Answer: 1035 cm^2
Step-by-step explanation:
Given that the shape s is exactly one quarter of solid sphere.
Where the volume of the shape s is 1994πcm^3.
The formula for volume of a sphere is
V = 4/3πr^3
The volume will be divided by 4 since the given solid is exactly quarter of solid sphere. Then equate it to the given value
1994π = 4/3πr^3 × 1/4
The π will cancel out
1994 = r^3/3
Cross multiply
5982 = r^3
r = cube root of 5982
r = 18.2 cm
The surface area of a sphere is
A = 4πr^2
Substitute r in the formula
A = 4× π × 18.2^2
A = 4141
Since the shape is exactly one quarter of solid sphere. Divide the answer by 4
A = 4141/4
A = 1035.3 cm^2
The surface area of s is therefore 1035.3 cm^2
The surface area of the shape s is approximately 329.53 cm².
Important information:
Shape s is exactly one-quarter of a solid sphere.The volume of the shape s is 1994π cm².Sphere:Volume of a sphere is:
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
The volume of one-quarter of a solid sphere is 1994π cm².
[tex]1994\pi=\dfrac{1}{4}\times \dfrac{4}{3}\pi r^3[/tex]
[tex]1994\pi=\dfrac{1}{3}\pi r^3[/tex]
[tex]\dfrac{1994\pi\times 3}{\pi}=r^3[/tex]
[tex]5982=r^3[/tex]
Taking cube root on both sides, we get
[tex]\sqrt[3]{5982}=r[/tex]
[tex]r\approx 18.153[/tex]
Surface area of a sphere is:
[tex]S=4\pi r^2[/tex]
Surface area of one quarter of solid sphere is:
[tex]S=\pi r^2[/tex]
[tex]S=\pi (18.153)^2[/tex]
[tex]S=329.5314\pi[/tex]
[tex]S\approx 329.53\pi[/tex]
Therefore, the surface area of the shape s is 329.53 cm².
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Kirk bought 2 1/4 punds of lemons. He used 1/4 of the lemons to make lemonade. Kirk completed his work and found that he hsed 9 pounds of lemons . Did hs do rhe work correctly?
Answer:
How could he have used 9 lbs of lemons when he only went and bought 2 1/4 lbs? So, his work was NOT correct.
Step-by-step explanation:
Answer:
it is d
Step-by-step explanation:
got it right
If f(x)=8-10x and g(x)=5x+4, what is he value of (fg)(-2)
Answer:
168
Step-by-step explanation:
We would like to multiply these two expressions together and then substitute -2 in for x to solve.
f(x) * g(x) = (8 - 10x) * (5x + 4)
We will use FOIL (first, outer, inner last):
(8 - 10x) * (5x + 4) = 8 * 5x + 8 * 4 + (-10x) * 5x + (-10x) * 4
Combining terms, we get:
f(x) * g(x) = 32 - 50x²
Plug -2 in for x:
32 - 50 * (-2)² = 32 - 50 * 4 = 32 - 200 = -168
The answer is thus 168.
~ an aesthetics lover
In the triangles, HG = MP and GK = PN. Triangles H G K and M P N are shown. Side H K has a length of 15 millimeters. Side M N has a length of 11 millimeters. Sides H G and M P are congruent. Sides G K and P N are congruent. Which statement about the sides and angles is true?
Answer:
m∠G > m∠P
Step-by-step explanation:
Given that:
HG = MP and GK = PN., Side H K has a length of 15 millimeters. Side M N has a length of 11 millimeters.
The triangle law for unequal sides states that if two sides are unequal. the angle opposite the longer side is greater than the angle opposite the shorter side. Since side HK has a length of 15 millimeters and Side MN has a length of 11 millimeters, the angle opposite side HK (which is m∠G) is greater than the angle opposite side MN (which is m∠P). That is m∠G > m∠P.
Answer:
A.
Step-by-step explanation:
Andre types 208 words in 4 minutes. Noah types 342 words and 6 minutes.who types faster explain?
