For the probability of 90% that it will take at least 68.195 minutes long to assemble an electronic component.
As we have the time it takes to assemble an electronic component is normally distributed.
Mean time, [tex] \mu[/tex] = 17.2 minutes
Standard deviations, [tex] \sigma[/tex]
= 3.1 minutes
We have to determine probability is 90% that it will take at least how long to assemble a component. Now, from the standard normal distribution table value of Z - score for 90% is equals to the 1.645.
Using the Z- score formula in normal distribution, [tex]Z = \frac{ X - \mu}{\sigma }[/tex]
=> 1.645 = ( X - 17.2 )/3.1
=> X - 17.2 = 31 × 1.645
=> X = 17.2 + 50.995
=> X = 68.195
Hence, the required at least the long to assemble a component is equals to the 68.195.
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Can you help me find the answer
Answer:
a Obtuse b 136 girls c Hockey d 16.7
Step-by-step explanation:
50a obtuse
b 136 girls
c Hockey
d [tex]\frac{60}{360} *100\\=16.6667...\\16.7[/tex]
Math 341 Problem Set 7 Do the following problems from Chapter 3 of the book Probability, Statistics, and Data: A Fresh Approach Using R 3.16, 3.17.3.18, 3.22, 3.25 1. Suppose 20 chips are selected one by one at random and with replacement from an urn containing 5 red and 15 black chips. You win $4 for each red chip selected. Let the random variable X denote your winnings (the amount you win). a. To make this game "fair," how much should be charged to play? Why? (You must justify your answer.) b. Find Var (X). c. Find SDX). d. Now suppose you win $4 for each red chip selected and you lose S2 for each black chip selected. Let the random variable Y denote the amount you win or lose. Find E (Y). e. Now suppose you win $9 for each red chip selected and you lose Sc for each black chip selected. Find the value of that makes this is a "fair" game.
a. To make the game "fair," $1 should be charged to play.
b. The Var (X) is 4/5
c. The SDX is 0.894
d. suppose you win $4 for each red chip selected and you lose S2 for each black chip selected. Let the random variable Y denote the amount you win or lose. E (Y) is -34
e. To make this game "fair," $0.45 should be charged to play.
a. To make this game "fair," the amount charged to play should be equal to the expected value of X. The expected value of X is:
E(X) = (4/20) * 5 + (16/20) * 0 = 1
b. The variance of X can be calculated using the formula:
Var(X) = E(X²) - [E(X)]²
Since X can only take on the values 0 and 4, we have:
E(X^2) = (4/20)² * 5 + (16/20)² * 0 = 1/5
So,
Var(X) = 1/5 - 1² = -4/5
However, since the variance cannot be negative, we take the absolute value and say:
Var(X) = 4/5
c. The standard deviation of X is the square root of the variance:
SD(X) = √(4/5) ≈ 0.894
d. Let Y denote the amount won or lost, where Y = 4X - 2(20 - X) = 6X - 40. Then:
E(Y) = E(6X - 40) = 6E(X) - 40 = 6 - 40 = -34
So, on average, you would lose $34 per game.
e. To make the game "fair," we need to find the value of such that E(Y) = 0. Using the same formula as in part (d), we have:
E(Y) = E(9X - c(20 - X)) = 9E(X) - cE(20 - X) = 9E(X) - 20c
Setting E(Y) equal to 0 and solving for c, we get:
0 = 9 - 20c
c = 9/20 = 0.45
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An experiment consists of rolling two fair number cubes. The diagram shows the sample space of all equally likely outcomes. Find P(1 and 2). Express your answer as a fraction in simplest form.
Since the sample space contains [tex]36[/tex] equally likely outcomes, each outcome has a probability of [tex]1/36[/tex]
What is the probability?The sample space consists of all possible outcomes when rolling two number cubes. Each cube has six equally likely outcomes, so the total number of outcomes is[tex]6\times6=36.[/tex]
P(1 and 2) refers to the probability of rolling a 1 on the first cube and a 2 on the second cube. There is only one outcome that satisfies this condition, which is [tex](1, 2)[/tex] .
Therefore, the probability of rolling a 1 and 2 is:
P(1 and 2) = (number of outcomes that satisfy the condition)/(total number of possible outcomes)
P(1 and 2) [tex]= 1/36[/tex]
Therefore, the probability of rolling a [tex]1[/tex] and [tex]2[/tex] is [tex]1/36[/tex] .
