Answers
Step-by-step explanation:
Oke so basically we can calculate volume like this
1st: v=
\( \frac{4}{3} \times \pi \times r {3}^{?} \)
Which equals:
\( \frac{4}{3} \times 3 \times {3}^{3} and \: it \: equals > 108 {\pi}^{3} \)
Related Questions
Prove : If p ≥ 5 is a prime number, show that p^2 + 2 is composite. (Hint: p takes one of the forms 6k + 1 or 6k + 5)
Answers
that if p ≥ 5 is a prime number, then p^2 + 2 is composite.
we can start by using the hint provided, which tells us that p takes one of the forms 6k + 1 or 6k + 5. If we consider these two forms separately and prove that p^2 + 2 is composite for each of them, then we will have shown that the statement is true for all values of p ≥ 5.
First, let's consider the case where p = 6k + 1. In this case, we can write p^2 + 2 as (6k + 1)^2 + 2 = 36k^2 + 12k + 3. Simplifying this expression, we get 3(12k^2 + 4k + 1). Since 3 is a factor of this expression, we know that p^2 + 2 is composite.
Now let's consider the case where p = 6k + 5. In this case, we can write p^2 + 2 as (6k + 5)^2 + 2 = 36k^2 + 60k + 27. Simplifying this expression, we get 3(12k^2 + 20k + 9). Since 3 is a factor of this expression, we know that p^2 + 2 is composite.
Therefore, we have shown that if p ≥ 5 is a prime number, then p^2 + 2 is composite, regardless of whether p takes the form 6k + 1 or 6k + 5.
we have proven the statement that if p ≥ 5 is a prime number, then p^2 + 2 is composite by considering two cases and showing that the expression is divisible by 3 in both cases.
To learn more about divisible visit:
https://brainly.com/question/21416852
#SPJ11
Thus, we have proved that if p is a prime number greater than or equal to 5, then p^2 + 2 must be composite.
Let p be a prime number greater than or equal to 5. We want to show that p^2 + 2 is composite.
Assume for the sake of contradiction that p^2 + 2 is a prime number.
Then p^2 + 2 cannot be divisible by any prime number less than or equal to p, since if it were, then p^2 + 2 would be composite by definition.
Now consider the two possible forms for p: 6k + 1 or 6k + 5, where k is a non-negative integer.
If p takes the form 6k + 1, then we have:
p^2 + 2 = (6k + 1)^2 + 2
= 36k^2 + 12k + 3
= 3(12k^2 + 4k + 1)
Notice that 12k^2 + 4k + 1 is an integer, so p^2 + 2 is divisible by 3. Since p^2 + 2 is assumed to be prime, this contradicts our assumption that it cannot be divisible by any prime number less than or equal to p.
Now consider the case where p takes the form 6k + 5. Then we have:
p^2 + 2 = (6k + 5)^2 + 2
= 36k^2 + 60k + 27
= 3(12k^2 + 20k + 9)
Notice again that 12k^2 + 20k + 9 is an integer, so p^2 + 2 is divisible by 3. This again contradicts our assumption that it cannot be divisible by any prime number less than or equal to p.
Therefore, we have shown that if p is a prime number greater than or equal to 5, then p^2 + 2 must be composite.
Know more about the prime number
https://brainly.com/question/145452
#SPJ11
It cost me $12 for 6 pounds of oranges.
How much is the cost per pound of oranges?
Answers
Answer:
$2 per pound.
Step-by-step explanation:
Find the area of the triangle given the base and height Base 14 feet height = 13 feet
a. 60 ft?
b. 89 ft?
c. 98 ft?
d. 91 ft?
Answers
Answer:
91
Step-by-step explanation:
how do you do that 52 + 19 = 71
Answers
Answer:
1
52
+ 19
____
71
Step-by-step explanation:
add 2+9 and get 11
carry the one
add 1+1+5 and get 7
71
Two major circus acts have agreed to perform at the stadium if they can get seven consecutive days each. On average, each performance will provide a profit margin of $35,000 for the stadium. How much will the stadium's profit margin be if it signs both acts to one-week deals?
A. $100,000
B. $250,000
C. 490,000
D. 500,000
Answers
The stadium's profit margin will be $490,000 if it signs both acts to one-week deals.
