Answer:
There is no relationship between voles and food preference (The food preferences among vole species are independent of one another)
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. The null hypothesis tries to establish that the old theory is true. So, for the case above, the old theory is that there is no relationship between voles species and food preference which is the null hypothesis.
The null hypothesis in Dr. Pagels' study is that there is no difference in the food preferences for peanut butter-oatmeal mixture and apple slices between meadow and common voles.
In the study conducted by Dr. Pagels for determining the food preference of meadow and common voles, the null hypothesis posits that there is no difference in preference for the peanut butter-oatmeal mixture or apple slices between the two species of voles. This implies that both meadow and common voles would choose either food option at an equal rate, suggesting that any observed preference could be attributed to random chance rather than a true preference.
The purpose of the null hypothesis is to establish a baseline expectation that no effect or difference is present, which can then be challenged by the experimental data. If significant differences in the vole populations' food choices are observed, the null hypothesis may be rejected, pointing to a potential preference for one food type over the other among the different vole species.
Using the digits 1 to 20, at most 1 time each, fill in the boxes to create equivalent expressions.
Answer:
There are many possible solutions. For example,
(2^3)^4 = ((2^5)^12)/((2^6)^8) = 2^10 x 2^2 = (2^19)/(2^7)
(2^2)^5 = ((2^6)^11)/((2^7)^8) = 2^1 x 2^9 = (2^20)/(2^10)
Step-by-step explanation:
You need to fill in boxes with the digits 1 to 20 to create equations where both sides yield the same numerical result. This will involve understanding of basic arithmetic operations and a bit of trial and error.
Explanation:The subject of this question is Mathematics. Specifically, it relates to the concept of equivalent expressions, which are an essential component of algebra and arithmetic. First, it's crucial to understand the concept of equivalent expressions: two expressions are considered equivalent if they share the same numerical value for each possible value of their variable(s).
Now, let's make an example with the numbers 1 to 10 (just to simplify the explanation). Consider the equations: 1+2+3+4 and 5+3+2+1. Even though the order of operations is different, both expressions yield the final numerical value of 10, making them equivalent expressions.
In the context of the question, you are being asked to fill in boxes with the digits 1-20, such that the expressions on either side of the equation sign are equivalent. This might involve a combination of operations like addition, subtraction, multiplication, and division.
It's a challenging task because it involves a bit of trial and error. Start by deciding on the operations for the expressions and then fill in the numbers. Make sure you check your results by calculating the numerical value of each expression.
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Which one is correct for this question need help please
Answer:
A is correct, 7 units. Hope this helps! :)
The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What is the probability that a randomly selected bill will be at least $39.10
Answer:
Probability that a randomly selected bill will be at least $39.10 is 0.03216.
Step-by-step explanation:
We are given that the daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.
Let X = daily dinner bills in a local restaurant
So, X ~ N([tex]\mu=28,\sigma^{2} =6^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount = $28
[tex]\sigma[/tex] = standard deviation = $6
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, the probability that a randomly selected bill will be at least $39.10 is given by = P(X [tex]\geq[/tex] $39.10)
P(X [tex]\geq[/tex] $39.10) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{ 39.10-28}{6}[/tex] ) = P(Z [tex]\geq[/tex] 1.85) = 1 - P(Z < 1.85)
= 1 - 0.96784 = 0.03216
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.85 in the z table which has an area of 0.96784.
Hence, the probability that a randomly selected bill will be at least $39.10 is 0.03216.
The probability that a randomly selected bill will be at least $39.10 is approximately 0.0323.
First, we calculate the z-score for a bill of $39.10 using the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where X is the value for which we want to find the probability, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.
Given:
[tex]\[ \mu = 28 \] \[ \sigma = 6 \] \[ X = 39.10 \][/tex]
Plugging in the values:
[tex]\[ z = \frac{39.10 - 28}{6} \] \[ z = \frac{11.10}{6} \] \[ z \approx 1.85 \][/tex]
Now, we look up the z-score of 1.85 in the standard normal distribution table or use a calculator to find the probability of a z-score being at least 1.85. This gives us the area to the right of the z-score on the standard normal curve.
Using a standard normal distribution table or calculator, we find:
[tex]\[ P(Z \geq 1.85) \approx 0.0323 \][/tex]
classify each pair of the angles as one of the following
Answer:
where are the angles? I can't see anything
Answer:
Please provide pictures!!
