Answer:
17,964.9 cubic meters
Step-by-step explanation:
Hey there!
The formula for finding the area of a sphere is:
[tex]V=(4/3)\pi r^3[/tex]
Where V is volume, and r is radius
The question already tells us that the diameter is 32.5m
*Remember, the diameter isn't the radius. It is the radius times two*
Now, we have to divide 32.5 by 2 to get the radius
32.5/2 is 16.25
Now we can plug this into the formula
16.25 cubed is 4291 after being rounded to the nearest tenth
Now we multiply 4291 by 3.14 (pi)
4291 x 3.14 is 13473.7 after being rounded to the nearest tenth
Now multiply 13473.7 by 4/3 and then you will get the volume to the sphere
13473.7 x 4/3 is 17964.93333333...
Since it is asking us to round to the nearest tenth of a cubic meter;
The volume of the sphere will be 17,964.9 cubic meters
[tex]\rule{300}{1}[/tex]
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter (m³)?
[tex]\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
We are asked to find the volume of a sphere, which we can find using the following formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Where:-V=volumeπ=pi (3.14…)r=radiusProvided information:-diameter (d)=32.5 mWhat we need in order to find the volume:-radiusWhat we need in order to find the radius:-Since the radius is exactly one-half of the diameter, we divide the diameter by 2 in order to find the radius:-[tex]\bold{r=d\div2}[/tex]
Replace d with 32.5:-
[tex]\bold{r=32.5\div2}[/tex]
Therefore, the sphere's radius is as follows:-
[tex]\bold{r=16.25}[/tex] m
[tex]\rule{300}{1}[/tex]
Now, let's find the sphere's volume, which, as I mentioned earlier, can be found with the help of this formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Replace r with 16.25:-
[tex]\bold{V=\dfrac{4}{3} \pi (4291)}[/tex] Next, we replace π with 3.14:-
[tex]\bold{V=\dfrac{4}{3} \times3.14\times4291}[/tex]
On simplification,
[tex]\bold{V=\dfrac{4}{3} \times13,473.74}[/tex]
On further simplification,
[tex]\bold{V=17,964.9\:m^3}\Longleftarrow\sf{volume\:of\:the\:sphere}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
Find the area of a circle with a diameter of 14 meters. Round your answer to the nearest hundredth of a square meter.
To find the area of the circle:
⇒ need to know the formula: [tex]\pi r^{2}[/tex]
r: radius or half of diameter's length ⇒ 7 metersLet's calculate:
[tex]Area = \pi (7)^2=49\pi =153.9380m^3[/tex]
The problem asks us to round to the nearest hundreth:
[tex]Area = 153.94m^3[/tex]
Answer: [tex]153.94m^3[/tex]
Hope that helps!
Anyone know the value of x for these
Emilia has a pencil box that is 12 inches long, 5 inches wide, and 3 inches tall. Richard's pencil box is 8 inches long and 5 inches wide, but it is twice as tall as Emilia's pencil box. How many cubic inches larger is Richard's pencil box than Emilia's pencil box?
Answer:
Twice as large, or 180 cubic inches more
Step-by-step explanation:
To find the volume/ cubic inches of Emilia's pencil box, multiply base x width x height.
12 · 5 · 3 = 180
Do the same with Richard's pencil box, but multiply the height by 2
12 · 5 · 3(2) = 360
Subtract 180 from 360 to get 180.
Richard's pencil box is 180 cubic inches larger than Emilia's
Hope this helps!
Help me please help me
the answer to that is -120
Step-by-step explanation:
-120+74=-46
Answer:
k = -120
Step-by-step explanation:
k + 74 = -46
Subtract 74 from both sides:
k + 74 = -46
- 74 - 74
k = -120
Final answer: k = -120
Hope this helps!
h(x) = x2 + 1 k(x) = x – 2
(h + k)(2) =
(h – k)(3) =
Evaluate 3h(2) + 2k(3) =
.
Some newer phones provide a screen time summary, which shows the amount of screen time for a user in a given week. A student would like to estimate the mean screen time for all phone users. She asks a random sample of 50 students at her school to share their screen time for the past 24 hours. The mean screen time for the chosen students is 2.73 hours. Which statement is an appropriate interpretation of the results?
A.)All students probably have screen times close to 2.73 hours.
B.)To obtain a better estimate of mean screen time, more students should be surveyed.
C.)Because of undercoverage, 2.73 likely underestimates the mean screen time of all phone users.
D.)2.73 hours is a suitable estimate for mean screen time of all phone users because a random sample was taken.
Answer:
c
Step-by-step explanation:
got it right on edge
Please, try to answer quickly Due in 1 hr!
