For the mean weight five boxes of cookies, the p-value is equals to 0.04189. If p-value is 0.233 > α, the conclusion is that mean weight of cookies is equals to 16.
We have total five boxes of cookies. Let population of weights is normally distributed, 15.91, 14.07 , 14.88, 16.07, 14.79. Use t.test to determine the p value and hypothesis testing for mean weight of product ( cookies). Let null and alternative hypothesis be defined as
[tex]H_0 : \mu = 16[/tex]
[tex]H_a : \mu<16[/tex]
degree of freedom, df = n - 1 = 5
Using the t-test formula, t value= -2.291,
Using t distribution table and the value p-value for t = -2.2907 and 4 degree of freedom is 0.04189. Hence, required value is 0.04189.
b) Now, p-value = 0.233 for mean weight varied from the specified value of 16.
Level of significance, [tex]\alpha[/tex] = 0.05
As we see p-value = 0.233 > 0.05 ( α), so, this is a significant region and null hypothesis can't be rejected. There is no enough evidence to conclude that the mean weight is actually less than 16 ounces.
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Complete question:
Following are the weights of 5 boxes of cookies, each of which is labeled as containing 16 ounces. Assume that the population of weights is normally distributed, 15.91, 14.07 , 14.88, 16.07, 14.79 . A quality control inspector wants to know whether the mean weight is actually less than 16 ounces. Compute the P-value of the test. Write down your P-value. Also, if he obtained a p-value of 0.233. which conclusion is appropriate?
5) What is the correct definition of a resume?
Question 5 options:
a letter listing all former employers, salaries and positions the applicant has ever had
a document listing detailed reasons why the applicant wants to work for the company and why he should be chosen
a letter serving as a sample of the applicant's writing skills and communication style
a document describing the applicant's experience, strengths, skills, education, and other qualifications
Answer:
The correction definition of a resume is a document describing the applicant's experience, strengths, skills, education and other qualifications.
Which scatter plot shows a negative nonlinear association?
A.
Scatter plot graph in quadrant 1 of a coordinate plane. 11 points are plotted approximated at (2, 5), (1.5, 11.5), (3.1, 6.1), (4, 9), (5.9, 12.5), (7, 6), (7.5, 8.5), (8, 11), (8.9, 4.1), (9, 8), and (11, 10).
B.
Scatter plot Graph on a coordinate plane. Closed points plotted at (3, 11), (3, 12), (4, 11), (4.2, 12), (5, 10.8), (5.4, 12), (6, 10), (6.5, 11), (6.9, 9), (7.1, 6), (7.1, 7.7), (7.8, 9), (8.1, 6.1), (8, 7.5).
C.
Scatter plot in quadrant 1 of a coordinate plane. 10 points are plotted at (2, 11), (2.5, 9), (3, 10), (4, 8), (5, 8.2), (5.5, 6.5), (6.5, 7), (6.5, 5), (8, 5.8), and (9, 4).
D.
Scatter plot in quadrant 1 of a coordinate plane. 10 points are plotted at (2, 3), (2.8, 4.2), (3.8, 3.2), (4, 4.6), (4, 6), (5, 5), (6, 8), (7, 7), (7.8, 9.2), and (8.9, 9.1).
The scatter plot that shows a negative nonlinear association is option C.
What is scatter plot?A scatter plot is a type of graph that displays the relationship between two variables. It is used to show how much one variable is affected by another variable. One variable is plotted on the horizontal axis (x-axis) and the other variable is plotted on the vertical axis (y-axis).
Here,
In this scatter plot, as the x-axis values increase, the y-axis values initially increase and then decrease. This type of association is referred to as a negative nonlinear association, where the direction of the association is negative (decreasing) and the shape of the association is nonlinear (not a straight line). The other options either show a positive association (increasing values of x and y) or a linear association (a straight line).
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A park has a large circle painted in the middle of the playground area. The circle is divided into 4 equal sections, and each section is painted a different color. The radius of the circle is 10 meters.
