Answer: 2.
Step-by-step explanation:
Number of samples = 121
Average speed (sample mean) = 65mph
Population standard deviation = 22 mph
The standard error of the mean is:
Standard error of the mean(S.Em)
Standard error of the mean is the proportion of the population standard deviation and the square root of the sample size.
S.Em = standard deviation / √same size
S.Em = 22 / √121
S.Em = 22 / 11
S.Em = 2
Two factory plants are making TV panels. Yesterday, Plant A produced 5000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 450 defective panels
Answer:
10,000 panels
Step-by-step explanation:
A TV panel is being produced by two factory plants
Plant A produced 5000 fewer panels than plant B
Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B
a= b-5000............equation 1
5% of the panels from plant A were defective
= 5/100
= 0.05
2% of the panels from plant B were defective
= 2/100
= 0.02
The total defective panels of both plants is 450
0.05a + 0.02b= 450..............equation 2
Substitute b-5000 for a in equation 2
0.05(b-5000) + 0.02b= 450
0.05b - 250 + 0.02b= 450
Collect the like terms
0.05b+0.02b= 450+250
0.07b= 700
Divide both side by the coefficient of b which is 0.07
0.07 b/0.07= 700/0.07
b= 10,000
Hence plant B produced 10,000 panels
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Complete question:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?
Answer:
Juice A = 15
Juice B = 35
Step-by-step explanation:
Given the following:
Juice A:
Let juice A = a
35% pure fruit juice
Juice B:
Let juice B = b
85% pure fruit juice
We need to make 50 pints of juice from both: that is ;
a + b = 50 -------(1)
In terms of pure fruit:
a = 0.35 ; b = 0.85 ;
Our mixed fruit juice from a and b should be 70% pure fruit = 0.7
Mathematically,
0.35a + 0.85b = 50(0.7)
0.35a + 0.85b = 35 -------(2)
Multiply (2) by 100
35a + 85b = 3500 --------(3)
We can then solve the simultaneous equation:
a + b = 50 -------(1)
35a + 85b = 3500 --------(3)
Multiply (1) by 35
35a + 35b = 1750 -----(4)
35a + 85b = 3500 ---(5)
Subtract (5) from (4)
-50b = -1750
b = 35
Substitute b = 35 into (2)
0.35a + 0.85(35) = 35
0.35a + 29.75 = 35
0.35a = 35 -29.75
0.35a = 5.25
a = 5.25/0.35
a = 15
Juice A = 15
Juice B = 35
i. For any uniform probability distribution, the mean and standard deviation can be computed by knowing the maximum and minimum values of the random variable.
a) true
b) false
ii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.
a) true
b) false
iii. The uniform probability distribution's shape is a rectangle
a) true
b) false
Answer: I. True
II. True
III. True
Step-by-step explanation:
Uniform probability distributions, this are probability distributions which have equally likely outcomes. There are two known types of uniform distributions:
1. discrete
2. continuous.
In the first type of distribution, each outcome is discrete. In a continuous distribution, outcomes are continuous this means they are usually infinite.
what is 92.5% of 200
Answer:
185
Step-by-step explanation:
All you have to do is multiply 200 by 92.5/100 (because it is 92.5%). This gives you 185.
Hope this helps!
Answer:
185
We know 92.5% of 100 is 92.5%, so 92.5 of 200 is just 92.5×2.
When using a calorimeter, the initial temperature of a metal is 70.4C. The initial temperature of the water is 23.6C. At the end of the experiment, the final equilibrium temperature of the water is 29.8C. What is the final temperature of the metal? C What is the temperature change of the water? C What is the temperature change of the metal? C
Answer:
29.8C6.2C-40.6CStep-by-step explanation:
a) "Equilibrium" means the final temperatures of everything in the calorimeter are the same. The final temperature of the metal is the same as that of the water: 29.8C.
