What is the standard deviation of a normal distribution, whose mean is 75, in which an x-value
of 68 has a z-score of -0.53?
Answers
The standard deviation of a normal distribution, whose mean is 75, in which an x-value of 68 has a z-score of -0.53 is σ = 13.207.
Given:
whose mean is 75, in which an x-value of 68 has a z-score of -0.53
μ = 75
x = 68
z = -0.53
we know that:
z = x-μ/σ
σ = x - μ / z
= 68 - 75 / -0.53
= -7/-0.53
= 7/0.53
= 7/53/100
= 7*100/53
= 700/53
= 13.207
Therefore The standard deviation of a normal distribution, whose mean is 75, in which an x-value of 68 has a z-score of -0.53 is σ = 13.207.
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Related Questions
ASAP help thanks if you help I appreciate it
Answers
The circumference of the circle in terms of π whose radius is given would be = 63π. That is option D.
How to calculate the circumference of a circle?To calculate the circumference of a circle, the formula that should be used would be given below.
That is;
circumference of circle= 2πr
The radius = 31½
circumference = 2×π × 31½
= 2×π× 63/2
= 63π
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Simplify
5^3 / 5 ^7
leaving your answer in index form
Answers
Answer:
\(5^{-4}\)
Step-by-step explanation:
\(\frac{5^3}{5^7}=5^{3-7}=5^{-4}\)
Answer: The answer is 0.0016 Or 1/625
Step-by-step explanation:
First step you Simplify 5^3 and 5^7 which is going to look like this:
5^3 = 5x5x5 = 25x5 = 125
and
5^7= 5x5x5x5x5x5x5=25x5x5x5x5x5= 125x5x5x5x5= 625x5x5x5=3125x5x5=15625x5= 78125
then divide 125 with 781225
you will get 0.000160005 but you would take out what goes after 16 and it would just have to grab 0.00016 and done
which of the following basic functions is equivalent to the piecewise-defined function f(x)= x if x≥0 −x if x<0 ? question content area bottom part 1 a. f(x)= 1 x b. f(x)=x c. f(x)=x2 d.
Answers
The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.
The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.
Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.
The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.
In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.
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Point A is located at –11. Point B is 5 less than Point A. Where is B located?
Answers
Answer:
We know that point A is at -11, and B is 5 less than it, so we only have to substract 5 to -11, and see what we get by doing this operation:
-11 - 5 = -16
So now, we know that point A is located at -11 and we also know point B is located at -16
In order to help ensure generalizability, which of the following should be true about your sample?
A. It is small
B. It is large
C. It is representative
D. It is not representative
Answers
To ensure generalizability, the sample should be representative, meaning that it should accurately reflect the characteristics of the population being studied.
The size of the sample, whether small or large, is not as important as the representativeness of the sample. A small or large sample that is not representative can lead to inaccurate conclusions about the population.
Therefore, it is important to carefully select a sample that is diverse and includes a range of characteristics that are relevant to the research question. By having a representative sample, researchers can increase the external validity of their findings and make more accurate generalizations about the population as a whole.
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pls give the answer with step by step explanation... :)
Answers
Answer:
Step-by-step explanation:
so you do 1150 x 115% to give you the answer and then you get the answer of that and take away 1150 and you should get your answer
f(x)=2x^-6 Find f(7)
Answers
Answer: 1/58824.5
Step-by-step explanation: 2x7^-6
2x1/117649
=1/58824.5
help asap
Determine the value of x.
Question 6 options:
1)
40°
2)
140°
3)
280°
4)
70°
Answers
Answer:
i think 1 but I am not sure
Step-by-step explanation:
#_Factor the quadratic binomial 3x2 - 48.
Then, find one of its factors.