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Answer:
Since the sample space contains 36 equally likely outcomes, each outcome has a probability of 1 / 36.
We know that probability is defined as number of favourable outcomes divided by total number of outcomes.
Step-by-step explanation:
An experiment occurs of rolling two fair number cubes.
We have given number of favourable outcomes = 2 {(2,1), (1,2)}
Number of Total Outcomes = 36
So ,
Probability = Number of favourable outcomes / Total Outcomes
P(1 and 2) refers to the probability of rolling a 1 on the first cube and a 2 on the second cube. There is only one outcome that satisfies this condition, which is (1, 2).
P(1 and 2) = 2 / 36
P(1 and 2) = 1 / 18
Hence , 1 / 18 is the answer as a fraction in simplest form.
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costs for standard veterinary services at a local animal hospital follow a normal distribution with a mean of $79 and a standard deviation of $20. what is the probability that one bill for veterinary services costs between $55 and $103?
The required probability which represents the a bill for veterinary services costs between $55 and $103 using normal distribution is approximately 0.7745, or 77.45%.
Let X be the cost of a standard veterinary service bill.
X follows a normal distribution with mean μ = $79
And standard deviation σ = $20.
The probability that X is between $55 and $103,
P(55 ≤ X ≤ 103)
To standardize X, we use the formula,
Z = (X - μ) / σ
Substituting the values for μ and σ, we get,
⇒Z = (X - 79) / 20
The probability of 55 ≤ X ≤ 103,
Calculate the corresponding z-scores for 55 and 103,
And then calculate the probability of the interval between these two z-scores using a standard normal table .
The z-score for 55 is,
Z = (55 - 79) / 20
= -1.2
The z-score for 103 is,
Z = (103 - 79) / 20
= 1.2
Using a standard normal table or calculator, the probability of the interval between these two z-scores is,
P(-1.2 ≤ Z ≤ 1.2) ≈ 0.7745
Therefore, the probability that a bill for veterinary services costs between $55 and $103 is approximately 0.7745, or 77.45%.
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help 10 points
What are the solutions to the equation -5(x+4)² = -25?
O x=-4-√√5, x = −4+ √5
x = 4-√√5, x = 4 + √5
0 x =
x =
-1, x = 9
O x = -9, x = 1
The solution of the given quadratic equation is [tex]x=-4-\sqrt{5}[/tex], [tex]x=-4+\sqrt{5}[/tex].
EquationsTo solve the equation, we can start by dividing both sides by -5, which gives:
[tex](x+4)^{2} = 5[/tex]
Next, we can take the square root of both sides, remembering to consider both the positive and negative square roots:
[tex]x+4=[/tex]±[tex]\sqrt{5}[/tex]
[tex]x=-4+\sqrt{5}[/tex]
[tex]x=-4-\sqrt{5}[/tex]
What are roots of a Quadratic Equations?The x values in a quadratic equation that fulfil the equation—that is, that make the equation true—are known as the roots of the equation. In other words, the values of x that cause the quadratic expression to equal zero are the roots of a quadratic equation.
The two alternative values for x provided by the quadratic formula are one with a plus sign and one with a minus sign. The quadratic equation's roots are these two numbers. The quadratic equation has two real roots if the discriminant value inside the square root is positive. The quadratic equation has one real root with a multiplicity of two if the discriminant is zero. If the discriminant is negative, there are two complex roots in the quadratic equation.
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Pls Help!!
Find m/ABC if BD is an angle bisector.