What is the area A of each section of the circle?
The area A of each of the section of the circle would be =78.5m²
How to calculate the area of each section of the circle given?To calculate the area of each section of the circle given, the formula for the area of circle is used which is given as follows;
Area of circle = πr²
Where;
π = 3.14
r = 10m
area = 3.14× 10×10
= 314m
But the circle is divided into 4 sections. Therefore, the area of a section = 314/4 = 78.5m²
Therefore, the area of each sector of the circle after being divided into four would be= 78.5m².
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The parallel line cannot have a y-intercept of c because then the lines would be
A. The same line
B. Perpendicular
C. Parallel
The parallel line cannot have a y-intercept of c because then the lines would be :- The same line.
Define parallel line.Parallel lines are two lines in the same plane that are equal distance apart and never intersect.
Two parallel lines have the same slope but different y-intercepts. If one of the parallel lines has a y-intercept of c, its equation is y = mx + c, where m is the slope. The other parallel line's equation would be y = mx + b, where b is a separate y-intercept.
If two lines have the same slope m and y-intercept c, their equations are the same: y = mx + c. As a result, they would be the same line rather than parallel lines.
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10. What is the answer in scientific notation?
(3.3 × 107) + (7.7 x 10")
A 8.03 × 10⁹
B 8.03 x 108
C 11 x 108
D 11 x 10⁹
The correct answer is C) 11 x 10^8.
What is scientific notation?Scientific notation is a way of writing very large or very small numbers in a compact and convenient form.
To add these two numbers, we need to make sure they have the same exponent. We can do this by converting 7.7 x 10^5 to scientific notation with an exponent of 7:
(3.3 x 10^7) + (7.7 x 10^5) = (3.3 x 10^7) + (7.7 x 10^5) x (10^2 / 10^2)
= (3.3 x 10^7) + (7.7 x 10^7) / 10^2
= (3.3 + 7.7 x 10^-2) x 10^7
= 11 x 10^8
Therefore, the answer is C) 11 x 108.
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if all these statistics were analyzed at the end of the season, the correlation between number of wins and each of the four baseball statistics would be an example of
The correlation between the number of wins and each of the four baseball statistics would be an example of bivariate correlation analysis, which measures the strength and direction of the relationship between two variables.
The correlation between number of wins and each of the four baseball statistics would be an example of a bivariate correlation, which measures the strength and direction of the linear relationship between two variables. In this case, the two variables would be the number of wins and each of the four baseball statistics. The correlation coefficient would provide a numerical value that represents the degree of association between the two variables
A positive correlation coefficient would indicate that as one variable increases, so does the other, while a negative correlation coefficient would indicate that as one variable increases, the other decreases.
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If all these statistics were analyzed at the end of the season, the correlation between the number of wins and each of
the four baseball statistics would be an example of bivariate analysis.
Bivariate analysis involves analyzing the relationship between two variables to determine if there is any correlation or
association between them.
In this case, the two variables are the number of wins and each of the four baseball statistics.
By conducting a bivariate analysis, you can identify if there is any significant relationship between these variables and
potentially draw conclusions about their impact on team performance.
If all these statistics were analyzed at the end of the season, the correlation between the number of wins and each of
the four baseball statistics would be an example of bivariate analysis.
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The length of Gwen's rectangular living room is 12 meters and the distance between opposite corners is 13 meters. What is the width of Gwen's living room?
Answer:
5 meters
Step-by-step explanation:
You want to know the width of a rectangular living room that is 12 m along one side and 13 m along the diagonal.
DiagonalThe diagonal of a rectangle is the hypotenuse of each of the right triangles it creates by dividing the rectangle in half. If one side length is 12 and the diagonal is 13, these measures are part of the {5, 12, 13} Pythagorean triple.
The width of the living room is 5 meters.
__
Additional comment
You can use the Pythagorean theorem to find the missing length:
13² = 12² +w²
169 -144 = w²
w = √25 = 5
The width of the living room is 5 meters.
