The statistical measures relative to each definition are given as follows:
The median is calculated by putting the data in order and selecting the middle value.The mode is the data value that occurs the most in a set of data.The range is the difference between the maximum and minimum values of a data set. The mean is the sum of the data divided by the number of data values.How to complete the sentences?The sentences are completed using four statistical measures, and their definitions, as follows:
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18. Are girls better at spelling than boys? An SRS of 200 boys and an SRS of 150 girls was administered a
spelling test. The average score for boys was 48.4 with standard deviation 12.96. The girls had an average
score of 48.9 with standard deviation 11.85. Construct and interpret a 95% confidence interval to estimate
the true mean difference in the scores of the spelling test between boys and girls. Does this interval
suggest a difference? Explain.
No, since interval contains 0, thus the difference between boys and girls is not significant.
This can be solved using the concept of standard deviation.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered.
We have given,
n₁ = 200, n₂ = 150
x₁ = 48.4 x₂ = 48.9
s₁ = 12.96 s₂ = 11.85
95% confidence interval for difference of mean scores of boys and girls
since, n₁ and n₂ are very large therefore we may use standard normal variate , thus 95% CI is given by:
x₁ - x₂ ± 2μ₂ √(s₁²/n₁ + s₂²/n₂)
now, 2μ₂ = 1.96
∴ CI = (48.4 - 48.9) ± 1.96 √(12.96)²/ 200 + (11.85)²/150
or, CI = (-3.119, 2.1119)
no, since interval contains 0, thus the difference between boys and girls is not significant.
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4. The U.S. Census Bureau calculated the homeownership rate in the United States for the second quarter of 2019
(April, May, and June) at 64.1 percent.
A. What does that mean? Please describe what a rate is and what that specific figure tells us.
B. How would they have calculated that rate? Please explain how rates are calculated and how this specific rate
would have been calculated.
A) The homeownership rate in the United States calculated by the U.S. Census Bureau for the second quarter of 2019 as 64.1 percent means that about 64% of the U.S. homes are owner-occupied instead of renting.
B) The homeownership rate is the quotient of the number of owner-occupied homes and the total number of U.S. homes.
What is the homeownership rate?The homeownership rate describes the percentage or proportion of U.S. homes occupied by owners instead of renters.
The rate refers to the ratio, which is the relative size of one quantity compared to another.
To compute the homeownership rate, the number of owner-occupied homes is divided by the total number of U.S. homes and multiplied by 100.
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The map shows air travel distances from Minneapolis to four other cities. Use the triangle
inequality to find the range of possible distances between:
Minneapolis
1584
San Francisco
355
1056
1018
Chicago
Houston
New York
Chicago and Houston
San Francisco and Chicago
New York and San Francisco
Houston and New York
The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.
Using this principle, we can calculate the range of possible distances between each of the following cities:
Minneapolis and San Francisco: The sum of the distances from Minneapolis to Chicago and from Chicago to San Francisco is 1584 + 355 = 1939. Therefore, the minimum distance between Minneapolis and San Francisco is 1939 - 1584 = 355. The maximum distance between Minneapolis and San Francisco is 1939.
Minneapolis and Houston: The sum of the distances from Minneapolis to Chicago and from Chicago to Houston is 1584 + 1056 = 2640. Therefore, the minimum distance between Minneapolis and Houston is 2640 - 1584 = 1056. The maximum distance between Minneapolis and Houston is 2640.
Minneapolis and New York: The sum of the distances from Minneapolis to Chicago and from Chicago to New York is 1584 + 1018 = 2602. Therefore, the minimum distance between Minneapolis and New York is 2602 - 1584 = 1018. The maximum distance between Minneapolis and New York is 2602.
Chicago and Houston: The sum of the distances from Chicago to Minneapolis and from Minneapolis to Houston is 1584 + 1056 = 2640. Therefore, the minimum distance between Chicago and Houston is 2640 - 1056 = 1584. The maximum distance between Chicago and Houston is 2640.
San Francisco and Chicago: The sum of the distances from San Francisco to Minneapolis and from Minneapolis to Chicago is 355 + 1584 = 1939. Therefore, the minimum distance between San Francisco and Chicago is 1939 - 355 = 1584. The maximum distance between San Francisco and Chicago is 1939.
