Answer:
(1024/3)r^3.
Step-by-step explanation:
Step one: So, we have that x^2 + y^2 = 4^2 × r^2(when z component = 0) . Hence, there is the need to make y^2 the subject of the formula.
Step two: 4y^2 = 16r^2 - x^2. Where 4 ×(16r^2 - x^2) is the the cross sectional area.
Step three: the next thing to do here is to integrate the cross sectional area making 4r and -4r the upper limit and lower limit for the integration.
Step four: the integration will then give a product (16 × 64)/3 A = (1024/3)r^3.
What is the equation of a line that goes through the point (0, 2) and has a slope of 1?
Answer: y=x+2
Step-by-step explanation:
The slope-intercept equation is y=mx+b. The m is slope, and the b is the y-intercept. Since we are given the slope, we can fill it into m. We also know that the y-intercept is on the y-axis, meaning the x-coordinate is 0. The point we were given is (0,2). This means the y-intercept is 2. Our equation is y=x+2.
Answer:
y=x+2
Step-by-step explanation:
Slope intercept form is:
y=mx+b
where m is the slope and b is the y-intercept.
We know that this line has a slope of 1. Therefore, we can substitute 1 in for m.
y=1x+b
1x is equal to just x, so change 1x to x.
y=x+b
Now we must find the y-intercept, or b.
Y-intercepts are where the line crosses the y axis. The x-coordinate is always a 0.
Therefore, (0,y) is the coordinates of a y-intercept, and the "y" is the y-intercept.
We are given the point:
(0,2)
Since the x-coordinate is a 0, the y-intercept is 2. Substitute 2 in for b.
y=x+b
y=x+2
The equation of the line is y=x+2
A nursing student is planning his schedule for next quarter. He needs to take three courses and one must be statistics. For his other courses, he can choose one of two science classes and one of three social sciences classes. What is the probability that his social sciences class is not Economics?
Answer: 0.66
Step-by-step explanation:
He must choose 2 courses.
The options are:
one of two science classes
one of three social sciences classes.
For the first class selection we do not have any restriction, so that selection can be ignored.
Now, we can assume that one of the 3 social sciences is economics, so we have 2 classes that are not economics.
Then, the probability that he does not select economics (if the selections are at random) is equal to the number of classes that are not economics divided the total number of classes:
p = 2/3 = 0.66
which linear is represented by the graph?
I need to find for both f(-1) and f(1) it’s
Answer:
f(-1) = -8
f(1) = -12
A regular hexagon is inscribed in a circle. The circle is inscribed in a square. If the side length of the square is 25 cm, what is the length of each side of the hexagon?
Answer:
12.5
Step-by-step explanation:
to find the length of one side of the hexagon, draw diagonal lines, which will be six diagonals, this will divide the hexagon into, 6 equilateral triangles. The diagonals are equal in length to the side of the square (25 cm.) and the sides of the equilateral triangles are just half of this (12.5 cm.)
25/2=12.5
Norah has $50,000 to invest. She is considering two investment options. Option A pays 1.5% simple interest. Option B pays 1.4% interest compounded annually. Drag dollar amounts to the table to show the value of each investment option after 5 years, 10 years, and 20 years rounded to the nearest dollar. the answer choices are: 58,027 53,500 53,750 57,458 66,028 65,000
Answer:
Option A
5 years: $53,750
10 years: $57,500
20 years: $65,000
Option B
5 years: $53,599
10 years: $57,458
20 years: $66,028
Answer:
the corrects answers
Option A
5 years: $53,750
10 years: $57,500
20 years: $65,000
Option B
5 years: $53,599
10 years: $57,458
20 years: $66,028
The second of two numbers is 7 times the first. Their sum is 72. Find the numbers.
Answer:
first number: 9 second number: 63
Step-by-step explanation
lets make a ratio!
since one number is 7 times less than the other, the ratio would be: 1:7.
now to find the answer, you'd have to do 1+7 divided by 72. so basically
x=72/8
then solving that should be simple!
x=9
so 7x would be 63.
Every new computer costs $702.37 from a local store. The nearby school has a policy that every 3 children must have at least 1 computer. If each class has 24 children, how much money should the school spend on computers if there is 17 classes?
