Using the normal distribution, it is found that:
a) [tex]Z_0 = -1.75[/tex].
b) [tex]Z_0 = 1.96[/tex].
c) [tex]Z_0 = 1.645[/tex].
d) [tex]Z_0 = -0.83[/tex].
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Each z-score has a p-value associated with it, which is the percentile of X, and is found at the z-table.Item a:
This is Z with a p-value of 0.0401, thus [tex]Z_0 = -1.75[/tex].
Item b:
Due to the symmetry of the normal distribution, the middle 95% is between the 2.5th and the 97.5th percentile.We want the positive value, so Z with a p-value of 0.975, which is [tex]Z_0 = 1.96[/tex]Item c:
Same logic as b, just middle 90%, thus [tex]Z_0 = 1.645[/tex].
Item d:
This is Z with a p-value of 1 - 0.2967 = 0.2033, thus [tex]Z_0 = -0.83[/tex].
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Final answer:
The value of the standard normal random variable Z that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.
Explanation:
The z-score that corresponds to the area 0.90 under the standard normal distribution can be found using a z-table or a calculator.
Using a z-table, locate the area 0.90. The corresponding z-score is approximately 1.28.Using a calculator, the invNorm(0.90) command can be used to find the z-score, which is also approximately 1.28.Therefore, the value of the standard normal random variable Z, denoted as Z0, that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.
There are five seniors in a class. For each situation, write how the binomial formula is used to calculate the probability.
a) In how many ways can I choose one senior to represent the group?
b) In how many ways can I choose two seniors to represent the group?
c) In how many ways can I choose three seniors to represent the group?
d) In how many ways can I choose four seniors to represent the group?
e) In how many ways can I choose five seniors to represent the group?
A baker bought some flour. He used to 2/5 of the flour to make bread and used the rest to make batches of muffins. If he used 16 pounds of flour making bread and 2/3 pound for each batch of muffins how many batches of muffins did he make
Find the number of years it would take for $1,200 to earn simple interest of $324 at an annual interest rate of 6% per year.
There are 13 fish in an aquarium. seven of the fish are guppies. how many non-guppies are in the aquarium
Factor completely and then place the factors in the proper location on the grid.
4y2 + 25y + 6
Answer:
factored form of given equation [tex]4y^2+25y+6[/tex] is [tex](4y+1)(y+6)[/tex]
Step-by-step explanation:
Given equation [tex]4y^2+25y+6[/tex]
We have to write the given equation in factors form and then represent the factors on grid.
Consider the given equation [tex]4y^2+25y+6[/tex]
25y can be written as 24y + y , we get
[tex]\Rightarrow 4y^2+24y+y+6[/tex]
Taking 4y common from first two term and 1 common from last two term, we get,
[tex]\Rightarrow 4y(y+6)+1(y+6)[/tex]
[tex]\Rightarrow (4y+1)(y+6)[/tex]
Thus, factored form of given equation [tex]4y^2+25y+6[/tex] is [tex](4y+1)(y+6)[/tex]
On grid it is shown as shown in attachment below.
After 3 years, what is the total amount of a compound interest investment of $5,000 at 4% interest, compounded quarterly?
$5,203.71
$5,360.68
$20,480,000
$5,634.13
Jared wrote an equation for the perimeter of an equilateral triangle as 3x = 20. What does x represent in his equation?
Answer:
The length of a side of the triangle.
Step-by-step explanation:
An equilateral triangle has 3 equal sides so the x would be equal to one side of the triangle.
What is 4/5 4/5 as a mixed number fraction?
A rectangle's length is 4 feet more than its width. If the area of the rectangle is 396 square feet, what is its width, in feet?
Solve for x.
x/7 = -3
1,) x = -21
2.) x = -10
3.) x = 4
4.) x = 21
Given that f(x) = 6x 2 and g(x) =2x=4/5 , solve for g(f(1))
Answer:
The answer would be 4.
