We are given two sets of paired observations, which we will use to calculate the sample mean difference and the standard error of the mean difference:
Sample mean difference = x1 -x2 = (214+186+182+200+210+204+187+210+190+182+215+198)/12 - (188+210+199+209+207+195+203+191+190+211+199+181)/12 = 4.75
Sample standard deviation of the differences = s = √[(Σd²)/(n-1)] where d = (x1 - x2) - (x1 - x2), and n is the number of pairs.
d1 = (214 - 188) - 4.75 = 21.25
d2 = (186 - 210) - 4.75 = -28.75
d3 = (182 - 199) - 4.75 = -22.75
d4 = (200 - 209) - 4.75 = -9.75
d5 = (210 - 207) - 4.75 = -1.75
d6 = (204 - 195) - 4.75 = 3.25
d7 = (187 - 203) - 4.75 = -20.75
d8 = (210 - 191) - 4.75 = 13.25
d9 = (190 - 190) - 4.75 = -4.75
d10 = (182 - 211) - 4.75 = -28.75
d11 = (215 - 199) - 4.75 = 10.25
d12 = (198 - 181) - 4.75 = 12.25
Σd² = 1734.875
s = √(1734.875/11) = 5.076
Standard error of the mean difference = s/√n = 5.076/√12 = 1.469
Using a t-distribution with 11 degrees of freedom and a 99% confidence level (α = 0.01), we find the t-value to be 3.106. Therefore, the 99% confidence interval for the true mean difference between the cholesterol levels for people who take the new drug is:
(4.75 - 3.106(1.469), 4.75 + 3.106(1.469))
= (0.885, 8.615)
So we are 99% confident that the true mean difference between the cholesterol levels for people who take the new drug lies between 0.885 and 8.615 mg/dL.
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Match each dilation to its correct function as it relates to the parent function(x)=x².
Nex
Instructions
uestion
j(x)=(1/2x)^2
k(x) = 2x²2
h(x)-(2x)²
g(x) = x²
horizontal compression
vertical compression
vertical stretch
horizontal stretch
The correct match of each dilation to its function is: j(x) = (1/2x)^2: vertical stretch, k(x) = 2x²: vertical compression, h(x) = (2x)²: horizontal compression, and g(x) = x²: no dilation, it is the parent function.
Each of the given functions is a dilation of the parent function f(x) = x^2, which means that they are obtained by stretching or compressing the graph of the parent function either vertically or horizontally.
- j(x) = (1/2x)^2: This function is a vertical stretch of the parent function, because the constant factor of 1/2 in front of the x causes the function to be stretched vertically by a factor of 2.
- k(x) = 2x²: This function is a vertical compression of the parent function, because the constant factor of 2 in front of the x^2 causes the function to be compressed vertically by a factor of 1/2.
- h(x) = (2x)²: This function is a horizontal compression of the parent function, because the constant factor of 2 inside the x^2 causes the function to be compressed horizontally by a factor of 1/2.
- g(x) = x²: This is the parent function, and it is not dilated in any way. Its graph is a parabola that opens upwards and has a vertex at the origin.
Thus, this is the correct match for the given scenario.
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Show that 20 is not a solution of the inequality in the example. Explain what this means about Fidel’s driving this week.
20 is not a solution of the inequality as the value is greater than 400 rather being less than 400.
We have the inequality
26g < 400
Now, for g = 20
26g
=26(20)
= 520 > 400
So, 20 is not a solution of the inequality as the value is greater than 400 rather being less than 400.
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What is the IQR of the aged, in years?
The IQR of the ages, in years include the following: B. 16.
How to interpret the box-and-whisker plot?Based on the information provided about the given box plot or box-and-whisker plot, the five-number summary for the given data set include the following:
Minimum (Min) = 12.First quartile (Q₁) = 22.Median (Med) = 32.Third quartile (Q₃) = 38.Maximum (Max) = 44.How to calculate the interquartile range (IQR)?In Mathematics and Statistics, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) of data set = Q₃ - Q₁
Interquartile range (IQR) of data set = 38 - 22
Interquartile range (IQR) of data set = 16.
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Other than translation, what transformation is used to create this frieze pattern?
