The total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.
To find the total cost of repayment, we need to calculate the total amount that Marvin will pay over the course of 5 years. Since he is making monthly payments, we need to first find the total number of payments he will make:
Total number of payments = 5 years x 12 months/year = 60 payments
The total amount Marvin will pay is then:
Total amount = 60 payments x $128.95/payment = $7,737.00
To find the total interest Marvin will pay, we need to subtract the original amount of the loan from the total amount he will pay:
Total interest = Total amount - Loan amount
Total interest = $7,737.00 - $6,800.00
Total interest = $937.00
Therefore, the total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.
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Frets are small metal bars positioned across the neck of a guitar so that the guitar can produce notes of a
specific scale. To find the distance a fret should be placed from the bridge, multiply the
string length by 2 " where nis the number of notes higher than the string 's root note.
Determine where to place a fret to produce an A note on a C string (5 notes higher) that is 70 cm long. Round
your answer to the nearest hundredth.
a. 52. 44 cm
C. 58. 33 cm
b. 93. 44 cm
d. 74. 92 cm
To produce an A note on a C string (5 notes higher) that is 70 cm long we should place a fret at a distance of 74.92cm from bridge.
To find where to place the fret, we use the formula:
distance from bridge = (string length) x [tex]2^{(n/12)[/tex]
In this case, the string length is 70 cm and we want to produce an A note on a C string, which is 5 notes higher. So n = 5.
distance from bridge = [tex]70 * 2^{(5/12)[/tex]
Using a calculator, we get:
distance from bridge ≈ 74.92 cm
Therefore, the answer is d. 74.92 cm, rounded to the nearest hundredth.
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Your doing practice 4
For a snowboard cost that was reduced by 40% by the end of the season, the snowboard cost $450 when it was new.
How to find original cost?To find the original cost of the snowboard, let the original price of the snowboard be x.
After a 40% reduction in price, the snowboard costs 60% of its original price, therefore the cost remaining percentage of the original prize times the reduction percentage = the price after reduction:
100% - 40% = 60%
60/100 = 0.6
0.6x = 270
Solving for x to get:
x = 270/0.6 = 450
Therefore, the original price of the snowboard was $450.
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Robin records the height of her plant for 3 months. If the pattern continues, what algebraic expression can Robin use to find the plant's height for any month? What will the plants height be at 12 months
The plant's height at 12 months would be 38 inches.
How to calculate the height?Assuming the plant's height follows a linear pattern, Robin can use the equation y = mx + b, where y is the height of the plant, x is the number of months, m is the slope or rate of growth, and b is the y-intercept or initial height.
To find the equation, Robin can use the data from the three months:
Month 1: Height = 5 inchesMonth 2: Height = 8 inchesMonth 3: Height = 11 inchesUsing these data points, Robin can calculate the slope m:
m = (11-5)/(3-1) = 3 inches/month
Then, using the point-slope form of the equation, Robin can find the y-intercept b:
y - 5 = 3(x - 1)
y = 3x + 2
Therefore, the algebraic expression to find the plant's height for any month x is y = 3x + 2.
To find the plant's height at 12 months, Robin can substitute x = 12 into the equation:
y = 3(12) + 2 = 38 inches
So the plant's height at 12 months would be 38 inches.
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Kaden invested $5,000 into a savings account. The interest was compounded
annually at 2. 5%. How much interest will Kaden earn in 30 months?
Kaden will earn $729.38 in interest in 30 months.
First, we need to calculate the annual interest rate equivalent to 2.5% for 1 year:
[tex]1 + r = (1 + 0.025)^1[/tex]
1 + r = 1.025
r = 0.025
So, Kaden's account earns 0.025 or 2.5% interest per year.