Take your values from the previous chart (in question 2) and convert them from Celsius to Fahrenheit follow the example below and use the conversion rule to fill out the chart for degrees Fahrenheit when t = 12 and t = 24 (2 points: 1 point for each row)
The previous chart from question 2 is below. The chart I am trying to fill out is the bigger one That has the above question written on the picture.
All other times this question has been asked it has gone unanswered or with incorrect and incomplete answers please answer the question no matter how old it is because even if I have figured it out someone else can get help from this.
The values of the temperature in degree Celsius (12 and 24) converted to degree Fahrenheit are 53.6°F and 75.2°F respectively.
How to convert the value of temperature?In this exercise, you're required to convert the value of temperature in degree Celsius to degree Fahrenheit. Thus, we would use the following mathematical expression to do the conversion:
F(t) = 9/5C(t) + 32
When t = 12, we have:
F(t) = (9/5 × 12) + 32
F(t) = 21.6 + 32
F(t) = 53.6°F.
When t = 24, we have:
F(t) = (9⁄5 × 24) + 32
F(t) = 43.2 + 32
F(t) = 75.2°F.
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Factor this trinomial
X^2 + 3x - 4
Answer:
(x - 1)(x + 4)
Step-by-step explanation:
What multiplies to (-4) but adds to (3)?
These two values are (4) and (-1). Therefore, these are the values that make up the factored trinomial.
x² + 3x - 4 -----> (x - 1)(x + 4)
You can check your answer by expanding the factors. This is done by multiplying each term within the first parentheses by each term within the second parentheses.
(x - 1)(x + 4) -----> x² - 1x + 4x - 4 -----> x² + 3x - 4
Use definition of a derivative to compute the derivative of g(x)= 1/3x^2
If g(x) = 1/(3x²), the by the definition of the derivative, we have
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{g(x+h) - g(x)}h[/tex]
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{\frac1{3(x+h)^2} - \frac1{3x^2}}h[/tex]
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{\frac{x^2}{3x^2(x+h)^2} - \frac{(x+h)^2}{3x^2(x+h)^2}}h[/tex]
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{x^2 - (x+h)^2}{3x^2(x+h)^2h}[/tex]
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{x^2 - x^2 - 2xh - h^2}{3x^2(x+h)^2h}[/tex]
[tex]\displaystyle g'(x) = - \lim_{h\to0} \frac{2xh + h^2}{3x^2(x+h)^2h}[/tex]
[tex]\displaystyle g'(x) = - \lim_{h\to0} \frac{2x + h}{3x^2(x+h)^2}[/tex]
[tex]\displaystyle g'(x) = - \frac{2x}{3x^4} = \boxed{-\frac2{3x^3}}[/tex]
I am thinking of a number. I multiply it by 8 and subtract 56.
I get the same answer if I multiply by 5 and subtract 8
What is my number?
Answer:
16
Step-by-step explanation:
[tex]8x-56=5x-8\\\\3x-56=-8\\\\3x=48\\\\x=16[/tex]
So, the number is 16
A 13-foot ladder is leaning against a building, forming a right triangle.
The height where the ladder touches the building is seven feet more
than the distance from the base of the ladder to the building. At what
height does the ladder touch the building?
The height from the ground at which the ladder touched the building is 12feet.
What is a right-angled triangle?A right-angled triangle is a type of triangle that has three sides and one of its three angles as 90°.
Analysis:
The ladder length, height of the ladder from the ground, and the distance of the foot of the ladder from the foot of the building form a right angle triangle.
let x, be the distance from the foot of the building to the foot of the ladder.
x+7 = height of ladder from building to foot of building.
length of ladder = 13 feet
using Pythagoras, we have
[tex](13)^{2}[/tex] = [tex]x^{2}[/tex] + [tex](x+7)^{2}[/tex]
169 = [tex]x^{2}[/tex] + [tex]x^{2}[/tex] + 7x + 7x + 49
169 = 2[tex]x^{2}[/tex] + 14x + 49
2[tex]x^{2}[/tex] + 14x = 169-49
2[tex]x^{2}[/tex] + 14x = 120
divide through by 2
[tex]x^{2}[/tex] + 7x - 60 = 0
[tex]x^{2}[/tex] +12x -5x - 60 = 0
(x+12) -5(x+12) = 0
(x+12)(x-5) = 0
x = -12 or 5
Since measurement cannot be negative, therefore x = 5
Height the ladder touches the building is x+7 = 5+7 = 12 feet
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A fish is 18 feet below the surface of a lake. The fish swims up 12 feet before diving 45 feet. What equation can be used to find the current depth of the fish in feet?