180° rotation
vertical reflection
horizontal reflection
glide reflection
The transformation to create the pattern is 180° rotation
Given data ,
Let the pattern be represented as figure A
Now , the figure A has footprints of the left leg
when rotating by 180° in the clockwise or anticlockwise direction , the sign only changes and it will be up side down
Hence , the transformation is 180° rotation
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the mean and standard deviation of salaries of players on the denver broncos were recorded. is it appropriate to use the methods of this section to perform a hypothesis test about the mean salary of players in the national football league? if not, why not?
It's important to consider the terms "deviation," "players," and the context of the question. The mean and standard deviation of the salaries of players on the Denver Broncos have been recorded. You'd like to know if it's appropriate to use these methods to perform a hypothesis test about the mean salary of players in the National Football League (NFL).
In this case, it may not be appropriate to use the methods of this section to perform a hypothesis test about the mean salary of players in the NFL. The reason is, the data collected only represents the players on the Denver Broncos and not the entire population of NFL players. The standard deviation and mean of the Denver Broncos' salaries may not accurately represent the salary distribution of the entire league, as there might be variations among different teams.
To perform a hypothesis test about the mean salary of players in the NFL, it would be necessary to gather data from a representative sample of players across all teams in the league. This would allow for a more accurate estimation of the true mean salary and standard deviation within the entire population of NFL players.
In conclusion, while the data collected for the Denver Broncos players provides useful information about that specific team, it is not sufficient to draw conclusions about the mean salary of players in the entire NFL without obtaining a representative sample from all teams.
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How to show the numbers 1/2 and 1/3 on the number line
Step-by-step explanation:
To represent 1 2/3 on a number line, we start by locating the integer 1 on the number line:
----|-----------|-----------|-----------|-----------|-----------|
-3 -2 -1 0 1 2
Next, we need to locate the fractional part 2/3 of a unit. To do this, we divide the interval between 1 and 2 into three equal parts, and then shade two of those parts:
----|-----------|-----------|-----------|-----------|-----------|
-3 -2 -1 0 1 2
1 4/3 5/3 2
Therefore, the point representing 1 2/3 on the number line is located at 5/3 units to the right of -1, as shown above.
The graph of f is translated a whole number of units horizontally and vertically to obtain the graph of g.
The function f is defined by f(x) = |x|
Write down the expression for g(x)
An expression for the function g(x) include the following: g(x) = |x - 3| + 4.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In order to write an expression that models g(x), we would have to apply a vertical translation to f(x) by 4 units up and a horizontal translation by 3 units right;
g(x) = f(x - 3) + 4
g(x) = |x - 3| + 4
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Sunny Town is symmetric
Mean, because Sunny Town is skewed
Median, because Beach Town is skewed
Mean, because Beach Town is symmetric
Median, because Beach Town is skewed. Therefore, option C is the correct answer.
The correct answer is Median, because Beach Town is skewed. The mean is the average of the data and works best when the data is symmetric, or evenly distributed around the center. Since the data for Beach Town appears skewed, with more temperatures on the higher end of the range, the median is a better measure for determining which location typically has a cooler temperature.
The median is the middle value of the data, so it is not affected by outliers as much as the mean.
The best measure of center to determine which location typically has the cooler temperature would be the median. The median is the best measure of center to use when comparing data because it is not affected by outliers or extreme values. Since both Sunny Town and Beach Town are skewed, the median is the more appropriate measure of center to use when comparing the data.
Therefore, option C is the correct answer.
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Read and answer the question circled in red
The sum of the numbers less than 3 is 5/4
What are fractions?Fractions are simply defined as part of a whole variable, element or number.
In mathematics, there are different types of fractions, they are;
Proper fractionsImproper fractionsSimple fractionsComplex fractionsMixed fractionsExamples of simple fractions are; 1/2, 1/3, 1/4
Examples of mixed fractions are; 2 1/3, 4 1/3
Examples of improper fractions are; 5/2, 4/2
From the information given, we have that;
the sum of the numbers less than 3 is written as
1/2 + 3/4
Add the values
2 + 3/4
Add the values
5/4
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how many ways are there for eight students and five professors to stand next to each other such that no two professors are standing next to each other
There are 8! (factorial) ways for the eight students to stand next to each other. However, since no two professors can stand next to each other, we need to alternate professors and students. We can start with a professor, then a student, then a professor, and so on.