Next, we can calculate the amount of interest Kaden will earn in 30 months, which is 2.5 years:
n = 2.5 (number of years)
P = $5,000 (principal)
r = 0.025 (annual interest rate)
We can use the compound interest formula to calculate the final amount A:
[tex]A = P(1 + r)^n[/tex]
[tex]A = 5000(1 + 0.025)^2^.^5[/tex]
A = $5,729.38
The interest earned is the difference between the final amount and the principal:
Interest = A - P
Interest = $5,729.38 - $5,000
Interest = $729.38
Therefore, Kaden will earn $729.38 in interest in 30 months.
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Which number line shows the sum of -8, 4, and -2?
o
a +++++
-15
10
-5
0
5
10
15
b the
- 15
- 10
-5
0
15
10
15
o
chef
15
-10
5
0
5
10
15
o
d
-15
-10
0
5
110
15
Add the given numbers: -8 + 4 + (-2) = -6. So, the sum of -8, 4, and -2 is -6.
Which number line shows the sum of -8, 4, and -2?To represent -6 on a number line, we need to find its position relative to zero. Since -6 is negative, it will be located to the left of zero. We count 6 units to the left of zero on the number line to represent -6. Therefore, the number line that shows the sum of -8, 4, and -2 is:
o----+----+----+----+----+----+----+----+----+----o
-15 -10 -5 0 5 10 15 20 25 30
-6
So, the complete answer is:
The sum of -8, 4, and -2 is -6.
To represent -6 on a number line, locate 6 units to the left of zero.
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Leroy is building a slide for his kids. If the ladder is 5 feet tall and he wants the bottom of the slide to be 12 feet from the ladder, how long does the slide need to be?
We can use the Pythagorean theorem to solve this problem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let x be the length of the slide. Then we have a right triangle with legs of length 5 (the height of the ladder) and x, and hypotenuse of length 12 (the distance from the ladder to the bottom of the slide).
Using the Pythagorean theorem:
12^2 = 5^2 + x^2
144 = 25 + x^2
Subtracting 25 from both sides:
119 = x^2
Taking the square root of both sides:
x ≈ 10.91
Therefore, the slide needs to be about 10.91 feet long.
A children's library has 5 storybooks for every 3 science books it has. The library also has the same number of picture books as science books. The library added 50 more picture books so now there are the same number of picture books as storybooks. How many of each of the book does the children's library have? Draw a model
The children's library has 75 science books, 125 picture books, and 125 storybooks.
How to solve for the number of booksz = 5x/3 (5 storybooks for every 3 science books)
y = x (the same number of picture books as science books)
y + 50 = z (the library added 50 more picture books so now there are the same number of picture books as storybooks)
Now, we can substitute the equations to solve for the number of each type of book:
From equation 2, we know that y = x. So, we can rewrite equation 3 as:
x + 50 = z
Now, we can substitute equation 1 into this equation:
x + 50 = 5x/3
Multiply both sides by 3 to eliminate the fraction:
3(x + 50) = 5x
3x + 150 = 5x
Subtract 3x from both sides:
150 = 2x
Divide both sides by 2:
x = 75
So, there are 75 science books in the library. Now we can find the number of picture books (y) and storybooks (z):
y = x = 75 (75 picture books before adding 50 more)
y = 75 + 50 = 125 (125 picture books after adding 50 more)
z = 5x/3 = (5 * 75) / 3 = 375 / 3 = 125 (125 storybooks)
So, the children's library has 75 science books, 125 picture books, and 125 storybooks.
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3. What is the range of the functiony = 3x + 1 for
the domain 2 ≤ x ≤ 67
6 ≤ y ≤ 18
sy≤2
7 ≤ y ≤ 19
1
5
sys 3
The volume of this cone is 339. 12 cubic feet. What is the height of the cone?
Answer:
Not enough info
Step-by-step explanation:
Volume of cone formula is: V = 1/3 π r²h
You did not give the radius so it is not possible to find the solution
If radius is given, isolate h by dividing the V by 1/3 π r²
Then simplify the left side of the equation and that is what h is
A meal program accepts online payments by the use of a credit card. for every payment processed, the person is charged a 2% processing fee.
if a person made a payment of $23.50, how much was the fee he or she paid?
