Answer:
20582.195 unitsStep-by-step explanation:
This problem is on the mensuration of solids.
A sphere is a solid shape.
Given data
radius of sphere = 17 units
The volume of a sphere can be expressed as below
[tex]volume = \frac{4}{3}\pi r^3[/tex]
Substituting our data into the expression we have
[tex]volume = \frac{4}{3}*3.142*17^3[/tex]
[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]
The volume of the sphere is given as
20582.195 units
A board of directors consists of eight men and four women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?
Answer:
Total probability = 0.002 or 1 / 495
Step-by-step explanation:
Given:
Number of men = 8
Number of women = 4
Total number of person = 12
Find:
All four members will be women
Computation:
1st women probability = (4/12)
2nd women probability = (3/11)
3rd women probability = (2/10)
4th women probability = (1/9)
Total probability = (4/12)×(3/11)×(2/10)×(1/9)
Total probability = 24 / 11,880
Total probability = 0.002 or 1 / 495
The probability that all four members of the search committee will be women is 1.42%.
Since a board of directors consists of eight men and four women, and a four-member search committee is randomly chosen to recommend a new company president, to determine what is the probability that all four members of the search committee will be women the following calculation should be performed:
4/8 x 3/7 x 2/6 x 1/5 = X 0.5 x 0.42857 x 0.333 x 0.20 = X 0.01428 = X 100X = 1.42
Therefore, the probability that all four members of the search committee will be women is 1.42%.
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Simplify (-8)2. please help
Answer:
-16
Step-by-step explanation:
This equation is showing -8 multiplied by 2, and when they are multiplied, the sum of those two numbers is -16.
Answer:
=-16
Step-by-step explanation:
(-8)2
= 2×-8
= -16
Jared hiked a trail that is 12 miles long. He hiked the trail in section that were 1.5
miles each. In how many sections did he complete the hike?
A. 12
B. 8
C. 10
D. 4
What is the probability of the complement of rolling a number less than 5 by using a six sided dye
Answer:
2/3
Step-by-step explanation:
Less than 5 is 1,2,3,4 and 4 out of 6 is also equal to 2/3
Consider the equation x2+4x+9=0 in standard form. Which equation shows the coefficients a, b, and c correctly substituted into the quadratic formula? Please show all steps to get to the answer, please!!
Answer:
x = -2+i√5 and -2i-√5Step-by-step explanation:
The general form of a quadratic equation is ax²+bx+c = 0
Given the quadratic equation x²+4x+9=0 in its standard form, on comparing with the general equation we can get the value of the constant a, b and c as shown;
ax² = x²
a = 1
bx = 4x
b = 4
c = 9
The quadratic formula is given as x = -b±√(b²-4ac)/2a
Substituting the constant;
x = -4±√(4²-4(1)(9))/2(1)
x = -4 ±√(16-36)/2
x = -4±√-20/2
x = -4±(√-1*√20)/2
Note that √-1 = i
x = -4±(i√4*5)/2
x = (-4±i2√5)/2
x = -4/2±i2√5/2
x = -2±i√5
The solution to the quadratic equation are -2+i√5 and -2i-√5
-3=n/2-6 help pleaseeee!!!!
Answer:
6 = n
Step-by-step explanation:
-3=n/2-6
Add 6 to each side
-3+6 = n/2 -6+6
3 = n/2
Multiply each side by 2
3*2 = n/2 *2
6 = n
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▹ Answer
n = 6
▹ Step-by-Step Explanation
-3 = n/2 - 6
Multiply both sides by 2:
-6 = n - 12
Rearrange the terms:
-n -6 = -12
Calculate:
-n = -6
Change the signs:
n = 6
Hope this helps!
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Where can parentheses be placed in the expression so that it has a value of 26? 4+2 ⋅ 14−3
Answer: 4+2 x (14-3)
Step-by-step explanation:
CLASSIFY THE TRIANGLES WHOSE SIDES MEASURE:
A. a = 15cm, b = 20cm and c = 25cm
B. a = 3cm, b = 3cm and c = 1cm
Problem 1
a^2+b^2 = 25^2+20^2 = 225+400 = 625
c^2 = 25^2 = 625
We get the same output of 625.
