Answer:
18 times bigger
Step-by-step explanation:
Bonny has 3 cards and a standard rolling cube. She wants to pick a card and spin the rolling cube at random. How many outcomes are possible?
There are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.
How to calculate How many outcomes are possibleThere are a total of 6 outcomes for the rolling cube and 3 outcomes for picking a card. To find the total number of outcomes, we can use the multiplication rule of counting:
Total number of outcomes = number of outcomes for picking a card x number of outcomes for rolling a cube
Total number of outcomes = 3 x 6 = 18
Therefore, there are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.
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The interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan
find the formula relating I and P
a) I when P = 800 b)P when I = 72
The formula relating I and P is I = kP
a) When P= $800, then I = $48
b) When I = $72, then P = $1200
If the interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan, we can write:
I = kP
where k is a constant of proportionality. To find the value of k, we can use the given information that the interest rate is 6%, or 0.06 as a decimal. We know that when P = 100, the interest I = 0.06 × 100 = 6. Therefore:
I/P = 6/100 = 0.06 = k
Now we can use this value of k to answer the given questions,
a) When P = 800, the formula relating I and P is:
I = kP
I = 0.06 × 800
I = 48
Therefore, the interest on a loan of $800 for a year at a rate of 6% is $48.
b) When I = 72, the formula relating I and P is:
I = kP
72 = 0.06P
Solving for P:
P = 72/0.06
P = 1200
Therefore, a loan of $1200 for a year at a rate of 6% would have an interest of $72.
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Darnel is studying the movement of glaciers, which are bodies of dense ice. The median
annual movement of the Blue Valley Glacier is about 300.2 feet, and the interquartile range is
14 feet. The median annual movement of the Silver Lake Glacier is about 300.4 feet, and the
interquartile range is about 14 feet.
4) What can you conclude from these statistics? Complete the sentence.
Over a year, the Blue Valley Glacier typically moves about
the Silver Lake Glacier, and Blue Valley has
its annual movement compared to Silver Lake.
as
▾ variability in its annual movement compared to silver lake
Over a year, the Blue Valley Glacier typically moves about the same distance as the Silver Lake Glacier, and Blue Valley has the same variability in its annual movement compared to Silver Lake.
How to interpret the statisticsThe median annual movement of the Blue Valley Glacier is 300.2 feet, and the interquartile range is 14 feet.
The interquartile range indicates the spread of the data within the middle 50% of the data
So we know that the annual movement of the Blue Valley Glacier falls within a range of 300.2 ± 7 feet (i.e. 293.2 to 307.2 feet)
Similarly, the median annual movement of the Silver Lake Glacier is 300.4 feet, and the interquartile range is also 14 feet
So the annual movement of the Silver Lake Glacier also falls within a range of 300.4 ± 7 feet (i.e. 293.4 to 307.4 feet)
Since the ranges for both glaciers overlap and have the same size, we can conclude that they typically move about the same distance over a year, and that the variability in the annual movement of Blue Valley is comparable to that of Silver Lake.
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Identify three points that are solutions to
each system.
The solutions for the systems of inequalities are:
a) (0, -100), (0, -150), (0, -1000)
b) (0, 50), (0, 55) , (0, 1,204).
How to identify 3 solutions of each system?When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.
The first one is:
y ≤ x - 8
y < -3x - 9
Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:
-100 ≤ 0 - 8 = -8
-100 < - 3*0 - 9 = -9
Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.
For the second system:
y > 5x + 1
y > 3
Let's do the same thing, x = 0 and y gets really large values, like y = 50
50 > 5*0 + 1 = 1 this is true.
50 > 3 this is true.
so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).
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The expression shown in red represents how many hockey pucks and hockey sticks come in one gym set. The expression shown in blue shows how many come in 3
sets.
Use the drop-down menus to complete the statements below to compare the values of the two expressions.
Answer:
three times
Step-by-step explanation:
find the number of ways of arranging the numbers ${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$ in a row so that the product of any two adjacent numbers is even.
Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.
What are the fundamental products?Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.
We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.
Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.
Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.
Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.
Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.
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8. Using only a compass and straightedge, find the image of A after a rotation by 180° counterclockwise about point B. Label the image A', please provide a picture of the answer
When a point is rotated, it must be rotated around a point.
