The confidence interval for the mean usage of water is (18.7,20.5).
Given population standard deviation of 2.4, mean of 19.5 gallons per day and confidence interval of 98%.
We have to find the confidence interval for the mean usage of water.
To find out the confidence interval we have to first find margin of error.
μ=19.5
σ=2.4
α=0.98
α/2=0.49
We have to find the z value for the p value 0.49 which is z=2.33
Margin of error=z*μ/[tex]\sqrt{n}[/tex]
=2.33*19.5/[tex]\sqrt{3034}[/tex]
=0.82
lower level=mean -m
=19.5-0.82
=18.68
after rounding upto 1 decimal
=18.7
upper mean = mean+m
=19.5+0.82
=20.52
Hence the confidence interval for the usage of water is (18.7,20.52).
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Julie bought 5 bottles of water for $5.35. Which of the following have the same unit rate? (Click all that apply.)
1 bottle for $1.07
3 bottles for $3.15
8 bottles for $8.56
6 bottles for $6.42
Answer: 1 bottle, 6 bottle, 8 bottle
Answer: 1 bottle for $1.07, 8 bottles for $8.56 and 6 bottles for $6.42
Two chains of clothing stores, Impulse Clothing and Opal Essence, were founded in the same year, although some outlets of Opal Essence were operating under a different name before Opal Essence was founded. The owner of Impulse Clothing uses the equation below to represent the number of clothing stores, C, he owns x years after the brand's founding. C = 2x The owner of Opal Essence uses the equation below to represent the number of clothing stores, C, she owns x years after the original brand's founding. C = x + 5 Using graphing technology, complete the statements.
By combining the equations we can found that the number of impulse clothing and Opal essence stores by equations be C (3x+5)/2 where x is the number of years after the brand's founding.
Given The equation showing number of impulse clothing stores is C=2x. The equation showing number of clothing stores be C=x+5.
We have to first plot both the equations on the graph.
For plotting we need points which can be calculated as
C=2x
when x=1 ,C or y=2
when x=3 , C or y=6
C=x+5
when x=0 ,C or y=5
when x=1 ,C or y=6
By combining both equations we get
C=(3x+5)/2
Plot this also and finding points
when x=0 , C=5/2
when x=1 , C=4
Hence the combination of both statements which shows the total stores owned is C=(3x+5)/2
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Answer:
So, after
3
years, Impulse Clothing and Opal Essence will own the same number of clothing stores.
The total number of stores during that year will be 8.
Find the surface area. Round to the nearest tenth.
Answer:
66.4 in^2
Step-by-step explanation:
Surface area is defined as the area around the surface of a 3-dimensional solid. The shape we are given here is a triangular prism with a square base. This means it contains one square and 4 triangles on the surface. To find the surface area, we just need to find the areas of all 5 surface shapes and add them up. We have been given that the square has a side length of 4 inches, meaning the area is 4^2 or 16. The area of a triangle is (1/2)base*height. The base length is 4 inches and the height is 6.3, and (1/2)*4*6.3 is 12.6. Note that, since there are four triangles, we have to multiply this value by 4 (12.6*4 = 50.4). Now we have the area of the square and the area of all the triangles put together, so we can just add them up:
16 + 50.4 = 66.4
For what values of x is the expression below defined?
√x+4÷√1-x
Answer:
x=1
Step-by-step explanation:
I need help with the question in the image, thank you.
Step-by-step explanation:
First, there is a vertical stretch by a factor of 3,
Next, there is a horizontal compression by a factor of 2.
Reflect about the y axis.
After, shift to the right 3 units horizontally,
Finally , shift upwards 7 units
In a group of 26 students, 4 study both art and biology. 5 study biology but not art. 5 study neither subject. given that a randomly selected student studies art, what is the probability the student studies art and biology?
[tex]\huge\boxed{25\%}[/tex]
We need to find the number of students that study art first. This includes the students who study both art and biology (4) and the students who study art but not biology.