This shows that a^2+b^2 = c^2 is true for (a,b,c) = (15,20,25). We have a pythagorean triple and this is a right triangle. This is also scalene as all three sides are different lengths.
Answer: Right scalene triangle=======================================
Problem 2
a^2+b^2 = 3^2+3^2 = 18
while c^2 = 1^2 = 1
So a^2+b^2 = c^2 is not a true equation for this a,b,c set of values. We do not have a right triangle. Instead we have an acute triangle based on these rules below
If a^2+b^2 = c^2, then we have a right triangleIf a^2+b^2 > c^2, then we have an acute triangleIf a^2+b^2 < c^2, then we have an obtuse triangleWe see that we have the form a^2+b^2 > c^2 since 18 > 1.
This acute triangle is also isosceles because a = b.
Answer: Isosceles acute triangleAnswer:
Triangle A is a scalene triangle.
Triangle B is an isosceles triangle
Exaplanation for the 1st Answer:
A scalene triangle is a triangle whose all side lengths are different.
Triangle A has the side lengths are 15, 20, 25. All these lengths are different, so this is a scalene triangle.
Explanation for the 2nd Answer:
An isosceles triangle has 2 sides lengths the same and the other side length different. Triangle B has side lengths of 3, 3, 1. Two side lengths are same, but 1 side length is different. So, this is an isosceles triangle.
Solve. 100+[12×{20−(10÷5)}]
Answer:
316
Step-by-step explanation:
12/6 and 4/2 state if each pair of ratios forms a proportion. helppppppp
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▹ Answer
This is proportional.
▹ Step-by-Step Explanation
[tex]\frac{12}{6} \\\\Divide each side by 3:\\\\12/3 = 4\\\\6/3 = 2\\\\= \frac{4}{2}[/tex]
Hope this helps!
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━━━━━━━☆☆━━━━━━━
Answer: yes
Step-by-step explanation: A proportion is a pair of equal ratios. So when we’re asked to determine whether two ratios form a proportion, what we’re really being asked to do is determine whether the two ratios are equal because i the ratios are equal, then we know they form a proportion.
So in this problem, we need to determine whether 12/6 = 4/2.
The easiest way to determine whether 12/6 = 4/2 is to use cross-products.
If the cross-products are equal, then the ratios are equal.
The cross products for these two ratios are (12)(2) and (6)(4).
Are these products equal?
Well (12)(2) is 24 and (6)(4) is 24.
Since 24 = 24, we can see that the cross-products are equal which means that the ratios are equal and since the ratios are equal, we know that they form a proportion. So the answer is yes, 12/6 and 4/2 form a proportion.
Use the motion map to answer the question.
Which scenario could be represented by the motion
map?
O A car speeds up to merge onto the freeway and
then continues at a constant velocity
O A car speeds up to pass a truck, then slows down
to a constant velocity.
O A car slows to stop at a stop sign. Once traffic is
clear, the car speeds up.
O A car slows to makes a U-turn, then continues in
the opposite direction.
Answer:
A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.
Step-by-step explanation:
Answer:
C.) A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.
Step-by-step explanation:
In a factory, two-thirds of the floor area is taken up by the production line. Out of the remaining floor area, three-fifths is taken up by office space. The rest is warehouse space. The warehouse space 2 occupies 2000 m . Work out the floor area of the production line.
Answer:
the floor area of the production line =20000 m^2
Step-by-step explanation:
From the question we were told two thirds of the floor of the factory is taken up by the production line.
If we denote the total area of the factory as "y" then
the Area of the production line can be express algebraically as
2/3 × y = 2y/3
The rest of floor area of warehouse space will be
y- 2y/3 = y/3
From the rest of floor area, we were told three fifths is taken up by the office space, then this office space's area can be expressed in m^3 as
3/5 × y/3 = y/5
The remaining space left will now be for
warehouse, by we were given warehouse space omas 2000m^2.
Then from here we can get value of y
2y/15 = 2000
2y = (2000×15)
2y= 30000
y= 15000m^2
Therefore, the floor area of the production line can be expressed as
(2 ×30000)/3
= 20000 m^2
Quit easily done!
