Answer:
Therefore the volume of the box is 13824 in³
Step-by-step explanation:
Given:
A spherical ball with is packaged in a box that is in the shape of a cube.
Volume of ball = 2304π in³.
Let 'r' be the radius of sphere
To Find:
Volume of Cube = ?
Solution:
Volume of sphere is given by
[tex]\textrm{Volume of sphere}=\dfrac{4}{3}\pi r^{3}[/tex]
Substituting the values we get
[tex]2304\pi=\dfrac{4}{3}\pi r^{3}\\\\\therefore r^{3}=1728\\\\Cube\ Rooting\\\\r=12\ in[/tex]
Now we know that diameter is given by
[tex]diameter=2\times r=2\times 12=24\ in[/tex]
it is given that,
The edge length of the box is equal to the diameter of the ball.
Therefore the length of cube = 24 in
Now the volume of the cube is given by
[tex]\textrm{Volume of cube}=(edge)^{3}[/tex]
substituting the values we get
[tex]\textrm{Volume of cube}=(24)^{3}=13824\ in^{3}[/tex]
Therefore the volume of the box is 13824 in³
1. Slove the system of equations, first by graphing, and then algebraically. (8 points) y=x-2 and y=-2x+7
The solution of the equation is [tex]x=3[/tex] and [tex]y=1[/tex]
Explanation:
The equations are [tex]y=x-2[/tex] and [tex]y=-2 x+7[/tex]
First we shall solve the equation graphically.
The image of the graph is attached below.
This contains the solution to the system of equations.
The equations [tex]y=x-2[/tex] and [tex]y=-2 x+7[/tex] are plotted on the graph.
The intersection of these two equations are the solutions of the system of equations.
Thus, the intersection of the two equations are [tex]x=3[/tex] and [tex]y=1[/tex]
Now, we shall solve the equation algebraically.
Let us solve the equation using substitution method.
Let us substitute [tex]y=x-2[/tex] in [tex]y=-2 x+7[/tex], we get,
[tex]x-2=-2x+7[/tex]
Adding both sides by 2x, we have,
[tex]3x-2=7[/tex]
Adding both sides by 2, we get,
[tex]3x=9[/tex]
Dividing both sides by 3,
[tex]x=3[/tex]
Thus, the value of x is 3.
Substituting [tex]x=3[/tex] in [tex]y=x-2[/tex], we get,
[tex]y=3-2\\y=1[/tex]
Thus, the value of y is 1.
Hence, The solution of the equation is [tex]x=3[/tex] and [tex]y=1[/tex]
Aaron invest $50 each month for 9 months in an account that pays 7.5% APR compounded monthly. What is the future value of Aaron's account after 9 months?
Answer: 461.45 APEX
Step-by-step explanation:
Answer:
its is $461.45
Step-by-step explanation:
A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7bt, where t is the time in weeks after the release and b is a positive unknown base. According to the model, how many fish of the new species were released initially? A) 2 B) 7 C) 12 D) 14
The initial amount of fish released would be the number shown in the equation.
The answer is 7
Final answer:
The initial number of fish released into the lake is 7, which is calculated by substituting t = 0 into the provided exponential growth function, P(t) = 7bt.
Explanation:
The growth of the fish population in the lake is modeled by the exponential function P(t) = 7bt, where t is the time in weeks after the release, and b is a positive unknown base. To find out how many fish were released initially, we need to consider the population at time t = 0. When we substitute t = 0 into the exponential function, we get P(0) = 7b0, and since any number raised to the power of 0 is 1, P(0) = 7. Therefore, the initial number of fish released was 7.
A shop sells one pound bags of peanuts for $2 and three pound bags of peanuts for $5. If 9 bags are purchased for a total of $36, how many three pound bags were purchased?
Answer:7
Step-by-step explanation:
5x7=35
Answer:
Six
Step-by-step explanation:
What do we know?
1 lb pack = $2
3 lbs pack = $5
9 packs are purchased for $36
Solve
The biggest amount of 3-pound bags can be 7. That cannot be because that would be $35, and there are no 1-pound bags.
Go down to 6. 6 bags of 3 pounds would cost $30. You can also get 3 2-pound bags to get to 36. Cost is reached. 6+3 = 9. Number of bags reached.
six 3-pound bags
Jolie uses the childcare facilities at her gym. Her monthly dues are $32, and childcare is $9 per visit. This month, she does not
wish to spend more than $122 for both dues and childcare. If x represents the number of times she can use childcare services,
which of the following inequalities symbolizes this situation?
A.
