Answer:
125 times larger
Step-by-step explanation:
Let's say the radius is 3, just as an example.
The formula of a sphere is V=4/3 pi r^3
Then we can just substitute and test it out.
V=4/3 pi (3)^3
V=4/3 pi (27)
V=36 pi
Then multiple the previous radius by 5 to test it out.
V=4/3 pi (15)^3
V=4/3 pi (3375)
V=4500 pi
Then divide the bigger one by the smaller one
You will get 125, therefore it is 125 times larger
hope this helps :D
If the first term of a geometric sequence is positive, and r>1, then the sequnce increases?
Answer:
Yes, if the first term of a geometric sequence is positive and r > 1, then the sequence increases
Step-by-step explanation:
* Lets talk about the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric sequence:
# U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
# Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms, and n is the position of
the number in the sequence
- V.I.N: The position of the number means the place of the
number like first , second , third , .......... so n must be positive integer
* Lets talk about the ratio r
- If r greater than 1 and a is positive, the sequence increases lets
take some different examples to explain that
# If the first term is 2 and the ratio between the consecutive
terms is 3/2, then the first four terms in the sequence are
∵ a = 2
∵ r = 3/2 ⇒ greater than 1
∴ First = a = 2
∴ Second = ar = 2 × 3/2 = 3
∴ Third = ar² = 2 × (3/2)² = 2 × 9/4 = 9/2 4.5
∴ Fourth = ar³ = 2 × (3/2)³ = 2 × 27/8 = 27/4 = 6.75
- From the answers the sequence increases
# If the first term is 1/2 and the ratio between the consecutive
terms is 4/3, then the first four terms in the sequence are
∵ a = 1/2
∵ r = 4/3 ⇒ greater than 1
∴ First = a = 1/2
∴ Second = ar = 1/2 × 4/3 = 2/3 ⇒ 2nd > 1st
∴ Third = ar² = 1/2 × (4/3)² = 2 × 16/9 = 8/9 ⇒ 3rd > 2nd
∴ Fourth = ar³ = 1/2 × (4/3)³ = 2 × 64/27 = 32/27 ⇒ 4th > 3rd
- From the answers the sequence increases
* Now we are sure if the first term of a geometric sequence is
positive and r > 1, then the sequence increases
Answer:
The given statement is TRUE.
Step-by-step explanation:
We are given that if the first term of a geometric sequence is positive, and r>1, then the sequence increases which is true.
If the first term of any geometric sequence is positive and its common ratio ( r ) is greater than 1 then the sequence will always increase.
[tex] a _ n = a r ^ n - 1 [/tex]
Jefferson played basketball in the park. He started playing basketball at 1:15 P.M and played for 1 hour and 25 minutes. What time did Jefferson play basketball until?
Final answer:
Jefferson played basketball until 2:57 P.M.
Explanation:
To find out what time Jefferson played basketball until, we need to add the duration of time he played to the starting time.
First, we convert the duration of time from minutes to hours. Since there are 60 minutes in an hour, 1 hour and 25 minutes is equal to 1.42 hours.
Next, we add 1.42 hours to the starting time of 1:15 P.M. This gives us the ending time of 2:57 P.M.
Calculate the value of x to the nearest degree
Answer:
x = 61.3°
Step-by-step explanation:
We are given the radius r = 9 cm and arc length l = 9.7 cm. We need to find the angle x in degrees.
The formula used is:
l = rФ
In our case Ф = x. So re writing the formula:
l= rx
9.7 = 9 x
=> x = 9.7 / 9
x = 1.07 radians
Converting radians into degree we need to multiply the value of x by
180/π where π = 3.14
x = 1.07 * 180/3.14
x = 61.3°
Which kind of function best models the data in the table? Graph the data and write an equation to model the data.
a. linear; y = –x – 2
b. linear; y = x – 2
c. exponential; y = 3^x – 2
d. quadratic; y = x^2 – 2
Answer:
Option A, linear; y = -x - 2
Step-by-step explanation:
Example-
x = 3
y = ?
? = -3 - 2 (add the negative number if in the case of subtracting a negative number)
? = -5
An animal shelter uses 41 cups of food each day to feed the dogs and cats. Each dog eats 2 cups per day. The cats eat a total of 17 cups per day. The diagram represents this situation. Which equation can be used to find d, the number of dogs at the shelter?