The fee paid by the person for a $23.50 payment with a 2% processing fee is $0.47.
As the meal program accepts online payments by the use of a credit card. for every payment processed and the processing fee for the credit card payment is 2% of the payment amount. To calculate the fee if a person made a payment of $23.50, we can multiply the payment amount by 2% or 0.02.
Fee = 23.50 x 0.02 = $0.47
Therefore, the fee paid by the person for a $23.50 payment is $0.47.
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3. Given f(x) = x² - 7x +13 and g(x) = x-2, solve f(x) = g(x) using the substitution method. Show your
work.
Answer:
The solutions for f(x) = g(x) are x = 5 and x = 3.
To solve f(x) = g(x) using substitution method, we need to substitute g(x) in place of x in the equation f(x) = x² - 7x + 13.
So, we have:
f(x) = g(x)
x² - 7x + 13 = x - 2 (Substituting g(x) = x - 2)
Now, we can solve for x by simplifying and solving the resulting quadratic equation:
x² - 8x + 15 = 0
Factoring the quadratic equation, we get:
(x - 5)(x - 3) = 0
So, x = 5 or x = 3.
Therefore, the solutions for f(x) = g(x) are x = 5 and x = 3.
To check, we can substitute each value back into the equations:
f(5) = 5² - 7(5) + 13 = 25 - 35 + 13 = 3
g(5) = 5 - 2 = 3
f(3) = 3² - 7(3) + 13 = 9 - 21 + 13 = 1
g(3) = 3 - 2 = 1
So, both solutions satisfy the original equation f(x) = g(x).
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Sikie Shoe Manufacturing Co. Was incorporated in the New York State on January 15, 2021 and received authorization to issue 100,000 shares of $25 par value, preferred stock 200,000 shares of $2 Par Value Common Stock. Prepare journal entries to record the following transactions. (40 POINTS)
1 What journal entry would you make on January 15, the authorization date?
2 On Jan. 20, 50,000 preferred stock were sold cash at $70 per share.
3 On February 1, 2021 Sikie Shoe Manufacturing Co. Issued 70,000 common shares with a Market price of $8
4 On February 15, 2021 Sikie Shoe Manufacturing Co. Issued 4,000 common shares to Delkab Consulting Co. In settlement of various Professional Services Provided at a fee of $100,000
5 On March 20, 2021 Mr. Park agreed to exchange a piece of land he owns with a fair value of $150,000 for 10,000 common shares. Sikie Shoe Manufacturing Co. Shares are actively traded at $10 per share on the stock exchange.