There are 5! ways to arrange the five professors among the eight spaces where a professor can stand. Once the professors are arranged, there are 8 - 5 = 3 spaces left for students to stand. There are 8P3 (permutations) ways to arrange the three students among the three spaces.
Therefore, the total number of ways for eight students and five professors to stand next to each other such that no two professors are standing next to each other is 5! * 8P3 = 5,760 ways.
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Calculate the area and circumference of a circle with diameter 8cm explain by step by step
Answer:
Area = 50.24 cm^2
Circumference = 25.12 cm
Step-by-step explanation:
To calculate the area and circumference of a circle with a diameter of 8cm, you can follow these steps:
Recall that the diameter of a circle is the distance across the circle passing through its center. In this case, the diameter is given as 8cm.
Recall that the radius of a circle is half of its diameter. To find the radius, you can divide the diameter by 2:
radius = diameter/2
radius = 8cm/2
radius = 4cmTo calculate the area of a circle, use the formula:
area = πr^2
where π is the mathematical constant pi (approximately 3.14) and r is the radius.
Substituting the values we have:
area = 3.14 x (4cm)^2
area = 3.14 x 16cm^2
area = 50.24cm^2
Therefore, the area of the circle with diameter 8cm is 50.24 square centimeters.
To calculate the circumference of a circle, use the formula:
circumference = 2πr
where π is again the mathematical constant pi and r is the radius.
Substituting the values we have:
circumference = 2 x 3.14 x 4cm
circumference = 25.12cm
Therefore, the circumference of the circle with diameter 8cm is 25.12 centimeters.
Answer:
the area is about 50.26548
the circumference is about 25.13274
Step-by-step explanation:
Divide the diameter by 2 to get the radius (4)
Then use this equation to find the area A=\pi r^{2}
A=\pi 4^{2}
A=16\pi
A= about 50.26548
Then use this equation to find the circumference C=\pi d
C=8\pi
C= about 25.13274
There is a pair of parallel sides in the following shape.
What is the area of the shape?
The area of the shape is 28 square units.
The shape you described is a trapezoid, which is a 4-sided shape with two parallel bases that are different lengths. The area of a trapezoid is given by the formula: A=21(b1+b2)h.
In this case we are given that;
b1=6, b2=8, and h=4.
Plugging these values into the formula, we get:
A=21(6+8)4
A=21(14)4
A=7×4
A=28
Therefore, by the area the answer will be 28 square units.
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The stem-and-leaf plot displays the amount of time, in minutes, that 10 players spent practicing their serving skills for an upcoming tennis tournament.
Part A: Calculate the mean, median, mode, and range for the data given. Show your work.
Part B: Should the tennis players report the mean or median value to show they have practiced enough for the tournament? Explain based on the scenario.
The mean of the stem leaf plot is 29.09, median is 29 , range is 46 and mode is 41.
The data from stem leaf plot is 19, 22,26, 29,30,31,41,41,43,52,6
Mean = (19 + 22 + 26 + 29 + 30 + 31 + 41 + 41 + 43 + 52 + 6) / 11
Mean = 320 / 11
Mean = 29.09
To find median let us arrange the data in ascending order
6, 19, 22, 26, 29, 30, 31, 41, 41, 43, 52
So the median of the data is 29.
To find the mode of the data, we need to find the value that appears most frequently.
Mode is 41
To find the range of the data, we need to subtract the smallest value from the largest value:
So the range of the data is 46.
The tennis players should report the median value to show they have practiced enough for the tournament, as it is a more robust measure of central tendency for this dataset.
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If a basketball team has lost 50 matches out of the 120 matches played in total. Find out their winning percentage?
The winning percentage for this team is 58.33 percent.
How to find the winning percentage?The formula for this percentage is:
P = 100%*(number of games won)/total number of games.
The total number of games is 120, and of these the team lost 50, then the number of games won is:
120 - 50 = 70
Now we can replace these two values in the formula given above, then we will find that the winning percentage is:
P = 100%*(70/120)
P = 58.33%
That is the percentage we wanted.
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Please write y = 4x -2
in Ax + By = C form
Then identify x-intercept, y-intercept, and slope
Thanks!
[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]
[tex]\begin{aligned} y &= 4x-2 \\ -4x+y &= -2 \end{aligned}[/tex]
Then, [tex]Ax+By=C \implies -4x+y=-2[/tex].
