Answers
= ∛1080
= 6∛5
answer
C. 6(∛5)
The simplified value of the product of [tex]\sqrt[3]{24}\times\sqrt[3]{45}[/tex] is [tex]6\sqrt[3]{5}[/tex].
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
We know when we have the same radical we can simply multiply the values.
Given, [tex]\sqrt[3]{24}\times\sqrt[3]{45}[/tex].
= [tex]\sqrt[3]{24\times45}[/tex].
= [tex]\sqrt[3]{2\times2\times2\times3\times3\times3\times5}[/tex].
= [tex]2\times3\sqrt[3]{5}[/tex].
= [tex]6\sqrt[3]{5}[/tex].
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Related Questions
Jessica is going to paint her patio. It is made up of two rectangles. One measures 7 ft x 4 ft x 5 ft, and the other measures 10ft x 8ft x 6ft. What is the total area of her patio?
Answers
Answer:
Jessica patio is made up of two rectangles.
Dimension of one rectangle which is in the shape of cuboid = 7 ft x 4 ft x 5 ft,
Dimension of Second rectangle which is also in the shape of cuboid =10 ft x 8 ft x 6 ft
→Total Area of Patio=Total Surface Area of Cuboid having Dimension 7 ft x 4 ft x 5 ft,+ Total Surface Area of Cuboid having Dimension 10 ft x 8 ft x 6 ft
= 2 ×[7×4+4×5+5×7]+2×[10×8+8×6+10×6]
=2×[28+20+35]+2×[80+48+60]
=2×83 +2×188
=166+376
=542 square feet
Upper face of larger cuboid is partially covered , with smaller cuboid.
Area of Lower face of smaller cuboid =7 ×4=28 square feet
Total Area of patio = 542- (Area of lower face of smaller cuboid)
= 542 - 28
=514 square feet
Bowling costs $4.50 per game (g). Shoe rental costs $3.75 each. The total cost is a function of the number of games. What function rule models the total cost of games and shoe rental? Evaluate the function for three games.
Answers
The cost function is an illustration of linear functions
The cost function is [tex]C(x) = 3.75 + 4.50x[/tex]The cost for three games is $17.25From the question, we have:
[tex]G = 4.50[/tex] --- cost per game
[tex]R = 3.75[/tex] --- cost per shoe rent
Since the cost is a function of number of games, it means that;
The cost of shoe rent is a fixed cost
Let x represents the number of games.
So, the cost function is:
[tex]C(x) = R + G \times x[/tex]
This gives
[tex]C(x) = 3.75 + 4.50 \times x[/tex]
[tex]C(x) = 3.75 + 4.50x[/tex]
Substitute 3 for x; to evaluate the function for 3 games
[tex]C(3) = 3.75 + 4.50 \times 3[/tex]
[tex]C(3) = 3.75 + 13.50[/tex]
[tex]C(3) = 17.25[/tex]
Hence, the cost for three games is $17.25
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according to a meteorologist rain gauge 2.785 centimeters of rain fell. which shows a way to represent the 7 in this number
Answers
7 * 10^-1
Hope that's right.
Another way is 7/10
Mary Ann is buying miniature cars. She wants to buy 20 cars total for a big race she and her friends are having. Black cars $6 dollars each. If she spends $104, how many white cars did she buy?
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Please help me with this question
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There are three trigonometric ratios you can use to find missing angles and sides, and the abbreviation is SOH CAH TOA. This just means that sine is paired with the opposite and the hypotenuse, cosine with the adjacent and the hypotenuse, and tangent with the opposite and the adjacent. You can search this up later to see how each aspect relates to the other in each trio.
The side X is the adjacent side of the triangle and you are given the opposite side as well, which measures 6 units. So if you have OA, the trigonometric ratio you are going to use is cosine as the group is TOA. Now, use the information to solve for X:
tan61=6/X
X=6/tan61
X=3.3ft (to the nearest 10th of a foot)
Find an for the arithmetic series with s16 = -288 And a1 =-21
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Given the sum of the sequence and the first term, we rearrange the formula for the sum to solve for 'd', the common difference. This will allow us to calculate the term at any given point in the arithmetic sequence.
Explanation:In an arithmetic sequence, the nth term can be represented by the formula a + (n-1)d where 'a' is the first term, 'n' is the number of terms and 'd' is the common difference between the terms.
