u = 2i - 6j
v = 3i + 9j
Take the dot product:
u • v = (2i - 6j) • (3i + 9j)
u • v = (2i • 3i) + (2i • 9j) + (-6j • 3i) + (-6j • 9j)
u • v = 6 (i • i) + 18 (i • j) - 18 (j • i) - 54 (j • j)
The dot product is defined so that for the orthogonal unit vectors i and j, we have i • i = j • j = 1, and i • j = 0. So the above reduces to
u • v = 6 + 0 - 0 - 54
u • v = -48
what is (2x - 4) - (6x + 6)
Answer:
Step-by-step explanation: (2x-4)-(6x+6)
= 2x -4 - 6x - 6 [ opening brackets]
= 2x-6x -4-6 [ bringing the same variables and numbers together]
= -4x-10
=2(2x-5)
Answer:
-4x-10
The 6x + 6 becomes negative due to the negative sign before the parenthesis. You then subtract 6x and 6 from 2x and -4 to get -4x-10
Ayudaaaa porfavorrrrrrrr
The length of the 'top' vector is sqrt(3^2 + 3^2) = 3sqrt2
The length of the 'bottom' vector is sqrt(4^2 + 1^2) = sqrt17
If sally walked 1/2 mile in 1/4 hour, how fast was she walking measured in miles per hour
2 mile per hour
Step-by-step explanation:
I use the equation :
[tex] \frac{ \frac{1}{2} }{ \frac{1}{4} } = \frac{x}{1} \\ x = \frac{ \frac{1}{2} \times 1}{ \frac{1}{4} } \\ x = \frac{ \frac{1}{2} }{ \frac{1}{4} } \\ x = \frac{1}{2} \times \frac{4}{2} \\ x = \frac{4}{2} \\ x = 2 \: mile[/tex]
So, she walked 2 mile per hour
Hope it helpful and useful :)
Help me not big brained
Answer:
33 yd
Step-by-step explanation:
To find the area of a triangle, you can follow the formula:
(base x height) / 2
By putting this formula into context, you can substitute the values of the terms with the information provided in the problem:
(base x height) / 2
(11 yd x 6 yd) / 2
66 yd / 2
33 yd
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Price in Dollars 25 33 34 45 48
Number of Bids 2 3 4 5 7
Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.
Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.Step 3 of 6: Find the estimated value of y when x = 34. Round your answer to three decimal places.Step 4 of 6: Determine the value of the dependent variable yˆ at x = 0.Step 5 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ.Step 6 of 6: Find the value of the coefficient of determination.
Answer:
1) b1=5.831
2) b0=12.510
3) y(34)=210.764
4) y(0)=12.510
5) y=12.510+5.831x
6) R^2=0.85
Step-by-step explanation:
We have the linear regression model [tex]y=b_0+b_1 x[/tex].
We start by calculating the all the parameters needed to define the model:
- Mean of x:
[tex]\bar x=\dfrac{1}{5}\sum_{i=1}^{5}(2+3+4+5+7)=\dfrac{21}{5}=4.2[/tex]
- Uncorrected standard deviation of x:
[tex]s_x=\sqrt{\dfrac{1}{n}\sum_{i=1}^{5}(x_i-\bar x)^2}\\\\\\s_x=\sqrt{\dfrac{1}{5}\cdot [(2-4.2)^2+(3-4.2)^2+(4-4.2)^2+(5-4.2)^2+(7-4.2)^2]}\\\\\\ s_x=\sqrt{\dfrac{1}{5}\cdot [(4.84)+(1.44)+(0.04)+(0.64)+(7.84)]}\\\\\\ s_x=\sqrt{\dfrac{14.8}{5}}=\sqrt{2.96}\\\\\\s_x=1.72[/tex]
- Mean of y:
[tex]\bar y=\dfrac{1}{5}\sum_{i=1}^{5}(25+33+34+45+48)=\dfrac{185}{5}=37[/tex]
- Standard deviation of y:
[tex]s_y=\sqrt{\dfrac{1}{n}\sum_{i=1}^{5}(y_i-\bar y)^2}\\\\\\s_y=\sqrt{\dfrac{1}{5}\cdot [(25-37)^2+(33-37)^2+(34-37)^2+(45-37)^2+(48-37)^2]}\\\\\\ s_y=\sqrt{\dfrac{1}{5}\cdot [(144)+(16)+(9)+(64)+(121)]}\\\\\\ s_y=\sqrt{\dfrac{354}{5}}=\sqrt{70.8}\\\\\\s_y=8.414[/tex]