6 On July 1, 2021 Sikie Shoe Manufacturing Co. Issued 45,000 common shares for cash at a Market price of $25
7 As of July 31, How many common shares have been issued?
8 As of July 31, How many common shares are outstanding?
The following treasury stock transactions were made by Sikie in 2021 Prepare the necessary journal entries to record the transactions in the financial records of the company. (25 POINTS)
9 1-Aug Purchased 5,000 shares of its own $2 par value common stock at $20 per share
10 1-Sep Sold 1,500 shares of treasury stock purchased on August 1 for $30 per share
11 21-Oct Sold 700 shares of treasury stock purchased on August 1 for $27 per share
12 1-Nov Sold 900 shares of treasury stock purchased on August 1 for $13,500
13 18-Nov Sold 600 shares of treasury stock purchased on August 1 for $9,600
Prepare the stockholders' equity section of Sikie Shoe Manufacturing Co as of December 31, 2021 including disclosure of all relevant information. (Hint: Refer to Learning Objective 3 Illustration 13. 11 page 13-18 of your text book). (35 points)
To help you with the journal entries and preparation of the stockholders' equity section for Sikie Shoe Manufacturing Co, let's start with the journal entries for the given transactions:
On January 15, the authorization date:
Journal entry:
Common Stock (200,000 shares * $2 par value) $400,000
Preferred Stock (100,000 shares * $25 par value) $2,500,000
Authorized Capital Stock $2,900,000
On January 20, 50,000 preferred stock were sold for cash at $70 per share:
Journal entry:
Cash $3,500,000
Preferred Stock (50,000 shares * $25 par value) $1,250,000
Common Stock $1,250,000
Paid-in Capital in Excess of Par - Preferred Stock $2,250,000
On February 1, 70,000 common shares were issued with a market price of $8:
Journal entry:
Cash $560,000
Common Stock (70,000 shares * $2 par value) $140,000
Paid-in Capital in Excess of Par - Common Stock $420,000
On February 15, 4,000 common shares were issued to Delkab Consulting Co. in settlement of professional services provided at a fee of $100,000:
Journal entry:
Common Stock (4,000 shares * $2 par value) $8,000
Paid-in Capital in Excess of Par - Common Stock $92,000
Accounts Payable/Professional Services $100,000
On March 20, Mr. Park exchanged a piece of land with a fair value of $150,000 for 10,000 common shares:
Journal entry:
Land (fair value) $150,000
Common Stock (10,000 shares * $2 par value) $20,000
Paid-in Capital in Excess of Par - Common Stock $130,000
On July 1, 45,000 common shares were issued for cash at a market price of $25:
Journal entry:
Cash $1,125,000
Common Stock (45,000 shares * $2 par value) $90,000
Paid-in Capital in Excess of Par - Common Stock $1,035,000
Now let's move on to the questions regarding common shares issued and outstanding:
As of July 31, the number of common shares issued is:
Calculation: 70,000 (February 1) + 4,000 (February 15) + 10,000 (March 20) + 45,000 (July 1) = 129,000 common shares
As of July 31, the number of common shares outstanding is the same as the number of common shares issued since there are no repurchases or retirements mentioned.
Moving on to the treasury stock transactions:
On August 1, purchased 5,000 shares of its own $2 par value common stock at $20 per share:
Journal entry:
Treasury Stock $100,000
Cash $100,000
On September 1, sold 1,500 shares of treasury stock purchased on August 1 for $30 per share:
Journal entry:
Cash $45,000
Treasury Stock $30,000
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A bridge is to be built across a small lake from a gazebo to a dock. The bearing from the gazebo to the dock is S 41° W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E, respectively (see figure). Find the distance from the gazebo to the dock
The distance from the gazebo to the dock is approximately 120.45 meters.
The given problem can be solved using the concept of trigonometry.
let the distance from the gazebo to the dock be "d".
According to the question it is known that the bearing from the gazebo to the dock is S 41° W which means that the angle between the line from the gazebo to the dock and due south is 41°.
Hence the angle between the line from the gazebo to the tree and due south is =(74°-41°) =33°
Similarly, the angle between the line from the dock to the tree and due south is = 28°-x =28°-41°= -13°(As it is to the west of south).
Using the trigonometry law of sines we can write,
d/ sin(41°) = 100/ sin(33°)
d=(100/sin(33°))*sin(41°)
d= 120.45 meters
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What's 2x = 20 if 4y = 80
Answer:
x=10 and y=20, 2x=20=y
Step-by-step explanation:
2x=20 | Divide by 2 on both sides
x=10
4y=80 | Divide by 4 on both sides
y=20
Answer: 40
80 ÷ 2 = 20, so x = 40.
To check your answer;
40 x 2 = 80
HELP!! I need the answer to pass 10th grade and im stumped D:
AB is dilated by a scale factor of 3 to form A'B'. Point O, which lies on AB, is the center of dilation.
The slope of AB is 3. The slope of A'B' is 3. A'B' passes through point O.
What is dilation in mathematics?Dilation is a process of transformation used to resize an object.
The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. The size of the form does differ, though.
By multiplying the x and y coordinates of the original figure by the scale factor, you may locate locations on the dilated image when a dilation in the coordinate plane has the origin as the center of dilation.
