Answer:
A perfect cube monomial must have three identical root , such that the product of the roots equal the perfect square monomial . The coefficient of the monomial must be divisible by 3 . Any monomial can be a perfect cube root .
Step-by-step explanation:
1.)1000=10 cube
2.) 729=9 cube
3.) 512=8 cube
4.) 343=7 cube
5.) 216=6 cube
6.) 125=5 cube
7.) 64=4 cube
8.) 27=3 cube
9.) 8=2cube
10.) 1=1 cube
One week, taylor earned $203.40 at her job when she worked for 9 hours. if she is paid the same hourly wage, how many hours would she have to work the next week to earn $881.40?
Answer:
39 hours
Step-by-step explanation:
First solve for how much Taylor would earn per hour which is to divide 203.40 by 9
= 203.40÷9 = 22.6
Let x represent the unknown hours
If 22.6 = 1 hr
Then 881.40 = x solving this simultaneously becomes
881.40 ÷ 22.6 = 39
x = 39, hence it'll take Taylor 39 hours to earn $881.40
She have to work 39 hours the next week to earn $881.40.
In simple terms, the unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.
In 9 hours she earned $203.40
∴ In 1 hour she earned $203.40/9 = $22.6
Let number of hours she worked to earn $881.40 be x.
∴ x = $881.40/ $22.6
x = 39 hours
Thus she have to work 39 hours the next week to earn $881.40.
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Helpppppppppp show your steps to the answer
Answer:
9
Step-by-step explanation:
you have to plug in the numbers and solve it, so it would go as follows:
-(-3^2)- 2(-5)(2) - /2/
-9 + 20 - 2 =
9
i hope this helps
Based on our Starbucks analysis report, 4 out of every 20 drinks are returned because of a customer complaint and 16/20 are not returned. Starbucks makes $4 on a typical drink not returned (probability of 16/20 ), but loses -$6 (probability of 4/20) when a drink is returned because the employee has to re-make it. What is the Expected Value of this problem and are they going to make a profit ?
Answer:
Step-by-step explanation:
the expected profit should be 2 dollars a drink
Ariel completed the work below to show that a triangle with side lengths of 9, 15, and 12 does not form a right triangle. 9 squared 15 squared = 12 squared. 81 225 = 144. 306 not-equals 144.
Answer:
Work is incorrect
Step-by-step explanation:
I'm assuming this question is asking whether the work is correct or not? In which case the work is not correct.
The Pythagorean Theorem states: [tex]a^2+b^2=c^2[/tex] where c=hypotenuse, and "a" and "b" are the other two sides. The main thing to note here, is that the hypotenuse is the largest side of all three sides.
So the equation Arial set up: [tex]9^2+15^2=12^2[/tex] is incorrect, since the 15 would need to be on the right side. This forms the correct equation: [tex]9^2+12^2=15^2[/tex] which then simplifies to: [tex]81 + 144 =225 \implies 225=225[/tex].
Thus a right triangle can be formed using these side lengths. You can of course set up a similar equation to Ariels, where the "c" or hypotenuse is not isolated, but you would have to rearrange the equation so that: [tex]a^2+b^2=c^2\implies b^2=c^2-a^2[/tex] but see how "a squared" is being subtracted from "c squared"? So it's a similar equation to Ariels, but not quite the same, and if she set it up like this, then she would reach the same conclussion
Which of the following alternatives are similar monomials?
a) 8x and -7x
b) 5a² and 5a
c) 4 and -17
d) 2ab and 3abc
e) -3ab and 9abc
f) - [tex]\frac{x}{3}[/tex] and 11x
The alternatives that are similar monomials are given as follows:
a) 8x and -7x.
c) 4 and -17.
f) -x/3 and 11x.
What are similar monomials?Similar monomials are monomials in which the part with the letters are equal. For example, 8x and -7x, as x = x, or even 9x²y and -2x²y, as x²y = x²y.
Hence options a, c and f are correct in this problem.
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How many 3-yard straight pieces does Vince need altogether to build the three slides?
Based on the dimensions of the support for the slides, the missing length and slide length is 15 yards.
The number of 3-yard straight pieces needed is 15 straight pieces.
