The volume of a sphere with a radius of 3 inches is [tex]\(36 \pi\)[/tex] cubic inches. Therefore, the correct option is [tex]\(36 \pi\)[/tex] cubic inches.
The volume V of a sphere with radius r is given by the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Given that the radius r is 3 inches, we can substitute this value into the formula:
[tex]\[ V = \frac{4}{3} \pi (3)^3 \]\[ V = \frac{4}{3} \pi (27) \]\[ V = \frac{4}{3} \times 27 \times \pi \]\[ V = 36 \pi \][/tex]
So, the volume of the sphere is [tex]\( 36 \pi \)[/tex] cubic inches.
Therefore, the correct option is: [tex]\( 36 \pi \)[/tex] cubic inches.
Complete Question:
The radius of a sphere is 3 inches. Which represents the volume of the sphere?
[tex]$12 \pi$[/tex] cubic inches
[tex]$36 \pi$[/tex] cubic inches
[tex]$64 \pi$[/tex] cubic inches
[tex]$81 \pi$[/tex] cubic inches
Mrs. Evans drove 24 miles on 3 gallons of gas. What is her unit rate in miles per gallon??
Answer: 8 miles
Step-by-step explanation:
24/3=8
PLZZZ HELP DUE BY MIDNIGHT
Tim answered all the questions on his math test but got 10 answers wrong. He received 4 points for every correct answer, and there was no penalty for wrong answers. His score was 76points.
Write an equation to determine the total number of questions (q) on Tim's math test.
Find the total number of questions on his math test.
Answer: (i) 4x - 40 = 76
(ii) 29 questions
Step-by-step explanation:
Let the total number of questions be x.
Since he received 4 points for every correct answer and he got 10 answers wrong , this means he lost 40 points , the equation thus become
4x - 40 = 76
To find the value of x , add 40 to both sides
4x = 116
divide through by 4
x = 29
Therefore , there are 29 questions on his math test
Which expression has a negative value?
Answer:
-3×3×-3×-3 is positive
Answer:
-3 x 3 x -3 x -3 because the answer is -81.
(Bottom Left)
CAN SOMEBODY PLEASE HELP ME??
Answer: According to the pattern i think its 66
Step-by-step explanation:
Which shows 50% of the area shaded?
Answer:
B shows 50% shaded
Step-by-step explanation:
Count how many triangles are in it (4) then see how many are shaded (2/4).
Simplify it to 1/2=50% then you got your answer.
Answer:
B
Step-by-step explanation:
because there is 2 trangle shaded and 2 trangle remain blank
Evaluate the expression 24/b+8 when b=9
To evaluate the expression 24/b+8 for b=9, substitute 9 for b to get 24/9 + 8, which simplifies to approximately 10.67.
Explanation:To evaluate the expression 24/b+8 when b=9, we substitute the value of b into the expression and perform the arithmetic operation.
First, we replace b with 9:
24/9 + 8
Then, we divide 24 by 9:
2.666... + 8
Next, we add 8 to the quotient:
2.666... + 8 = 10.666...
The result of evaluating the expression 24/b+8 for b=9 is approximately 10.67.
( y + 1 ) + 4 = ?
Use one or more properties to rewrite each expression that dose not use parentheses.
To rewrite the expression (y + 1) + 4 without using parentheses, we can distribute 4 to the terms inside the parentheses and then combine like terms.
Explanation:
To rewrite the expression without using parentheses, we can use the distributive property. The distributive property states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding them together. In this case, we have (y + 1) + 4, and we can distribute the 4 to both terms inside the parentheses. So, (y + 1) + 4 can be rewritten as y + 1 + 4.Next, we can combine like terms. The terms y and 1 do not have any common variable factors, so they cannot be combined. However, 1 and 4 are both constants, so they can be added together to give us 5. Therefore, y + 1 + 4 simplifies to y + 5.
So, the expression (y + 1) + 4 can be rewritten as y + 5.