So, [tex]A=-4, B=1, C=-2[/tex].
Now, identify the x-intercept (y = 0):
[tex]y=4x-2\\0=4x-2\\2=4x\\x=\dfrac{2}{4}\\x=\dfrac{1}{2}\\ \therefore \left( \dfrac{1}{2} , 0 \right)[/tex]
y-intercept (x = 0):
[tex]y=4x-2\\y=4(0)-2\\y=2\\\therefore (0,2)[/tex]
Slope:
We know that [tex]y=4x-2[/tex]. the the slope [tex]m=4[/tex] (x coefficient).
[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\boxed{\mathfrak{answered \: by: \: akbarsdtazm}}}}[/tex]
Your goal is to find a better procedure for microwaving a bag of popcorn to cook the best in terms of proportion of popped kernels) popped bag. You plan to design an experiment to determine which bran
Make sure to keep all other variables constant, such as the brand and size of the popcorn bag, the amount of oil and seasoning used, and the type of microwave used.
1. Select multiple brands of microwave popcorn to test in the experiment.
2. For each brand, follow the recommended cooking instructions found on the packaging. This will serve as the control group.
3. Next, for each brand, design alternative microwaving procedures, such as adjusting the cooking time, using different power settings, or including a pre-heating step.
4. Randomly assign these alternative procedures to different bags of each brand, ensuring that you have at least one bag per procedure per brand.
5. Microwave each bag following its assigned procedure.
6. After microwaving, carefully count the number of popped kernels and unpopped kernels in each bag.
7. Calculate the proportion of popped kernels for each bag by dividing the number of popped kernels by the total number of kernels (popped and unpopped).
8. Compare the results for each procedure within each brand and identify which procedure yields the highest variable proportion of popped kernels.
9. Further, compare the results across all brands to determine if any particular procedure is consistently effective for multiple brands.
By following this experimental design, you should be able to determine the most effective microwaving procedure for achieving the highest proportion of popped kernels in a bag of popcorn.
Complete Question:
Your goal is to find a better procedure for microwaving a bag of popcorn to cook the best in terms of proportion of popped kernels) popped bag. You plan to design an experiment to determine which brand to use, how long to cook each bag in the microwave and what power setting to use. Some reasonable ranges for the factors from past experience: Cooking time (3 and 5 minutes), Power levels on the microwave oven (settings 5 and 10) and Popcorn brand (Kroger or Orville) (1) What type of design of experiment you will suggest for this study. (ii) Do you suspect that the effect of any factor on the proportion of popped kernels may depend on the value of some other factor? If yes, how will you add such an effect in the model? (iii) You decide to include all possible two-factor interactions besides main effects. (a) Write down the statistical model and its assumptions. (b) What will be the minimum number of runs needed to perform the experiment based on the effects you have added to the model?
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a rectangular painting has a diagonal measure of inches and an area of square inches. use the formula for the area of a rectangle and the pythagorean theorem to find the length and width of the painting.
A rectangular painting has a diagonal measure of 20 inches and an area of 192 square inches. Using the formula for the area of a rectangle and the Pythagorean theorem the length and width of the painting are 8 inches and 24 inches respectively.
To solve this question, we will use the given information: the area of the rectangle (192 square inches) and the diagonal length (20 inches), along with the formula for the area of a rectangle and the Pythagorean theorem.
Step 1: Recall the formula for the area of a rectangle:
Area = length × width
We know that the area of the painting is 192 square inches. So, we have:
192 = length × width
Step 2: Recall the Pythagorean theorem for a right triangle:
a² + b² = c²
In this case, a and b represent the length and width of the rectangle, and c represents the diagonal. We know that the diagonal is 20 inches. So, we have:
length² + width² = 20²
length² + width² = 400
Step 3: Solve the system of equations:
192 = length × width
400 = length² + width²
We will solve the first equation for length:
length = 192 ÷ width
Step 4: Substitute the expression for length in the second equation:
(192 ÷ width)² + width² = 400
Step 5: Solve the equation for width:
width² - 400 = -(192 ÷ width)²
width⁴ - 400width² + 192² = 0
Step 6: Factor the equation and solve for width:
(width² - 64)(width² - 576) = 0
Two possible values for width are 8 and 24.