What number of straight pieces are needed?The length of a single slide is the hypotenuse of the triangle which can be found using the Pythagoras theorem as:
Hypotenuse² = 9² + 12²
Hypotenuse = √(81 + 144)
= 15 yards
If a single slide is 15 yards, then 3 slides would be:
= 15 x 3
= 45 yards
The number of 3-yard straight pieces needed are:
= 45 / 3
= 15 pieces
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Answer: 39
Explain:
The length of each slanted area for each slide is 15 yards. The length of each straight piece is 3 yards. So, the number of straight pieces needed for 15 yards is 15 - 3, or 5. There are two slanted areas on each slide.
The number of straight pieces required for the flat area at the bottom of each slide is 3.
Adding them up, the total number of straight pieces required for one slide is 5 + 5 + 3, or 13. Because there are three slides, the total number of straight pieces needed is 13 • 3, or 39
Vince needs 39 straight pieces to build the three slides.
From ED
Suppose that w varies directly as the product of x and the square of y and inersely as z. when x = 2, y = 3, and z = 36, the value of w is 1/2. find the value of w when x = 5, y = 5, and z = 10.
The value of w is 12.5 when x = 5 , y= 5 and z = 10.
What is Equation of variation?
A variation is a relation between a set of values of one variable and a set of values of other variables. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.Equation of variation w = [tex]\frac{kxy^{2} }{z}[/tex]
Constant of variation k = [tex]\frac{wz}{xy^{2} }[/tex]
Find k when w = 1/2, x = 2 and z = 36
k = [tex]\frac{wz}{xy^{2} }[/tex]
[tex]k = \frac{\frac{1}{2} * 36 }{2 * 3^{2} }[/tex]
[tex]k = \frac{18}{2 * 9}[/tex]
[tex]k = \frac{18}{18}[/tex]
k= 1
find the value of w when x = 5 , y = 5 and z = 10
[tex]w = \frac{kxy^{2} }{z} \\w= \frac{1 * 5 * 5^{2} }{10}[/tex]
[tex]w = \frac{5^{3} }{10}[/tex]
w = 125 /10
w = 25 /2
w = 12 . 5
Therefore, the value of w is 12.5 when x = 5 , y= 5 and z = 10
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Use the graph to write the explicit rule of the arithmetic sequence.
Question 19 options:
A)
ƒ(n) = 9 + 2(n – 1)
B)
ƒ(n) = 5 + 3(n – 1)
C)
ƒ(n) = –3 + 2(n – 1)
D)
ƒ(n) = 3 + 2(n – 1)
Answer: D
Step-by-step explanation:
The first term is 3 and the common difference is 2.
Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.
What step would be necessary if you wished to conduct a poll with a margin of error of zero?
The necessary step would be we would have to get every respondent in the population to participate if you wished to conduct a poll with a margin of error of zero.
What is a poll?An opinion poll, often known as a poll or a survey, is a human research survey of public opinion from a specific sample. Opinion polls are often designed to depict a population's opinions by asking a series of questions and then extrapolating generalities in ratio or within confidence intervals. A pollster is somebody who conducts polls.If we were to conduct a poll with a margin of error of zero, we would need to recruit every responder in the population to participate.As it is given in the description itself, if we were to conduct a poll with a margin of error of zero, we would need to recruit every responder in the population to participate.
Therefore, the necessary step would be we would have to get every respondent in the population to participate if you wished to conduct a poll with a margin of error of zero.
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The measure of angle is 5. The equivalent measurement in degrees is...
Answer:
300 degrees
Step-by-step explanation:
pi should be 180 degrees so 5*180/3 = 5*60=300
Which graph represents the function f(x)=(x+4)(x+1)(x−3)?
Answer:
your answer will be C .
Step-by-step explanation:
At the end of the soccer season, the player who scored the most goals had 8 more goals than the player who had the second most goals. The player who had the second most goals had 15 more goals than the third player. The total number of goals scored by all three of the players was 98. Determine the number of goals scored by the player with the most goals. Show your working out.
Step-by-step explanation:
x = the number of goals of the top scorer.
y = the number of goals of the second top scorer.
z = the number of goals of the third top scorer.
x + y + z = 98
x = y + 8
y = z + 15
using the third in the second equation we get
x = z + 15 + 8 = z + 23
and now using this and the third equation in the first equation gives us
z + 23 + z + 15 + z = 98
3z + 38 = 98
3z = 60
z = 20
y = z + 15 = 20 + 15 = 35
x = y + 8 = 35 + 8 = 43
the player with the most goals scored 43 goals.
.
Find the value of x for which ABCD must be a parallelogram.