We know the counts for every category except for "art but not biology", so we can use subtraction.
[tex]26-4-5-5=12[/tex]
This means that 12 students study art but not biology, which combines with the 4 who study both subjects to give us 16 art-studying students.
Now, we just need to find the probability that a student studies both subjects (4 students) given that they study art (16 students).
This is simple division.
[tex]4/16=0.25=25\%[/tex]
The area of a square is 64 n Superscript 36square units. What is the side length of one side of the square?
8 n Superscript 6 units
8 n Superscript 18 units
64 n Superscript 6 units
64 n Superscript 18 units
The correct answer is option D which is the side length will be (64n)¹⁸.
What is the area of the square?The square is defined as a quadrilateral having all four sides equal to each other and the area of the square is the product of its sides.
Given that:-
The area of the square is given as- A = (64n)³⁶.The sides of the square will be calculated as follows:-
A = (64n)³⁶
a² = (64n)³⁶ Here a = Side of the square.
a = √ (64n)³⁶
a = 64n¹⁸
Therefore the correct answer is option D which is the side length will be (64n)¹⁸.
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In a recent survey of 1002 people, 701 said that they voted in a recent presidential election. voting records show that 61% of eligible voters did not vote. how would the confidence interval change if we increased the confidence level to 99%? find the 99% confidence interval estimate to support your answer.
The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).
Given sample size=1002 and confidence level of 99%.
In a sample with a number n of people surveyed with a probability of a success of π and a confidence level of 1-α, we have the following confidence interval of proportions.
π±z[tex]\sqrt{}[/tex]π(1-π)/n
in which z is the z score that has a p value of 1-α/2
n=1002,π=701/1002
So α=0.01, z is the value of Z that has a p value of 1-0.01/2=0.995, so Z=2.575.
Lower limit=π-[tex]z\sqrt{}[/tex]π(1-π)/n
=0.6996-2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]
=0.6623
Upper limit=π+[tex]z\sqrt{}[/tex]π(1-π)/n
= 0.6996+2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]
=0.7369
Hence the 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).
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Six more than a number
cubed.
n^3 + 6
I'll make n stand for the number
Six more means adding extra 6 onto our number cubed.
So, n x n x n = n^3
(n^3 means n cubed)
Thus, answer is n^3 + 6
Hope this helps!
Drag the tiles to the correct boxes to complete the pairs
68% of the data lies within one standard deviation from the mean
95% of the data lies within two standard deviation from the mean
99.7% of the data lies within three standard deviation from the mean
What is empirical rule?The empirical rule states that for a normal distribution, 68% of the data lies within one standard deviation from the mean, 95% of the data lies within two standard deviation from the mean and 99.7% of the data lies within three standard deviation from the mean
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9. The length of a rectangle is 2p cm and its breadth is p cm. When the length of the rectangle is increased by 25% and the breadth is decreased by 25%, determine the percentage change in (i) its perimeter, (ii) its area.