Answer:
Noah
Step-by-step explanation:
Find how many words each person types in one minute. Andre types 208/4=52 words/min and Noah types 342/6=57 words/min. The answer is Noah.
Answer:
noah types faster
Step-by-step explanation:
Andre
208 words/ 4 minutes =
52 words per minute
Noah
342 words / 6 minutes = 57 words per minute
Simplest form w^3-w(w^2+2w-1)+2w
Answer:
[tex] - 2 {w}^{2} + 3w[/tex]Solution,
[tex] {w}^{3} - w( {w}^{2} + 2w - 1) + 2w \\ = {w}^{3} - {w}^{3} - 2 {w}^{2} + w + 2w \\ = - 2 {w}^{2} + 3w[/tex]
Some rules:
[tex]( + ) \times ( + ) \ = ( + ) \\ ( - ) \times ( + ) = ( - ) \\ ( + ) \times ( - ) = ( - ) \\ ( - ) \times ( - ) = ( + )[/tex]
Hope this helps...
Good luck on your assignment..
Can someone please help me I really need help please help me thank you
Answer:
(-1,-1), (2,1), (5,3)
Step-by-step explanation:
We can use the formula: rise/run to solve x and y. Since we know the slope is 2/3, 2 will be rise (going up on y axis), and 3 will be run (moving right on x axis).
We are given the point, (2,1) which we can use to find the 2 points that are needed. By using rise/run, we can find the highest point which is (5,3)
How to get the highest point:
(2 + 3, 1 + 2)
Now we can find the lowest point: (-1,-1)
(2 - 3, 1 - 2)
Can someone help me with this question please?
Answer:
If the ratio of edge lengths is 3:5, I'm going to assume that the perimeters are going with the same ratio.
Therefore, the ratio would be 345:575.
Hope this is right and helps :)
Helppp!!!! please!!!
Answer:
[tex]128m^{2}[/tex]
Step-by-step explanation:
[tex]A=\frac{1}{2} (\frac{b}{h} )\\A=\frac{1}{2} (\frac{8}{8} )\\A=\frac{1}{2} (64)\\A= 32 m^{2} \\[/tex]
So, the area of 1 triangle is 32m^2.
To find the whole area, you will have to multiply 32 by 4.
Hence, your answer is [tex]128m^{2}[/tex]
Draw a picture of the standard normal curve and shade the area that corresponds to the requested probabilities. Then use the standard normal table to find the following probabilities. Enter the probabilities as decimals. Enter the final answer only.
1.P(z>1.38)=
2.P(1.233.P(z<−0.42)=
3.P(z<−0.42)=
4. P(−2.645.P(z<3.04)=
5. P(z<3.04)
6.P(07.P(z>−2.43)=
7.P(z>−2.43)=
Answer:
(1) P (z > 1.38) = 0.08379
(2) P (z < - 0.42) = 0.33724
(3) P (z < 3.04) = 0.99882
(4) P (z > -2.43) = 0.00755
Step-by-step explanation:
(1)
Compute the value of P (z > 1.38) as follows:
[tex]P(z>1.38)=1-P(z<1.38)\\=1-0.91621\\=0.08379[/tex]
(2)
Compute the value of P (z < -0.42) as follows:
[tex]P(z<-0.42)=1-P(z<0.42)\\=1-0.66276\\=0.33724[/tex]
(3)
Compute the value of P (z < 3.04) as follows:
[tex]P(z<3.04)=0.99882[/tex]
(4)
Compute the value of P (z > -2.43) as follows:
[tex]P(z>-2.43)=1-P(z<2.43)\\=1-0.99245\\=0.00755[/tex]
A baker is making cookies. She uses 3 cups of flour for every 8 oz of chocolate chips
How many cups of flour are needed with 192 oz of chocolate chips?