__
b) The temperature change of the water is ...
final temp - initial temp = 29.8C -23.6C = 6.2C
__
c) The temperature change of the metal is ...
final temp - initial temp = 29.8C -70.4C = -40.6C
Answer:
29.8C
6.2C
-40.6C
Step-by-step explanation:
A company offering online speed reading courses claims that students who take their courses show a 5 times (500%) increase in the number of words they can read in a minute without losing comprehension. A random sample of 100 students yielded an average increase of 415% with a standard deviation of 220%. Calculate a 95% confidence interval for the average increase in number of words students can read in a minute without losing comprehension. Choose the closest answer.
Answer:
C.I = (371.88 , 458.12)
Step-by-step explanation:
Given that:
sample size n = 100
sample mean [tex]\overline x =[/tex] 415
standard deviation = 220
The objective is to calculate the 95% confidence interval for the average increase in number of words students who can read in a minute without losing comprehension.
At 95% confidence interval; level of significance ∝ = 1 - 0.95
level of significance ∝ = 0.05
[tex]z_{\alpha/2} = 0.05/2[/tex]
[tex]z_{\alpha/2} = 0.025[/tex]
The critical value at [tex]z_{\alpha/2} = 0.025[/tex] is 1.96
C.I = [tex]\overline x \pm M.O,E[/tex]
C.I = [tex]\overline x \pm z_{\alpha/2} \dfrac{\sigma }{\sqrt{n}}[/tex]
C.I = [tex]415\pm 1.96 \dfrac{220 }{\sqrt{100}}[/tex]
C.I = [tex]415\pm 1.96 *\dfrac{220 }{10}[/tex]
C.I = [tex]415\pm 1.96 *22[/tex]
C.I = [tex]415\pm 43.12[/tex]
C.I = (371.88 , 458.12)
If f(x) = 2x2 - 5 and g(x) = x2 - 4x - 8, find (f - g)(x).
O A. (f- g)(x) = x2 - 4x - 3
O B. (f- g)(x) = x2 + 4x + 3
O C. (f- g)(x) = 3x2 - 4x - 13
O D. (f - g)(x) = -x2 - 13
The value of (f - g)(x) is x² + 4x + 3 if f(x) = 2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 2x² - 5
g(x) = x² - 4x - 8
(f - g)(x) = f(x) - g(x)
= (2x² - 5) - (x² - 4x - 8)
= 2x² - 5 - x² + 4x + 8
= x² + 4x + 3
(f - g)(x) = x² + 4x + 3
Thus, the value of (f - g)(x) is x² + 4x + 3 if f(x) = 2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.
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Two angles form a linear pair. The measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘ . Find the measure of each angle.
Answer:
70° and 110°
Step-by-step explanation:
If two angles forms a linear pair, this means that the sum of the angles is 180°. If the measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘
Let A be the first angle = x°
Let B be the second angle = (1.4x+12)°
Since they form a linear pair, then
A+B = 180°
x + 1.4x+12 = 180°
2.4x = 180-12
2.4x = 168
x = 168/2.4
x = 70°
The measure of angle A = 70°
The measure if angle B = 1.4x+12
B = 1.4(70)+12
B = 98+12
B = 110°
The measure of both angles are 70° and 110°
Explain how to solve the equation |2x-3| = x^2 graphically. Using a graphing calculator to find all real number solutions to the equation.
Answer:
x = -3 , x = 1
Step-by-step explanation:
Hello,
you need to draw the graph of the two functions and then find the intersection points.
please see below
So the solution is the two points A and B
(-3,9) and (1,1)
Hope this helps
Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M. Which angle is an adjacent interior angle to ∠JKM? ∠JKL ∠MKL ∠KLM ∠LMK
Answer:
The correct option is;
∠MKL
Step-by-step explanation:
From the construction of the line LKJ to form the exterior angle ∠JKM, we have that the segment MK of triangle KML forms two adjacent angles on JKL which are ∠JKM and ∠MKL, therefore, the adjacent interior angle to angle ∠JKM is angle ∠MKL
PLease find attach The drawing of triangle KML showing the extended point J
Answer:
B) ∠MKL
Step-by-step explanation:
Took the quiz on edge
If 3, x, y, -9 are in A.P, find the values of x and y.
