Using the normal distribution, the percentages are given as follows:
a) 9.18%.
b) 97.72%.
c) 50%.
d) 4.27%.
e) 0.13%.
f) 59.29%.
g) 2.46%.
h) 50%.
i) 50%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 247, \sigma = 60[/tex]
For item a, the proportion is the p-value of Z when Z = 167, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (167 - 247)/60
Z = -1.33.
Z = -1.33 has a p-value of 0.0918.
Hence the percentage is of 9.18%.
For item b, the proportion is the p-value of Z when Z = 367, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (367 - 247)/60
Z = 2.
Z = 2 has a p-value of 0.9772.
Hence the percentage is of 97.72%.
For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (247 - 247)/60
Z = 0
Z = 0 has a p-value of 0.5.
Hence the percentage is of 50%.
For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (350 - 247)/60
Z = 1.72
Z = 1.72 has a p-value of 0.9573.
1 - 0.9573 = 0.0427.
Hence the percentage is of 4.27%.
For item e, the proportion is the p-value of Z when Z = 67, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (67 - 247)/60
Z = -3.
Z = -3 has a p-value of 0.0013.
Hence the percentage is of 0.13%.
For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:
X = 300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (300 - 247)/60
Z = 0.88.
Z = 0.88 has a p-value of 0.8106.
X = 200:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (200 - 247)/60
Z = -0.78.
Z = -0.78 has a p-value of 0.2177.
0.8106 - 0.2177 = 0.5929.
Hence the percentage is 59.29%.
For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:
X = 400:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (400 - 247)/60
Z = 2.55.
Z = 2.55 has a p-value of 0.9946.
X = 360:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (360 - 247)/60
Z = 1.88.
Z = 1.88 has a p-value of 0.97.
0.9946 - 0.97 = 0.0246
Hence the percentage is 2.46%.
For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.
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a. The cardinal number of {213, 214, 215, 216, ..., 912) is
Answer:
Step-by-step explanation:
a=213
l=912
let cardinal number=n
let c.d.=d
d=214-213=1
l=a+(n-1)d
912=213+(n-1)1
912=213+n-1
912-212=n
n=700
cardinal number=700
how do I get the answer to blank space in the picture below
Answer:
Answer is 1Step-by-step explanation:
Using addition(Left hand side) 5 + 1 = 6
(Right hand side) 5 + 1 = 6
Hope this helpsGood luck ✅3
bec
At the end of the mini-golf game Heather was 2 over par, Alphonso was 3 under par,
Jackie was par, Wanda was I under par, and Trevor was 4 over par. Write an integer to
represent each of their golf scores. Then order the golfers from 1st to 5th place.
(Remember that the LOWEST score in golf wins!)
the order of golfers from 1st to 5 th is Trevor, Heather, Wanda, Jackie and Alphonso.
we are given that:
at the end of amini golf match,
Heather was 2 over par
So, Heather = 2
Alphonso was 3 under par
Alphonso = - 3
Jackie was par
Jackie = 0
Wanda was I under pa
Wanda = 1
Trevor was 4 over par.
Trevor = 4
Now arranging the integers from 1st to 5th place,
Trevor = 4 is 1st
Heather = 2 is 2 nd
Wanda = 1 is 3rd
Jackie = 0 is 4th
and Alphonso = - 3 is 5th
Therefore, the order of golfers from 1st to 5 th is Trevor, Heather, Wanda, Jackie and Alphonso.
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What is the solution to -2(8x-4) < 2x + 5?
x > 2/1/20
x < 1/1/20
x>6
x<6
The solution to the given Inequality i.e. -2(8x-4) < 2x + 5 is x>[tex]\frac{1}{6}[/tex]
Inequality:
Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Equations can be used to address Inequality problems when they are stated as questions or as declarations of fact in the form of theorems.
Given that a Inequality i.e. -2(8x-4) < 2x + 5 and asked to find the solution of the given Inequality.
⇒ -2(8x-4) < 2x + 5
⇒ -16x+8 < 2x+5
⇒3< 18x
⇒x>[tex]\frac{1}{6}[/tex]
Therefore,The solution to the given inequality i.e. -2(8x-4) < 2x + 5 is x>[tex]\frac{1}{6}[/tex]
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let U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4,5,6}, B = {2,4,5,6}, And C = {1,6,7}. find
Given;
U = {1,2,3,4,5,6,7,8,9},
A = {1,2,3,4,5,6},
B = {2,4,5,6},
C = {1,6,7}.