The value of x that would make ABCD a parallelogram is x = 5
How to find the interior angle of a parallelograms?A parallelogram, opposite sides are equal and parallel, which means opposite interior angles are equal.
Opposite sides of a parallelogram are congruent and parallel
Therefore,
5x - 3 = 14x - 48
subtract 5x from both sides
5x - 5x - 3 = 14x - 5x - 48
-3 = 9x - 48
add 48 to both sides
-3 + 48 = 9x - 48 + 48
45 = 9x
x = 45 / 9
x = 5
Therefore, the value of x that would make ABCD a parallelogram is x = 5
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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=3y2−3x2; 2x y=9
There is a minimum value of -81 located at (x, y) = (6, -3).
The function given to us is f(x, y) = 3y² - 3x².
The constraint given to us is 2x + y = 9.
Rearranging the constraint, we get:
2x + y = 9,
or, y = 9 - 2x.
Substituting this in the function, we get:
f(x, y) = 3y² - 3x²,
or, f(x) = 3(9 - 2x)² - 3x² = 3(81 - 36x + 4x²) - 3x² = 243 - 108x + 12x² - 3x² = 243 - 108x + 9x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = - 108 + 18x ... (i)
Equating to 0, we get:
- 108 + 18x = 0,
or, 18x = 108,
or, x = 6.
Differentiating (i), with respect to x again, we get:
f''(x) = 18, which is greater than 0, showing f(x) is minimum at x = 6.
The value of y, when x = 6 is,
y = 9 - 2x,
or, y = 9 - 2*6 = 9 - 12 = -3.
The value of f(x, y) when (x, y) = (6, -3) is,
f(x, y) = 3y² - 3x²,
or, f(x, y) = 3*(-3)² - 3*6² = 3*9 - 3*36 = 27 - 108 = -81.
Thus, there is a minimum value of -81 located at (x, y) = (6, -3).
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please answer this I give u thanks and f0ll0w u and mark brainiest
Use of identity for sum of cubes:
x³ + y³ = (x + y)(x² - xy + y²)Change it as:
x³ + y³ = (x + y)(x² + 2xy + y² - 3xy) = (x + y)[(x + y)² - 3xy)]It is easy to notice that:
64a³ = (4a)³ and125b³ = (5b)³.So the sum of cubes for the given expression will be:
64a³ + 125b³ = (4a + 5b)[(4a + 5b)² - 3(4a*5b)] =(4a + 5b)[(4a + 5b)² - 60ab]Now substitute the values and calculate each of these:
(a) 4a + 5b = 5, ab = -1.
(4a + 5b)[(4a + 5b)² - 60ab] = 5[5² - 60(-1)] = 5(25 + 60) = 5(85) = 425(b) 4a + 5b = -2, ab = 1/15.
(4a + 5b)[(4a + 5b)² - 60ab] = -2[(-2)² - 60(1/15)] =-2(4 - 4) = -2(0) = 0(c) 4a + 5b = 1/3, ab = -1/9.
(4a + 5b)[(4a + 5b)² - 60ab] = (1/3)[(1/3)² - 60(-1/9)] =(1/3)(1/9 + 60/9) = (1/3)(61/9) = 61/27 = 2 7/27(d) 4a + 5b = -1, ab = 1.
(4a + 5b)[(4a + 5b)² - 60ab] = -1[(-1)² - 60(1)] = -1(1 - 60) = -1(-59) = 59What is the equation for the line of best fit on the scatter plot below?
We've got a negative slope, but it doesn't look steep enough to go through 6 on the y-axis.
So, it's the last option:
y = - 1.25x + 5.75
Hope this helps!
Which solution finds the value of x in the triangle below?
A right triangle is shown. The hypotenuse has a length of 8. Another side has a length of x. The angle between the hypotenuse and the other side is 60 degrees.
Secant 60 degrees = StartFraction 8 Over x EndFraction. 2 = StartFraction 8 Over x EndFraction. 2 x = 8. x = 4.
Cosecant 60 degrees = StartFraction 8 Over x EndFraction. StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction = StartFraction 8 Over x EndFraction. x times 2 StartRoot 3 EndRoot = 24. x = StartFraction 24 Over 2 StartRoot 3 EndRoot EndFraction. x = StartFraction 12 Over StartRoot 3 EndRoot EndFraction times StartFraction StartRoot 3 EndRoot Over StartRoot 3 EndRoot EndFraction. x = StartFraction 12 StartRoot 3 EndRoot Over 3 EndFraction. x = 4 StartRoot 3 EndRoot.
