The volume of the given sphere is 32 cm³. Thus, the correct answer is option (A) 32 cm³.
Given that the diameter of the sphere is 4 cm, the radius is half of that or 2 cm.
The formula for the volume of a sphere is:
V = (4/3)πr³
Where r is the radius of the sphere.
Here, r = 2
Substituting these values into the formula, we get:
The volume of a sphere = (4/3) × π × (2)³
The volume of a sphere = (4/3)π(8)
The volume of a sphere = 32π/3
Using π = 3.14, we get:
The volume of a sphere ≈ 33.51 cm³
Therefore, the closest option to the volume of the sphere is 32 cm³.
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Carly and Gina read the following problem in their math class:
Seven cereal bars were shared equally by 3 children. How much did each child receive?
Carly and Gina solve the problem differently. Carly gives each child 2 whole cereal bars and then divides the remaining cereal bar among the 3 children. Gina divides all the cereal bars into thirds and shares the thirds equally among the 3 children.
a. Illustrate both girls’ solutions.
b. Explain why they are both right.
Answer:
Part a) and Part b) see the explanation
Step-by-step explanation:
Part a) Illustrate both girls’ solutions
Carly
Carly gives each child 2 whole cereal bars and then divides the remaining cereal bar among the 3 children
so
1) Each child receive first 2 whole cereal bars
the remaining is
[tex]7-(2+2+2)=7-6=1\ cereal\ bar[/tex]
2) Divides the remaining cereal bar among the 3 children
Each child receive 1/3 cereal bar
3) Each child receive in total
[tex]2+\frac{1}{3}=2\frac{1}{3}\ cereal\ bar[/tex]
Gina
Gina divides all the cereal bars into thirds and shares the thirds equally among the 3 children.
so
1) Divide the total bars by 3
Each child receive
[tex]\frac{7}{3}\ cereal\ bar[/tex]
Part b) Explain why they are both right
Compare the results
Carly ----> [tex]2\frac{1}{3}\ cereal\ bar[/tex]
Gina ----> [tex]\frac{7}{3}\ cereal\ bar[/tex]
Convert mixed number to decimal number
[tex]2\frac{1}{3}\ cereal\ bar=2+\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}\ cereal\ bar[/tex]
so
[tex]2\frac{1}{3}\ cereal\ bar=\frac{7}{3}\ cereal\ bar[/tex]
therefore
Carly and Gina are right
Use rounding to estimate the product
Question: 4 3/4 * 7 2/17
A. About 28
B. About 32
C. About 35
D. About 40
Answer:
The estimate of the product is about 35 answer C
Step-by-step explanation:
- We use rounding to estimate the product of two fractions
- The mixed number has whole number and fraction
- To round the mixed number we look to the fraction
- If the numerator is half or greater than half the denominator, then we
add the whole number by 1 and cancel the fraction
- If the numerator is less than half the denominator, then we keep the
whole number as it and cancel the fraction
- Ex: If the mixed number is [tex]2\frac{3}{4}[/tex], 3 is more than
half 4 then we will add 2 by 1 and cancel the fraction part, the
mixed number [tex]2\frac{3}{4}[/tex] after rounding is 3
- Ex: If the mixed number is [tex]5\frac{1}{4}[/tex], 1 is less than
half 4 then we will keep 5 as it and cancel the fraction part, the
mixed number [tex]5\frac{1}{4}[/tex] after rounding is 5
* Lets solve the problem
∵ In the part [tex]4\frac{3}{4}[/tex] 3 is more than half 4
∴ The rounding value of [tex]4\frac{3}{4}[/tex] is 5
∵ In the part [tex]7\frac{2}{17}[/tex] 2 is less than half 17
∴ The rounding value of [tex]7\frac{2}{17}[/tex] is 7
∴ [tex]4\frac{3}{4}*7\frac{2}{17}=5*7=35[/tex]
* The estimate of the product is about 35
t varies inversely as the square root of u.
t = 3 when u = 4.
Find t when u = 49.