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Bob and Anna are planning to meet for lunch at Sally's Restaurant, but they forgot to schedule a time. Bob and Anna are each going to randomly choose from either 1\text{ p. M. }1 p. M. 1, start text, space, p, point, m, point, end text, 2\text{ p. M. }2 p. M. 2, start text, space, p, point, m, point, end text, 3\text{ p. M. }3 p. M. 3, start text, space, p, point, m, point, end text, or 4\text{ p. M. }4 p. M. 4, start text, space, p, point, m, point, end text to show up at Sally's Restaurant. They must both choose exactly the same time in order to meet. Bob has a "buy one entree, get one entree free" coupon that he can only use if he meets up with Anna. If he successfully meets with Anna, Bob's lunch will cost him \$5$5dollar sign, 5. If they do not meet, Bob's lunch will cost him \$10$10dollar sign, 10. What is the expected cost of Bob's lunch?
The expected cost of Bob's lunch is $9.69, rounded to the nearest cent.
To figure out the probability of Bob and Anna successfully meeting up, we need to use a unitary method. The probability of Bob choosing a specific time is 1/4, and the probability of Anna choosing the same time is also 1/4. Since they both need to choose the same time, we can multiply their individual probabilities to find the probability of them meeting up:
1/4 x 1/4 = 1/16
This means that the probability of Bob and Anna successfully meeting up is 1/16 or 0.0625.
Now we can use this probability to find the expected cost of Bob's lunch. If Bob and Anna meet up, Bob will get a discount on his lunch and pay $5. If they don't meet up, he'll have to pay the full price of $10. So the expected cost of Bob's lunch is:
(Probability of meeting up x Cost if they meet) + (Probability of not meeting up x Cost if they don't meet)
(1/16 x $5) + (15/16 x $10) = $0.3125 + $9.375 = $9.69
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hich of the following lists the range and IQR for this data?
The range is 10, and the IQR is 14.
The range is 10, and the IQR is 13.
The range is 14, and the IQR is 13.
The range is 14, and the IQR is 10
Answer:
The range is 10, and the IQR is 13.
Step-by-step explanation:
The range is the difference between the maximum and minimum values in a dataset, and the interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of the dataset.
Since the range is the difference between the maximum and minimum values in the dataset, the range cannot be 14 and the IQR be 10, since 14 is greater than 10.
Therefore, the correct answer is:
The range is 10, and the IQR is 13.
A student is solving the problem |2−9x|=29. They know that one answer can be found by solving the equation 2−9x = 29. They subtract 2 to get −9x=27 and then divide by -9 to get x=−3. They think that this is one answer, and then take the absolute value of this to get their other answer of x=3. Did this student solve this problem correctly? If so, how can you show that they got it correct. If not, what mistake did they make and what should they have done instead?
The student did not solve the problem correctly. The student only discovered one of two solutions and made the mistake of presuming that the absolute value of -3 was the other solution without investigating the second situation.
When solving absolute value equations, we have to consider both cases:
|2-9x| = 29 can be rewritten as
2-9x = 29 or 2-9x = -29
Solving the first equation as the student did:
2-9x = 29
Subtracting 2 from both sides:
-9x = 27
Dividing both sides by -9:
x = -3
This is one solution, but we also need to solve the second equation:
2-9x = -29
Subtracting 2 from both sides:
-9x = -31
Dividing both sides by -9:
x = 31/9
So the two solutions are x = -3 and x = 31/9.
Taking the absolute value of -3 gives us 3, which is one of the solutions the student found. However, the other solution is x = 31/9, not |-3|.
Therefore, the student only found one of the two solutions and made an error in assuming that the absolute value of -3 was the other solution without considering the second case.
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Determine the values of a, b, and c in the following matrix equation.
4 a
[34]
30
52
[3
2 b5
1 8
LC
a.
b.
C.
54=
16.