Since each major circus act will perform for seven consecutive days, the stadium will have a total of 14 performance days (7 days for each act). Each performance provides a profit margin of $35,000 for the stadium. To calculate the stadium's profit margin if it signs both acts, we need to multiply the profit margin per performance by the total number of performances.
Profit per performance = $35,000
Total number of performances = 14 (7 days for each act)
To find the stadium's profit margin, we multiply the profit per performance by the total number of performances:
Profit margin = $35,000 * 14 = $490,000
Therefore, the stadium's profit margin will be $490,000 if it signs both acts to one-week deals. The correct answer is option C: $490,000.
Learn more about profit here:
https://brainly.com/question/29785257
#SPJ11
NEED HELP ASAP
Is 100 part of the solution?
1.25(x+16)_> 140.75
Answers
100 is part of the solution to the inequality 1.25(x + 16) ≥ 140.75.
What is an inequality equation?
An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
To determine if 100 is part of the solution to the inequality 1.25(x + 16) ≥ 140.75, we can substitute 100 for x and see if the inequality holds true.
1.25(x + 16) ≥ 140.75
1.25(100 + 16) ≥ 140.75
1.25(116) ≥ 140.75
145 ≥ 140.75
Since 145 is greater than or equal to 140.75, the inequality holds true when x = 100.
Therefore, 100 is part of the solution to the inequality 1.25(x + 16) ≥ 140.75.
To know more about inequality equations visit:
https://brainly.com/question/30238989
#SPJ1
Determine whether the geometric series is convergent or divergent. [infinity] en 4n − 1 n = 1 convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)
Answers
The geometric series is divergent and The sum of the series is: S = e/3/(1-1/3) = e/2
The given series is: ∑ (en/(4n-1)), n=1 to infinity
To determine if this series is convergent or divergent, we can use the ratio test:
= lim n→∞ \(|(en+1/(4(n+1)-1))/(en/(4n-1))|\)
= lim n→∞ \(|en+1(4n-1)/en(4n+3)|\)
= lim n→∞ \(|(4n-1)/(4n+3)|\)
Since e is a positive constant, it does not affect the convergence or divergence of the series. Taking the limit, we get:
lim n→∞ \(|(4n-1)/(4n+3)|\)
= 1
Since the limit is equal to 1, the ratio test is inconclusive. We need to use another test to determine the convergence or divergence of the series.
Next, we can try the root test:
= lim n→∞ \((en/(4n-1))^(1/n)\)
= lim n→∞ \(e^(1/n) / (4-1/n)^(1/n)\)
= 1/4
Since the limit is less than 1, the series converges by the root test.
To find the sum of the series, we can use the formula for the sum of a convergent geometric series:
S = a/(1-r)
where a is the first term of the series and r is the common ratio.
The first term is e/(4-1) = e/3. The common ratio is e/(4n-1) multiplied by its inverse, which is (4n-1)/e. Simplifying, we get:
r = \((4n-1)/(3(4n)) = (1-1/(4n))/(3/4)\)
Taking the limit as n approaches infinity, we get:
lim n→∞ r = 1/3
Therefore, the sum of the series is: S = e/3/(1-1/3) = e/2
For such more question on divergent:
https://brainly.com/question/30904030
#SPJ11
Helpp ASAP I’m timed I give Brainly things so hurry;)))
Answers
Answer: Its A
Step-by-step explanation: The square root of 88 is 9.3.... add 2/5 and you get 9.78083151 and its not rational
Answer this set of easy math questions to get a good rating and to be the brainiest (check the attached file)
Answers
Answer:
its easy
Step-by-step explanation:
so basically,
The distance between two lines measured along a perpendicular line to the line is always the same.
Answers
The distance between two lines measured along a perpendicular line to the line is always the same is called as equidistant .
Given :
The distance between two lines measured along a perpendicular line to the line is always the same.
What is Equidistant ?
Distances between two points from a common points are equal then it is called as equidistant .
Formulas :
Midpoint = ( x1 + x2 / 2 , y1 + y2 / 2 )
Distance = \(\sqrt{(x2 - x1 )^2 - (y2 - y1)^2 }\)
These are two main formulas are used to find whether equidistant or not.