To find;
A∩B, A∪C, (AUB)∩(A∪C), A'∩B', (A∩C)', A∪C, A∩(B∪C), A', A'∪B', A-B, A∪B, A∪(B∪C), B', (AUB)', B-C
A∩B = {2,4,5,6,}
A∪C = {1,2,3,4,5,6,7}
(AUB)∩(A∪C) = {1,2,3,4,5,6}
A'∩B' ={7,8,9}
(A∩C)' = {2,3,4,5,7,8,9}
A∪C = {1,2,3,4,5,6,7}
A∩(B∪C) = {1,2,4,5,6}
A' = {7,8,9}
A'∪B' = {1,3,7,8,9}
A-B = {2,4,5,6}
A∪B = {1,2,3,4,5,6}
A∪(B∪C) = {1,2,3,4,5,6,7}
B' = {1,3,7,8,9}
(AUB)' = {7,8,9}
B-C = {6}
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A 3-gallon bottle of bleach costs $19.56. What is the price per quart?
The price per quart is 0.40 dollars
Given that A 3-gallon bottle of bleach costs $19.56 and asked to find out the price per quart.
There are 16 quarts for a gallon
For a 3-gallon bottle, price is 19.56 dollars
For a one-gallon bottle, the price is [tex]\frac{19.56}{3}[/tex] dollars.
⇒The price of the one-gallon bottle is 6.52 dollars.
The price of 16 quarts is 6.52 dollars.
The price of one quart is [tex]\frac{6.52}{16}[/tex]
The price of one quart is 0.40 dollars.
Therefore,the price of the one quart is 0.40 dollars.
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Pls help it’s just one answer
Answer:
its 5 good luck
Step-by-step explanation:
Answer:
40 - 35 = 5 dollars more
Jennie median = 40
Markos median = 35
Subtract and it equals = 5
Hope this helps with your question :)
Points P and S are located the same distance from 0 on the
number line shown.
The expression which has a negative value according to the number line drawn in the task content where points P and S are as given is; Choice D; P + 1.
Which expression has a negative value according to the number line drawn in the task content?It follows from the task content that the expression which has a negative value among the given answer choices is to be identified.
As evident in the number line, the number S is greater than 1, and hence, is a positive number.
Also, the number P is less than -1 and hence, is a negative number.
Since, the task content requires that the expression with negative value be identified, it follows that the required expression is; Choice D.
This follows from the fact that, hypothetically, the value of P is -1.8, hence; P + 1 = -1.8 + 1
= -0.8
Ultimately, The expression which has a negative value according to the number line drawn in the task content where points P and S are as given is; Choice D; P + 1.
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SA school has 900 concert tickets for sale. Some of them are for reserved seats (x) and the
rest are for general admission (y). No more than 600 reserved seat tickets can be sold. They
know they will sell at least 200 general admission tickets. Write a system of inequalities that
shows how many of each type of ticket can be sold and then graph the feasible region.
Answer:
x ≤ 600y ≥ 200x +y ≤ 900see the attachment for a graphStep-by-step explanation:
Given 900 tickets for sale and restrictions on the numbers of reserved and general admission seats, you want a system of inequalities that models the possible sales. You also want a graph of the feasible region.
The variables are defined as ...
x = number of reserved seat ticketsy = number of general admission ticketsInequalitiesThe limits give rise to these inequalities:
x ≤ 600 . . . . . no more than 600 reserved seats can be sold
y ≥ 200 . . . . . at least 200 general admission tickets will be sold
x + y ≤ 900 . . . . at most, 900 tickets can be sold
GraphThese inequalities can be graphed simply by giving them as input to a graphing calculator. The result is attached. The feasible region is that area of the graph where the three solution spaces overlap. Here, it is outlined in black.
(BRAINLIESTING ANYONE WHO SOLVES THIS AND POSTS AN IMAGE OF SOLVED QUESTION)
Red and green lines are Parallel lines. and black line is perpendicular to the blue line.
How are parallel straight lines related?Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.
Since the parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.
In the given figure, we have a set of lines which are parallel and perpendicular to each others.
We know that Parallel lines are lies in the same plane which when extended do not meet and are always same distance apart from each other.
The Perpendicular lines are two non-vertical lines in the same plane that intersect at right angles.
From the figure given,
Red and green lines are Parallel lines. and black line is perpendicular to the blue line.
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Fission of 1 kg of element B releases ? times as much energy as burning 1 kilogram of element A. (Round to the nearest whole number as needed.)
Fission of 1 kg of element B releases 26 times as much energy as burning 1 kilogram of element A.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
What is a proportion?A proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Next, we would determine the ratio of the energy released by elements A and B:
EB : EA = EB/EA
Ratio = 1.3 × 10¹⁰/5.1 × 10⁸
Ratio = 25.49 ≈ 26.0
Therefore, fission of 1 kg of element B releases 26 times as much energy as burning 1 kilogram of element A.
