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.
three less than the product of 4 and the number is equal to 5
Answer:
4n-3=5
Step-by-step explanation:
If you read it step by step the product of and a number is basically 4* any variable.( In this case I use n.) Next the beginning part is 3 less than the product part so it is 4n-3. And finally the whole equation is equal to 5 so itis 4n-3=5.
Answer the question bellow
Answer:
The old version awards 50 more points for each level
Step-by-step explanation:
Function Modeling
Two models are being compared: The old model relates the total number of points awarded in a computer game (y) with the number of levels completed (x) as
[tex]y=175x+150[/tex]
The new model is given as a graph. To find the equation of the line we must locate a couple of 'good' points. The graph is very clear, so we select the extreme points (1,250) (9,1250)
Find the equation of the line with the point-point formula
[tex]\displaystyle y-250=\frac{1250-250}{9-1}(x-1)[/tex]
[tex]\displaystyle y-250=\frac{1000}{8}(x-1)[/tex]
[tex]y=250+125x-125[/tex]
[tex]y=125x+125[/tex]
Comparing the new function with the old function we can note the coefficient of x (the slope of the line) is 50 points more in the old version than the points in the new version.
Thus the answer is
The old version awards 50 more points for each level
Answer: the answer is B
Step-by-step explanation:
Layla and Sam are both dog sitters. Layla charges $2 per day plus a sign-up fee of $3. Sam charges a flat rate of $3 per day. The system of linear equations below represents y, the total amount earned in dollars for x days of dog sitting.
A. Write the equation to represent Layla’s fees
B. Write the equation to represent Sam’s fees
C. After how many days do Layla and Sam earn the same amount for dog sitting?
What is that amount?
Answer:Correct Answer: A
Explanation: Choice A is the correct answer. Let x be the number of hours that the babysitter worked. Since the babysitter earns money at a rate of $8 per hour, she earned 8x dollars for the x hours worked. If the babysitter gets both children to bed on time, the babysitter earns an additional $3 tip. Therefore, the babysitter earned a total amount of 8x + 3 dollars.
Choice B is incorrect since the tip and the rate per hour have been interchanged in the expression. Choices C and D are incorrect since the number of children is not part of how the babysitter’s earnings are calculated.
g a. A 99% confidence level and a sample of 24 observations. 2.807 2.807 Correct b. A 90% confidence level and a sample of 24 observations. 1.714 1.714 Correct c. A 99% confidence level and a sample of 20 observations. 2.845 2.845 Incorrect d. A 90% confidence level and a sample of 20 observations.
Answer: b. A 90% confidence level and a sample of 24 observations. 1.714 1.714 Correct
Step-by-step explanation:
A cylinder with height 2x is inscribed in a sphere with radius 8 meters. The center of the sphere is the midpoint of the altitude that joins the centers of the bases of the cylinder. What is the volume of the cylinder? *
The volume of the cylinder is 401.92 cube m.
Step-by-step explanation:
Given,
A cylinder of height 2x inscribed in a sphere of radius 8 m.
The center of the sphere is the midpoint of the altitude that joins the centers of the bases of the cylinder.
To find the volume of the cylinder.
Formula
The volume of a cylinder with h as height and r as radius is = πr²h
Since,
The cylinder is inscribed in the sphere
The radius (r) of the cylinder = 4 m
The height (h) of the cylinder = 8 m
So,
The volume of the cylinder = π×4²×8 cube m
= 128π cube m [ taking π=3.14]
= 128×3.14 cube m
= 401.92 cube m
Hence,
The volume of the cylinder is 401.92 cube m.
The volume of the cylinder is 128πx.
Explanation:The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the cylinder's base and h is the height of the cylinder. In this case, the cylinder is inscribed in a sphere with radius 8 meters and the center of the sphere is the midpoint of the altitude that joins the centers of the bases of the cylinder. Since the cylinder is inscribed in the sphere, the diameter of the cylinder is equal to the diameter of the sphere, which is twice the radius of the sphere. Thus, the diameter of the cylinder is 16 meters and the radius is 8 meters.
Since the height of the cylinder is given as 2x, we can substitute this value into the formula to find the volume:
V = π(8)²(2x) = 128πx
Therefore, the volume of the cylinder is 128πx.