Step-by-step explanation:
What you have to do here is you have to substitute
So the problem told you the f(x) = 1. So what you want to do is plug that into the function f(x).
So:
f(x) = 6(1)2
= 8
Now we know that f(x) = 8, so what we going to do now is plug f(x) into g(x).
So:
g(f(8)) = 2(8) + 4/5
= 4
The value of g(f(1)) is 4.
Composite function -Composition of functions is the process of plugging one function into another, and simplifying or evaluating the result at a given x-value. Another way to read it is "f circle g of x." It is a process that joins two functions to create a third, unique function.Given ,
f(x) = 6x + 2
g (x) = 2x + 4 /5
To get value of g(f(1)) first we have to solve f(x).
f(x) = 6x + 2 .......................(1)
We simply put x = 1 in equation 1 .
Then, F(1) = 6 × 1 + 2 ⇒ 8
Now , we put value of f(1) in g(f(1)) ,
So, g(f(1)) = [tex]\frac{2x + 4}{5}[/tex]
= [tex]\frac{2 * 8 + 4}{5}[/tex]
= [tex]\frac{16 + 4}{5}[/tex]
= 20/5 ⇒ 4
Therefore, the value of g(f(1)) is 4 .
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which is greater 14 ounces or 0.4 kilograms
After converting 0.4 kilograms to ounces using the appropriate conversion factors, it is determined that 0.4 kilograms is slightly greater than 14 ounces.
Explanation:To determine which is greater, 14 ounces or 0.4 kilograms, we first need to use the appropriate conversion factors to compare the two measurements in the same unit. Since 1 pound is equivalent to 0.4536 kilograms, and 1 pound is also equal to 16 ounces, we need to convert one of the measures so that both are in either ounces or kilograms for a direct comparison.
Converting 0.4 kilograms to ounces:
1 kilogram is approximately 2.20462 pounds (since 1 pound is 0.4536 kg).So, 0.4 kilograms is 0.4 * 2.20462 pounds, which is approximately 0.882 pounds.Next, we convert 0.882 pounds to ounces by multiplying by the conversion factor of 16 ounces per pound: 0.882 * 16 = 14.11 ounces (approximately).Now we have both weights in ounces, and we can see that 14.11 ounces is slightly more than 14 ounces. Therefore, 0.4 kilograms is greater than 14 ounces.
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A piece of furniture has a retail price of $3,200 and is on sale at a 30% discount. how much money will be saved if the piece of furniture is purchased at the sale price?
I need help finding the slope for AB, BC, CD and DA
A class of 18 students took a math test. Seven students had an average of 90. The other students had an average of 82.
What is the average for the whole class? Round to the nearest whole percent.
A) 80
B) 83
C) 85
D) 87
Answer: C- 85%
Step-by-step explanation:
7x11=630
Remaining Students: 18-7=11
11x82=902
Aveage:
630+902=1532
1532/18=85.1111
A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line.
f(x) = - 1 over 4x + 4
f(x) = - 1 over 10x + 4
f(x) = - 1 over 10x + 10
f(x) = - 1 over 4x + 10
Answer:
Option D is correct
[tex]y =-\frac{1}{4}x+10[/tex]
Step-by-step explanation:
Slope intercept form:
The equation of line is given by:
[tex]y=mx+c[/tex] .....[1]
where, m is the rate or slope and c is the y-intercept or initial value.
As per the statement:
Here, y represents the distance in kilometer and x represents the time in minutes.
A student is running a 10-kilometer race
⇒y(0) = b = 10 km
It is also given that he runs 1 kilometer every 4 minutes.
Now, with each passing minute the student is getting closer and closer to the finish line which was 10 kilometers away when the race started. Thus, as the race progresses, the distance between the student and the finish line will decrease.
[tex]m =-\frac{1}{4}[/tex]
Substitute these in [1] we have;
[tex]y = -\frac{1}{4}x+10[/tex]
Therefore, the function that describes his distance from the finish line is, [tex]y = -\frac{1}{4}x+10[/tex]
Please help me
All of the following are equivalent except _____.
