Answer:
Step-by-step explanation:
-9
A study of a local high school tried to determine the mean amount of money that each
student had saved. The study surveyed a random sample of 69 students in the high
school and found a mean savings of 5000 dollars with a standard deviation of 1400
dollars. At the 95% confidence level, find the margin of error for the mean, rounding
to the nearest whole number. (Do not write ).
Using the t-distribution, it is found that the margin of error for the 95% confidence interval is of $336.
What is a t-distribution confidence interval?The confidence interval is:
\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)
In which:
\(\overline{x}\) is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The margin of error is given by:
\(M = t\frac{s}{\sqrt{n}}\)
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 69 - 1 = 68 df, is t = 1.9955.
The standard deviation and sample size are given, respectively, by:
s = 1400, n = 69.
Hence, the margin of error in dollars is given by:
\(M = t\frac{s}{\sqrt{n}}\)
\(M = 1.9955\frac{1400}{\sqrt{69}}\)
M = 336.
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A painter bought 14 gallons of paint just enough to cover 2 room
7
Step-by-step explanation:
\(Based\ on\ the\ given\ conditions,\ formulate:\)
\(14\div 2\)
\(\frac{14}{2}\)
Creoss out the common factor
\(7\)
I hope this helps you
:)
Consider the inequality b >-2.
Which best describes the values of b that are solutions of the inequality?
any value that is less than or equal to - 2
any value that is less than -2 - any value that is greater than or equal to -2
any value that is greater than -2
I'm thinking it's
I'm thinking it's"Any value that is greater than -2."
Please mark brainliest...
Which term of the sequence 1/4;-1;-21/4;...is equal to -131/2
11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).
Step-by-step explanation:
the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the
As part of a board game, players choose 5 unique symbols from 9 different symbols to create their secret password. How many different ways can the players create a specific 5 symbol password?
Give your answer in simplest form.
Answer:
\(15,120\)
Step-by-step explanation:
For the first symbol, there are 9 options to choose from. Then 8, then 7, and so on. Since each player chooses 5 symbols, they will have a total of \(9\cdot 8 \cdot 7 \cdot 6\cdot 5=\boxed{15,120}\) permutations possible. Since the order of which they choose them matters (as a different order would be a completely different password), it's unnecessary to divide by the number of ways you can rearrange 5 distinct symbols. Therefore, the desired answer is 15,120.
Answer:15,120
Step-by-step explanation:
Mark all of the statements that are true.
A. All real numbers are in the range of this function.
B. The domain for this function is the set {-5).
C. The range for this function is the set {-5).
D. The domain for this function is all real numbers,
E. This graph is not a function because the value of y is the same for
every value of x.
The correct statements regarding the domain and the range of the function are given as follows:
C. The range for this function is the set {-5}.
D. The domain for this function is all real numbers.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.In this problem, the function is defined as y = 5 for all values of x. It is a function because each value of x is associated with only one value of y, hence the correct statement is given by:
C. The range for this function is the set {-5}.
D. The domain for this function is all real numbers.
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What do you want to find out? > The rate at which Bill puts shringles on a rood. What do you know? > Bill and Chip each finished half of the roof. > Bill needs 7 hours to put the same number of shingles on the roof that Chip does in 4 hours. > For each worker, the time multiplied by the rate equals the number of shringles > Chip's rate is 30 shringles more per hour than Bill's rate. What is Chip's rate in terms of Bill's rate? Let b = Bill's rate. Chip's rate = Bill's rate (b) ( - ) ( 4 ) ( 30 ) ( 7 ) ( + )
Answer:
(a) b = (4/7)c
(b) Bill: 40 shingles/hour; Chip: 70 shingles/hour
Step-by-step explanation:
Let b and c represent Bill's and Chip's rates in shingles per hour, respectively. Then we have ...
7b = 4c
c - b = 30 . . . . shingles per hour difference in rates
(a) Bill's rate in terms of Chip's rate can be found by dividing the first equation by 7
b = (4/7)c . . . . . Bill's rate is 4/7 of Chip's rate
__
(b) To find the rates, we can multiply the second equation by 7 and substitute using the first equation:
7c -7b = 210
7c -4c = 210
c = 210/3 = 70
b = (4/7)(70) = 40
Bill's rate is 40 shingles per hour; Chip's rate is 70 shingles per hour.
