2034.72ft³ is the required cylinder volume.
What do we mean by the volume of the cylinder?The capacity of a cylinder determines how much material it can carry, or we may say that the volume of a cylinder is the total number of unit cubes that can fit inside of it.
The volume of a cylinder is r²h, and its surface area is 2πrh+2πr².
The volume of cylinder Formula: V = A × h
We will assume the cylinder is a right circular cylinder.
Then, we have the formula:
V = πr²h
We already know:
Radius = 6ft
Height = 18ft
Now, calculate the volume as follows:
(V) = π× 6² × 18
(V) = 2034.72ft³
Therefore, 2034.72ft³ is the required cylinder volume.
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dominic has a family history of hypertension. according to the chronic disease risk reduction intakes (cdrr) for sodium, dominic should lower or maintain his sodium intake to below mg/day to reduce his risk of chronic disease, including hypertension
Dominic should lower or maintain his sodium intake to below 2,300 mg/day.
Chronic disease :The Chronic Disease Risk Reduction (CDRR) consumption of 2,300 mg/day was recently developed due to connections between high sodium intake and the risk of hypertension. It is anticipated that sodium intake below this level will lower the risk of chronic diseases.
Adults may be at risk for chronic diseases if their sodium intake exceeds their CDRR intake. The population's cardiovascular health may be improved by efforts to reduce sodium consumption. Among healthy individuals, lowering daily sodium intake to CDRR is anticipated to lower the risk of developing chronic diseases, primarily by lowering blood pressure.
Hence, sodium intake to below 2,300 mg/day can reduce his risk of chronic disease.
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Identify the expression or expressions equivalent to -5 + 4(-3x+6) -4x
The equivalent expression of -5 + 4(-3x+6) -4x is -29 - 16x
How to determine the equivalent expression?From the question, we have the following parameters that can be used in our computation:
-5 + 4(-3x+6) -4x
Open the bracket in the above expression
This gives
-5 + 4(-3x+6) -4x = -5 - 12x - 24 -4x
Collect the like terms in the above expression
This gives
-5 + 4(-3x+6) -4x = -5 - 24 - 12x -4x
Evaluate the like terms in the above expression
This gives
-5 + 4(-3x+6) -4x = -29 - 16x
Hence, the equivalent expression is -29 - 16x
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y+5-1/3x=7 find y and then x to find the corresponding values
Answer:
y+5-1/3x=7 find y and then x to find the corresponding values
y = 5 - 1/3x + 7
y = 5 - 1/3(x) + 7
y = 5 - (1/3)x + 7
y = (5 - 1/3x) + 7
y = (5 + 7) - (1/3)x
y = 12 - (1/3)x
For y = 12,
12 - (1/3)x = 12
(1/3)x = 0
x = 0
Therefore, when y = 12, x = 0.
what is the probability of rolling a die ten times and obtaining odd digits on eight or less of the rolls?
The probability of rolling a die 10 times and obtaining odd digit 8 or less of the rolls is 529/512 = 1.033
Let us call, getting an odd no. on a roll of die, Success.
The, clearly, the probability p of Success is 3/6 = 1/2.
Hence, q = 1 −p = 1/2
If, X = x denotes the no. of success in n trials, then, X is a
Binomial Random Variable, with parameters
n = 10, and, p = 1/2.
Binomial Random Variable:
This is a specific type of discrete random variable. A binomial random variable counts how often a particular event occurs in a fixed number of tries or trials. For a variable to be a binomial random variable, ALL of the following conditions must be met:
There are a fixed number of trials (a fixed sample size).On each trial, the event of interest either occurs or does not.The probability of occurrence (or not) is the same on each trial.Trials are independent of one another.Then, the Probability of x success out of n trials, i.e.,
P (X = x), is,
P (X = x) = p(x) =ⁿCₓ pˣ , qⁿ⁻ˣ, x = 0,1,2, ........, n
In our case,
P (X = x) = ¹⁰Cₓ (1/2)ˣ (1/2)¹⁰⁻ˣ ,x = 0,1,2,..., 10, i.e.,
P (X = x) = p(x) = ¹⁰Cₓ (1/2)¹⁰ = ¹⁰Cₓ /1024, x = 0, 1, ..., 10.