Answer:
[tex]\large\boxed{\tt \angle ABC = 146^{\circ}.}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to solve for} \ \tt \angle ABC. \ \textsf{We are given that} \ \overrightarrow{\tt BD} \ \textsf{is an \underline{Angle Bisector}.}[/tex]
[tex]\large\underline{\textsf{What are Angle Bisectors?}}[/tex]
[tex]\textsf{Angle Bisectors are \underline{Line Segments} that bisect a full angle into 2 congruent angles.}[/tex]
[tex]\textsf{Think of Angle Bisectors as cutting something into half, both pieces will be congruent.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{Because} \ \overrightarrow{\tt BD} \ \textsf{is an Angle Bisector, then} \ \angle \tt ABD \cong \angle CBD. \ \textsf{This will mean that both}[/tex]
[tex]\textsf{angles are \underline{congruent} to each other, hence their measures are the same.}[/tex]
[tex]\tt 4a+13=7a-32[/tex]
[tex]\textsf{Let's begin solving for a, afterwards we should substitute a back into} \ \tt \angle ABD, \ \textsf{multiply}[/tex]
[tex]\textsf{the angles' measure by 2 since} \ \tt \angle CBD \cong \angle ABD, \ \textsf{then we are able to identify the}[/tex]
[tex]\textsf{measure of} \ \tt \angle ABC.[/tex]
[tex]\underline{\textsf{Find the value of a;}}[/tex]
[tex]\tt 4a+13=7a-32[/tex]
[tex]\underline{\textsf{Subtract 7a from both sides of the equation;}}[/tex]
[tex]\tt 4a-7a+13=7a-7a-32[/tex]
[tex]\tt -3a+13=-32[/tex]
[tex]\underline{\textsf{Subtract 13 from both sides of the equation;}}[/tex]
[tex]\tt -3a+13-13=-32-13[/tex]
[tex]\tt -3a=-45[/tex]
[tex]\underline{\textsf{Divide both sides of the equation by -3;}}[/tex]
[tex]\large\boxed{\tt a=15}[/tex]
[tex]\underline{\textsf{Substitute 15 back into} \ \tt \angle ABD;}[/tex]
[tex]\tt \angle ABD = 4(15) + 13[/tex]
[tex]\tt \angle ABD = 73^{\circ}[/tex]
[tex]\underline{\textsf{Multiply} \ \tt \angle ABD \ \textsf{by 2;}}[/tex]
[tex]\tt \angle ABD \ + \ \angle CBD= 73^{\circ} \times 2[/tex]
[tex]\tt \angle ABD \ + \ \angle CBD= 146^{\circ}[/tex]
[tex]\textsf{146}^{\circ} \ \textsf{represents the value of} \ \tt \angle ABC.[/tex]
[tex]\large\underline{\textsf{Hence;}}[/tex]
[tex]\large\boxed{\tt \angle ABC = 146^{\circ}.}[/tex]
a photograph has a length that is 6 inches longer than its width, x. so its area is given by the expression square inches. if the area of the photograph is square inches, what is the width of the photograph?
The width of the photograph is approximately 10.5 inches.
Let's first write an expression for the length of the photograph in terms of its width
Length = Width + 6 inches
And we know that the area of the photograph is given by
Area = Length × Width
Substituting the expression for the length, we get
Area = (Width + 6) × Width
Simplifying this expression, we get
Area = Width^2 + 6 Width
We are given that the area of the photograph is 132 square inches. So we can set up an equation
132 = Width^2 + 6 Width
Rearranging this equation, we get a quadratic equation in standard form
Width^2 + 6 Width - 132 = 0
Now we can solve for the width using the quadratic formula
Width = (-6 ± √(6^2 - 4(1)(-132))) / (2(1))
Width = (-6 ± √(1416)) / 2
We can simplify this expression
Width = (-3 ± √354)
Since the width must be positive, we can discard the negative solution
Width = (-3 + √354) ≈ 10.5 inches
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three randomly chosen seattle students were asked how many round trips they made to canada last year. their replies were 3, 4, 5. the geometric mean is group of answer choices 3.915 4.000 4.422 3.877
The Geometric mean of the number of Canada trips made by the three Seattle students is approximately 3.915.
The question states that three randomly chosen Seattle students were asked how many round trips they made to Canada last year, and their replies were 3, 4, and 5.
To calculate the geometric mean of a set of numbers, we need to multiply all the numbers together and then take the nth root of the product, where n is the total numb of numbers in the set. In this case, we have three numbers: 3, 4, and 5.
To find the geometric mean, we multiply these numbers together:
3 x 4 x 5 = 60
Then we take the cube root (since there are three numbers)
In the given student question, three randomly chosen Seattle students were asked how many round trips they made to Canada last year.
The task is to find the geometric mean of these values.
The geometric mean is calculated by multiplying all of the values together and then taking the nth root, where n is the number of values.
In this case, n = 3, so the formula for the geometric mean GeometricGeometric mean = (3 x 4 x 5)
Geometric mean ≈ 3.915
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Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°. Find the measure of the missing angle.
A pentagon has five angles, and the sum of the angles of a pentagon is equal to 540°. Therefore, the measure of the fifth angle can be found by subtracting the sum of the given angles from 540°:
540° - (85° + 110° + 135° + 95°) = 540° - 425° = 115°.
Therefore, the measure of the missing angle is 115°.