Answer:
The equation that can be used to find d is [tex]2d+17=41[/tex]
[tex]d=12\ dogs[/tex]
Step-by-step explanation:
Let
d -----> the number of dogs
we know that
The linear equation that represent this situation is
[tex]2d+17=41[/tex]
Solve for d
Subtract 17 both sides
[tex]2d=41-17[/tex]
[tex]2d=24[/tex]
Divide by 2 both sides
[tex]d=12\ dogs[/tex]
Final answer:
The equation to find the number of dogs at the shelter is 2d + 17 = 41, where 2d represents the total cups of food eaten by the dogs and 17 represents the cups eaten by the cats per day.
Explanation:
To find d, the number of dogs at the animal shelter, we can use the information provided to set up an equation. We know the shelter uses 41 cups of food each day in total, and that cats eat 17 cups in total per day. Since each dog eats 2 cups per day, we can represent the number of cups dogs eat as 2d, where d is the number of dogs. We can then express the total food used as the sum of the food eaten by the cats and the food eaten by the dogs, which gives us the equation:
2d + 17 = 41
This equation can be used to find the number of dogs at the shelter since solving for d would give us the total number of dogs based on their food consumption.
write the equation for the cosine function that has been compressed vertically by a factor of 2, stretched horizontally by a factor of 4, and shifted down one unit
Answer:
[tex]f(x)=\frac{1}{2}Cos(\frac{1}{4}x)-1[/tex]
Step-by-step explanation:
Consider the function f(x) = cos x. Noted below are the points of transformations of the cos function
The function f(x) = [tex]\frac{1}{a}[/tex] cos x is a vertical compression of the original by a factor of aThe function f(x) = cos [tex](\frac{1}{b}x)[/tex] is a horizontal stretch of the original function by a factor bThe function f(x) = cosx - c is the original function shifted down c unitsConsidering the points above, we can now write down the "transformed" cosine function's equation:
f(x) = [tex]\frac{1}{2}Cos(\frac{1}{4}x)-1[/tex]
Answer:
Hope this helps :)
Step-by-step explanation:
A statistics student is doing a project for her class. She wants to make a prediction for the outcome of an upcoming national election. Since there are only two candidates, she decides that her question is "Which candidate do more people favor in the upcoming election?" She decides to randomly interview 100 students crossing the courtyard on campus about their preference. Is this sample good for drawing general conclusions about the results of the election?
Final answer:
Interpreting the preference of 100 college students on campus to predict an election result is unlikely to yield a representative sample of the national electorate. A more scientific poll requires a larger, random, and demographically diverse sample of the voting population.
Explanation:
The student's approach of interviewing 100 students on a college campus to predict the outcome of a national election may not provide a representative sample of the general voting population. A sample to make general predictions about national elections should reflect the demographics and political distribution of the entire nation, which is unlikely to be the case for a sample drawn solely from a college campus.
Furthermore, the sample may also suffer from selection bias if, for instance, those who choose to walk through the courtyard are not representative of the entire student body, let alone the country's electorate.
To conduct a more accurate and scientific poll, a larger and more diverse sample size would need to be chosen randomly from among all potential voters in the nation and it should include a mix of individuals with a history of voting and other demographic characteristics that align with the broader population.
Solved + 3d = 6.
isolate the variable
You can sum like terms:
[tex]d+3d=4d[/tex]
The equation becomes
[tex]4d = 6[/tex]
Divide both sides by 4:
[tex]d=\dfrac{6}{4}=\dfrac{3}{2}[/tex]
A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she
serves 6 times, what's the probability that she gets...
All 6 serves in?
Exactly 4 serves in?
At least 4 serves in?
No more than 4 serves in?
this is a binomial problem: p = 0.7 and q = 0.3
a) (0.7)^6
b) (6C4)(0.7)^4(0.3)^2
c) Pr ( at least 4) = Pr(4) + Pr(5) + Pr(6) = (6C5)(0.7)^5(0.3) + (0.7)^6
d) Pr (no more than 4) = 1 - Pr(at least 4) = 1 - (answer from c)
The question requires understanding of binomial probability. The probability of all 6 serves, exactly 4 serves, at least 4 serves, and no more than 4 serves can be calculated using binomial distribution when each serve is an independent event.
Explanation:The subject of this question relates to probability involved in binomial distribution. Binomial distribution applies when there is a fixed number of independent trials, each with a constant probability of success. Here, a tennis player making a successful serve can be considered a success, with a probability of 0.70.