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Complete Question:
Use the table to the right to answer the following question.
Compare the energy released by fission of 1 kilogram of element B to that released by burning 1 kilogram of element A.
Energy released by burning 1 kilogram of element A is 5.1 × 10⁸
Energy released by fission of hydrogen in 1 kilogram of element B is 1.3 × 10¹⁰
Fission of 1 kg of element B releases ____ times as much energy as burning 1 kilogram of element A. (Round to the nearest whole number as needed.)
Eight less than the product of six and the difference of a number and two is twice the number. What is the number?
If 8 less than the product of 6 and the difference of a number and 2 is twice the number, then the number is 5.
As per the question statement, 8 less than the product of 6 and the difference of a number and 2 is twice the number.
We are required to calculate the number.
To solve this question, let us assume that our concerned number is "x". Now, we will form a linear equation of single variable, based on the conditions mentioned in the question statement, and solving for "x", we will obtain our desired answer.
[tex][6(x-2)-8]=2x\\or, 6x-12-8=2x\\or,6x-(12+8)=2x\\or,6x-20=2x\\or,6x-2x=20\\or, 4x=20\\or, x=\frac{20}{4} =5[/tex]
Product: In mathematics, a product is the result of multiplication of two or more numbers or factors.Linear Equation: A linear equation is an algebraic equation when graphed, always results in a straight line and each term has an exponent of 1.To learn more about Linear Equations, click on the link below.
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What’s the correct answer answer asap for brainlist
Answer:The answer is a.
Step-by-step explanation:I hope this helps.
Find the distance between ( -3,4) and (2,-4)
Answer: exact form: √89 decimal form: 9.43398113…
Step-by-step explanation:
the distance between (-3,4) and (2,-4) is
exact form: √89 decimal form: 9.43398113…
The two beakers below contain pure water.
Which of the following properties is the same for both of these samples?
A
Mass
B
Weight
C
Volume
D
Boiling Point
•FIA: bid 2 =6
2- Given the 12 term of an arithmetic sequence which is 13
and d=2. Find the A1.
The first term of the arithmetic sequence [tex]a_{1}[/tex] is -9
As per the question statement, we are given an arithmetic sequence whose 12th given term is 13 and common difference is 2. We are supposed to find the first term [tex]a_{1}[/tex].
We know that the [tex]n_{th}[/tex] term in an arithmetic sequence is given by:
[tex]a_{n} = a_{1}+(n-1)d[/tex]
where "n" is the number of terms and "d" is the common difference.
Now in question, [tex]a_{n} =a_{12} =13[/tex]
[tex]d=2[/tex]
[tex]n=12[/tex] and we have to find [tex]a_{1}[/tex]
Substituting values,
[tex]13=a_{1} +(12-1)*2\\13=a_{1} +11*2\\13=a_{1}+22\\a_{1} = -9[/tex]
Hence [tex]a_{1} = -9[/tex]
Arithmetic sequence: Arithmetic Progression (AP) or arithmetic sequence is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value known as common difference.To learn more about Arithmetic sequence, click on the link given below:
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Write and solve a subtraction word problem using the numbers 34,508 and 8,529
Answer:
Jack and Jill look at all their savings, Jack has £34,508 and Jill has £8,529. How much more does Jack have than Jill?
Step-by-step explanation:
34,508 - 8529 = 25979
Answer:
lay lay and jay went to the store and bout some candy they had 34,508 dollers and spent 8,529 dollers how much money do they have left
Step-by-step explanation:
hey did i help pls mark brainliest
Beth walk two blocks in 15 minutes how many blocks or bad word if she walked at the same rate for an hour
The answer for this given question is 8 blocks
Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
basic rules of algebra
• Commutative Rule of Addition.
• Commutative Rule of Multiplication.
• Associative Rule of Addition.
• Associative Rule of Multiplication.
• Distributive Rule of Multiplication.
15*4= 60, meaning a full hour.
15 minutes = 2 blocks
15 minutes = 2 blocks
15 minutes = 2 blocks
15 minutes = 2 blocks
add them all up and we get that in 60 minutes (an hour) Beth walked 8 blocks.
Hence, Beth walked 8 blocks in 60 minutes of time.
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5. Find the product: 26.4 x 0.15
A. 2.64
B. 3.96
C. 26.4
D. 29.6
please explain in number form and as little as possible but still explaining.
Answer:
B. 3.96
Step-by-step explanation:
use a calculator to solve the answer unless it's a sentence
You are solving a measurement problem where the numbers 2.058 × 109 and 3.0571 × 10−4 are divided. How many significant digits should the quotient have?
The number of significant digits is 4
What is quotient?Quotient can be defined as the number that results from the division of a number by another number.
