Answer:
3ab
Step-by-step explanation:
area = length * width
width = area/length
width = (12ab^2)/(4b)
width = 3ab
If f(x)=2x−1, show that f(f(x))=4x−3. Find f(f(f(x))).
Answer: f(f(f(x)))=8x-7
Step-by-step explanation:
Since we were given f(x) and f(f(x)), We plug that into f(x) again to get f(f(f(x))).
2(4x-3)-1 [distribute]
8x-6-1 [combine like terms]
8x-7
Select the correct answer from each drop-down menu. The given equation has been solved in the table.
Answer:
1). SUBTRACTION property of equality
2). MULTIPLICATION property of equality
Step-by-step explanation:
Step 2:
When we subtract the same number from both the sides of an equation it represents the subtraction property of equality.
[tex]\frac{x}{4}+5-(5)=23-(5)[/tex]
Here 5 has been subtracted from both the sides.
Therefore, SUBTRACTION property of equality was applied.
Step 4:
If the same number is multiplied to both the sides of an equation, multiplication property of equality is applied.
[tex]4\times \frac{x}{4}=4\times (18)[/tex]
Here 4 has been multiplied to both the sides.
Therefore, MULTIPLICATION property of equality was applied.
Arrange the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity. Please see picture attached.
Answer:
see attached
Step-by-step explanation:
The limit as x gets large is the ratio of the highest-degree terms. In most cases, the limit can be found by evaluating that ratio. Where an absolute value is involved, the absolute value of the highest-degree term is used.
If the ratio gives x to a positive power, the limit does not exist. If the ratio gives x to a negative power, the limit is zero.
The arrangement of functions according to the given condition
[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]
[tex]h(x)=\frac{x^{3} -x^{2} +4}{1-3x^{2} }[/tex]
[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]
[tex]i(x)=\frac{x-1}{|1-4x| }[/tex]
[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]
[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]
[tex]f(x)=\frac{x^{2} -1000}{x-5}[/tex]
[tex]j(x)=\frac{x^{2}-1 }{|7x-1|}[/tex]
What is limit?A limit is the value that a function approaches as the input approaches some value.
According to the given question
[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]
⇒[tex]\lim_{nx\to \infty} \frac{5x^{2} -1}{x^{2} +1}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x^{2} }{x^{2} } \frac{5-\frac{1}{x^{2} } }{1+\frac{1}{x^{2} } }[/tex]
= 5 ([tex]\frac{1}{x^{2} } = 0[/tex] ,as x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0)
[tex]i(x)=\frac{x-1}{|1-4x|}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x-1}{|1-4x|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{1-\frac{1}{x} }{|\frac{-1}{4}+\frac{1}{x} | }[/tex] =[tex]\frac{1}{\frac{1}{4} }[/tex] =[tex]\frac{1}{4}[/tex]
As x tends to infinity 1/x tends to 0, and |[tex]\frac{-1}{4}[/tex]| gives 1/4
[tex]f(x)= \frac{x^{2} -1000}{x--5}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x^{2} -1000}{x-5}[/tex]= [tex]\lim_{x \to \infty} \frac{x^{2} }{x} \frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex]= [tex]\lim_{x \to \infty} x\frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex] ⇒ limit doesn't exist.
[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]
⇒[tex]\lim_{x\to \infty} \frac{4x^{2} -6}{1-4x^{2} }[/tex]=[tex]\lim_{x\to \infty} \frac{x^{2} }{x^{2} } \frac{4-\frac{6}{x^{2} } }{\frac{1}{x^{2} } -4}[/tex] [tex]= \lim_{n \to \infty} \frac{4}{-4}[/tex] = -1
As x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0.