- Sample correlation coefficient
[tex]r_{xy}=\sum_{i=1}^5\dfrac{(x_i-\bar x)(y_i-\bar y)}{(n-1)s_xs_y}\\\\\\r_{xy}=\dfrac{(2-4.2)(25-37)+(3-4.2)(33-37)+...+(7-4.2)(48-37)}{4\cdot 1.72\cdot 8.414}\\\\\\r_{xy}=\dfrac{69}{57.888}=1.192[/tex]
Step 1
The slope b1 can be calculated as:
[tex]b_1=r_{xy}\dfrac{s_y}{s_x}=1.192\cdot\dfrac{8.414}{1.72}=5.831[/tex]
Step 2
The y-intercept b0 can now be calculated as:
[tex]b_o=\bar y-b_1\bar x=37-5.831\cdot 4.2=37-24.490=12.510[/tex]
Step 3
The estimated value of y when x=34 is:
[tex]y(34)=12.510+5.831\cdot(34)=12.510+198.254=210.764[/tex]
Step 4
At x=0, the estimated y takes the value of the y-intercept, by definition.
[tex]y(0)=12.510+5.831\cdot(0)=12.510+0=12.510[/tex]
Step 5
The linear model becomes
[tex]y=12.510+5.831x[/tex]
Step 6
The coefficient of determination can be calculated as:
[tex]R^2=1-\dfrac{SS_{res}}{SS_{tot}}=1-\dfrac{\sum(y_i-f_i)}{ns_y^2}\\\\\\\sum(y_i-f_i)=(25-24.17)^2+(33-30)^2+(34-35.83)^2+(45-41.67)^2+(48-53.33)^2\\\\\sum(y_i-f_i)=0.69+ 8.98+ 3.36+ 11.12+ 28.38=52.53\\\\\\ ns_y^2=5\cdot 8.414^2=353.98\\\\\\R^2=1-\dfrac{52.53}{353.98}=1-0.15=0.85[/tex]
6x-2(x+1)>0 a. X>2 b. X<2 c. X>1/2 d. X<1/2
Answer:
c. x>1/2
Step-by-step explanation:
Distribute the -2 to eliminate parentheses:
6x -2x -2 > 0
4x -2 > 0 . . . . . . combine terms
Now, you can divide by 4:
x -2/4 > 0
and add 1/2
x > 1/2 . . . . . matches choice C
Answer:
[tex]x > \frac{1}{2} [/tex]
Find the circumference of each circle. Use your calculator's value of 1. Round your answer to
the nearest tenth for
[tex]area = 50.3 in^{2} [/tex]
Answer:
25.1
Step-by-step explanation:
area = pi x r x r
r x r = 50.3 / pi = 16.0109
r = 4.00137
circumference = pi x 2 x r = pi x 2 x 4.00137 = 25.141
For 16 and 17, use the dot plot of the number
of cars sold at a car dealership per week
during the first half of the year.
8
121 16
Cars Sold
20 24
2
16. Find the mean, median, and range.
Mean =
Median
Range -
Answer:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.
i hope i helped a bit
Step-by-step explanation:
Find the value of X to the nearest tenth.
Choices are: 3, 6, 9, 12
Answer:
Here, we have BC // ST, by applying Thales theorem:
UB/US = UC/UT
=>UB = UC x US/UT =6 x 12/(6 + 18) = 3
=> x = US - UB = 12 - 3 = 9
=> Option C is correct.
Hope this helps!
:)
During a recent election, a clerk was responsible for the placement of candidates names on election ballots for a particular voting precinct. Party A candidates were selected for the first position in 30 of 40 ballots. Because the clerk was supposed to use a method of random selection, Party B claimed that instead of using randomness, the clerk used a method favoring Party A. Use a 0.05 significance level to test the claim that the method favored Party A. [Note: Favored means a proportion greater than 50%.]
Answer:
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha > 0.50
z = 3.16
P value = P(Z>3.16) = 0.0008
Decision: we reject the null hypothesis and accept the alternative hypothesis. That is, the clerk used a method favoring Party A.