See attachment for the image of the rotation about point K
How to construct triangles?We should note the following:
In order to construct triangles, you will need a protractor, a pair of compasses and a ruler. To draw the triangle, three properties must be taken into account: length, angle and shape
The given parameters are:
ΔEFG
The angle of rotation is
∅ = 180⁰
The above angle of rotation means that:
The translated triangle will be 180 degrees from ΔEFG about point K.
It also means that:
ΔEFG and ΔE'F'G' will be equidistant from point K
See attached image for ΔE'F'G'
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What is an equation of the line that passes through the points ( 3 , 6 ) (3,6) and ( − 1 , − 6 ) (−1,−6)?
Answer:
y = 3x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (- 1, - 6 )
m = [tex]\frac{-6-6}{-1-3}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3 , then
y = 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 6 )
6 = 3(3) + c = 9 + c ( subtract 9 from both sides )
- 3 = c
y = 3x - 3 ← equation of line
In order to make the same amount of money, they would have to each sell ______ bicycles. They would both make $______.
They would each need to sell 5 bicycles to make the same amount of money and if they both sell 5 bicycles, they would each make $500.
What do you mean by finding the break-even point ?
The key concept used here is the idea of finding the break-even point between two scenarios. In this case, the break-even point is the number of bicycles that Jim and Tom each need to sell in order to make the same amount of money. This is found by setting their total earnings equal to each other and solving for the number of bicycles. Once the break-even point is found, the total earnings for that number of bicycles can be calculated by plugging it back into the original equations. This concept is commonly used in business and finance to determine the minimum level of sales needed to cover costs and make a profit.
Calculating the number of bicycle and money :
To make the same amount of money, Jim and Tom would have to each sell the same number of bicycles, let's call it "b".
So Jim would make a total of:
250 + 50b dollars
Tom would make a total of:
400 + 20b dollars
To find the value of "b" where they both make the same amount of money, we can set the two expressions equal to each other and solve for "b":
250 + 50b = 400 + 20b
30b = 150
b = 5
Therefore, they would each need to sell 5 bicycles to make the same amount of money.
To find out how much they would make, we can substitute "b=5" into either of the expressions above:
Jim:
250 + 50(5) = $500
Tom:
400 + 20(5) = $500
Therefore, if they both sell 5 bicycles, they would each make $500.
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plain why the statistic is misleading.
Wilson was 42 inches tall on Jan 1, 2000, and 51 inches tall on Jan 1, 2002. William was 5 feet tall on Jan 1, 2000, and 6 feet tall on Jan 1, 2002.
Conclusion: The difference between 42 and 51 is greater than the difference between 5 and 6, so Wilson grew more during one year.
Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect and the statistics is misleading.
What is descriptive statistics?Inferential statistics and descriptive statistics are two disciplines of statistics with distinct applications.
Summarizing and characterizing gathered data is the focus of descriptive statistics. It uses techniques including graphical presentations, measurements of variability, and measures of central tendency, such as mean, median, and mode (e.g., histograms, box plots). The purpose of descriptive statistics is to shed light on a sample's or population's properties, such as its distribution, dispersion, and shape.
Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect.
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48 identical looking bags of lettuce were delivered to Circle J grocers. Unfortunately, 12 of these bags of lettuce are contaminated with listeria. Joe, from Joes Cafe randomly selects 4 bags of the lettuce for his cafe. Let X equal the number of the selected packets which are contaminated with listeria. a. How many possible ways are there to select the 4 out of 48 packets (order does not matter) without replacement? b. What is the probability thatX=0
c. What is the probability thatX=4? d. What is the probability thatx>2? e. What is the expected value ofX? f. What is the standard deviation ofX? g. What is the probability that X is smaller than its expected value?
h. What is the probability thatX=5?
Probability that X = 5:Since, Joe selects only 4 bags of lettuce. X can't be 5.P(X=5) = 0Hence, the probability that X = 0 is 0.3164 and the probability that X = 5 is 0.
The given problem can be solved using the concept of binomial distribution.
In the given question, there are 48 bags of lettuce out of which 12 bags are contaminated with listeria.
Joe selects 4 bags of lettuce. X is the random variable which represents the number of contaminated bags of lettuce selected by Joe. X can take values from 0 to 4. (as Joe selects only 4 bags).
Part A)Number of ways to select 4 bags of lettuce out of 48:This can be solved using the concept of combinations. The formula to calculate the number of combinations is[tex]:nCr = n! / r!(n-r)![/tex]Here, n = 48 and r = 4.