[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]
⇒[tex]\lim_{x\to \infty} \frac{|4x-1|}{x-4}[/tex] = [tex]\lim_{x \to \infty} \frac{|x|}{x} \frac{4-\frac{1}{x} }{1 -\frac{4}{x} } }[/tex] = 4
as x tends to infinity 1/x tends to 0
and |x|=x ⇒[tex]\frac{|x|}{x}=1[/tex]
[tex]h(x)=\frac{x^{3}-x^{2} +4 }{1-3x^{3} }[/tex][tex]\lim_{x \to \infty} \frac{x^{3} -x^{2} +4}{1-3x^{3} }[/tex][tex]= \lim_{x \to \infty} \frac{x^{3} }{x^{3} } \frac{1-\frac{1}{x}+\frac{4}{x^{3} } }{\frac{1}{x^{3} -3} }[/tex] = [tex]\frac{1}{-3}[/tex] =[tex]-\frac{1}{3}[/tex]
[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]
[tex]\lim_{x \to \infty} \frac{5x+1000}{x^{2} }[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{5+\frac{1000}{x} }{x}[/tex] =0
As x tends to infinity 1/x tends to 0
[tex]j(x)= \frac{x^{2}-1 }{|7x-1|}[/tex]
[tex]\lim_{x \to \infty} \frac{x^{2}-1 }{|7x-1|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{|x|}\frac{x-\frac{1}{x} }{|7-\frac{1}{x}| }[/tex] = [tex]\lim_{x \to \infty} 7x[/tex] = limit doesn't exist.
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Find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (1 comma 0 ), (3 comma 2 ), and (1 comma 2 )about the y-axis. Use the washer method to set up the integral that gives the volume of the solid.
Answer: Volume = [tex]\frac{20\pi }{3}[/tex]
Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be
V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]
For this case, the region generated by the conditions proposed above is shown in the attachment.
Because it is revolting around the y-axis, the formula will be:
[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]
Since it is given points, first find the function for points (3,2) and (1,0):
m = [tex]\frac{2-0}{3-1}[/tex] = 1
[tex]y-y_{0} = m(x-x_{0})[/tex]
y - 0 = 1(x-1)
y = x - 1
As it is rotating around y:
x = y + 1
This is R(y).
r(y) = 1, the lower limit of the region.
The volume will be calculated as:
[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]
[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]
[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]
[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]
[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]
[tex]V=\frac{20\pi }{3}[/tex]
The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].
1. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Berwick sample is________.
a. 60
b. 75
c. 80
d. 90
2. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Milton sample is________.
a. 60
b. 75
c. 80
d. 90
3. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Leesburg sample is________.
a. 60
b. 75
c. 80
d. 90
4. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square test statistic for these samples is_______.
a. 1.49
b. 2.44
c. 4.15
d. 5.33
5. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The degrees of freedom for the chi-square critical value is_______.
a. 1
b. 2
c. 3
d. 4
6. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square critical value using alpha = 0.05 is_______.
a. 2.706
b. 3.841
c. 5.991
d. 7.815
7. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
Using alpha = 0.05, the conclusion for this chi-square test would be that because the test statistic is
A. More than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
B. Less than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
C. More than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
D. Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Answer:
1) Option B is correct.
Expected frequency of satisfied customers from the Berwick sample = 75
2) Option D is correct.
Expected frequency of satisfied customers from the Milton sample = 90
3) Option A is correct.
Expected frequency of satisfied customers from the Leesburg sample = 60
4) Option B is correct.
The chi-square test statistic for these samples = 2.44
5) Option B is correct.
The degrees of freedom for the chi-square critical value = 2
6) Option C is correct.
The chi-square critical value using alpha = 0.05 is 5.991
7) Option D is correct.
The conclusion for this chi-square test would be that because the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Step-by-step explanation:
Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Since this is a chi test that aims to check if there are differences in the proportion of expected number of customers for each location, we state the null and alternative hypothesis first.
The null hypothesis usually counters the claim we hope to test and would be that there is no difference between the proportion of expected frequency of satisfied customers at the three locations.
The alternative hypothesis confirms the claim we want to test and is that there is a significant difference between the proportion of expected frequency of satisfied customers at the three locations.
So, the total proportion of satisfied customers is used to calculate the expected number of satisfied customers for each of the three locations.