How many students in the survey were in the age category of 18 to 22?
Answer:
82
Step-by-step explanation:
78 + 4 = 82
Answer:
82 students
Step-by-step explanation:
The chart has a total of 82 students in the 18 to 22 age category, as 78 + 4 = 82.
how to solve this equation
x2-5x=0
Answer:
x = 5
Step-by-step explanation:
x² - 5x = 0
(x² - 5x) /x = 0/x
x²/x - 5x/x = 0
x - 5 = 0
x = 5
Check:
x² - 5x = 0
5² - 5*5 = 0
25 - 25 = 0
The solution to the equation is:
x = 0 or x = 5
How to solve the equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
We have:
x²-5x = 0
We can solve the equation as follow:
x²-5x = 0
Factorize:
x(x - 5) = 0
x = 0 or (x -5) = 0
x = 0 or x = 5
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Simplify $\frac{3}{2 \sqrt 3 - 3}.$[tex]Simplify $\frac{3}{2 \sqrt 3 - 3}.$[/tex]
Answer:
[tex]2\sqrt{3}+3[/tex]
Step-by-step explanation:
[tex]$\frac{3}{2 \sqrt 3 - 3}$[/tex]
Rationalize the fraction.
[tex]$\frac{3}{2 \sqrt 3 - 3}\cdot \frac{2 \sqrt 3 + 3}{2 \sqrt 3 + 3} =\frac{6\sqrt{3}+9 }{12-9} =\frac{6\sqrt{3}+9 }{3} =2\sqrt{3}+3 $[/tex]
Note that I used the positive signal because we would have a difference of squares.
Of the 34 cars in a parking lot, 20 are green, 8 are gold, and the rest are black. What are
the odds against the next car leaving the lot being black?
A) 3:14
B) 3:28
C) 28:3
D) 14:3
Answer:c
Step-by-step explanation:
Write the coefficient of x2 in the following a) 2 + x2 + x b) 2 – 4x2 + x solution pls I will mark as brainliest
Answer:
The coefficient of x²
a) 1
b) -4
the coefficient of x² is the number in front of the x²(variable).
Coefficient= Constanta
I hope this helps
if u have question let me know in comments ^_^
Answer:
a) 1.
b) -4.
Step-by-step explanation:
The coefficient is the number multiplying x2. If it is 1 it is usually omitted.
A man died leaving property
worth 49000 for his three daughters and a son. Find out the share of each in inheritance?
Answer:
49000
Step-by-step explanation:
since it's the same worth
Answer:
49000
Step-by-step explanation:
since there was the same worth given to all
a man bought a set of furniture listed 2350. he received a discount of 5% and then paid 3 % sales tax on the selling price. the sales tax was
Answer:
Sales tax on selling price: $2232.50(0.03) = $66.98
Step-by-step explanation:
List price: $2350
5% discount: 0.05($2350) = $117.50
Sale (selling) price: List price less discount: $2350 - $117.50 = $2232.50
Sales tax on selling price: $2232.50(0.03) = $66.98
if it takes a half of a cup of oil to make 20 cookies how much oil is needed to make 5 cookies?? please help.
Answer:
We need 1/8 cup
Step-by-step explanation:
We can use ratios to solve
1/2 cup x cups
------------ = -----------------
20 cookies 5 cookies
Using cross products
5 * 1/2 = 20x
Divide each side by 20
5/2 * 1/20 = 20x/20
5/40 =x
1/8 =x
We need 1/8 cup
Answer:
Step-by-step explanation:
step 1: you know that 1/2 c of oil makes 20 cookies.
step 2: if you only have 1/4 c (half of 1/2 cup), then you can make 10 cookies.
Step 3: 1/8 c would make 5 cookies.
What type of number is 17?
There may be more than one correct answer.
Select all that apply.
If only one answer is correct, select "only" and the answer that applies.
rational
only
integer
natural
whole
Rational Numbers
Answer:
Rational, integer, natural, whole, rational numbers
Step-by-step explanation:
17 is a rational, integer, natural, whole, and is a rational number. I'm not totally sure why rational is on there, since rational and rational number should be the same thing. Basically it's everything but "only". If rational is supposed to mean irrational, then it's not irrational.