Number of ways = 48C4 = 194,580
Part B)Probability that X = 0:This can be calculated using the formula for the binomial distribution :
[tex]P(X = r) = nCr * p^r * q^(n-r)[/tex]
Here, p = probability of selecting contaminated bag = 12/48 = 0.25q = probability of selecting non-contaminated bag = 1-0.25 = 0.75Also, n = 4 and r = [tex]0P(X=0) = 4C0 * 0.25^0 * 0.75^4= 0.3164[/tex]
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An avid gardener wants to know which of two brands of fertilizer is best for her tomatoes. The two brands of fertilizer are A and B. She plants five pairs of tomato plants in two rectangular planters and places them beside one another. She gives each set of tomato plants the same amount of water each day, only she gives one set of plants fertilizer A and the other set of plants fertilizer B. At the end of the growing season, she counts the number of tomatoes each plant has yielded. Assume that all conditions for inference have been met. The rectangular planters are lined up so that plant 1 is beside plant 6, and plant 2 is beside plant 7, and so on. The yield for the five pairs of tomato plants are given. Plant 1 2 3 4 5 Yield with Fertilizer A 7 6 5 8 10 Plant 6 7 8 9 10 Yield with Fertilizer B 4 7 6 5 3 The gardener believes that fertilizer A enhances the yield of her tomatoes more than fertilizer B. She uses the following order of subtraction when determining the difference in the yields for the two brands: A- B (a) We would like to carry out a t test for the population mean difference. Calculate the point estimate. (b) Calculate the standard deviation of the differences. (Round your answer to three decimal places.) (c) Calculate the test statistic. (Round your answer to two decimal places.)
(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.
To perform a t-test for the population mean difference, follow these steps:
(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.
Mean difference = (Sum of differences) / Number of pairs
Using the given data gives:
Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5
Subtracting gives:
Mean difference = (3 - 1 - 1 + 3 + 7) / 5
Solving gives:
Mean difference = 11 / 5
Dividing gives:
Mean difference = 2.2
(b) Calculate the standard deviation of the differences:
To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.
Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]
Solving gives:
Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)
Solving gives:
The sum of squared differences = 48.36
The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]
Solving gives:
The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]
Rounded to three decimal places
The standard deviation of the differences ≈ 3.47
c) Calculate the test statistic:
The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))
Let's assume the null hypothesis is that there is no difference between the two fertilizers
(i.e., mean difference = 0).
[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]
Substituting [tex]\sqrt 5 = 2.236[/tex]
t = 2.2 / (3.47 / 2.236)
Rounded to two decimal places
t ≈ 1.378
So, the test statistic is approximately 1.378.
The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma
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Find the value of N.
4 + 5 -3 = N
8 x 3 - 5 = N
15 ÷ 3 + 10 = N
8 + 3 -1 x 2 = N
14 x 3 - 2 = N
( 3 + 5 ) x 2 = N
10 + 7 + 2 x 1 = N
16 ÷ 8 + 4 = N
7 + 5 ÷ 5 = N
20 ÷ 4 x 6 = N
Answer:
1. n=6
2. n=19
3. n=15
4. n=20
5. n=40
6. n=16
7. n=19
8. n=6
9. n=2.4
10. n=30
Step-by-step explanation:
remember the priorities :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
inside every category you go usually from left to right, but you can use the commutative property where applicable.
4 + 5 - 3 = 4 + 5 - 3 = 4 + 5 - 3 = 4 - 3 + 5 = 6
8×3 - 5 = 24 - 5 = 19
15/3 + 10 = 5 + 10 = 15
8 + 3 - 1×2 = 8 + 3 - 2 = 9
14×3 - 2 = 42 - 2 = 40
(3 + 5)×2 = 8×2 = 16
10 + 7 + 2×1 = 10 + 7 + 2 = 19
16/8 + 4 = 2 + 4 = 6
7 + 5/5 = 7 + 1 = 8
20/4×6 = 5×6 = 30
please help me I have attached a photo below. thanks for your time
Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.
What is slope?In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Here,
To find the slope of a line, we use the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
Using the given coordinates, we have:
x1 = 0, y1 = 5
x2 = 2, y2 = 0
slope = (0 - 5) / (2 - 0)
slope = -5/2
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Y=3x+3 what is the slope and y intercept
Answer:
y-intercept is (0,3) and the slope is 3
Step-by-step explanation:
Answer: the slope is 3x while 3 is the y-intercept.