80+85+60= 225
Total number of customers = 100 + 120 + 80 = 300
Proportion of satisfied customers = (225/300) = 0.75
1) Expected frequency of satisfied customers from the Berwick sample = np = 100 × 0.75 = 75
2) Expected frequency of satisfied customers from the Milton sample = np = 120 × 0.75 = 90
3) Expected frequency of satisfied customers from the Leesburg sample = np = 80 × 0.75 = 60
4) Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Proportion for unsatisfied ccustomers = 0.25
So, expected number of unsatisfied customers for the three branches are 25, 30 and 20 respectively.
Chi square test statistic is a sum of the square of deviations from the each expected value divided by the expected value.
χ² = [(X₁ - ε₁)²/ε₁] + [(X₂ - ε₂)²/ε₂] + [(X₃ - ε₃)²/ε₃] + [(X₄ - ε₄)²/ε₄] + [(X₅ - ε₅)²/ε₅] + [(X₆ - ε₆)²/ε₆]
X₁ = 80, ε₁ = 75
X₂ = 85, ε₂ = 90
X₃ = 60, ε₃ = 60
X₄ = 20, ε₄ = 25
X₅ = 35, ε₅ = 30
X₆ = 20, ε₆ = 20
χ² = [(80 - 75)²/75] + [(85 - 90)²/90] + [(60 - 60)²/60] + [(20 - 25)²/25] + [(35 - 30)²/30] + [(20 - 20)²/20]
χ² = 0.3333 + 0.2778 + 0 + 1 + 0.8333 + 0 = 2.4444 = 2.44
5) The degree of freedom for a chi-square test is
(number of rows - 1) × (number of columns - 1)
= (2 - 1) × (3 - 1) = 1 × 2 = 2
6) Using the Chi-square critical value calculator for a degree of freedom of 2 and a significance level of 0.05, the chi-square critical value is 5.991.
7) Interpretation of results.
If the Chi-square test statistic is less than the critical value, we fail to reject the null hypothesis.
If the Chi-square test statistic is unusually large and is greater than the critical value, we reject the null hypothesis.
For this question,
Chi-square test statistic = 2.44
Critical value = 5.991
2.44 < 5.991
test statistic < critical value
The test statistic is Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Hope this Helps!!!
Phil Nelson deposited $35,000 at Wachovia Bank at 3.5% interest
compounded quarterly. How much money will be in this account at
the end of the year?
Answer:
$36,241.20
Step-by-step explanation:
Compounded Interest Rate Formula: A = P(1 + r/n)^nt
Since we are given P, r, n, and t, simply plug it into the formula:
A = 35000(1 + 0.035/4)⁴⁽¹⁾
A = 35000(1 + 0.00875)⁴
A = 35000(1.00875)⁴
A = 35000(1.03546)
A = 36241.2
A rookie quarterback is negotiating his first NFL contract.His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows:________.
1 2 3 4
Contract 1 $3,000,000 $3,000,000 $3,000,000 $3,000,000
Contract 2 $2,000,000 $3,000,000 $4,000,000 $5,000,000
Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,000
As his advisor, which contract would you recommend that he accept?
Answer:
He should accept contract 2 because it has a higher present value.
Step-by-step explanation:
we need to find the present value of each contract:
Contract 1 = $3,000,000/1.1 + $3,000,000/1.1² + $3,000,000/1.1³ + $3,000,000/1.1⁴ = $2,727,273 + $2,479,339 + $2,253,944 + $2,049,040 = $9,509,596
Contract 2 $2,000,000/1.1 + $3,000,000/1.1² $4,000,000/1.1³ + $5,000,000 /1.1⁴ = $1,818,182 + $2,479,339 + $3,005,259 + $3,415,067 = $10,717,847
Contract 3 $7,000,000/1.1 + $1,000,000/1.1² + $1,000,000/1.1³ + $1,000,000/1.1⁴ = $6,363,636 + $826,446 + $751,315 + $683,013 = $8,624,410
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 meters cubed A sphere with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? 10 meters cubed 20 meters cubed 30 meters cubed 40 meters cubed
Answer:
30 m^3
Step-by-step explanation:
Answer:
B. 20m3
Step-by-step explanation:
i dont know if its correct, hope it is tho
20. The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of units over the ten-year span, (number of units sold, profit) for specific recorded years: (46,250), (48, 305), (50,350), (52, 390), (54, 410) a) Use linear regression to determine a function y, where profit in thousands of dollars depends on the number of units sold in hundreds. b) Predict when the profit will exceed one million dollars.