Learn more about the perpendicular here:
https://brainly.com/question/29268451
#SPJ4
PLEASE SHOW WORK A coffee distributor needs to mix a(n) Gualtemala Antigua coffee blend that normally sells for $10.30 per pound with a Tanzanian coffee blend that normally sells for $13.80 per pound to create 60 pounds of a coffee that can sell for $12.46 per pound. How many pounds of each kind of coffee should they mix? Answer: They must mix ________ pounds of the Gualtemala Antigua Blend ________pounds of the Tanzanian Blend. (Round your answers to the nearest whole number of pounds.)
Answers
Answer:
23 pounds of the Gualtemala Antigua Blend and 37 pounds of the Tanzanian Blend
Step-by-step explanation:
you need to make a system of equations to solve this.
First lets make x be the pounds of Gualtemala Antigua coffee blend and y the pounds of Tanzanian coffee blend
we know we need 60 pounds total so first equation is
x+y=60
Next we will make an equation based on the money information
10.30x + 13.80y = 12.46(60)
10.30x + 13.80y = 747.60
So our system of equations is
x + y = 60
10.30x + 13.80y = 747.60
I will solve this by using substitution. first rewrite x+y=60 to y=60-x
now i can substitute that into the other equation for y and solve for x
10.30x + 13.80(60-x) = 747.60
10.30x + 828 -13.80x = 747.60
-3.5x + 828 = 747.60
-3.5x = -80.4
x = 23 (rounded from 22.9714 since they requested that)
now I can use this solution to solve for y by plugging into one of the original equations
x + y =60
23 + y =60
y = 37
Finally we can say that they must mix 23 pounds of the Gualtemala Antigua Blend and 37 pounds of the Tanzanian Blend.
Adi bought a bag for $25 and sold it at a loss of 10%. Find the selling price of the bag.
Answers
Answer:
The selling price of the bag is $22.5
Step-by-step explanation:
Buying Price = $25,
Selling Price = ?
Since they sold it at a loss of 10%,
So, they sold it for a price 10% less than the buying price,
or at 90% or 0.9 of the buying price,
so,
Selling Price = (0.9)(25) = $22.5
∛a² does anyone know it
Answers
The equivalent expression of the rational exponent ∛a² is \((a)^{\frac{2}{3}\).
What is a rational exponent?Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root.
So rational exponents (fractional exponents) are exponents that are fractions or rational expressions.
To determine the rational exponent equivalent to the expression given, we will apply the power rule of indices as shown below.
The given expression is ;
∛a²
The rational exponent is calculated as follows;
∛a² = \((a)^{\frac{2}{3}\)
Thus, based on exponent power rule, the given expression is equivalent to ∛a² = \((a)^{\frac{2}{3}\)
Learn more about rational exponents here: brainly.com/question/30603002
#SPJ1
The complete question is below:
Find the equivalent expression of the rational exponent ∛a². does anyone know it
1 Write the area as a sum:
2 Write the area as a product:
Answers
The area of the shape as a sum is 2x^2 + 5x + 2.
The area of the shape as a product is (x+2) (2x+1).
What is area of a shape?
A figure surrounded by a barrier is referred to as a shape. Numerous things in shapes like square, rectangle, round, etc. are all around us.
The space around by a shape's perimeter or boundary is known as its area. Using particular mathematical methods, we may determine the area of shape for various geometric shapes.
Area as a sum
For this, we will simply add all the values given in the figure
⇒ x^2 + x^2 + x + x + x + x + x + 1 + 1
⇒ 2x^2 + 5x + 2
So, the area of the shape as a sum is 2x^2 + 5x + 2.
Area as a product
The shape given is a rectangle
Area of a rectangle is length * width
Now, the length is x+2 and the width is 2x+1
So, the area is
⇒(x+2) (2x+1)
So, the area of the shape as a product is (x+2) (2x+1).
Hence, the area of the shape as a sum and as a product are obtained.
Learn more about area of a shape from the given link
https://brainly.com/question/25965491
#SPJ1
what are the three choices equivalent to 27^4/3
a. 4^3
b. (27^1/3)^4
c. 3^1/4
d. 81
e. 3 √4
f. (^3 √27)^4
Answers
the answers are B,D and F
Find the function that represents the relationship on the chart
Answers
Answer:
last one f(x) = 7x-5
Step-by-step explanation:
7(0)-5 = -5
7(1)-5 = 2
7(2) - 5 = 9
...
_____ is the tendency to emit repeatedly the same verbal or motor response to varied stimuli.
Answers
Answer:
perseveration
Step-by-step explanation:
The term you are looking for is "perseveration."