Answer:
x = -1y = -5Step-by-step explanation:
The common difference (d) can be found using the first and 4th terms:
a1 = 3
a4 = a1 +d(4 -1)
-9 = 3 +3d . . . . . simplify
-3 = 1 + d . . . . . . divide by 3
-4 = d . . . . . . . . . subtract 1
Then ...
x = a1 + d = 3 -4 = -1
y = x + d = -1 -4 = -5
The values of x and y are -1 and -5, respectively.
Find the surface area of the regular pyramid shown to the nearest whole number
Answer:
740 m^2
Step-by-step explanation:
¿por qué no está definida la raíz de índice par de un número negativo?
Answer:
Porque se convierte en positivo cada vez que haces la raíz cuadrada.
Help please!!! Thanksss
Answer:
6:00 p.m.
hope this helps :)
-4x-7+10x=-7+6x−4x−7+10x=−7+6xminus, 4, x, minus, 7, plus, 10, x, equals, minus, 7, plus, 6, x Choose 1 answer: Choose 1 answer: (Choice A) A No solutions (Choice B) B Exactly one solution (Choice C) C Infinitely many solutions
Answer:
(Choice C) C Infinitely many solutions.
Step-by-step explanation:
First of all, let us learn about solutions of linear equations in one variable.
The linear equations in one variable usually have one solution.
For example:
[tex]2x =x+3[/tex]
When we solve this:
[tex]2x-x=3\\\Rightarrow x=3[/tex]
One solution is [tex]x = 3[/tex]
But there can be situations when there are
1. No solutions:
For example:
[tex]x =x+9[/tex]
It means that value x is equal to value of x+9 which can never be true.
Truth is the term on Right Hand Side is always 9 greater than the value of Left Hand Side.
Such situations are called Contradictions.
Here, no solution exists.
2. Infinitely many solutions:
For example:
[tex]x+2x+8=3x+8[/tex]
The Right hand Side is just the simplification of the LHS.
And LHS is always equal to RHS no matter what is the value of variable [tex]x[/tex].
It means there are infinitely many solutions for this equation.
-----------------------------------------------------
Now, let us have a look at the given equation in the question:
[tex]-4x-7+10x=-7+6x[/tex]
Taking LHS: [tex]-4x-7+10x[/tex]
Taking the terms with [tex]x[/tex] on one side:
[tex]-7+10x-4x\\\Rightarrow -7+6x[/tex]
which is equal to Right Hand Side.
Hence, as we discussed in case 2 above.
For every value of [tex]x[/tex] the equation holds true.
[tex]\therefore[/tex] There exists infinitely many solutions to the given equation.
Correct answer is:
(Choice C) C Infinitely many solutions
Answer:
C Infinitiy solutions
Step-by-step explanation:
1. In triangle ABC. A-54.2° B=71.5º, a=12 4cm. Find b
Answer:
13
Step-by-step explanation:
What is the value of this expression when a = 2 and b = -3?
5
Answer:
5 is the answer..
Step-by-step explanation:
simply by calculating
How many three-digit numbers can you make if you are not allowed to use any other digits except 1 and 2? (You may use 1 and 2 in a number more than once or not at all!)
The first digit can be 1 or 2.
For each one ...
The second digit can be 1 or 2.
For each one ...
The third digit can be 1 or 2.
That's (2•2•2)= 8 different possibilities.
Select the correct answer. A parabola has a minimum value of 0, a y-intercept of 4, and an axis of symmetry at x = -2. Which graph matches the description?
Answer:
The third graph
Step-by-step explanation:
The following data points represent the number of children in each household on Maple Street. \qquad 0, 1, 2, 1, 20,1,2,1,20, comma, 1, comma, 2, comma, 1, comma, 2 Find the mean number of children.
