Answer: [tex]\displaystyle \frac{10}{3}\left(\frac{1}{3}\right)^{n-1}[/tex]
======================================================
Explanation:
a = 10/3 is the first term
r = 1/3 is the common ratio
Multiply each term by r = 1/3 to get the next term.
Example:
(10/3)*(1/3) = 10/9
We then plug those two items into the formula
[tex]a_n = a(r)^{n-1}[/tex]
to end up with the answer shown above.
The value of n is a positive integer.
The probability generating function of the dis- crete nonnegative integer valued random variable X having probability mass function pj, j = 0, is defined by ø(s) = E[s] =Σp;si j=0 Let Y be a geometric random variable with param- eter p 1 s, where 0 < s < 1. Suppose that Y is independent of X, and show that ø(s) = P{XY}
The probability generating function of a discrete nonnegative integer valued random variable X is defined by ø(s) = E[s] = Σp;si j=0, where pj is the probability mass function of X. P{XY} = P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij,Therefore, ø(s) = Σ pi pj sij = P{XY}
In this problem, we are also given a geometric random variable Y with parameter p 1 s, where 0 < s < 1. Y is independent of X. To show that ø(s) = P{XY}, we must show that the two expressions are equal.
First, we note that the probability of X and Y being equal to i and j, respectively, is given by P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij. This is because the probability of X being equal to i is pi, and the probability of Y being equal to j is pj (where p is the parameter of the geometric distribution). Since sij is the product of i and j, the probability of both X and Y being equal to i and j, respectively, is pi pj sij.
We can now substitute this expression into the probability generating function for X. We have that ø(s)
= E[s] = Σp;si j=0
= Σ pi pj sij
= P{XY}
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In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.35 and SSR = 4.18. What is the error sum of squares?
Multiple Choice
1.07
0.17
0.320
8.74
In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.35 and SSR = 4.18. What is the error sum of squares is 0.17.
What do you meant by squares?A square is a figure with four equal sides and four right angles. It's a popular shape for windows and record albums, among many other things.Square has many different metaphorical uses. Old towns had square open areas for meetings, so now "town square" means meeting place, even if it's not shaped exactly like a square. If you settle your debts, you square them, and if someone calls you a square, they mean you're boring, rule-abiding, and lame. In math, a square is the product of something multiplied by itself. If you square your plans with someone, you line them up.To learn more about square refer to:
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A drug-testing laboratory produces false negative results 2% of the time and false positive results 5% of the time. Suppose that the laboratory has been hired by a company in which 10% of the employees use drugs.
a) If an employee tests positive for drug use, what is the probability that they actually use drugs?
b) What is the probability that a nondrug user will test positive for drug use twice in a row?
c) What is the probability that someone who tests positive twice in a row is not a drug user?
a) The probability that they actually use drugs, if an employee tests positive for drug use is 69%
b) The probability that a nondrug user will test positive for drug use twice in a row is 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user is 23%
What is Bayes' theorem in probability?Based on past knowledge of circumstances that might be relevant to the event, Bayes' theorem estimates the likelihood of an event.
The theorem explains how a degree of belief, stated as a probability, should logically alter to account for the presence of relevant data using Bayesian probability interpretation.
The question state that
Pr(D) = 0.10
Pr(D') = 0.90
Pr (P/D) = 0.98 ( (2% False negatives means for drug users, 2% will get a negative result, so 98% will get positive result)
Pr(P/D') = 0.05
a) The probability that they actually use drugs, if an employee tests positive for drug use Pr(D/P) = Pr(D)*Pr (P/D) / Pr(D)*Pr (P/D)+Pr(D')*Pr(P/D')
⇒ Pr(D/P) = (0.10*0.98)/(0.10*0.98 + 0.90*0.05)
⇒ Pr(D/P) = 0.098/(0.098+0.045)
⇒ Pr(D/P) = 0.098/0.143
⇒ Pr(D/P) ≈ 0.6853
⇒ Pr(D/P) ≈ 69%
b) The probability that a nondrug user will test positive for drug use twice in a row Pr (P*2/D') = Pr(P/D')*Pr(P/D')
⇒ Pr (P*2/D') = 0.05*0.05
⇒ Pr (P*2/D') = 0.0025
⇒ Pr (P*2/D') = 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user Pr (D'/P*2) = Pr(D')*Pr (P*2/D') / Pr(D')*Pr (P*2/D')+Pr(D)*Pr (P*2/D)
⇒ Pr (D'/P*2) = (0.90*.0.05²)/(0.90*0.05²+0.10*0.98²)
⇒ Pr (D'/P*2) = 0.00225/ 0.00225+0.09604
⇒ Pr (D'/P*2) = 0.00225/0.09829
⇒ Pr (D'/P*2) ≈ 0.2289
⇒ Pr (D'/P*2) ≈ 23%
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Jaquan bought an RV for $95,000. He made a down payment of $72,000 and paid $650 monthly for 60 months. What's the total finance charge?