Step-by-step explanation:
How do I graph y=3 sin0+1
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12% chose chocolate pie, and the margin of error was given as plus or minus3 percentage points. What values do ModifyingAbove p with caret, ModifyingAbove q with caret, n, E, and p represent? If the confidence level is 99%, what is the value of alpha?
Answer:
Step-by-step explanation:
.01 (subtract confidence level from 100)
Michelle borrows a total of $2500 in student loans from two lenders. One charges 4.2% simple interest and the other charges 6.8% simple interest. She is not required to pay off the principal or interest for 3 yr. However, at the end of 3yr, she will owe a total of $354 for the interest from both loans. How much did she borrow from each lender?
Let x represent amount borrowed at 4.2% and y represent amount invested at 6.8%.
We have been given that Michelle borrows a total of $2500 in student loans from two lenders. We can represent this information in an equation as:
[tex]x+y=2500...(1)[/tex]
[tex]y=2500-x...(1)[/tex]
We are also told that at the end of 3 years, she will owe a total of $354 for the interest from both loans.
Amount of interest earned at a rate of 4.2% in 3 years would be [tex]0.042\cdot 3\cdot x=0.126x[/tex].
Amount of interest earned at a rate of 6.8% in 3 years would be [tex]0.068\cdot 3\cdot y=0.204y[/tex].
We can represent this information in an equation as:
[tex]0.126x+0.204y=354...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]0.126x+0.204(2500-x)=354[/tex]
[tex]0.126x+510-0.204x=354[/tex]
[tex]-0.078x+510=354[/tex]
[tex]-0.078x+510-510=354-510[/tex]
[tex]-0.078x=-156[/tex]
[tex]\frac{-0.078x}{-0.078}=\frac{-156}{-0.078}[/tex]
[tex]x=2000[/tex]
Therefore, Michelle borrowed $2000 at 4.2%.
Upon substituting [tex]x=2000[/tex] in equation (1), we will get:
[tex]y=2500-2000=500[/tex]
Therefore, Michelle borrowed $500 at 6.8%.
She borrowed $ 2000 from the 4.2% lender and $ 500 from the 6.8% lender.
Since Michelle borrows a total of $ 2500 in student loans from two lenders, and one charges 4.2% simple interest and the other charges 6.8% simple interest, and she is not required to pay off the principal or interest for 3 yr, but at the end of 3yr, she will owe a total of $ 354 for the interest from both loans, to determine how much did she borrow from each lender, the following calculation must be performed:
4.2 x 3 = 12.6 6.8 x 3 = 20.4 2500 x 0.126 + 0 x 0.204 = 315 2000 x 0.126 + 500 x 0.204 = 354
Therefore, she borrowed $ 2000 from the 4.2% lender and $ 500 from the 6.8% lender.
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Percent of discount 15%
Sale price $146.54
find the illegal values of b in the fraction 2b2+3b-10/ b2-2b-8
Answer:
-2 and 4
Step-by-step explanation:
When you look for values that make an expression “illegal” the first step is to look for 3 things.
1) a variable in a denominator
- we have b, a variable, in the denominator of this expression
- values in the denominator cannot be 0
2) variables under even roots
- variables under even roots are a restriction because even roots are undefined when there are negative values under them
- there are no roots in this case so we dont have to worry about that
3) the literal letters: “log” in the expression
- there’s no “log” in the expression so we dont have to worry about that
—moving on—
We have a variable in the denominator, b.
The expression is a quadratic:
b^2 - 2b - 8
You have to find values that make this quadratic 0.
So you can make an equation setting the quadratics equal to 0.
b^2 - 2b - 8 = 0
Solve for b
Factor:
(b - 4)(b + 2) = 0
Because of zero product property we can say:
b = -2, b = 4.
If these values are plugged into your expression, it will be “illegal,” or “undefined,”
Use the interactive tool to create the three-dimensional
solid from the net.
What is the surface area of the three-dimensional solid
you created?
35 cm2
56 cm2
72 cm2
90 cm2
The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.
Step-by-step explanation:
The given is,
Detailed view or net diagram of the three dimensional diagram.
Step:1
Three dimensional diagram of the given net diagram is attached.
From the three dimensional diagram given net diagram is rectangular prism.
