Answer:
Step-by-step explanation:
Which statement best compares and contrasts the two formats?
The infographic shows the movement of water visually, while the text describes it.
The infographic would be less appealing to visual learners than the text.
It is impossible to understand the infographic without the text.
The text is more accurate than the infographic.
1) What is the total amount in the account if the interest rate is 4.5% each year?
2) After 6 years $275 is added to the account. What does R(x) equal after 6 years ? What is the new expression for A(x) ?
The simple interest has an expression and the total amount after an year at an interest rate of 4.5% is approximately $2478.33. The value of R(x) after 6 years is 275 and the new expression for A(x) is 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x + 275
What is the total amount in the account if the rate is 4.5%1. To find the total amount in the account after 5 years with an interest rate of 4.5%, we can simply plug in x = 1.045 (1 + 0.045) into the expression for A(x):
A(1.045) = 525(1.045)^5 + 450(1.045)^4 + 375(1.045)^3 + 500(1.045)^2 + 300(1.045)
≈ 2478.33
So the total amount in the account after 5 years with an interest rate of 4.5% is approximately $2478.33
2. After 6 years, the expression for A(x) would become:
A(x) + 275
We can find the new expression for R(x) by subtracting the original expression for A(x) from the new expression:
R(x) = A(x) + 275 - A(x)
= 275
So the new expression for R(x) after 6 years is simply R(x) = 275.
3. The original expression for A(x) was:
A(x) = 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x
To find the new expression for A(x) after 6 years, we can simply plug in x = 1.045 (1 + 0.045) and add 275:
A(1.045) + 275 = 525(1.045)^5 + 450(1.045)^4 + 375(1.045)^3 + 500(1.045)^2 + 300(1.045) + 275
≈ 2923.97
So the new expression for A(x) after 6 years is:
A(x) = 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x + 275
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Compare the dimensions of the prisms. How many times greater is the surface area of the red prism than the surface area of the blue prism?
4 m
3m
2m
12 m
The dimensions of the red prism are
The surface area of the red prism is
9 m
6 m
times the dimensions of the blue prism.
times the surface area of the blue prism.
Answer:
3, 9
Step-by-step explanation:
Surface A = 2(wl + hl + hw)
Where in the red prism, l is 12, w is 6, h is 9 and in the red prism l is 4, w is 2, h is 3
Lenght 12/4 =3
Width 6/2 =3
Height 9/3 =3
Calculate surface are of red prism
SA = 2( 6x12 + 9x12 + 9x6)
SA = 2( 72 +108+54)
SA = 2(234) = 468 m²
Calculate surface area of blue prism
SA = 2(2x4 + 3x4 + 3x2)
SA = 2(8 +12+6)
SA = 2(26)
SA =52
Area of red /area of blue = 468/52
Ans =9
Finding values of an Inverse Using a Table values. =.31.f−1(5) 34. f(f−1(6)) ax. f−1(f(1)) 36. f−1(f−1(0)) 37−48= Inverse Function Property we une inverse Funge . Property to show that f and g are inverses of each other. 37. f(x)=x−6:g(x)=x+6 38. f(x)=3x,g(x)=3x e.39. f(x)=3x+4;g(x)=3x−4 40. f(x)=2−5x;g(x)=52−x 41. f(x)=x1;g(x)=x1 42. f(x)=x5;g(x)=5x
43. f(x)=x2−9,x≥0;g(x)=x+9
,x≥−9 44. f(x)=x3+1;g(x)=(x−1)1/3 45. f(x)=x−11;g(x)=x1+1
31.f(f-1(6)) = 6
34.f-1(f(1)) = 1
36.f-1(f-1(0)) = 0
37.f(g(x)) = f(x + 6) = x + 6 - 6 = x g(f(x)) = g(x - 6) = x - 6 + 6 = x
39.f(g(x)) = f(3x) = 3(3x) = x g(f(x)) = g(3x) = 3(3x) = x
40.f(g(x)) = f(3x - 4) = 3(3x - 4) + 4 = x g(f(x)) = g(3x + 4) = 3(3x + 4) - 4 = x
41. f(g(x)) = f(5/2 - x) = 2 - 5(5/2 - x) = x g(f(x)) = g(2 - 5x) = 5/2 - (2 - 5x) = x
42. f(g(x)) = f(x2) = (x2)1/2 = x g(f(x)) = g(x1/2) = (x1/2)2 = x
43.f(g(x)) = f(x + 9) = (x + 9)2 - 9 = x g(f(x)) = g(x2 - 9) = x2 - 9 + 9 = x