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
Given;
n = 40 represent the number of samples taken
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha > 0.50
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 40
po = Null hypothesized value = 0.50
p^ = Observed proportion = 30/40 = 0.75
Substituting the values we have
z = (0.75-0.50)/√(0.50(1-0.50)/40)
z = 3.16227766
z = 3.16
To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.
P value = P(Z>3.16) = 0.0008
Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 3.16) which doesn't falls with the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0008 which is lower than 0.05. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.
PLZ HELP FAST WILL MARK BRAINLIEST
The box plots show the number of hours that Mr. Yan’s biology class spent studying for a test. It also shows the number of hours Mrs. Gonzalez’s class spent studying for a geography test. Mr. Yan’s Class 2 box plots. The number line goes from 0 to 10. For Mister Yan's class, the whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4. For Misses Gonzalez's Class, the whiskers range from 1 to 9, and the box ranges from 4 to 7. A line divides the box at 5.5. Mrs. Gonzalez’s Class Four students compared the data in the box plots. Nadine Kendrick Tahara Dean The medians are the same because both sets of data have the same minimum and maximum values. Mr. Yan’s class has a greater median because the box in that box plot is larger. Mrs. Gonzalez’s class has a greater median because the line inside that box is located at a greater value. The medians are both 7 because the upper quartile for the sets of data is 7. Which student is correct?
Nadine
Kendrick
Tahara
Dean
The correct student is Dean.
To determine which student is correct, let's analyze the information given in the box plots for both classes:
For Mr. Yan's class, the box plot shows:
- Minimum value (lower whisker): 1
- Maximum value (upper whisker): 9
- Lower quartile (Q1): 2
- Median (Q2): 4
- Upper quartile (Q3): 7
- Interquartile range (IQR): Q3 - Q1 = 7 - 2 = 5
For Mrs. Gonzalez's class, the box plot shows:
- Minimum value (lower whisker): 1
- Maximum value (upper whisker): 9
- Lower quartile (Q1): 4
- Median (Q2): 5.5
- Upper quartile (Q3): 7
- Interquartile range (IQR): Q3 - Q1 = 7 - 4 = 3
Now let's evaluate each student's statement:
- Nadine: The medians are the same because both sets of data have the same minimum and maximum values. This statement is incorrect because the medians are different. Mr. Yan's class has a median of 4, while Mrs. Gonzalez's class has a median of 5.5.
- Kendrick: Mr. Yana's class has a greater median because the box in that box plot is larger. This statement is incorrect because the size of the box does not determine the median. The median is the value that divides the data into two equal halves, and it is indicated by the line inside the box.
- Tahara: Mrs. Gonzalez's class has a greater median because the line inside that box is located at a greater value. This statement is correct. The median for Mrs. Gonzalez's class is 5.5, which is greater than the median for Mr. Yan's class, which is 4.
- Dean: The medians are both 7 because the upper quartile for the sets of data is 7. This statement is incorrect because the median is not determined by the upper quartile but by the value that separates the higher half from the lower half of a data sample.
Therefore, the only correct statement is made by Tahara, who correctly identifies that Mrs. Gonzalez's class has a greater median because the line inside the box is located at a greater value (5.5) compared to Mr. Yan's class (4).
A student was asked to find a 95% confidence interval for widget width using data from a random sample of size n = 21. Which of the following is a correct interpretation of the interval 10.6 < μ < 29.1? Check all that are correct.
A. With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.
B. With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.
C. The mean width of all widgets is between 10.6 and 29.1, 95% of the time.
D. We know this is true because the mean of our sample is between 10.6 and 29.1.
E. There is a 95% chance that the mean of the population is between 10.6 and 29.1.
F. There is a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean. A 95% confidence interval does not mean 95% probability. It is used to express how confident we are that the true population parameter lies within the confidence interval.
With a lower limit of 10.6 and an upper limit of 29.1, and confidence interval of 95%, the correct option is
With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.
Final answer:
The 95% confidence interval represents the range within which the true mean of all widgets is likely to fall, not the individual sample mean.
Explanation:
A 95% confidence interval for widget width of 10.6 < μ < 29.1 means:
With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.
There is not a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.
Therefore, the correct interpretations are A and F.
Point A is (-7, 5) and point M is at (0, 4)
Point M is the midpoint of point A and Point B
What are the coordinates of point B
Answer: (7,3)
Step-by-step explanation:
The coordinates of point B(7, 3).