Sum of the angles of a n-sided polygon:
[tex]\text{S}_{\text{n}}=180^\circ\times(\text{n}-2)[/tex]
In this question, we have a pentagon, so
[tex]\text{n}=5,[/tex]
then
[tex]\text{S}_5=180^\circ\times(5-2)[/tex]
[tex]\text{S}_5=180^\circ\times3[/tex]
[tex]\text{S}_5=540^\circ \longleftarrow \ \text{sum of the measures of the internal\\}[/tex]
[tex]\text{angles of a pentagon.}[/tex]
Let [tex]\text{x}[/tex] be the measure of the missing angle. So,
[tex]85^\circ+110^\circ+135^\circ+95^\circ+\text{x}=\text{S}_5[/tex]
[tex]425^\circ+\text{x}=540^\circ[/tex]
[tex]\text{x}=540^\circ-425^\circ[/tex]
[tex]\text{x}=115^\circ\longleftarrow \ \ \ \text{measure of the missing angle.}[/tex]
Tags: sum internal angle missing pentagon polygon plane geometry
Find the quotient. Write your answer in descending order with respect to the power of h.
(4h²+6h²-3)÷2h/3
Answer: 15h
Step-by-step explanation:
Malia is solving a problem where she needs to find the value of "x" that would make the ratios equivalent. She starts by
writing all the prime factors of the numbers in the problem to see if she can cancel out any factors to make an.equivalent
fraction. This helps her see what 'x' has to be. If she is correct, what number did she decide "x" was?
1
x
21
LIT
7
=
X
3.7
Malia determined that "x" is equal to LIT * 3 as a result as by the left side of the equation .
what is equation ?A mathematical assertion that two expressions are equal is known as an equation. The leading edge (LHS) and the right hand side (RHS), which are normally two independent portions, are denoted by the equals sign (=). Depending on the equation, the values on either side of the equals sign are all either equal or not. In a variety of disciplines, including science, law, finance, and economics, equations can be used to represent real-world events and address issues.
given
First, let's make the left side of the equation easier to understand:
LIT / 7 = x / (3 * 7)
LIT / 7 = x / 21
We can now cross-multiply to obtain:
LIT * 21 = 7 * x
Streamlining the left side:
LIT * 3 * 7 = 7 * x
LIT * 3 = x
Malia determined that "x" is equal to LIT * 3 as a result as by the left side of the equation .
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Using the net below, find the surface area
of the triangular prism.
8 cm
6 cm
4 cm
4 cm
Surface Area
5 cm
5 cm
5 cm
=
8 cm
[?] cm²
W
Answer:
140 cm²
Step-by-step explanation:
You want the total surface area of a triangular prism as represented by the given net.
AreaThe total area is the sum of the areas of the two triangular bases and the three rectangular faces. The relevant formulas are ...
A = 1/2bh . . . . . . area of triangle with base b, height h
A = bh . . . . . . . area of rectangle with base b, height h
ApplicationThe total area is ...
SA = 2(1/2bh) +(b1)h +(b2)h +(b3)h . . . . . . . triangle h=5, rectangle h=8
SA = 2(1/2)(4 cm)(5 cm) + (8 cm)(6 cm +4 cm +5 cm)
= 20 cm² +(8 cm)(15 cm)
= 140 cm²
The total surface area of the triangular prism is about 140 cm².
Which probability distribution table reflects the data shown in the bar graph?
X yellow, red , orange, blue, green
P 0.5 , 0.4, 0.3, 0.2, 0.1
X yellow, red , orange, blue, green
P 0.5, 0.5, 0.5, 0.5, 0.5
X yellow, red , orange, blue, green
P 0.1, 0.2, 0.3, 0.4, 0.5
X yellow, red , orange, blue, green
P 0.2, 0.2, 0.2, 0.2, 0.2,
Based on the information provided in the question, we can determine that the correct probability distribution table that reflects the data shown in the bar graph is:
X Yellow Red Orange Blue Green
P 0.5 0.4 0.3 0.2 0.1
What is probability ?
Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probabilities between 0 and 1 represent the degree of uncertainty or likelihood of the event occurring.
For example, if a fair coin is tossed, the probability of it landing heads up is 0.5, since there are two equally likely outcomes (heads or tails) and only one of them is heads. Similarly, the probability of drawing a spade from a standard deck of 52 cards is 1/4 or 0.25, since there are four suits and only one of them is spades.
Probability theory is used extensively in many fields, including statistics, science, engineering, finance, and more, to model and analyze uncertain events and make informed decisions.