The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12. The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is:
Answer:
0.0668
Step-by-step explanation:
Assuming the distribution is normally distributed with a mean of $75,
with a standard deviation of $12.
We can find the z-score of 78 using;
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]\implies z=\frac{78-75}{\frac{12}{36} } =1.5[/tex]
Using our normal distribution table, we obtain the area that corresponds to 0.25 to be 0.9332
This is the area corresponding to the probability that, the average is less or equal to 78.
Subtract from 1 to get the complement.
P(x>78)=1-0.9332=0.0668
The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is 0.0668.
Calculation of the probability:Since The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12.
Here we need to find out the z score
= [tex]78-75\div 12\div 36[/tex]
= 1.5
Here we considered normal distribution table, we obtain the area that corresponds to 0.25 to be 0.9332
So, the average is less or equal to 78.
Now
Subtract from 1 to get the complement.
So,
P(x>78)=1-0.9332
=0.0668
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help, will give brainliest
Answer:
10.0
Step-by-step explanation:
4.0+8.0=12.0-2.0=10.0
What is the probability that a domestic airfare is $560 or more (to 4 decimals)? b. What is the probability that a domestic airfare is $260 or less (to 4 decimals)? c. What if the probability that a domestic airfare is between $320 and $500 (to 4 decimals)? d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)
Without sufficient data, we cannot calculate the probabilities or the cost for the 3% highest domestic airfares. The calculations require details about the total number of observed airfares and the number that falls in the specified price ranges.
Explanation:I regret to inform you that I cannot provide a factual answer to your question regarding domestic airfares as you have not provided sufficient data. Probability depends on the sample space and given conditions which are not provided in your question. For instance:
For the probability of a domestic airfare being $560 or more, we need to know the total number of observed airfares and the number that were $560 or more. The same applies to a domestic airfare of $260 or less (to 4 decimals). The total fares and the ones falling under this range are required. The probability of a fare being between $320 and $500 is calculated from the total fares within this range divided by the total fares observed. For the 3% highest fares, we need to know the distribution of airfares to calculate this value. Learn more about Probability here:
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Suppose that 60% of employees at a particular corporation participate in the optional retirement plan. If a random sample of 50 employees is selected, what is the probability that at least 25 employees in the sample will participate in the optional retirement plan?
Answer:
94.41% probability that at least 25 employees in the sample will participate in the optional retirement plan
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 50, p = 0.6[/tex]
So
[tex]\mu = E(X) = np = 50*0.6 = 30[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.6*0.4} = 3.46[/tex]
What is the probability that at least 25 employees in the sample will participate in the optional retirement plan?
Using continuity correction, this is [tex]P(X \geq 25 - 0.5) = P(X \geq 24.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 24.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.5 - 30}{3.46}[/tex]
[tex]Z = -1.59[/tex]
[tex]Z = -1.59[/tex] has a pvalue of 0.0559
1 - 0.0559 = 0.9441
94.41% probability that at least 25 employees in the sample will participate in the optional retirement plan
Please help, I don’t know the answer
Answer:
The answer is A.
Step-by-step explanation:
Which points on the graph represent values that could be in the table? A B C D
Answer:
uhhh
Step-by-step explanation:
uh I don't see the graph
Answer:
D and B
Step-by-step explanation:
A bag of walnuts sells for$1.95 Estimate the cost of 8 bags of walnut
Answer:
$15.6
Step-by-step explanation:
one bag= $1.95
8 bags = 8×1.95=15.6
so answer is $15.6.
-2/5x - 5 = -25
solve X QUICKKKKLY
Answer:
50
Step-by-step explanation:
add 5 to -25 to get -2/5x by itself.
Which equation has the components of 0 = x2 - 9x - 20 inserted into the quadratic formula correctly?
O
x
= -9 V(-9)2 - 4(1)(-20)
x= 91V(- 9)2 - 4(1)(20)
2(1)
x= 9:(-92 - 4(1)(-20).
2(1)
x= -9 1(-9)2 + 4(1)(-20)
2(1)
Answer:
c
Step-by-step explanation:
just did it on the assignment
Drag each tile to the correct cell in the table.