44.f(g(x)) = f((x - 1)1/3) = (x - 1)1/33 + 1 = x g(f(x)) = g(x3 + 1) = (x3 + 1 - 1)1/3 = x
45.f(g(x)) = f(x1/2 + 1) = x1/2 + 1 - 11 = x g(f(x)) = g(x - 11) = (x - 11)1/2 + 1 = x
To answer your questions, here is the following information:
1. Finding values of an Inverse Using a Table values: f-1(5) = 0.31
f(f-1(6)) = 6
f-1(f(1)) = 1
f-1(f-1(0)) = 0
2. Inverse Function Property: To show that f and g are inverses of each other, you must use the Inverse Function Property which states that if f and g are two inverse functions, then f(g(x)) = x and g(f(x)) = x.
3. Examples:
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PLEASE HELP ME ASAP PLEASEEE
Answer:
Step-by-step explanation:
B and E
Henry has 3 bunches of flowers. If there are 5 flowers in each bunch, which of the following shows how to find the total number of flowers he has?
A) 3 divided by 5
B) 3 times 5
C) 3 plus 5
Which describes a possible independent variable for the given dependent variable?
The amount of money you earn
1. Who you call most often each day
2. The number of miles you run each day
3. The number of hours you work
4. The color of your new car
Answer:
3. The number of hours you work.
Step-by-step explanation:
Independent variable means that the occurrence of the event is not dependent on another event occurring.
In this case, the independent variable is the amount of hours you work, as you can, assumingly for the question, can work any amount you would like. However, the pay would be on the basis of how much work you do, and is dependent on the amount of hours you do (assuming you are on hourly).
~
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Alex’s printer can print 8 photos in 12 minutes. Khalid printer can print 24 photos in 1 hour. which process could you use to help determine how much longer will it take khalils printer to print 120 photos than Alex’s. select all that apply.
A. write an equation that adds the number of photos that each print prints in 1 hour
B. make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference
C. Subtract the number of photos that khalil printer prints in two hours from the number of photos that alex’s printer print in 2 hours.
D. graph a table of values for each printer and compare the number of minutes when the number of photos is 120.
Answer:
B. Make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference would be an appropriate process to determine how much longer it will take Khalil's printer to print 120 photos than Alex's.
Step-by-step explanation:
To use this process, we can set up a table showing the ratio of photos printed to time taken for each printer. Then we can use these ratios to find how long it would take each printer to print 120 photos, and find the difference between the two times to determine how much longer it would take Khalil's printer.
For the expression
15x² + 25x² + 5x+2/
(5x +1)
which sum represents the correct form of the partial fraction decomposition?
Answer:
15×2
Step-by-step explanation:
5×+2/(5× +1) =15×2^
Which expression is equivalent to the expression 10a - 14c
The expression 10a - 14c is factorized and then found to be equivalent to 2(5a - 7c)
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
Given the equation:
10a - 14c
We are to solve the equation by factorizing the expression. To factorize the expression, we need to find the term that is common to both 10a and -14c. The common term is 2, hence:
10a - 14c
2(5a - 7c)
The expression 10a - 14c is equivalent to 2(5a - 7c)
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what would the answer to y = 11.7x + 96.7 be?
The answer to given linear equation will be When y = 200, x = 8.82.
The values of x and y utilised will determine the solution to the equation y = 11.7x + 96.7.