Hence,
The Required Probability = P( X< 8),
⇒ P (X = 0)+ P( X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) +P(X = 6) + P(X= 7) + P(X =8)
⇒ 1/1024 ( 1 + 10 + 45 + 120 +210 + 252 + 210 + 120 +90)
⇒ 1/1024 ×1058
⇒ 529 / 512
⇒ 1.033
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the base of a right triangle is 6 and the perpendicular height is 8, what is the length of a hypotenuse
The length of hypotenuse is 10. It can be obtained by using Pythagorean Theorem.
What is Pythagorean theorem?
It is a theorem which gives the relationship between the length of base, perpendicular height, and hypotonus. This relationship is valid only for a right angled triangle.
The length of hypotenuse is given by the following formula:
[tex]h=\sqrt{b^2+p^2}[/tex]
Here, h is the length of hypotenuse, b is the length of base, and p is the length of perpendicular.
Substitute 6 for b and 8 for p in the above equation.
[tex]h=\sqrt{6^2+8^2}\\=\sqrt{36+64}[/tex]
Now, take the square root of 100.
[tex]h=\sqrt{100}\\=10[/tex]
Hence, the length of hypotenuse is 10.
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samantha is considering job offers from two companies. company a offered her a starting salary of $48,000 with a $2100 raise at the end of each year. company b offered her a starting salary of $48,000 with a 3.7% raise at the end of each year.
Let f(t) represent Rosa's salary at Company A, t years after accepting a position at Company A, and let g(t) represent Rosa's salary at Company B t years after accepting a position at Company B.
Complete the table of values below:
t f(t) g(t)
0 50000 50000
1
2
3
The value of f(t) are 48000, 52200, 54300, 56400, and g(t) are 48000, 49776, 51617.71, and 53527.56.
She was given a starting wage of $48,000 from Company A, with annual raises of $2100.
The formula for Company A is
f(t) = 48000 + 2100t
She was given a starting wage of $48,000 from Company B, with an annual rise of 3.7%.
The formula for Company B is
g(t) = 48000 × [tex](1 + 0.037)^t[/tex]
The value of f(t) and g(t),
t ------- f(t) ------- g(t)
0 ----- 48000 ----- 48000
1 ------ 52200 ----- 49776
2 ----- 54300 ----- 51617.71
3 ----- 56400 ----- 53527.56
The graphical representation of both the linear equations of company A and company B.
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a robotic machine fills containers with an acid solution at the rate of 140 3 t milliliters ( ml ) per second, where t is in seconds and 0 ≤ t ≤ 60 . how many ml are put into a container in 60 seconds? round to the nearest whole number.
The container put 320 ml amount of the acid in 60 seconds.
Given, a robotic machine fills containers with an acid solution at the rate of 140 + 3t milliliters ( ml ) per second, where t is in seconds and 0 ≤ t ≤ 60 .
we have to find the amount of acid solution put into the container in 60 sec
As, Amount of acid be A(t)
A(t) = 140 + 3t
A(60) = 140 + 3(60)
A(60) = 140 + 180
A(60) = 320
So, the container put 320 ml amount of the acid in 60 seconds.
Hence, the container put 320 ml amount of the acid in 60 seconds.
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The dimensions of a box have been doubled. How many times greater is the volume of the box?
8, 6, 4, or 2
Answer:
The volume increases 8-fold or by 700%.
Step-by-step explanation:
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Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2x
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A tax of 5% is applied to the bill.
Zoe decides to leave a tip of 15% on the entire bill (including the tax).
let the bill cost $x.