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Complete the equation of the line through (-10,3) and (-8,-8)
Answer: 2y + 11x = -104
Step-by-step explanation:
The formula for calculating equation of line given two points is :
[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = -10
[tex]x_{2}[/tex] = -8
[tex]y_{1}[/tex] = 3
[tex]y_{2}[/tex] = -8
substituting the values into the formula , we have :
[tex]\frac{y-3}{x-(-10)}[/tex] = [tex]\frac{-8-3}{-8-(-10)}[/tex]
[tex]\frac{y - 3}{x + 10}[/tex] = [tex]\frac{-11}{2}[/tex]
2(y - 3 ) = -11 ( x +10 )
2y - 6 = -11x - 110
2y + 11x = -110 + 6
2y + 11x = -104
Therefore : the equation of the line in standard form is 2y + 11x = -104
Two people bought 46 apples. Chris bought 5 times more than Brian. How many apples did Brian buy?
Answer:
7.6667
Step-by-step explanation:
46÷6=7.6667
brian buys 7.6667 apples i believe.
but please round depending on question
Help me please and thank you
Answer:
The required answer is 218 degree.Step-by-step explanation:
∠AOB = 90 degree.
∠BOC = 52 degree.
Arc CDE = 180 degree, since CE is the diameter.
Hence, Arc EAC = 180 degree.
Besides, Arc EAC = Arc EA + Arc AB + Arc BC = Arc EA + 90 + 52 = Arc EA + 142.
Thus, Arc EA = 180 - 142 = 38 degree.
Arc ADC = 180 + 38 = 218 degree.
Help me please..... .......thanks
Answer:
Step-by-step explanation:
3/8
Three different car dealers advertised the
same make and model car at the following
prices: $14,280; $14,195; and $14,275.
(A) How much can be saved by buying the
least expensive car instead of the most ex-
pensive? (B) What is the average price?
Final answer:
Buying the least expensive car can save $85, and the average price of the car from the three dealers is $14,250.
Explanation:
To address the question concerning the savings and the average price of a car being advertised by three different dealers, we perform the following calculations:
First, identify the least and most expensive cars. The lowest price is $14,195, and the highest price is $14,280.To find out how much can be saved, subtract the least expensive car's price from the most expensive car's price: $14,280 - $14,195 = $85. So, buying the least expensive car instead of the most expensive can save $85.To find the average price of the car based on the three dealers' prices, add all the prices together and divide by the number of prices: ($14,280 + $14,195 + $14,275) / 3 = $42,750 / 3 = $14,250. The average price of the car is $14,250.pls help 10 points!!!
Answer:
3rd one
Step-by-step explanation:
will give brainiest In △ABC, angle bisectors
AK
and
BL
are drawn. It is known that m∠BAC =m∠AKC and m∠ABC=m∠ALB. Find all the angles of △ABC.
Answer:
[tex]m\angle CAB=102\dfrac{6}{7}^{\circ}\\ \\m\angle ABC=51\dfrac{3}{7}^{\circ}\\ \\m\angle ACB=25\dfrac{5}{7}^{\circ}[/tex]
Step-by-step explanation:
AK is angle A bisector, then
[tex]m\angle BAK=m\angle KAC=x^{\circ}[/tex]
BL is angle B bisector, then
[tex]m\angle ABL=m\angle CBL=y^{\circ}[/tex]
Consider triangle ABL. The sum of the measures of all interior angles in this triangle is [tex]180^{\circ},[/tex] then
[tex]m\angle BAL+m\angle ALB+m\angle LBA=180^{\circ}\\ \\2x+2y+y=180\\ \\2x+3y=180[/tex]
Consider triangle ABK. In this triangle,
[tex]m\angle AKB=180^{\circ}-2x^{\circ} \ [\text{Supplementary angles}][/tex]
The sum of the measures of all interior angles in this triangle is [tex]180^{\circ},[/tex] then
[tex]m\angle BAK+m\angle AKB+m\angle KBA=180^{\circ}\\ \\x+(180-2x)+2y=180\\ \\2y-x=0[/tex]
Hence,
[tex]x=2y\\ \\2(2y)+3y=180\\ \\4y+3y=180\\ \\7y=180\\ \\y=\dfrac{180}{7}=25\dfrac{5}{7}\\ \\x=\dfrac{360}{7}=51\dfrac{3}{7}[/tex]
Find the measures of the triangle ABC:
[tex]m\angle CAB=2x^{\circ}=102\dfrac{6}{7}^{\circ}\\ \\m\angle ABC=2y^{\circ}=51\dfrac{3}{7}^{\circ}\\ \\m\angle ACB=180^{\circ}-102\dfrac{6}{7}^{\circ}-51\dfrac{3}{7}^{\circ}=25\dfrac{5}{7}^{\circ}[/tex]
The problem is asking to find all angles of an isosceles triangle ABC with angle bisectors AK and BL. The given conditions imply that the triangle has angles of 45°, 45°, and 90°.