You can solve for y by substituting a particular value of x into the equation. For instance, if x equals 2, then:
y = 11.7(2) + 96.7
y = 23.4 + 96.7
y = 120.1
Hence, at x = 2, y = 120.1.
Nevertheless, you might choose a different value of y and solve for x by substituting it into the equation. For instance, if y equals 200, then
200 = 11.7x + 96.7
103.3 = 11.7x
x = 8.82
Hence, x equals 8.82 when y is 200.
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Given the following profit payoff table: s1�1 s2�2 s3�3 d1�1 130 100 330 d2�2 230 -50 310 d3�3 70 -100 370 Construct an opportunity loss (regret) table by completing the following table. s1�1 s2�2 s3�3 d1�1 d2�2 d3�3 Given the probabilities of the states of nature are P(s1)�(�1) = 0.2, P(s2)�(�2) = 0.3, and P(s3)�(�3) = 0.5, calculate the minimum expected opportunity loss. Minimum EOL��� = What is the best alternative based on expected opportunity loss? d1�1 d2�2 d3�3 s1�1 s2�2 s3�3 What is the EVPI����?
Minimum EOL = 72Best alternative based on expected opportunity loss = d3EVPI = 520
Answer:To solve this problem, we will have to first calculate the regret for each option. We will do that by finding the maximum payoff for each column and subtracting the current payoff from that. That gives us the opportunity loss. We will then multiply the opportunity loss with the probabilities of the events to calculate the expected opportunity loss. We will find the minimum expected opportunity loss by selecting the minimum value in each row. We will then add the minimum expected opportunity loss to the minimum payoff for each option to calculate the maximum regret. Finally, we will calculate the EVPI by subtracting the maximum regret from the maximum payoff. Here are the tables that we need to construct: Regret table: Minimum expected opportunity loss table: Minimum EOL = 72Best alternative based on expected opportunity loss = d3EVPI = 520
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An employer provides two payment options for employees.
Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.
Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.
(Score for Question 1: ___ of 2 points)
1. Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.
Option A:
Week
1
2
3
4
5
6
Amount Paid
Option B:
Week
1
2
3
4
5
6
Amount Paid
Answer:
(Score for Question 2: ___ of 8 points)
2. Suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.
(a) Determine the iterative rule for each sequence. Show your work.
(b) Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show two calculations to convince your friend that both your rules work.
Answer:
(Score for Question 3: ___ of 5 points)
3. Consider the iterative rules you wrote in Problem 2.
(c) Explain why the rules are functions.
(d) Your friend says that because the rules are functions, they can be graphed and must have y-intercepts. How would you respond to your friend’s comment?
(e) Your friend uses your rules to determine the outputs when the inputs are 18.5. Explain why her outputs are meaningless in this situation. What would you tell her about the inputs she can use?
Answer:
(Score for Question 4: ___ of 5 points)
4. The longest amount of time employees can work under Option A or Option B is 20 weeks. After employees work 20 weeks, they can either quit or keep making the same amount they made during Week 20. If an employee plans on quitting after 20 weeks, which payment option gives the greatest total income? Explain.
Answer: A
Week Amount Paid
1 $200
2 $250
3 $300
4 $350
5 $400
6 $450
Option B:
Week Amount Paid
1 $200
2 $220
3 $242
4 $266.20
5 $292.82
6 $322.10
Your welcome stranger. (:
(6e−3f−4)⋅2=left parenthesis, 6, e, minus, 3, f, minus, 4, right parenthesis, dot, 2, equals
The final result of the expression (6e−3f−4)⋅2 is e3f−8.
The calculation is as follows: (6e−3f−4)⋅2 = (6e-3f-4)*2. In order to calculate this expression, it is necessary to use the Order of Operations. The Order of Operations is a set of rules that determine the order in which operations should be performed when evaluating an expression. First, any parentheses need to be evaluated. In this expression, there are parentheses surrounding 6e−3f−4. This means that any operations within the parentheses should be done first. Inside the parentheses, there is an exponent, e−3f, and a subtraction, 4. Exponents should be done first, so e−3f should be evaluated first. This is equivalent to e multiplied by e multiplied by e, multiplied by f, which is equal to e3f. Then, 4 should be subtracted from e3f, which is equal to e3f−4. After the parentheses have been evaluated, the remaining multiplication should be done. This is equivalent to (e3f−4)*2, which is equal to e3f−8.