Answer:
20
Step-by-step explanation:
The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015.
What is a linear function?
A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given pair of (number of units sold y, profit x)
Linear equation slope and y-intercept
A linear equation or function is given as ;
y = mx + c
Here, c is the y-intercept and m is the slope.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope m = (y₂ - y₁)/(x₂ - x₁)
Therefore slope of (46,250), (48, 305)
m = (305 - 250)/(48 - 46) = 27.5
Put, m = 27.5 and (46,250)
250 = 27.5(46) + c
c = -1015
y = 27.5x - 1015
Hence "The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015".
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g A catering service offers 7 %E2%80%8b Appetizers, 9 main%E2%80%8B courses, and 5 desserts. A banquet committee is to select 2 %E2%80%8b Appetizers, 8 main%E2%80%8B courses, and 4 desserts. How many ways can this be%E2%80%8B done
Answer:
945 ways
Step-by-step explanation:
Total
Number of Appetizers = 7Number of main courses = 9Number of desserts =5Required Selection
Number of Appetizers = 2Number of main courses = 8Number of desserts =42 Appetizers out of 7 can be selected in [tex]^7C_2[/tex] ways
8 main courses out of 9 can be selected in [tex]^9C_8[/tex] ways
4 desserts out of 5 can be selected in [tex]^5C_4[/tex] ways
Therefore, the number of ways this can be done
[tex]=^7C_2 \times ^9C_8 \times ^5C_4[/tex]
=945 ways
The price of a vase was increased by 10% to £22.What was the price before the increase
Answer: £20.
Step-by-step explanation:
Let the old price = £x
Percent increase. = 10%
Increment. = 10% of £x
= 10x/100
Now new price = £22
To determine the old price we have
x + 10x/100. = 22
We now multiply everything by 100 to make it a linear expression
100x + 10x = 2200
110x = 2200, therefore
x. = 2200/110
= £20
Therefore, the price before the increase. = £20.
A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl
Answer: 7/8
Step-by-step explanation:
Let the boy is letter B and the girl is letter G.
So the possible outcomes are as follows below
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG
SO the number of possible outcomes is 8
The number of outcomes where is at least 1 girl ( triples where is 1 girl, 2 girls or all 3 children are the girls) is 7
So the probability, that family with 3 kids has at least 1 girl is
P(number of girls >=1)= 7/8
Find the value of c such that the three points (5,5), (-3,1), and (6,c) lie on the same line. Note: Three points are on the same line if the slope of the line through any two points is always the same.
Answer:
c = 5.5
Step-by-step explanation:
We can find the slope of the line using the given points (5,5) and (-3,1) using rise over run:
-4/-8 = 1/2
Now, we can plug in the slope and a point into the equation y = mx + b to find b:
5 = 1/2(5) + b
5 = 2.5 + b
2.5 = b
Then, we can plug in 6 in the point (6,c) to find c:
y = (1/2)(6) + 2.5
y = 3 + 2.5
y = 5.5
c = 5.5
Answer:
c = 5.5
Step-by-step explanation:
Find the slope with two points
m = (y2-y1)/(x2-x1)
m = (1-5)/(-3-5)
= -4/-8
= 1/2
If all the points are on the same line, then they have the same slope
m = (y2-y1)/(x2-x1)
Using the first and third points
1/2 = (c-5)/(6-5)
1/2 = (c-5)/1
1/2 = c-5
Add 5 to each side
5+1/2 = c
5.5 =c
I don't know what to do.