Answer:
The mean number of the children is 1.2
Step-by-step explanation:
Given
Children: 0, 1, 2, 1, 2
Required
Determine the Mean number
The mean of a set is calculated as follows;
[tex]Mean = \frac{\sum x}{n}[/tex]
Where x is the given set and n is the number of sets
In this case, n = 5 children
Hence;
[tex]Mean = \frac{0 + 1 + 2 + 1 + 2}{5}[/tex]
[tex]Mean = \frac{6}{5}[/tex]
[tex]Mean = 1.2[/tex]
Hence, the mean number of the children is 1.2
Find the area a. 530 b. 779 c. 390 d. 1060
Answer:
a. 530 ..I think.. i'm pretty sure
Step-by-step explanation:
40*26.5 is 1060
1060/2=530
area=530
Which statement is true about the equation fraction 3 over 4z = fraction 1 over 4z − 3 + 5?
Answer:
It has two solutions.
Step-by-step explanation:
Let as consider the given options are
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
The given equation is
[tex]\dfrac{3}{4z}=\dfrac{1}{4z-3}+5[/tex]
Multiply both sides by 4z(4z-3).
[tex]3(4z-3)=4z+5(4z(4z-3))[/tex]
[tex]12x-9=4z+80z^2-60z[/tex]
[tex]0=-12x+9+80z^2-56z[/tex]
[tex]0=80z^2-68z+9[/tex]
It is a quadratic equation.
Therefore, it has two solutions.
Answer:
It has 1 solution
Step-by-step explanation:
I did the test I put the guys above me in and got it wrong
If you vertically stretch the exponential function, f(x) = 2^x, by a factor of 4, what is the equation of the new function?
Answer:
f( x ) = 4( [tex]2^x[/tex] )
Step-by-step explanation:
If we vertically stretch a graph by a factor of 4, the " exponential slope " extending from the x - axis, should increase by a factor of 4 as well.
Therefore, the previous function is expressed by the following ...
f( x ) = [tex]2^x[/tex] ... then this new function should be -
f( x ) = 4( [tex]2^x[/tex] )
The equation of this new function is f( x ) = 4( [tex]2^x[/tex] )
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A.6
B.7
C.3
D.4
E.5
=======================================================
Explanation:
The distribution is perfectly symmetrical about the center 6. Notice how the left side is a mirror copy of the right side, due to the heights being the same. Because of this, the mean, median and mode are all the same value and that is 6. The mode is equal to 6 as this is the most frequent value.
The longer way to do this problem is to add up each value shown. We have four copies of '2', six copies of '3', and so on. The total sum you would get is 372. Divide this over 62 because there are 62 smaller green squares. The final result is the mean of 6.
The number closest to the mean of the given distribution is 6. Therefore, option A is the correct answer.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
From the given histogram,
Number Frequency
2 4
3 6
4 7
5 9
6 10
7 9
8 7
9 6
10 4
Here, the mean = [2(4)+3(6)+4(7)+5(9)+6(10)+7(9)+8(7)+9(6)+10(4)]/[4+6+7+9+10+9+7+6+4]
= [8+18+28+45+60+63+56+54+40]/62
= 372/62
= 6
Therefore, option A is the correct answer.
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The sports car travels along a straight road such
that its acceleration is described by the graph. Construct the
v-s graph for the same interval and specify the velocity of
the car when s = 10 m and s = 15 m.
Answer:
at s = 10m, v(t_1) = 7.663 m/s
at s = 15m, v(t_2) = 10.041 m/s
Step-by-step explanation:
for the interval 0-10 seconds,
a(t) = t m/s^2
v(0) = 0
v(t) = v(0) + integral(a(t)dt)
= 0 + [t^2/2]
= (1/2) t^2
s(0) = 0 .................. arbitrary
s(t) = s(0) + integral(v(t)dt)
= 0 + integral ((1/2)t^2)
= (1/6)t^3
When s(t) = 10 m,
(1/6)t^3 = 10
t^3 = 60
t_1 = 60 ^(1/3) = 3.9149 s approx.
v(t_1) = (1/2) t_1^2 = (1/2)3.9149^2 = 7.663 m/s
When s = 15 m
(1/6)t^3 = 15
t^3 = 90
t_2 = 4.4814 s approx.