So, the price after tax and tip
= x+ 5% of x+ 15% of x
= x + 0.05x + 0.15x
= x + 0.20x
= 1.2x
Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x
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the mean score of 888 players in a basketball game was 14.514.514, point, 5 points. if the highest individual score is removed, the mean score of the remaining 777 players becomes 121212 points. what was the highest score?
The highest score is 32 points.
Given,
Mean score of 8 players =14.5
After removing highest score then,
Mean score of 7 players =12
let
the sum of all score be 'x'
highest score be 'y'
At first,
[tex]Mean=\frac{sum\ of\ all\ scores}{total\ number\ of\ scores}\\\\14.5=\frac{x}{8}\\\\x=116[/tex]
after removing the highest score, mean will be
[tex]Mean=\frac{sum\ of\ all\ scores-highest\ score}{number\ of\ scores}\\\\12=\frac{x-y}{7}\\\\x-y=84[/tex]
substituting 'x'
[tex]116-y=84\\\\116-84=y\\\\y=32[/tex]
Thus, the highest score is 32 points.
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what can you change in 3 (x + 4) - 2(x+4) + 0.5(x + 4) to get 1.5
Please Help!
To make the expression 3(x + 4) - 2(x + 4) + 0.5(x + 4) equals 1.5, we make x in the linear equation equals -3
Linear EquationA linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
There are linear equations in one variable and linear equations in two variables.
In this problem given we have to simplify and equation the expression to 1.5 to make it an equation.
3(x + 4) - 2(x + 4) + 0.5(x + 4) = 1.5
3x + 12 -2x -8 + 0.5x + 2 = 1.5
3x - 2x + 0.5x + 12 - 8 + 2 = 1.5
1.5x + 6 = 1.5
Collect like terms
1.5x = 1.5 - 6
x = -3
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Data Island is a beautiful beach resort. It has been a premier touristic destination for over 80 years, and the earliest holiday homes have been built just a few steps away from the beach itself. You work for a real estate agency that sells and rents holiday homes in Data Islands. Recently, one of the interns working on the Data Science Team presents you a report. According to the linear regression model they have run, the price of a house is proportional to its age. But this does not make any sense: after all, newer houses should be worth more.
1. Comment the regression output, noticing that the Sig. column is reporting the p-value of the coefficient. What can you tell about the sign of Age’s slope?
2. Why do you think the model forecasts an higher price for old holiday homes? Think carefully about all the information you have concerning Data Island.
3. Assuming that more data and variables are available, what would you suggest your intern to do to fix their report?
A lovely beach resort is Data Island. Since it first became a popular tourist destination more than 80 years ago, the earliest vacation homes have been constructed just a few steps from the beach. You are a real estate agent for a company that deals in vacation rentals and sales in the Data Islands. A report was recently presented to you by one of the interns on the data science team. The age of a house affects its price, according to the linear regression model they have ran. But this is absurd because newer homes ought to be more valuable.
1. As the coefficient of Age is positive, so the older the house, the more price it is. Sig. (or p-value) = 0.000 which implies that the co-efficient of Age is significant.
2. This may be that the people who live there are reluctant to sell it, so they quote a higher price or the size of old houses are large or they may be located at prime location.
3. We would ask new interns to consider other independent variables for the regression equation like size of house, location, etc.
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How much would you pay monthly on a $6,000 loan if you pay 12. 5 percent for 10 years?.
If we pay 12.5 percent for 10 years, our monthly payment for a $6000 loan will be about (C) $55.58.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.
A % is a number that has neither dimensions nor a defined unit of measurement.
To calculate the percentage, we must divide the value by the entire amount and then multiply the result by 100.
So, if the interest rate is 12.5%, our total loan payment would be:
112.5/100 × 6,000 = $6,750.