Answer: 72cups
Step-by-step explanation:
there are 8oz in a cup, so 8oz x 3cups = 24oz
[tex]\\ \frac{24}{8} \ = \frac{x}{192} \\(24) (192) = 8x\\(3) (192) = x\\576=x\\[/tex]
[tex]\frac{576}{8} = 72cups[/tex]
The baker will need 72 cups of flour for 192oz of chocolate chips.
The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day
Answer:
The second option.
Step-by-step explanation:
We are trying to find what is W(x) - D(x).
(4x^3 + 6x^2 - 11x + 7) - (x^3 + 2x^2 + 15)
= 4x^3 - x^3 + 6x^2 - 2x^2 - 11x + 7 - 15
= 3x^3 + 4x^2 - 11x - 8
This corresponds to the second option.
Hope this helps!
A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8
What is an equation?
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
The water usage at a car wash is modelled by the equation W(x) = 4x³ + 6x² − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The amount of decrease in water used is modelled by D(x) = x³+ 2x² + 15, where D is the amount of water in cubic feet and x is time in hours.Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.
We are trying to find what
C(x) = W(x) - D(x)
C(x) = ( 4x³ + 6x² − 11x + 7, ) - ( x³ + 2x² + 15 )
C(x) = 4x³ - x² + 6x² - 2x³ - 11x + 7 - 15
C(x) = 3x³ + 4x² - 11x - 8
Therefore A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8
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Identify the fallacies of relevance, weak induction, presumption, ambiguity, and illicit transference committed by the following arguments, giving a brief explanation for your answer. If no fallacy is committed, write "no fallacy." When I visited Dr. Ames about my cholesterol, she insisted that I go on a statin drug. She says everybody should be on a statin. And when I saw Dr. Collins for depression, he prescribed Prozac. And when the Prozac gave me nausea, he prescribed Zofran to stop the nausea. Doctors are all the same. They all take their orders from the pharmaceutical industry.
Answer:
Hasty generalization fallacy
Step-by-step explanation:
Fallacy can be said to be a reasoning which leads to the wrong interpretation of a statement or an argument. Although some people intentionally make fallacious statements just to score cheap points or to please the listening audience, but some make fallacious unknowingly, either due to carelessness or by being lackadaisical.
In this case the writer, without enough investigation and proof, comes to a very hasty conclusion that "all doctors are the same". This is termed a hasty conclusion because the writer only had dealings with just two docotors(Dr. Ames and Dr. Collins). So saying all doctors are the same just because of two instance is a rather rash statement.
Therefore, the fallacy commited by the writer here is a fallacy of hasty generalization.
Hasty generalization fallacy occurs when someone has a limited information on a population but makes a conclusion based on a larger population than he/she should.
what is the y intercept of the line x -72 -54 -35 y 25 13 1
Answer:
can you retype the equation
I think it is not correctly typed
The origin is at (1, 1): that is, the origin is at position 1 on the x-axis and at position 1 on the y-axis.
Answer: What is the question? If you could be more specific I could try to help but there is no question here.
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
just did it
Pleas Help 9th grade work
Consider the reflectional symmetry of the shape.
How many lines of symmetry does the shape have?
2
3
4
5
Answer:
4.
Step-by-step explanation:
One line of symmetry is horizontal ( through the centre of the horizontal part of the cross).
Another is a vertical line through the centre of the vertical part.
Then there are 2 diagonal lines of reflectional symmetry.
What is the length of arc FE?
Answer:
4.42
Step-by-step explanation:
Angles A and C are identical because the two circles are similar.
The arc length formula is s = rФ, where r is the radius and Ф is the central angle.
If we know s and r, then the central angle Ф is s/r, or, in this case,
Ф = 8.84/5.
Now let's find the length of the arc EF: s = rФ becomes:
s = (2.5)(8.84/5) = 4.42
Jennifer has 75 pounds of strawberry ice cream. Jennifer is going to serve the ice cream at her birthday party. If every serving is $\frac{2}{3}$ of a pound of ice cream, how many servings of strawberry ice cream can Jennifer make? Express your answer as a fraction.