Secant 60 degrees = StartFraction 8 Over x EndFraction. One-half = StartFraction 8 Over x Endfraction. x = 16
Cosecant 60 degrees = StartFraction 8 Over x EndFraction. StartFraction StartRoot 3 EndRoot Over 2 EndFraction = StartFraction 8 Over x EndFraction. x times StartRoot 3 EndRoot = 16. x = StartFraction 16 Over StartRoot 3 EndRoot EndFraction. x = StartFraction 16 Over StartRoot 3 EndRoot EndFraction times StartFraction StartRoot 3 EndRoot Over StartRoot 3 EndRoot EndFraction. x = StartFraction 16 StartRoot 3 EndRoot Over 3 EndFraction.
The value of x in the triangle is 4
How to determine the solutions?The complete question is added as an attachment
From the question, the given parameters are as follows:
Hypotenuse = 8
Adjacent = x
Angle = 60
The cosine of the angle is then calculated as:
cos(angle) = Adjacent/Hypotenuse
Substitute the known values in the above equation
cos(60) = x/8
Multiply both sides by 8
x = 8 * cos(60)
Evaluate the product
x = 4
Hence, the value of x in the triangle is 4
So, the complete parameters are:
Hypotenuse = 8
Adjacent = x
Angle = 60
x = 4
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Answer:
Secant 60 degrees = StartFraction 8 Over x EndFraction. 2 = StartFraction 8 Over x EndFraction. 2 x = 8. x = 4.
Step-by-step explanation:
The answer above is correct.
Could somebody help me with this? I'm terrible at these problems
Answer:
1. to add 9 to both sides
2. to multiply by 2 to both sides (horrible English)
3. x = -8
Step-by-step explanation:
why do you feel you are terrible at this ?
this is like a riddle or puzzle to solve. like a magic cube or changing a match in a pattern of matches to create another pattern.
let's try and explain this to you.
an equation is like a balance, where both cups are in perfect balance.
whatever value is on the left side, is exactly also on the right side. although it is not plainly visible and explainable, why they are equal.
so, to find out we need to transform the equation. and to keep the balance while transforming you have to do the same changes on both sides of the balance. until you find out what makes the cups equal.
if we destroy the balance at any point, we have no more chance to find out what made both sides equal in the first place, because there is no more original balance.
we can do all mathematical operations in the transformation.
we can add things, subtract things, multiply by a factor, divide by something, ... - anything.
x/2 - 9 = -13
to get clarity in our search for the reason of the equality we try to combine the same type of terms on one side of the equation, and the other type (or types) on the other side.
what types of terms do we have here ?
there is one with a variable (x/2), and there are constant terms (-9, -13).
so, what do I need to do to get rid of the constant term (-9) on the side of the variable term (so that this becomes the side with only variable terms) ?
I need to add 9, so the constant term on that side turns 0 and therefore disappears in the sum. but remember, the action has to be done on both sides.
so,
x/2 - 9 = -13 | + 9 on both sides
x/2 - 9 + 9 = -13 + 9
x/2 = -4
what else is now blocking our view on what x is ?
there is this 1/2 factor of x.
how do we get rid of this 1/2 ? by multiplying by 2. because 2× 1/2 = 1, and a factor of 1 disappears in a multiplication.
x/2 = -4 | ×2 on both sides
x/2 × 2 = -4 × 2
x = -8
and now we see what it is that kept both cups or sides in balance : x = -8
Find the center of a circle with the equation: x2 y2−32x−60y 1122=0 x 2 y 2 − 32 x − 60 y 1122 = 0
The equation of a circle exists:
[tex]$(x-h)^2 + (y-k)^2 = r^2[/tex], where (h, k) be the center.
The center of the circle exists at (16, 30).
What is the equation of a circle?
Let, the equation of a circle exists:
[tex]$(x-h)^2 + (y-k)^2 = r^2[/tex], where (h, k) be the center.
We rewrite the equation and set them equal :
[tex]$(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2- 32x - 60y +1122=0[/tex]
[tex]$x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0[/tex]
We solve for each coefficient meaning if the term on the LHS contains an x then its coefficient exists exactly as the one on the RHS containing the x or y.
-2hx = -32x
h = -32/-2
⇒ h = 16.
-2ky = -60y
k = -60/-2
⇒ k = 30.
The center of the circle exists at (16, 30).