New York and San Francisco: The sum of the distances from New York to Minneapolis and from Minneapolis to San Francisco is 1018 + 355 = 1373. Therefore, the minimum distance between New York and San Francisco is 1373 - 1018 = 355. The maximum distance between New York and San Francisco is 1373.
Houston and New York: The sum of the distances from Houston to Minneapolis and from Minneapolis to New York is 1056 + 1018 = 2074. Therefore, the minimum distance between Houston and New York is 2074 - 1056 = 1018. The maximum distance between Houston and New York is 2074.
There will be 2,375 campers at a state summer camp this year. If each cabin has 2 counselors for every 50 campers, what prediction can you make about the number of counselors who will be at the state camp?
There will be about 1,163 counselors there.
There will be about 1,188 counselors there.
There will be about 95 counselors there.
There will be about 48 counselors there.
There will be about 95 counselors there with the help of expression 2375/50.
What are expressions exactly?
In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.
Now,
Given that Total campers = 2375
and for each cabin there are 2 counselors and 50 campers
then no. of cabins = 2375/50
No. of counselors= 2*no. of cabins
=2*2375/50
=95
Hence,
There will be about 95 counselors there with the help of expression 2375/50.
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Yasmin is participating in a 5-day cross-country biking challenge. She biked for 45,60,68 and 52 kilometers on the first four days. How many kilometers does she need to bike on the last day so that her average (mean) is 58 kilometers per day?
Step-by-step explanation:
The total distance biked by Yasmin on the first four days can be calculated as follows:
45 + 60 + 68 + 52 = 225 km
To find out how many kilometers she needs to bike on the last day to achieve an average of 58 km per day over the 5 days, we can set up an equation based on the formula for the mean:
(45 + 60 + 68 + 52 + x) / 5 = 58
Where x is the number of kilometers Yasmin needs to bike on the last day. Expanding the equation:
225 + x = 5 * 58
225 + x = 290
Subtracting 225 from both sides:
x = 65
So Yasmin needs to bike 65 kilometers on the last day to achieve an average of 58 kilometers per day over the 5 days
Last question: Find the volume of a cylinder where the circular base has a diameter of 7km, and the height of the cylinder is 13.08km.
Note: Find the indicated volumes. Use 3.14 for pi and round your final results two decimal places as needed
Answer:
503.1222
rounded: 503.12
Tomas estimated that he would need to throw 22.52m in fact he threw 21.36m what is the percentage error
Answer:
5.15%
Step-by-step explanation:
Difference between estimated throw and actual throw
= estimated - actual
= 22.52 - 21.36
= 1.16 m
As a fraction of estimated throw:
1.16/22.52
As a percentage:
1.16/22.52 x 100 = 5.15%
Write a recursive formula for an, the nth term of the sequence 50, -10, 2, ....
a1
an
11
Answer:do homework
Step-by-step explanation:
help me pls and thank you :)
Answer:
350
Step-by-step explanation:
∑ (xy) means the sum of the products of x and y , that is
∑ (xy)
= (7 × 2) + (2 × 5) + (5 × 7) + (9 × 4) + (6 × 2) + (10 × 9) + (9 × 9) + (8 × 4) + (4 × 10)
= 14 + 10 + 35 + 36 + 12 + 90 + 81 + 32 + 40
= 350
Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the car was set to 60 miles per hour by cruise control, and the mpg were recorded at random times. Here are the mpg values from the experiment:
37.2 21.0 17.4 24.9 27.0 36.9 38.8 35.3 32.3 23.9
19.0 26.1 25.8 41.4 34.4 32.5 25.3 26.5 28.2 22.1
Suppose that the standard deviation of the population of mpg readings of this vehicle is known to be σ=6.5mpg
a) What is σx¯, the standard deviation of x¯ (x Bar)?
b) Based on a 95% confidence level, what is the margin of error for the mean estimate?
c) Given the margin of error computed in part (b), give a 95% confidence interval for μμ, the mean highway mpg for this vehicle. The vehicle sticker information for the vehicle states a highway average of 27 mpg. Are the results of this experiment consistent with the vehicle sticker?
a) The standard deviation of 1.45 mpg.
b)The margin of error for the mean estimate 3.03 mpg
c) A 95% confidence interval for μμ is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg, the mean highway mpg for this vehicle is 27 mpg.
a) Using the formula for the standard error of the mean, σx¯ = σ/√n, where σ is the standard deviation of the population, n is the sample size, we can calculate σx¯ = 6.5/√20 ≈ 1.45 mpg.