What is Section Formula?The formula below gives the coordinates of the point A(x, y), which internally splits the line segment between the points P([tex]x_1[/tex], [tex]y_1[/tex]) and Q([tex]x_2[/tex], [tex]y_2[/tex]) in the ratio [tex]m_1[/tex]: [tex]m_2[/tex],
A (x, y) = [tex]((m_1 x_2 + m_2 x_1) / ( m_1 + m_2), \;\; (m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]
Given:
Point A is (-7, 5) and point M is at (0, 4).
and, Point M is the midpoint of point A and Point B.
A (x, y) = [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]
So, x= [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]
0 = ( 1 x [tex]x_2[/tex] + 1 x (-7)) / (1 + 1)
0 = [tex]x_2[/tex] - 7
[tex]x_2[/tex] =7
and, y= [tex](m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]
4= ( 1 x [tex]y_2[/tex] + 1 x 5)/ 2
8 = [tex]y_2[/tex] + 5
[tex]y_2[/tex] = 3
Hence, the coordinates of B(7, 3).
Learn more about Section formula here:
https://brainly.com/question/11888968
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Assume that when adults with smartphones are randomly selected, 42% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 24 of them use their smartphones in meetings or classes.
Answer:
0.00205%
Step-by-step explanation:
Use binomial probability:
P = nCr p^r q^(n-r)
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
n = 30, r = 24, p = 0.42, and q = 0.58.
P = ₃₀C₂₄ (0.42)²⁴ (0.58)³⁰⁻²⁴
P ≈ 0.00205%
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let AAA be the event that the six-sided die is an even number and BBB be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions. What is P(A)P(A)P, (, A, ), the probability that the six-sided die is an even num
Answer:
0.5
Step-by-step explanation:
The sample space of a fair six-sided die and a fair four-sided die rolled simultaneously is given below:
[tex](1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\[/tex]
where in each pair (x,y), x represents the four-sided die and y represents the six sided die.
Total Number of Possible Outcomes =24
Event A is the event that the six-sided die is an even number.
n(A)=12
Therefore, the probability that the six-sided die is an even number:
P(A)=12/24=0.5
On a coordinate plane, a graph has number of hours on the x-axis and number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).
The graph represents the number of haircuts, y, a hair stylist can give over time, x. Use the graph to find the constant of proportionality and write an equation.
The constant of proportionality is .
The equation that represents the number of haircuts the stylist can give in an hour is .
The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
On a coordinate plane, a graph has a number of hours on the x-axis and a number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).
We know that the equation of the line passing through the two-point is given as
[tex]\rm (y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Then we have
[tex]\rm y-1 = \dfrac{2-1}{4-2} \times (x-2)\\\\y = \dfrac{1}{2}\ x - 1+1 \\\\y = \dfrac{1}{2}\ x[/tex]
The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.
More about the linear system link is given below.
https://brainly.com/question/20379472
Answer:
first one is 1/2 second one is y = 1/2 x
Hope it helps!!!
(((HELP ASAP)))
Graph the line your equations using the slope of the line and y-intercept taken from the slope intercept form of the equation. Find the intersection of the two graphs. Check that your solution is correct. Watch your place and minus slopes! In y=mx+b, m Is the slope of the line and b is the y-intercept.
Answer: (-2,3)
Step-by-step explanation:
Two solution of salt water contain 0.03% and 0.23 salt respectively. A lab technician
wants to make 1 liter of Solution which contains
0.18% salt. How much of each solution should
She use?
Amount of 0.3% solution-milliliter
Amount of 0.23% solution - Milliliter
Answer:
750 mL of 0.23% solution250 mL of 0.03% solutionStep-by-step explanation:
Let x represent the quantity (in liters) of the higher percentage solution, the 0.23% solution. Then 1-x will be the quantity of 0.03% solution. The amount of salt in the mix is ...
0.23%·x +0.03%·(1 -x) = 0.18%·1
Multiply by 100% and subtract 3:
20x = 15
x = 15/20 = 0.75 . . . . liters of 0.23% solution
1-x = 1-0.75 = 0.25 . . liters of 0.03% solution
The lab tech needs 750 mL of 0.23% solution and 250 mL of 0.03% solution.
