Therefore, the formula for the volume of the sphere can be derived by writing an expression that represents the volume of C. The solid between the two cones and the cylinder
What is the Volume of a Sphere?
This refers to the capacity of a sphere, which is the maximum that can be contained in the sphere. This is denoted as V=4/3πr3
Hence, we can see that based on Cavalieri’s principle that states that if two solids of equal height have equal cross-sectional areas, then the two solids have equal volume.
Therefore, the two shaded solids both have a height of 2r units, and thus, to derive the function, we would have to write an expression that represents the volume of the solids between the two cones and the cylinder
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Answer: B
Step-by-step explanation: just did it
Need help please answer ASAP!
(22-23)
Answer:
Question 22 is
[tex]x - 3[/tex]
Question 23 is
[tex]1.67 \times {10}^{ - 21} g[/tex]
Which biconditional statement is NOT true?
The biconditional statement that is not true from the given option is "a triangle is equilateral if and only if it has three sides.
What is a Biconditional Statement?A biconditional statement is one of the logical statements that contain the words "if and only if."
A biconditional statement is true for p ⇔ q provided that both p and q have an exact truth value, and it is false if otherwise.
The biconditional statement that is not true from the given option is "a triangle is equilateral if and only if it has three sides. For a triangle to be equilateral, it is supposed to have three equal angles and three equal sides.
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Answer:
A quadrilateral is rectangle if and only if it has at least two right angles
Step-by-step explanation:
IMAGINE mATH!
PLEASE HELP ASAP TYSM
Answer:
306=192-361xj.
Hope this helps!
(URGENT) Maurice and Rhonda a are traveling in the same direction along the same road. Maurice is traveling at 55 mph and is exactly 15 miles ahead of Rhonda, who is traveling at 65 mph. How many hours will it take Rhonda to catch Maurice?
Answer:
Step-by-step explanation:
Givens
Maurice
55 miles an hour
15 miles ahead of Rhonda
d1
Rhonda
65 miles per hour
d2
The distance has to be the same for both in order to meet.
Formula
d1 = d2
d = r * t where r is the speed.
65*t = 55t + 15 Subtract 55t from both sides
Solution
65t - 55t = 55t - 55t + 15 Combine
10t = 15 Divide both sides by 10
10t/10 = 15t/10
t = 1.5 hours
Answer
They will meet in 1.5 hours.
Which of these describes how the function is increasing and decreasing?
Answer:
increasing from -2 to +∞
Step-by-step explanation:
The graph starts at -2 and continues to the right which means it increases from -2.
Answer:
Increasing from -2 to positive infinity.
Step-by-step explanation: This is because this is the graph of the square root of x + 2. It will increase from -2 in the x range and eventually hit every single x value from -2 to positive infinity.
Use the information in the diagram to find the length of segment AD. Round your answer to the nearest hundredth.
Two triangles, A B C and C B D, with segment C D connecting vertex C with a point D on side A C. Angle C D B is a right angle. Segment C B is 23.2, segment B D is 14.6 and segment C A is 28.6.
Group of answer choices
36.83
22.20
18.03
7.20
Based on the lengths of the given triangles and the length of segment BD, the length of segment AD is 22.20.
What is the length of segment AD?The triangle ABC is a right angled triangle with segment AB being the hypothenuse.
We can therefore find this length using the Pythagoras Rule:
Hypothenuse ² = a² + b²
Hypothenuse ² = 28.6² + 23.2²
Hypothenuse ² = 1,356.20
Hypothenuse = √1,356.20
= 36.83
Length of AD:
= AB - BD
= 36.83 - 14.60
= 22.2
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Factor using the greatest common factor.
6x^4 + 15x^2 + 24x
show work.
Answer: [tex]3x(2x^{3} + 5x + 8)[/tex]
Step-by-step explanation:
[tex]6x^{4} + 15x^{2} + 24x[/tex]
↓
[tex]3x(2x^{3} + 5x + 8)[/tex]
The factored expression is 3x(2x³ + 5x + 8).