The sum, 's', of the first 'n' terms in an arithmetic sequence is given by the formula s = n/2 * (2a + (n - 1)d).
Given the sum, 's', and the first term in the sequence, 'a', we can rearrange the sum formula to find 'd', the common difference, which will then allow us to find any term in the sequence.
We have s16 = -288 and a1 = -21. So, our problem reduces to solve for 'd' in s = n/2 * (2a + (n - 1)d) The solution with most relevance to the student's question will be the calculated 'd' value.
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Leo bought a used car for x dollars. one year later the value of the car was 0.88x. which expression is another way to describe the change in the value of the car?
A)0.12% decrease
B)0.88% decrease
C)12% decrease
D)88% decrease
Answers
Initial price of car = $x
After one year the price of car = $0.88x
to find the change in price we subtract the price after one year from initial price.
It means change in price = (x-0.88x)= 0.12x
By this we can easily see that , price dropped by 0.12
Or we can say that price dropped by 12%
So option C is the correct answer
C) 12% decrease
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Answers
How many ways can you pick 4 students from 10 students (6 men, 4 women)?
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for 4 person from 10: C⁴₁₀.
It means C₁₀⁴ = [tex] \frac{10!}{4!6!}= \frac{7*8*9}{4!}= \frac{7*8*9}{24}=21.[/tex]
Answer: 21 ways.
Answer:
There are 210 ways in which you can pick 4 students from 10 students (6 men, 4 women).
Step-by-step explanation:
We use the combination formula because the order does not matter.
For example, John, Laura,... is the same way as Laura, then John, then ...
Combinations formula
[tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
Combinations of 4 students from a set of 10. So
[tex]C_{10,4} = \frac{10!}{4!(10-4)!} = 210[/tex]
There are 210 ways in which you can pick 4 students from 10 students (6 men, 4 women).
The data set below consists of the scores of 15 students on a quiz. for this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? explain your thinking. 90 90 91 91 89 90 89 91 91 90 60 90 89 90 91
Answers
In the given data set, the standard deviation is the more appropriate measure of variation as it takes all the scores into account and provides a better insight into the data compared to the range.
Explanation:In the given data set, both range and standard deviation can be used to measure the variation. However, the standard deviation might be a better measure in this instance. The standard deviation provides a numerical measure of the overall amount of variation in the data set. It indicates how far the values are from their average, or mean. In contrast, the range only provides the difference between the highest and lowest values, potentially overlooking the distribution of all the values.
When calculating the standard deviation for your dataset, it becomes evident that most scores are concentrated around the 90s, but there's one score dramatically lower at 60. This single score skews the data set and increases the standard deviation, indicating a larger spread around the mean than what might first be observed. As such, the standard deviation gives us a more detailed understanding of the spread within this set of quiz scores, making it the more useful measure in this case compared to the range.
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The two cones below are similar. What is the value of x?
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The values of x is 0.8 and the right option is O A. 0.8.
What are similar shapes?Similar shapes are enlargements of two shapes using scale factor.
The ratio of the corresponding lengths of similar shapes is equal.
Formula:
Height of the larger cone/Height of the smaller cone = Radius of the larger cone/Radius of the smaller coneFrom the diagram,
10/2 = 4/xmake x the subject of the equation
x =(4×2/10)x = 8/10x = 0.8.Hence, the values of x is 0.8 and the right option is O A. 0.8.
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Which digit is in the hundredths place in the number 742.891?
Answers
Place value is the value of a digit in a number.
Before the decimal i.e on the left-hand side, the place values we have are called:
Units, Tens, Hundreds, Thousands, Ten Thousands e.t.c
After the decimal i.e on the right-hand side, the place values we have are called:
Tenth, Hundredth, Thousandth. Ten thousandth e.t.c
We are given the number: 742.891
The digit in the hundredths place is 9
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My friend needs help with her homework. The problem she is on is: There is 11 sandwiches. 2 children shares each sandwich. How many children share the sandwiches?
Answers
A particular security's default risk premium is 2 percent. for all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.5 percent. the security's liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. the security has no special covenants. calculate the security's equilibrium rate of return.
Answers
ij*=2.00%+1.75%+3.50%+0.25%+0.85%
ij*=8.35%
The equilibrium rate of return is 8.3%.
The equilibrium rate of return of a security is the sum of the real risk-free rate, the inflation risk premium, the default risk premium, the liquidity risk premium, and the maturity risk premium.
In this case, the equilibrium rate of return is:
3.5% + 1.75% + 2% + 0.25% + 0.85% = 8.3%
So the answer is 8.3%.
Here is a breakdown of the calculation:
The real risk-free rate is the rate of return that investors would expect to earn on an investment with no risk of default or inflation.
The inflation risk premium is the additional return that investors demand to compensate them for the risk of inflation.
The default risk premium is the additional return that investors demand to compensate them for the risk of default on a security.
The liquidity risk premium is the additional return that investors demand to compensate them for the difficulty of selling a security quickly and easily.
The maturity risk premium is the additional return that investors demand to compensate them for the risk that the value of a security will decline as it approaches maturity.
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[tex] \frac{3}{4} - \frac{3}{8} \\ [/tex]
Answers
two fractions have the same denominator. Which is greater fraction: the fraction with the greater
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the fraction with the greater numerator is the greater fraction, and
the fraction with the smaller numerator is the smaller fraction.
The area of the shaded circle below is 78.5 square inches. The area of the large circle is 314 square inches.
What is the probability that a point chosen at random will be in the shaded region? Round the answer to two decimal places.
0.25
0.33
0.66
0.75
Answers
The probability that a point choosen at random lies within the shaded area = Area of shaded region / Total area of the bigger cricle
So,
Probability = 78.5/314 = 0.25
Thus there is 0.25 or 25% probability that the point chosen at random will lie inside the shaded region.
Answer:
A. 0.25
Step-by-step explanation:
How many sequences of outcomes are possible if one rolls two identical dice 10 successive times?
Answers
So 252 is your final answer.
By the way I used • to represent multiplication
Mr Connors drove 78 1/3 miles on Monday, 77 1/12 miles on Tuesday, and 75 5/6 miles on Wednesday. If he continues this pattern on Thursday and Friday, How many fewer miles will he drive on Friday then don't Tuesday
Answers
Answer:
3 3/4 miles
Step-by-step explanation:
Mr. Connors' pattern is to drive 1 3/12 fewer miles each day. The third day after Tuesday (on Friday), he wll drive 3×(1 1/4) = 3 3/4 fewer miles than on Tuesday.
Final answer:
Mr. Connors will drive 1/12 mile fewer on Friday compared to Tuesday.
Explanation:
To find how many fewer miles Mr. Connors will drive on Friday compared to Tuesday, we need to calculate the difference in the distances driven.
On Tuesday, he drove 77 1/12 miles.
On Friday, he will continue the pattern of subtracting a fraction from the distance driven each day. Therefore, we can subtract the same fraction (1/12) from the distance driven on Friday.
So, the difference in miles driven between Friday and Tuesday will be 77 1/12 - (77 1/12 - 1/12), which simplifies to 1/12 mile.
Therefore, Mr. Connors will drive 1/12 mile fewer on Friday compared to Tuesday.
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Which statements about the ellipse are true? Check all that apply.
The center is at (−2, −5).
The distance between the center and each vertex is 10 units.
The covertices are at (−2, −4) and (−2, −6).
The distance between the center and each focus is units.
The directrices are horizontal lines approximately 5.1 units from the center.
Answers
1.) The center is at (-2,-5).
3.) The con vertices are at (-2,-4) and (-2,-6).
4.) The distance between the center and each focus is 2√6 units.
Statements 1,3 and 4 about the ellipse are true. Ellipse is the result of carving a cone with an oblique plane that does not intersect the base.
What is an ellipse?The asymmetrical oval shape is drawn by a spot advancing along a plane so that the sum of its distance from foci is kept the same known as an ellipse.
1.) The center is at (-2,-5).
3.) The cone vertices are at (-2,-4) and (-2,-6).
4.) The distance between the center and each focus is 2√6 units.
Hence statements 1,3 and 4 about the ellipse are true.
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A minor league baseball team plays 101 games in a season. If the team won 17 more than twice as many games as they lost, how many wins and losses did the team have? How many games did the team lose? How many games did they win?
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Find the thirtieth term of the following sequence.
-6, -4, -2, 0, ...
52
64
66
Answers
Answer:
The thirtieth term of sequence is 52
Step-by-step explanation:
Given the A.P series
-6, -4, -2, 0, ...
we have to find the thirtieth term of the following sequence.
The A.P is -6, -4, -2, 0, ...
which implies
Common difference, d=-4-(-6)=-4+6=2
First term=a=-6
n=30
[tex]a_n=a+(n-1)d[/tex]
[tex]a_{30}=a+29d[/tex]
[tex]a_{30}=-6+29(2)=-6+58=52[/tex]
hence, the thirtieth term of sequence is 52
An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. The yard has 3 sprinkler heads that each cover a circular area with no overlap. What is the approximate total area that will be watered?
Answers
Answer:
Approximate Total area that will be watered is 5887.5 feet²
Step-by-step explanation:
Radius of the Circular area that sprinkler cover , r = 25 feet
Number of sprinkler = 3
Area covered by 1 sprinkler = Area of circle
= πr²
= 3.14 × (25)²
= 3.14 × 625
= 1962.5 feet²
Area covered by 3 sprinkler = 3 × 1962.5 = 5887.5 feet²
Therefore, Approximate Total area that will be watered is 5887.5 feet²
The approximate total area that will be watered will be 5887.5 feet². Square centimeters and other similar units are used to measure area.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area.
The given data in the problem is;
r is the radius of the Circular area that sprinkler cover = 25 feet
n is the number of sprinklers = 3
The sprinkler executes a circular motion ;
Area covered by sprinkler = Area of the circle
The area covered by sprinklers is found as;
[tex]A_S = \pi r^2 \\\\ A_S = 3.14 \times (25)^2 \\\\\ A_S = 3.14 \times 625 \\\\ A_S= 1962.5 \ feet^2[/tex]
The area covered by the three sprinklers will be;
[tex]\rm A_S = 3 \times 196.25 \\\\ \rm A_S =5887.5 \ feet^2[/tex]
Hence approximate total area that will be watered will be 5887.5 feet².
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Seven friends picked 7 quarts of blueberries. Three of the friends will share 4 quarts blueberries equally and the other 4 friends will share 3 quarts of the blueberries equally. In which group does each friend get a greater amount of blueberries? Explian your reasoning
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In the group of 4 friends, each gets 3/4 quart.
The friends in the first group get a greater amount of blueberries. Reasoning: 4/3 > 3/4.
The football and soccer teams at Juans middle school are selling movie tickets. He wants to determine the average number of tickets sold at the school. First he surveyed eight random players on tge football team. Then he surveyed every third athlete on the football and soccer team. Which sampling technique should produce a more representative sample
Answers
Answer:
D is the answer.
"The second sampling method, surveying the both teams, is the most representative. "
Step-by-step explanation:
A stretch of highway that is 12 1/4 kilometers long has speed limit signs every 7/8 of a kilometer. How many speed limit signs are on this stretch of highway?
Answers
= (49/4)*(8/7)
= 2*7
= 14
There are 14 speed limit signs on that highway.
Answer:
the answer is 14 speed limit signs
Step-by-step explanation:
Future googling man, am I ever gonna get married?
Answers
how to find the area of 2 half circles and a rectangle
Answers
We use different formulas to calculate the areas of different shape.
RECTANGLE:
To find the area of a rectangle, we must simply multiply its length by its width. The formula for its area is:
A = l × w
SEMICIRCLE:
Since the formula for a circle is pi × r × r, we must use the same formula but divide it in half, because a semicircle is a half circle, which is why its area would also be half of a circle's. The formula for a semicircle's area is:
A = 1/2 pi × r × r
Tip:
Write these formulas down and memorize them so that you don't forget them. You'll have to use these formulas quite often when finding the area of these shapes.
Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x − 1 , y = 0, x = 9; about the x-axis v = incorrect: your answer is incorrect.4
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Four consecutive integer numbers add to 2. What are the numbers?
Answers
Hope this helps
The numbers are consecutive, meaning they are in arithmetic progression.
Sum of Arithmetic Progression = (n/2)[2a + (n- 1)d]
Where, n = total number of numbers and d = common difference between two successive numbers
Therefore n = 4 and d = 1 ( as the numbers are consecutive )
now (4/2)(2a + (4 - 1)1) = 2
i.e. 2(2a + 3) = 2
i.e. 4a + 6 = 2
i.e. 4a = - 4
i.e. a = - 1
Therefore nos are -1, -1+1 , -1+1+1 , -1+1+1+1
i.e. -1, 0 , 1 , 2
Hope this helps..!!
Thank you :)