This week Emma earned ten more than half the number of dollars she earned last week a babysitting. If this week she earned 100 dollars how much did she earn last week
Answer:180
Step-by-step explanation:
100 - 10 is 90
90 x 2 is 180
I did a reverse calculation you can also check this is correct by knowing that half of 180 is 90 and 100 dollars is 10 more than 90 dollars.
Quiana has 7 times more text messages from Yolanda than from Pierre. Quiana has 56 text messages from Yolanda. Which equation can be used to find how many text messages Quiana has from Pierre, p?
Answer:
Quiana has 8 text messages from Pierre.
Step-by-step explanation:
This question can be solved using a rule of three.
Quiana has 7 times more text messages from Yolanda than from Pierre.
This means that for each message that she receives from Pierre, she receives 7 from Yolanda.
She received 56 from Yolanda.
So
7 messages from Yolanda - 1 messages from Pierre
56 messages from Yolanda - x messages from Pierre
[tex]7x = 56[/tex]
[tex]x = \frac{56}{7}[/tex]
[tex]x = 8[/tex]
Quiana has 8 text messages from Pierre.
Quiana has 8 text messages from Pierre.
To find how many text messages Quiana has from Pierre, represented as p, given that Quiana has 7 times more text messages from Yolanda than from Pierre, and she received 56 text messages from Yolanda, we can set up the following equation:
p × 7 = 56
To solve for p, we divide both sides of the equation by 7:
p = 56 ÷ 7
p = 8
So, Quiana has 8 text messages from Pierre.
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught.
Step 2 of 2 : Suppose a sample of 1390 suspected criminals is drawn. Of these people, 514 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 1390
x = 514
p = 514/1390 = 0.37
q = 1 - 0.37 = 0.63
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.01 = 0.99
The z score corresponding to the area on the z table is 2.33. Thus, confidence level of 98% is 2.33
Therefore, the 98% confidence interval is
0.37 ± 2.33√(0.37)(0.63)/1390
Confidence interval = 0.37 ± 0.0302
Which two values are greater then 3/5
Answer:
4/5 and 1
Step-by-step explanation:
4/5 is greater then 3/5 and 5/5=1 whole which is greater than 3/5, 4/5 and 1 is greater than 3/5 and 1 1/5, 1 2/5 so on and so on it could go forever but 4/5, and 1 is the only ones that our after 3/5 so those are the two greatest ones in this quistion.
Hope this helps.
The two values are 4 by 5 and 1
The following information should be considered:
4 by 5 is greater then 3 by 5 and 5 by 5 = 1 whole which is more than 3 by 5, 4 by 5 and 1 is greater than 3 by 5 and 1 1 by 5.However 4 by 5, and 1 is the only ones that after 3 by 5 so those are the two greatest ones in this given question.Learn more:
https://brainly.com/question/17429689?referrer=searchResults
If the volume of the pyramid shown is 216 inches cubed, what is the area of its base?
A rectangular pyramid with a height of 6 inches.
12 inches squared
36 inches squared
72 inches squared
108 inches squared
Answer:
D.) 108 in.2
Step-by-step explanation:
Use the equations you know to help you figure this out. It may not be easy, but for you to understand, you need to learn how to do it. If you want work, try it out.. Not to be rude...
Answer:
D) 108 inches squared.
Step-by-step explanation:
When you have the height of a pyramid, you must find the area of the base. Then multiply the base and height. When you find the product, divide this by three. There's your answer.
SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school are given below. 380 520 480 510 560 630 670 490 500 550 400 350 440 490 620 660 700 730 740 560 Test if the standard deviation of the reading and writing section SAT score of the students in this school is higher than 100. What is the value of the test statistic (round off to the nearest integer)
Answer:
The value of test statistics is 25.
Step-by-step explanation:
We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;
380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560
Let [tex]\sigma[/tex] = population standard of the reading and writing section SAT score of the students in this school
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \leq[/tex] 100 {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma[/tex] > 100 {means that the reading and writing section SAT score of the students in this school is higher than 100}
The test statistics that would be used here is One-sample Chi-square test statistics;
T.S. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2} __n_-_1[/tex]
where, [tex]s^{2}[/tex] = sample variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex] = 13135.8
n = sample of 11th-grade students = 20
So, the test statistics = [tex]\frac{(20-1)\times 13135.8^{2} }{100^{2} }[/tex]
= 24.96 ≈ 25
Hence, the value of test statistics is 25.