Other Pythagorean triples you see in algebra, trig, and geometry problems are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41} and their multiples.
Madison owns a bakery named Cakes and Happiness Bakery. She sells cakes for $20 and sells additional baked goods for $5. How much money should she be making in 2 months if she sells an average of 5 cakes a week and 10 baked goods?
A- $1,050
B- $4,200
C-16,800
(this is just for fun, it's made up. feel free to ask questions fr tho :)
Answer:
The total amount Madison should be making in 2 months can be calculated as follows:
Number of cakes sold in 2 months: 5 cakes/week x 4 weeks/month x 2 months = 40 cakes
Number of baked goods sold in 2 months: 10 baked goods/week x 4 weeks/month x 2 months = 80 baked goods
Total revenue from cake sales: 40 cakes x $20/cake = $800
Total revenue from baked goods sales: 80 baked goods x $5/baked good = $400
Total revenue from both cake and baked goods sales: $800 + $400 = $1,200
Therefore, the correct answer is not listed among the options provided. The correct answer should be $1,200.
Did i get it right?
Simplify the radical
[tex]\sqrt{x} 245[/tex]
The radical expression √45 when simplified has a value of 3√5
Simplifying the radical expressionFrom the question, we have the following parameters that can be used in our computation:
The radical expression √45
Express 45 as the product of 9 and 5
So, we have the following representation
√45 = √(9 * 5)
Expand the expression
This gives
√45 = √9 * √5
Take teh square roots of 9
This gives
√45 = 3 * √5
Lastly, we have
√45 = 3√5
Hence, the radical expression when simplified is 3√5
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Complete question
Simplify the radical √45
The Udderly Delicious Cheese Factory produces 200 blocks of cheddar cheese and 200 blocks of Swiss cheese each day. The factory uses 5 quarts of milk to make a block of cheddar cheese and 6 quarts of milk to make a block of Swiss cheese. How many total gallons of milk does the factory use each day?
the Udderly Delicious Cheese Factory uses a total of 550 gallons of milk each day to produce 200 blocks of cheddar cheese and 200 blocks of Swiss cheese.
How to calculate the question?
To calculate the total gallons of milk used by the Udderly Delicious Cheese Factory each day, we need to determine the total quarts of milk used to produce 200 blocks of cheddar cheese and 200 blocks of Swiss cheese.
For the cheddar cheese production, we know that each block requires 5 quarts of milk, so for 200 blocks, the factory would need:
200 blocks x 5 quarts/block = 1000 quarts of milk
For the Swiss cheese production, we know that each block requires 6 quarts of milk, so for 200 blocks, the factory would need:
200 blocks x 6 quarts/block = 1200 quarts of milk
To find the total quarts of milk used by the factory each day, we can add the amount of milk used for cheddar cheese production to the amount used for Swiss cheese production:
1000 quarts + 1200 quarts = 2200 quarts
To convert quarts to gallons, we divide the total quarts by 4, since there are 4 quarts in 1 gallon:
2200 quarts / 4 = 550 gallons
Therefore, the Udderly Delicious Cheese Factory uses a total of 550 gallons of milk each day to produce 200 blocks of cheddar cheese and 200 blocks of Swiss cheese.
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Convert 5.00 x 102 milliliters to quarts. (1L = 1.06 qt)A) 1.88 qt B) 0.472 qt C) 0.528 qt D) 4.72 × 105 qt E) 5.28 × 105 qt
In the context of the question, concerning the convertion of 5.00 x 10² milliliters to quarts is 0.528qt. Hence, the required answer for the given question is Option C.
In order to convert milliliters to quarts, we can implement the conversion factor of 1L = 1.06 qt .
Now using the principles of simple conversion we have
5.00 x 10² milliliters = 0.500 L .
Hence,
0.500 L x (1.06 qt / 1 L) = 0.530 qt .
In the context of the question, concerning the convertion of 5.00 x 10² milliliters to quarts is 0.528qt. Hence, the required answer for the given question is Option C.
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At Sam's Kookie shop there is an unlimited number of chocolate chip, sugar, oatmeal, and snickerdoodle cookies. How many ways can Angelina choose six cookies?
Answer:
84
Step-by-step explanation:
This is a combination problem with repetition. Since there is an unlimited number of each type of cookie, we can choose 6 cookies from a pool of 4 types of cookies.
The formula for choosing r items from n types with repetition is:
(n + r - 1)C(r)
Where C is the combination function.
Using this formula, we can calculate the number of ways to choose 6 cookies:
(4 + 6 - 1)C(6) = 9C6 = 84
Therefore, there are 84 ways for Angelina to choose 6 cookies from Sam's Kookie shop, if she can choose any combination of chocolate chip, sugar, oatmeal, and snickerdoodle cookies with unlimited supply.
A box contains 3 pens, 2 markers, and 1 highlighter. Tara selects one idem randomly and does not return it to the box. She then selects a second idem randomly. What is the probability that Tara selects 1 pen and then 1 marker? A. ) 5/36 B. ) 6/30 C. ) 6/36 D. ) 27/30
The probability that Tara selects 1 pen and then 1 marker is 6/30 (option b).
To solve this problem, we need to first find the total number of ways that Tara can select two items from the box without replacement.
In this case, we have n = 6 (3 pens, 2 markers, and 1 highlighter) and r = 2. Therefore, the total number of ways that Tara can select two items is:
6C2 = 6! / 2! (6 - 2)! = 15
Next, we need to find the number of ways that Tara can select a pen first and then a marker.
Therefore, the number of ways to select a pen first is 3, and the number of ways to select a marker second is 2. The total number of ways to select a pen first and then a marker is:
3 x 2 = 6
Finally, we can find the probability of selecting a pen first and then a marker by dividing the number of ways to select a pen first and then a marker by the total number of ways to select two items:
6 / 15 = 2 / 5
Therefore, the correct answer is option B) 6/30, which can be simplified to 2/5.
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Over the previous three weeks a work center produced 36,43 , and 35 standard hours of work. What is the measured capacity? (10pts) a. 114 standard hours b.36 standard hours c. 38 standard hours d. 43 standard hours e. cannot be determined with this data
The correct answer is (a) 114 standard hours.
To find the measured capacity of the work center, we need to add up the standard hours of work produced over the previous three weeks.
36 + 43 + 35 = 114
Therefore, the measured capacity of the work center is 114 standard hours.
The answer is (a) 114 standard hours.
To determine the measured capacity of the work center, you need to sum up the standard hours of work produced over the three weeks.
Here's the calculation:
36 standard hours (week 1) + 43 standard hours (week 2) + 35 standard hours (week 3) = 114 standard hours
So, the measured capacity of the work center is 114 standard hours. The correct answer is (a) 114 standard hours.
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The measured capacity of the work center is 114 standard hours. The correct answer is (a) 114 standard hours.
The correct answer is (a) 114 standard hours.
We must tally up the standard hours of work completed during the preceding three weeks in order to determine the measured capacity of the work center
36 + 43 + 35 = 114
Therefore, the measured capacity of the work center is 114 standard hours.
You must total the standard hours of work completed over the course of the three weeks in order to calculate the measured capacity of the work center.
Here's the calculation:
36 standard hours (week 1) + 43 standard hours (week 2) + 35 standard hours (week 3) = 114 standard hours
So, the measured capacity of the work center is 114 standard hours. The correct answer is (a) 114 standard hours.
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Use the formula 6p + 3q = t to find the value of q when p = 4 and t = 24. 6
Can I have some help please
When p=4 and t=24 then substituting these values into the equation 6p + 3q = t we get q=0.
To find the value of q in the equation 6p + 3q = t when p = 4 and t = 24, you can substitute the given values into the equation and solve for q. First, replace p with 4 and t with 24
6(4) + 3q = 24
Simplify the left side of the equation
24 + 3q = 24
Subtract 24 from both sides
3q = 0
Divide both sides by 3
q = 0
Therefore, when p = 4 and t = 24, q is equal to 0.
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For three seasons each year, a travel agent accommodates a certain number of people in four different tours: Tours A, B, C and D. This is shown as matrix S below. The cost ($) per tour, and the number of brochures printed for each person’s information pack per tour, is shown below as matrix T.
How much did the travel agency make for Summer Tour B?
a. 17,325
b. 22,050
c. 26,775
d. 29,400
e. 61,200
Answer: 22,050.
Step-by-step explanation: The number of individuals who went on Summer Visit B is given within the moment push of lattice S as 150.
The fetched per individual for Summer Tour B is given within the moment push of matrix T as $145.
Hence, the whole income created from Summer Visit B is:
150 individuals × $145 per individual = $21,750
express the double integral d f (x, y) da as an iterated integral for the given function f and region d.
An iterated integral for the given function f and region d is [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex].
What is integral?
An integral is the continuous equivalent of a sum in mathematics, where sums are used to compute areas, volumes, and their generalizations. One of the two basic operations in calculus, along with differentiation, is integration, which is the process of computing an integral.
Here, we have
Given: Consider the following F(x, y) = x + y YA (1,1) D 0 2 x
Equation of line passes through (2,0),(1,1)
= (y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)
= (y - 0)/(1 - 0) = (x - 2)/(1 - 2)
= y/1 = (x-2)/(-1)
y = -x + 2
x = 2-y
∫∫F(x,y)dA = [tex]\int\limits^0_1 \int\limits^2_y {f(x,y)} \, dx dy[/tex]
∫∫F(x,y)dA = [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex]
Hence, an iterated integral for the given function f and region d is [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex].
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What is 270% of 136ft?
Answer:
367.2
Step-by-step explanation:
Basically 270% is 2.7 so if you multiply 2.7 by 136 you will get 367.2
(Part 1 of 2) Please Help there is not much time left (Look at photo)
The average rate of change of each function on the interval 2 ≤ x ≤ 6 is given as follows:
f(x): -1.25.g(x): -0.715.How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For the function f(x), we have that:
When x = 2, y = 7.When x = 6, y = 2.Hence the rate is given as follows:
r = (2 - 7)/(6 - 2)
r = -5/4
r = -1.25.
For the function g(x), we have that:
When x = 2, y = 2(-5/7) - 6 = -7.43.When x = 6, y = 6(-5/7) - 6 = -10.29.Hence the rate is given as follows:
r = (-10.29 - (-7.43))/(6 - 2)
r = -0.715
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Can i have help please
Answer:
All new reflected coordinates
T (-3, 6)
S (-2, 4)
U (-4, 4)
R (-3, 2)
Step-by-step explanation:
This is because the are reflected sideways on x = 1. This works like a mirror or opening a page of a book if that helps visualise it.
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The area of the composite figure comprising of a semicircle and a parallelogram is about 110.3 square units.
What is a composite figure?A composite figure is a figure comprising of two or more simple geometric figures.
The figure consisting of a parallelogram and a semicircle is a composite figure, which indicates that the area of the figure is the sum of the area of the parallelogram and the area of the semicircle
The dimensions of the semicircle includes;
Diameter length, D = 8 units
The area of the circle = π·D²/4
Therefore; Area of the circle = π × (8 units)²/4 = 16·π square units
The dimensions of the parallelogram are;
The length of the base, b = 10 units
The height of the parallelogram, h = 6 units
The area of the parallelogram = b × h
Therefore; Area of the parallelogram = 10 units × 6 units = 60 square units
The area of the figure = 16·π square units + 60 square units ≈ 110.3 square units
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The mean on a Biology test was 78. What is your score on the test if you scored 2 deviations above the mean with a standard deviation of 8?
Your score on the Biology test is 94.
How to find your score on the test if you scored 2 deviations above the mean with a standard deviation of 8?If you scored 2 deviations above the mean, that means your score is 2 standard deviations above the mean. Since the standard deviation is 8, 2 standard deviations above the mean is:
2 * 8 = 16
Thus, your score on the test is:
78 + 16 = 94
Therefore, your score on the Biology test is 94 if you scored 2 deviations above the mean with a standard deviation of 8.
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Grayson measured a line to be 10.9 inches long. If the actual length of the line is 13.4
inches, then what was the percent error of the measurement, to the nearest tenth of a
percent?
The calculated value of the percent error of the measurement is 18.7%.
Calculating the percentage errorPercent error is calculated by subtracting the measured value from the actual value, dividing the result by the actual value, and then multiplying by 100 to get a percentage.
Using this formula, we have:
Error = Actual Value - Measured Value = 13.4 - 10.9 = 2.5
So, we have
Percent Error = (Error / Actual Value) * 100 = (2.5 / 13.4) * 100 ≈ 18.7%
Therefore, the percent error of the measurement is approximately 18.7%.
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Triangle ABC with vertices at A(-3, -3), B(3, 3), C(0, 3) is dilated to create triangle A'B'C' with vertices at A'(-12, -12), B'(12, 12), C'(0, 12). Determine the scale factor
used
The scale factor used to dilate triangle ABC to triangle A'B'C' is approximately 4. So, correct option is C.
To determine the scale factor used to dilate triangle ABC to triangle A'B'C', we can use the formula:
scale factor = distance(A', B') / distance(A, B)
We can choose any pair of corresponding vertices to calculate the distance, but it's usually easiest to use the endpoints of a side. Let's use points A and A', and points B and B', respectively:
distance(A', B') = √[(12 - (-12))² + (12 - (-12))²] = √(24² + 24²) ≈ 34
distance(A, B) = √[(3 - (-3))² + (3 - (-3))²] = √(6² + 6²) = 6√2
Substituting these values into the formula, we get:
scale factor = 34 / (6√2) ≈ 4
This means that every length in triangle A'B'C' is 4 times the corresponding length in triangle ABC.
Therefore, Correct option is C.
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Indicate which operation is performed with the exponents 2 and 3 in order to simplify the expression.
Select the correct answer in each row.
The operations that are performed with the exponents 2 and 3 in order to simplify the expression include the following:
x²x³ = addition.
(x²)³ = multiplication.
x³/x² = subtraction.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the addition, division, and multiplication law of exponents for powers to each of the expressions, we have the following:
x²x³ = x⁽³⁺²⁾ = x⁵ (addition).
(x²)³ = x⁶ (multiplication).
x³/x² = x⁽³⁻²⁾ = x (subtraction).
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Charlie jumped a distance of 81/feet. His younger 1 brother jumped a distance of 35/L feet and then jumped 21 feet Who jumped farther? How much farther? Explain how you found your answer.
Charlie jumped farther than his younger brother, by a distance of (60L + 35)/L - 81 feet.
To compare the distances that Charlie and his younger brother jumped, we need to find a common unit of measurement. We can convert the mixed numbers into improper fractions to make the calculation easier.
Charlie jumped 81/1 feet, which is the same as 81 feet.
His younger brother jumped 35/L feet and then 21 feet. We don't know the exact value of L, but we can still compare the distances by assuming L is a constant value. So, the total distance his younger brother jumped is:
35/L + 21 feet
We can simplify the expression by finding a common denominator:
(35 + 21L)/L feet
To compare the distances, we can subtract the distances jumped by Charlie and his younger brother:
81 - (35 + 21L)/L
To determine who jumped farther, we need to simplify this expression by finding a common denominator:
(81L - 35 - 21L)/L
Simplifying further:
(60L + 35)/L
We don't know the exact value of L, but we can say that if L is any positive value, then 60L + 35 is greater than 81. Therefore, Charlie jumped farther than his younger brother, by a distance of (60L + 35)/L - 81 feet.
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Solve for the Social Security contribution if the percentage deduction is 8.5% for the income of $112, 000
Answer:$9,520.