Answer:
The answers are:
(i) 108.33%
(ii) 93.75%
Step-by-step explanation:
The original area and perimeter are as follow:
Perimeter = 2l + 2w
= 2(2p) + 2(p)
= 4p + 2p
= 6p cm
Area = l * w
= 2p * p
= 2p^2 cm^2
A 25% increase of the length is = 2p * (1 + 25%) = 2p * 1.25 = 2.5p cm
A 25% decrease of the breadth is = p * (1 - 25%) = p * 0.75 = 0.75p cm
Perimeter = 2l + 2w
= 2(2.5p) + 2(0.75p)
= 5p + 1.5p
= 6.5p cm
Area = l * w
= 2.5p * 0.75p
= 1.875p^2 cm^2
Now that we have found the changes, let's calculate the percentage changes
Percentage change of perimeter:
x% * 6p = 6.5p
x/100 * 6p = 6.5p
x * 6p = 6.5p * 100
x = 650p/6p
x = 108.33
Percentage change of area:
x% * 2p^2 cm^2 = 1.875p^2 cm^2
x/100 * 2p^2 cm^2 = 1.875p^2 cm^2
x * 2p^2 cm^2 = 1.875p^2 cm^2 * 100
x = 187.5p^2 cm^2 / 2p^2 cm^2
x = 93.75
Answer:
i = 8 1/3%
ii = -6 1/4%
Step-by-step explanation:
The previous answer is wrong this is the correct one:
Because they are using the same variable P let's assume P = 10
Length increase 25% = 10 + (10 x 25%) = 10 + 2,5 = 12,5 cm
Breath decreased 25% = 10 - (10 x 25%) = 10 - 2,5 = 7,5 cm
i. Original Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x10) + 2(10) = 2(20) + 2(10) = 60cm
Modified Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x12,5) + 2(7,5) = 2(25) + 2(7,5) = 65cm
The percentage change is
65-60/60 x 100
= 5/60 x 100
= 500/60
= 8 2/6% simplified 8 1/3%
ii. Original Area: L x B = 2p x p = 2(10) x 10 = 20 x 10 = 200 cm^2
Modified Area: L x B = 2p x p = 2(12,5) x 7,5 = 25 x 7,5 = 187,5 cm^2
The percentage change is
187,5-200/200x 100
= - 12,5/200 x 100
= - 1250/200 = - 6 1/4 %
That is the Correct answer. Hope that help
please assist me wit this question
Answer: 65
Step-by-step explanation:
By the geometric mean theorem, the length of the altitude to the hypotenuse has length [tex]\sqrt{25 \cdot 144}=60[/tex]
So, by the Pythagorean theorem,
[tex]x=\sqrt{60^2 + 25^2}=65[/tex]
(a) Find the three-digit number that increases by 30% when each of its
digits are increased by 1.
(b) Show that no three-digit number increases by 40% when each of its
digits are increased by 1.
Step-by-step explanation:
So a three digit number can be expressed as: [tex]100a + 10b + c[/tex] where a is the third digit, b is the second digit, and c is the first digit. Or in other words a is the hundreds place, b is the tens place, and c is the ones place. When something "increases" by 30%, it is 130% it's original value, and to calculate how much that is, you simply convert 130% to a decimal by dividing by 100, which gives you 1.30. And since all the digits are increased by 1, you have the equation:
[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.30(100a+10b+c)[/tex]
Distribute the multiplication on the left side:
[tex]100a+100+10b+10+c+1=1.30(100a+10b+c)[/tex]
Distribute the multiplication on the right side:
[tex]100a+100+10b+10+c+1=130a+13b+1.3c[/tex]
Add like terms on the left side:
[tex]100a+10b+c+111=130a+13b+1.3c[/tex]
Subtract 100a, 10b, and c from both sides
[tex]111=30a+3b+0.3c[/tex]
So "technically" you can just plug in any two values, and then solve for the last value, but since you have a 3 digit number, you have the restriction of a < 10, b < 10, and c < 10, and also a, b, and c, should only be integers and all have the same sign or it wouldn't be a 3 digit number.
So let's start with a, since it has the highest coefficient, well you can fit 30 into 111, 3 times without going over so that's the first value
111 = 30(3) + 3b + 0.3c
111 = 90 + 3b + 0.3c
Now subtract the 90 from both sides
21=3b+0.3c
Well 3 can fit into 21, 7 times!
21 = 3(7) + 0.3c
21 = 21 + 0.3c
subtract 21 from both sides
0 = 0.3c
and now obviously c is 0, if you want you can divide both sides by 0.3 but it's a bit redundant
c = 0
This gives you the three values, a=3, b=7, c=0. which is the number 370. Now let's double check. Adding 1 to each digit would give you 481 and 481/370 = 1.3, so it is correct!
part b:
So to prove there is no three digit number, is to realize there is no solution, given the restriction or integers, greater than or equal to 0, and less than 10, and all of them must have the same sign.