Division is one of the four fundamental arithmetic operations. The amount of money the school needs to spend on computers is $95,522.32.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
The number of students in a class is 24, while the number of classes is 17. Therefore, the number of students in the classes should be,
[tex]\text{Total number of students} = 24 \times 17 = 408[/tex]
Now, since, there should be a computer for every 3 students, therefore, the number of computers that will be needed are,
[tex]\text{Number of computer} = \dfrac{\text{Number of students}}{3} = \dfrac{408}{3} = 136[/tex]
The cost of a single computer is $702.37, therefore, the cost of 136 computers will be,
[tex]\rm Total\ cost= (\text{Cost of a single computer}) \times 136\\\\ Total\ cost= (\$702.37) \times 136\\\\ Total\ cost= \$95,522.32[/tex]
Hence, the amount of money the school needs to spend on computers is $95,522.32.
Learn more about Division:
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9q + –23 = –77 q = _______
Answer:
q = -6
Step-by-step explanation:
given:
9q + (–23) = –77 (add 23 to both sides)
9q = -77 + 23
9q = -54 (divide both sides by 9)
q = (-54)/9
q = -6
Write and solve the equation and then check your answer. A number increased by twenty-six is forty-two. Which statements are correct? Check all that apply. This is an addition problem. This is a subtraction problem The correct equation is s + 26 = 42. The correct equation is s – 26 = 42. To solve the equation, add 26 to both sides. To solve the equation, subtract 26 from both sides.
Answer:
equation= s+26=42
to solve,subtract 26 from both sides
Step-by-step explanation:
lets say the number is S
to increase is to add
S+26=42
solution
S+26(-26)=42-26
S=16
Answer:
A: This is an addition problem.C: The correct equation is s + 26 = 42. F: To solve the equation, subtract 26 from both sides.Explanation: Correct on Edg 2020.
Pls help me I really need help
Answer:
26 - 7(n-1)
Step-by-step explanation:
subtract n times 7 from the start value.
But if we want to call the first term n=1, we have to subtract 1 from n.
www.g "A political discussion group consists of 6 Democrats and 10 Republicans. Three members are selected to attend a conference. Find the probability that the group will consist of all Republicans."
Answer:
[tex]Probability = \frac{3\\}{14}[/tex]
Step-by-step explanation:
Given
Republicans = 10
Democrats = 6
Total = Republicans + Democrats = 10 + 6 = 16
Selection = 3
Required
Probability that all selected members are Republicans
This implies that all selected members are republicans and none are republicans
This is calculated by (Number of ways of selecting 3 republicans * Number of ways of selecting 0 Democrats) / (Total number of possible selections)
First; the number of ways the 3 republicans from 10 can be selected needs to be calculated;
[tex]^{10}C_3 = \frac{10!}{(10-3)!3!}[/tex]
[tex]^{10}C_3 = \frac{10!}{7!3!}[/tex]
[tex]^{10}C_3 = \frac{10*9*8*7!}{3!7!}[/tex]
Divide numerator and denominator by 7!
[tex]^{10}C_3 = \frac{10*9*8}{3*2*1}[/tex]
[tex]^{10}C_3 = \frac{720}{6}[/tex]
[tex]^{10}C_3 = 120[/tex]
Next, the number of ways that 0 republicans can be selected from 6 will be calculated
[tex]^6C_0 = \frac{6!}{(6-0)!0!}[/tex]
[tex]^6C_0 = \frac{6!}{6!0!}[/tex]
[tex]^6C_0 = 1[/tex]
Next, the total number of possible selection will be calculated; In other words number of ways of selecting 3 politicians fro a group of 16
[tex]^{16}C_3 = \frac{16!}{(16-3)!3!}[/tex]
[tex]^{16}C_3 = \frac{16!}{13!3!}[/tex]
[tex]^{16}C_3 = \frac{16*15*14*13!}{13!3!}[/tex]
[tex]^{16}C_3 = \frac{16*15*14}{3!}[/tex]
[tex]^{16}C_3 = \frac{16*15*14}{3*2*1}[/tex]
[tex]^{16}C_3 = \frac{3360}{6}[/tex]
[tex]^{16}C_3 = 560[/tex]
Lastly, the probability is calculated as follows;
[tex]Probability = \frac{^{10}C_3\ *\ ^6C_0}{^{16}C_3}[/tex]
[tex]Probability = \frac{120\ *\ 1}{560}[/tex]
[tex]Probability = \frac{120\\}{560}[/tex]
Simplify fraction to lowest term
[tex]Probability = \frac{3\\}{14}[/tex]
Suppose Melissa borrows $3500 at an interest rate of 14% compounded each year,
Assume that no payments are made on the loan.