Solve each system of equations by substitution
x + 4y = 19
x - 2y = 1
What is the product of x and y ?
The value of product of x and y is, 21
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
WE have to given that;
System of equation ae,
x + 4y = 19 .. (i)
x - 2y = 1 .. (ii)
From (i);
x + 4y = 19
x = 19 - 4y
substitute it for the (ii) equation;
x - 2y = 1
19 - 4y - 2y = 1
19 - 6y = 1
-6y = -18
y = 3
Hence, From (i);
x + 4y = 19
x + 12 = 19
x = 7
So, The value of product of x and y is,
x × y = 3 × 7 = 21
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Which of the following has the greatest value? *
5/12
4/9
3/7
7/13
3/5
Answer:
3/5
Step-by-step explanation:
You'll get 0.6 if you divide it
Answer:
3/5
Step-by-step explanation:
5/12 = 0.41666
4/9 = 0.4444
3/7 = 0.4285714
7/13 = 0.538461
3/5 = 0.6
A tower that is 107 feet tall casts a shadow 112 feet long. Find the angle of elevation of the sun to the nearest degree.
Draw the picture.
You have a right triangle with height = 107 and base = 131
-----
angle = tan^-1(107/131) = 39.24 degrees
==============================
How is this problem to be solved?
Step-by-step explanation:
I hope this helps you!!!!!!
Factor 21x^2 - 14x - 56
Answer:
7((x-2)(3x+4))
Step-by-step explanation:
Common factor of 7 in this quadratic formula. \(7(3x^2-2x-8)\); -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product. You get 7((x-2)(3x+4))
Solve the inequality for x
Answer:
see below
Step-by-step explanation:
\(\frac{x-c}{d} > y\)
x - c > dy
x > dy + c
b) How many times would you expect the
spinner to land on a shaded section if it were
spun 40 times?
The number of times the spinner lands on a shaded section are 8 times.
What is the probability?
Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true.
We have,
2 Shaded sections are on a spinner,
8 unshaded sections are on a spinner,
10 total sections are on a spinner,
Therefore,
The probability of the spinner to land on a shaded section:
P = 2 ÷ 10 = 1 ÷ 5
consider x, the number of times the spinner lands on a shaded section.
If the spinner were spun 40 times:
so, \(\frac{x}{40} = \frac{1}{5}\)
By cross multiplying we get,
5x = 40
x = 8
Hence, the number of times the spinner lands on a shaded section are 8 times.
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To apply Central Limit Theorem on sample proportions in One Sample Proportion test, the sample size and the population proportion under null hypothesis need to satisfy certain conditions. Which of the following scenarios meet the requirement?
A. The sample size is 50 and the population proportion under null hypothesis is 25%.
B. The sample size is 70 and the population proportion under null hypothesis is 90%.
C. The sample size is 50 and the population proportion under null hypothesis is 15%.
D. The sample size is 200 and the population proportion under null hypothesis is 4%.
Answer:
The sample size is 50 and population proportion under null hypothesis is 25% ( A ) meets the requirement
Step-by-step explanation:
when applying the central limit theorem on sample proportions in one sample proportion test .The conditions needed to be satisfied are np > 10, and n( 1-p ) > 10
A) sample size ( n ) = 50
population proportion = 25%
np = 50 * 0.25 = 12.5 which is > 10 ( 1st condition met )
n( 1 - p ) = 50( 1 - 0.25 ) = 37.5 which is > 10 ( second condition met )
B ) sample size (n) = 70
population proportion = 90%
np = 70*0.9 = 63 which is > 10 ( 1st condition met )
n(1-p) = 70 ( 1 - 0.9 ) = 7 which is < 10 ( second condition not met )
C) sample size ( n ) = 50
population proportion = 15% = 0.15
np = 50 * 0.15 = 7.5 which is < 10 ( 1st condition not met )
n ( 1 - p ) = 50 ( 1 - 0.15 ) = 50 * 0.85 = 42.5 which is > 10 ( second condition met )
D) sample size ( n ) = 200
population proportion = 4% = 0.04
np = 200 * 0.04 = 8 which is < 10 ( 1st condition not met )
n ( 1 - p ) = 200 ( 1 - 0.04 ) = 192 which is > 10 ( second condition met )
hence : The sample size of 50 with population proportion under null hypothesis of 25% meets the requirement
How many different sums of money can be made from 4coins of different denomination
Answer:
15 different sums----------------------
There are various combinations of coins.