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Question 6 of 10 Which of the following is the correct factorization of the polynomial below? p³-125q³ A. (p-5q) (p² + 5pq+25q²) B. (p-25q) (p2 + 25pq+25q²) C. (p² +10g)(p³ +25pq+5q²) D. The polynomial is irreducible.
Answer:
the answer is A
Step-by-step explanation:
p³-125q³
(p-5q)³
but if expand A
it will give the same p³-125q³
(p-5q)(p²+5pq+25q²)
expanding will give
p3+5p²q+25pq²-5p²q-25pq²-125q³
C.L.T
p³+5p²q-5p²q+25pq²-25pq²-125q³
p³-125q³
What value of x makes 23x+5=11 true?
A. 4
B. 513
C. 9
D. 1023
E. 24
6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true. The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.
We must find x in order to determine what value of x results in the equation 23x + 5 = 11 being true.
Initially, we must remove 5 from both sides of the equation to isolate the variable x:
23x + 5 - 5 = 11 - 5
When we combine the left and right sides, we obtain:
23x = 6
Then, by multiplying both sides of the equation by 23, we must find x:
23x/23 = 6/23
When we combine the left and right sides, we obtain:
x = 6/23
As a result, 6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true.
The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.
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Find the surface area of a cylinder with a base diameter of 8 feet and a height of 8 feet right your answer in terms of pi and be sure to include the correct unit
Answer:
96π cubic feet
Step-by-step explanation:
Surface area of a cylinder
A = 2πr(h+r)
where r = radius, h = height
Here
r = diameter/w = 8/2 = 4 feet
h = 8 feet
A = 2π · 4 (8 + 4)
= 8π (12)
= 96π cubic feet
which way does shift
g(x)=lx+9l-5
Answer:
g(x) was shifted 9 units to the left and 5 units down
Step-by-step explanation:
Horizontal shifts take place when the x value is changed within the parentheses, or in this case, absolute value.
The graph is shifted 9 units left because of the + 9.
Vertical shifts happen when the entire equation is added or subtracted to.
The graph is shifted 5 units down because of the - 5.
See the graph for a visualization.
Find the area of the rhombus
If the length of one side of the rhombus is 6m and the radius of the rhombus as 4 m then the area of the rhombus is 24 m².
What is the area of the rhombus?
The Area of a Rhombus = A = ½ × d1 × d2,
Where d1 and d2 are the diagonals of the rhombus.
The area of a rhombus can be found using the formula:
Area = (diagonal 1 x diagonal 2) / 2
or
Area = (base x height) / 2
We are given the length of one side of the rhombus as 6 m, which means the length of the other side is also 6 m since all sides of a rhombus are congruent. We are also given the radius of the rhombus as 4 m, which is half the length of the diagonal.
Using the Pythagorean theorem, we can find the length of the other diagonal:
diagonal 2 = 2(radius) = 2(4) = 8 m
Now we can use the formula to find the area of the rhombus:
Area = (diagonal 1 x diagonal 2) / 2
Area = (6 m x 8 m) / 2
Area = 24 m²
Therefore, the area of the rhombus is 24 m².
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How long is this triangles hypotenuse?
Answer:
17.
Step-by-step explanation:
[tex]a^2+b^2 = c^2[/tex] is the formula used to find the hypotenuse (also known as the Pythagora's Theorem).
Substitute the given values into the equation.
[tex]8^2+15^2=c^2[/tex]
64 + 225 = [tex]c^2[/tex]
289 = [tex]c^2[/tex]
[tex]\sqrt{289}[/tex] = c
c = 17
Mary works for a company that pays time and a half for hours over 40 in a week and double time for holidays. This week she worked 8 hours on Monday (which was a holiday), 10 hours on Tuesday, 10 hours on Wednesday, 9 hours on Thursday, and 8 hours on Friday. If Mary earns $8 per hour, what is the total of Mary’s earnings for the week?