Answer:
104.93 in
Step-by-step explanation:
When we draw out a picture of our triangle, we should see that we need to use sin∅ to solve:
sin23° = 41/x
xsin23° = 41
x = 41/sin23°
x = 104.931
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 3 0 -4 2 0 6 -3 0 8
a. The matrix is invertible. The columns of the given matrix span R^3.
b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
c. The matrix is invertible. The given matrix has 2 pivot positions.
d. The matrix is not invertible. If the given matrix is A, the equation Ax = 0 has only the trivial solution.
Answer:
b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
Step-by-step explanation:
A square matrix is said to be invertible if the product of the matrix and its inverse result into an identity matrix.
3 0 -4
2 0 6
-3 0 8
Since the second column elements are all zero, the determinant of the matrix is zero ad this implies that the inverse of the matrix does not exist(i.e it is not invertible )
A square matrix is said to be invertible if it has an inverse.
The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
The matrix is given as:
[tex]\left[\begin{array}{ccc}3&0&-4\\2&0&6\\-3&0&8\end{array}\right][/tex]
Calculate the determinant
The determinant of the matrix calculate as:
[tex]|A| = 3 \times(0 \times 8- 6 \times 0) - 0(2 \times 8 - 6 \times -3) -4(2 \times 0 - 0 \times -3)[/tex]
[tex]|A| = 3 \times(0) - 0(34) -4(0)[/tex]
[tex]|A| = 0 - 0 -0[/tex]
[tex]|A| = 0[/tex]
When a matrix has its determinant to be 0, then
It is not invertibleIt does not form a linear independent set.Hence, the correct option is (b)
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In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two exam scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third exam that will give an A? What about a B?
Answer:
a) The student cannot receive an A in the class.
b) The student must score 119 in the third exams to make an A. This is clearly not possible, since he cannot make 119 in a 100-points exam.
c) The student can make a B but he must score at least 84 in the third exam.
Step-by-step explanation:
To make an A, the student must score 315 (350 x 90%) in both home and the three exams.
The student who scored 35 (7 + 8 + 7 + 5 + 8) in the homework and 161 (81 + 80), getting a total of 196, is short by 119 (315 - 196) scores in making an A.
To make a B, the student must score 280 (350 x 80%) or higher but not reaching 315.
B ≥ 280 and < 315.
Since, the student had scored 196, he needs to score 84 and above to make a B in the last exam.
Find the lateral area of a regular square pyramid if the base edges are of length 12 and the perpendicular height is 8.
Answer:
Lateral area of the pyramid = 120 square units
Step-by-step explanation:
In the figure attached,
A pyramid has been given with square base with edges of 12 units and perpendicular height as 8 units.
Lateral area of a pyramid = Area of the lateral sides
Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]
= [tex]\frac{1}{2}(\frac{b}{2})(\sqrt{(\frac{b}{2})^2+h^2})[/tex] [Since l = [tex]\sqrt{r^{2}+h^{2}}[/tex]]
= [tex]\frac{1}{2}(6)(\sqrt{6^2+8^2})[/tex]
= [tex]3\sqrt{100}[/tex]
= 30 units²
Now lateral area of the pyramid = 4 × 30 = 120 square units
Answer: 240 units^2
Step-by-step explanation:
LA= 1/2 Pl
P= perimeter of base
l= lateral height
l= 8^2 + (12/2)^2 = 10^2
P= 12 x 4 = 48
48 x 10 = 480
480/2 = 240
240 units^2
plz answer question in screen shot
Answer: 342.32
Step-by-step explanation: sin(25) = h/a
Sin(25)= h/27
27*sin(25) = h
b*h = area
www.g A survey of athletes at a high school is conducted, and the following facts are discovered: 19% of the athletes are football players, 79% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player
Answer:
84%
Step-by-step explanation:
The probability that the selected player is a football player, P(F)=19%
The probability that the selected player is a basketball player, P(B)=79%
The probability that the selected player play both football and basketball,
[tex]P(B \cap F)=14\%[/tex]
We want to determine the probability that a randomly chosen athlete is either a football player or a basketball player, [tex]P(B \cup F)[/tex]
In probability theory
[tex]P(B \cup F)=P(B)+P(F)-P(B \cap F)\\=79\%+19\%-14\%\\=84\%[/tex]
The probability that a randomly chosen athlete is either a football player or a basketball player is 84%.