1 coin:4 options2 coins:4C2 = 4!/(2!2!) = 6 options3 coins:4C3 = 4!/(3!1!) = 4 options4 coins: 1 optionIn total there are:
4 + 6 + 4 + 1 = 15 different sumsThe following scatterplot shows two variables, x and y, along with a least-squares model.
Which of the following is a high leverage point with respect to the regression?
A (5,8)(5,8)
B (20,31)(20,31)
C (27,22)(27,22)
D (30,60)(30,60)
E (80,70)
Answer:
D(30,60)
Step-by-step explanation:
It was way outside the other points that are around the line.
The point (30,60) is a high leverage point on the regression plot.
What is High leverage points?High leverage points are those that are extreme but follow the regression equation's trend.
High leverage points are distinct from outliers, which deviate from the graph's or plot's pattern or trend.
Looking closely at the regression plot, the coordinate (30,60) follows the trend of the plot, however, it is farther from the majority of the points on the graph.
Hence, the point (30,60) is a high leverage point on the regression plot.
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What is the difference?
-3 2/3 - (-2 1/4)
let's firstly convert the mixed fractions to improper fractions.
\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{11}{3}-\left( \cfrac{9}{4} \right)\implies -\cfrac{11}{3}+\cfrac{9}{4}\implies \cfrac{-(4)11~~ + ~~(3)9}{\underset{\textit{using this LCD}}{12}} \\\\\\ \cfrac{-44+27}{12}\implies \cfrac{-17}{12}\implies {\Large \begin{array}{llll} -1\frac{5}{12} \end{array}}\)
There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
How many people use at least two
facilities?
Answer:
he total number of people who use at least two facilities is 4 + 45 = 49
Step-by-step explanation:
To find the number of people who use at least two facilities, we can find the number of people who use all three facilities and add the number of people who use only two facilities.
The number of people who use all three facilities is 4, and the number of people who use only two facilities is 27 + 23 + 31 - 3 * 4 = 45.
Therefore, the total number of people who use at least two facilities is 4 + 45 = 49.
University trailer sales company sold 356 utility trailers during a recent year. If the gross annual sales for the company was $328,132, what was the average selling price for each trailer? The average selling price of each trailer was nearly?
Answer:
The average selling price of each trailer was nearly $922
Step-by-step explanation:
University trailer sales company sold 356 utility trailers during a recent year.
If the gross annual sales for the company was $328,132.
For the average selling price of each trailer, we will divide the gross annual sales by utility trailers.
= 328132 ÷ 356
= 921.7 ≈ 922
Thus, The average selling price of each trailer was nearly $922
-TheUnknownScientist
3.f(-4)-3.g(-2) please help me with this problem
A tennis ball can in the shape of a right circular cylinder holds three tennis balls snugly. If the radius of a tennis ball is
3.5 cm, what percentage of the can is not occupied by tennis balls?
The percentage of the can that is not occupied by tennis balls is______%.
(Type an integer, fraction, or mixed number.)
The percentage of the can that is not occupied by tennis balls is approximately 80.14%.
We have,
The volume of the can = The volume of the cylinder - The volume of the three tennis balls.
The volume of the cylinder.
V(cylinder) = πr²h
where r is the radius and h is the height of the cylinder.
Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.
= 3 × 2(3.5 cm)
= 21 cm.
V(cylinder)
= π (3.5 cm)² (21 cm)
= 2709.38 cm³
The volume of one tennis ball.
V (ball) = (4/3)πr³
where r is the radius of the tennis ball. Thus,
V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³
The total volume of the three tennis balls is:
V(3balls) = 3 V(ball)
= 3(4/3) π (3.5 cm)³
= 538.782 cm³
The volume of the can not be occupied by tennis balls.