Total Earnings = (8 x 1.5 x 8) + (10 x 2) + (10 x 1) + (9 x 1) + (8 x 1) = $136. Once we have all the calculations, we can add them together to find Mary’s total earnings amount for the week. In this case, Mary’s total earnings is $136.
To calculate Mary’s total earnings for the week, we need to take into account the time and a half for hours over 40 and the double time for holidays. First, we multiply the 8 hours worked on Monday (a holiday) by 1.5 to calculate the time and a half earnings for that day. Then we multiply the 10 hours worked on Tuesday and Wednesday by 1 to calculate the regular earnings for those days. We multiply the 9 hours worked on Thursday by 1 to calculate regular earnings for that day. Finally, we multiply the 8 hours worked on Friday by 1 to calculate regular earnings for that day. Once we have all the calculations, we can add them together to find Mary’s total earnings for the week. In this case, Mary’s total earnings is $136 amount.
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Write (10 + √2)÷(14+ √2) in the form a+b√2/c
where a, b and c are all integers.
Answer:
[tex]\frac{69+2\sqrt{2}}{97}[/tex]
Step-by-step explanation:
(10 + √2)÷(14+ √2)= [tex]\frac{10+\sqrt{2} }{14+\sqrt{2} }[/tex]
= [tex]\frac{(10+\sqrt{2}) x (14-\sqrt{2})}{(14+\sqrt{2}) x (14-\sqrt{2}) }[/tex]
= [tex]\frac{(10+\sqrt{2}) x (14-\sqrt{2})}{14^{2}-(\sqrt{2}^{2})}[/tex]
= [tex]\frac{{(10+\sqrt{2}) x (14-\sqrt{2})}}{196-2}[/tex]
= [tex]\frac{140-10\sqrt{2}+14\sqrt{2}-2}{194}[/tex]
= [tex]\frac{138+4\sqrt{2}}{194}[/tex]
= [tex]\frac{2 x (69+2\sqrt{2})}{194}[/tex]
= [tex]\frac{69+2\sqrt{2}}{97}[/tex]
∴ the answer is [tex]\frac{69+2\sqrt{2}}{97}[/tex] in the form [tex]\frac{a+b\sqrt{2}}{c}[/tex]
(10 + √2)÷(14+ √2) can be written in the form (69 + 3√2) ÷ 97, where a = 69, b = 3, and c = 97, and all are integers.
What are integers?A number that includes zero, positive numbers, and negative numbers, is an integer. Integer's can never be a fraction, a decimal, or a percent, it should be noted.
To write (10 + √2)÷(14+ √2) in the form a+b√2/c, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is 14 - √2.
[(10 + √2) ÷ (14 + √2)] x [(14 - √2) ÷ (14 - √2)]
= [(10 + √2) x (14 - √2)] ÷ [(14 + √2) x (14 - √2)]
= [140 + 8√2 - 2√2 - 2] ÷ [196 - 2]
= (138 + 6√2) ÷ 194
= (69 + 3√2) ÷ 97
Therefore, (10 + √2)÷(14+ √2) can be written in the form (69 + 3√2) ÷ 97, where a = 69, b = 3, and c = 97, and all are integers.
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could use some help, think this might be right(new to precalculus
Find dxdy . y= cosx1+ tanx7dxdy =
Answer:
y= 1/cosx+7/tanx
dy/dx = 1secxtanx-cosec^2x
In a school, 220 students offer Biology or Mathematics or both. 125 offer biology and 110 Mathematics. How many offer Biology but not Mathematics?
The number of students are 110 students offer Biology but not Mathematics.
Let's use a Venn diagram to solve this problem. We know that 125 students offer Biology and 110 offer Mathematics, and we want to find out how many offer Biology but not Mathematics.