In a survery of 154 households, a Food Marketing Institute found that 106 households spend more than $125 a week on groceries. Please find the 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries.
Answer:
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 154, \pi = \frac{106}{154} = 0.6883[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 - 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.6151[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 + 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.7615[/tex]
The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).
Using Volume Formulas: Tutorial
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Question 2
Suppose that you want to design a set of four congruent square pyramids whose combined volume is the same as the volume of a single
rectangular pyramid. What values of land h for the four square pyramids and what values of I, w, and h for the rectangular pyramid will produce
identical volumes? There is more than one correct answer.
B
TUX
X
Font Sizes
A. A
E JE
Square Pyramids
Rectangular Pyramid
Volume
Base Length Height
Volume
Volume x4 Base Length Base Width Height
(2x)
3
(lxwh
3
I
Characters used: 110 / 15000
Submit
Answer:
For the Square
Base length is 6 units
Height is 4 units
Volume is 48 cubic units
Volume of 4 square pyramids is 192 cubic units
(Rectangular)
Base length is 12 units
Base width is 8 units
Height is 6 units
Volume is 192 cubic units
Step-by-step explanation:
Square pyramids is a geometric shape having square base. The appex is perpendicularly at the center of the square. If all the edges are equal it is equilateral square pyramid.
Rectangular pyramids have four sided base and four triangle sides that are coming together to the appex. Each base and appex form a triange called lateral face. The triangular faces are non rectangular base. Pyramid with n side have n + 1 vertices and 2n edges.
3. A tunnel is 300 feet deep and makes an angle of 30° with the ground, as shown below.
30°
300 feet
Tunne
How long is the tunnel?
Answer:
173.20 ft
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]
Want Brainliest? Get this correct Which of the following is the product of the rational expressions shown below?
We multiply the numerators together to get x*2x = 2x^2 as the numerator for the answer.
The denominators pair up and multiply to get (x-5)(x+4) = x^2+4x-5x-20 = x^2-x-20. You can use the distributive property, FOIL, or the box method to expand out (x-5)(x+4)
So that's how we end up with (2x^2) all over (x^2-x-20) as the answer.
What is y - 8 = 4(x - 4) in slope intercept form?
Answer:
y=4x-8
Step-by-step explanation:
First you must use the distributive property and get y-8=4x-16.
Then you have to add 8 on both sides so just y is left on the left side.
This will get you y=4x-8 in slope-intercept form.
Find the value of x geometry
Answer:
x = 22
Step-by-step explanation:
Since the the 2 bisectors are equal, that means the chords are also equal. Since bisector splits into 2 equal parts, 11 + 11 equals 22
forex is the name of the U.S. stock exchange.
-true
-false
Answer:
false
Step-by-step explanation:
hello
this is false
FOREX means Foreign Exchange
it refers to the foreign exchange market
hope this helps
Answer:
true, forex trading is a profitable than staking cryptocurrency. forex trading is the best thing I will refer someone I love because learning never stops and no on is above blowing accounts when beginning Forex
To get from North to East, you walk 12 meters south and 16 meters east, as shown
in the diagram below. If you wanted to walk straight from North to East, what would
the distance be? Solve for x
Answer:
ur pito is to small
Step-by-step explanation:
it to little
What is the area of this composite shape? Enter your answer in the box. in²
Answer:
53 in.
Step-by-step explanation:
to find the area u do 8 times 6 and 1/2 2(5)
triangle = 1/2bh
rectangle = bh
hope this helps
A biologist samples and measures the length of the fish in a lake. What is the level of measurement of the data?
Answer:Ratio
Step-by-step explanation:
The ratio data because length has a true zero, and ratios of lengths are meaningful.
Please help ASAP thanks in advance
Answer:
Make a point at (3pm, 45), (4.5 pm, 45), (5.5pm, 30), (6.5pm, 15), and (7.5pm, 0). Then connect the dots starting at (0,0) Then you have your graph :)
Step-by-step explanation: