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Related Questions
Simplify the expression [tex]\sqrt[3]{32a^{7} }b\fracx^{9}[/tex] . Assume a ≠ 0 and b ≠ 0.
Enter the correct answer in the box.
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The result obtained when we simplify the expression ³√(32a⁷b⁹) is ³√(2⁵ × a⁷) × b³
How to simplify ³√(32a⁷b⁹)The simplification of ³√(32a⁷b⁹) can be obatined as illustrated below:
³√(32a⁷b⁹)
We shall simplify the individual term. This is shown below
³√32 = ³√2⁵
³√a⁷ = ³√a⁷
³√b⁹ = b^(9/3) = b³
Combining the above, we have
³√(32a⁷b⁹) = ³√2⁵ × ³√a⁷ × b³
³√(32a⁷b⁹) = ³√(2⁵ × a⁷) × b³
From the above illustration, we can conclude that simplifying ³√(32a⁷b⁹) results in ³√(2⁵ × a⁷) × b³
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please help meeeee!!!!!
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The S₄ is 3/125 .
A sequence could be a list of numbers that have been arranged sequentially whereas series can be exceedingly generalized as the sum of all the terms in a sequence be that as it may, there must be a clear relationship between all the terms of the sequence. An infinite arrangement is given by all the terms of an unbounded grouping, included together and the sum of the series is just adding the n number of terms
Since we are provided with an infinite series, where n starts from 0 till infinite.So we need to find the sum for 4 terms, just replacing the n in the given formula to 4
S⁴=3(1/5) ^(n-1)
= 3(1/5) ^(4-1)
= 3(1/5) ^3
= 3/125
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How far is each planet from the st
Mercury-51,000,000
Venus-10000000
Earth-150000000
Susan said, "Venus is more than twice as far from the sun as Mercury is."
Is Susan correct? If so, write yes. If she is wrong, rewrite the statement to make it true.
You could change more to less, change the planets-do whatever you need to do to
make a TRUE statement for Susan.
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A TRUE statement for Susan is: "Venus is less than twice as far from the Sun as Mercury is."
Given:
The distance of each planet from the Sun,
Mercury - 51,000,000
Venus - 10000000
Earth - 150000000
Susan said, "Venus is more than twice as far from the sun as Mercury is."
51,000,000 × 2 = 102,000,000
When we calculate twice the distance of Mercury from the Sun it is much greater than the actual distance of Venus from the Sun.
(102,000,000 > 10000000)
Hence, the statement is incorrect and so is Susan.
The correct statement should be:
"Venus is less than twice as far from the sun as Mercury is."
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EO GEOMETRYVolume of a sphereThe diameter, D, of a sphere is 19.8 m. Calculate the sphere's volume, V.Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.
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Remember that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
r=19.8/2=9.9 m -----> the radius is half the diameter
pi=3.14
substitute given values
[tex]V=\frac{4}{3}\cdot3.14\cdot9.9^3[/tex]V=4,062.3 m3you are buying one flower for each member of the swim team to wear at an awards tonight there are 19 members on the team you have decided to buy pink roses and yellow roses the pink roses cost $3 and the yellow roses cost $2 you will spend $50 Let x represent pink roses and y represent yellow roses . If there's a solution graph them
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Let:
x = Number of pink roses
y = Number of yellow roses
there are 19 members on the team, so:
[tex]x+y\le19[/tex]the pink roses cost $3 and the yellow roses cost $2 you will spend $50, so:
[tex]3x+2y\le50[/tex]so:
[tex]\begin{gathered} y\le19-x \\ y\le\frac{1}{2}(50-3x) \end{gathered}[/tex]12⋅(1/4+1/3)to the 2nd power+2/3
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Answer: 19/4 or 4 3/4 or 4.75
Step-by-step explanation:
calculate the sum
12(7/12)^2+(2/3)
use the properties of exponents
12x(49/144)+(2/3)
simplify the expression
(49/12)+(2/3)
calculate the sum
19/4 or 4 3/4 or 4.75
have a GREAT day!!
The length of a rectangle is 17 meters and the width is 12 meters. What is the perimeter of the rectangle? Do not include units in your answer.
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We have that the perimeter is the addition of all the sides of the rectangle, so we have that
[tex]\begin{gathered} p=2\cdot l+2\cdot w \\ p=2\cdot17+2\cdot12 \\ p=34+24=58 \end{gathered}[/tex]I got 58 for my answer
The question is below! I think the answer is: 10(8-i)
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Notice that the GCD between 80 and 10 is 10. Therefore, we can factor the expression as following:
[tex]80-10i\rightarrow10(8-i)[/tex]Which relation shown is not a function?
O {(14, 15). (5. 7). (3. 10). (11, 1). (3.8)}
O {(1, 1), (2, 2), (3, 3), (4. 4), (5,4)}
O {(14, 15). (5, 7), (3, 10), (11, 1), (6, 10)}
O {(14, 15). (5. 15). (3. 15). (11, 15). (5, 15)}
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Answer: the last one
Step-by-step explanation:
the easiest way to do this is the vertical line test. Graph the relation separately and then roll a pencil over each one. If the pencil touches two points at the same time, then it is not a function. Or you can look at the x inputs and if any are the same, it’s not a function.
Using the line of best fit, estimate a person's hourly rate when he or she has 5 years of experience.es )
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It will be aproximately equal to 11$, because when you take x=5 then the heigh of the y coordinate will be aproximately equal to 11.
Carol says that 83 + 96 + 74 is greater than 300.
Is Carol correct? Why or why not?
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Answer:
that girl is wrong because if you add 83+96+74 it equals 253, and that is not greater than 300
Step-by-step explanation:
A person's stride length is the distance covered by one step. On average, a person's stride is
approximately 2.5 feet long. How many steps would the average person take to travel 50 feet?
Set up the division problem.
. What number is your dividend (the number being divided)?
O The dividend is
. What number is the divisor (the number doing the dividing)?
. The divisor is
4
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Answer:
2.5 ft long= one step
1 ft long=1/2.5
50 ft= 50 x 1/2.5=20 steps
20 steps to travel 50 steps
Step-by-step explanation:
the net of a rectangular prism is shown below each Square represents one square unit what is the total surface area of the cone
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Given:
Area of each sqaure = 1 square unit
Let's find the total surface area of the net image.
From the image, the total number of squares we have is = 52.
The total surface area will be the total number of squares since each square represents one square unit.qu
We have 52 squares in total.
Therefore, the total surafce area of the rectangular prism is 52 square units.
ANSWER:
B. 52 square units
In the diagram , AB and BC are both tangent to P
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Since AB and BC are both tangent to the circle P, their length is the same.
So we have the following equation:
[tex]2x+7=31[/tex]Solving this equation for x, we have:
[tex]\begin{gathered} 2x=31-7 \\ 2x=24 \\ x=\frac{24}{2} \\ x=12 \end{gathered}[/tex]So the value of x is 12, therefore the correct option is the first one.
Hello! I need answer 1 solved, for geometry this is a question sheet!
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1) We have to solve for x.
We have a right triangle, so we can apply the Pythagorean theorem to relate the side lengths.
As x is the hypotenuse, we can write:
[tex]\begin{gathered} x^2=9^2+15^2 \\ x^2=81+225 \\ x^2=306 \\ x=\sqrt{306} \\ x\approx17.5 \end{gathered}[/tex]Answer: x = 17.5
I need help asap I will give a lot of point for it
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Answer:
x = 65°
Step-by-step explanation:
Question 19 of 25Which of these frequency counts would be represented by the tallest bar on ahistogram?OA. 15OB. 17O C. 18O D. 16SUBMIT
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18 (option C)
Explanation:Given:
Frequency counts: 15, 17, 18, 16
To find:
the frequency count that would be represented by the tallest bar on a histogram
The tallest bar on a histogram is the highest frequency in a given set of dataset
We have been given 4 frequencies: 15, 17, 18, and 16
The highest value in the frequency is 18
Hence, the frequency count that will have the tallest bar on a histogram is 18 (option C)
Enter your answer as a number without units, like this: 42
Answers
Answer:
perimeter: 88
area: 246
Step-by-step explanation:
6 x 32 = 192
32 - 20 = 12 12 x 9 = 108 108 / 2 = 54
54 + 192 = 246
QUICK ANSWERS ONLY! No graph* 39. What are three pairs of corresponding angles?A. angles 1 & 2, 3 & 8, and 4 & 7B. angles 1 & 7, 2 & 4, and 6 & 7C. angles 1 & 7, 8 & 6, and 2 & 4D. angles 3 & 4, 7 & 8, and 1 & 6
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The "same side interior angle theorem" states: If a transversal intersects two parallel lines, each pair of same-side interior angles are supplementary (their sum is 180∘ ).
In the image uploaded, the same side interior angleS are 1 and 4, also 2 and 3.
Therefore, in the question, the same side interior angle is option B
I need to use the formula value, A = P(1 + rt), and elementary algebra to find the Principal
Answers
P= $1300
Explanation
when you have the rate, the time and the initial value , you can find the principial by using the formula
[tex]\begin{gathered} A=P(1+rt)^ \\ where\text{ P is the principal} \\ A\text{ is the amounnt} \\ r\text{ is the rate \lparen in decimal\rparen} \\ t\text{ is the number of periods} \end{gathered}[/tex]so
Step 1
a)let
[tex]\begin{gathered} A=1508 \\ r=4\text{ \%=}\frac{4}{100}=0.04 \\ t=4\text{ \lparen years\rparen} \end{gathered}[/tex]now, replace in the formula
[tex]\begin{gathered} A=P(1+r)^ \\ 1508=P(1+0.04*4) \\ 1508=P(1.16) \\ divide\text{ both sides by 1.16} \\ \frac{1,508}{1.16}=\frac{P(1.16)}{1.16} \\ 1300=P \end{gathered}[/tex]therefore, the answer is
P= $1300
I hope this helps you
1 Which of the following situations can be represented by 14? Circle all the correct answers. А Renee has 14 feet of ribbon that she will cut into 5 pieces of equal length. B. Michael has 14 packs of trading cards with 5 cards in each pack. C Logan opens S bags of trail mix, which she will split equally into 14 bowls. D Patrick takes 5 oranges from a bag containing 14 oranges E Tim walks 14 blocks from the library to a friend's house and then walks another 5 blocks to home. Arianna pours 5 equal servings of lemonade from a bottle containing 14 ounces. AA BB C C D D FF
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Answer:
A.
F.
Explanation:
14/5 represents situation where we have 14 objects and we need to divide it in 5 equal parts. Therefore, these situations are
A. Renee has 14 feet of ribbon that she will cut into 5 pieces of equal lenght
F. Arianna pours 5 equal servings of lemonade from a bottle containing 14 ounces
For the first case, 14/5 will be the length of the pieces and for the second case 14.5 represents the amount of ounces in each serving.
Convert 1.6 x 10-2 to standard notation.
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Recall that:
[tex]b\times a^{-x}=\frac{b}{a^x}.[/tex]Therefore:
[tex]1.6\times10^{-2}=\frac{1.6}{10^2}=\frac{1.6}{100}.[/tex]Simplifying the above result we get:
[tex]\frac{1.6}{100}=0.016.[/tex]Answer: 0.016.
write 783.94 using exponential form
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Answer:
62727262 is the awnser your welcome thank me later
Final and of the unknown side rania answer to the nearest whole number 7 mm to 7 mm what is the answer
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Round to the nearest whole number means round the tenth digit to the one digit, so
Divide 1 by 2
1/2 = 0.5, so we will add 0.5 and subtract 0.5 from 7
7 - 0.5 = 6.5
7 + 0.5 = 7.5, so
[tex]6.5\text{ }\leq\text{ 7 mm <7.5}[/tex]You can choose any number between them
[tex]6.5\approx\text{ 7}[/tex][tex]7.49\approx\text{ 7}[/tex]Greg bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7.5% per year, and for the laptop it was 8% per year. The total finance charges for one year were $400. How much did each computer cost before finance charges?
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the cost of laptop and cost of desktop is $1,800 and $2,100 respectively does each computer cost before finance charges.
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
From the question above, we can see that the laptop costs $350 more than the desktop, therefore, we say:
let x represent the cost of the laptop ;
then x-350 will be the cost of the desktop .
We can also see that the total finance charge of $400 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as follows:
400 = 0.08(x) + 0.075(x - 350)
252 = 0.08x + 0.075x - 26.25
252 26.75 = 0.155x
278.75 = 0.155x
x = 278.75/0.155
x = 1798
Recall that:
cost of desktop = x -350
therefore:
1,798- 350 = 1448
cost of laptop = $1798
cost of desktop = $1448
Thus, the cost of laptop and cost of desktop is $1,800 and $2,100 respectively does each computer cost before finance charges.
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Sabreena is playing a card game, and the odds of her winning after drawing the next card are 5:7.
What is the probability of her not winning?
Enter your answer as a decimal rounded to the nearest thousandth, like this: 0.423
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Giving that her probability of winning is 5:7, Her Probability of not winning is; 0.286
What is the Probability of not winning?
According to binomial probability distribution, the probability is usually given by the formula;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
where;
p is probability of success
n = number of trials, or the sample size
x = the number of "successes" in the probability
Now, we are told that the probability of winning in the next card is 5:7. Writing this in fraction form is 5/7.
Now, we know that percentage of winning + percentage of losing equals to 1. Thus;
Percentage of not winning + 5/7 = 1
Percentage of not winning = 1 - 5/7
Percentage of not winning = 2/7
In percentage form, this gives us;
2/7 * 100% = 28.57% = 0.286
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What is (-4x²-3x+8) subtracted from (2x2² + 5x - 7)?
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Answer:
6x² + 8x - 15
Step-by-step explanation:
2x² + 5x - 7 - (- 4x² - 3x + 8) ← distribute parenthesis by - 1
= 2x² + 5x - 7 + 4x² + 3x - 8 ← collect like terms
= 6x² + 8x - 15
Answer:
[tex]6x^2+8x-15[/tex]
Step-by-step explanation:
Given expression:
[tex](2x^2+5x-7)-(-4x^2-3x+8)[/tex]
[tex]\textsf{Apply\:the\:distributive\:law}\quad \:-\left(-a-b\right)=a+b:[/tex]
[tex]\implies 2x^2+5x-7+4x^2+3x-8[/tex]
Collect like terms:
[tex]\implies 2x^2+4x^2+5x+3x-7-8[/tex]
Combine like terms:
[tex]\implies 6x^2+8x-15[/tex]
I am having trouble with this equation & how to correctly use the [ & ) when it comes to writing in interval notation.
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We need to solve the inequality:
[tex]4\left(2-x\right)>\left(5x-7\right)-\left(x-10\right)[/tex]In order to do so, we can expand the expressions on each side, then apply the same operations on both sides of the inequality until we isolate the variable x and find the solution.
By expanding the expression, we obtain:
[tex]\begin{gathered} 4(2)+4(-x)>5x-7-x-(-10) \\ \\ 8-4x>5x-x-7+10 \\ \\ 8-4x\gt4x+3 \end{gathered}[/tex]Now, adding 4x to both sides, we obtain:
[tex]\begin{gathered} 8-4x+4x>4x+3+4x \\ \\ 8>8x+3 \end{gathered}[/tex]Subtracting 3 from both sides, we obtain:
[tex]\begin{gathered} 8-3>8x+3-3 \\ \\ 5>8x \end{gathered}[/tex]Then, dividing both sides by 8, we obtain:
[tex]\begin{gathered} \frac{5}{8}>\frac{8x}{8} \\ \\ \frac{5}{8}>x \\ \\ x<\frac{5}{8} \end{gathered}[/tex]Notice that x must be less than 5/8. Thus, 5/8 does not belong to the solution set. We represent this using (..., ...) for interval notation (open interval). Also, since there is no beginning to the interval solution, we write -∞ in replacement of the left boundary of the set.
Therefore, the solution set is:
Answer
[tex]\left(-\infty,\frac{5}{8}\right)[/tex]Options1. is -2, -1, 2, 52. is subtract 25/2, add 25/2, subtract 25/4, add 25/4 and the second box is the same thing.6. is -5/2, -11/2, 5/2, 11/2.