For all 6 serves in, the calculation is simply the product of the successful probability raised to the power of 6, which is (0.70)^6.For exactly 4 serves in, the calculation uses a binomial probability formula P(x=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where n is the total number of trials, k is the desired number of successes, and p is the probability of a single success. Here, C(6,4) * (0.70^4) * (0.30^2).For at least 4 serves in, it's the sum of the probabilities of getting exactly 4, 5, and 6 serves in.For no more than 4 serves in, it's the sum of the probabilities of getting exactly 0, 1, 2, 3, and 4 serves in.Learn more about Binomial Probability here:https://brainly.com/question/39666605
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The radius of the circle whose equation is (x-3)^2 + (y+1)^2 = 16 is
Answer:
4
Step-by-step explanation:
The general equation of a circle with center (a, b) and radius r is given by the equation;
[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]
The constant in the right hand side of the equation is simply the square of the radius;
We have been given the following equation;
(x-3)^2 + (y+1)^2 = 16
Comparing this with the general equation above;
[tex]r^{2}=16\\\\r=\sqrt{16}=4[/tex]
Can you guys help my with this problem? thanks.
Answer:
$3,750
Step-by-step explanation:
Find how much 3% of 125,000 is. Divide 3 by 100 and then multiply that by 125,000. You get 3,750, which is how much interest Moran will earn.
Find the product. (A^3 + 8)(a^3 -8)
a^6-64
I used the foil method
(a^3+8)(a^3-8)
a^6-8a^3+8a^3-64 middles cancel out
a^6-64
A rectangular swimming pool that is 10 ft wide by 16 ft long is surrounded by a cement sidewalk of uniform width. If the area of the sidewalk is 155 ft2, what is its width? A = lw 2.5 ft 5.0 ft 6.2 ft 15.5 ft
The pool has area [tex]160\,\mathrm{ft}^2[/tex].
Let [tex]x[/tex] be the width of the sidewalk. Then the combined area of the pool and sidewalk is [tex](10+x)(16+x)=160+26x+x^2[/tex], so that the area of the sidewalk alone is [tex]26x+x^2[/tex].
We're told this area is [tex]155\,\mathrm{ft}^2[/tex], so
[tex]26x+x^2=155\implies x^2+26x-155=(x-5)(x+31)=0\implies x=5[/tex]
Answer:
The width of the sidewalk is 5.0 ft.
Step-by-step explanation:
Given,
The dimension of the rectangular swimming pool is 16 ft × 10 ft,
So, the area of the pool = 16 × 10 = 160 ft²,
Let x be the uniform width of the cement sidewalk,
So, the dimension of the area covered by both swimming pool and sidewalk = (16+x) ft × (10+x) ft,
Thus, the combined area of the swimming pool and sidewalk = (16+x)(10+x) ft²
Also, the area of the sidewalk = The combined area - Area of the pool,
= (16+x)(10+x) - 160
According to the question,
[tex](16+x)(10+x)-160 = 155[/tex]
[tex](16+x)(10+x)=315[/tex]
[tex]160+16x+10x+x^2=315[/tex]
[tex]x^2+26x-155=0[/tex]
By the quadratic formula,
[tex]x=\frac{-26\pm \sqrt{676+620}}{2}[/tex]
[tex]x=\frac{-26\pm 36}{2}[/tex]
[tex]\implies x=5\text{ or } x = -31[/tex]
Side can not be negative,
Hence, the width of the sidewalk is 5.0 ft.
The volume of a rectangular prism is (x^3-3x^2 +5x-3) and the area of its base is (x^2-2) if the volume of a rectangular prism is the product of its base area and height what is the height of the prism?
A)x-3 + 7x-9/x^2-2
B) x-3 + 7x-9/x^3 -3x^2+5x -3
C) x-3 + 7x +3 /x^2-2
D)x-3 + 7x+3/x^3-3x^2 +5x-3
Answer:
option A.
Step-by-step explanation:
We know that the volume of a rectangular prism is the product of its base area and height. That is to say:
Volume = Base Area x Height
Where: x^3-3x^2 +5x-3
Height: x^2-2
Volume =
Solving for "Height" we have:
Height = Volume / Base Area
Height = (x^3-3x^2 +5x-3) / (x^2-2)
Using ruffinis law we have that the solution is:
x-3 with a remainder of 7x-9
That is to say:
x-3 + (7x-9)/(x^2 - 2)
That is option A.