b) Using a 95% confidence level, we can find the critical value for the t-distribution with 19 degrees of freedom (n-1), which is 2.093. The margin of error for the mean estimate is then t*σx¯ = 2.093 x 1.45 ≈ 3.03 mpg.
c) The 95% confidence interval for μ is given by x¯ ± margin of error, which is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg. Since the vehicle sticker information states a highway average of 27 mpg, the results of this experiment are not consistent with the vehicle sticker, as the 95% confidence interval does not contain the value of 27 mpg. This suggests that the vehicle may not be performing as well as expected, or that the sample of mpg readings was not representative of the overall population.
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Can anyone please solve this
The answers include the following:
61324318111566What is Addition?This is referred to as a mathematical operation in which two or more numbers or quantities are added together to form a sum.
3x = 18
x = 18/3 = 6
x+9 =22
x = 22-9 = 13
x/4 = 6
x = 6 × 4 = 24
x-12 =19
x = 19+12 =31
2x + 9 = 25
2x = 25-9 =16
x=16/2 = 8
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In simple terms, please explain to me what is the difference between horizontal shrink and vertical stretch.
Answer:
see attached
Step-by-step explanation:
You want the difference between horizontal shrink and vertical stretch.
Horizontal shrinkA horizontal shrink compresses a graph horizontally. In the attached figure, the original graph is the red circle. The blue ellipse is that circle shrunk horizontally by a factor of 3. It retains the same height, but is compressed sideways.
Vertical stretchA vertical stretch expands the graph vertically. The green ellipse in the attached figure is the original circle stretched vertically by a factor of 3. The horizontal dimension remains unchanged.
InterchangeableYou will notice that replacing a variable x by x/k effectively accomplishes a stretch by a factor of k in that variable's direction. Similarly, replacing a variable x by kx accomplishes a compression by a factor of k.
Your question suggests that you have noticed the similarities between vertical stretch and horizontal compression. For some figures, there is basically no difference.
Here are a couple of examples of that:
line y = x. Vertical stretch by 2: y/2 = x, or y = 2x. Horizontal compression by 2: y = 2x. These equations are identical.
parabola y = x². Vertical stretch by 4: y/4 = x² or y = 4x². Horizontal compression by 2: y = (2x)² = 4x². These equations are identical.
DifferencesThe differences between stretch in one direction and compression in the other direction are more apparent for figures with multiple reversals of direction. The second attachment shows the sine function (red) vertically stretched (blue) and horizontally compressed (green).
What is the value of x? enter your answer, as a decimal, in the box. Do not round your answer.
The "value of x" in algebraic expression represented as "3x + 2 = 8" , in decimal form is 2.0 .
We have to solve the algebraic expression "3x + 2 = 8" for value of x, we first need to separate the "variable x" on one side of the equation.
So , we subtract "2" from both sides of expression ,
we get ;
⇒ 3x + 2 - 2 = 8 - 2 ;
Simplifying the left hand side, we get:
⇒ 3x = 6 ;
To solve for the variable x, we on divide both sides by 3 ;
⇒ 3x/3 = 6/3 ;
Simplifying, we get:
⇒ x = 6/3 = 2 .
Therefore, the value of x in the algebraic expression "3x + 2 = 8" is 2 , which is 2.0 when expressed as a decimal.
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The given question is incomplete , the complete question is
What is the value of x in the algebraic expression "3x + 2 = 8" ? Enter your answer, as a decimal . Do not round your answer.
37
B
12
35
Find cos(o) in the triangle.
A
Answer:
cos α = 35/37-------------------------------
Definition:
cosine = adjacent leg / hypotenuseSubstitute for cos α:
cos α = 35/37This table shows the results of a survey on how students get to school.
A circle graph is to be used to display the data.
Calculate the sector angle, to the nearest degree, for each method of transportation.
Transportation Number of Students
Bus 39
Bike 12
Walk 25
Car 24
The sector angle are 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.
What is a Pie Chart?A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.
We have to show the given data in a pie chart where each sector represents a proportion of a type of transportation.
39 students uses bus for transportation.
12 students uses bike for transportation.
25 students walk for transportation.
24 students uses car for transportation.