Answer:
²²⁵/₂ servings or 112 ¹/₂ servings
Step-by-step explanation:
assuming that Jennifer will serve ²/₃ of a pound of ice cream per serving, then the maximum amount of servings that she can make = total pounds of ice cream / individual serving of ice cream
= 75 pounds / (²/₃ pound)
= (75 pounds x 3) / 2 pounds
= ²²⁵/₂ servings or 112 ¹/₂ servings
Match each polynomial expression to its additive inverse.
6x²-x-2
6x2 - x+2
6x2 - x+2
6x2 + x + 2
6x²+x-2
6x2 + x-2
6x2+x-2
-6,2-x+2
Answer:
Step-by-step explanation:
To find the additive inverse of polynomial expression, flip the sign of each term.
6x² ----> -6x²
-x -----> +x
-2 -----> +2
Additive inverse:
-6x² + x + 2
The Mississippi River flows at a rate of 16,790 cubic meters per second. Choose the best approximation of the flow rate of the Mississippi River. Choose 1 answer: A:2 * 10^3 B: 2*10^4
Answer:
B, 2(10^4)
Step-by-step explanation:
2(10^3)= 2000
2(10^4)= 20000
2(10^4) Is closer to 16790 than 2(10^3)
Which of the following numbers is not part of the solution to x ≤ -2? * -2 * -2.45 * -8 * -1.76
Answer:
-1.76
Step-by-step explanation:
-2 is equal to -2, so it works (greater or less than -2)
-2.45 is less than -2, so it works
-8 is less than -2, so it works
-1.75 is greater than -2, so it doesn't work
HELP ASAP HELP PLEASE ASAP
Answer:
WXYZ can not be a rectangle because consecutive sides are not perpendicular to each other.
Step-by-step explanation:
The given vertices are W(-4,3), X(1,5), Y(3,1) and Z(-2,-1).
Plot these points on coordinate plane and draw the quadrilateral as shown below.
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using this formula, we get
[tex]m_{WX}=\dfrac{5-3}{1-(-4)}=\dfrac{2}{5}[/tex]
[tex]m_{XY}=\dfrac{1-5}{3-1}=\dfrac{-4}{2}=-2[/tex]
Now,
[tex]m_{WX}\times =\dfrac{2}{5}\times (-2)=-\dfrac{4}{5}\neq -1[/tex]
Here, WX and XY are two consecutive sides of quadrilateral but the product of their slopes is not equal to -1. It means they are not perpendicular to each other.
Since, all interior angles of a rectangle are right angles, therefore, WXYZ can not be a rectangle.
Henry wants to double a cake recipe that uses 2 cups and 10 tbsp of flour. How much flour will he need?
9514 1404 393
Answer:
5 cups and 4 tbsp
Step-by-step explanation:
Double the quantity (2 c, 10 T) is ...
2 × (2 c, 10 T) = (4 c, 20 T)
A cup is equal to 16 tablespoons, so this quantity can be rewritten as ...
(5 c, 4 T)
Five cups and four tablespoons of flour are needed for the double recipe.
Which figure shows a line of reflectional symmetry for the letter T? A letter T is folded at the horizontal line. A letter T is folded diagonally. A letter T is folded vertically through the middle. A letter T is folded diagonally through its center.
Answer:
A letter T is folded vertically through the middle.
Step-by-step explanation:
Reflectional symmetry refers to the symmetry of line that divides the given shape into two equal halves. The halves represent the mirror reflection of each other. The line of symmetry is drawn to show the reflection and it acts as a mirror. For the letter 'T', the reflectional symmetry will be drawn vertically in the middle of the letter. The line divides the letter into two equal halves with mirror images.
The figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
What is a Line of Reflectional Symmetry?A line of reflectional symmetry can be described as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.
When a line divides letter T vertically, two mirror images are created.
Thus, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
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The product of a number and its inverse is 1. Represent it in algebraic form.