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-6(4x + 5) = -24x - 30 associative property of addition commutative property of multiplication distributive property inverse property of addition
Answer:
distributive property
Step-by-step explanation:
86cm, 132cm,1m 6cm, 1.6m, 1m 20cm, 1.15m Arrange the heights in order of size, starting with the smallest to the Tallest
Answer:
6cm,20cm,80cm,1m,1m,1.15m,132cm
Step-by-step explanation:
Hence,1 m=100 cm
The floor of a rectangular room measures 5m by 4m and the ceiling is 3m from the floor. An ant is at the top of a corner of the room and crawls to the opposite bottom corner of the room. Find the shortest distance it can travel. (Cannot do its diagonal distance)
Answer:
12 m
Step-by-step explanation:
Well, imagine you got this nice room. How can it reach the other corner? It has to go along the 3 dimensions. So the shortest path would be: 5 + 4 + 3 12m
Answer:
3 + √(41) = 9.4 m (nearest tenth)
Step-by-step explanation:
The room can be modeled as a rectangular prism with:
width = 4 mlength = 5 mheight = 3 mIf the ant is at the top of a corner of a room and crawls to the opposite bottom corner of the room, the shortest distance will be to travel down one vertical edge of the room then to travel the diagonal of the floor of the room (or to travel the diagonal of the ceiling and then one vertical edge).
Vertical edge = height of room = 3m
The diagonal of the floor (or ceiling) is the hypotenuse of a right triangle with legs of the width and length. Therefore, to find the diagonal, use Pythagoras Theorem.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleGiven:
a = width = 4 mb = length = 5 mc = diagonalSubstitute the given values into the formula and solve for c:
[tex]\implies 4^2+5^2=c^2[/tex]
[tex]\implies c^2=41[/tex]
[tex]\implies c=\sqrt{41}[/tex]
Therefore, the shortest distance the ant can travel is:
⇒ 3 + √(41) = 9.4 m (nearest tenth)
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each series with the equivalent series written in sigma notation
The series and the sigma notations are[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex], [tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex], [tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex] and [tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]
How to match each series with the equivalent series written in sigma notation?To do this, we simply expand each sigma notation.
So, we have:
[tex]\sum\limits^4_0 3(5)^n[/tex]
Next, we set n = 0 to 4.
So, we have:
3(5)^0 = 3
3(5)^1 = 15
3(5)^2 = 75
3(5)^3 = 375
3(5)^4 = 1875
So, we have:
[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex]
[tex]\sum\limits^4_0 4(8)^n[/tex]
Next, we set n = 0 to 4.
So, we have:
4(8)^0 = 4
4(8)^1 = 32
4(8)^2 = 256
4(8)^3 = 2048
4(8)^4 = 16384
So, we have:
[tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex]
[tex]\sum\limits^4_0 2(3)^n[/tex]
Next, we set n = 0 to 4.
So, we have:
2(3)^0 = 2
2(3)^1 = 6
2(3)^2 = 18
2(3)^3 = 54
2(3)^4 = 162
So, we have:
[tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex]
[tex]\sum\limits^4_0 5(3)^n[/tex]
Next, we set n = 0 to 4.
So, we have:
5(3)^0 = 5
5(3)^1 = 15
5(3)^2 = 45
5(3)^3 = 135
5(3)^4 = 405
[tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]
Hence, the series and the sigma notations are[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex], [tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex], [tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex] and [tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]
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Please help with this question asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
no solution
Step-by-step explanation:
We can think of an absolute value as the magnitude of the number. We can also define it as how far the number is from 0 on the number line. Thus, absolute value must always be positive (or 0).
Solve
Start by adding 1 to both sides:
[tex]\frac{|m|}{2}=-2[/tex]
Multiply both sides by 2:
[tex]|m|=-4[/tex]
The absolute value of a number is always positive (with the exception of 0), therefore there is no solution.
Additional CommentsNotice we can only add/multiply (or subtract/divide) an equation because of the Addition/Subtraction/Multiplication/Division Property of Equality which state that if you add/subtract/multiply/divide one side of the equation by a certain value, you must do the same to the other side of the equation.
John has a 3/4 of a quart of orange juice and needs to fill it equally in cups that hold 1/10 of a quart. how many cups can he fill?
Answer: 7 1/2 cups
Step-by-step explanation:
We first need to make both fractions have an equal denominator. Cross Multiply 3/4 and 1/10. You will end up with 30/40 and 4/40.