High school students were surveyed about which math and
science topics they preferred. They were asked to choose
algebra or geometry, and biology or chemistry. The results are
shown in the frequency table below.
QUI 73%DC 100%
C
70%
30%
30%
100%
100%
28%
72%
Use this table to create a relative frequency table by row.
27%
Algebra
Geometry
Total
Algebra
Geometry
Total
Biology
67
92
Biology
Chemistry
46
66
Chemistry
Total
113
45
158
Total
Answer:
Step-by-step explanation:
Table(2) shows the relative frequency opted from the table(1).
What is the frequency?It is defined as the number of waves that crosses a fixed point in one second known as frequency. The unit of frequency is per second.
We have a table in which data has shown:
To find the relative frequency:
For the first cell:
[tex]=\frac{67}{92} \times100 \approx 73\%[/tex]
For the second cell:
= 100 - 73 ⇒ 27%
For the third cell:
[tex]\rm = \frac{46}{66} \times 100 \approx 70\%[/tex]
For the fourth cell:
= 100 - 70 = 30%
Thus, table(2) shows the relative frequency opted from table(1).
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3•(7+10)=G+30 use the distributive property to solve
Answer: G=21
Step-by-step explanation:
Solve for G by simplifying both sides of the equation, then isolating the variable.
Which of the following equations represents a hyperbola with a vertical transverse axis and foci at (0, −10) and (0, 10)?
Answer: A
Step-by-step explanation:
Answer:
the first opition is the correct answer
The reaction times for a random sample of 9 subjects to a stimulant were recorded as 2.5, 3.6, 3.1, 4.3, 2.9. 2.3, 2.6, 4.1, and 3.4 seconds. Calculate (a) the mean; (b) the median. 8.4 The number of
Answer:
Mean is 3.2
Median is 3.1
Step-by-step explanation:
a) mean
= (2.5+3.6+3.1+4.3+2.9+2.3+2.6+4.1+3.4)/9
= 28.8/9
= 3.2
b) median: we will arrange in ascending order and pick the middle term.
2.3 2.5 2.6 2.9 3.1 3.4 3.6 4.1 4.3
From the above order, 3.1 is the middle term and is the median
a) The mean reaction time of the 9 subjects is 3.2 seconds.
What is a mean?A mean is an average of a set of values.
The mean is computed by summing the values and then dividing the sum by the number of subjects.
b) The median reaction time for the random sample of 9 subjects to a stimulant is 3.1 seconds.
What is the median?The median is the middle number in an arranged list of values. The arrangement takes into consideration their ascending or descending orders.
The median is simple to determine when the list of values is not too long and well-arranged.
Data and Calculations:Variables Reaction Times
in seconds
1. 2.5
2. 3.6
3. 3.1
4. 4.3
5. 2.9
6. 2.3
7. 2.6
8. 4.1
9. 3.4
Total 28.8
Mean = 3.2 (28.8/9)
Determination of the Median:6. 2.3
1. 2.5
7. 2.6
5. 2.9
3. 3.1
9. 3.4
2. 3.6
8. 4.1
4. 4.3
Thus, the mean and the median have been calculated.
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Suppose 40% of DC area adults have traveled outside of the United States. Nardole wants to know if his customers are atypical in this respect. He surveys 40 customers and finds 60% have traveled outside of the U.S. Is this result a statistically significant difference?
Answer:
We conclude that % of DC area adults who have traveled outside of the United States is different from 40%.
Step-by-step explanation:
We are given that 40% of DC area adults have traveled outside of the United States. Nardole wants to know if his customers are typical in this respect. He surveys 40 customers and finds 60% have traveled outside of the U.S.
We have to test is this result a statistically significant difference.
Let p = % of DC area adults who have traveled outside of the United States
SO, Null Hypothesis, [tex]H_0[/tex] : p = 40% {means that 40% of DC area adults have traveled outside of the United States}
Alternate Hypothesis, [tex]H_a[/tex] : p [tex]\neq[/tex] 40% {means that % of DC area adults who have traveled outside of the United States is different from 40%}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = % of customers who have traveled outside of the United States
in a survey of 40 customers = 60%
n = sample of customers = 40
So, test statistics = [tex]\frac{0.60-0.40}{\sqrt{\frac{0.60(1-0.60)}{40} } }[/tex]
= 2.582
Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical value of 1.96 for two-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.