The student is asking about an angle bisector problem in triangle geometry. In triangle ABC, the angle bisectors AK and BL are drawn such that m∠BAC = m∠AKC and m∠ABC = m∠ALB. To solve this problem, we need to use the properties of angle bisectors and triangles.
Since AK is an angle bisector, it bisects ∠BAC into two equal angles. Similarly, BL bisects ∠ABC into two equal angles. We also know that the sum of angles in a triangle is 180 degrees.
Let's denote m∠BAC and m∠AKC as 'x'. Similarly, let's denote m∠ABC and m∠ALB as 'y'. Since AK and BL are bisectors, m∠BAK = m∠CAK = x and m∠ABL = m∠CBL = y. Hence, ∠ACB would be 180 - 2x - 2y (sum of angles in a triangle).
We are given that m∠BAC is equal to m∠AKC and m∠ABC is equal to m∠ALB. This implies that the triangle is isosceles with the following angle measurements: m∠BAC = m∠ABC = x (equal base angles in an isosceles triangle), and m∠ACB = 180 - 2x.
Now, since m∠BAC and m∠ABC are equal, we can say that 2x + (180 - 2x) = 180. Simplifying, we find that x = 45 degrees, and thus, all angles of triangle ABC are 45°, 45°, 90°.
I don't understand what this means.
Rewrite the polynomial function (in standard form), classify by its degree, and then determine the end behavior of its graph.
y=2x+3x^3+10
a)Standard form:____
b)Classification:____
c)End Behavior:____
Answer:
a) -3x^3 - 2x + y - 10 = 0
b) it a trinomial
c) not sure. sorry. :(
hope this helps.:)
Joey has 3 liters of lemonade to share with 6 friends. He
decides put 0.5 liter of lemonade in each of his friends'
6 cups, then drink any leftover lemonade himself. How
much lemonade will Joey get to drink?
A. O liters
B. 0.2 liter
C. 0.5 liter
D. 0.8 liter
E. 1 liter
N
Answer:
bruh dis ni gga should keep all his lemonade forget his friends
Step-by-step explanation:
PLEASE HELP ASAP! THANK YOU LOTS! <3
Answer:
C
Step-by-step explanation:
12 divided by 3 is 4 and 30 divided by 3 is 10
30 cm on the smaller figure corresponds to 12 meters on the larger figure.
We can write the ratio 30 cm : 12 m
If we divide both parts by the GCF 6 then,
30/6 = 5
12/6 = 2
This means the ratio 30 cm : 12 m reduces to 5 cm : 2 m
Telling us "2 meters on the real house correspond to 5 cm on the doll house"
Answer: Choice B. 5 cm : 2 mSociologists want to determine the probability of exactly 4 out of the next 7 individuals they survey earning over
$50,000 dollars per year. The probability of an individual earning over $50,000 a year is 30%. What is the probability of
exactly 4 out of the next 7 individuals that they survey earning over $50,000?
A. 0.07859
B. 0.07651
C. 0.08311
D. 0.09724
Answer:
the probability of exactly 4 out of next 7 individuals that the sociologists survey earning over $50000 is given by
= [tex]\binom{7}{4} \cdot (0.3)^4(0.7)^{7-4}[/tex] = 0.09724
Step-by-step explanation:
i) This problem is solved by using the Binomial Probability distribution as the sample size is less than 30.
ii) The sample size is 7
iii) It is given that the probability of an individual earning over $50000 is 30% or 0.3 and therefore the probability of an individual not earning over $50000 is ( 1 - 0.3) = 0.7
iv) Therefore the probability of exactly 4 out of next 7 individuals that the sociologists survey earning over $50000 is given by
= [tex]\binom{7}{4} \cdot (0.3)^4(0.7)^{7-4}[/tex] = 0.09724
Damien landers 10K race in 30 minutes Kyle Tucker one-and-a-half times as long as Damien how long did kyle take to run the race
Answer:
45 minutes
Step-by-step explanation:
1.5 × (30 min) = 45 min
It took Kyle 45 minutes to run the race.