Answer:
t = [tex]\frac{6}{7}[/tex]
Step-by-step explanation:
Given that t varies inversely as the square root of u then the equation relating them is
t = [tex]\frac{k}{\sqrt{u} }[/tex] ← k is the constant of variation
To find k use the condition t = 3 when u = 4, thus
k = t[tex]\sqrt{u}[/tex] = 3 × [tex]\sqrt{4}[/tex] = 3 × 2 = 6
t = [tex]\frac{6}{\sqrt{u} }[/tex] ← equation of variation
When u = 49, then
t = [tex]\frac{6}{\sqrt{49} }[/tex] = [tex]\frac{6}{7}[/tex]
The value of 't' when 'u = 49' in the equation [tex]'t = k/\sqrt(u)[/tex]' is approximately '0.86'. This was calculated using the concept of inverse variation in mathematics.
Explanation:The question is dealing with the concept of inverse variations in math. The given expression states that 't' varies inversely with the square root of 'u'. This can be represented mathematically as [tex]'t = k/\sqrt(u)',[/tex] where 'k' is the constant of variation.
From the problem we know that 't = 3' when 'u = 4'. Substituting these terms in into the equation above, we can solve for 'k'. Doing this yields [tex]'k = 3\times \sqrt(4) = 6.'[/tex]
Now that we have found 'k', we can find the value of 't' when 'u = 49'. We can do this by plugging in the known values into the equation. So [tex]'t = 6/\sqrt(49)'.[/tex] It simplifies to 't = 6/7' or about '0.86'.
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What is 8363 x 9374)?
Answer:7,836,664
Step-by-step explanation:I used a calculator
Answer:
Step-by-step explanation: 36,211,762
In the problem 5 divided 3/5 instead of dividing 5 by 3/5 we can find the answer by multiplying 5 by what number
Answer:
5/3
Step-by-step explanation:
If you do 5/ 3/5 what youre really doing is just doing two division problems which by the way equals 5/0.6 or 8.3333333
But one thing i realized when i was doing division by fractions is that if you flip the fraction then you can multiply and you get the same exact answer. SO lets try: 5/3 = 1.6666
1.6666*5=8.3333333
So you can use that trick when dividing a whole number by fractions. It makes it a lot easier.
The official answer is instead of dividing 5 by 3/5 you can instead multiply 5 by 5/3 and get the same answer!
How do you do scientific notation with the number 0.2058
Answer:
2.058 x 10 to the -1st
Step-by-step explanation:
Help!!! Easy apparently? Right answers only!!
Answer:
It is A
Explanation:
Two points will always be collinear, but the same can't be said for three, since in some occasions one point is outside the line.
What is the answer for A?
Answer:
a=2B/d-l
Step-by-step explanation:
da-la=2B
1) Factor out an a from (da-la):
a(d-l)=2B
2) Divide both sides by (d-l):
a=2B/d-l
please help me
500+150+20+6=
1. Write the product using exponents. (1 point)
7.7.7
When multiple of the same number are multiplied together, this can be represented as an exponent. An exponent is a way to write repeated multiplication of a number by itself. In your case, 7 multiplied by itself 3 times (7*7*7) can be written using exponents as 7^3.
Explanation:In mathematics, when you multiply the same number multiple times, you can express that multiplication as an exponent. An exponent tells you how many times to multiply the number, or the base, by itself. For example, in your question, the number 7 is multiplied by itself 3 times (7*7*7), so this multiplication can also be written with exponents. The correct way to express this multiplication using exponents is 73.
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Someone plzzz help I’m lost :(
Answer:
j = (h-4) / k
Step-by-step explanation:
Unless there is more information given about this question somewhere else in the assignment, I'm assuming you are being asked to solve this equation for j.
If so, then its just a matter of rearranging the equation so that it is in the form
j = (expression containing other variables)
(h-4) / j = k (multiply both sides by j)
(h-4) = jk (divide both sides by k)
j = (h-4) / k
Which number is between 21 and 3π 2 ? A π + 1 B 14 3 C 5 D 26
The answer is D, 26. [tex]3\pi^2[/tex] is about 26.6!
Final answer:
The number that is between 21 and 3π/2 is 5.
Explanation:
To find the number that is between 21 and 3π/2, we need to determine the value of 3π/2 first. Since π is approximately 3.14, 3π/2 is approximately (3)(3.14)/2 = 4.71.
Now we can compare this value to 21. Since 4.71 is less than 21, we need to find a number that is greater than 4.71 but less than 21. The only option in the given choices that fits this criteria is Option C, 5.
Katie collects stamps. She has stamps from Canada, the U.S.A, and the rest of the world in a ratio of 1: 1.2: 1.5. She has 135 stamps from the rest of the world.
a) How many stamps are from Canada?
b) How many stamps are from the U.S.A?
c) What is the total number of stamps in Katie's collection?
(Please explain and show how you got those answers.)
Answer:
Step-by-step explanation:
: I got A)90
B)108
C)333
Hope that's right. I checked it 4 times.
Answer:
Step-by-step explanation:
A) 90
B) 108
C)333
What values could be substituted for x to make a true number sentence in x + 4 = x + 8
The number of campers who sign up for archery each week is listed in the table. If the relationship is proportional, how many campers will sign up for archery in Week 3?
Archery Sign Up Total Campers
Week 1 36 120
Week 2 45 150
Week 3 ? 130
A. 54
B. 40
C. 41
D. 39
Answer:
[tex]\boxed{39}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcc}& \textbf{Archery Sign Up} & \textbf{Total Campers}\\\textbf{Week 1} & 36 & 120\\\textbf{Week 2} & 45 & 150\\\textbf{Week 3} & ? & 130\\\end{array}[/tex]
Let x = Total campers
and y = Archery sign up
In a direct proportionality,
y = kx
1. Calculate the value of k
Substitute a pair of values for x and y
150 = k × 45
Divide each side by 45
k = 150/45 = 10/3
2. Calculate the value of x in Week 3
[tex]\begin{array}{rcl}130& = & \dfrac{10}{3}x\\\\390 & = & 10x\\x & = & \mathbf{39}\\\end{array}[/tex]
[tex]\boxed{\textbf{39 campers}} \text{ will sign up for archery in Week 3}[/tex]
The diagram is a graph of your proportionality. It shows that y = 130 when x = 39.
Manuel spent a total of $40 at the grocery store. Of this amount, he spent $36 on fruit. What percentage of the total did he spend on fruit?
Final answer:
Manuel spent 90% of his total grocery expenses on fruit. To calculate this, the amount spent on fruit ($36) is divided by the total spent ($40), and then multiplied by 100%.
Explanation:
Manuel spent a total of $40 at the grocery store and out of that, $36 was spent on fruit. To find out the percentage that he spent on fruit, you can use the formula:
Percentage = (Amount spent on fruit / Total amount spent) x 100%
Plugging in the values gives us:
Percentage = ($36 / $40) x 100% = 0.9 x 100% = 90%.
Thus, Manuel spent 90% of his total grocery expenses on fruit.
In the figure below, the arc x is formed on the unit circle by angle θ . What is the measure of angle θ in radians? A x B π−x C π/2 D π
Answer:
A. x radians
Step-by-step explanation:
The circumference of the unit circle is
[tex]2\pi r=2\pi \cdot 1=2\pi[/tex]
The full rotation angle has the measure [tex]2\pi[/tex] radians.
So,
[tex]\begin{array}{cc}\text{Angle}&\text{Arc length}\\ \\2\pi &2\pi \\\theta &x\end{array}[/tex]
Write a proportion:
[tex]\dfrac{2\pi }{\theta}=\dfrac{2\pi }{x}[/tex]
Cross multiply:
[tex]2\pi x=2\pi \theta\\ \\\theta=x[/tex]
I need help please?!!!
What is the answer to M- 7 =1?
Answer:
m=8
Step-by-step explanation:
m-7=1
+7 +7
m=8
(A) Write an expression for a number that is five
times greater than two
Easy middle school number line plotting!! Please help!! Can you tell me if I plotted the ones right? And plot the 3.11
Answer:
3.11 is infinite so we would plot that 1 tick past 3 as the graph is going in increments of .50 and the square root of 7 is 2.64 which we would round to 2.7 (i could be wrong about rounding) soo in your case i would go with 2.6 which is 1 tick past 2.5
Step-by-step explanation:
its been a long time since ive done this and im currently in pre calc 11th grade math so if i got some of the wrong im very sorry :-(
fritz drew an array with 5 rows of dots . he drew 15 dots altogether. how many dots are in each row of fitz's array ? how do you know ?
There are 3 dots in each row of Fritz's array. This conclusion is reached by dividing the total number of dots (15) by the number of rows (5). This is an exercise in simple division and understanding arrays in mathematics.
Explanation:The subject of this question from Fritz is Mathematics, specifically, it's about arrays and simple division.
To find out how many dots are in each row of Fritz's array, we need to use division. In this case, the total number of dots (15) would be divided by the number of rows (5).
So, we calculate: 15 ÷ 5 = 3.
So, there are 3 dots in each row of Fritz's array. We know this is correct because the definition of an array in mathematics is a collection of objects or numbers arranged in rows, and each row has the same number of items.
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Ar which root does the graph of P(x) = (x + 4)(x + 7) cross the x-axis?
Answer:
(-4,0)(-7,0)
Step-by-step explanation:
The x axis is crossed when y = 0.
That happens in two places.
x +4=0 is one place
x = - 4 when it does.
x + 7 =0 is the other.
x = - 7
Which of the following expressions are equivalent? Please explain so I can understand.
Answer:
B and D
Step-by-step explanation:
Expression B = 1/[tex]x^{-1}[/tex] = 1/ (1/x) = x
Expression D = [tex]x^{1/3}[/tex] [tex]x^{1/3}[/tex] [tex]x^{1/3}[/tex]
= [tex]x^{1/3 + 1/3 + 1/3}[/tex]
= [tex]x^{1}[/tex]
= x
as shown above the both the value of B and D are equal to x and hence the expressions are equivalent
A pallet of boxes weighed
738 kilograms. If there
were 6 boxes on the pallet
and each box weighed the
same amount, how much
did each weigh?
An archi
hotel do
bought
the roor
gets 7 la
rooms d
have?
Answer:
4428
Step-by-step explanation:
—-
PB. It has endpoints at -2 and 12. What is the coordinate of its midpoint
Answer:
The midpoint is 5
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two numbers is
[tex]M=(\frac{x1+x2}{2})[/tex]
we have
[tex]x1=-2, x2=12[/tex]
substitute
[tex]M=(\frac{-2+12}{2})[/tex]
[tex]M=(\frac{10}{2})[/tex]
[tex]M=5[/tex]
therefore
The midpoint is 5
What is the next term of the geometric sequence. 135,45,15
Answer:
5
Step-by-step explanation:
Each term is 1/3 of the preceding term
135 / 3 = 45
45 / 3 = 15
15 / 3 = 5
Answer:
Keep dividing the number by 3.
The next number is 5.
Step-by-step explanation:
-3(1 + 6x) = 14 - x
How do you solve this?
Raj is mixing different colors of paint. The table shows the amount of each color paint Raj uses for each mixture. Select the two mixtures that will create the same color.
Answer:
Mixture 1 and Mixture 2 will create the same color
Step-by-step explanation:
we know that
If two mixtures create the same color, then the proportion of the painting in the mixtures must be the same
Let
x ----> the ounces of a red paint in the mixture
y ----> the ounces of a blue paint in the mixture
Verify the proportion of the paints in each mixture
Mixture 1) x=2, y=1
[tex]\frac{2}{1}=2[/tex]
Mixture 2) x=7, y=3.5
[tex]\frac{7}{3.5}=2[/tex]
Mixture 3) x=4.5, y=2
[tex]\frac{4.5}{2}=2.25[/tex]
Mixture 4) x=5.5, y=2.5
[tex]\frac{5.5}{2.5}=2.2[/tex]
therefore
Mixture 1 and Mixture 2 will create the same color, because have the same ratio
Answer:
Mixture 1 and Mixture 2
Step-by-step explanation:
It is given that Raj is mixing different colors (blue and red) of paint to make a new color.
If two mixtures have same ratio of red and blue color, then that will create the same color.
The ratio of red and blue color in each mixture is shown below:
Mixture 1: [tex]\frac{Red}{Blue}=\frac{2}{1}=2:1[/tex]
Mixture 2: [tex]\frac{Red}{Blue}=\frac{7}{3.5}=\frac{2}{1}=2:1[/tex]
Mixture 3: [tex]\frac{Red}{Blue}=\frac{4.5}{2}=\frac{9}{4}=9:4[/tex]
Mixture 4: [tex]\frac{Red}{Blue}=\frac{5.5}{2.5}=\frac{11}{5}=11:5[/tex]
From the above calculation it is clear that the ratio of red and blue color in mixture 1 and mixture 2 is same.
Therefore, Mixture 1 and Mixture 2 will create the same color.
Write the value of the underlined digit 7,270
I am sorry but I do not see the underlined digit, but I will put it this way. 7 in the thousands place is worth 7000, 2 in the hundreds place is worth 200, 7 in the tens place is worth 70, and 0 in the ones place is worth 0.
Hope this helped!
Nate