Total number of students = 39 + 12 + 25 + 24 = 100
Total sector angle of a circle = 360°
Sector angle for bus = (39 / 100) × 360 = 140.4°
Sector angle for bike = (12 / 100) × 360 = 43.2°
Sector angle for walk = (25 / 100) × 360 = 90°
Sector angle for car = (24 / 100) × 360 = 86.4°
Hence the sector angle for each mode of transportation is 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.
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5.3A Find Two Numbers Whose Product and Sum is as Indicated
For product=6 and sum=7, the numbers or integers are 1 and 6.
What exactly are integers?
In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.
now,
As given product=6 and sum=7
make factors for 6 i.e 1,2,3,6
from these choose the numbers whose sum=7
and they are 1,6.
Hence,
For product=6 and sum=7, the numbers are 1 and 6.
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Solve for x
.............
Answer:
3
Step-by-step explanation:
BT ≅ TD
[tex]19=5x+4\\15=5x\\3=x[/tex]
the sum of two fractions is 5 3/8 one of the numbers is 7/9 what is the other number
Answer:
[tex]\boxed{\mathrm\bold {4\dfrac{43}{72}}}[/tex]
Step-by-step explanation:
Let the unknown fraction be x
We are given sum of the fractions = 5 3/8 and one of the fractions is 7/9
First convert 5 3/8 to an improper fraction for easier calculation
[tex]5 \dfrac{3}{8} = \dfrac{5\times 8 + 3}{8} = \dfrac{43}{8}[/tex]
Therefore we get:
[tex]\dfrac{7}{9} + x = 5\dfrac{3}{8}\\\\\dfrac{7}{9} + x = \dfrac{43}{8}\\\\[/tex]
Subtract [tex]\dfrac{7}{9}[/tex] on both sides to isolate x:
[tex]\dfrac{7}{9} - \dfrac{7}{9} + x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]
[tex]x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]
To compute the right side
Find the LCM of 8 and 9: 8 x 9 = 72Adjust the fractions based on LCM so we get 72 as a common denominator:[tex]\dfrac{43}{8}=\dfrac{43\cdot \:9}{8\cdot \:9}=\dfrac{387}{72}\\\\\\\dfrac{7}{9}=\dfrac{7\cdot \:8}{9\cdot \:8}=\dfrac{56}{72}\\\\[/tex]A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 22 mg every six hours. This antihistamine also comes in a liquid form with a concentration of 12.3 mg/ 6mL. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person take in a week?
On solving the provided question, we can say that equation is 532/13.5 = 39.4 doses.
What exactly is an equation?A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2.
the equation is the week * 7 (weekdays) * 24 (hours/day) * 19/6 (MILIGRAMS/HOURS)
532 mg per week (532/13.5 = 39.4 doses)
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hi, can i get an answer? please and thank you
Answer:
[tex]x=-2(y+3)^2-4:[/tex]
Vertex: (-4, -3)
Focus: (-33/8, -3)
[tex]x=2(y-3)^2+4:[/tex]
Vertex: (4, 3)
Directrix: (x=31/8)
Step-by-step explanation:
Due to the formula being squared, you know it's going to be a parabola. The 4 at the end is to shift the parabola (-4 = left 4, 4 = right 4). From there you can deduce the vertex and from there the focus and directrix.
Find the difference between the simple interest
and compound interest on 16000 at 5%
per annum at the end of one and a half year
if the interest is compounded half yearly.
Answer: The simple interest on 16000 at 5% per annum for 1.5 years is calculated as:
I = P * r * t
I = 16000 * 0.05 * 1.5
I = 1200
The compound interest on 16000 at 5% per annum compounded half yearly for 1.5 years is calculated as:
A = P * (1 + r/n)^(nt)
A = 16000 * (1 + 0.05/2)^(2 * 1.5)
A = 16000 * (1.0253)^3
A = 16000 * 1.07897
A = 17253.576
The difference between the compound interest and simple interest is:
17253.576 - 1200 = 16053.576
So the difference between the simple interest and compound interest is 16053.576.
Step-by-step explanation:
Which equation shows how to rewrite the sum of 42 and 54 using their greatest common factor?
Answer:69
Step-by-step explanation:
31+38=69
Please help me with this please
Answer:
He will need 64 ft of fencing
Step-by-step explanation:
To determine the amount of fencing, we need to find the perimeter.