Example;
The quotient of 4 and 2 is expressed as;
= 4/ 2
= 2
From the information given, we have the numbers as;
2.058 × 10^93.0571 × 10^−4To determine the quotient, we have;
= 2.058 × 10^9/ 3.0571 × 10^−4
= 6. 731 × 10^12
The number of significant digits is 4
Thus, the number of significant digits is 4
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What Is the term -3x and 5x combined to?
Answer:
Step-by-step explanation:
2x
Compare 4/5, 8/10, and 12/15 using ratios
On simplifying the equation this show that the ratio are equal:
4/5 = 4/5 = 4/5 .
What is the relationship between two ratios?To obtain the comparative ratio, find the LCM of both the consequents of both ratios, divide the LCM with both the consequents and then multiply the numerator and denominator of both ratios with the answer.
What does the ratio formula mean?The ratio is a relationship between the amounts of two or more things that indicates how much of one is contained in the other. The ratio formula can be used to convert a ratio into a fraction. a:b = a/b is the ratio formula for just about any two quantities, say a and b.
According to the given data:4/5, 8/10, and 12/15
dividing the ration to simplify it:
4/5, 8/10, and 12/15
8/10 = 4/5 on dividing by 2
12/15 = 4/5 on dividing by 3
So,
On simplifying the equation this show that the ratio are equal:
4/5, 8/10, and 12/15
4/5 = 4/5 = 4/5 .
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Destiny wants to spend at most $240 on a video games. If each video game cost $30, what are all the possible number of games Destiny can buy?
Part A: Translate the situation into an Inequality
The inequality that best matches the situation is
Answer Choices: (30x) (x/30) (240x) (x/240)
Answer Choices: (<) (>) (> or =) (> or =)
Answer Choices: (240) (30)
Part B: Solve the Inequality from Part A
Remember to use x < or > or < underline or > underline
Answer:
30x <= 240
Step-by-step explanation:
Given the definitions of f(x) and g(x) below, find the value of (fog)(-3).
f(x) = 3x² - 7x-3
g(x) = -4x - 10
The value of the composite function (f o g)(3) is 1603
How to evaluate the composite function?The functions are given as
f(x) = 3x² - 7x - 3
g(x) = -4x - 10
Next, calculate (f o g)(x) using
(f o g)(x) = f(g(x))
So, we have
(f o g)(x) = 3(-4x - 10)² - 7(-4x - 10) - 3
Substitute 3 for x.
So, we have
(f o g)(3) = 3(-4 x 3 - 10)² - 7(-4 x 3 - 10) - 3
Evaluate
(f o g)(3) = 1603
Hence, the value of the composite function (f o g)(3) is 1603
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7^x^2=7^3X+10 SOLVE FOR X
Answer:
x= -0.9
Step-by-step explanation:
Assuming you did a typo by saying 7 to the power of x that's also to the power of 2.
This is the answer for 7x^2 = 7x^3+10
A 100kg bag of granulated sugar is to
be put into smaller polythene (nylon)
bags each containing 250g. How
many polythene bags will needed?
100 kg = 100000 g
∴ bags needed = [tex]\frac{100000}{250}[/tex] = 400
Please help me.I'll give brainliest.
Answer:
24cm
Step-by-step explanation:
24÷2=12
1/2×b×h=1/2×12×10
=60cm
60-24=36
36-12=24cm
AustralianFish=24cm
A triangle has lengths 29, 29, and 40. Can you find another isosceles triangle with the same perimeter and area and also with sides of integral length but not congruent to the given one? (Hint: the use of Heron’s formula will help).
PLEASE HELP!!!
The mathematical form of perimeter and area formulas allows us to find obtain the same values from triangles not congruent to each other due to commutative property for addition and multiplication.
Is it possible to obtain the same perimeter and area from triangles with same sides but not congruent to each other?
The perimeter is equal to the sum of the lengths of the three sides of the triangle and the Heron's formula allows us to calculate the areas in term of the three side lengths:
A = √[s · (s - a) · (s - b) · (s - c)]
s = 0.5 · (a + b + c)
Where:
s - Semiperimetera, b, c - Side lengthsThe mathematical form of perimeter and area formulas allows us to find obtain the same values from triangles not congruent to each other due to commutative property for addition and multiplication.
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help for brainliest please
Answer:
5/9
Step-by-step explanation:
When you divide 5 by 9, you will get 0.5 repeating. I know the answer because I had this question on Acellus.
Olivia is trying to get her friends to go swimming. She says it is 959595 degrees to convince them, but she rounded the temperature to the nearest one.
Which could be the temperature before Olivia rounded it? PLEASE ANSWER QUICKLY!!!
Answer:
t > 94.5
Step-by-step explanation: