The probability that the sample mean would be higher than 88.4 or smaller than 84.4 is 0.85582
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = 86
sample size, n = 140
standard deviation, σ = 11
The probability
P(z > 88.4) + P(z < 84.4)
z score for z < 88.4
z = (88.4 - 86) / 11
= 0.21818 p value = 0.41364
z score for z < 84.4
z = (84.4 - 86) / 11
= -0.14545
p value for z < -0.14545 = 0.44218
The probability required = 0.41364 + 0.44218 = 0.85582
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2. One plane
points_____
passes through three noncollinear
A. Point, Line, and Plane Postulates do not
address this topic directly.
B. always
C. never
D. sometimes
4) Identify all the zeros that make the function
true. f(x) = 2x² - 8
0
-2
2
-4
4
-8
The zero of the function f(x) = 2x² - 8 is ± 2.
Zeros of the function
Zero of the function means the values of x when f(x) is equal to 0. Which means that when f(x) = 0, x is a zero of the function.
Given,
Here we have the function f(x) = 2x² - 8.
Here we need to find the zero of the function.
As per the definition of the zeros of the function,
We have to apply the value of f(x) = 0, then we get,
2x² - 8 = 0
Now, we need the value of x only, so we have to move the other numbers to the other side , then we get,
2x² = 8
Now, move the number 2 to the right hand side then it will be dividing the number 8,
x² = 8/2
x² = 4
x = √4
Therefore, the value of x is ± 2.
So, the zeros of the function is either +2 or -2.
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1. Harper is going to create a graph of the equation y = -0.5x + 12. Which of the following will be true about the graph?
The graph will contain the origin.
The graph will increase from left to right.
The graph will cross the x-axis at (12, 0).
The graph will have a slope of -0.5.
The statement that would be true concerning the graph would be that the graph will have a slope of -0.5.
What is a slope?A slope is defined as the difference between a chosen point on the vertical and horizontal axis.
The slope of a straight line graph has a constant equation that is used to determine its slope. Thus;
y = mx + b
Where m = the measure of the steepness of the straight line graph.
From the equation of the graph that was given;
y = -0.5x + 12. The slope of the graph which is represented by 'm' would be -0.5.
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Determine whether the function is one-to-one. If it is, find a formula for its inverse.
f(x) = 4/9x+8
Answer:
87c
Step-by-step explanation:
How long will it take for $3, 900 to double if it is invested at 8% annual interest compounded 2 times a year?
Enter in exact calculations or round to 3 decimal places.
It will take___years to double.
How long will it take if the interest is compounded continuously?
Compounded continuously, it would only take___ years.
The number of years to double the investment is 8.824 years.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $3,900
R = 8%
n = 2
A = 2P = 2 x 3,900 = $7,800
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]
78/39 = [tex](1.04)^{2t}[/tex]
2 = [tex](1.04)^{2t}[/tex]
Taking logs on both sides.
log 2 = 2t log(1.04)
0.30 = 2t x 0.017
0.30/0.017 = 2t
17.65 = 2t
Divide both sides by 2.
t = 17.65 / 2
t = 8.824 years.
Thus,
The number of years to double the investment is 8.824 years.
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Ibram got a job selling bags of peanuts at the local fairground. He is paid a fixed amount of $340 per week plus $0.84 per item sold. This is represented by the equation P = 0.84 + 340 where P is the amount he is paid for the week and n is the number of bags of peanuts he sold. How much will Ibram be paid if he sells 380 bags of peanuts? If Ibram sells 380 bags of peanuts, he will earn S How many bags of peanuts did Ibram sell if he earned $1,087.60? for the week. If Ibram has earned $1,087.60, he sold bags of peanuts.
Answer:
Assuming the bags sold were for 1 week period.
1. $659.20 for 1 week and 380 bags of peanuts
2. 890 bags
Step-by-step explanation:
The equation is missing the variable, n (the number of bags sold). I'll take the liberty to add it after the $0.84/bag term, where it belongs:
P = 0.84n + 340
The 340 is $340/week. n must be in units of "bags/week."
1. How much will Ibram be paid if he sells 380 bags of peanuts?
P = $0.84n + $340
n = 380 bags (we will assume in 1 week).