P = 2 (l+w) where l is the length and w is the width
P = 2(22+10)
P = 2(32)
P = 64
He will need 64 ft of fencing
please help me with math i’ll give you brainlist
The linear functions for this problem are classified as follows:
a. Parallel.
b. Neither parallel nor perpendicular.
c. Perpendicular.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.They are classified as parallel, perpendicular or neither according to their slopes as follows:
Parallel: same slope.Perpendicular: multiplication of the slopes is of -1.Neither: slopes are different with a multiplication different of -1.More can be learned about linear functions at https://brainly.com/question/24808124
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You borrow $900 and agree to repay it with 11% interest.
How much interest will you owe?
The interest to be paid is $99
What is simple interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Simple Interest = P×R×T/100
where P is the principal,
R is the rate
and T is the time
P = $900
R = 11%
T= 1
I = 900× 11/100
I = $99
therefore the interest to be paid is $99
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Classify the following triangles as obtuse, acute, or right triangle, using the sidelength relationship. A. 15,16,17. B 20,18,7. C 17,144,145. D 24,32,40
A. Obtuse Triangle
B. Acute Triangle
C. Right Triangle
D. Right Triangle
What is meant by an obtuse triangle?
Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or greater than 90°. Only 180° is equal to the internal angles of an acute triangle.
Given triangles are A. 15,16,17. B 20,18,7. C 17,144,145. D 24,32,40.
If the sum of squares of least two sides is greater than the square of the largest side then it is an obtuse triangle.
If the sum of squares of least two sides is less than the square of the largest side then it is an acute triangle.
If the sum of squares of least two sides is equal to the square of the largest side then it is a right triangle.
A. side lengths are 15,16,17
[tex]15^{2}+16^{2} =481\\17^{2} =289\\481 > 289[/tex]
Therefore this triangle is an obtuse triangle.
B. side lengths are 7,18,20
[tex]7^{2} +18^{2} =373\\20^{2}=400 \\373 < 400[/tex]
Therefore this triangle is an acute triangle.
C. side lengths are 17,144,145
[tex]17^{2} +144^{2} =21025\\145^{2}=21025 \\21025=21025[/tex]
Therefore this triangle is a right triangle.
D. side lengths are 24,32,40
[tex]24^{2} +32^{2} =1600\\40^{2}=1600 \\1600=1600[/tex]
Therefore this triangle is a right triangle.
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check all of the following that are possible units for measuring mass in the metric system. A. Pound B. Kilogram C. Anagram D. Gram
The following that are possible units for measuring mass in the metric system include the following below:
B. Kilogram
D. Gram.
What is Mass?This is a quantitative measure of inertia and it is referred to as the amount of matter which is present in a given body.
Options B and D both have the suffix "gram" which represents a metric system and are used in measuring mass unlike anagram which isn't a form of measurement which was why they were chosen as the correct set of options.
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Solve for B, please.
Answer:
b = 30
Step-by-step explanation:
You want the value of b given line y = 20x +b passes through the points (6, 150) and (11, 250).
Solve for bThe equation y = 20x +b can be solved for b:
b = y -20x . . . . . . . . subtract 20x
Using the given point (x, y) = (6, 150), you have ...
b = 150 -20(6) = 150 -120
b = 30
Part B
Landon thinks that the answer is
12 guests. He says, "10+ 4 = 14, and
14 rounds to 10. Then 10 X 12=120."
Do you agree with his reasoning? Explain
why or why not.
The number of guests that shared one platter is 10.
How to solve thisA. Since 3 people bring a total of 4 platters each, there are a total of 3 x 4 = 12 platters.
If the 120 guests share the platters equally, then each platter is shared by 120/12 = 10 guests. Therefore, 10 guests share 1 platter.
B. Landon's reasoning is incorrect.
While it is true that 3 people bring 4 platters each, the total number of platters is 3 x 4 = 12, not 7.
Therefore, 7 guests cannot be the correct answer. The correct answer is 10 guests share 1 platter, as explained in part A.
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Three people each bring 4 platters of food to a family reunion. The 120 guests all share the platters equally. A. How many guests share 1 platter? Explain your answer. 3.AR.1.2 B. Landon thinks that the answer is 7 guests. He says, " 3+4=7, and 7 rounds to 10 . Then 10×12=120." Do you agree with his reasoning
Find the value of x that makes AABC~ADEF.
B
8
12
光
A x+7 C
X =
D
24
E
48
3(x+3)
F
Answer:e
Step-by-step explanation:t