Donavan and Jones are randomly choosing chalices to drink from. 4 of the chalices contain purified water, 5 contain spoiled milk, and 6 contain diluted flat soda. Jones gets to choose a chalice from the remaining ones after Donavan drinks from 3 of them. If the chances of Jones choosing a chalice with purified water is then 1/3, how many of the chalices that Donavan drank out of contained purified water?
Answer:
0
Step-by-step explanation:
Chalice with purified water = 4
With spoiled milk = 5
With flat soda = 6
Probability of Jones drinking from a chalice with purified water after Donovan had drank from 3 = 1/3
Probability = required outcome / Total possible outcomes
Total possible outcomes = (4 + 5 + 6) = 15
After Donovan drinks 3 :
Total possible outcomes = (15 - 3) = 12
If the probability of Jones choosing a chalice with purified water is 1/3 then :
(Required outcome / Total possible outcomes) =1 /3
(Required outcome / 12) = 1 / 3
Required outcome * 3 = 12
Required outcome = 12 / 3
Required outcome = 4
Therefore, since initial number of chalice with purified water is 4,
4 - 4 = 0
Then Donovan did not drink from a chalice containing purified water.
how do you find the length of the hypotenuse when you have only the length of the altitude of the hypotensuse and a length of a leg?
Answer:
By using The Pythagorean Theorem:
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex]
/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]
Step-by-step explanation:
The Pythagorean theorem states that: Given a Right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides ( Here, being the length of the altitude and length of leg). That is,
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex] and hence,
/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]
For example, If the length of the altitude is 4m and the length of leg is 3m. Using The Pythagorean theorem, the length of the hypotenuse will be
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \\\/Hypotenuse/ = \sqrt{/Length of altitude/^{2} + /Length of leg/^{2}} \\/Hypotenuse/ = \sqrt{4^{2} + 3^{2} }[/tex]
[tex]/Hypotenuse/ = \sqrt{16+9} \\/Hypotenuse/ = \sqrt{25} \\/Hypotenuse/ = 5m[/tex]
The length of the hypotenuse for the given example will be 5m.
This is how to find the length of an hypotenuse.
Please answer this question now
Answer:
Arc BC = 117°
Step-by-step explanation:
Angle D is an inscribed angle that intercepts arc ABC. According to the Inscribed angle theorem of a circle, m<D = ½ of arc ABC.
Thus,
104° = ½(AB + BC)
104° = ½(91° + BC)
Multiply both sides by 2
104*2 = 91 + BC
208 = 91 + BC
Subtract both sides by 91
208 - 91 = BC
117 = BC
Arc BC = 117°
please solve this question.
[tex]\left(\dfrac{1}{1+2i}+\dfrac{3}{1-i}\right)\left(\dfrac{3-2i}{1+3i}\right)=\\\\\left(\dfrac{1-2i}{(1+2i)(1-2i)}+\dfrac{3(1+i)}{(1-i)(1+i)}\right)\left(\dfrac{(3-2i)(1-3i)}{(1+3i)(1-3i)}\right)=\\\\\left(\dfrac{1-2i}{1+4}+\dfrac{3+3i}{1+1}\right)\left(\dfrac{3-9i-2i-6}{1+9}\right)=\\\\\left(\dfrac{1-2i}{5}+\dfrac{3+3i}{2}\right)\left(\dfrac{-3-11i}{10}\right)=\\\\\left(\dfrac{2(1-2i)}{10}+\dfrac{5(3+3i)}{10}\right)\left(\dfrac{-3-11i}{10}\right)=[/tex]
[tex]\dfrac{2-4i+15+15i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{17+11i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{-51-187i-33i+121}{100}=\\\\\dfrac{70-220i}{100}=\\\\\dfrac{70}{100}-\dfrac{220i}{100}=\\\\\boxed{\dfrac{7}{10}-\dfrac{11}{5}i}[/tex]
Mr.Snyder gave his four children $35 to split equally for each car they cleaned out. The children cleaned put 3 cars. Mr.Snyder does not have any coins. He only had dollar bills. How much money should each child get?