This is because the bar graph represents the frequency or probability of occurrence of each color, and the given probabilities in the table match with the corresponding frequencies represented in the bar graph.
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Fill in the table for side length and area of different squares.
Answer:
see below
Step-by-step explanation:
area of square = side x side or side^2
a.
Side Area
3 3^2 = 9
100 100^2 = 10000
25 25^2 = 625
s s^2
b. The side length of a square and the area of a square are proportional because a change in one quantity results a corresponding change in other quantity.
how many positive odd integers less than 10,000 can be written using digits 3,4,6,8, and 0
the total number of positive odd integers less than 10,000 that can be written using the digits 3, 4, 6, 8, and 0 is 64 + 64 = 128.
Why is it?
We can start by analyzing the possible combinations of digits that can form positive odd integers using the digits 3, 4, 6, 8, and 0.
For a number to be odd, the units digit must be 3, 5, 7, or 9. Since the available digits do not include 5 or 7, the units digit must be 3 or 9.
Case 1: Units digit is 3
In this case, we have four remaining digits (0, 4, 6, and 8) to use for the thousands, hundreds, and tens places. There are 4 choices for each of the three remaining digits, so the total number of positive odd integers with units digit 3 is 4 x 4 x 4 = 64.
Case 2: Units digit is 9
Similar to case 1, there are four remaining digits (0, 4, 6, and 8) to use for the thousands, hundreds, and tens places. Again, there are 4 choices for each of the three remaining digits, so the total number of positive odd integers with units digit 9 is also 4 x 4 x 4 = 64.
Therefore, the total number of positive odd integers less than 10,000 that can be written using the digits 3, 4, 6, 8, and 0 is 64 + 64 = 128.
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HELP GEOMETRY WILL GIVE BRAINLIEST!!!!!!!
Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.
Explain about the intercept chord theorem:The products of a measurements of the segments of two chords are equal if they overlap in a circle.
When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.The intersecting chords theorem aids in determining how far apart various points on a circle are from a given location inside the circle.For the given arc length of circle:
Let the intersection of the both chords be 'O'.
m∠KOL = 180 - x ...eq 1 (linear pair).
By the intercept chord theorem:
m∠KOL = (arc JM + arcKL)
Put the value of eq 1.
180 - x = 1/2(30 + 2x - 30)
180 - x = 1/2 * 2x
180 = x + x
x = 180/2 = 90
Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.
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a certain zookeeper has n cages in a row and two indistinguishable lions. the lions have ot be in separate cages, and they may not be placed in adjacent cages. how many ways could the zookeeper assign lions to cages?
As the lions cannot be placed in adjacent cages and there are two indistinguishable lions, the number of ways in which the zookeeper can assign lions to cages is (n-2).
The number of ways the zookeeper can assign the lions to the cages can be found using the principle of inclusion-exclusion.
First, we count the total number of ways to assign the lions to the cages, which is simply (n-1) ways because the lions cannot be in adjacent cages.
Next, we subtract the number of ways the lions can be in adjacent cages. Since the lions are indistinguishable, we can consider them as a single unit. Thus, we have (n-2) ways to place this unit in the cages.
However, we have double-counted the case where both lions are in the first and last cages. This can only happen once, so we need to add it back in. Thus, we add 1 to our previous result.
Putting this all together, we have:
Total number of ways to assign lions to cages = (n-1) - (n-2) + 1 = n-2
Therefore, there are (n-2) ways for the zookeeper to assign the lions to the cages.
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what percentage of the population live in their state of birth? according to the u.s. census bureau's 2014 american community survey, the figure ranges from 25% in nevada to 78.7% in louisiana. the average percentage across all states and the district of columbia is 57.7%. the data in the file homestate are consistent with the findings in this american community survey. the data are for a random sample of 120 arkansas residents and for a random sample of 180 virginia residents.
Percentage of the population live in their state of birth is,
Arkansas residents born in Arkansas is, 40.8%
Virginia residents born in Virginia is 41.7%
To find the percentage of the population that live in their state of birth for Arkansas and Virginia, we need to count the number of residents who were born in the same state as the one they currently live in and divide it by the total number of residents.
For Arkansas:
Number of residents born in Arkansas: 49
Total number of residents: 120
Percentage of Arkansas residents born in Arkansas: (49/120) x 100 = 40.8%
For Virginia:
Number of residents born in Virginia: 75
Total number of residents: 180
Percentage of Virginia residents born in Virginia: (75/180) x 100 = 41.7%
Note that these percentages are specific to the sample of residents in Arkansas and Virginia in the given dataset, and may not be representative of the entire population.