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. The appropriate hypotheses to determine if the manufacturer's claim appears reasonable are
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W
Step-by-step explanation:
We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.
They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Let [tex]\mu[/tex] = mean power consumption of microwave ovens.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W
Here, null hypothesis states that the mean power consumption of microwave ovens is no more than 250 W.
On the other hand, alternate hypothesis sates that the mean power consumption of microwave ovens is more than 250 W.
The test statistics that would be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.
What is the difference between the circumference and area of a circle?
Answer
The circumference of a circle is the length of its side, the area is the amount of space within it.
Step-by-step explanation:
The circumference of a circle represents the distance around the circle's boundary, while the area represents the surface area enclosed by the circle.
The difference between the circumference and area of a circle lies in their respective measurements and what they represent.
Circumference: The circumference of a circle is the measurement of the distance around the outer boundary of the circle. It is essentially the perimeter of the circle. The circumference is calculated using the formula:
Circumference = 2πr or πd
Where r represents the radius of the circle and d represents the diameter. It is a linear measurement and is typically expressed in units such as centimeters, inches, or meters.
Area: The area of a circle is the measurement of the region enclosed by the circle's boundary. It represents the total surface area within the circle. The area of a circle is calculated using the formula:
Area = πr²
Where r represents the radius of the circle. The area is a two-dimensional measurement and is typically expressed in square units such as square centimeters, square inches, or square meters.
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Two different samples will be taken from the same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values, and the second sample will have 64 data values. A 95% confidence interval will be constructed for each sample to estimate the population mean. Which confidence interval would you expect to have greater precision (a smaller width) for estimating the population mean?
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - α)% confidence interval for population mean μ is:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
n₁ = 25
n₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Width for n = 64:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Thus, the sample consisting of 64 data values would give a greater precision
Answer:
Confidence Interval with sample size 25 = Broader, less precision; Confidence Interval with sample size 64 = Narrower, more precision
Step-by-step explanation:
Confidence Interval is the range around sample statistic, which contains the actual population parameter. Confidence level is the percentage probability, with which the population parameter is expected to be in confidence interval.
When sample size increases : the margin of error, ie sampling error between population parameter & sample statistic decreases. The reduced margin of error increases the level of confidence & precision in confidence interval range. So, the confidence interval range becomes narrower.
Hence, confidence interval becomes narrower & has more precision, when sample size increases from sample number = 25 to sample number = 64.
-2x-8y= -32 slope intercept form
Answer:
y = -1/4x +4
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
-2x-8y = -32
Add 2x to each side
-2x+2x-8y =2x -32
-8y = 2x-32
Divide each side by -8
-8y/-8 = 2x/-8 -32/-8
y = -1/4x +4
is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is direct or inverse write a function to model it.
x 2 5 20 40
y 40 20 5 2
Answer:
Neither
Step-by-step explanation:
In direct variation, as one number increases, the other number also increases and as one number decreases, the other number also decreases. In inverse variation, as one number increases, the other number decreases and as as one number decreases, the other number increases.
For direct variation, [tex]y=kx[/tex] and for indirect variation, [tex]y=\frac{k}{x}[/tex] where k is a constant.
x 2 5 20 40
y 40 20 5 2
Here,
[tex]\frac{2}{40}=\frac{1}{20}\\ \frac{5}{20}=\frac{1}{4}\\ \frac{20}{5}=4 \\\frac{40}{2} =20[/tex]
So, this is neither a direct variation nor an indirect variation.
The City of Decatur finds that salaries for residents working in the technology sector follow an approximately normal distribution with a mean of $42,800 and a standard deviation of $8,365.
To the nearest hundredth, what Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000?
Answer:
- 1. 15
Step-by-step explanation:
Z score is used in statistic to calculate deviation of an observed value from mean value of sample of observation.
Mathematically it is given by
[tex]z = observed \ value - mean\ value/ standard\ deviation[/tex]
using the above formula and substituting the value of of
mean = $42,800
standard deviation = $8,365
observed value =$30,000
Z = (8,365 - 42,800) / $30,000
= - 34,435/ 30,000 = - 1. 14783
= - 1. 15 ( to the nearest hundredth)
- 1. 15 Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000