
Please answer this correctly
Answer: Rectangular pyramid
Step-by-step explanation:
When you think about it, a pyramid has 3 faces that are triangular!
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