The values of a, b, and c in the matrix equation are a = 3, b = 1 and c = 8
Determining the values in the matrix equation.To determine the values of a, b, and c in the matrix equation:
4 a + 3 0 = 7 3
3 4 5 b c 5
By addition operation, we have
a + 0 = 3
3 + 5 = c
4 + b = 5
When the equations evaluated, we have
a = 3
c = 8
b = 1
The above are the values of a b and c
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Complete question
Determine the values of a, b, and c in the following matrix equation.
4 a + 3 0 = 7 3
3 4 5 b c 5
The cafeteria staff made sandwiches. Each sandwich had either rye or white bread, either ham or turkey, and either cheese or no cheese. The staff made an equal number of each type of sandwich. The sandwiches were placed on a tray. Without looking, Mary will choose a sandwich. What are the chances that Mary will get a sandwich with cheese?
Responses
one eighth
one sixth
one third
one half
Answer:
Step-by-step explanation:
There are 8 equally likely sandwich options: rye and ham, rye and turkey, white and ham, white and turkey, rye and ham with cheese, rye and turkey with cheese, white and ham with cheese, white and turkey with cheese.
Since each type of sandwich was made in equal number, there are 4 sandwiches with cheese.
Therefore, the chances that Mary will get a sandwich with cheese is 4/8 or 1/2.
Answer: one half
16.
The image of point (3,-5) under the translation that shifts (x, y)
to (x-1, y-3) is
Answer:
The answer would be D.
(3,-5) is the original image.
To find your X, use the x from the first image and fill in the x which would be (3-1) which gives you (2,y)
to find Y, use the y from the first image and fill it it which is ( (-5) - 3 ) which gives you (x,-8)
therefore the full answer would be D. (2,-8)
Step-by-step explanation:
Write three different pairs of coordinate points that form a line segment with a slope greater than 2.
Three pairs of coordinate points that form a line segment with a slope greater than 2 are: (x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 7), (x₁, y₁) = (1, 3) and (x₂, y₂) = (5, 13), (x₁, y₁) = (-2, 1) and (x₂, y₂) = (2, 9)
To find three pairs of coordinate points that form a line segment with a slope greater than 2, we need to choose pairs of points where the difference in y-coordinates is at least twice the difference in the corresponding x-coordinates.
Here are three pairs of coordinate points that satisfy this condition:
1. (x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 7)
Using the slope formula, we get:
slope = (y₂ - y₁) / (x₂ - x₁) = (7 - 0) / (3 - 0) = 7/3, which is greater than 2.
2. (x₁, y₁) = (1, 3) and (x₂, y₂) = (5, 13)
Using the slope formula, we get:
slope = (y₂ - y₁) / (x₂ - x₁) = (13 - 3) / (5 - 1) = 10 / 4 = 5 / 2, which is also greater than 2.
3. (x₁, y₁) = (-2, 1) and (x₂, y₂) = (2, 9)
Using the slope formula, we get:
slope = (y₂ - y₁) / (x₂ - x₁) = (9 - 1) / (2 - (-2)) = 8 / 4 = 2, which is exactly 2, but if we extend the line segment beyond these two points, the slope will become greater than 2.
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under a time crunch, you only have time to take a sample of 15 water bottles and measure their contents. the sample had a mean of 20.05 ounces with a sample standard deviation of 0.3 ounces. what would be the 90% confidence interval, when we assumed these measurements are normally distributed? g
The 90 % confidence interval is ( 19.92 , 20.18 )
What is confidence interval?A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the number of samples n = 15
Let the mean of the sample be μ = 20.05
Let the standard deviation σ = 0.3
Now , the z score of 90 % confidence interval is z = 1.645
The 90% confidence interval is calculated by the equation
A = μ ± z ( σ / √n )
Substituting the values in the equation , we get
P = μ + z ( σ / √n )
Q = μ - z ( σ / √n )
Now , the value of P is
P = 20.05 + 1.645 ( 0.3/√15 )
P = 20.05 + ( 0.4935 / 3.873 )
P = 20.05 + 0.12742
P = 20.18
Now , the value of Q is
Q = μ - z ( σ / √n )
Q = 20.05 - 1.645 ( 0.3/√15 )
Q = 20.05 - ( 0.4935 / 3.873 )
Q = 20.05 - 0.12742
Q = 19.92
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Homework 8: Problem 5 Previous Problem Problem List Next Problem (1 point) Find all points of intersection (r, θ) of the curves t = 6 cos(θ), r= 2 sin(θ). Note. In this problem the curves intersect at the pole and one other point. Only enter the answer for nonzero r in the form (r, θ) with θ measured in radians.