V(not occupied) = V(cylinder) - V(3 balls)
= 2709.38 - 538.782
= 2170.598 cm³
The percentage of the can that is not occupied by tennis balls.
percentage = (V(not occupied / V(cylinder)) × 100%
= (2170.598 cm^3/2709.38 cm^3) × 100%
= 80.14%
Therefore,
The percentage of the can that is not occupied by tennis balls is approximately 80.14%.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
100°
Step-by-step explanation:
tThe sum of all arc measures that make up that circle is 360 degrees.
QS + RQ + RS = 360
QS = 360 - 120 - 140 = 100
An arc angle is the degree measurement of that angle inside the circle, opposite the arc
m∠R = arc QS = 100°
Answer:
∠ R = 50°
Step-by-step explanation:
the inscribed angle R is half the measure of its intercepted arc QS
the sum of the arcs on a circle is 360° , that is
RQ + QS + SR = 360°
120° + QS + 140° = 360°
QS + 260° = 360° ( subtract 260° from both sides )
QS = 100°
Then
∠ R = \(\frac{1}{2}\) × 100° = 50°
Question is down below
Answer:
g(x) = -|x+12|
Step-by-step explanation:
Simplify as much as possible. 4u√80w^5 - w^2√20wu^2 Assume that all variables represent positive real numbers.
4u√80w^5 - w^2√20wu^2 can be simplified to 4u^2w^4√5 - w^2u√20.
You can simplify it further by combining the constant factors 4u^2 and -w^2u, resulting in 4u^2w^4√5 - w^2u√20 = (4u^2w^4-w^2u)√5.
What does it mean to simplify in mathematics?Simplifying an expression in mathematics means to rewrite it in a form that is more clear, concise, and/or easy to understand. This can involve a variety of techniques such as combining like terms, factoring, canceling out common factors, or applying mathematical rules and identities.
The goal is to express the expression in the simplest form possible, which makes it easier to perform calculations and understand the underlying concepts.
In the case of the above Express, the given expression was simplified by combining the constant factors 4u^2 and -w^2u and canceling out the common factor √5 from both terms. This resulted in a new expression that is still equivalent to the original one but written in a more condensed and transparent form.
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Which expression is equivalent to 3x2+(5x−8x2)+4−(5x+2)
Answer: -5x^2 + 2
Step-by-step explanation:
x²+8x-16 by factorising method
what is the ans pls I need it fast ASAP
Answer:
this cannot be factored since nothing shares factorable groups/values
Step-by-step explanation:
hope this helps:)
PLEASE HELP
The table of values represents an exponential function.
What is the y-coordinate of -3f(x-1) when x = 0
Enter your answer in the box.
SEE PHOTO
The y-coordinate of -3f(x-1) when x = 0 is -63
What is the y-coordinate of -3f(x-1) when x = 0From the question, we have the following parameters that can be used in our computation:
The table of values
So, we have
-3f(x - 1)
When x = 0, we have
y = -3f(0 - 1)
This gives
y = -3f(-1)
From the table, we have
y = -3 * 21
Evaluate
y = -63
Hence, the y-coordinate is -63
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Quick answer please!!!! Brodie hires a technician to fix his air conditioning unit. The total cost includes $26.50 for parts and $50.00 per hour the technician works on the job. Which equation can be used to find y, the total cost Brodie pays, given x represents the number of hours the technician works on the job? y=26.50x−50 y = 26.50x + 50 y = 50x + 26.50 y=26.50(x+50)
Answer:
y = 50x + 26.50
Step-by-step explanation:
we put the x after 50 be cause we don't know how many hours he worked
then add 26.50 the cost of the parts.
Hoped this helped.
Answer:
C: y=50x+26.50
Step-by-step explanation:
I just took the test and i got it right!!! 100%
do i get brainlest
Mr. Layton needs to buy some oil for his central heating. He can put up to 2500 litres of oil in his oil tank. There are already 750 litres of oil in the tank. Mr. Layton is going to fill the tank with oil. The price of oil is 58.4 p per litre. Mr. Layton gets 6% off the price of the oil. How much does Mr. Layton pay for the oil he needs to buy
Answer:
Step-by-step explanation:
If the tank holds 2500 liters and there are already 750 liters in there, he only needs to buy 1750 liters.
If he is saving 6%, he is still spending 94%, so
.94(58.4) = 54.896 (what he'll be paying per liter after the 6% comes off, then
54.896(1750) = $96,068