$32x+ $9 > $122
B. $32x + $9 < $122
C. $9x + $32> $122
D. $9x + $32 < $122
Answer:
The answer is D
Step-by-step explanation:
Answer:
D. $9x + $32 < $122
Step-by-step explanation:
given :
x is the number of visits
$9 is the cost per visit
$32 is the monthly dues
the amount she pays each month
= monthly dues + (cost per visit x number of visits)
= 32+ 9x (rearrange)
= 9x + 32
given that she does not wish to spend more than $122, that means she wants to spend LESS than $122, i.e
amount spent < $122
or
9x + 32 < 122 (answer D)
-4/4+160%+1/5 as an exact decimal
Answer:
0.8
Step-by-step explanation:
-4/4=-1
160%=1.6
1/5=0.2
--------------
-1+1.6+0.2
0.6+0.2
0.8
Janelle ate 82% of the pie. What fraction of the pie remained? help meee
Answer:
There is 18% left of the pie.
Step-by-step explanation:
There is only 100% of a pie. If she at 82% then there is 18% left. 100-82=18
Answer:
9/50
Step-by-step explanation:
for a percentage to turn into a fraction all u have to do put the percent over 100 so in this case first subtract total 100-82= 18% so then 18/100 simplified it would be 9/50
On a random Monday in the spring, 95% of students are present at school. If there are 589 students present, then how many total students are enrolled?
Answer:
620
Step-by-step explanation:
Which step is included in the graph of the function f(x)=[x-1]? (the brackets are ceiling functions symbols)
Answer:
The correct step is y = - 5 for, - 4 ≤ x < - 3.
Step-by-step explanation:
From the definition of a box function y = [x], we know that
y = 0 for, 0 ≤ x < 1
y = - 1 for, - 1 ≤ x < 0
y = - 2 for, - 2 ≤ x < - 1
Here, we are given another box function y = [x - 1], and we have to choose from options the steps which is included in the graph of the this function.
So, the correct step is y = - 5 for, - 4 ≤ x < - 3. (Answer)
Given the following geometric sequence, find the common ratio: {16, 64, 256, ...}.
Answer:
The common ratio is 4
Step-by-step explanation:
We need to divide a term by the previous term to find the common ratio in a geometric sequence:
64 ÷ 16 = 4
256 ÷ 64 = 4
By doing it twice we can confirm that the common ratio is 4
Given the following geometric sequence, the common ratio would be 4.
janice is asked to solve0=64x^2+16x-3 what is x
Answer:
x=-1/8 or 3/8
Step-by-step explanation:
64x^2+16x-3=0
By Mid term breaking
64x^2-24x+8x-3=0
8x(8x-3)+1(8x-3)=0
(8x+1)(8x-3)=0
Either
8x+1=0 OR 8x-3=0
8x=-1 OR 8x=3
x=-1/8 OR x=3/8
ak = v+w solve for a
Answer:
a = [tex]\frac{v+w}{k}[/tex]
Step-by-step explanation:
Given
ak = v + w ( isolate a by dividing both sides by k )
a = [tex]\frac{v+w}{k}[/tex]
What is the total weight of Trail Mix used in all bags
To find the total weight of trail mix used in all bags, more information is needed.
Explanation:To find the total weight of trail mix used in all bags, we need more information. The information provided in the question does not mention the weight of trail mix or the number of bags. Without this information, we cannot calculate the total weight.
The circumference of a circle is about 37.7 cm and the diameter is about 12 cm. What expression best represents the value of π?
6/37.7
37.7/12
37.7/6
12/37.7
Answer:
The best expression represents the value of π is [tex]\frac{37.7}{12}[/tex] ⇒ 2nd answer
Step-by-step explanation:
π is the ratio between the circumference of the circle and the length of its diameter
[tex]\frac{C}{d}=\pi[/tex] , where
C is the circumference of the circled is the diameter of the circle∵ The circumference of the circle is about 37.7 cm
∵ The diameter of the circle is about 12 cm
- Find the ratio between them
∴ [tex]\frac{C}{d}=\frac{37.7}{12}[/tex]
∵ [tex]\frac{C}{d}=\pi[/tex]
- Equate the two right hand sides
∴ [tex]\frac{37.7}{12}=\pi[/tex]
∴ The best expression represents the value of π is [tex]\frac{37.7}{12}[/tex]
Marco has baked and frosted 4 dozen heart-shaped sugar cookies to bring to his class party. He wants to
put 3 gumdrops on each cookie. He has 4 bags of 40 gumdrops. Does he have enough gumdrops to put 3
on each cookie? Explain.
Answer:
16Step-by-step explanation:
4 x 12=48 48 divided by 3=16
what did the beaver say to the tree
Answer:
It’s been nice gnawing you
Step-by-step explanation:
While beavers don't 'speak' to trees in human terms, they interact with them by using their teeth to fell trees for food and building materials.
Explanation:The question, 'what did the beaver say to the tree?', is somewhat humorous due to its anthropomorphic implication of a beaver communicating with a tree in human language. But, from a biological perspective, we could interpret this as asking about the interactions between beavers and trees. Beavers, as known dentition specialists, utilize trees for building dams and lodges and as a source of food. So, if a beaver could 'speak', it might 'tell' the tree that it's hungry, or that it needs materials for its dam. Of course, this is all figuratively speaking.
Learn more about Beaver-Tree Interaction here:https://brainly.com/question/28678269
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Which best describes the function on the graph?
A. direct variation; k = 3
B. direct variation; k = 1/3
C. inverse variation; k = 3
D. inverse variation; k = 1/3
Answer:A i think
Step-by-step explanation:
Answer:
B. Direct Variation: k = 1/3
Step-by-step explanation:
Your Welcome
P divided by 28 = -26
Answer:54 when ever you have a positive and plus you always add
Step-by-step explanation:
4/6 x - 6 = - 24
Solve for X
Answer:
-27
Step-by-step explanation:
4/6x-6=-24
+6 +6
4/6x=-18
6/4×4/6x=-18×6/4 ->multiply by reciprocal to get rid of x
x=-108/4
x=-27
1. Which of the following shows the correct use of the Distributive Property when solving 1/3( 33
- y) = 135. 2
• (33 - y) = 1/3 * 135.2 (your response)
. (1/3*33) - 1/3y = 1/3* 135.2
. (1/3 * 33) - 1/3y = 135.2
. (1/3 * 33) + 1/3y = 135.2
Please I need this asp
Answer:
The option [tex](\frac{1}{3}\times 33)-\frac{1}{3}y=\frac{1}{3}135.2[/tex] is correct
Step-by-step explanation:
Given equation is [tex]\frac{1}{3}(33-y)=135.2[/tex]
The option shows correct usage of distributive property is
[tex](\frac{1}{3}\times 33)-\frac{1}{3}y=\frac{1}{3}135.2[/tex]
( by distributive property [tex]a(x+y)=ax+ay [/tex] here [tex]a=\frac{1}{3}[/tex], x=33 and y=-y )
Therefore the option [tex](\frac{1}{3}\times 33)-\frac{1}{3}y=\frac{1}{3}135.2[/tex] is correct.
The correct use of the Distributive Property for the equation 1/3(33 - y) = 135.2 is to apply multiplication to each term inside the parentheses by 1/3, resulting in (1/3 * 33) - (1/3)y = 135.2.
The question is asking for the correct use of the Distributive Property when solving the equation 1/3(33 - y) = 135.2.
The correct application of the Distributive Property to solve the equation would involve multiplying both terms inside the parentheses by 1/3. Here's how the property is correctly applied:
(1/3 * 33) - (1/3 * y) = 135.2
(33/3) - (1/3)y = 135.2
11 - (1/3)y = 135.2
Hence, the correct option that uses the Distributive Property properly is:
(1/3 * 33) - (1/3)y = 135.2
Select is a subset of or is not a subset of for the blank so that the resulting statement is true.
{ 1, 3, 5 } ___ { 1, 2, ..., 10 }
Answer:
Step-by-step explanation:
Subset(1,3,5) because it is found in another set.
not subset(2,4,6,7,8,9,10) they are not found in the other set.
If the angular size of a tree at a distance of 0.5 miles is 1/2, how tall is the tree
The tall of the tree is 23.048 ft.
Solution:
Given data:
Angular size of a tree = [tex]\left(\frac{1}{2}\right)^{\circ}[/tex]
Distance = 0.5 miles = 2640 feet
To find the tall of the tree:
Formula to calculate the height of the tree is
[tex]$\text{Physical size}= \text{Angular size}\times\frac{2\pi\times \text{distance}}{360^{\circ}}[/tex]
[tex]$ = \left(\frac{1}{2}\right)^{\circ}\times\frac{2\pi\times 2640}{360^{\circ}}[/tex]
[tex]$ = \left(\frac{1}{2}\right)^{\circ}\times\frac{44\pi}{3^{\circ}}[/tex]
[tex]$ = 23.048[/tex]
Physical size = 23.048 ft
Hence the tall of the tree is 23.048 ft.
A school football team is selling raffle tickets As a fundraiser it cost them $155 to print the tickets and they would like to make at least a $2500 profit how much money do they need to raise to cover the cost of the printing and meet their goals
Answer:
They need $2655 to raise to cover the costs of the printing and meet their goal.
Step-by-step explanation:
Consider the provided information.
As a fundraiser it cost them $155 to print the tickets and they would like to make at least a $2500 profit
Let x (in dollar) represents the fund raised.
The money spent on printing ticket is $155.
The profit they would like to make at least is $2500.
Therefore, the required inequality is:
[tex]x-155\geq 2500[/tex]
Simplify the inequality.
[tex]x\geq 2500+155\\x\geq 2655[/tex]
Therefore, they need $2655 to raise to cover the costs of the printing and meet their goal.
What is the area of this figure?
Enter your answer in the box
What is X plus 11 equals 15
Answer:
X plus 11 equals 15 is 4. X equals 4.
Step-by-step explanation:
X + 11 = 15
4 + 11 = 15
X = 4
to find X you needed to subtract 11 from 15 and what you got would be X
factor this expression completely. 18x^2 - 32
Answer:
2(3x - 4)(3x + 4)
Step-by-step explanation:
Factorizing the below expression requires factoring common term.
[tex]18 {x}^{2} - 32[/tex]
Obviously 2 is common to both 18 and 32. Thus, the answer is:
[tex] = 2(9 {x}^{2} - 16)[/tex]
=2(3x - 4)(3x + 4)
Answer:
the answer above was a little confusing to me so i thought i would just give the answer straight up: 2(3x+4)(3x-4)
Step-by-step explanation:
just did the test! :)
If Kayla ran 9/10 mile yesterday today she ran 8/9 the distance she ran yesterday which day did Kayla run more miles? Explain your reasoning
Answer:
Kayla ran longer miles yesterday than today
Step-by-step explanation:
Distance Kayla ran yesterday be x
Then x = [tex]\frac{9}{10}[/tex] mile
That is x = 0.9 miles
The Distance she ran today be y
Then y = [tex]\frac{8}{9}[/tex] of the distance she ran yesterday
So the distance Kayla ran today
= [tex]\frac{8}{9}[/tex] [tex]\times \text { the distance she ran yesterday }[/tex]
On substituting the value
y = [tex]\frac{8}{9} \times\frac{9}{10}[/tex]
y = [tex]\frac{8}{10}[/tex]
y = 0.8 miles
x is greater than y
0.9 > 0.8
How do you do this question?
Answer:
x={1,2,3}
Step-by-step explanation:
The given inequality is
[tex]1 \leqslant \frac{6x - 1}{3} \: < \: 7[/tex]
We multiply through by the LCM of 3 to get:
[tex]3\leqslant 6x - 1\: < \: 21[/tex]
We add 1 to both sides to get:
[tex]3 + 1\leqslant 6x \: < \: 21 + 1[/tex]
[tex]4\leqslant 6x \: < \: 22[/tex]
Divide through by 6 to get:
[tex] \frac{4}{6} \leqslant x \: < \: \frac{22}{6} [/tex]
This gives us:
[tex]\frac{2}{3} \leqslant x \: < \: \frac{11}{3} [/tex]
[tex]0.67 \leqslant x \: < \:3.67[/tex]
Since x is an integer, the possible values are:
x={1,2,3}
Maggie has a circular table cloth with a 72-inch diameter that she plans to sew lace around. if the lace comes in 3-foot rolls, how many rolls will she need?
She will need 7 rolls of lace
Step-by-step explanation:
The given is:
Maggie has a circular table cloth with a 72-inch diameterShe plans to sew lace aroundThe lace comes in 3-foot rollsWe need to find how many rolls she will need
∵ The diameter of the table is 72 inches
- Change the inches to feet because the length of the lace in
the rolls by feet
∵ 1 foot = 12 inches
∴ 72 inches = 72 ÷ 12 = 6 feet
∵ She plans to sew lace around the table
∴ The length of the lace is equal to the circumference of the table
∵ The circumference of a circle = π d, where d is its diameter
∴ The length of the lace = π(6)
∴ The length of the lace = 18.84955592 feet
∵ The lace comes in 3-foot rolls
- Divide the length of lace by 3 to find the numbers of the rolls
∴ The number of rolls = 18.84955592 ÷ 3
∴ The number of rolls = 6.283185
∴ She must buy 7 rolls
She will need 7 rolls of lace
Learn more:
You can learn more about the circumference of a circle in brainly.com/question/8929610
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What is the approximate area of the circle shown? Use 3.14 to approximate pi. Round your answer to the nearest hundredth.
Answer:
[tex]A=153.86\ cm^2[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ cm[/tex] ----> the radius is half the diameter
substitute
[tex]A=(3.14)(7)^{2}=153.86\ cm^2[/tex]
Answer:
C
Step-by-step explanation
THE ANSWER IS C