a triangle ABC like the one below suppose that a=40, B = 62 and c= 23 (the figure is not drawn to scale) solve the triangle carry your intermediate computations to at least four decimal places , and round your answers to the nearest tenth . if there is more than one solution , use the button labeled "or"
Answer:
Answer:
A =24.7° ; B = 40.6° ; C =114.7°
Step-by-step explanation:
Cosine Law
a² = b²+c²-2bc cos A
b² = c²+a² -2ca cos B
Sum of three angles of a triangle is 180°.
a = 34 ; b= 53; c = 74
Substituting the given values in the cosine law, we have
34² = 53² + 74² - 2*53 *74 * cos A
7844 cos A = 2809 + 5476 - 1156 = 7129
cos A = 7129/7844 = 0.9088
A = cos⁻¹ (0.9088) = 24.6600° = 24.7°
53² = 74² + 34² - 2 (74)(34) cos B
5032 cos B = 5476 + 1156 - 2809 = 3823
cos B = 3823/5032 = 0.7597
B = cos⁻¹ (0.7597) = 40.5622° = 40.6°
Also, A + B + C = 180°
24.7 + 40.6 + C =180
C =180 - 65.3 = 114.7°
∴ A =24.7° ; B = 40.6° ; C =114.7°
Step-by-step explanation:
Im not sure if it is right. But hope it helps
please help me with this
Answer:
In the explanation
Step-by-step explanation:
AB = line segment
ABC = angle
AB = line segment
CD = intersecting line
AC = line segment
AB = line segment
EBC = angle
BC = line segment
Does anyone know how to do this please help
Step-by-step explanation:
the photo should explain
A convoy must carry 44 tons of goods. Because there are 3 trucks that are assigned to other jobs, each of the remaining trucks has to carry an additional 1.5 tons. How many cars did the group have at the beginning? (Know that each truck carries the same number of goods).
please help me!!
Which of the following is in standard form of quadratic?
One morning the temperature in Bangor, Maine was 18 degrees. By afternoon, it had dropped 20 degrees. What was the afternoon temperature? Show your work.
One morning the temperature in Bangor, Maine was 18 degrees. By afternoon, it had dropped 20 degrees. The afternoon temperature in Bangor, Maine, was -2 degrees.
To find the afternoon temperature, we need to subtract 20 degrees from the morning temperature of 18 degrees.
Afternoon temperature = Morning temperature - Temperature drop
Afternoon temperature = 18 degrees - 20 degrees
To perform the subtraction, we have to handle negative numbers:
Afternoon temperature = 18 degrees - 20 degrees
Afternoon temperature = -2 degrees
So, the afternoon temperature in Bangor, Maine, was -2 degrees.
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An equilateral triangle has all sides the same length and all angles the same measure.
Which is the measure of one angle of an equilateral triangle?
30°
45°
60°
90°
Find uv.
v
u
640
10
w
write your answer as an integer or as a decimal rounded to the nearest tenth.
uv =
The value of uv to the nearest tenth or as an integer is 3.1 units
How to find side of a right triangle?uv is the adjacent side of the right triangle.
uv can be found using trigonometric ratios as follows:
Therefore,
tan 63 = opposite / adjacent
Hence,
tan 63 = 6 / adjacent
cross multiply
uv tan 63 = 6
divide both sides by tan 63
uv = 6 / tan 63
uv = 6 / 1.96261050551
uv = 3.05716906145
uv = 3.1 units
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The coordinates of a parallelogram are given segment AB is parallel to the x-axis determine the values for a,b,c,d
Answer:
a=3 d=1 b and c cant be solved
Step-by-step explanation:
because segment AB is parallel to x axis . So the slope of ABco is 0. So the y value is congruent
a=3 d=1
We know AB=CO b+2=8-C
we can only find ad, but we could not get b,c
Angle C is inscribed in circle O. AB start overline, A, B, end overline is a diameter of circle O. What is the measure of \angle B∠Bangle, B?
The measure of ∠angle B when Angle C is inscribed in circle O and AB is a diameter of circle O, is 19 degrees.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.
In the image attached below:
Angle C is inscribed in circle O. AB is a diameter of circle O.The measure of the angle A is,
[tex]m\angle A=71^o[/tex]
The measure of the angle C in a semicircle is,
[tex]m\angle C=90^o[/tex]
The sum of all the angle(interior) of a triangle is equal to the 180 degrees. Thus,
[tex]\angle A+\angle B+\angle C=180\\90+\angle B+71=180\\\angle B=180-90-71\\\angle B=19^o[/tex]
Thus, the measure of ∠angle B when Angle C is inscribed in circle O and AB is a diameter of circle O, is 19 degrees.