Answers
Answer:
3(x - 4)(x + 4)
Step-by-step explanation:
\(3 {x}^{2} - 48 \\ = 3( {x}^{2} - 16) \\ = 3( {x}^{2} - {4}^{2} ) \\ = 3(x - 4)(x + 4)\)
Amy is draining an aquarium. The graph shows the amount of water (in liters) in the aquarium versus time (in minutes)
Answers
From the graph, we have the amount of water (in liters) on the y-axis and the time (in minutes) on the x-axis
a)
To obtain the amount of water at zero minutes, we will trace the y-value that corresponds with the value of zero on the x-axis: we will see this to be 270 liters
Therefore, at time zero minutes, the amount of water is 270 liters
b)
We will answer this by picking two points that lie along the straight line and calculate the slope. We pick the points:
\(\begin{gathered} (x_1,y_1)=(0,270) \\ (x_2,y_2)=(2,90) \end{gathered}\)We will proceed to calculate the slope as shown below:
\(\begin{gathered} slope(m)=\frac{y_2-y_1}{x_2-x_1} \\ \text{Substitute the values of the variables into the equation, we have:} \\ slope(m)=\frac{90-270}{2-0} \\ slope(m)=-\frac{180}{2} \\ slope(m)=-90l\text{/}min \end{gathered}\)The slope is -90 liters per minute.
The negative sign (-) means that as time increases, the amount of water in the aquarium decreases
The water decreases at a rate of 90 liters per minute
passes through (-2,6) with a slope of - 1/4
Answers
The equation of the line is y = x/4 + 13/2 .
What is a slope?A line's slope, sometimes referred to as its gradient in mathematics, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
And here we have the slope,
m = 1/4
And (x₁ ,y₁) = (-2,6)
then the equation of line is
y - y₁ = m (x - x₁)
y - 6 = (1/4) (x +2)
y = x/4 + 13/2
Therefore, the equation is y = x/4 + 13/2.
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Yea I can do tomorrow it would take me to get the money back to you
Answers
Given, the equation that represents the height of an object:
\(y(t)=100t-16t^2\)First, we will find the velocity of the object which is the first derivative of the height using the method of the limits
\(\frac{dy}{dt}=\lim_{h\to a}\frac{y(3+h)-y(3)}{(3+h)-(3)}\)We will find the value of the function y(t) when t = 3, and when t = 3+h
\(\begin{gathered} y(3+h)=100(3+h)-16(3+h)^2 \\ y(3+h)=300+300h-16(9+6h+h^2) \\ y(3+h)=300+300h-144-96h-16h^2 \\ y(3+h)=156+4h-16h^2 \\ y(3)=100(3)-16(3)^2=156 \end{gathered}\)Substitute y(3+h) and y(3) into the expression of the limit
\(\begin{gathered} \frac{dy}{dt}|_{t=3}=\lim_{h\to a}\frac{156+4h-16h^2-156}{3+h-3}=\lim_{h\to a}\frac{4h-16h^2}{h} \\ \\ \frac{dy}{dt}|_{t=3}=\lim_{h\to a}(4-16h) \end{gathered}\)Where a = 0
d) compute the instantaneous velocity at t = 3
\(\frac{dy}{dt}|_{t=3}=100-16*2*3=4\)So, the answer will be:
\(\begin{gathered} \frac{dy}{dt}|_{t=3}=\lim_{h\to a}(4-16h) \\ a=0 \\ \\ \frac{dy}{dt}|_{t=3}=4\text{ ft/sec} \end{gathered}\)David made a scale drawing of an Olympic-sized pool the pool is 20.5 in long and the drawing that I can shoot pool is 164 ft long what is the correct scale of the drawing
Answers
Answer:
\(Scale = 1\ in : 8\ ft\)
Step-by-step explanation:
Given
\(Scale\ Measurement = 20.5in\)
\(Actual\ Measurement = 164ft\)
Required
Determine the scale
The scale is calculated using the following ratio:
\(Scale = Scale\ Measurement : Actual\ Measurement;\)
Substitute values for Scale and Actual Measurements
\(Scale = 20.5\ in : 164\ ft\)
Divide ratio by 20.5
\(Scale = 20.5/20.5\ in : 164/20.5\ ft\)
\(Scale = 1\ in : 8\ ft\)
This implies that: 1 inch on scale represents 8 ft in actual measurement
Answer:
1.8
Step-by-step explanation:
just wondering if anyone wanted to play with me
Im only at young age so dont be mean to me :c
Answers
And lots more games just name one
How do cows count
[riddle]
Answers
Answer:
Step-by-step explanation:
I think the answer is utterly perfect
Lol or its a 'cow'nter
This year there were more than 800 entrants in the Kangaroo Hop race. Exactly 35% of the entrants were female and there were 252 more males than females. How many entrants were there in total?