Step:2
From the three dimensional diagram
Formula for surface area of the rectangular prism,
[tex]A = 2(wl + lh + hw)[/tex]..............................(1)
Where, w - Width
l - Length
h - Height
From the attachment,
l = 6 cm
w = 2 cm
h = 3 cm
Equation (1) becomes,
[tex]A = 2((6)(2) + (6)(3) + (3)(2))[/tex]
= 2 ( 12 + 18 + 6 )
= 2 ( 36 )
A = 72 squared centimeters
( or )
From the net diagram,
Surface area, A = ((6×3)+(2×3)+(2×6)+(2×3)+(3×6)+(2×6))
= 18 + 6 + 12 + 6 + 18 + 12
= 72
Surface area, A = 72 squared centimeters
Result:
The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.
Answer:72 cm2
Step-by-step explanation:
You come up with what you think is a great idea for a new advertising campaign for your company. Your boss is worried that the ads will cost a lot of money and she wants to be 99% confident that the ads increase sales before rolling the new ads out nationwide. You run the ads in a typical city and take a random sample to see if people who saw the ad are more likely to buy the product. When you reported the results to your boss, you made a Type II error. 18. Explain in words the statistical meaning of this type of error.
Answer:
Type II error will be made if we conclude that the new advertising campaign does not increases the sales when in fact the sales are increased after the advertising campaign.
Step-by-step explanation:
A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.
β = Probability of accepting H₀ when H₀ is false.
In this case we need to test the hypothesis whether the new advertising campaign increases the sales or not.
The hypothesis can be defined as:
H₀: The new advertising campaign does not increases the sales.
Hₐ: The new advertising campaign increases the sales.
The confidence level wanted here is 99%.
The type II error will be made if we conclude that the new advertising campaign does not increases the sales when in fact the sales are increased after the advertising campaign.
The type II error could have been made because of the following reasons:
The sample size selected is too small. The smaller the sample size, greater is the probability of type II error. Significance level of the test must be small. If the significance level is small then the rejection regions decreases. Thus, reducing the chances of correctly rejecting the null hypothesis.Thus, the type II error might have been committed because of small sample size or small significance level.
what is x= 0.393 as a fraction
Answer:
393/1000
Step-by-step explanation:
Answer:
Step-by-step explanation:
393/1000
Solve:
3(4 – 2x) = -x+1
Answer:
11/5 =x
Step-by-step explanation:
3(4 – 2x) = -x+1
Distribute
12 -6x = -x+1
Add 6x to each side
12 -6x+6x = 6x-x +1
12 = 5x +1
Subtract 1 from each side
12-1 = 5x+1-1
11= 5x
Divide each side by 5
11/5 =5x/5
11/5 =x
Steps to solve:
3(4 - 2x) = -x + 1
~Distribute
(3 * 4) + (3 * -2x) = -x + 1
~Simplify
12 - 6x = -x + 1
~Subtract 12 to both sides
12 - 12 - 6x = -x + 1 - 12
~Simplify
-6x = -x - 11
~Add x to both sides
-6x + x = -x + x - 11
~Simplify
-5x = -11
~Divide -5 to both sides
-5x/-5 = -11/-5
~Simplify
x = 11/5
Best of Luck!
What is the lowest terms of 36 and -18?
Answer:
49
Step-by-step explanation:
36 minus -18 is 49
Answer:
-1/2
Step-by-step explanation:
The fraction is not reduced to lowest terms. We can reduce this fraction to lowest
terms by dividing both the numerator and denominator by 18.
Suppose cattle in a large herd have a mean weight of 1217lbs1217 lbs and a variance of 10,40410,404. What is the probability that the mean weight of the sample of cows would differ from the population mean by more than 11lbs11 lbs if 116116 cows are sampled at random from the herd? Round your answer to four decimal places.
Answer:
0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 1217, \sigma = \sqrt{10414} = 102, n = 116, s = \frac{102}{\sqrt{116}} = 9.475[/tex]
What is the probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd?
This is 2 multiplied by the pvalue of Z when X = 1217 - 11 = 1206. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1206 - 1217}{9.475}[/tex]
[tex]Z = -1.16[/tex]
[tex]Z = -1.16[/tex] has a pvalue of 0.1230
2*0.1230 = 0.2460
0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.
To calculate the probability, we can use the Central Limit Theorem. Calculate the standard error using the formula: standard error = standard deviation / sqrt(n), then use the z-score formula to find the probability.
Explanation:To find the probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs, we can use the Central Limit Theorem. Since the sample size is large (n > 30), the distribution of sample means will be approximately normally distributed. First, we calculate the standard deviation of the sampling distribution, also known as the standard error, using the formula: standard error = standard deviation / sqrt(n). In this case, the standard error is sqrt(10404)/sqrt(116).
Finally, we can use the z-score formula to calculate the probability. The z-score is given by z = (x - mean) / standard error. We want to find the probability that the mean weight differs from the population mean by more than 11 lbs, so we calculate the z-score for both 11 and -11 and use the z-table or a calculator to find the probability of z being greater than the positive z-score and less than the negative z-score. Adding these two probabilities gives us the final answer.
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Find a polynomial equation that has zeros at x = −2, x = 0, x = 3 and x = 5
If a polynomial "contains", in a multiplicative sense, a factor [tex](x-x_0)[/tex], then the polynomial has a zero at [tex]x=x_0[/tex].
So, you polynomial must contain at least the following:
[tex](x-(-2)),\quad (x-0),\quad (x-3),\quad (x-5)[/tex]
If you multiply them all, you get
[tex]x(x+2)(x-3)(x-5)=x^4 - 6 x^3 - x^2 + 30 x[/tex]
Now, if you want the polynomial to be zero only and exactly at the four points you've given, you can choose every polynomial that is a multiple (numerically speaking) of this one. For example, you can multiply it by 2, 3, or -14.
If you want the polynomial to be zero at least at the four points you've given, you can multiply the given polynomial by every other function.
To find a polynomial with given zeros, each zero can be plugged into the format (x - a). Doing so with the provided zeros in this question, i.e., -2, 0, 3, and 5, represents the zeroes of the polynomial equation x(x + 2)(x - 3)(x - 5) which simplifies to x4 - 6x3 + 3x2 + 60x.
Explanation:The subject of this question is polynomial equations in mathematics. In order to find a polynomial equation that has zeroes at x = -2, x = 0, x = 3, and x = 5, you can use the fact that the equation (x - a)(x - b)(x - c)(x - d) will have zeros at a, b, c, and d.
By substituting the values for a, b, c, and d into the equation with the zeroes provided (-2, 0, 3, and 5), the polynomial equation that satisfies these zeroes can be expressed as: (x - (-2))(x - 0)(x - 3)(x - 5). Simplifying, this gives: x(x + 2)(x - 3)(x - 5).
To further simplify, we need to multiply these expressions: x*(x+2)*(-x+15)-(2*x-10),which simplifies to: x4 - 6x3 + 3x2 + 60x. This is the polynomial equation that has zeros at x = -2, x = 0, x = 3, and x = 5.
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The length of the base of an isosceles triangle is x. The length of a leg is 3x-6. The perimeter of the triangle is 51. Find x
Answer:
x = 9
Step-by-step explanation:
The perimeter is the sum of the lengths of the base and the two equal legs:
51 = x + 2(3x -6)
51 = 7x -12 . . . . . eliminate parentheses
63 = 7x . . . . . . . . add 12
9 = x . . . . . . . . . . divide by 7
A book normally costs $21.50. Today it was on sale for $15.05. What percentage discount was offered during the sale?
Answer:
The answer is 30% off
Step-by-step explanation:
if you do 21.50 - 30% = 15.05
The coach of an age group swim team needs to assign swimmers to a 200-yard medley relay team to send to the Junior Olympics. Since most of his best swimmers are very fast in more than one stroke, it is not clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and the best times (in seconds) they have achieved in each of the strokes (for 50 yards) are
Answer:
a) add a dummy stroke to make the problem as an assignment problem of adding 5 strokes to 5 swimmers. see first attachment.
b) applying the Hungarian method.
4.8 0 0.9 4.1 2.5
10.3 0 9.1 1.6 8.7
4.8 0 10.4 1.9 5.1
2.8 0 3.2 2.1 4.7
0 0 0 0 0
Deduct the smallest element in each column from the other elements of the column.
2 0 0 2.5 0
7.5 0 8.2 0 6.2
2 0 9.5 0.3 2.6
0 0 2.3 0.5 2.2
0 0 0 0 0
Which implies:
2 8.2 2.5 6.2
7.5 9.5 0.3 2.6
2 2.3 0.5 2.2
33.8 + 34.7 + 28.5 + 29.2 = 126.2
David = Back Stroke
tony = Breast Stroke
Chris = Butterfly
Carl = Free Style
The question is about assigning swimmers in a team to different strokes to achieve the best total time. It's a combinatorial optimization problem which can be solved by considering all the permutations of swimmers' assignments to each stroke and selecting the one with least total time.
Explanation:The subject of this question is an optimization problem in Mathematics, specifically in the field of Combinatorics. Deciding the arrangement of swimmers to minimize the total time spent can be approached using techniques from this field. Unfortunately, the information provided does not give the exact times of the swimmers, so achieving a detailed solution isn't possible. However, the problem could hypothetically be solved by enumerating all possible assignments of swimmers to strokes and selecting the assignment that has the least total time.
This problem resonates with high school level math, where students begin to tackle optimization problems and permutations.
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Subract 8 from the quotient of 15
Answer: These would be my two thoughts.
Step-by-step explanation:
ANSWER #1. 15-8= 7
ANSWER #2. 3-8= -5
In the United States, 41% of the population have brown eyes. If 14 people are randomly selected, find the probability that at least 12 of them have brown eyes. Is it unusual to randomly select 14 people and find that at least 12 of them have brown eyes? Why or why not?
Answer:
0.000773 is the probability that atleast 12 out of 14 will have brown eyes.
Step-by-step explanation:
We are given the following information:
We treat people having brown eyes as a success.
P(people have brown eyes) = 41% = 0.41
Then the number of people follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 14
We have to evaluate:
[tex]P(x \geq 12) = P(x = 12) + P(x = 13) + P(X = 14) \\= \binom{14}{12}(0.41)^{12}(1-0.41)^2 + \binom{14}{13}(0.41)^{13}(1-0.41)^1 + \binom{14}{14}(0.41)^{14}(1-0.41)^0\\= 0.0007 + 0.00007 + 0.000003\\= 0.000773[/tex]
0.000773 is the probability that atleast 12 out of 14 will have brown eyes.
Yes, it is an unusual event due to small probability values.
An online gaming site conducted a survey to determine the types of games people play online. if 1500 people participated in the study how many more would play card games than arcade games (Page 824)
Answer:
315
Step-by-step explanation:
The missing percentages of the given scenario are;
Adventure Games: 22%
Puzzles: 28%
Card Games: 30%
Arcade Games: 9%
Board Games: 11%
So in order to solve the problem, we simply use the pie chart distributions to get the result
Now if look at the percentages, we that card games percentage is 30 while arcade games is 9 so, 21 % of people play more card games.
In terms of number of people = 21/100 x 1500 = 315
Hence out of 1500, 315 people play card games more than arcade
Answer:
The number of more people that played card games than arcade games is 150 people
Step-by-step explanation:
Here we have a pie chart showing games people play in the following proportions
Assumption; Card games = 49%
Arcade games = 32%
Classic = 15%
Kids = 4%
Therefore. if 49% played card games, we have 49% of 1500 which is 735 people, while 32% that played arcade games, we have 39% of 1500 = 0.39×1500 = 585
Therefore, the number of more people that played card games than arcade games = 735 - 585 = 150 people.
In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank
are the same size and packed wall-to-wall. If each of the tanks are filled to the top with water, which
tank would contain the most water. Prove your answer algebraically using x to represent the edge
length of the tanks.
Answer:
Step-by-step explanation:
Let represent the edge of the tank with x and the radius of the first sphere with x/2;
The amount of the water = Volume of the tank - Volume of the sphere
= [tex]x^3 - \frac{4}{3} \pi (\frac{x}{2})^3[/tex]
on the second cube ; the radius of the sphere = [tex]\frac{x}{4} \ units[/tex] ;
Also the number of sphere here is = 8
The amount of water = [tex]x^3 -8*\frac{4}{3} \pi (\frac{x}{4})^3[/tex]
For the third figure ; the radius of the sphere is = [tex]\frac{x}{8} \ units[/tex]
Also the number of sphere here is = 64
The amount of water = [tex]x^6 -64*\frac{4}{3} \pi (\frac{x}{8})^3[/tex]
= [tex]x^3 - \frac{4}{3} \pi (\frac{x}{2})^3[/tex]
In the fourth tank ; 512 sphere illustrates that in a single row; that more than one 8 sphere is present i.e 8³ = 512
then the radius will be = [tex]\frac{x}{16}[/tex]
The amount of water = [tex]x^3 -512*\frac{4}{3} \pi (\frac{x}{16})^3[/tex]
= [tex]x^3 -\frac{4}{3} \pi (\frac{x}{2})^3[/tex]
This implies that alll the three cube shaped tanks are identical and hold equal amount of water.
HELP ASAP PLEASE!!!
Which of the following lines are parallel?
a. line c and line d
b. line b and line c
c. line a and line b
d. line d and line e
You may pick more than one.
Answer:
The answer is d: LINE D AND LINE E
The other answer is c LINE A AND LINE B
Step-by-step explanation:
Jimmy bought a 5-kilogram can of peanuts for $4.50. What is the unit price?
Answer:
$0.90 per kilogram
Step-by-step explanation:
4.5/5=.9
the scores on a test given to all juniors in a school district are normally distributed with a mean of 80 and a standard deviation of 8. Find the percent of juniors whose score is at least 80. The percent of juniors whose score is at or above the mean is_____% PLZ HELP!
Answer:
The percent of juniors whose score is at or above the mean is 50%
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 80, \sigma = 8[/tex]
Find the percent of juniors whose score is at least 80.
This is 1 subtracted by the pvalue of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 80}{8}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
1 - 0.5 = 0.5
So
The percent of juniors whose score is at or above the mean is 50%
Find the quotient. Round to the nearest tenth. 3784 divided by 18
Answer:
210.22
Step-by-step explanation:
first you need to divide 3785 divided by 18 which is 210.22222222 then u need to round to the nearest tenth which is equaled to 210.22. I hope this helped
Round 43.3333 to the nearest hundredth.
A) 43.3
B) 43.33
C) 43.34
D) 43.4
Answer: B
Step-by-step explanation:
Can't really explain it. A tenth is .1, a hundredth is .01
A __________ determines how far a particular value is from the mean relative to the data set's standard deviation. a. percentile b. coefficient of variation c. z-score d. variance
Answer:
z-score
Step-by-step explanation:
Z-score gives the relative value of any data population in relation to its mean. It depicts at what distance any data is from the mean. In technical terms it can be termed as the number of times a data is data away from the mean. Positive value of z score means value is more than mean while a negative value signifies data is less than that of mean.
Z – score is primarily used in qualitative analysis of numerical data by the statistician after data is arranged in normal distribution form. Z score of 0 means the value is same as mean while z-score of value 1 means data is one standard deviation away from the mean.
The z-score is the measure that determines the distance of a value from the mean in terms of standard deviations which is option c.
A z-score determines how far a particular value is from the mean relative to the data set's standard deviation. Given an experimental value, X, the mean, μ (mu), and the standard deviation, σ (sigma), the z-score is calculated using the formula Z = (X - μ) / σ. A z-score represents the number of standard deviations an experimental value is above or below the mean. For example, if a data value has a z-score of 2, it is two standard deviations above the mean. Contrarily, a z-score of -1.5 indicates that the value is one and a half standard deviations below the mean. Z-scores are used across various fields to compare different values within a data set or among different data sets with different means and standard deviations.
The triangle shown below has an area of 121212 units^2
2
squared.
Find xxx.
Answer:
4
Step-by-step explanation:
Let's set up an equation using the formula for the area of a triangle.
Hint #22 / 3
\begin{aligned} \text{Area of a triangle} &= \dfrac12 \cdot \text{base} \cdot \text{height}\\\\ 12&= \dfrac12 \cdot 6 \cdot x \\\\ 12&= 3x \\\\ \dfrac{12}{\blueD{3}}&= \dfrac{3x}{\blueD{3}} ~~~~~~~\text{divide both sides by } {\blueD{ 3}}\\\\ \dfrac{12}{\blueD{3}}&= \dfrac{\cancel{3}x}{\blueD{\cancel{3}}}\\\\ x &=\dfrac{12}{\blueD{3}}\\\\ x &=4\end{aligned}
Area of a triangle
12
12
3
12
3
12
x
x
=
2
1
⋅base⋅height
=
2
1
⋅6⋅x
=3x
=
3
3x
divide both sides by 3
=
3
3
x
=
3
12
=4