To factor the expression 6x⁴ + 15x² + 24x using the greatest common factor (GCF), we first need to identify the common terms or factors that can be factored out from each term.
Step 1: Find the GCF of the coefficients (numbers).
The GCF of 6, 15, and 24 is 3.
Step 2: Find the GCF of the variables (x terms).
The GCF of x⁴, x², and x is x.
Step 3: Combine the GCF of the coefficients and variables.
The GCF of the entire expression is 3x.
Now, factor out 3x from each term:
3x * (2x³ + 5x + 8)
The factored expression is 3x(2x³ + 5x + 8).
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Can somebody help me with this? Please and Thank you
[tex]\text{Given that,}~ p(x) = x^2 +3 ~ \text{and}~ h(x) = \sqrt{x-3} \\\\(p \circ h)(x)\\\\=p(h(x))\\\\=p\left(\sqrt{x-3}\right)\\\\=\left(\sqrt{x-3} \right)^2 +3\\\\=x-3 +3\\\\=x[/tex]
She would also like to tour genoa as well, which would cost her €60.85. if the conversion rate of us dollars to euros at the time of kari’s visit is 1:0.6859, how will this affect her budget? round all dollar values to the nearest cent. a. kari can see genoa and have $60.33 left in her budget. b. kari can see genoa and have $41.38 left in her budget. c. kari has almost exactly enough left in her budget to see genoa. d. kari cannot afford to see genoa, because it would put her $84.48 over budget.
The conversion rate will affect her budget as C. Kari has almost exactly enough left in her budget to see Genoa.
How to illustrate the budget?From the information given, it should be noted that a trip to Genoa will cost her €60.85.
This will be converted to dollars which will be:
= 60.85/0.6859
= 88.72
Therefore, out of the $585 budget, only $88.72 is used.
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PLEASE HELP
a41= 5 7 2
wha is 10% of 695,000
Answer:
[tex]69500[/tex]
Step-by-step explanation:
[tex] \frac{695000}{1} \times \frac{10}{100} \\ \\ = 69500[/tex]
At what point does the line given by the following equation cross the y-axis?
y = 6/9x+3
a. (0,3)
b. (3,0)
c. (0,-)
d. (-9/2,0)
Answer:
A
Step-by-step explanation:
In a slope-intercept equation, the format goes like this:
y = mx + bM = Slope
B = Y-intercept
In the equation, y = 6/9x + 3:
The slope is 6/9
The y-intercept is 3.
So what the question means by "cross the y-axis" is when the line on the graph is going through the y-intercept point.
Because the y-intercept is 3, the ordered pair would look like this:
(0, 3)
Note: The y-intercept is when the x-intercept has a value of 0 and the y-intercept is only on the y-axis, never the x-axis.
Therefore, the answer would be Option A. (0, 3)
Carl is covering the rectangular prism-shaped
box with cloth.
5 in.
2 in.
-
12 in.
what is the minimum amount of cloth carl
needs to cover the entire box?
The minimum amount of cloth carl needs to cover the entire box will be 188 square inches.
What is a surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called the surface area.
Given that:-
The length width and the height of the prism are 5 , 2 , and 12 inches respectively.The minimum amount of cloth carl needs to cover the entire box will be the surface area of the prism
Surface area = 2 [ (5 x 2)+ (12 x 5) + (12 x 2)]
Surface area= 188 square inches
Therefore the minimum amount of cloth carl needs to cover the entire box will be 188 square inches.
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A store buys 17 sweaters for $68 and sells them for $561. How much profit does the store make per sweater?
He makes a profit in total of $8381
The store makes a profit of $29 per sweater.
Here, we have to calculate the profit per sweater, we need to find the difference between the selling price and the cost price (purchase price) of each sweater.
Given:
Number of sweaters bought = 17
Cost of buying 17 sweaters = $68
Selling price of 17 sweaters = $561
Profit per sweater = Selling price per sweater - Cost price per sweater
First, calculate the cost price per sweater:
Cost price per sweater = Total cost / Number of sweaters
Cost price per sweater = $68 / 17
Cost price per sweater = $4.