So let's start with the same equation except this time instead of 1.3 it's 1.4
[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.40(100a+10b+c)[/tex]
Distribute on the left side;
[tex]100a+100+10b+10+c+1=1.40(100a+10b+c)[/tex]
Distribute on the right side:
[tex]100a+100+10b+10+c+1=140a + 14b + 1.4c[/tex]
Add like terms on left side:
[tex]100a + 10b + c + 111 = 140a + 14b + 1.4c[/tex]
Subtract 100a, 10b, and c from both sides:
[tex]111 = 40a + 4b + 0.4c[/tex]
Now to do the same process, let's start by finding how many times we can fit 40 into 111, and if you're wondering why we start with 40, it's because let's say for example I just say, I can fit another 40 into it, but I decide not to, and let b do that, well even if it's just 40, b will have be at least 10, which does not fit our restrictions, so you have to fit as many 40's into the number first then go the other numbers.
So only 2 40's can fit in 111 without going over the value
111 = 40(2) + 4b + 0.4c
Subtract 80 from both sides
[tex]31=4b+0.4c[/tex]
4 can fit into 31, 7 times
31 = 4(7) + 0.4c
31 = 28 + 0.4c
subtract 28 from both sides
3 = 0.4c
divide both sides by 0.4
7.5 = c.
Since c is not an integer there is no 3 digit number that exists that increases by 40% whenever you increase it by 1.
a man is walking a 300 foot long field at the same time his daughter is walking towards him from the opposite end . The man is walking 9 feet per second and the daughter is moving 6 feet per second . How many seconds will it take them to meet somewhere in the middle?
Answer:20ft
Step-by-step explanation:Because you add the numbers up 9 and 6 you get 15 so 300/15=20
20x15 equals 300 so it goes both ways
PLEASE HELP
The graph of g(x) is shown.
The graph has...
#1.
a. the same horizontal asymptote as function g
b. a horizontal asymptote at y = 5
c. a horizontal asymptote at y = 8
#2. The graph has...
a. the same vertical asymptote as function g
b. a vertical asymptote at x = -7
c. a vertical asymptote at x = -5
d. a vertical asymptote at x = 3
On the given graph, we can see that we have:
Horizontal asymptote at y = 3Vertical asymptote at x = -2The correct option would be a in both cases.
What can we conclude about the graph of g(x)?We want to study the asymptotes of the graph
If we look at the graph, we can see that the horizontal asymptote (denoted by the horizontal dashed line) is at y = 3.
the graph has a horizontal asymptote (or two actually) at y = 3.
For the vertical asymptote we just look at the vertical dashed line, it is at x = -2
Notice that none of these coincides with the options, so the only options that can be correct (depending on the graph of g(x), which is not shown) are option "a" in both cases.
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Solve for x. NEED HELP
Answer:
22.470
Step-by-step explanation:
In this example you have to use the trigonometric function sine which is defined as [tex]sin(\theta) = \frac{opposite}{hypotenuse}[/tex]
Plug in known values:
[tex]sin(64) = \frac{x}{25}[/tex]
Multiply both sides by 25
[tex]sin(64) * 25 = x[/tex]
Approximate sin(64) using a calculator:
[tex]0.89879 * 25 = x[/tex]
Simplify
[tex]22.470 \approx x[/tex]
James bought a cake that weighs 3 and 1 over 4 pounds. How many ounces does the cake weigh? Show your work. (5 points)
[16 ounces = 1 pound]
Part B: A running tap dispenses 0.15 gallons of water every second. How many pints of water is dispensed after 20 seconds? Show your work. (5 points)
[1 gallon = 4 quarts, 1 quart = 2 pints]
The weight of James cake in ounces is 52 ounces and the Pint of water dispensed in 20 seconds is 24 pints
WeightWeight of cake = 3 1/4 pounds1 pound = 16 ounces
Number of ounces the cake weigh = 3 1/4 pounds × 16 ounces
= 13/4 × 16
= (208) / 4
= 52 ounces
Water dispensed per second = 0.15 gallonsNumber of seconds = 20 seconds1 gallon = 4 quarts
0.15 gallon = 0.6 quarts
1 quart = 2 pints
0.6 quart = 1.2 pints
Pint of water dispensed in 20 seconds = 1.2 × 20
= 24 pints of water
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Complete the statement to describe the expression a b c + d e f abc+defa, b, c, plus, d, e, f. the expression consists of terms, and each term contains factors.