Answers
Answer:
840
Step-by-step explanation:
m = number of males
f = number of females
t = total entrants
t = m + f
m = f + 252
0.35(m + f) = f (×20)
7(m + f) = 20f
These are simultaneous which can be solved:
7(m + f) = 20f
7m + 7f = 20f
7m = 13f
Substitute:
7(f + 252) = 13f
7f + 1764 = 13f
6f = 1764
f = 294
m = 546
t = 294 + 546
t = 840
for a two-tailed test, if 2.36 is in the rejection region and the test statistic is -3.11, and the null hypothesis is true, do we have a correct decision? give an explanation for your answer.
Answers
If the test statistic is -3.11, it means that the observed data is 3.11 standard deviations below the mean of the null distribution.
Since 2.36 is in the rejection region, it means that the critical value for the test is greater than 2.36 in absolute value. This implies that the null hypothesis would be rejected if the test statistic is either less than the negative critical value or greater than the positive critical value.
However, since the test statistic of -3.11 is smaller than the negative critical value, we would fail to reject the null hypothesis. This means that we would conclude that there is not enough evidence to support the alternative hypothesis and we accept the null hypothesis. Therefore, we would have made an incorrect decision if we rejected the null hypothesis based on the given information.
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A plane flying horizontally at an altitude of 1 mile and a speed of 570 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 3 miles away from the station. (Round your answer to the nearest whole number.)
Answers
The rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.
We assume the station to be at point A.
The plane when directly over the station, takes point C.
As it is flying horizontally continuously at an altitude of 1 mile, AC = b = 1 mile.
The plane flies continuously, and when it is at a distance of 3 miles from the station, it is at point B.
The distance between the plane and the station of 3 miles can be shown as AB = c = 3 miles.
The movement of the plane from C to B can be shown as BC = a.
Now, from the given case, we get a right triangle ABC.
By Pythagoras' Theorem,
a² + b² = c² ... (i).
or, a² + 1² = 3²,
or, a² = 9 - 1 = 8,
or, a = 2√2 miles.
We are told that the plane is moving at a speed of 570 miles/hour.
This can be shown as, da/dt = 570 miles/hour.
As the plane is moving horizontally, the vertical distance between the plane and the station doesn't change, that is, db/dt = 0.
In the question, we are asked to find the rate at which the distance from the plane to the station is increasing, that is, we are asked to find dc/dt.
Differentiating (i), with respect to time t, we get:
2a(da/dt) + 2b(db/dt) = 2c(dc/dt).
Substituting values of a = 2√2 miles, b = 1 mile, c = 3 miles, da/dt = 570 miles/hour, and db/dt = 0, we get:
2(2√2)(570) + 2(1)(0) = 2(3)(dc/dt),
or, 2280√2 + 0 = 6(dc/dt),
or, dc/dt = 380√2 miles/hour = 537.40 miles/hour ≈ 537 miles/hour.
Thus, the rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.
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How to factor 3x^2-10x-8?
Answers
\(answer \\(x - 4)(3x + 2) \\ solution \\ {3x}^{2} - 10x - 8 \\ = {3x}^{2} - (12 - 2)x - 8 \\ = {3x}^{2} - 12x + 2x - 8 \\ = 3x(x - 4) + 2(x - 4) \\ = (x - 4)(3x + 2) \\ hope \: it \: helps\)
Answer:
Step-by-step explanation:
A blueprint is 1" 12'. The width of a building is 48'. What is the width of the building on the blueprint?
Answers
The width on the blueprint is 4 inches.
What is the width of the building on the blueprint?The blueprint is a scale drawing of the building.
A scale drawing is a reduced form in terms of dimensions of an original image / building / object.
The scale of a drawing is usually written in this format; length in the drawing, a colon, then the matching length on the original image.
For example of a scale is 1 inch 12 feet means that 1 inch of the blueprint represents 12 feet of the building.
Therefore, Width of the building on the blueprint = 48 / 12 = 4 inches
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Find the area of the surface. The part of the plane x+2y+3z=1 that lies inside the cylinder x2 + y2=3.