2%
0.2
1/50
0.02
77 decreased by twice of a number
The algebraic expression for '77 decreased by twice of a number' is 77 - 2x, where x is the unknown number.
Explanation:The question '77 decreased by twice of a number' involves creating an algebraic expression. This expression will have the form 77 - 2x, where x represents the unknown number. To decrease 77 by twice a number means to subtract two times that number from 77.
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What is the unit rate of 50.4 feet in 14 years?
5,893,402 + 19,392,009 =
Write the trigonometric expression in terms of sine and cosine, and then simplify.
csc2 x − cot2 x
Egypt is 386,700 square miles and wyoming is about 97,818 square miles egypt is about how many times as large as wyoming
Egypt is approximately 4 times as large as Wyoming when comparing their areas.
Explanation:To calculate how many times larger Egypt is compared to Wyoming, we divide the area of Egypt by the area of Wyoming. The area of Egypt is 386,700 square miles, and the area of Wyoming is about 97,818 square miles.
Dividing the area of Egypt by the area of Wyoming gives us: 386,700 / 97,818 ≈ 3.95.
Therefore, Egypt is approximately 4 times as large as Wyoming.
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How do you fine arccot(-sqrt(3))?
Answer:The answer is be And i’m Strongly positive about this because i just got it right!
Step-by-step explanation:
A company introduces a new product for which the number of units sold S is
S(t)= 200 ( 5- 9/(2+t))
where t is the time in months
(a) Find the avg. value of S(t) during the first year.
(b) During what month does S'(t) equal the avg value during the first year? ...?
Select all ratios equivalent to 20:4
4:20, 2:10, 15:3, 1:2
Final answer:
The only ratio equivalent to 20:4 from the given choices is 15:3 because, when simplified, both ratios reduce to 5:1.
Explanation:
To determine which ratios are equivalent to 20:4, we need to find ratios that can be simplified or scaled to form the same relationship. An equivalent ratio maintains the proportion when both terms are multiplied or divided by the same number.
First, the given ratio of 20:4 can be simplified by dividing both terms by 4, which gives us 5:1. Now, we can compare this to the choices provided:
4:20 is not equivalent because when simplified (divided by 4), it gives 1:5, which is the inverse of 5:1.2:10 simplifies to 1:5 (dividing by 2), also not equivalent for the same reason.15:3 simplifies to 5:1 (dividing both terms by 3), which is equivalent to 20:4.1:2 is already in simplest form and is not equivalent to 5:1 or 20:4.Therefore, the only ratio equivalent to 20:4 given in the choices is 15:3.
The difference between five times a number and twelve times the number is –35.
The lengths of two sides of a triangle are 9 and 15. What can be said about the length of the third side?
It must be geater than or equal to 6 and less than 24.
It must be greater than or equal to 6 and at most 24.
It must be greater than 6 and less than 24.
It must be greater than 6 and at most 24.
Answer:
Your answer is B
As the sum of any 2 lengths of a triangle is always greater than the third length
Step-by-step explanation:
It must be greater than or equal to 6 and at most 24.
Given that
The lengths of the two sides of a triangle are 9 and 15.
We have to determine
What can be said about the length of the third side?
According to the question
The lengths of the two sides of a triangle are 9 and 15.
By the properties of the triangle, the sum of the square of two lengths is equal to the third side length of the triangle.
Always remember that when you add two sides to a triangle, the sum will come out to be higher than the third side’s length.
Hence, It must be greater than or equal to 6 and at most 24.
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A giant salmon skier uses skies that are one sixth her height. if she is 174 cm tall how long are her skies?
A copy machine makes 44 copies per minute. How many copies does it make in 4 minutes and 30 seconds?
To cover A rectangle region of her yard penny needs atleast 170.5 square feet of sod. The length of the region is 15.5 feet. What are the possible widths of the region?