Now, calculate the profit per sweater:
Profit per sweater = Selling price per sweater - Cost price per sweater
Profit per sweater = $561 / 17 - $4
Profit per sweater = $33 - $4
Profit per sweater = $29.
The store makes a profit of $29 per sweater.
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look at the image below lol
Answer:
1.7.
Step-by-step explanation:
2x^3 + 9x^2 - 2x + 8 = 40
Substituting values for x in the range 1 to 2:
when x = (1.1):
f(1.1) = 2(1.1)^3 + 9(1.1)^2 - 2(1.1) + 8 = 19.32.
x = 1.3:
f(1.3) = 25.004
F(1.5) = 32
F(1.6) = 36.032
F(1.7) = 40.436 which is just greater than 40.
So the root is between 1.6 and 1.7.
f(1.65) = 38.19
Therefore the root is > 1.65 and < 1.7
and to 1 DP it is 1.7.
To join the game club, you must pay $7 a month plus
$3 per game (x) that you download. Write an
expression to show the total cost per month to be a
member of the game club.
Answer: Total cost/month = 7 + 3x
Step-by-step explanation:
This is only the total cost per month that is why it is only 7 and 3x since the number of downloaded games is not given.
I'm not sure about my answer but I hope that it helps.
Select the correct answer. if you roll a single six-sided die, what is the probability of rolling an odd number? a. b. c. d. 3
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
P(odd number)= [tex]\frac{3}{6}[/tex]
=[tex]\frac{1}{2}[/tex]
What is the volume of this aquarium?
Answer:
9000 in³
Step-by-step explanation:
Small cube:
Volume = length x width x height
= 10 x 10 x 10 = 1000 in³
Big cube:
width (front) = 20
length (side) = 10 + 10 = 20
height (back) = 10 + 10 = 20
V = 20 x 20 x 20 = 8000 in³
Total volume: 1000 + 8000 = 9000 in³
Can someone please solve for me
Let x = 0.263263263…
Then 1000x = 263.263263263…
Subtracting x gives
1000x - x = 263.263263263… - 0.263263263…
999x = 263
x = 263/999
help meeeeee 1/2 X (6 X 4)+3 + 2
6x4=24
24x1/2=12
12+3=15
15+2=17
17 is the answer
What is the value of s to the nearest whole number? 10 12 13 14
The value of s to the nearest whole number is 14. The correct option is the last option 14
TrigonometryFrom the question, we are to determine the value of s
Using the laws of cosines
a² = b² + c² -2bc Cos A
Then,
s² = 8² + 9² -2(8)(9) cos111°
s² = 64 + 81 - 144 cos111°
s² = 145 - (-51.605)
s² = 145 + 51.605
s² = √196.605
s = 14.0216
s ≅ 14
Hence, the value of s to the nearest whole number is 14. The correct option is the last option 14
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Tim, Ryan, and Joe are brothers. Their mom, Lisa gives them each a weekly allowance. Since Tim is older, she gives him 4 more dollars than Joe. Ryan is the youngest and receives 2 less dollars than Joe. Lisa gives a total of 20 dollars a week in allowance. With Joe receiving m dollars, which equation demonstrates the situation?
Answer:
m + (m+4) + (m-2) = 20 or 3m + 2 = 20
Step-by-step explanation:
19. A soccer field is a rectangle 90 meters wide and 120 meters long. If you were
asked to run from one corner to the other corner diagonally across, what is the
distance?
a. 150 meters
b. 1500 meters
c. 15 meters
d. 200 meters
Find the zeroes of the polynomial 100x^2 - 81
Answer:
x = ±0.9Step-by-step explanation:
The algebraic identity to be used here :
a² - b² = (a + b)(a - b)We know that :
100x² = (10x)²81 = 9²Therefore,
100x² - 81 (10x + 9)(10x - 9)The zeros are :
10x + 9 = 0 ⇒ 10x = -9 ⇒ x = -9/10 ⇒ x = -0.910x - 9 = 0 ⇒ 10x = 9 ⇒ x = 9/10 ⇒ x = 0.9Answer:
[tex]x=-\dfrac{9}{10} \quad x=\dfrac{9}{10}[/tex]
Step-by-step explanation:
[tex]\begin{aligned}100x^2-81 & =(10^2)x^2-9^2\\ & = (10x)^2-9^2\end{aligned}[/tex]
[tex]\textsf{Difference of Two Squares Formula}: \quad a^2-b^2=\left(a+b\right)\left(a-b\right)[/tex]
[tex]\implies a=10x \: \textsf{ and } \: b=9[/tex]
[tex]\implies 100x^2-81=(10x+9)(10x-9)[/tex]
[tex]\begin{aligned}\textsf{To find the zeros}: \quad 100x^2-81 & = 0\\\\\implies (10x+9)(10x-9) & =0\\\implies 10x+9 & =0 \implies x=-\dfrac{9}{10}\\\implies 10x-9 & =0 \implies x=\dfrac{9}{10}\end{aligned}[/tex]
Roadstone Limited can resurface 7/8km of a road in a day. How many days will it take
to resurface a road of length 14 km?
Answer:
16 daysStep-by-step explanation:
Let x be the number of days that it will take.
7/8 km per 1 day
14 km per x day
We have to solve the equation:
[tex]\frac{x}{1} =\frac{14}{\left( \frac{7}{8} \right) }[/tex]
[tex]\Longrightarrow x=14\times \frac{8}{7} =2\times 8=16[/tex]
the units of a two-digit numeral is 5 more then the tens digit. the number is three times the sum of its digits. find the numeral
Answer:
27
Step-by-step explanation:
Let x = ten's digit
Let y = units' digit
Given: the units of a two-digit numeral means
that our final answer will be a 2 digit number (xy)
Given: 5 more than the tens digit means
y is 5 more than x (y = x + 5)
Given: the number is three times the sum of its digits.
xy is 3 times x + y
A two digit positive integer can be written as 10x + y, where x is the tens digit and y is the ones digit
y = x + 5 and 10x + y = 3(x + y)
x - y = -5
7x - 2y = 0
Multiply the first equation by -2:
-2x + 2y = 10
7x - 2y = 0
Add the equations to get 5x = 10
So, x = 2 and y = x + 5 = 7
Reminder:
Let x = ten's digit
Let y = units' digit
The number is 27
A person can read 24 pages of a book in 1/3 of an hour. What is this person's reading rate in pages per hour?
48
12
72
8
Answer:
72
Step-by-step explanation:
If he reads 24 pages in 1/3 of an hour, he reads 3 times as many pages in 1 hour.
3 × 24 pages = 72 pages
Answer: 72
If X=3 and y= -2, find xy + 2y.
-2
-9
-10
-1
Answer:
-10 is the answer
Step-by-step explanation:
[tex]xy + 2y \\ putting \: the \: value \: of \: x \: and \: y \\ 3 \times ( - 2) + 2 \times ( -2 ) \\ - 6 - 4 \\ = - 10[/tex]
(4a^3 - 36a^2 + 60a^2 + 72) \ (a - 6)
Answer:
4a^2+48a+288+(fraction)1800/a-6
Step-by-step explanation:
HELP FAST ITS EASY I JUST NEED TO MAKE SURE PLEASE SOMEONE WHO HAS REAL SKILL AND CAN FINSH THIS ANSWER IT PLEASE I BEG U GUYS I NEED TO FINISH (GIVING BRAINLIEST!!)
Answer: 71/28 or 2 15/28
Step-by-step explanation:
Turn both fractions into improper fractions.
5 1/4 = 21/4
2 5/7 = 19/7 multiply the denominator with the whole then add the numerator, same denominator.
21/4 - 19/7 = ? find common denominator to subtract
4 x 7 = 28 common denominator
Divide the new denominator by previous denominators then multiply by each respective numerator. 28 divided by 4 is 7 multiplied by 21 is 147, the same happens with 19/7.
147/28 - 76/28 = 71/28 or 2 15/28