Answers
After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.
To find the area of the surface of the part of the plane x + 2y + 3z = 1 that lies inside the cylinder x^2 + y^2 = 3, we can use a parametric representation for the plane and cylinder intersection.
Let x = r * cos(θ) and y = r * sin(θ), where r^2 = 3 (from the cylinder equation). Now, we can find z in terms of r and θ using the plane equation:
z = (1 - x - 2y) / 3
z = (1 - r * cos(θ) - 2r * sin(θ)) / 3
Now, we have the parametric representation of the intersection: (r * cos(θ), r * sin(θ), (1 - r * cos(θ) - 2r * sin(θ)) / 3). To find the surface area, we need to calculate the partial derivatives with respect to r and θ and then find the magnitude of the cross product.
After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.
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Determine whether the statement below is true or false. If it is false, explain. Least squares means that the square of the largest residual is as small as it could possibly be. Choose the correct answer below. O A. The statement is false. It is the sum of the squares of all the residuals that is minimized. OB. The statement is true. O C. The statement is false. It is the difference of the squares of all the residuals that is minimized.
Answers
C. The statement is false. It is the sum of the squares of all the residuals that is minimized.
In the context of least squares, the goal is to minimize the sum of the squares of the residuals, not the square of the largest residual alone. The residuals are the differences between the observed values and the corresponding predicted values obtained from a regression model.
By minimizing the sum of the squares of the residuals, the least squares method ensures that all residuals contribute to the overall measure of fit, rather than just focusing on the largest residual. This approach provides a balanced and comprehensive assessment of the overall goodness of fit between the model and the observed data.
Therefore, the statement that the square of the largest residual is as small as it could possibly be is false. The least squares method aims to minimize the sum of the squares of all the residuals, leading to the best overall fit between the model and the data.
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Two similar triangles are shown. What is the measure of ∠P?
Answers
Answer:
68.2
Step-by-step explanation:
if the triangles are similar then all of the angles are the same. The only thing that changes is the side lengths.
Answer:
\(63.2\)°
Step-by-step explanation:
since the triangles are similar they have identical angle measures are the same
however you could solve it this way too:
\(A+B+C=180\)
all measures of a triangle add up to 180
\(23.8+90+C=180\)
\(116.8+C=180\)
\(C=63.2\)
. Belle decided to start a new retirement
account. She deposits $1,000 into an account
that earns 3.5% interest, compounded
quarterly, for 10 years. How much more would
she have earned, in interest, if she invested the
same amount into an account earning 3.8%
interest, compounded monthly, for the same
number of years? EL MP
A $44.50
B $350
© $1,416.91
D $1,461.41
amo
Answers
Answer:
44.50
Step-by-step explanation:
461.41-416.91
Simplify the expression: - 3+ 60 x 10 6 . 97 130 103 103 HELP
Answers
Answer:
597,
Step-by-step explanation:
what is 6 . 97 130 103 103 please specify
am I multiplying dividing...
Paula bought 8 pairs of socks. She paid $104. Two pairs of socks cost the same amount. How much did each of the others pairs of socks cost?
Answers
Answer:
The other socks cost 9$.
Step-by-step explanation:
Find the equation of the line shown.
(Please help me)
Answers
Answer:
2y=x
Step-by-step explanation:
How many pint are in 28 cups
Answers
Answer:
14 pints are in 28 cups
Step-by-step explanation:
Answer:
14 pints in 28 cup
Step-by-step explanation:
If a car's gas tank has 15 gallons of gas in it, and the gauge says the tank is 75% full, then how many gallons can the entire tank hold?
12
20 gallons
24
11.25
Answers
Answer:
20 gallons
Step-by-step explanation:
set up proportion
15/x=75/100
cross multiply
75x=1500
x=20 gallons
Bài 2: Cho ∆ABC có AB AC = , M là trung điểm của BC . Trên tia đối của tia MA lấy điểm D sao cho MA = MD .
a) Chứng minh : ∆ ABM =∆ DCM .
b) AB // DC
c) AM ⊥ MC
d) Tìm điều kiện ∆ABC để góc ADC =30 °
Answers