The monthly payment would be if there was no buildup and other agreement in payment:
6750/12*10
6750/120
$56.25
Therefore, if we pay 12.5% for 10 years, our monthly payment for a $6000 loan will be about (C) $55.58.
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Complete question:
How much would you pay monthly on a $6,000 loan if you pay 12.5 percent for 10 years?
a. $87.90
b. $70.32
c. $55.58
d. $125.00?
A certain type of car has room for 4 passengers.
How many passengers could fit in 78 cars?
How many cars would be needed to fit 78 passengers?
Answer:
1) 312
2) 20
Step-by-step explanation:
4x78=312
78 divided by 4=19.5 rounded up =20
The following inequalities form a system. y is greater than or equal to two-thirds times x plus 1 y is less than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (−6, 3.5) (−6, −3) (−4, 3) (−4, 4)
The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given phrase,
y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1
y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2
Substitute, point (−6, −3)
-3 ≥ (2/3)(-6) + 1
-3 ≥ -3
Substitute in second inequality,
-3 < (-1/4)(-6) + 2
-3 < 7/2
Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".
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Find the values of the variables in each parallelogram
Adjacent angles of a parallelogram are supplementary.
[tex]x+2x=180 \\ \\ 3x=180 \\ \\ x=\boxed{60}[/tex]
Help help help help help I will give 20 points
Answer:
Step-by-step explanation:
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If 5x + 2 = 7x - 7, then x =
Answer:
if 5x + 2 = 7x - 7 then the answer is x = 9/2.
identify the type i error and the type ii error that corresponds to the given hypothesis. the proportion of people who write with their left hand is equal to 0.29 .
Type I error is:
" Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29 "
Type II error is:
"Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29 "
What is proportion?
An equation in which two ratios are made equal is called a proportion. For instance, you could write the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.
In Statistics, a type I error is the rejection of a true null hypothesis
and a type II error is the non-rejection of a false null hypothesis
Given that p = 0.29 is accepted
Now type I error is
C. Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29
i.e. (false positive)
and type II error here is
B. Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29.
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if n people of different heights are lined up in a queue, what is the probability that at least one person is just behind a taller person?
Probability of at least one people behind taller person = n-1/n.
From the question, we have
n people of different heights are lined up in a queue
Probability of at least one people behind taller person = 1 - 1/n =n-1/n
Probability:
The term probability refers to possibility. The occurrence of a random event is the focus of this mathematical field. There is a 0 to 1 value range. To determine the possibility of certain events, probability has been employed in mathematics. The likelihood of anything happening is often referred to as probability. You can better understand the outcomes of a random experiment by applying this fundamental theory of probability, which also holds true for the probability distribution. Utilize probability to gauge a situation's likelihood of happening. Numerous factors are difficult to forecast with absolute precision. Using it, we can only speculate on whether or how likely it is that an event will occur.
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Need help asap now please!!!!!!!!
Answer:
C. 150
Step-by-step explanation:
Divide 1,350 by 9, which gives you 150 (with no remainders)
Answer:
150
Step-by-step explanation:
1350 divided by 9
C. If this is Thursday, then I do not go to church.
Converse:
Inverse:
Contrapositive:
x + 2y = -6
6x +2y =4
Step-by-step explanation:
um, I'm going to use elimination method to solve this simultaneous equation
x+2y=-6.......... equation 1
6x+2y=4........ equation 2
subtract equation 2 from equation 1
-5x = -10
x = -10/-5
x=2
substitute x=2 in equation 1
therefore equation 1 becomes
2+2y=-6
2y=-6-2
2y=-8
y=-8/2
y=-4
suppose that a random sample of 25 measurements is selected from a population with mean 70 and standard deviation 10. what is the mean and standard deviation of the sampling distribution of the sample mean?
The mean and standard deviation of the sampling distribution is 70 and 2 respectively.
Given a random sample of 25 measurements means
n = 25.
Population with mean(µ) 70 means
µ = 70.