Answer:
$26 for each child
Step-by-step explanation:
35 * 3 = 105 / 4 = 26.25
Given the range (1, 1),(4,2), (2, -1), with a coordinate transformation of f(x, y) = (x+1, y-1), what is the
domain?
=============================================
Explanation:
The rule f(x,y) = (x+1,y-1) says to add 1 to the x coordinate and subtract 1 from the y coordinate. So let's say the input point is (7,2). This would move it to (8,1).
Now let's say that you accidentally erased the "(7,2)", but you still have the "(8,1)". You'd have to work through the steps backwards to get back to (7,2)
So you'll effectively use this rule g(x,y) = (x-1, y+1) which is the inverse transformation. Whatever f(x,y) does, the g(x,y) function will undo it and go opposite. We'll subtract 1 from the x coordinate and add 1 to the y coordinate.
------------
So that's what we'll do with the set of points { (1,1), (4,2), (2,-1) }
We have (1,1) become (0,2) after applying the g(x,y) rule
(4,2) becomes (3,3) after using g(x,y)
(2,-1) becomes (1,0) after using g(x,y)
Therefore, the domain is { (0,2), (3,3), (1,0) }
-------------
The mapping diagram is shown below.
Solve for x 3x - 4 = 2x - 10
Answer:
-6
Step-by-step explanation:
To solve this problem, you should move all of the variables onto one side, and all of the constants onto the other side as such:
3x-4=2x-10
+10 +10
3x+6=2x
-3x -3x
6=-x
/-1 /-1
x=-6
Hope this helps!
P.S. Please give me brainliest. Thanks :)
Answer:
[tex]x = -6[/tex]
Step-by-step explanation:
Looking at the expression [tex]3x - 4 = 2x - 10[/tex], our goal is to get rid of the x term on one side.
To do this, we can subtract 2x from both sides which gets us
[tex]x - 4 = -10[/tex]
Add 4 to both sides:
[tex]x = -6[/tex]
Hope this helped!
Help is needed please!!! Thanks Find the number of pairs of integers (x,y) with 0 1-(5/y)
Answer:
Técnicas orales y de cálculo mental de multiplicación y división entera . ... conjunto de múltiplos de 10 es un subconjunto de los números pares. Si ... La clase vacía ∅ se representa por la notación 0, la clase unitaria por 1, la clase binaria por 2, etc. En ... 5 x (5 x (5 x (5 + 4) + 3 ) + 2) + 1 ; x significa el signo de multiplicar. 8.
Step-by-step explanation:
Técnicas orales y de cálculo mental de multiplicación y división entera . ... conjunto de múltiplos de 10 es un subconjunto de los números pares. Si ... La clase vacía ∅ se representa por la notación 0, la clase unitaria por 1, la clase binaria por 2, etc. En ... 5 x (5 x (5 x (5 + 4) + 3 ) + 2) + 1 ; x significa el signo de multiplicar. 8.
Your car gets 15 miles per gallon and your friend's car averages 25 mpg. You decide
head off to St. George Island on vacation, 361 miles away. If gas costs $2.79/gallon and you decide to split the
gas costs, how much money will you save by driving your friend's car?
Answer:
the answer is $27.90
Step-by-step explanation:
if you do 15 times 2.79 you will get $41.85
then do 25 times 2.79 and you will get $69.75
then subtract 69.75 from 41.85 and your answer will be $27.90
i hope this helps this is the only way i could find the answer!
$29.4864 money will you save by driving your friend's car.
Given that, your car gets 15 miles per gallon and your friend's car averages 25 mpg.
You decide to go on a road trip to St. George Island, which is 361 miles away.
What are Gallons?A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters exactly.
Gallons needed for your car =361/15=24.06 gallons
Cost of 24.06 gallons of gas=24.06×2.79=$69.774
Gallons needed for friends car =361/25=14.44 gallons
Cost of 4.44 gallons of gas=14.44×2.79=$40.2876
Hence, while driving a friend's car you will save 69.774-40.2876=$29.4864
Therefore, $29.4864 money will you save by driving your friend's car.
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