Point of intersection= Need find the area inclosed in the intersection of the two graphs. Area =
The two points of intersection are (0, θ) and (0.247, θ).
The area enclosed in the intersection of the two graphs is 7π/2 square units.
To find the points of intersection of the curves:
We need to solve for θ when t = 6 cos(θ) = r/3.
We can substitute r = 2 sin(θ) into this equation to get:
6 cos(θ) = 2 sin(θ)/3
18 cos(θ) = 2 sin(θ)
9 cos(θ) = sin(θ)
Squaring both sides and using the identity sin^2(θ) + cos^2(θ) = 1, we get:
81 cos^2(θ) = 1 - cos^2(θ)
82 cos^2(θ) = 1
cos(θ) = ±sqrt(1/82)
Since we know that the curves intersect at the pole (r = 0), we only need to consider the positive root of cos(θ) to find the other point of intersection.
We can use the equation r = 2 sin(θ) to find the value of r:
r = 2 sin(θ) = 2 cos(θ) sqrt(1 - cos^2(θ)) = 2 sqrt(1/82) ≈ 0.247
So the two points of intersection are (0, θ) and (0.247, θ) where cos(θ) = sqrt(1/82) and θ is measured in radians.
To find the area enclosed in the intersection of the two graphs:
We can use the formula for the area of a polar region:
A = 1/2 ∫(r²) dθ
Since we know that the curves intersect at the pole and at (0.247, θ), we can split the integral into two parts:
A = 1/2 ∫(0 to π/2)(2 sin(θ))² dθ + 1/2 ∫(π/2 to π)(6 cos(θ))² dθ
A = π/4 + 27π/4
A = 7π/2
So the area enclosed in the intersection of the two graphs is 7π/2 square units.
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Choose all the expressions that are equal to 45×67 4 5 × 6 7. A. 2435 24 35 B. 4×75×6 4 × 7 5 × 6 C. 4×56×7 4 × 5 6 × 7 D. 6×54×7 6 × 5 4 × 7 E. 6×45×7 6 × 4 5 × 7
None of the given expressions (A, B, C, D, E) are equal to 45 x 67.
How to find which expressions are equal to multiplication?To find which expressions are equal to 45 x 67, we simply need to simplify each of the expressions given.
Starting with option A, 24 x 35, this is not equal to 45 x 67.Moving on to option B, we have 4 x 75 x 6. Simplifying this, we get 1,800, which is not equal to 45 x 67.Option C is 4 x 56 x 7, which simplifies to 1,568, not equal to 45 x 67.Option D is 6 x 54 x 7, which simplifies to 2,268, not equal to 45 x 67.Finally, option E is 6 x 45 x 7, which simplifies to 1,890, also not equal to 45 x 67.Therefore, none of the expressions are equal to 45 x 67.
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The product of 5 & 10 is equal to a third of a number
Write as an equation and solve.
The equation that represents the statement is
50 = x/3 and x is 150
What is word problem?A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
Word problem are brain teaser that allows people to think properly. The first step is to represent the unknown by a letter.
Representing the number by x
therefore:
The product of 5 and 10 is 5 × 10
5 × 10 = 1/3 × x
50 = x/3
therefore the equation is 50 = x/3 and the value of x is 150.
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The following two-way table shows the distribution of daily traffic and weather issues in a certain large city.