Do not do any rounding.
(a) Find the amount owed at the end of 1 year
(b) Find the amount owed at the end of 2 years.
PLEASE HELPPP!!!
The probability that a grader will make a marking error on any particular question of a multiple-choice exam is 0.10. If there are ten questions and questions are marked independently, what is the probability that no errors are made
Answer:
0.9^10
Step-by-step explanation:
The probability to make an error in 1 question =0.1 => The probability that this one particular question will be answered correctly is P=1-0.1=0.9
There are 10 questions that are independent from each other .
The probability to be answered correctly is 0.9 each. So the probability to answer correctly to all of them is
P(10quest=correct) =0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9=0.9^10
Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time of firing are normally distributed random variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively. Assume the time of wheel throwing and time of firing are independent random variables.
A) What is the probability that a piece of pottery will befinished within 95 minutes?
B) What is the probability that it will take longer than 110minutes?
Answer:
a) 8.23% probability that a piece of pottery will be finished within 95 minutes
b) 0.28% probability that it will take longer than 110 minutes.
Step-by-step explanation:
Normal distribution:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Two variables:
Means [tex]\mu_{a}, \mu_{b}[/tex]
Standard deviations [tex]\sigma_{a}, \sigma_{b}[/tex]
Sum:
[tex]\mu = \mu_{a} + \mu_{b}[/tex]
[tex]\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}}[/tex]
In this question:
[tex]\mu_{a} = 40, \mu_{b} = 60, \sigma_{a} = 2, \sigma_{b} = 3[/tex]
So
[tex]\mu = \mu_{a} + \mu_{b} = 40 + 60 = 100[/tex]
[tex]\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}} = \sqrt{4 + 9} = 3.61[/tex]
A) What is the probability that a piece of pottery will befinished within 95 minutes?
This is the pvalue of Z when X = 95.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{95 - 100}{3.61}[/tex]
[tex]Z = -1.39[/tex]
[tex]Z = -1.39[/tex] has a pvalue of 0.0823
8.23% probability that a piece of pottery will befinished within 95 minutes.
B) What is the probability that it will take longer than 110 minutes?
This is 1 subtracted by the pvalue of Z when X = 110.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 100}{3.61}[/tex]
[tex]Z = 2.77[/tex]
[tex]Z = 2.77[/tex] has a pvalue of 0.9972
1 - 0.9972 = 0.0028
0.28% probability that it will take longer than 110 minutes.
A grocery store estimates that customers arrive at the rate of 15 per hour. The cashier can serve customers at a rate 20 per hour. Calculate the average number of customers in a line. Group of answer choices
Answer:
The average number of customers in a line = 2.25
Step-by-step explanation:
We are given;
Mean arrival rate;a = 15 customers per hour
Mean service rate;s = 20 customers per hour
Now, we want to find the average number of customers in the line. It is given by the formula;
N_q = a(W_q) = a²/(s(s - a)
Plugging in relevant values, we have;
N_q = 15²/(20(20 - 15))
N_q = 225/100
N_q = 2.25
What is the solution to the following equation?
X/3 - 14 = -2
Answer:
x = 36
Step-by-step explanation:
x/3 - 14 = -2
x - 42 = -6
x = -6 + 42
x = 36
Hope this helps! :)
Answer:
x= 36
Step-by-step explanation:
X/3 - 14 = -2
Add 14 to each side
X/3 - 14+14 = -2+14
x/3 = 12
Multiply each side by 3
x/3 * 3 = 12*3
x = 36
In a survey of 1309 people, 825 people said they voted in a recent presidential election. Voting records show that 60% of eligible voters actually did vote. Given that 60% of eligible voters actually did vote,
(a) find the probability that among 1309 randomly selected voters, at least 825 actually did vote.
(b) What do the results from part (a) suggest?
Answer:
a) P(X>825)
b) This low value of probability of the sample outcome (as 825 voters actually did vote) suggests that the 60% proportion may not be the true population proportion of eligible voters that actually did vote.
Step-by-step explanation:
We know a priori that 60% of the eligible voters did vote.
From this proportion and a sample size n=1309, we can construct a normal distribution probabilty, that is the approximation of the binomial distribution for large samples.