The scale factor of Triangle A to triangle B is 1:2 1/2
Answers
If the scale factor of Triangle A to Triangle B is 1:2, it means that the ratio of the corresponding sides of the two triangles is 1:2.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
If the scale factor of Triangle A to Triangle B is 1:2, it means that the ratio of the corresponding sides of the two triangles is 1:2.
More specifically, it means that for any given pair of corresponding sides of Triangle A and Triangle B, the length of the side in Triangle B is twice as long as the length of the corresponding side in Triangle A.
For example, if Triangle A has sides of length 3, 4, and 5 units, and Triangle B is similar to Triangle A with a scale factor of 1:2, then the corresponding sides of Triangle B will have lengths of 6, 8, and 10 units.
Learn more about Scale factors here:
https://brainly.com/question/22312172
#SPJ1
When comparing two group means, the _____ refers to the number of scores free to vary once the means are known. A. null hypothesis B. research hypothesis C. statistical significance D. degree of freedom
Answers
When comparing two group means, the degree of freedom refers to the number of scores free to vary once the means are known. Correct option is D.
What is the degree of freedom?The degree of freedom (df) is the number of independent pieces of information available in a study that may be used to estimate the value of the population parameter in question.
In layman's terms, the degree of freedom is the number of independent pieces of information that can be used to calculate a population parameter estimate in a statistical study. The degree of freedom (df) refers to the number of scores free to vary once the means are known.
This implies that there are a certain number of scores (or values) in the study that can be changed freely without affecting the mean of the study's scores. For instance, if the study's mean score is 75, the degree of freedom is the number of scores that may be adjusted without altering the mean score of 75.
As a result, the degree of freedom represents the number of values that can be varied to get a given statistic, such as the mean.
To know more about degree of freedom, visit:
https://brainly.com/question/31178740#
#SPJ11
1. In the 400-meter race, Hade ran in 54.3 seconds, Porter ran in 55.6
seconds, Harry ran in 52.7 seconds and Andy ran in 54.1 seconds. Who is
the fastest? *
Answers
Answer:
Harry
Step-by-step explanation:
he has the lowest time
Is 43 square root plus 5 rational or irrational?
Answers
Answer:
square root of 43 is irrational and thus square root of 43 + 5 is also irrational.
Step-by-step explanation:
To know more about square root questions -
https://brainly.com/app/ask?q=squareroot
the number of employees for a certain company had been decreasing each year by 8%. If the company currently has 860 employees and this rate continues, fund the number of employees in 19 years.
Answers
Answer:
approximately 684 employees
Step-by-step explanation:
So this is an exponential equation since there is a dividing decrease, not just subtracting. The standard equation is,
\(y = a(b)^{x} \). \(a\) is initial value (860 employees) and \(b\) is the change \(-8%\) or \(0.92\). The \(x\) would be the period of time, \(19\). This equation would be \(y = 860(0.92)^{19} \).
After solving, the equation would become the following: \(y = 860(0.92)^{19} = 176.387242442≈176\). After subracting the number of lost employees from orginal employees (\(860-176=684\)), we see that the company will have approximately 684 employees left after 19 years.
The question is.. "The expression 5(3r - 10) means the product of 5 and the difference of three times r minus 10. If r = 4, the value of the expression is [?] This is 6th grade math and im kinda stuck here
Answers
Answer:
10
Step-by-step explanation:
5(3r - 10)
Let r = 4
5(3*4 - 10)
5( 12 - 10)
5 (2)
10
Answer:
10
Step-by-step explanation:
5(3r-10)
5(3(4)-10)
so forget the 5 and solve inside first
3*4= 12
12-10= 2
now bring the 5 back and multiply
5*2= 10
Jen Butler has been pricing Speed-Pass train fares for a group trip to New York Three adults and four children must pay $120. Two adults and three children must pay $85. Find the price of the adult's
ticket and the price of a child's ticket.
Answers
The adult's ticket will cost $20 while the children's ticket will cost $15.
To find the cost of the ticketsFrom the question, we have that;
Three adults and four children must pay $120
Representing this in an equation
Let adults = a
Let children = c
3a + 4c = 120 -----1
Also;
Two adults and three children must pay $85.