Answer:
Step-by-step explanation:
Hello
first of all we assume that this number is different from 0 as dividing by 0 is not allowed
let's not n this number
its inverse is
[tex]\dfrac{1}{n}[/tex]
and we can write
[tex]n*\dfrac{1}{n}=1[/tex]
hope this helps
Answer:
x * 1/x = 1
Step-by-step explanation:
Let x be the number
1/x is the inverse
x * 1/x = 1
What is the area of the triangle below?
3
16
O A. 24 sq. units
O B. 19 sq. units
O C. 48 sq. units
O D. 16 sq. units
Answer:
answer is 24
area of triangle=1/2 base*height
1/2*16*3=24
Answer:
24 sq. units
Step-by-step explanation:
Area of a triangle = Base x height ÷ 2
Base = 16
Height = 3
Therefore 16 x 3= 48 ÷2 = 24
I really hope this helps:)
A wooden clock is made in the shape of a triangular pyramid. The net of the pyramid is shown. A triangular pyramid. The base has a base of 8 inches and height of 6.9 inches. The 3 sides have a base of 8 inches and height of 7.4 inches. [Not drawn to scale] How much wood is needed to build the clock?
Answer:
116.4 Square Inches
Step-by-step explanation:
Base Area of the Triangular Pyramid
[tex]=\dfrac12 \times 8 \times 6.9\\\\=27.6$ square inches[/tex]
Surface Area of the three sides
[tex]=3 \times \dfrac12 \times 8 \times 7.4\\\\=88.8$ square inches[/tex]
Therefore, the area of wood needed to build the clock
=27.6+88.8
=116.4 Square Inches
Answer:
C
Step-by-step explanation:
I hope it helps
A train leaves Miami at 3:00 PM. A second train leaves the same city in the same direction at 8:00 PM. The second train travels 145 mph faster than the first. Of the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains
Answer:
The first train travels at 58 mph and the second train travels at 203 mph.
Step-by-step explanation:
The first train left Miami at 3:00 PM.
The second train left Miami at 8:00 PM.
Let the speed of the first train be x.
The second train travels 145 mph faster than the first, that is 145 + x
The second train overtakes the first at 10:00 PM
This means that at 10:00 PM, they were both at the same location.
That is 7 hours after the first train left and 2 hours after the second train left.
Speed is given as:
s = d / t
where d = distance traveled and t = time taken
For the first train, after 7 hours traveling at speed x:
x = d / 7
=> d = 7x _______(1)
For the second train, after 2 hours, traveling at speed 145 + x:
145 + x= d / 2
=> d = 290 + 2x ____(2)
Equating (1) and (2):
7x = 290 + 2x
=> 7x - 2x = 290
5x = 290
=> x = 290/5 = 58 mph
Therefore, the first train travels at 58 mph and the second train travels at 203 mph (58 + 145)
EXTRA POINTS! Evaluate the expression 7x2y, when x = 3 and y = 4. A.168 B.252 C.336 D.794
Answer:
A
Step-by-step explanation:
Put the values of x and y into the expression, then multiply the values.
7 x 3 x 2 x 4 = 168
Answer:
B. 252
Step-by-step explanation:
[tex]7x^2y[/tex]
Put x as 3 and y as 4.
[tex]7\left(3\right)^2\left(4\right)[/tex]
Evaluate.
[tex]7(9)(4)[/tex]
[tex]=252[/tex]
For every 1000 hits a channel gets it makes £16 from ad revenue. How much will the channel make from each hit?
Hi there! Hopefully this helps!
The answer is: 0.016
Here is how I got that answer:
16/1000=0.016
Answer:
Step-by-step explanation:
£16÷1000=0.016p
Find the distance between the points (4, 0) and (–3, 4).
Answer:
[tex]\huge\boxed{\sqrt{65}\approx8.062}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have two points (4, 0) and (-3, 4).
Substitute:
[tex]d=\sqrt{(-3-4)^2+(4-0)^2}=\sqrt{(-7)^2+4^2}=\sqrt{49+16}=\sqrt{65}[/tex]