find the 25th, 50th, and 75th percentile from the following list of 32 data. please enter exact answers.
the 25th, 50th, and 75th percentile from the following list of 32 data are 25th percentile: 13 , 50th percentile: 21 , 75th percentile: 29.
To find the 25th percentile:
25th percentile: 25% of 32 = 8th number = 13
Count the total number of values in the data set, which is 32
Calculate 25% of 32, which is 8
Count 8 numbers from the beginning of the list and the 25th percentile is the 8th number, which is 13
To find the 50th percentile:
50th percentile: 50% of 32 = 16th number = 21
Count the total number of values in the data set, which is 32
Calculate 50% of 32, which is 16
Count 16 numbers from the beginning of the list and the 50th percentile is the 16th number, which is 21
To find the 75th percentile:
75th percentile: 75% of 32 = 24th number = 29
Count the total number of values in the data set, which is 32
Calculate 75% of 32, which is 24
Count 24 numbers from the beginning of the list and the 75th percentile is the 24th number, which is 29
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PLEASE HELP ASAP!!!
A machine at a bakery poured out flour for 16 minutes. At the end of that time, the machine was empty. The graph shows the amount of flour (in grams) remaining in the machine versus time (in minutes). Find the range and the domain of the function shown.
Answer:
R = 0≤ y ≤ 800
D = 0≤ x ≤ 16
.
.
.
.
Select the correct answer. When using the binomial formula, which of the following is a correct step in the expansion of (x + y)? 4(4-1)(4-2) (4-³)³ + 31 24 + 24 + 24 + ○ D. x + Ο Α. OB. C. x(4-¹)y + 4(4-¹) (4-2) y² + 2(4-¹)y + 4(4-¹) x(4-2) y² + x(4-1)y + 4(4-¹)(4-2)² + (4-1)(4-2)(4-3)3 + 4(4-1)(4-2)(4-3) (4-4) z 4(4 − 1)(4 − 2)(4 — 3) (4-4) - 3 4(4-1)(4-2) (4-3)³ + 3 4(4-1)(4-2)(4-3) (4-4) 41 4(4 − 1)(4 − 2)(4 — 3) (4-4) (4-1)y + 4(4-1)(4-2) (4-3)³ +
Hi, Can anyone help me solve this please?
Ma'am there is nothing to solve...
Emoji::<
Answer:
Step-by-step explanation:
Yes there is literally nothing to solve:(
Which of the following represents a nonlinear function?
y=x²
y=x
y=-2 x
y=5 x+7
The equation that represents a non linear function is y = x² , the correct option is (a) .
In the question ,
four functions are given ,
we have to select the option that is non linear ,
we know that ;
A Linear Function is an equation in which the the highest degree of the equation is 1 , and the graph is a straight line . and
A Non Linear Function ,is an equation in which the highest degree of the equation is more than 1 , and the graph is not a straight line .
So , from the given options
we can see that all the options have degree 1 except the equation y = x² which has highest degree 2 .
Therefore , The Non Linear Function is (a) y = x² .
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Last year, Alan opened an investment account with $7200. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in his account at the end of the year?
Answer:
1) $468
2) 7668
Step-by-step explanation:
1) 6.5% of 7200 is 468. Therefore, this is the amount it had increased.
2) 7200+468=7668 Total for the end of the year
A rivet is to be inserted into a hole. If the standard deviation of hole diameter exceeds 0.02 mm, there is an unac- ceptably high probability that the rivet will not fit. A random sample of n = 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s = 0.016 mm. (a) Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 mm? Calculate a P-value to draw conclusions. State any necessary assumptions about the underlying distribution of the data. (b) Construct a 95% lower confidence bound for o. (c) Use the confidence bound in part (b) to test the hypothesis.