P = $0.84n + $340
P = $0.84(380) + $340
P = $659.20
2. How many bags of peanuts did Ibram sell if he earned $1,087.60?
P = $0.84n + $340
P = $1087.60
$1087.60 = $0.84n + $340
$1087.60 - $340 = $0.84n
$0.84n = $1087.60 - $340
$0.84n = $747.60
n = 890 bags ( ! - I'm impressed)
196 prime factorization pls help
a shelf in the metro department store contains 80 colored ink cartridges for a popular ink-jet printer. seven of the cartridges are defective. (a) if a customer selects 2 cartridges at random from the shelf, what is the probability that both are defective? (round your answer to five decimal places.)
The probability that both are defective when a customer selects 2 cartridges at random from the shelf will be 0.00766.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The probability of choosing defective cartridge=7/80
So, the probability of choosing 2 defective cartridge=(7/80)²
=0.00765625
=0.00766
When a customer randomly chooses two cartridges from the shelf, the likelihood that both are flawed is 0.00766.
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(jk−1)÷j when j=−4 and k=−0.9
The evaluation of the expression for the given values of j and k is -0.65
Evaluating an ExpressionFrom the question, we are to evaluate the given expression for the given values of j and k.
From the given information,
The given expression is
(jk - 1) ÷ j
and
j = -4 and k = -0.9
Now, substitute the values of j and k into the expression
(jk - 1) ÷ j
((-4)(-0.9) - 1) ÷ -4
= (3.6 - 1) ÷ -4
= 2.6 ÷ -4
= - 0.65
Hence, the value of the expression is -0.65
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two foods contain proteins, carbohydrates, and fats. food a costs $1 per pound and contains 30% protein, 10% fat, and 50% carbohydrates. food b costs $1.50 per pound and contains 20% protein, 4% fat, and 75% carbohydrates. what is a combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat at the lowest cost? (x, y)
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given,
Function:
C = x + 1.5y
Subjected to:
30x + 20y ≥ 13/10 ×100 ≥ 130
10x + 4y ≥ 1/5 × 100 ≥ 20
50x + 75y ≥ 3 × 100 ≥ 300
Feasible region:
(0, 13/2), (3,2) (6,0)
C = x + 1.5y
(0, 13/2) ⇒ C = 0+ (1.5)(13/2)
(0.13/2) ⇒ C = 9.75
(3,2) ⇒ C = 3+ (1.5)(2)
(3,2) ⇒ C = 6
(6,0) ⇒ C = 6 + 0
(6,0)⇒ C = 6
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
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which number line shows -4, -1, 1, and 2 correctly plotted.
A number line which shows -4, -1, 1, and 2 correctly plotted on a graph is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical values -4 and -1 would be plotted on the left hand side of zero (0) while the numerical values 1 and 2 would be plotted on the right hand side of zero (0) using a number line.
In this scenario, a number line would be used for the comparison of two or more numbers such as -4, -1, 1, and 2, and this is plotted in the graph shown in the image attached below.
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if a seed is planted, it has a 65% chance of growing into a healthy plant. if 12 seeds are planted, what is the probability that exactly 3 don't grow?
There is a 136.13 probability that 3 won't increase.
Only 0.65% of seeds will grow into robust plants.
There is a 0.35 probability that a seed won't grow into a robust plant.
In this case, n = 12 and r = 3.
11 seeds will sprout if 1 seed doesn't germinate. Raising 0.65 to the power of 11 and 0.35 to the power of 3 will result in the following: 11 seeds develop, and we use the 11th power; 3 seeds do not grow, so we use the power of 3:
So, the response is:
[tex]{}^{12}C_3[/tex] × [tex]{(chance of successful growth) }^{11}[/tex]x [tex](chance of Unsuccessful growth)^3[/tex]
= [tex]{}^{12}C_3[/tex] × [tex]0.65^{11}[/tex] × [tex]{0.35}^3[/tex]
= 362880 × 0.008750 × 0.042875
= 136.13
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Help! Consider the following three systems of linear equations.
Answer:
b & d
Step-by-step explanation:
which is a reasonable estimate for the amount of kernels serena needs to make 6 cups of popcorn
Answer:
four tablespoons to make 6 cups of popcorn.