First, we can fill in the number of students who offer both Biology and Mathematics, which is the overlap between the two circles. We can do this by subtracting the total number of students who offer both from the total number of students who offer either:
220 (total) - (125 + 110) = 220 - 235 = -15
Wait a minute! A negative number of students doesn't make sense in this context. What this tells us is that there must be some double-counting going on - in other words, some students are being counted twice, once in each of the Biology and Mathematics categories.
To correct for this, we need to add back in the number of students who are counted twice, which is the overlap between the two circles. We can calculate this by adding the number of students who offer Biology and Mathematics together:
125 + 110 = 235
Now we can redo the calculation:
220 (total) - 235 (double-counted) = -15
This tells us that there are 15 students who are being counted twice. To find the number of students who offer Biology but not Mathematics, we need to subtract this number from the number of students who offer Biology:
125 - 15 = 110
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Answer: if im correct i think its 95
Jill bakes an apple pie in a pie
pan that is 10" in diameter. What is
the circumference of Jill's pie?
2
Answer: the circumference of Jill's pie is 31.4 inches.
Step-by-step explanation:
The circumference (C) of a circle is given by the formula C = πd, where d is the diameter of the circle and π (pi) is a constant approximately equal to 3.14.
In this case, the diameter of Jill's pie is 10", so we can use the formula to find the circumference:
C = πd
C = 3.14 x 10
C = 31.4 inches
Therefore, the circumference of Jill's pie is 31.4 inches.
Answer:
10pi or 31.42
Step-by-step explanation:
the formula for circumference of a circle is 2pir (yes, i can't find the symbol for pi... sorry...) (and r = the radius)
since the diameter is 2*r, the radius is 5 inches.
2*5*pi = 10pi, which is about 31.42
Use a property to write an equivalent expression 12 times (100-5).which property did you use?
Answer: distributive property
Step-by-step explanation:1 2 times 95 can indeed be rewritten as 12(100-5) and we can use the distributive property IN OUR HEADS, so we get 1200 - 60 = 1140.
A group consists of men and women. people are selected to attend a conference.
a. In how many ways can people be selected from this group of ?
b. In how many ways can women be selected from the women?
c. Find the probability that the selected group will consist of all women.
a) The number of ways to choose three people from a set of eleven is given as follows: 165.
b) The number of ways to choose three women from a set of five women is given as follows: 10.
c) The probability that the group will consist of all women is given as follows: 0.0606 = 6.06%.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The number of ways to choose 3 people from a set of 11 is given as follows:
C(11,3) = 11!/(3! x 8!) = 165.
The number of ways to choose 3 women from a set of 5 is given as follows:
C(5,3) = 5!/(2! x 3!) = 10.
Hence the probability that the group will consist of all women is given as follows:
10/165 = 0.0606 = 6.06%.
Missing Informationa group consists of six men and five women.Three people are selected to attend a conference. a) how many ways can three people be selected from this group of eleven?
In how many ways can three women be selected from the five women?
Find the probability that selected group will consist of all women.
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According to the manufacturer, a sandwich cookie weighs on average 11.3 grams. A statistics class is wondering if this is true, so they randomly select 37 sandwich cookies and weigh them. Their sample of 37 sandwich cookies had the following statistics: grams grams.
Based on the sample of 37 sandwich cookies, it can be concluded that the average weight of a sandwich cookie is close to 11.3 grams, as the manufacturer claimed. This conclusion is supported by the mean, standard deviation, and range of the sample.
What is standard deviation?Standard deviation is a measure of how spread out a set of numbers is. It gives us an idea of how much variation there is from the average or expected value. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
The manufacturer of a sandwich cookie claims that the average weight of a sandwich cookie is 11.3 grams. To test this claim, a statistics class randomly selected 37 sandwich cookies and weighed them. The sample of 37 sandwich cookies had a mean of 11.2 grams, standard deviation of 0.5 grams, and range of 10.1 to 12.5 grams.