Since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),
there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.
Given that;
H₀ : σ = 0.02
H₁ : σ > 0.02
The test statistics is;
X² = ( n-1 )s² / σ² = ( 15 - 1)(0.016)² / (0.02)²
= 0.003584 / 0.0004
= 8.96
degree of freedom
df = n - 1 = 15 - 1 = 14
For right tailed test, critical value at 0.01 level of significance is 29.141.
Now since our test statistics ( 8.96 ) is less than the critical value (29.141 ),
Therefore, there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.
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let $d$ be any positive integer not equal to $2, 5$ or $13$. show that one can find distinct $a,b$ in the set $\{2,5,13,d\}$ such that $ab-1$ is not a perfect square.
The statement given in the question holds true . We get this result after analyzing the given data set .
Given , hypothesis is ,
Let d be any positive integer not equal to2 , 5 or 13 .
Show that one can find distinct a , b in the set {2,5,13,d} such that ab-1 is not a perfect square.
Using the modular way to solve this question we get ,
d = 0 , 3 = | 4 |
Then , we get the result as ,
13d - 1 , which is not a perfect square.
d = 2|4|
we get , 2d -1
which again is not a perfect square.
Similarly after checking the value for all the possible cases , we will get the result that the hypothesis is correct.
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Describe and correct the error.
By midpoint segment theorem DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
A line segment that connects two midpoints of the sides of a triangle is called a midsegment.
DE is the midsegment of AB and AC.
AD≅BD and AE≅EC.
The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.
DE=1/2BC
5=1/2(10)
5=5
Hence, DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.
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with the given vertices.
4. E(-3, 3), F(1, 3), G (3, -3), H(-5, -3)
Answer:
sorry new don't understand the app
you are measuring a process, and you are given the following information: overall average: 131 population stdev: 5 sample size: 11 determine the upper control limit if your desired confidence interval is 99.73%. enter your answer to one decimal place. it's ok if you get a negative number; in that case, just enter the minus sign in front of it.
The upper control limit is 16.4 if our desired confidence interval is 99.73%.
What is Confidence interval?In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.
Given 131 population
Standard deviation = 5
sample size = 11.
mean = 131/11 = 11.9.
Determine the upper control limit if desired confidence interval is 99.73%
Confidence interval = sample mean ± margin of error
Upper limit = sample mean + margin of error.
Margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex]
Margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].
Value of z* for 99.73% confidence interval is 3.00.
So margin of error = 4.5.
Upper limit = 11.9 + 4.5
Upper limit = 16.4
If we want a confidence level of 99.73%, the top control limit is 16.4.
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what is a 500 doller diposet for 20 years witha intrest rate of 2%
The value of the amount will be $721.40.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
500 dollar deposit for 20 years with a interest rate of 2%.
Now,
We know that;
The formula for amount is,
⇒ [tex]A = P (1 + r)^n^t[/tex]
Where, A is total amount, P is principle amount, r is interest rate.
Here, We have;
P = $500
t = 20 years
r = 2%
Substitute all the values, we get;
⇒ [tex]A = P (1 + r)^n^t[/tex]
⇒ [tex]A = 500 (1 + 0.02)^2^0[/tex]
⇒ A = 500 × 1.02²⁰
⇒ A = 500 × 1.44
⇒ A = $721.40
Thus, The value of the amount = $721.40
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two events, a and b are independent if and only if . recall that a reorganization of the multiplication rule will yield . suppose for some events a and b, . which of the following statements is true of a and b? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a events a and b are independent since and . b events a and b are not independent, but they are mutually exclusive since . c events a and b are independent since ; however . d events a and b are not independent since and .
The two events a and b are independent if and only if (a) Events a and b are independent .
What are Independent Events ?
Two events A and B are said to be independents if the occurrence of event A does not affect the chance of occurrence of the other event B .
The probability of two independent events can be mathematically represented as P(A and B) = P(A) × P(B) .
So, we can conclude that , Two events, a and b are independent if and only if Events a and b are independent .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
Two events, a and b are independent if and only if
Which of the following statements is true of a and b?
(a) Events a and b are independent
(b) Events a and b are not independent, but they are mutually exclusive
(c) Events a and b are not independent since and .
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Hello can someone please help me find x. Im getting stuck. Thanks!