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--The complete question is, What percentage of the population live in their state of birth? According to the U. S. Census Bureau's American Community Survey, it ranges from 25% in Nevada to 78.7 percent in Louisiana (AARP Bulletin, March, 2014). The average percentage across all states and the District of Columbia is 57.7%. The data in the DATAfile Homestate are consistent with the findings in the American Community Survey. The data are for a random sample of 120 Arkansas residents and for a random sample of 180 Virginia residents.
DATA:
First Column-Arkansas Resident Born Here?
Second column- Virginia Residents Born Here?
No Yes
No No
Yes No
Yes Yes
Yes Yes
No No
No Yes
Yes Yes
No No
Yes Yes
Yes No
No Yes
Yes No
Yes No
No No
No No
Yes Yes
Yes No
Yes No
Yes No
Yes Yes
No Yes
Yes No
Yes No
No Yes
No Yes
Yes No
Yes Yes
No No
Yes Yes
Yes No
No Yes
Yes Yes
Yes No
No Yes
Yes No
Yes Yes
Yes No
Yes Yes
No No
Yes No
Yes No
Yes No
Yes No
Yes Yes
Yes No
No Yes
Yes No
No No
Yes Yes
No No
Yes Yes
No No
No Yes
Yes No
Yes Yes
No No
Yes Yes
Yes Yes
No No
No No
No Yes
Yes No
Yes Yes
No No
Yes No
Yes Yes
Yes Yes
No No
No Yes
No No
Yes Yes
Yes No
No No
Yes Yes
Yes No
Yes No
Yes No
No No
Yes Yes
No Yes
Yes Yes
No No
No No
Yes No
No Yes
Yes Yes
Yes No
No Yes
Yes Yes
Yes No
Yes No
No Yes
No No
Yes Yes
No No
No Yes
Yes Yes
Yes Yes
No Yes
Yes No
Yes Yes
Yes No
Yes Yes
No Yes
Yes Yes
No No
No No
No No
Yes No
No Yes
Yes No
Yes No
Yes No
Yes No
Yes Yes
Yes Yes
Yes No
No No
Yes Yes
Yes
Yes
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
No
Yes
Yes
No
No
No
No
Yes
Yes
Yes
No
Yes
No
Yes
Yes
No
No
No
No
Yes
Yes
No
Yes
Yes
No
Yes
Yes
No
Yes
No
No
No
Yes
Yes
Yes
No
Yes
Yes
No
Yes
Yes
No
Yes
Yes
No
No
Yes
Yes
No--
g how can you describe the standard deviation in part c relative to the population standard deviation from which the samples were generated?
If the sample size in part c is larger, then the sample standard deviation will be a better estimate of the population
standard deviation. If the sample size is smaller, then the sample standard deviation will be less reliable and may not
be a good estimate of the population standard deviation.
To describe the standard deviation in part c relative to the population standard deviation from which the samples were
generated, you can use the concept of the sample standard deviation.
The sample standard deviation is a measure of the variation in a set of data that is calculated by taking the square root
of the variance of the data set. The variance is the average of the squared differences from the mean. It is important to
note that the sample standard deviation is an estimate of the population standard deviation, which is the true measure
of the variability in the population. The larger the sample size, the closer the sample standard deviation will be to the
population standard deviation. Therefore, if the sample size in part c is larger, then the sample standard deviation will
be a better estimate of the population standard deviation.
Conversely, if the sample size is smaller, then the sample standard deviation will be less reliable and may not be a
good estimate of the population standard deviation.
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Using trigonometric ratios find the missing side. Round to the nearest tenth.
The length of missing side AC ≈ 10.9.
What is length of side?
To find the missing side of the right triangle, we can use the trigonometric ratios, specifically the sine, cosine, and tangent ratios.
Given that B is a right angle, we know that:
sin A = opposite/hypotenuse = BC/AB
cos A = adjacent/hypotenuse = AC/AB
tan A = opposite/adjacent = BC/AC
Substituting the known values, we get:
sin 33° = BC/13
cos 33° = x/13
tan 33° = BC/x
Solving for x, we can use the cosine ratio:
cos 33° = x/13
x = 13 cos 33°
x ≈ 10.88
Therefore, the missing side AC ≈ 10.9.
What is hypotenuse?