Answer:
45 minutes
Step-by-step explanation:
If it is one and a half it would be a whole so 30 but the half, is half of 30, so 15. 30+ 15= 45
28.71 is what percent of 6.6?
Answer:
28.71 is 435% of 6.6
Step-by-step explanation:
100%/x%=6.6/28.71
(100/x)*x=(6.6/28.71)*x - we multiply both sides of the equation by x
100=0.229885057471*x - we divide both sides of the equation by (0.229885057471) to get x
100/0.229885057471=x
435=x
x=435
The price of an item yesterday was 115. Today the price fell to 69. Find the percentage decrease
Answer:
Step-by-step explanation:
40%
The formula is
Old-new/old *100
115-69/115*100
The percentage decrease is 40% if the price of an item yesterday was 115. Today the price fell to 69.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
The price of an item yesterday was 115. Today the price fell to 69.
The difference in price = 115 - 69 = 46
Percentage decrease = (46/115)×100 = 40%
Thus, the percentage decrease is 40% if the price of an item yesterday was 115. Today the price fell to 69.
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8x^2 - 2x = 1 quadratic simplification
Answer:
x = -1/4 = -0.250
Step-by-step explanation:
SOME ONE PLEASE HELP
Answer
6,000x
Explanation
To work out how many times greater something is compared to another, we have to divide the larger number by the smaller
To put it more simply, imagine you had 30 apples and I had 6. To work out how many times greater your apple collection was than mine, you would divide your 30 by my 6, and find that you had 5 times as many apples as me (30 ÷ 6 = 5).
The principle is the same here, how many more viruses (3 x 10⁹) are there compared to protozoa (5 x 10⁵)?
We do 3 x 10⁹ ÷ 5 x 10⁵
3 x 10⁹ = 3,000,000,000
5 x 10⁵ = 500,000
3,000,000,000 ÷ 500,000 = 6,000 times more
f
(
x
)
=
−
x
2
+
6
x
+
13
f(x)=−x
2
+6x+13, determine the average rate of change of the function over the interval
−
1
≤
x
≤
5
−1≤x≤5.
Answer:
The average rate of change of [tex]f(x) = x^2 +6x+13[/tex] is 12
The average rate of change of [tex]f(x) =- x^2 +6x+13[/tex] is 10
Step-by-step explanation:
The average rate of change of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the secant line connecting the 2 points.
We can calculate the average rate of change between the 2 points by
[tex]\frac{f(b) - f(a)}{b -a}[/tex]-------------------(1)
(1) The average rate of change of the function [tex]f(x) = x^2 +6x+13[/tex] over the interval 1 ≤ x ≤ 5
f(a) = f(1)
[tex]f(1) = (1)^2 +6(1) + 13[/tex]
f(1) =1+6+13
f(a) = 20---------------------(2)
f(b) = f(5)
[tex]f(5) = (5)^2 +6(5)+13[/tex]
f(5) = 25 +30 +13
f(5) = 68-----------------------(3)
The average rate of change between (1 ,20) and (5 ,68 ) is
Substituting eq(2) and(3) in (1)
=[tex]\frac{f(5) - f(1)}{5-1}[/tex]
=[tex]\frac{68 -20}{5-1}[/tex]
= [tex]\frac{48}{4}[/tex]
=12
This means that the average of all the slopes of lines tangent to the graph of f(x) between (1 ,20) and (5 ,68 ) is 12
(2) The average rate of change of the function [tex]f(x) = -x^2 +6x+13[/tex] over the interval -1 ≤ x ≤ 5
f(a) = f(-1)
[tex]f(1) = (-1)^2 +6(-1) + 13[/tex]
f(1) =1-6+13
f(1) = 8---------------------(4)
f(b) = f(5)
[tex]f(5) = (5)^2 +6(5)+13[/tex]
f(5) = 25 +30 +13
f(5) = 68-----------------------(5)
The average rate of change between (-1 ,8) and (5 ,68 ) is
Equation (1) becomes
[tex]\frac{f(5) - f(-1)}{5-(-1)}[/tex]
On substituting the values
=[tex]\frac{68 - 8}{5-(-1)}[/tex]
=[tex]\frac{60}{5+1}[/tex]
=[tex]\frac{60}{6}[/tex]
= 10
This means that the average of all the slopes of lines tangent to the graph of f(x) between (-1 ,8) and (5 ,68 ) is 10
PLS HELP - What is the product?