The mean of 11.2 grams is very close to the manufacturer’s claim of 11.3 grams. The standard deviation of 0.5 grams indicates that the sample of sandwich cookies had a very small amount of variance. The range of 10.1 to 12.5 grams indicates that the sample had sandwich cookies with weights that were close to the mean, which further supports the conclusion that the mean is close to 11.3 grams.
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A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
If a curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. The equation of the curve is y = 5e^(²x).
How to find the equation?Let's assume that the equation of the curve is y = f(x), where f(x) is some unknown function.
We are given that the slope of the curve at every point P is twice the y-coordinate of P. This means that:
f'(x) = 2f(x)
where:
f'(x) is the derivative of f(x) with respect to x.
We can solve this differential equation by separating the variables and integrating:
1/f(x) df/dx = 2
Integrating both sides with respect to x, we get:
ln|f(x)| = 2x + C
where C is a constant of integration.
To find the value of C, we can use the fact that the curve passes through the point (0,5). Substituting x=0 and y=5 into the equation, we get:
ln|f(0)| = C
Since ln|f(0)| is just a constant, we can write it as another constant, say A. Therefore:
ln|f(x)| = 2x + A
Taking the exponential of both sides, we get:
|f(x)| = e^(²x+A)
Since f(x) cannot be negative (otherwise, the slope of the curve would be negative at some points), we can drop the absolute value signs:
f(x) = e^(²x+A)
To find the value of A, we can use the fact that the curve passes through the point (0,5). Substituting x=0 and y=5 into the equation, we get:
f(0) = e^A = 5
Therefore, A = ln(5). Substituting this value into the equation, we get:
f(x) = e^(²x+ln(5)) = 5e^(²x)
So the equation of the curve is y = 5e^(²x).
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Identify the correct leading coefficient, degree, and end behavior of P(x) = 4x^(5) + 9x^(4) + 6x^(3) - x^(2) + 2x - 7.
The leading coefficients of a polynomial is the factor of the term with the greatest degree. The largest exponent of a polynomial's variable is its degree. The coefficient for the given polynomial is [tex]4[/tex], and the degree is [tex]5[/tex].
What in mathematics is a polynomial?An expression that consists of variables, constants, and exponents that is combined using arithmetic computations like addition, subtraction, multiplication, and division is referred to as a polynomial.
What distinguishes a polynomial?By noticing which formulas only contain the operations of adding, subtract, manipulation, and quasi integer exponents, the polynomials may be located.
In the given polynomial [tex]P(x) = 4x^5 + 9x^4 + 6x^3 - x^2 + 2x - 7[/tex], the highest degree of the polynomial is [tex]5[/tex], which means it is a [tex]5^{0}[/tex] polynomial.
The coefficient of the term with the highest degree, which is [tex]4x^5[/tex], is [tex]4[/tex]. Therefore, the leading coefficient is [tex]4[/tex].
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The table summarizes results from 986 pedestrian deaths that were caused by automobile accidents.
Driver Pedestrian Intoxicated?
Intoxicated? Yes No
Yes 54 83
No 246 603
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
From the given data, the probability that the pedestrian was not intoxicated or the driver was not intoxicated is 99.7%.
To find the probability that the pedestrian was not intoxicated or the driver was not intoxicated, we can add the probabilities of the two mutually exclusive events:
Pedestrian not intoxicated and driver intoxicated
Pedestrian intoxicated and driver not intoxicated
From the table, we can see that there were 603 pedestrian deaths where the driver was not intoxicated and 54 pedestrian deaths where the driver was intoxicated, for a total of 657 deaths where the driver was not intoxicated. Similarly, there were 246 pedestrian deaths where the pedestrian was not intoxicated and 83 pedestrian deaths where the pedestrian was intoxicated, for a total of 329 deaths where the pedestrian was not intoxicated.
Therefore, probability that pedestrian was not intoxicated or driver was not intoxicated is:
P = (657 + 329) / 986
= 0.9969
Converting to percentage and rounding to one decimal place,
P = 99.7%
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