Step-by-step explanation:
o solve for the Social Security contribution, you can use the following formula:Social Security contribution = (percentage deduction/100) x incomeSubstituting the given values:Social Security contribution = (8.5/100) x $112,000
= $9,520Therefore, the Social Security contribution for an income of $112,000 with a percentage deduction of 8.5% is $9,520.
given u=5i+4j and v = 4i-3j, determine -9u-v
-9u - v = -49i - 33j
To find -9u - v, you need to multiply the vector u by -9 and subtract the vector v from the result.
Given u = 5i + 4j and v = 4i - 3j, first multiply u by -9:
-9u = -9(5i + 4j) = -45i - 36j
Now, subtract the vector v from -9u:
-9u - v = (-45i - 36j) - (4i - 3j) = (-45i - 4i) + (-36j + 3j) = -49i - 33j
7B Math: Efficiency Expert Portfolio
Directions:
You will mathematically and experimentally show how 4 figures made from the SAME size paper will produce different volumes.
Take 4 sheets of paper (I used 8 ½ x 11 printer paper you will use 8x10 in) and create:
-A: tall rectangular prism
-B: short rectangular prism
-C: tall cylinder
-D: short cylinder
Mathematically you will figure the dimensions of your shapes just using your paper dimensions versus a ruler.
A: B: C: D:
Volume of Prism: l x w x h
Volume of Cylinder: r x r x 3.14 x h
So we will use our paper dimensions to find the shape measurements needed to find the volume of each one.
A and B….the prisms are easy. We just take the dimension and divide it by 4 to find our measurement.
C and D ….the cylinders are a bit more tricky. We know the circumference of our circle tops and the heights of our cylinders but we need to find the radius of our circle top.
Circumference = diameter x 3.14
11 = d x 3.14
Divide both sides by 3.14 to find the diameter
11/3.14 = d
3.5 = d but in finding the volume of the cylinder we need the radius.
d/2 = r 3.5/2 = 1.75 in
According to the information, we can infer that the dimension of each shape is A are 8 x 8.5 x 2, B are 8 x 2 x 10, olume of 401.9 cubic inches, height of 2 inches and a radius of 4 inches.
How to calculate the dimensions of each shape?For shape A, the height of the rectangular prism is equal to the length of the paper (8 inches) and the width is equal to one-fourth of the width of the paper (2 inches). Therefore, the dimensions of shape A are 8 x 8.5 x 2.
For shape B, the height of the rectangular prism is equal to one-fourth of the length of the paper (2 inches) and the width is equal to the width of the paper (8 inches). Therefore, the dimensions of shape B are 8 x 2 x 10.
For shape C, the height of the cylinder is equal to the length of the paper (8 inches) and the radius of the circle top is equal to one-half of the width of the paper (4 inches). Therefore, the dimensions of shape C are a height of 8 inches and a radius of 4 inches, giving a volume of 401.9 cubic inches (rounded to one decimal place).
For shape D, the height of the cylinder is equal to one-fourth of the length of the paper (2 inches) and the radius of the circle top is equal to one-half of the width of the paper (4 inches). Therefore, the dimensions of shape D are a height of 2 inches and a radius of 4 inches, giving a volume of 100.5 cubic inches (rounded to one decimal place).
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The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would a) increase the sample size to 200. b) increase the sample size to 400. c) decrease the sample size to 50. d) decrease the sample to 25.
In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.
The given standard error of the mean for a sample of 100 is 30. So to cut the standard error of the mean to 15, we have to proceed by increasing the sample size to 400.
The formula for evaluating the standard error of mean
SEM = SD / √(n)
here, SEM = standard error of the mean,
SD = standard deviation
n = sample size
Staging the values
15 = SD / √(100)
15 x √(100) = SD
SD = 150
Now evaluating for the value of n
15 = 150 / √(n)
15 x √(n) = 150
√(n) = 10
n = 100
Now looking at the formula, we need to decrease SEM by half,
So we proceed by increasing the sample size by a factor of 4.
In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.
To learn more about standard error,
https://brainly.com/question/1191244
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