Representing this in an equation
2a + 3c = 85 -----2
From equation 1
a = \(\frac{120 - 4c}{3}\) ----- 3
Substituting a in equation 2
\(2 (\frac{120 - 4c}{3} ) + 3c = 85\)
\(\frac{240 - 8c}{3} + 3c = 85\)
Multiplying through by 3
240 - 8c + 9c = 255
c = 15
To find a when c = 15
Substitute c = 15 in equation 3
\(a = \frac{120 - 4(15)}{3}\)
\(a = \frac{120 - 60}{3}\)
a = 20
Therefore, the Adult's ticket is $20 and the children's ticket is $15.
To find more about cost: https://brainly.com/question/28147009
#SPJ1
if ₱60,000.00 was deposited in a bank and became ₱61,625.00 at the end of 150 days, find the interest rate using exact and ordinary days.
Answers
Days exactly: The rate of interest is 4.17%. The interest rate of amount is 4.21% on regular days.
I = P x R x T/365, where I is the interest, P is the principal, R is the rate, and T is the duration, can be used to determine the interest rate using exact days.
I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows: 625 = 60000 x R x 150/365. By multiplying both sides by 365/150, we may find R. As a result, R = 625 x 365/90000 = 4.17%.
I = P x R x T/360, where I is the interest, P is the principal, and R is the rate of return, can be used to get the interest rate using regular days.T stands for time, and R represents the rate. I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows:
625 = 60000 x R x 150/360. By dividing both sides by 360/150, we may find R. As a result, R = 625 x 360/90000 = 4.21%.
I = P x R x T/365, which means that R = I x 365/P x T = 625 x 365/60000 x 150 = 4.17%. Exact days
I = P x R x T/360 on typical days, which means that R = I x 360/P x T is 625 x 360/60000 x 150, or 4.21%.
Learn more about amount here
https://brainly.com/question/28970975
#SPJ4
Helppp find the slope of the line
Answers
Answer:
2
Step-by-step explanation:
change in y ÷ change in x
4÷2=2
help lol
The FOIL method helps you remember how to multiply each term in one ____________ by each term in the other ____________.
Answers
The FOIL method helps you remember how to multiply each term in one binomial by each term in the other binomial.
What is FOIL method?FOIL is the standard method of multiplying two binomials.
The word FOIL is an acronym for the four terms of the product:
First (“first” terms of each binomial are multiplied together)Outer (“outside” terms are multiplied—that is, the first term of the first binomial and the second term of the second)Inner (“inside” terms are multiplied—second term of the first binomial and first term of the second)Last (“last” terms of each binomial are multiplied)We try to explain this using an example.
\(= (2x+1)(3x+ 5)\\\\=(2x * 3x) + (2x * 5) + (1* 3x) + (1 *5)\\\\= 6x^{2} + 10x + 3x + 5\\\\= 6x^{2} + 13x + 5\)
Learn more about FOIL method here
https://brainly.com/question/27785127
#SPJ2
What does the x equal
Answers
I need to know the answer
Answers
The compound interval for the given interval is (-∞, ∞).
What is compound inequality?A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".
The given intervals are (-∞, -2] or [-3, ∞).
Now, the compound interval is (-∞, ∞)
Thus, the interval notation is -∞<x<∞
Therefore, the compound interval for the given interval is (-∞, ∞).
Learn more about the compound inequality here:
https://brainly.com/question/29004091.
#SPJ1
Emily has papayas and apples in a ratio of 6:100. How many apples does she have if
she has 3 papayas?
Answers
0.06 apples does she have if,She has 3 papayas.
If theIf the ratio is provided, how do you find the number?Calculate the item's quantity. P:Q = p/Q should be used as the format.
The total quantities for the two objects would be equal to the sum of "p" and "q."
If you can, reduce the complexity of the object ratios.
Final outcome is the ratio in its simplest form.
Much like fractions, ratios can be entirely simplified. Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.
Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.
Explanation:
6/100 = 0.06.
To learn more about ratio refer to:
https://brainly.com/question/12024093
#SPJ1
0.06 apples does she have if,She has 3 papayas.
If theIf the ratio is provided, how do you find the number?Calculate the item's quantity. P:Q = p/Q should be used as the format.
The total quantities for the two objects would be equal to the sum of "p" and "q."
If you can, reduce the complexity of the object ratios.
Final outcome is the ratio in its simplest form.
Much like fractions, ratios can be entirely simplified. Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.
Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.
6/100 = 0.06.
To learn more about ratio refer to:
brainly.com/question/12024093
#SPJ1