Step-by-step explanation:
Where did my dad go? He went to get milk but never came back
The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.
The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.
However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.
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when performing a hypothesis test based on a 95% confidence level, what are the chances of making a type ii error?
When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.
The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.
Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.
The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.
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I need help, what does this mean
Answer:
2125 ft/min
33,000 ft
y = -2125x + 33,000
Step-by-step explanation:
A. -2125 feet per minute. You get this number when you divide 17,000 by 8 (rise over run). You could also use the formula y2-y/x2-x1 with the points (0, 33,000) and (8, 17,000).
B. 33,000 feet is the height of the plane before it starts descending, so it must be the starting value.
C. Plug in the values you got for A and B into the slope formula y = mx + b
y = -2125x + 33,000
The rectangular garden is 175 m long and 96 m broad . find the cost of fencing it at 17.50per m.also find the cost of ploughing it at 4.50 paise per square metre
Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.
What is perimeter?Perimeter is the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.
Here,
The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:
2 × (length + width) = 2 × (175 m + 96 m) = 542 m
Therefore, the cost of fencing the garden at 17.50 per meter is:
Cost of fencing = length of fence × cost per meter
= 542 m × 17.50
= 9485
Hence, the cost of fencing the garden is ₹9485.
To find the cost of plowing the garden, we need to first calculate its area, which is given by:
Area = length × width
= 175 m × 96 m
= 16800 m²
Therefore, the cost of plowing the garden at 4.50 paise per square meter is:
Cost of plowing = area of garden × cost per square meter
= 16800 m² × 0.045
= 756
Hence, the cost of plowing the garden is ₹756.
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Hi. Please help me convert this non-linear to linear form y=mx+c. The answer is square root of y= 6/p x - 2/q .
Thank you so much.
Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:
Square both sides of the equation to eliminate the square root:
√y = (6/p)x - (2/q)
√y^2 = (6/p)x - (2/q)^2
Simplifying the right-hand side, we get:
y = (36/p^2)x - (4/q) + 4/q^2
Rearrange the equation to the form y = mx + c:
y = (36/p^2)x + (4/q^2 - 4/q)
So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).
Step-by-step explanation:
during the computer daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. there are 8 different software packages from which to select. how many different groups of software packages can be selected?
Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.
There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.
To calculate this, the total number of possibilities can be found by using the formula nPr,
where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]
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A rectangle has a length of (x+4)cm and a width of (3x-1)cm. It’s perimeter is 78cm
Calculate the value of x
Answer:
X≈ 2,37 cm
x= (-11+√637)/6 cm
Step-by-step explanation:
Salaries for teachers in a particular state have a mean of $ 52000 and a standard deviation of $ 4800. a. If we randomly select 17 teachers from that district, can you determine the sampling distribution of the sample mean? Yes If yes, what is the name of the distribution? normal distribution The mean? 52000 The standard error? b. If we randomly select 51 teachers from that district, can you determine the sampling distribution of the sample mean? ? If yes, what is the name of the distribution? The mean? The standard error? C. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer? ? v d. Assuming a sample size of 51, what is the probability that the sampling error is within $1000. (In other words, the sample mean is within $1000 of the true mean.) e. Assuming a sample size of 51, what is the 90th percentile for the AVERAGE teacher's salary? f. Assuming that teacher's salaries are normally distributed, what is the 90th percentile for an INDIVIDUAL teacher's salary?
a. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{17}}$.
b. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{51}}$.
c. You would need to know that the population distribution of X, teacher salaries, is normal in order to answer the questions regarding any sample size.
d. Assuming a sample size of 51, the probability that the sampling error is within $1000 is approximately 0.84 or 84%.
e. Assuming a sample size of 51, the 90th percentile for the average teacher's salary is approximately $54488.
f. Assuming that teacher's salaries are normally distributed, the 90th percentile for an individual teacher's salary is approximately $56396.
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A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 600 liters of 21% acid solution?