The value of the x is 3.26556.
What is the Intersecting Chord Theorem?
When two chords intersect each other inside a circle, the products of their segments are equal.
We have,
It is a little easier to see this in the diagram, each chord is cut into two segments at the point where they intersect.
One chord is cut into two line segments A(x+10) and B(x+1). The other is into segments C(x) and D(5x+1).
According to Intersecting Chord Theorem:
This theorem states that A×B is always equal to C×D no matter where the chords are.
A.B = C.D
(x+10) * (x+1) = (x) * (5x+1).
x² + x + 10x + 10 = 5x² + x
x² + x + 10x + 10 - 5x² - x = 0
-4x² + 10x + 10 = 0
using the Quadratic Formula where, a = -4, b = 10, and c = 10, we get
x=−0.765564
x = 3.26556
Hence, the value of the x is 3.26556.
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Select all of the equations for the line that passes through (5, −2) and (0, 18).
Multiple select question.
A)
y+2=−4(x−5)
B)
x+4y=−12
C)
y−6=−4(x+1)
D)
y=−4x−12
E)
y=−4x+18
F)
4x+y=18
Answer:
Need more info please
Step-by-step explanation:
let c and d be disjoint compact subspaces of the hausdorff space x. then there exist disjoint open sets u and v containing c and d, respectively.
The statement "let c and d be disjoint compact subspaces of the Hausdorff space x and then there exist disjoint open sets u and v containing c and d, respectively." is proved.
Here we have given the let A and B be disjoint compact subspaces of the Hausdorff space X.
And we have to prove the statement.
According to the given question, let us consider that x be an arbitrary coordinate of A and here the points of x isn't in Y because A and B are disjoint.
Then according to Lemma 26.4 disjoint open sets Ux and Vx such that x Î Ux and Ux contain B.
Here the collection {Ux} is a covering of A by sets open in X.
And the finite collection of them {U1, ..,Un} covers A because A is compact.
Here the open set U = U1 U....U Un contains A and it is disjoint from
V = V1 I.....I Vn that contains B because it's the finite intersection of the corresponding open sets containing.
Therefore, here there exists disjoint open sets U and V containing A and B, respectively.
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Armando divided 6 and 258
Answer:
43
Step-by-step explanation:
258 divided by 6 equals 43
Look below
Armando divided 6 and 258
258 is the bigger number, so we will keep that on the right, and then add the dividing symbol. Next, we will add the 6. That should look like this:
258÷6
then just put it on a calculator and you get the answer 43. hope that helps
write an equation of the line that passes through the given point and is parallel to the given line. (see example 2.) 7. (0, 2); x
Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.
What is EQUATIONS?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
Equations come in two varieties: identities and conditional equations.
According to our question-
Given line: 2x+5y−7=0
the mid - point of the line segment joining point (2,7) and (−4,1) is
( 2(2−4 )2(7+1))=(−1,4)
the equation of the line will be
y−y 1=m(x−x 1)y−4=( 5−2 )(x+1)
5y−20=−2x−2
2x+5y=18
Hence, Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.
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Liam accidentally charged more on his debit card than he had in his checking account. His balance is now -$12.75. He is charged a $10 overdraft fee each day his account balance is below $0. He makes no other withdrawals or deposits. Which equation accurately represents his balance, y, after x days?
Answer:
The equation that accurately represents Liam's balance, y, after x days is y = -12.75 - 10x.
This equation takes into account the fact that Liam's balance is already -$12.75 and that he is charged a $10 overdraft fee each day his balance is below $0. As the number of days, x, increases, the total amount of overdraft fees he is charged will also increase, resulting in a decrease in his balance.
For example, if Liam's balance is -$12.75 after 0 days, his balance will be -$22.75 after 1 day (y = -12.75 - 10(1) = -22.75), and his balance will be -$32.75 after 2 days (y = -12.75 - 10(2) = -32.75).
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean ?, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses H0: ? = 115 Ha: ? ? 115. The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students. Based on the P-value computed choose the correct choice. Group of answer choices the data are statistically significant at level ? = .05 and at level ? = .01. the data are not statistically significant at level ? = .05 and not statistically significantat level ? = .01. the data are statistically significant at level ? = .05, but not at level ? = .01 the data are statistically significant at level ? = .01, but not at level ? = .05
The data are statistically significant at level = 0.05, but not at level = 0.01.