What is the value of a in the polynomial
Answer: a= 16
Step-by-step explanation:
We have the following expression:
[tex](y-4)(y^2 +4y +16)[/tex]
To find the value of the coefficient "a" you must use the distributive property to multiply the expression:
[tex](y-4)(y^2 +4y +16)[/tex]
until you transform it to the form:
[tex]y^3 +4y^2 +ay -4y^2 -ay-64[/tex]
Then we have
[tex](y-4)(y^2 +4y +16)\\\\(y^3 +4y^2 +16y -4y^2 -16y-64)\\\\[/tex]
Therefore the value of a in the polynomial is 16
Which side lengths form a right triangle 30 POINTS!!
Answer:
A. 3, 4, 5
Step-by-step explanation:
Option A:
LHS = 3² + 4² = 9 + 16 = 25
RHS = 5² = 25
(3, 4, 5) is a right triangle.
Option B:
LHS = 7² + 8² = 49 + 64 = 113
RHS = 9² = 81
(7, 8, 9) is NOT a right triangle.
Option C:
LHS = 3² + 9² = 9 + 81 = 90
RHS = √95² = 95
(3, 9, √95) is NOT a right triangle.
Hope this help!!!
Have a nice day!!!
how many square feet of outdoor carpet will we need for this hole?
Answer:
40
Step-by-step explanation:
12x4 = 48
3x2 = 6
2x1 = 2
6+2 = 8
48-8= 40
HOPE THIS HELPS!
For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed that 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic (to 1 decimal) that could be used to estimate the number of women out of 1,000 in this population who have tissue abnormalities.
Answer: 15.8 Women out of 1,000 have tissue abnormalities.
Step-by-step explanation:
It's pretty simple, all you need to do is set up a proportion with the variables you already have
63/3980 = x/1000
Do Cross products so
63000=3980x
Divide both sides by 3980 to get x by itself and you get 15.82914573 which reduced to 1 decimal is 15.8
Answer:
Answer is 16
Step-by-step explanation:
Given that for the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed that 63 developed tissue abnormalities that might lead to cancer.
From the given information, we find the proportion of women who took the drug and developed tissue abnormalities
Proportion p = [tex]\frac{63}{3980} =0.015829[/tex]
Assuming the same proportion continues constantly for any population, we find
the number of women out of 1,000 in this population who have tissue abnormalities, estimated = [tex]1000(0.015829)\\=15.829\\=16[/tex]
Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah’s account, y, after x years?
Answer:
[tex]y=\$360(1+0.03x)[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]y=P(1+rx)[/tex]
where
y is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
x is Number of Time Periods
in this problem we have
[tex]P=\$360\\r=0.03[/tex]
substitute in the formula above
[tex]y=\$360(1+0.03x)[/tex]
Answer:
y = 360(0.03)x
Step-by-step explanation:
incorrect and how do i erase a answer
Are these permutation or combination problems?
1. Suppose you need to choose a new combination for your combination lock. You have to choose three numbers, each different and between 0 and 40. How many combinations are there?
2. You want to construct a 3 digit number from the digits 4,6,8,9. How many possible numbers are there?
Answer: You just bought a new briefcase and need to pick a four digit combination out of 10 possible numbers for the lock. If order does matter how many possible lock combinations can you choose from?
Step-by-step explanation:
The frequency table below represents the 30 best batting averages for a semi-peo baseball league. Which range of batting averages was most common among the players?
Answer:
A. .350-.359
Step-by-step explanation:
It has the highest frequency of all the ranges (14).
Answer: [tex]0.350-0.359[/tex]
Step-by-step explanation:
From the given table, it can be seen that the largest frequency in the data table = 14
Thus, there are 4=14 players which have the common range.
The range corresponding to the frequency 14 = [tex]0.350-0.359[/tex]
Hence, the range of batting averages which was the most common among the players = [tex]0.350-0.359[/tex]
Big Ed’s car dealership is running a special on 2008 trucks. Big Ed offers financing at a rate of 6.71% on a loan with a term of 36 months, but he requires the customer to make a down payment of 15% of the cost of the vehicle. You are interested in a Car Crusher truck that costs $25,230. Not including the down payment, how much will you pay over the lifetime of the loan? a. $27,924.84 c. $23,735.88 b. $25,789.32 d. $21,445.50 Please select the best answer from the choices provided A B C D
Answer: C
Step-by-step explanation:
25,230 x .15= 3,784.50
25,230- 3,784.50= 21,535
21,535/36= 598.20833
598.20833 x 1.0671= 638.348109
638.348109 x 36= 22,980.5319
Answer:
Letter C $23,735.84.The result varies a few dollars, because during the solution an adjustment was made to the decimals.