v(t_2) = (1/2)t_2^2 = (1/2)4.4814^2 = 10.041 m/s
Answer:
at s = 10m, v(t_1) = 7.663 m/s
at s = 15m, v(t_2) = 10.041 m/s
Step-by-step explanation:
I took the test and got it right
Which equation represents the line that passes through (-6, 7) and (-3, 6)?
y=-*x+9
y=-*x+5
y=-3x – 1ly
y=-3x + 25
Answer:
y = -3x - 11
Step-by-step explanation:
(y - y1)/(x - x1) = (x2 - x1)/(y2 - y1)
(y - 7)/(x + 6) = (-3 + 6)/(6 - 7)
(y - 7)/(x + 6) = 3/-1 = -3
y - 7 = -3(x + 6)
y - 7 = -3x - 18
y = -3x -18 - 7
y = -3x - 11
This graph shows how the length of a time kayak is rented is related to the rental cost. What is the rate of change shown in the graph?
Answer:
A.
Step-by-step explanation:
Which number is the additive inverse of –5? A.– 1/5 B.0 C.1/5 D.5
Answer:
Hey there!
The additive inverse means the number opposite to five.
The additive inverse of negative five is positive five.
Hope this helps :)
Answer:
The additive inverse of negative five is positive five.
explanation:
T models the temperature (in degrees Celsius) in New York City when it's t hours after midnight on a given day. Match each statement with the feature of the graph that most closely corresponds to it.
Answer:
Y Intercept: It was 3C at the beginning of the day.
Positive or negative interval: The temperature was above zero between 8 am and 8 pm.
Increasing or decreasing interval: It was getting warmer between 2 am and 2 pm
Step-by-step explanation:
Features matching the correct statements are:
y intercept: It was ₋3°C at the beginning of the day.
Positive or negative interval: The temperature was above zero between 8 am and 8 pm.
Increasing or decreasing interval: It was getting warmer between 2am and 2 pm.
What is the temperature graph over time?
The x-axis in a time-temperature graph, sometimes known as a "x-y graph," depicts time, and the y-axis the temperature. The temperature's relationship to time is depicted on the graph.
we can notice in the given graph that T(t) represents the time and t represents the temperature of the city.
So we see when lowercase t when time is zero(0), zero hours after midnight the temperature in the New York city is negative 3°C(₋3°C) so it was ₋3°C at the beginning of the day since the true beginning of the day is right at midnight. Hence y intercept tells us that it was ₋3°C at the beginning of the day. Then about the positive or negative interval we can notice from the graph that we have a negative interval from time equals zero to time equals eight which means the temperature is negative as it goes below zero and from 8 am to 8 pm we can see that the temperature goes positive and then it dips down to negative again. So a positive or negative interval tells us about when the temperature was above xero between 8 am and 8 pm.The increasing and decreasing interval, here we see that the function is increasing as t increases so does the temperature, all the way to 2 pm. Hence, we are just using the increasing interval to match the statement that it was getting warmer between 2 am and 2 pm.Hence we get the statements match to their features.
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PLEASEEEEEE HELPPPPP Which of the following is the surface area of the right cylinder below?
The correct answer is D. [tex]72 \pi[/tex] [tex]units^{2}[/tex]
Explanation:
The surface area refers to the sum of the area of all sides in a 3D shape such as a cube or cylinder. Additionally, the formula used to calculate the surface area varies with the shape. In the case of cylinders, the general formula is [tex]A = 2\pi r h + 2\pi r^{2}[/tex]. Moreover in this, the r represents the radius (measure from the center of a circle to any side), while the h represents height. Below, all the process is shown:
[tex]A = 2\pi r h + 2\pi r^{2}[/tex]
[tex]A = 2\pi (8 x 3) + 2\pi 8^{2}[/tex]
[tex]A = 2\pi 24 + 2\pi 64[/tex]
[tex]A = 48\pi + 128\pi[/tex]
[tex]A = 176\pi[/tex]
In this point, you have the answer without solving [tex]\pi[/tex] (3.1416). This makes option A the correct answer.