Step 7: Find the corresponding lengths:
If width = 8, then length = 192 ÷ 8 = 24
If width = 24, then length = 192 ÷ 24 = 8
So, the length and width of the painting are 8 inches and 24 inches.
The complete question is:-
A rectangular painting has a diagonal measure of 20 inches and an area of 192 square inches. use the formula for the area of a rectangle and the Pythagorean theorem to find the length and width of the painting.
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We want the margin of error to be 2% while we are 95% confident. What sample size is
needed?
The sample size needed for the margin of error to be 2% while we are 95% confident is 9604.
Margin of error = 2%
Confidence interval = 95%
The formula to calculate the margin of error is,
MOE = z σ/√n
Here z is the test statistic, σ is the population standard deviation and n is the sample size.
For a normal distribution,
z value for 95% confidence interval = 1.96
Population standard deviation = 1
Substituting,
0.02 = 1.96 / √n
√n = 1.96 / 0.02
n = (1.96/0.02)² = 9604
Hence the sample size is 9604.
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A transportation authority conducts a survey of users of a commuter railroad. A random sample of passengers is selected, and each passenger in the sample is given a questionnaire. There are two questions on the questionnaire. The first question asks whether the passenger paid for the journey at the ticket office. using a machine located on the platform, or online. The second question asks how happy the passenger is with the transportation service (very happy, happy, neutral, or unhappy). A hypothesis test will be conducted to determine whether there is a association between the method of payment and happiness with the service. The test will use a chi-square distribution with k degrees of freedom. What is the value of k?
The value of k, or the degrees of freedom for this hypothesis test, is 6.
The value of k in this scenario would depend on the number of categories or levels for each of the variables being tested. Since the first question has three possible answers (ticket office, platform machine, online), and the second question has four possible answers (very happy, happy, neutral, unhappy), the degrees of freedom would be (3-1) x (4-1) = 6. Therefore, the chi-square distribution used in the hypothesis test would have 6 degrees of freedom.
To find the value of k, we need to determine the degrees of freedom for this chi-square test. The formula for calculating degrees of freedom in a chi-square test is:
k = (number of rows - 1) x (number of columns - 1)
In this case, the number of rows corresponds to the method of payment (ticket office, machine on the platform, or online), which gives us 3 rows. The number of columns corresponds to the levels of happiness (very happy, happy, neutral, or unhappy), which gives us 4 columns.
Using the formula:
k = (3 - 1) x (4 - 1)
k = 2 x 3
k = 6
The value of k, or the degrees of freedom for this hypothesis test, is 6.
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Find the parallel line
Js need a simple answer
Answer:
the tenth letter of the alphabet.
Step-by-step explanation:
Js is just the plural version of J.
Answer:a simple answer
Step-by-step explanation:the question asks: "Js need a simple answer"
So what they need is "a simple answer"!
What is the component form of the vector that translates the top house figure to the bottom house figure?
(7, -2)
(6, -4)
(5, -1)
(-4, 5)
Answer:
Mark me the brainliest
Step-by-step explanation:
Okay, let's break this down step-by-step:
The top figure represents the original vector: (7, -2)
To translate it to the bottom figure: (6, -4)
We need to determine the component form of the translation.
The x-component is 7 - 6 = 1 (it decreased by 1)
The y-component is -2 - (-4) = -2 (it decreased by 2)
Therefore, the component form of the translation is: (1, -2)
So the translation vector that transforms the top figure (7, -2) into the bottom figure (6, -4) is (1, -2).
Does this make sense? Let me know if you have any other questions!
A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find the probability of drawing a yellow chip, not replacing it, and then choosing a blue chip.
A)13/49
B)7/10
C)42/625
D)13/50
The probability of first drawing a yellow chip without replacement and then drawing a blue is equal to 3/100.
Probability of an event without replacementThe probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.
total number of chips = 7 + 9 + 3 + 6
total number of chips = 25
yellow chips = 3
blue chips = 6
probability of drawing a yellow chip = 3/25
probability of drawing a blue without replacing the first yellow drawn = 6/24
probability of drawing a yellow without replacement and then a blue = 3/25 × 6/24
probability of drawing a yellow without replacement and then a blue = 3/100.
Therefore, the probability of first drawing a yellow chip without replacement and then drawing a blue is equal to 3/100.