Step-by-step explanation:
1.5 is nine Equals 2.25 x. And then divide both sides by 2.25. That gives you four tablespoons to make 6 cups of popcorn.
11. Write an equation in vertex form for the parabola below.
Answer:
Step-by-step explanation:
1. The vertex is where the parabola is changing from increasing to decreasing
2. From the picture, we can see that the vertex is at (1,2)
3. The formula for vertex form is f(x)=a(x-h)^2+k
4. Vertex is (1,2) or (h,k)
5. You can see that the parabola opens upside down like a "n" so it has been reflected in the x axis
6. So, your equaltion is f(x)=-(x-1)^2+2
7. In this cause you can see that a=-1, but if not given you would choose a random point on the parabola and plug it in :). Example:(0,1): 1 = a(0-1)^2+2
a=-1.
8. Your answer: f(x)=-(x-1)^2+2
tan 30 x cos 30 in exact value
what is the function rule in slope intercept form
Answer:
The picture is not Clear. Please provide a better view of the question.
Step-by-step explanation:
a circular curve is to be constructed with a 225 ft radius and an interior angle of 55 degrees. the separation between the stakes along the arc is 50 ft. assuming the curve is laid out from point to point, what is the last deflection angle?
The curve is laid out from point to point, the last deflection angle of circular curve is 26.5°
In the given question we have,
Radius of circular curve (R) = 225 ft
intersection or central angle in circular curve (I or delta) = 55°
separtion between stakes alaong arc = 50 ft
Angle of deflection is measured from tangent at PC or PT to any point .
deflection angle formula
deflection angle = (Lc /L)(I/2)
where, Lc is long chord and L is lenth of arc , I is central angle
first we find out the value of Lc and L
using formula , R = Lc / 2sin(I/2)
Lc = 225× 2 sin(55°/2) = 208 ft
L = R × I ×π/180°
L = 225 × 3.14 ×55/180 = 215.8 ~ 216 ft
put all the vales in deflection angle formula we get ,
deflection angle= (208/216)(55°/2) = 26.48° ~ 26.5°
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What was the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64
the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64 was $ 68.73
We have the insurance coverage amount for men of 30 years and for women of 50 years. Therefore, to find the percentage that represents the cost of coverage of the 50-year-old woman based on the cost of coverage of the man, we need to perform the following operation:
Xw= Cw/Cm * 100%
Where:
Cw: cost of coverage for a woman of 50 years.
Cm: coverage cost for a 30-year-old man.
Xw= 819.73/1192.64 *100%
= 68.73
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elect the correct answer. A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?
The expected value of a player's winnings on each roll is: $30.
How can we calculate the expected value of a player's winnings on each roll?We can calculate the expected value of a player's value on each winning by first understanding that there are only two multiples of three on the six-sided die. These multiples are 3 and 6.
So, if 3 is obtained facing upward, the player wins 3 × 20 = $60
Also, if the player obtained 6 facing upward, the player wins 6 × 20 = $120
So, the total amount is $180.
However, the question expects us to calculate the expected value of a player's winnings on each roll. Thus, we will have $180 ÷ 6 = $30.
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Help me in this proportion maths problems
y is inversely proportional to the square of x, here y in terms of x is 2/5.
From the given problem y is inversely proportional to the square of x.
A table of values for x and y is shown.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
From the table:
(a) As we know that, y is inversely proportional to the square of x,
Here k is proportionality constant.
y∝1/x²
y= k/x²
4=k/1²
k=4
So, y in terms of x is y=4/x²
(b) Putting the value of y=25, we get:
25=4/x²
x²=4/25
x=2/5
Therefore, y is inversely proportional to the square of x, here y in terms of x is 2/5.
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Please can someone answer this question it would be much appreciated
Thanks so much :)
I need help too on this one
Answer:
you lowest tempeture in the mesosphere is -96
Step-by-step explanation:
4/9 - 1/2 Subtract.
- Simplest form.
-1/9 - (-2/5) Evaluate.
- Simplest form.
Answer:
Step-by-step explanation:
Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18
The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.
An astronaut has an annual income of $161,141.00.
The income tax an astronaut must pay is 8%.