[tex]x=\textit{Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~x\implies \cfrac{20}{100}(x)\implies 0.2 (x) \\\\\\ y=\textit{Liters of solution at 50\%}\\\\ ~~~~~~ 50\%~of~y\implies \cfrac{50}{100}(y)\implies 0.5 (y) \\\\\\ \textit{600 Liters of solution at 21\%}\\\\ ~~~~~~ 21\%~of~600\implies \cfrac{21}{100}(600)\implies 126 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{acid only}}&\stackrel{\textit{Liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.2&0.2x\\ \textit{2nd Sol'n}&y&0.5&0.5y\\ \cline{2-4}&\\ mixture&600&0.21&126 \end{array}~\hfill \begin{cases} x + y = 600\\\\ 0.2x+0.5y=126 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=600}\implies x=600-y \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.2(600-y)+0.5y=126}\implies 120-0.2y+0.5y=126 \\\\\\ 120+0.3y=126\implies 0.3y=6\implies y=\cfrac{6}{0.3}\implies \boxed{y=20} \\\\\\ \stackrel{\textit{since we know that}}{x=600-y}\implies \boxed{x=580}[/tex]
Find $\sin X,\ \sin Z,\ \cos X,\ $ and $\cos Z$. Write each answer as a simplified fraction and rounded to four decimal places
The result of each trigonometric functions are:
a) sin X = 7√149 / 149
b) sin Z = 10√149 / 149
c) cos X = 10√149 / 149
d) cos Z = 7√149 / 149
In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows
sin X = YZ / XZ = 7 / √149
cos X = XY / XZ = 10 / √149
sin Z = XY / XZ = 10 / √149
cos Z = YZ / XZ = 7 / √149
To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:
sin X = 7√149 / 149
cos X = 10√149 / 149
sin Z = 10√149 / 149
cos Z = 7√149 / 149
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The given question is incomplete, the complete question is:
Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.
Solve the triangle MNO (find the measure of ∠O and the lengths of sides MO and NO).
(I need help finding both side measures and angle measure please and thank you
Answer:
Step-by-step explanation:
m∠O = 90° - 34° = 56°
cos M = [tex]\frac{MN}{MO}[/tex] ⇒ MO = [tex]\frac{12}{cos34}[/tex] ≈ 14.5 cm
tan M = [tex]\frac{ON}{MN}[/tex] ⇒ ON = 12 × tan 34° ≈ 8.1 cm
You ate 4/12 of the pizza your family bought for dinner. Your brother ate 3/12 of the pizza. Which equation represents the fraction of pizza both you and your brother ate?
Answer:
7/12 pizzas have been eaten
Step-by-step explanation:
3 + 4= 7
7/12
7-12=5
5 pizzas left
Given the lengths of two sides of a triangle, write an equality to indicate between which two numbers the length of the third side must fall.
The sides are:
8 and 13
I will award brainliest to the first correct answer with a decent explanation
The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
if one response is selected at random, what is the probability the response indicated that the dog is small-sized given that they enjoyed the treat? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.
What is Bayes' theorem?Bayes' theorem is used to update probabilities of a hypothesis or an event in light of new data or evidence. It is used to calculate the conditional probability of an event based on prior knowledge of the conditions that might be relevant to the event.In the given problem, we have to find the probability that the response indicated that the dog is small-sized given that they enjoyed the treat.
The probability that the dog is small-sized given that they enjoyed the treat is the conditional probability P(S|T), where S is the event that the dog is small-sized and T is the event that they enjoyed the treat. To find the value of P(S|T), we will use Bayes' theorem. Bayes' theorem states that P(S|T) = P(T|S) * P(S) / P(T) where P(T|S) is the probability that they enjoyed the treat given that the dog is small-sized, P(S) is the prior probability that the dog is small-sized, and P(T) is the probability that they enjoyed the treat.
P(S) = 3/7P(T|S) = 2/3P(T) = (2/3 * 3/7) + (1/4 * 4/7) = 18/84 + 4/28 = 1/3
(adding the probabilities of T given S and T given L)Therefore, P(S|T) = (2/3 * 3/7) / (1/3) = 2/7 = 0.285714...Rounding off to the nearest millionth, the probability is 0.286. Therefore, the probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.
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Use substitution to solve -4x + y = 3, 5x - 2y = -9
Using the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)
We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:
-4x + y = 3 (Equation 1)
5x - 2y = -9 (Equation 2)
Solving Equation 1 for y, we get:
y = 4x + 3
Now, we substitute this expression for y into Equation 2 and solve for x:
5x - 2(4x + 3) = -9
5x - 8x - 6 = -9
-3x = -3
x = 1
We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:
-4(1) + y = 3
y = 7
Therefore, the solution to the system of equations is (x, y) = (1, 7)
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