Next we divided 30 by 4, and we will end up with 7 1/2. 7 times 4 is 28, and half of 4 is 1/2, or in this case 2/10. John can fill 7 and 1/2 cups of orange juice.
A data value is considered _______ if its z-score is less than 2 or greater than 2.
A data value is considered significantly low or significantly high if its z-score is less than -2 or greater than 2.
What does it mean if z-score is 2?
A positive z-score indicates the raw score is higher than the mean average.For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.A negative z-score reveals the raw score is below the mean average.For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.What does a standard deviation of 2 mean?
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean.In any distribution, about 95% of values will be within 2 standarddeviations of the mean.
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The correct question is -
A data value is considered _______ if its z-score is less than minus−2 or greater than 2.
find the domain and range
Answer:
domain should be x=1
range is all real numbers
Step-by-step explanation:
Answer:domain should be x=1
range is all real numbers
Step-by-step explanation:
25. A chocolate bar which weighs of a pound is 9/16 cut into seven equal parts. How much do three parts weigh? (A) pound 21/112 (B) pound/27/112 (C) pound 16/63 (D) pound 47/63
The three parts weigh 27/112 pound ( letter B).
Rules for Multiplication and Division of FractionsFor Multiplication - First, you should multiply both numerators after that you should multiply both denominators. Finally, you can simplify if it is necessary.For Division- First, you should repeat the numerator and after that you should multiply the numerator by the reciprocal of denominators. Finally, you can simplify if it is necessary.The question gives:
A chocolate bar that weighs = 9/16A chocolate bar cut into seven equal parts.Therefore, each part will be [tex]\frac{\frac{9}{16} }{7} =\frac{9}{16} *\frac{1}{7} =\frac{9}{112}[/tex].
For knowing the three parts weigh, you should mulitiply the previous value for 3. Thus,
[tex]\frac{9}{112}*3=\frac{27}{112}[/tex].
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The weight of three parts is 27/112 pounds
How to determine the weight of three parts?The weight of the chocolate bar is given as:
Weight = 9/16
When it is cut into 7 equal parts, the weight of each part is
Each = Weight/7
This gives
Each = 9/16 * 1/7
Evaluate the product
Each = 9/112
The weight of three parts is then calculated as:
Three parts = Each * 3
This gives
Three parts = 9/112 * 3
Evaluate the product
Three parts = 27/112
Hence, the weight of three parts is 27/112 pounds
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Suppose 5 different integers are randomly chosen from between 20 and 69, inclusive. What is the probability that they each have a different tens digit?
The probability that they each have a different tens digit is 0.047.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The probability of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.
Solution:- The collection contains 50 integers, hence there are [tex]^{50}C_5[/tex] different ways to select 5 different integers.
Sample space = [tex]^{50}C_5[/tex]
Each of the five numbers must correspond to one of the five available tens-digits, which are 2 through 6. There are a total of 105 ways to choose the five numbers that satisfy these properties because there are 10 ways to choose a number with a particular set of ten digits (such as 30, 31, or 39).
Therefore,
probability that each have a different tens digit = [tex]\frac{10^5}{^{50}C_5}[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{^{50}C_5}[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{(50-5)!5!} }[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{45!5!} }[/tex]
= 0.047
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The figure below is made of 222 rectangular prisms.
What is the volume of this figure?
A shape made up of two rectangular prisms. The first rectangular prism has a base that measures 9 inches length by 6 inches width, and has a height of 3 inches. The second rectangular prism sits behind the first rectangular prism. It has a base that measures 10 inches length by 7 inches width and has a height of 3 inches.
please help its a khan question and i have a timer :'D
Answer:
372 in^3.
Step-by-step explanation:
The volume of the first prism = 9*6*3
= 162 in^3.
Volume of second prism
= 10*7*3
= 210 in^3.
Total vol = 162 + 210
= 372 in^3.
The required volume of the composite prism is 372 cubic inches,
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
To determine the volume of the composite prism,
As we can see there is two rectangular prisms,
Calculate the volume of two individual prisms and add their volume to the composite volume of the figure.
The volume of the first prism
= lenght × width × height
= 9 × 6 ×3 = 162 in³
The volume of the second prism
= lenght × width × height
= 10 × 7 ×3 = 210 in³
The total volume of the composite figure = 162 + 210 = 372 in³.
Thus, the required volume of the composite prism is 372 cubic inches,
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