The statement of expressions is two terms and three factors.
The statement and expressions:According to the question, the statement that teaches us about expression is made up of two terms, each of which has three factors.
The ABC and DEF expressions define the expression of two terms, each of which comprises two elements.
As a result, the answer is two terms and three factors.
The terms of the expressions are connected by mathematical signs like addition and subtraction. Variables are combined using multiplication signs to form the factor.The three components are found in each word. Looking at the first term ABC, we can see that it has three variables, a, b, and c, which is multiplied together.Therefore, the answer is two terms and three factors.
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Explain in your own words why you think a tangent of a circle is always perpendicular to the radius at the point of tangency
Explain in your own words why you think angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle
A radius and diameter are parts of a circle. Thus the reasons required in the question are given as;
i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.
ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.
A circle is a figure that is bounded by a curved line which is called its circumference. Some of its parts are radius, diameter, chord, sector, etc.
A diameter is a line from one point on the circumference of a circle to another through its center.A radius is a line drawn from the center of a circle to its circumference. Thus a radius is half of the diameter.A tangent is an external line drawn to meet the circumference of a circle at a point,Thus the reasons required in the question are given as;
i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.
ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.
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The __________ is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.
The standard deviation is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.
In statistics, the same old deviation is a degree of the amount of variation or dispersion of a hard and fast of values. A low well-known deviation suggests that the values tend to be close to the suggested of the set, while an excessive widespread deviation shows that the values are spread out over a much broader range.
It tells you, in common, how some distance every rating lies from the suggestion. In everyday distributions, a high well-known deviation approach that values are typically far from the implied, while a low popular deviation suggests that values are clustered close to the mean.
Fashionable deviation tells you ways to unfold out the statistics is. It is a degree of the way some distance each location cost is from the suggest. In any distribution, about ninety-five% of values may be inside 2 preferred deviations of the suggested.
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If (x – 3)(x + 5) = 49, then what is the value of the expression (x – 4)(x + 6)?
HELPP‼️‼️
21. Out of 500 people in a room, 200 of them are
wearing red shirts. Of the people wearing red
shirts, 15% are wearing red pants. What percentage of the people in the room are wearing both red shirts and red pants?
500 people
200 people wearing red shirts
200x15%= 30 people
30 =6% of 500
Made Eyewear wants to conduct a survey on consumers who wear glasses. It wants to give every person who wears glasses in the United States an equal chance of being chosen for the survey. First, though, it needs to separate those who wear glasses from those who do not. What type of sampling should Made Eyewear use
Stratified sampling is used by Made Eyewear
Stratified sampling is is where we divide the population into groups by some characteristic such as age or occupation or gender. Then make sure our survey includes people from each group in proportion to how many there are in the whole population.
Example of this sampling is A stratified sample is one that ensures that subgroups (strata) of a given population are each adequately represented within the whole sample population of a research study. For example, one might divide a sample of adults into subgroups by age and use of eyeglasses, like 18–29, 30–39, 40–49, 50–59, and 60 and above
So, Stratified sampling is used by Made Eyewear
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1) The rational function shown could be used to the number of arrests, f(x), per 100,000 drivers, for driving under the influence of alcohol, as a function of a driver’s age, x.