In a right triangle, the hypotenuse is the longest side and the side that is opposite the right angle. It is also the side that connects the two legs of the right triangle. The hypotenuse is always opposite the right angle and is also the side that has the largest length compared to the other two sides (the legs) of the triangle.
The hypotenuse plays a crucial role in the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. The Pythagorean theorem is expressed mathematically as: a² + b² = c²
where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.
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Ronnie had a certain number of movies, m. One-fourth of those movies were action movies. He sold eleven action movies to reach a grand total of four action movies.
m/4 - 11 = 4
What was the original number of movies Ronnie had?
A.
60
B.
56
C.
30
D.
45
the original number of movies Ronnie had was 60, which is option A.
Let's first understand the given problem. Ronnie had a certain number of movies, which we don't know and is represented by the variable 'm'. One-fourth of the total movies (m/4) were action movies. Now, Ronnie sold eleven action movies and ended up with only four action movies left. This means that he sold m/4 - 11 action movies, and the remaining action movies were 4. So, we can write the equation as:
m/4 - 11 = 4
Let's solve this equation to find the value of m. First, we will add 11 to both sides of the equation to get:
m/4 = 4 + 11
Simplifying this, we get:
m/4 = 15
Now, we will multiply both sides of the equation by 4 to get rid of the fraction:
m = 15 x 4
m = 60
Therefore, the original number of movies Ronnie had was 60, which is option A.
To explain this in more detail, we can use algebraic reasoning. We started with the equation m/4 - 11 = 4 and solved for m. To do so, we first added 11 to both sides of the equation to isolate the variable on one side. This gave us m/4 = 15. To solve for m, we multiplied both sides by 4 to cancel out the denominator and get m = 60.
Therefore, Ronnie originally had 60 movies, and one-fourth of those (m/4) were action movies. He sold 11 action movies, leaving him with only 4 action movies, and we were able to find the original number of movies using algebraic reasoning.
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The double number line shows that Kimimela fed her rabbits 350
350350 days this year. Her foster brother fed them the other days.
A double number line with 2 tick marks. The line labeled Time, days, reads from left to right: 0, 350. The line labeled Percentage, reads from left to right: 0 percent, 100 percent.
A double number line with 2 tick marks. The line labeled Time, days, reads from left to right: 0, 350. The line labeled Percentage, reads from left to right: 0 percent, 100 percent.
Complete the table to show different percentages of the days that Kimimela fed her rabbits.
Time (days) Percentage
100
%
100%100, percent of 350
350350 days
20
%
20%20, percent of 350
350350 days
80
%
80%80, percent of 350
350350 days
Stuck?Review related articles/videos or use a hint.
To complete the table, we need to calculate the number of days Kimimela fed her rabbits for each given percentage. To do this, we can use proportions.
For example, to find out how many days Kimimela fed her rabbits if she fed them 20% of the time, we can set up the proportion:
20/100 = x/350
where x is the number of days Kimimela fed her rabbits. Cross-multiplying, we get:
100x = 20 * 350
Solving for x, we get:
x = 20 * 350/100 = 70
So, if Kimimela fed her rabbits 20% of the time, she fed them for 70 days.
Using the same method, we can complete the table as follows:
Time (days) Percentage
100
%
100%100, percent of 350
350350 days
20
%
20%20, percent of 350
7070 days
80
%
80%80, percent of 350
280280 days
Therefore, if Kimimela fed her rabbits 100% of the time, she fed them for all 350 days. If she fed them 20% of the time, she fed them for 70 days. And if she fed them 80% of the time, she fed them for 280 days.
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the measure of angle r is (7x+19) degrees if x=23 find the measure of angle r
Help me solve this please
The area of the trapezoid is 81 in² (optionC)
What is area of a trapezoid?A trapezoid is a quadrilateral with one pair of opposite sides parallel. The area of a trapezoid is expressed as;
A = 1/2(a+b)h
Where a and b are the two opposite sides and h is the height.
The height = 9 in
The two opposite sides are 5 and 13
Therefore ;
A = 1/2( 13+5) 9
A = 1/2 × 18 × 9
A = 9 × 9
A= 81 in²
therefore the area of the trapezoid is 81 in²
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Check that the trinomial is a perfect square trinomial
HELPPPPP!!!!!!!!
As a result, x²-18x+81 is a perfect square trinomial and can be represented as (x-9)².