Therefore, we conclude that % of DC area adults who have traveled outside of the United States is different from 40%.
FIND THE AREA OF THE SHADED REGION
Answer: 40in²
Step-by-step explanation:
To find the area of the shade region, considering the diagram, the diagonal of the rectangle has divided the figure into two equal half. So, one is shaded and the other not shaded. So the shaded region is a right angled triangle,. So the formula for finding the area of a triangle need to be applied.
Area. = 1/2 × b × h
= 1/2 × 10 × 8
= 40in²
What fraction is equivalent to 0.997
What is the median of the following data set?
{6, 3, 9, 1, 7}
3
6
8
9
I know the answer just seeing what you guys know and giving points:)
Answer:
The median of the following set of data is 9 since the question is implying, which is the center of the data distribution.
Step-by-step explanation:
Which expression is equivalent to 15x – 2(3x + 6)?
Answer: 3(3x−4) is the answer
Answer:
3(3x-4) is the answer
Step-by-step explanation:
A manager recorded how many hours each of 11 cashiers worked in a week. Which interval contains the median number of hours worked?
Answer:
Step-by-step explanation:
Hello!
In descriptive statistics, the median is a measurement of center position. It separates the sample in halves. (bottom 50% from upper 50%)
The manager took a sample of 11 cashiers and recorded the worked hours in a week
To identify the median you have to calculate it's position:
The position is calculated as
PosMe= (n+1)/2= (11+1)/2= 6 cashier
This means that the Median of hours worked is a week observed corresponds to the 6th cashier (after ordering the data from lowest to highest)
If you observe the histogram, the x-axis corresponds to worked hours and the y-axis shows the number of workers.
The workers were already arranged from least hours worked to most hours worked.
The first interval corresponds to 0-10 worked hours and two workers recorded these working times.
The second interval corresponds to 10-20 worked hours and three workers recorded these working times.
In the third interval of 20-30 hours, no workers recorded these working times.
The fourth interval corresponds to 30 - 40 worked hours and 5 workers recorded these working times.
The fifth interval corresponds to 40 - 50 worked hours and only one worker recorded these working hours.
The first five workers were recorded in the first two intervals and the sixth worker was recorded in the fourth interval. So the interval that contains the median number of hours worked is "30 - 40 hours"
I hope this helps!
The interval that contains the median number of hours worked is "30 - 40 hours"
The manager took a sample of 11 cashiers and recorded the worked hours in a week
To identify the median you have to calculate it's position:
The position is calculated as
PosMe= (n+1)/2= (11+1)/2= 6 cashier
The fourth interval corresponds to 30 - 40 worked hours and 5 workers recorded these working times.
The first five workers were recorded in the first two intervals and the sixth worker was recorded in the fourth interval. So the interval that contains the median number of hours worked is "30 - 40 hours"
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Please help
What is the slope of a line that is parallel to the line shown?
Answer:
m=2/3
Step-by-step explanation:
your answer would be A.
Given a family with four children, find the probability of the event.
The oldest is a girl and the youngest is a boy, given that there is at least one boy and at least one girl.
Answer:
28.57% probability that the oldest is a girl and the youngest is a boy, given that there is at least one boy and at least one girl.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
These are all the possible outcomes: from youngest to oldest, b is boy and g is girl
b - b - b - g
b - b - g - b
b - b - g - g
b - g - b - b
b - g - b - g
b - g - g - b
b - g - g - g
g - b - b - b
g - b - b - g
g - b - g - b
g - b - g - g
g - g - b - b
g - g - b - g
g - g - g - b
The nuber of total outcomes is 14.
Desired outcomes:
Oldest(last) girl, youngest(first) boy
b - b - b - g
b - b - g - g
b - g - b - g
b - g - g - g
So 4 desired outcomes
Probability:
4/14 = 0.2857
28.57% probability that the oldest is a girl and the youngest is a boy, given that there is at least one boy and at least one girl.
