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3 years ago

A students work to simplify a radical is shown below. Select the statemmebt which best applies to rhe sample mathematical work

Mathematics

1 answer:

Citrus2011 [14]3 years ago

4 0

Answer:

D. The work shown above is correct, and $y^5.\sqrt[4]{y^3}$ may not be simplified further.

Step-by-step explanation:

$\sqrt[4]{y^{23} } = \sqrt[4]{y^4 . y^4 . y^4.y^4.y^3}$

$\sqrt[4]{y^4. y^4.y^4. y^4.y^3} = y^5 . \sqrt[4]{y^3}$

When we simplify, we get

$\sqrt[4]{y^{23} } = y^5.\sqrt[4]{y^3}$

The answer: D. The work shown above is correct, and $y^5. \sqrt[4]{y^3}$ may not be simplified further.

Thank you.

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The base of an isosceles triangle is one and a half times the length of the other two sides.A smaller triangle has a perimeter t

Anna11 [10]

Answer:

Perimeter of the smaller triangle = 1.75x

Step-by-step explanation:

Let the two equal sides of an isosceles triangle = x

Therefore, length of the base = $(1\frac{1}{2})x$

Perimeter of this isosceles triangle = x + x + $(1\frac{1}{2})x$

= 2x + $(1+\frac{1}{2})x$

= 2x + x + $\frac{x}{2}$

= $\frac{5x}{2}$

Since, smaller triangle has a perimeter that is half the perimeter of the larger triangle,

Length of each corresponding side of smaller triangle will be half of the larger triangle.

Length of sides of the smaller triangle = $\frac{x}{2},\frac{x}{2},(1\frac{1}{2})\frac{x}{2}$

Perimeter of the smaller triangle = $\frac{x}{2}+\frac{x}{2}+(1\frac{1}{2})\frac{x}{2}$

= x + $\frac{x}{2}+\frac{x}{4}$

= $\frac{3}{2}x+\frac{x}{4}$

= $\frac{6}{4}x+\frac{x}{4}$

= $\frac{7}{4}x$

= 1.75x

Therefore, expression that represents the perimeter of the smaller triangle is (1.75x)

4 0

3 years ago

What is a 15% tip on a meal that costs $25.00

nataly862011 [7]

$25.00/ 10= 2.50
 \\ 2.50*1.5= 3.75 \\ 25.00+3.75= 28.75$
As you've got 15%, the best thing to do is to find 10%, then multiply it by 1.5. Once you've found the tip, you add this onto the cost of the meal.
Therefore, the total cost of $25 meal with a 15% tip is $28.75
Hope this helps :)

8 0

3 years ago

Read 2 more answers

11. What is the reciprocal of 6/5?<br> OA. 12/20<br> OB.11/5<br> OC.1<br> OD.576

Elanso [62]

Answer: The answer is D, 5/6.

Step-by-step explanation: The reciprocal of a fraction is that fraction but the numerator and denominater swapped places.

3 0

3 years ago

Read 2 more answers

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mou

VikaD [51]

Complete Question

The complete question is shown on the first uploaded image

Answer:

$P(X = 8) = 0.0037$

$P(X < 5) = 0.805$

$P(X > 6) = 0.0206$

I would be surprised because the value is very small , less the 0.05

Step-by-step explanation:

From the question we are told that

The probability a randomly selected individual will not cover his or her mouth when sneezing is $p = 0.267$

Generally data collected from this study follows binomial distribution because the number of trials is finite , there are only two outcomes, (covering , and not covering mouth when sneezing ) , the trial are independent

Hence for a randomly selected variable X we have that

$X \ \ \~ \ \ { B ( p , n )}$

The probability distribution function for binomial distribution is

$P(X = x ) = ^nC_x * p^x * (1 -p) ^{n-x}$

Considering question a

Generally the the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as

$P(X = 8) = ^{12} C_8 * (0.267)^8 * (1- 0.267)^{12-8}$

Here C denotes combination

$P(X = 8) = 495 * 0.000025828 * 0.28867947$

$P(X = 8) = 0.0037$

Considering question b

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as

$P(X < 5 ) =[P(X = 0 ) + \cdots + P(X = 4)]$

=> $P(X < 5 ) =[ ^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0} + \cdots + ^{12} C_4 * (0.267)^4 * (1- 0.267)^{12-4} ]$

=> $P(X < 5 ) = 0.02406 + 0.10516 + 0.21067 + 0.25580 + 0.20964$

=> $P(X < 5) = 0.805$

Considering question c

Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

$P(X > 6) = 1 - p(X \le 6)$