(2x-1)(x+4)
A- O 2x² - 4
B- O zx²+4
C- 2x?+7x-4
D- O 2x² - 7x-4
Answer:
C. 2x² + 7x - 4
Step-by-step explanation:
Given:
(2x-1)(x+4)
= 2x * (x+4) + (-1) * (x+4) ⇒ Distributive property.
= 2x² + 8x - x - 4 ⇒ Combine like terms.
= 2x² + 7x - 4
The answer is option C. 2x² + 7x - 4
14pqr+35pqr factorise
Answer:
14pqr+35pqr = pqr×(14+35)
Solve each compound inequality and graph the solutions. -2 < x - 3 < 5
Answer:
See attachment.
Step-by-step explanation:
The given inequality is -2 < x - 3 < 5.
We add 3 to each part of -2 +3< x - 3+3 < 5+3
We now simplify to get: 1 < x < 8.
To represent this on the number line, we have to draw open circles at 1 and 8 and connect them as shown in the attachment.
Which answer represents the series in sigma notation? −5+(−1)+3+7+11
The series in sigma notation is: representing terms increasing by 4 starting from -5.
To represent the series in sigma notation, let's first examine the pattern of the terms.
The given series starts with -5 and each subsequent term increases by 4. We can express this pattern using the formula:
[tex]\[ a_n = -5 + (n - 1) \times 4 \][/tex]
Here, [tex]\( a_n \) represents the \( n \)th term of the series[/tex].
Now, let's break down the components of the formula:
-[tex]\( -5 \) is the initial term of the series.- \( (n - 1) \) accounts for the position of each term in the series. When \( n = 1 \), \( (n - 1) = 0 \), so the first term is \( -5 \). As \( n \) increases, \( (n - 1) \) increases by 1, causing the series to increase by 4 each time.- \( 4 \) is the common difference between consecutive terms in the series.[/tex]
Next, we represent the series using sigma notation:
[tex]\[ \sum_{n=1}^{5} (-5 + (n-1) \times 4) \][/tex]
This notation indicates that we sum up the expression [tex]\( -5 + (n-1) \times 4 \) for \( n \)[/tex] ranging from 1 to 5, which covers all the terms of the given series.
In summary, the series is represented in sigma notation as described above, capturing the pattern of increasing terms starting from -5.
Write the next three terms of the geometric sequence.
A. 32, 8, 2, 1/2, ...
B. 16/9, 8/3, 4, 6, ...
The correct statement is that the terms are
A. The next three numbers are 1/8, 1/32, and 1/128.
B. The next three-term will be 9, 13.5, and 20.5.
What are sequence and series?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after. A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.
Given
A. 32, 8, 2, 1/2, ...
B. 16/9, 8/3, 4, 6, ...
How to find the next three numbers?A. 32, 8, 2, 1/2... can be expressed as [tex]2^{2n - 1}[/tex]
Then For n= -1, -2, and -3, Then the next three numbers will be
[tex]2^{-2 - 1} \ \ \ \ \ , \ 2^{-4 - 1} \ \ \ \ \ , \ 2^{-6 - 1}\\\dfrac{1}{8} \ \ \ \ \ \ \ \ \ \ \ , \dfrac{1}{32} \ \ \ \ \ \ \ \ \ \ , \dfrac{1}{128}[/tex]
The next three numbers are 1/8, 1/32, and 1/128.
B. 16/9, 8/3, 4, 6... each term increases by 2/4. So the next three-term will be 9, 13.5, and 20.5.
Thus, the terms are 9, 13.5, and 20.5.
More about the sequence and the series link is given below.
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Describe the relationship between the two quantities.
Distance traveled by car; Amount of gas in the car.
a. inverse
c. joint
b. direct
d. compound
Please select the best answer from the choices provided
The relationship between the distance traveled by a car and the amount of gas in the car is inverse. As the distance increases, the gas decreases
Explanation:The relationship between the distance traveled by a car and the amount of gas in the car is inverse. This means that as one quantity increases, the other decreases. In this case, as the distance traveled by a car increases, the amount of gas in the car decreases, because the car uses gas to move. In other words, the more you drive, the less gas you have left in your car.
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