Final answer:
The probability that a family with four children will have the oldest being a girl and the youngest being a boy, given that there is at least one boy and one girl, is 1/4.
Explanation:
To solve this probability question, we need to consider all possible combinations of children while adhering to the given conditions: the oldest child must be a girl (G), the youngest must be a boy (B), and there must be at least one boy and at least one girl in the family.
The possible genders for the four children can be represented as a sequence of G (girl) and B (boy) like this: G---B. There are two positions in the middle that can be either a boy or a girl. Since each position can be filled independently with either a boy or a girl, there are 2 options for each of the middle children, giving us 2 x 2 = 4 combinations: GBGB, GBBB, GGBB, GGBG.
To calculate the probability of any single one of these combinations occurring, we need to remember that the probability of giving birth to a boy or a girl is equal, which means each event (birth of a child) has a probability of 1/2. Thus, the probability of each combination is (1/2)^4 since there are four independent events (births). However, since we have 4 combinations that meet the criteria, we multiply this probability by 4. So, the probability is 4 * (1/2)^4 = 1/4.
Therefore, the probability that a family with four children will have the oldest being a girl and the youngest being a boy, given that there is at least one boy and at least one girl, is 1/4.
What is the volume, in cubic in, of a rectangular prism with a height of 5in, a width of 12in, and a length of 14in?
Answer:
840
Step-by-step explanation:
the volume of a rectangular prism is the base(width)height
A school has two kindergarten classes. There are 21 children in Ms. Toodle's kindergarten class. Of these, 17 are "pre-readers" children on the verge of reading. There are 19 children in Mr. Grimace's kindergarten class. Of these, 13 are pre-readers. Using the plus four confidence interval method, a 90% confidence interval for the difference in proportions of children in these classes that are pre-readers is â0.104 to 0.336.
Which of the following statements is correct?
A) This confidence interval is not reliable because the samples are so small.
B)This confidence interval is of no use because it contains 0, the value of no difference between classes.
C)This confidence interval is reasonable because the sample sizes are both at least 5.
D) This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.
Answer:
Answer : D
Step-by-step explanation:
A school has two kindergarten classes. There are 21 children in Ms. Toodle's kindergarten class. Of these, 17 are "pre-readers" children on the verge of reading. There are 19 children in Mr. Grimace's kindergarten class. Of these, 13 are pre-readers. Using the plus four confidence interval method, a 90% confidence interval for the difference in proportions of children in these classes that are pre-readers is â0.104 to 0.336.
Which of the following statements is correct?
A) This confidence interval is not reliable because the samples are so small.
B)This confidence interval is of no use because it contains 0, the value of no difference between classes.
C)This confidence interval is reasonable because the sample sizes are both at least 5.
D) This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.
The Answer is D - This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.
In this setup, all the students are already involved in the data. This is not a sample from a larger population, but probably, the population itself.
Please solve it as fast as possible
find an equation equivalent to r= 1+2 = sin theta in rectangular coordinates
Answer:
C
Step-by-step explanation:
[tex]x^{2}[/tex]+[tex]y^{2}[/tex]= [tex]\sqrt{x^{2}+y^{2} }[/tex]+2y
Answer:
The equation of equivalent is,[tex]x^{4}+ y^{4} +3 y^{2} +2x^{2} y^{2} -4y^{3} -4 x^{2} y-x^{2} =0[/tex]
Step-by-step explanation:
Definition of equivalent equation:If two systems of equations have the same solution, they are equivalent (s). This article explains how to determine whether two systems are equal. Equivalent systems are sets of equations that have the same solution.
Given, r = 1+2sinФ
[tex]r^{2} =r+2rsin[/tex]θ
[tex]x^{2}+ y^{2} =r+2y\\x^{2} + y^{2} -2y=r\\[/tex]
Squaring, both side:
[tex](x^{4} +y^{4} -2 y^{2}) = r^{2} \\x^{4}+ y^{4} + 4y^{2}+2 x^{2} y^{2} - 4y^{3} -4x^{2} y =x^{2} +y^{2} \\x^{4} + y^{4} +3 y^{2} +2 x^{2} y^{2} -4y^{3} -4x^{2} y^}-x^{2} =0[/tex]
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