Population with standard deviation(σ) 10 means
σ = 10.
mean of sampling distribution is itself same as mean of population
so mean of sampling distribution is 70.
standard deviation of sampling distribution is
σ/[tex]\sqrt{n}[/tex].
put the value of σ= 10 and n =25.
10/[tex]\sqrt{25}[/tex] = 10/5 = 2
So mean of sampling distribution is 70 and standard deviation of sampling distribution is 2.
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which term below is a number that describes how the data is dispersed across the entire range of data? a.) shape b.) outlier c.) spread d.) center
the spread data is dispersed across the entire range of data.
What is range of data?
In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.
When we plot data, we are considering the shape of the data. We plot the data based on the histogram, for example. The data's shape is Shape.
Outliers are different observations from the majority of the observations and are clustered in the center. Spread is the dispersion of the data throughout the entire range.
Hence, the spread data is dispersed across the entire range of data.
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B. The President uses technology to produce the following random numbers.
26 17 58 68 2 17 1 29 33 51
Determine the numbers for 9 faculty members who will be included in the sample.
The numbers for 9 faculty members who will be included in the sample are 26, 17, 58, 68, 2, 1, 29, 33, 51
What is a simple random sample?
A subset of a statistical population called a simple random sample is one in which each member has an equal chance of being chosen. A straightforward random sample is intended to offer an unbiased representation of a group.
Given, the President uses technology to produce the following numbers:
26 17 58 68 2 17 1 29 33 51
Now, 9 faculty members will be included in the sample is:
26, 17, 58, 68, 2, 17, 1, 29, 33, 51
In the above data, 17 occurs with repeated frequency then we will make 17 once.
Hence, the required answer is 26, 17, 58, 68, 2, 1, 29, 33, 51
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Find the distance between (2, 3) and (−4, −9). Round your answer to the nearest hundredth, if necessary.
Answer:
I think it would be 13.42 because round 13.41640786… would be 13.42
I hope this helps
in a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. if 10 boys and 14 girls are competing, how many different ways could the six medals possibly be given out?
answer: 72 or 1572480 depends on how you do the math
at a deli counter, there are 9 sandwiches with meat and 10 vegetarian sandwiches. dante is at the counter buying sandwiches for a picnic. in how many ways can he choose 9 sandwiches if 8 or more must be vegetarian sandwiches?
There are two different ways in which he can choose 9 sandwitches. It can be solve by the concept of permutation and combination.
What is permutation and combination?
A permutation is an arrangement of several items taken one at a time or all at once in a specific order.
Combinations are based entirely on grouping. Combinations can be used to determine how many different groups that can be created from the available items.
Since all vegitarian sandwiches looks like same and all sandwitches with meat looks like same hence, their order will not affect the number of choice.
If 8 sandwitches are vegitarian then 1 sandwitch must be with meat. So that total sandwithches becomes 9.
If all 9 sindwitches are vegetarian then there is no option to choose another sandwitch. Because he can choose only 9 sandwitches.
Hence, there are two different ways in which he can choose 9 sandwitches.
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one sample has n = 8 scores and m = 2. a second sample has n = 4 and m = 8. if the two samples are combined, then what is the mean for the combined sample?
The combined sample mean for sample one, whose size equals 8 scores and mean equals 2, and for sample second, whose size equals 4 scores and mean equals 8, is 4..
A combined sample mean is calculated by taking the mean of each group and combining (adding) the results of each average.
We have given that,
For First sample :
Sample size ,n₁ = 8 scores
sample mean, m₁ or X₁-bar = 2
Sample 2 :
Sample size, n₂ = 4
sample mean , m₂ or X₂-bar = 8
Combined sample mean is given by,
M or X-bar =( n₁× x₁-bar + n₂ × x₂-bar)/(n₁+n₂)
plug all the known values in above formula
=> M = (8×2 + 4×8 )/12
=> M = 48/12 = 4
Hence, combined sample mean is 4 .
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