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Given the equation:
[tex]7=-2x^2+10x[/tex]Step 1: Factor -2 out of the variable terms
[tex]7=-2(x^2-5x)[/tex]Step 2: Divide both sides by -2.
[tex]\frac{7}{-2}=x^2-5x[/tex]If R^2 = 0.62, then how much of the sample variation is y
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In equation [tex]r^{2}[/tex] = 0.62 we get the variation of r is [tex]r = \frac{\sqrt{62} }{10 } }[/tex] or [tex]r =- \frac{\sqrt{62} }{10 } }[/tex]
According to the question, given that
Variation [tex]r^{2}[/tex] = 0.62
Split into two equation
[tex]r = \sqrt{0.62}[/tex] or, [tex]r = -\sqrt{0.62}[/tex]
First equation
[tex]r = \sqrt{0.62}[/tex]
convert decimal to fraction
[tex]r =\sqrt{\frac{62}{100} }[/tex]
[tex]r =\sqrt{\frac{31}{50} }[/tex]
rewrite the expression using
[tex]\sqrt[n]{ab} = \sqrt[n]{a}* \sqrt[n]{b}[/tex]
[tex]r = \frac{\sqrt{31} }{\sqrt{50} }[/tex]
[tex]r = \frac{\sqrt{31} }{\sqrt{5^{2} * 2} }[/tex]
[tex]r = \frac{\sqrt{31} }{\sqrt{5^{2} * \sqrt{2} } }[/tex]
[tex]r = \frac{\sqrt{31} }{5 \sqrt{2} } }[/tex]
Rationalize the denominator
[tex]r = \frac{\sqrt{31}* \sqrt{2} }{5 \sqrt{2} * \sqrt{2} } }[/tex]
[tex]r = \frac{\sqrt{31}* \sqrt{2} }{5 *2} } }[/tex]
[tex]r = \frac{\sqrt{31}* \sqrt{2} }{10 } }[/tex]
[tex]\sqrt[n]{ab} = \sqrt[n]{a}* \sqrt[n]{b}[/tex]
[tex]r = \frac{\sqrt{31 *2} }{10 } }[/tex]
[tex]r = \frac{\sqrt{62} }{10 } }[/tex]
Second equation
[tex]r = -\sqrt{0.62}[/tex]
[tex]r =-\sqrt{\frac{31}{50} }[/tex]
[tex]r =- \frac{\sqrt{31} }{\sqrt{50} }[/tex]
[tex]r = - \frac{\sqrt{31} }{\sqrt{5^{2} * 2} }[/tex]
[tex]r = - \frac{\sqrt{31} }{\sqrt{5^{2} * \sqrt{2} } }[/tex]
rewrite the expression using
[tex]\sqrt[n]{ab} = \sqrt[n]{a}* \sqrt[n]{b}[/tex]
[tex]r = - \frac{\sqrt{31} }{\sqrt{5^{2} * \sqrt{2} } }[/tex]
[tex]r = -\frac{\sqrt{31} }{5 \sqrt{2} } }[/tex]
Rationalize the denominator
[tex]r = -\frac{\sqrt{31}* \sqrt{2} }{5 \sqrt{2} * \sqrt{2} } }[/tex]
[tex]r = -\frac{\sqrt{31}* \sqrt{2} }{5 *2} } }[/tex]
[tex]r = -\frac{\sqrt{31}* \sqrt{2} }{10 } }[/tex]
[tex]r = -\frac{\sqrt{31 *2} }{10 } }[/tex]
[tex]r =- \frac{\sqrt{62} }{10 } }[/tex]
[tex]r = \frac{\sqrt{62} }{10 } }[/tex] or [tex]r =- \frac{\sqrt{62} }{10 } }[/tex]
Therefore, equation [tex]r^{2}[/tex] = 0.62 we get the sample variation of r is [tex]r = \frac{\sqrt{62} }{10 } }[/tex] or [tex]r =- \frac{\sqrt{62} }{10 } }[/tex]
A relationship between a set of values for one variable and a set of values for other variables is known as a variation.
Direct variation
The function y = mx (commonly written y = k x), which is referred to as a direct variation, can be obtained from the equation y = mx + b if m is a nonzero constant and b = 0.
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