A 4-column table with 3 rows. Column 1 has entries bad weather, good weather, total. Column 2 is labeled heavy traffic with entries 25, 55, 80. Column 3 is labeled Light traffic with entries 5, 15, 20. Column 4 is labeled Total with entries 30, 75, 100. The columns are titled daily traffic and the rows are titled weather conditions.
Suppose a day from this city is selected at random. Let event A = heavy traffic and event B = bad weather. Are events A and B independent?
No, P(A) = P(B|A).
No, P(A) ≠ P(A|B).
Yes, P(A) = P(A|B).
Yes, P(A) ≠ P(B|A)
The correct answer is "No, P(A) ≠ P(A|B)".
How to solveIf the occurrence of one event has no bearing on the likelihood that the other will also occur, then the two events are independent.
The likelihood that both occurrences A and B will occur is defined mathematically as being equal to the product of the probabilities of A and B (i.e., P) (A and B).
Let event A = heavy traffic and event B = bad weather.
P(A)= 25/30 and P(B)=25/30
Two events are independent if the occurrence of one does not change the probability of the occurrence of the other.
This means P(A) = P(A|B) or P(B) = P(B|A).
For event A (heavy traffic), P(A) = 80/100 = 0.8.
For event B (bad weather), P(A|B) = 25/30 = 0.833.
Since P(A) ≠ P(A|B), events A and B are not independent.
So, the correct answer is "No, P(A) ≠ P(A|B)".
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Mrs. Carter baked a cake that was in the shape of a rectangular prism. The cake was 24 inches long, 15 inches wide and 3 inches high. She spread frosting on all four sides and the top. How many square inches of frosting did she use?
477 inches squared
594 inches squared
954 inches squared
1080 inches squared
Mrs. Carter used 954 square inches of frosting.
To find the surface area of the rectangular prism cake, we need to find the area of all six sides and then subtract the bottom since frosting was not applied to it.
The area of the top and bottom sides is 24 x 15 = 360 square inches each.
The area of the two side faces is 24 x 3 = 72 square inches each.
The area of the two end faces is 15 x 3 = 45 square inches each.
So, the total surface area of the cake is:
2(360) + 2(72) + 2(45) = 720 + 144 + 90 = 954 square inches.
Since frosting was applied to all sides, including the top, we use this surface area to find the amount of frosting used.
Therefore, Mrs. Carter used 954 square inches of frosting.
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Already Know The Vertex but need help on the opens and axis of symmetry
Answer: x = -3
Step-by-step explanation:
Hope this helps.
April’s grandmother bought her a set of Russian dolls from St. Petersburg. The dolls stack inside of each other and are similar to each other. The diameters of the two smallest dolls are 1. 9 cm and 2. 85 cm. The scale factor is the same from one doll to the next. April estimates that the volume of the smallest doll is 7 cm^ 3. Determine the volume of the 4th doll
The volume of the 4th doll is approximately [tex]130.1 cm^3.[/tex]
The diameter of the smallest doll is 1.9 cm, so its radius is 0.95 cm (half of the diameter).
Similarly, the radius of the second smallest doll is (2.85/2) = 1.425 cm.
Since the scale factor is the same from one doll to the next, the ratio of the radius of the second smallest doll to the radius of the smallest doll is:
1.425 cm / 0.95 cm = 1.5
Similarly, the ratio of the radius of the third smallest doll to the radius of the second smallest doll is also 1.5.
Using this pattern, we can find the radius of the 4th doll as:
Radius of 4th doll = 1.5 × (Radius of 3rd doll) = 1.5 × 2.1375 cm = 3.2063 cm (rounded to 4 decimal places)
The volume of the 4th doll can then be calculated as:
Volume of 4th doll = (4/3) × π ×[tex](Radius of 4th doll)^3[/tex]
= (4/3) × π × [tex](3.2063 cm)^3[/tex]
≈ [tex]130.1 cm^3[/tex]
Therefore, the volume of the 4th doll is approximately [tex]130.1 cm^3.[/tex]
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