Its mean and standard deviation are:
[tex]\mu=n\cdot p=1309\cdot 0.6=785.4\\\\\sigma =\sqrt{np(1-p)}=\sqrt{1309\cdot 0.6\cdot 0.4}=\sqrt{314.16}=17.7[/tex]
Now, we have to calculate the probabilty that, in the sample of 1309 voters, at least 825 actually did vote. This is P(X>825).
This can be calculated using the z-score for X=825 for the sampling distribution we calculated prerviously:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{825-785.4}{17.7}=\dfrac{39.6}{17.7}=2.24\\\\\\P(X>825)=P(z>2.24)=0.0126[/tex]
This low value of probability of the sample outcome (as 825 voters actually did vote) suggests that the 60% proportion may not be the true population proportion of eligible voters that actually did vote.
3/(2x-1)+4=6x/(2x-1)
X=?
A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s equals negative 16 t squared plus 256 t. After how many seconds will the ball be 1008 feet from the ground?
Answer:
7 seconds
Step-by-step explanation:
Given the height equation of the motion;
s = -16t^2 + 256t
At s = 1008 ft
The equation becomes;
1008 = -16t^2 + 256t
16t^2 - 256t + 1008 = 0
Solving the quadratic equation for t;
Factorising, we have;
16(t-7)(t-9) = 0
t = 7 or t = 9
When the ball is going up it would reach the given height at time t = 7 seconds.
When it is coming down it would reach the given height at time t = 9 seconds.
how do you graph y=–7/3x+2. PLEASE HELP ME
Graph the line using the slope and y-intercept, or two points.
Slope: -7/3
y-intercept: 2
Please mark me as brainliest if possible. Stay safe and God bless you!!
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- Eli
What is the solution to the inequality below?
x < 5
A. x< 25 or x>-25
B. x < 25 or x>0
O C. x< 25 and x > 0
O D. x < 25 and x>-25
Answer:
C. x < 25 and x ≥ 0
Step-by-step explanation:
Fastest and easiest way to do this is to graph the inequality and find out the lines.
PLEASE ANSWER U NEED HELP!! determine which numbers The equations need to be multiplied by to form opposite terms of the y variable. 3x - 1/4y equals 15 2/3x - 1/6y equals 6 which number should be the first equation be multiplied by? which number should the second equation be multiplied by?
Answer:
4 -6
Step-by-step explanation:
have a great day!
Multiply the first equation by 2/3 and the second equation by -1.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
3x - (1/4)y = 15
(2/3)x - (1/6)y = 6
Multiply the equation 1 by 2/3, then we have
(2/3) · 3x - (2/3) · (1/4)y = (2/3) · 15
x - (1/6)y = 10
Multiply the equation 2 by -1, then we have
(-1) · (2/3)x - (-1) · (1/6)y = (-1) · 6
- (2/3) x + (1/6)y = - 6
Multiply the first equation by 2/3 and the second equation by -1.
More about the solution of the equation link is given below.
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A baseball card collector buys and opens 360 packs of 1989 Fleer baseball cards. He is told that there is a 2.3% chance of anyone pack containing the coveted Billy Ripken error card. Find the mean and standard deviation of the random variable "number of Billy Ripken error cards ound", where n-360
Answer:
Mean: 8.28
Standard deviation: 2.84
Step-by-step explanation:
This random variable "number of Billy Ripken error cards found" can be described by the binomial distribution, with sample size n=360 (number of packs) and probability of success p=0.023 (probabillity of a pack containing the coveted Billy Ripken error card).
Then, the mean and standard deviation are calculate as for the binomial distribution:
[tex]\mu=np=360\cdot 0.023=8.28\\\\\sigma=\sqrt{np(1-p)}=\sqrt{360\cdot 0.023\cdot 0.977}=\sqrt{8.08956}\approx2.84[/tex]
which of the following is the correct factorization of the trinomial below?
-7x^2 + 5x + 12
a. 7(x+1) (-x + 12)
b. -1 (7x - 12) (x+1)
c. (-7x + 12) (x - 1)
d. -7 (x - 6) (x+1)
Answer:
The answer is option B.
Hope this helps you
Answer:
The answer is B
Step-by-step explanation:
Use the Pythagorean theorem to calculate the diagonal of a TV is it's length is 36 inches and its width is 15 inches. Round your final answer to one decimal place.