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What is the sum? startfraction x over x 3 endfraction startfraction 3 over x 3 endfraction 2 over x 3 endfraction five-thirds startfraction x 5 over x 3 endfraction startfraction x 5 over 3 x 27 endfraction startfraction 6 x over x 3 endfraction
The value of the sum expression [tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex] is 1
How to determine the sum?The expression is given as:
[tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex]
Take the LCM of terms of the expression
[tex]\frac{x}{x +3} + \frac{3}{x + 3} = \frac{x + 3}{x +3}[/tex]
Evaluate the quotient of x + 3 and x + 3
[tex]\frac{x}{x +3} + \frac{3}{x + 3} = 1[/tex]
Hence, the value of the sum expression [tex]\frac{x}{x +3} + \frac{3}{x + 3}[/tex] is 1
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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!
Which expression is equivalent to the one that is modeled?
Answer:
What are the equivalent expressions?
Two expressions are said to be equivalent if they have the same value regardless of the value of the variable(s) in them.
Step-by-step explanation:
Graph on the same axes: y =x^2-4 and y=4-x^2. Write an equation for the part of the graph which is above of the x-axis.
The upper part of the x-axis is a quadratic function and the equation of the upper part is: y = 4 - x^2; -2 < x < 2
How to determine the equation of the graph?The equations are given as:
y = x^2 - 4
y = 4 - x^2
When these equations are plotted, the upper part of the x-axis is a quadratic function that has the following properties:
Zeros = -2 and 2
Because the upper x-axis is open upwards, the equation of the graph is:
y = -(x - zeros)
So, we have:
y - (x - 2)(x + 2)
Evaluate
y = 4 - x^2
Hence, the equation of the upper part is:
y = 4 - x^2; -2 < x < 2
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Mario borrows $620 from his parents and agrees to pay them back the same amount each month without interest. After 6 months of payments, he still owes them $320. Write a linear function to model the remaining amount over time that Francisco has to repay. Identify the slope and the y-intercept in terms of the context.
A linear function that models the remaining amount he would have to repay is y =620 - 50x. The slope is -50 and the y-intercept is 620.
What is the linear function?A linear function is a function in which there is only one variable that is raised to the power of one. Linear functions usually have the form: mx + b.
Where:
x = slope b = y -interceptThe first step is to determine the amount that would be repaid each month: (620 - 320) / 6 = $50
The linear function: =620 - 50x.
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[tex]\huge\color{yellow}\underline \colorbox{violet} {\color{red}{QUESTION}}[/tex]
need answer guys
Answer:
26. c. 6 cm
27. c. 70 cm³
Step-by-step explanation:
Question 26
Volume = Length × Width × Height360 = 10 × 6 × WidthWidth = 6 cmc. 6 cmQuestion 27
Volume = Length × Width × HeightVolume = 7 × 5 × 2Volume = 70 cm³c. 70 cm³Question 28 (not entirely visible)
Solve:
1)
Find Width
10 * W * 6 = 360
W = 360/60
W = 6 cm
2)
Volume
LWH
(2)(7)(5)
70 cm³
3)
Volume
LWH
(7)(3)(4)
84 m³
the factory makes light bulbs the probability that a bulb is defective is 1/15 if 300 light bulbs are tested about how many are expected to be defective
a 20
b 66
c 15
d 30
can you help me solve this equation? 20 POINTS
Answer:
x = 63
Step-by-step explanation:
In [tex]\odot \:O, [/tex] ML and MN are tangents from external points M at points L and N respectively. OL and ON are radii of the circle.[tex]\implies ML\perp OL,\:\&\: MN \perp ON[/tex] (By tangent theorem)[tex]\implies m\angle MLO = m\angle MNO = 90\degree[/tex][tex]m\angle LON = 117\degree[/tex] (Given)In quadrilateral LMNO, by interior angle sum theorem, we have:[tex] m\angle LON+m\angle MOL +m\angle MON +m\angle LMN= 360\degree[/tex][tex] \implies 117\degree+90\degree +90\degree +x\degree= 360\degree[/tex][tex] \implies 297\degree+x\degree= 360\degree[/tex][tex] \implies x\degree= 360\degree-297\degree[/tex][tex] \implies x\degree= 63\degree[/tex][tex] \implies\red{\boxed{\bold{ x= 63}}}[/tex]Answer:
63°
Step-by-step explanation:
The central angle is 117°The angles at the tangent are 90° each (property of tangents)Applying the Angle Sum of Quadrilaterals,
117° + 2(90°) + x° = 360°180° + x° = 243°x° = 63°