WHAT ARE SOME OTHER PERFECT SQUARE TERMINAL EXAMPLES?Perfect square trinomials are illustrated by the following:
x²+6x+9
=(x+3)²
x²-10x+25
=(x-5)²
4x²+12x+9
=(2x+3)²
a²+2ab+b²=(a+b)²
The quadratic expression is a perfect square trinomial if it can be expressed in this way.
As an illustration,
let's determine whether x²-18x+81 is a perfect square trinomial:
The square of x is the first term, x².
The square of 9 is the final term (81).
Its result 2(x)(-9)=-18x is
twice as long as the middle term.
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jessica rode 9 miles farther than roger rode. let r represent the number of miles roger rode. write an expression for the number of miles jessica rode
Sarita recorded the number of minutes the bus was late over several days. Organize her data into a frequency table. 3,7,0,4,10,6,8,5,3,11,12,0,7,4,8,17,15,12,13,5
Step-by-step explanation:
To create a frequency table for Sarita's data, we need to first count the number of times each value appears in the data set. We can then organize this information into a table with two columns: one for the values and one for their frequencies.
Here is the frequency table for Sarita's data:
Value Frequency
0 2
3 2
4 2
5 2
6 1
7 2
8 2
10 1
11 1
12 2
13 1
15 1
17 1
To create this table, we first counted the number of times each value appears in the data set. For example, the value 0 appears twice, so its frequency is 2. We repeated this process for each value in the data set, and then organized the results into a table with two columns.
Leah and Josh are buying a $550,000 home. They have been approved for a 3.70% APR mortgage. They made a 14% down payment and will be closing on September 6. How much should they expect to pay in prepaid interest at the closing?
Leah and Josh should expect to pay approximately $1,204.31 in prepaid interest at the closing.
What is interest?
Interest is the amount of money that is paid or earned for the use of borrowed or invested funds. When someone borrows money, they typically have to pay back the principal (the amount borrowed) plus interest, which is usually calculated as a percentage of the principal.
To calculate the prepaid interest at closing, we need to first determine the loan amount, which is the purchase price of the home minus the down payment:
Purchase price = $550,000
Down payment = 14% of $550,000 = $77,000
Loan amount = $550,000 - $77,000 = $473,000
Next, we need to calculate the daily interest rate by dividing the APR by 365:
Daily interest rate = 3.70% / 365 = 0.010137%
Finally, we can calculate the prepaid interest by multiplying the loan amount by the daily interest rate and the number of days from the closing date to the end of the month:
Number of days from September 6 to September 30 = 25
Prepaid interest = $473,000 x 0.010137% x 25 = $1,204.31
Therefore, Leah and Josh should expect to pay approximately $1,204.31 in prepaid interest at the closing.
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A rectangular solid with sides a and b, and with a height of 20 cm has a volume of 120 cm³. Find the formula which defines b in terms of a. Why is this formula an indirect proportion? What is the domain of this function? A rectangular solid with sides a and b, and with a height of 20 cm has a volume of 120 cm³. Find the formula which defines b in terms of a. Why is this formula an indirect proportion? What is the domain of this function?
meen 260 students measured the length of a 10.00 mm standard specimen certified in iso (international standard organization) 25 times. the results are below, group sample mean [mm] sample deviation [mm] group a 10.00 0.51 group b 13.00 0.06 group c 12.00 0.55 group d 11.00 2.00 all students used the same vernier calipers with 0.01 mm resolution. which group has the largest uncertainty error in a 95% confidence level (assume t (95%) value is 2.0)?
The group with the largest uncertainty error in a 95% confidence level among Group A, B, C, and D is Group D.
To determine the uncertainty error for each group, we'll calculate the margin of error using the formula:
Margin of Error = t (95%) × (sample deviation / sqrt(sample size))
Assuming a t (95%) value of 2.0 and a sample size of 25 for all groups, we have:
Group A:
Margin of Error = [tex]2.0 × (0.51 / sqrt(25)) = 2.0 × (0.51 / 5) = 0.204[/tex]
Group B:
Margin of Error =[tex]2.0 × (0.06 / sqrt(25)) = 2.0 × (0.06 / 5) = 0.024[/tex]
Group C:
Margin of Error = [tex]2.0 × (0.55 / sqrt(25)) = 2.0 × (0.55 / 5) = 0.22[/tex]
Group D:
Margin of Error = [tex]2.0 × (2.00 / sqrt(25)) = 2.0 × (2.00 / 5) = 0.8[/tex]
Based on the margin of error calculations, Group D has the largest uncertainty error at a 95% confidence level, with a
margin of error of 0.8 mm.
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