[tex]f(x)=\frac{27725(x-14)}{x^2+9} -5x[/tex]
a) Describe the trend you see in the graph, in context.
b)Use a graphing utility to determine the age that corresponds to the greatest number of arrests.
The age that has the maximum number of arrest is 25 years
The trend on the graphThe equation of the function is given as:
[tex]f\left(x\right)\ =\ \frac{27725\left(x\ -\ 14\right)}{x^{2\ }+\ 9}-5x[/tex]
See attachment for the graph of the function.
The end behavior of the graph is
[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]
This means that:
As the age of the driver increases, arrested drivers decreases and as the age of the driver decreases, arrested drivers increases
The age that has the maximum arrest
From the graph, the maximum is:
Maximum = (25.388, 356.166)
Remove the y values
Maximum = 25.388
Approximate
Maximum = 25
Hence, the age that has the maximum arrest is 25
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Logarithmic Functions
Can anyone help?
The equation [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex] has x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞). Thus Option A,B and C are correct.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
Given function,
= [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex]
Domain of the above function is grater than -2 because at -2 system goes to infinity. Domain can be given as(-2, ∞).
Given function has x intercept at (14, 0) and y intercept at (0, 6).
Thus, the given function of log has following characteristic i.e.
x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞).
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3,
Which expression is equivalent to
56x7y5, if x #0 and y# 0?
Answer:
1960
Step-by-step explanation:
1960
times 56 times 7 time 5 = 1960
An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?
2 < s < 18
6 < s < 12.8
s < 2 or s > 18
s < 6 or s > 12.8
Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.
What is the Triangle Inequality Theorem?According to the triangle inequality theorem, the sum of any two sides of a given triangle must be greater than the length of the measure of the third side of the triangle.
Thus, given an acute triangle has sides, 8 cm and 10 cm, applying the triangle inequality theorem, the range of sides would be calculated as shown below:
10 - 8 < s > 8 + 10
2 < s > 18
The range of values for the third side is: A. 2 < s < 18.
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Answer: A. 2 < s < 18.
Step-by-step explanation:
Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.
CAN ANYONE HELP PLEASE
Answer:
x = 8
Step-by-step explanation:
Every angle in an EQUILATERAL triangle = 60°
so 9x -12 = 60
9x = 72
x = 8
Step-by-step explanation:
[tex]9x - 12 = \frac{180}{3} = 60 \\ [/tex]
[tex]9x = 60 + 12[/tex]
[tex]9x = 72[/tex]
[tex]x = \frac{72}{9} \\ [/tex]
[tex]x = 8[/tex]
hence the value of x is 8...
Which of the following options is a polynomial with a root 2i and exactly 2
real roots?
A. F(x)=x²-x²³ +2x² - 4x-8
B. F(x)=x²-x² + 4x-4
C. F(x)=x²-x³-6x² +4x+8
OD. F(x)= x³ + x² + 4x+8
The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
Factorizing polynomial functionsGiven the polynomial function below
F(x)=x³-x² + 4x-4
Group
F(x)=(x³-x²) + (4x-4)
f(x) = x²(x-1)+4(x-1)
f(x) = (x²+4)(x-1)
If f(x) = 0
x²+4 = 0 and x -1. = 0
x² = -4 and x = 1
x = ±2i and -1
Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
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Steve can complete 100m dash in 10 seconds paul can run it in 12 seconds how does their times compare?
Steve is 1.2 times faster than Paul.
What is a ratio?The quantitative relationship between two values indicating how frequently one value is contained within the other.
For example: Speed = Distance / Time
Total distance covered by both Steve and Paul = 100m
Total time taken by Steve = 10s
Steve's speed = 100 / 10 = 10m/s
Total time taken by Paul = 12s
Paul's speed = 100 / 12 = 8.33m/s
Ratio of Steve's speed to Paul's speed = 10 / 8.33 = 1.2
Hence we can say that Steve is 1.2 times faster than Paul.
Learn more about ratios on:
https://brainly.com/question/2328454
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