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Factor the polynomial. 5s5 − 15s3 − 25s
Answer:
5s(s4−3s2−5)
Step-by-step explanation:
if x+y= Z/2
& x-y=zero so..
a) Z = 2xy
b) y = 2z-4y
c) 2x = 2z
d) 2x = z-2y
Answer:
D
Step-by-step explanation:
x + y = [tex]\frac{z}{2}[/tex]
multiply through by 2 to clear the fraction
2x + 2y = z ( subtract 2y from both sides )
2x = z - 2y
12. Lucy earned $400 and
$550 in interest the last 2
years. How much interest
must she earn this year so
that her average earnings
over the three year period
is more than $600?
Inequality:
Answer:
Answer:
Check Screenshot for answer and explanation
Step-by-step explanation:
In circle M, MN = 3 and the length of NO = 37. Find the area shaded below.
-
Express your answer as a fraction times 7.
M
0
N
The shaded area on the circle in this problem is given as follows:
A = 13/2π.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
[tex]C = 2\pi r[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it is given as follows:
r = MN = 3.
Thus the circumference of the circle is of:
C = 6π.
NO = 5π/3, hence the proportion of the shaded area is given as follows:
p = (6π - 5π/3)/6π
p = (13π/3)/6π
p = 13/18.
Thus the area of the shaded region is given as follows:
A = 13/18 x π x r²
A = 13/18 x π x 9
A = 13/2π.
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T/F : Span{a1,a2} contains only the line through a1 and the origin, and the line through the a2 and the origin.
False.
The span of {a1, a2} is the set of all linear combinations of a1 and a2. A linear combination of two vectors is of the form c1a1 + c2a2, where c1 and c2 are constants.
The span of {a1, a2} is the set of all linear combinations of a1 and a2. A linear combination of two vectors is of the form c1a1 + c2a2, where c1 and c2 are constants.
If a1 and a2 are linearly independent, then the span of {a1, a2} is the plane that contains a1 and a2. If a1 and a2 are linearly dependent, then the span of {a1, a2} is the line that contains a1 and a2.
So, in general, the span of {a1, a2} does not contain only the line through a1 and the origin, and the line through a2 and the origin. It can be a line, a plane, or all of R^3, depending on whether a1 and a2 are linearly dependent or independent.
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A student is graduating from college in 12 months but will need a loan in the amount of $9,529 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 5.95%, compounded monthly, and a payment grace period of six months from time of graduation
PLUS loan: annual interest rate of 6.55%, compounded monthly, with a balance of $10,172.23 at graduation
Which loan will have a lower balance, and by how much, at the time of repayment?
Answer:
To compare the balances of the two loans at the time of repayment, we need to calculate the future value of the loan amount for each loan option after 12 months of compounding.
For the Unsubsidized Stafford Loan:
Principal (P) = $9,529
Annual interest rate (r) = 5.95%
Compounding period (n) = 12 (monthly compounding)
Time period (t) = 1 year
Using the formula for future value of a loan (FV), we get:
The formula is:
FV = P * (1 + r/n)^(nt) = $9,529 * (1 + 0.0595/12)^(121) = $10,087.14
For the PLUS Loan:
Principal (P) = $10,172.23
Annual interest rate (r) = 6.55%
Compounding period (n) = 12 (monthly compounding)
Time period (t) = 1 year
Using the same formula, we get:
FV = P * (1 + r/n)^(nt) = $10,172.23 * (1 + 0.0655/12)^(121) = $10,774.71
Therefore, the Unsubsidized Stafford Loan will have a lower balance at the time of repayment, by $687.57 ($10,087.14 - $10,774.71).
Please help hard problem big reward of 12 points please help. If your can solve it please show me how you got the answer.Thanks
The measure of the intercepted arc is equal to 134 degrees
How to find the measure of arc BDThe measure of arc BD is calculated using the inscribed angle theorem, this theorem have that the measure of the inscribed angle is equal to half the measure of the intercepted arc.
This is represented mathematically as
inscribed angle = 1/2 x intercepted arc
Where
inscribed angle = 67
intercepted arc = ?
then we have that
inscribed angle = 1/2 x intercepted arc
67 = 1/2 x intercepted arc
intercepted arc = 2 x 67
intercepted arc = 134 degrees
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