Step-by-step explanation:
1. Define the price of the vehicle you are going to buy with the dealer or seller
Principal: $25230
Rate= 6.71%
N= 36 months
Down payment=15% of the cost of the vehicle= (25230*0.15)=$3784.50
25230-3784.50=21445.5
2. Apply the amortization formula to determine the monthly payments. With this taxation, you will determine the payments applied to the principal and the copper of interest.
A=P*(r(1+r)^{n})/((1+r)^{n}-1).
A= amortization or monthly payments.
P=Principal
R=interest rate
N= the total number of months
a. Calculate the monthly interest rate. The annual interest rate is 6.71% percent. Divide it by 12 to get the monthly interest rate. The monthly interest rate is 0.5592 percent (6.71/12 = 0.5592)
A=21445.5*(0,005592 (1+0,005592)^{{36}})/(1+0,005592)^{{36}}-1.
A=21445.5*(0,00683/0,2223)
A=21445.5*0,03072=658.90
Total of the payment= 658.90*36=23720.40
which expressions are equivalent to 2-(-6+3)+4c
A..-8c+6
B.3(-4+2)+4c
c. None of the above
Answer:
c. none of the above
Step-by-step explanation:
(-6+3)= -3
2--3=2+3=5
5+4c cant add them since they arent like terms
final answer 5+4c and that option isnt here
44 is 55% of what number?
Enter your answer in the box.
|___|
Whoever answers it correctly gets branliest :)
Answer:
44 is 55% of 80
Step-by-step explanation:
44 is 55% of what number
LEt the unknown number be x
44 is 55% of x
Write the given sentence in equation form
[tex]44= 55 \ percent \ times \ x[/tex]
To remove percentage we divide by 100
55 divide 100 is 0.55
[tex]44=0.55 \cdot x[/tex]
Divide both sides by 0.55 to solve for x
[tex]80=x[/tex]
The value of x is 80. It means 44 is 55% of 80
The number is 80 and 44 is 55 percentage of the number 80
Given data ,
To find out what number 27 is 30 percent of, we can set up the equation:
55% of x = 44
To solve for x, we can divide both sides of the equation by 55% (or 0.55), which is the equivalent of dividing by 0.55:
x = 44 / 0.55
On dividing the numerator of the fraction by the denominator , we get
Evaluating the expression on the right side gives:
x = 80
Therefore , the value of the number is x = 80
Hence , 44 is 55 percent of number 80
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What is the equation of the circle shown below?
A.
(x ‒ 4)2 + (y + 5)2 = 34
B.
(x ‒ 5)2 + (y ‒ 4)2 = 5.83
C.
(x + 4)2 + (y ‒ 5)2 = 34
D.
(x ‒ 5)2 + (y + 4)2= 5.83
I am definitely willing to assist you, but without an illustration is a tough challenge.
What is the square root of 9 plus the square root of 9 plus the square root of 9 plus the square root of 9, etc
[tex] \sqrt{9} + \sqrt{9} + \sqrt{9} + \sqrt{9} [/tex]
3+3+3+3
=18
hope that helped you
Answer: 18
Step-by-step explanation:
square root of 9 equals 3+3+3+3+3+ = 18 (3x6)
if x is 5, then what does 6x =
Answer:
x=30
Step-by-step explanation:
More math help please im lazy ._.
there are no real square roots of 25,36
Find the value of x for which line a is parallel to line b
Answer:
20
Step-by-step explanation:
Since we are told that line a is parallel to line b, even if it's not visible in the image, we can say that ∠5 = ∠1, since they are formed by the same line crossing parallel lines.
So, we have
∠4 = 3x
∠5 = ∠1 = 6x
Since ∠4 and ∠5 are complementary angles formed by line t, we know their sum is 180 degrees. So,
∠4 + ∠5 = 180
3x + 6x = 180
9x = 180
x = 20
Answer is 20.
Sam wrote these four expressions .
1 . n + n + n + n + 2
2 . n + n + n + 2
3 . 4n + 2
4 . 2n + 2n + 2n
PART A- Which expressions are equivalent? Write your answer in the space provided .
PART B- Choose two of Sam’s expressions that are not equivalent . Explain how you know they are not equivalent . Write your answer in the space provided .
Part A) the first and the third answer are equivalent because.
n+n+n+n+2= 4n+2 which is the same as the third answer.
Part B) 2 and 4 are not equivalent because
2) n+n+n+2= 3n+2
4) 2n+2n+2n= 6n
as we can see they are not the same. Therefore they are not equivalent.
hope this helps