Given-
H0: μ = 115
HA: μ ≠ 115
The sample mean = 120
The standard deviation = 25
Standard error of mean 2.5
Solution-
If z = (xbar- μ ) / SE
Then the solution would be
z = (120-115) / 2.5
z = 2
P of the value = 2 P( z > 2) = 2(0.0228) = 0.0456 is the statistically significant level.
Therefore the answer is technically at .05 level of significance.
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In evaluating a double integral over a region D. a sum of iterated integrals was obtained as follows: Sketch the region D and express the double integral as an iterated integral with reversed order of integration.
Let D be the region bounded by the lines y = 0, y = x, x = 1, and x = 2. In order to express the double integral as an iterated integral with reversed order of integration, we first need to sketch the region D.
The double integral could be expressed as an iterated integral with reversed order of integration as follows:
[tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex]
The region is bounded by the lines y = 0, y = x, x = 1, and x = 2. This forms a triangle-like shape with 1 and 2 being the x-coordinates of the vertices and y = 0 being the base of the triangle. Then, we can express the double integral as: [tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex], where the order of integration is reversed from the original double integral. This means that first we are integrating with respect to y from 0 to x, and then we are integrating with respect to x from 1 to 2.
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Question
Newton's Law of Universal Gravitation: The gravitation attraction, f , between two objects of masses x and y is proportional to the product of the masses and inversely proportional to the square of the distance, d , between the objects.
Write an equation for the constant of variation, k, in terms of f, x, y, and d.
Complete the equation in the space below (do not enter “k=“)
The required equation for the variation of k is given as k = Fd² / xy.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Newton's Law of Universal Gravitation states that the gravitational attraction, f, between two objects with masses x and y is proportional to the product of their masses and inversely proportional to the square of their distance, d.
So,
F ∝ x × y - - - - (1)
And
F ∝ 1 / d² - - - - - (2)
Combining equations 1 and 2
F ∝ xy / d²
Or
F = kxy / d²
Now,
Formulate the above expression with subject to constant k.
K = Fd² / xy
Thus, the required equation for the variation of k is given as k = Fd² / xy.
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what is the area of this triangle
30POINTS
Answer:
81.74 cm²
Step-by-step explanation:
Use tan(x) to find x
tanθ = opposite/adjacent
tan(36) = x/15
15tan(36) = x
area of triangle = [tex]\frac{1}{2}[/tex]*b*h
[tex]\frac{1}{2}[/tex]*15tan(36)*15 = 81.74 cm² (2 d.p.)
Round the answer to the nearest tenth please
Answer:
19.9 m
Step-by-step explanation:
Cone: r= 1m Height= 2m (You will use the radius for the Cylinder)
1/3 x π x 1^2 × 2 = 2.0943951023932
2.0943951023932 x 2 = 4.1887902047864 (Just use the hundreths place if writing down.)
Cylinder: r= 1m Height= 5m
π x 1^2 x 5 = 5π = 15.707963267949
Now add both together then round to tenths.
4.1887902047864 + 15.707963267949 = 19.8967534727354
(Remember use hundreths place if writing down)
19.8967534727354 --> 19.9 m
Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6 ?
A
2/36
B
3/36
C
3/15
D
2/9
E
4/6
Answer:
e
Step-by-step explanation:
because it's number is common
Your company creates haircare and skincare products in large quantities. You have a cylindrical storage tank that’s going to be used for a new batch of shampoo. The tank is 170 feet across in diameter and 60 feet high.
Use this formula sheet for your calculations.
Part A
To calculate the volume of this cylindrical tank, what preliminary calculations must be done with the information given in the problem?
To calculate the volume of a cylindrical tank, you will need to use the formula for the volume of a cylinder, which is:
V = πr^2h
Where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
To use this formula, you will need to first calculate the radius of the base of the tank. To do this, you will need to divide the diameter of the tank (170 feet) by 2.
Once you have calculated the radius, you can plug the value into the formula along with the height of the tank (60 feet) to find the volume of the tank.
Answer:
Step-by-step explanation:
height of the tank= 60 feet
diameter = 170 feet.
as we know, radius = 2 *diameter
therefore radius = diameter /2
= 170/2
=85 feet
volume of cylinder = πr²h
π =3.14
= 3.14 ×85×60
=10927.2 feet²