What is the amount of income tax in dollars and cents that the
astronaut must pay?
3 math questions for 50 points.
The points (4, -3) and (x, 3) lie on the same straight line.
If the slope of the line is 2, what is the value of x ?
answer:
(1,3)
step-by-step explanation:
desmos.
The value of x will be equal to 7 for the given slope of 2 for the line.
What is the slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Given that the points (4, -3) and (x, 3) lie on the same straight line. The slope of the line is 2.
The slope of the line is calculated by the formula,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
2 = ( 3 + 3 ) / ( x - 4)
2(x-4) = 6
2x - 8 = 6
2x = 8 + 6
2x = 14
x = 14 / 2
x = 7
Therefore, the value of x will be equal to 7 for the given slope of 2 for the line.
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Mr karki divided a sum of Rs 1,80,000 between his son and daughter in the ratio of 4:5 find the sum obtained by eachof them.
Answer:
Rs 80,0000 and Rs 100,000
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
divide the amount by 9 to find the value of one part.
Rs 1,80,000 ÷ 9 = Rs 20,000 , then
4 parts = 4 × Rs 20,000 = Rs 80,000 ← amount son receives
5 parts = 5 × Rs 20,000 = Rs 100,000 ← amount daughter receives
The sum obtained by the son is Rs. 80,000 and the daughter is Rs. 1,00,000.
Mr. Karki divided Rs. 1,80,000 in a ratio of 4:5 between his son and daughter.
Let the common multiple be x
∴ The son obtained Rs. 4x --------1
And daughter obtained Rs. 5x --------2
As the total sum is Rs. 1,80,000
∴ 4x + 5x = 180000
9x = 180000
x = 180000/9
∴ x = Rs. 20000
Putting the value of x in 1 and 2 we get,
The sum obtained by son = 4x = 4*20000 = Rs. 80000
And the sum obtained by daughter = 5x = 5*20000 = Rs. 100000
Thus, the son obtained Rs. 80,000 while the daughter obtained Rs. 1,00,000 which is in the ratio of 4:5.
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a sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. determine the decision rule for rejecting the null hypothesis, h0, at the 0.10 level.
The alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
Given that;
A sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.
To get decision rule for rejecting the null hypothesis, h0, at the 0.10 level;
n = 900
P = 0.34
p = 0.31
α = 0.10
Claim: More than 31% do not malfunction within the first 1000 hours of operation.
The null and alternative hypothesis must be stated.
This is a right-tailed test because the claim is directional to the right side (> type).
Therefore, the alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
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The altitude y in feet of a hawk that is descending can be represented by the equation y=−20x+350, where x represents the time in minutes. The equation y=−10x+400 represents the altitude y in feet of an eagle after descending x minutes.
Which bird is closer to the ground after 8 minutes?
The
eagle
is closer to the ground.
How much closer?
feet
hurry
The hawk is closer to the ground after 8 minutes
It is 130 feet closer
How to determine the valuesWe have the equation as;
y = −20x+350. This represents the altitude y in feet of a hawky=−10x+400. This represents the altitude y in feet of the eagleAlso, x represents the descending time in minutes
Now, let's substitute the value of x as 8 minutes in the equations
If x = 8
For equation (1)
y = - 20(8) + 350
expand the bracket
y = - 160 + 350
y = 190 feet
For equation (2)
y = -10(8) + 400
expand the bracket
y = -80 + 400
y = 320 feet
The hawk is closer after 8 minutes
The distance from the ground(eagle) - The distance from the ground(hawk)
320 - 190
130 feet
Hence, the hawk is closer to the ground
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A collector of rare books has a first-edition book worth $262, which he anticipates will grow in
value at a rate of 15% per year. How much will this book be worth 10 years from now?
If necessary, round your answer to the nearest cent.
Que
ans
2
The worth of the book after 10 years is $1061.1
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First edition book worth = $262
Rate of increase per year = 15%
The worth of the book after t years can be given by the expression.
= 262 x [tex]1.15^{t}[/tex]
Now,
The worth of the book when t = 10.
= 262 x [tex]1.15^{10}[/tex]
= 262 x 4.05
= $1061.1
Thus,
The book is worth $1061.1 after 10 years.
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