Answer:
39 inches
Step-by-step explanation:
sqrt(15^2 + 36^2) = 39
Express the confidence interval 0.555 less than 0.777 in the form Modifying above p with caret plus or minus Upper E.
Complete Question
Express the confidence interval 0.555 less than p less than 0.777 in the form Modifying above p with caret plus or minus Upper E.
Answer:
The modified representation is [tex]\r p \pm E = 0.666 \pm 0.111[/tex]
Step-by-step explanation:
From the question we are told that
The confidence interval interval is [tex]0.555 < p < 0.777[/tex]
Now looking at the values that make up the up confidence interval we see that this is a symmetric confidence interval(This because the interval covers 95% of the area under the normal curve which mean that the probability of a value falling outside the interval is 0.05 which is divided into two , the first half on the left -tail and the second half on the right tail as shown on the figure in the first uploaded image(reference - Yale University ) ) which means
Now since the confidence interval is symmetric , we can obtain the sample proportion as follows
[tex]\r p = \frac{0.555 + 0.777}{2}[/tex]
[tex]\r p =0.666[/tex]
Generally the margin of error is mathematically represented as
[tex]E = \frac{1}{2} * K[/tex]
Where K is the length of the confidence interval which iis mathematically represented as
[tex]K = 0.777 -0.555[/tex]
[tex]K = 0.222[/tex]
Hence
[tex]ME = \frac{1}{2} * 0.222[/tex]
[tex]ME = 0.111[/tex]
So the confidence interval can now be represented as
[tex]\r p \pm E = 0.666 \pm 0.111[/tex]
A survey was conducted to determine the amount of time, on average, during a given week SCAD students spend outside of class on class work (projects, homework, and studying). The data shows: 5, 7, 11, 14, 18, 22 (in hours). Calculate the standard deviation by using the appropriate formula. Round your answer to three decimal places.
Answer:
Standard Deviation = 5.928
Step-by-step explanation:
a) Data:
Days Hours spent (Mean - Hour)²
1 5 61.356
2 7 34.024
3 11 3.360
4 14 1.362
5 18 26.698
6 22 84.034
6 days 77 hours, 210.834
mean
77/6 = 12.833 and 210.83/6 = 35.139
Therefore, the square root of 35.139 = 5.928
b) The standard deviation of 5.928 shows how the hours students spend outside of class on class work varies from the mean of the total hours they spend outside of class on class work.
I NEED HELP PLEASE, THANKS! :)
Answer:
7/2
Step-by-step explanation:
notice that if you substitute x by five you get 0/0 wich a non-defined form
The trick is to simplify by x-5
(x²-3x-10)/(2x-10)You get using the Euclidien division : x²-3x-10 = (x-5) (x-2)so : (x-2)(x-5)/2*(x-5) = (x-2)/2 substitute x by 5 to get 7/2 [tex]\lim_{x\to \5} \frac{x^{2} -3x-10}{2x-10}[/tex] = 7/2Hey there! :)
Answer:
[tex]\lim_{x \to 5} = 7/2[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\frac{x^{2}-3x-10 }{2x-10}[/tex]
Factor the numerator and denominator:
[tex]\frac{(x - 5)(x+2) }{2(x-5)}[/tex]
'x - 5' is on both the numerator and denominator, so it gets cancelled out and becomes a "hole".
This means that at x = 5, there is a hole. There is a limit at x ⇒ 5. Find the hole by plugging 5 into the simplified equation:
[tex]\frac{((5)+2) }{2}[/tex] = 7/2
Therefore:
[tex]\lim_{x \to 5} = 7/2[/tex]
Flying against the wind, a jet travels 3000 miles in 4 hours. Flying with the wind, the same jet travels 7500 miles in 6 hours. What is the rate of the jet in still air and what is the rate of the wind? g
Answer:
The rate of the jet in still air is 1125 miles per hour, and the rate of the wind is 375 miles per hour.
Step-by-step explanation:
Flying against the wind, the speed of the airplane is 750 miles per hour (3000/4), while flying with a downwind, its speed is 1500 miles per hour (7500/6). Therefore, the difference between the two speeds is 750 miles per hour, so since the distance traveled is the same, the midpoint between the two speeds is 375 miles per hour. Then, without wind, the plane would travel the same distances at a speed of 1125 miles per hour.
In conclusion, the rate of the jet in still air is 1125 miles per hour, and the rate of the wind is 375 miles per hour.