MATHEMATICS COLLEGE

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Answers

Answer 1

Answer:

answer:

I gotdas the answer

decimal format = 29.25

mixed number = 29 1/4

Improper fraction = 117/4

Step-by-step explanation:

Make the denominators equal after simplifying the denominators*. The denominators are currently 2 and 4. So you can just make your life easier by making the denominator of the first number a 4. Multiply both sides by 2.

1. Simplify

12*2+1 = 25/2

25/2*2/2 = 50/4

2. Simplify second number

16*4+3 = 67/4

3. Add the improper fractions

50/4 + 67/4 = 117/4

Total answer:

29.25 = decimal format

mixed number = 29 1/4

Improper fraction = 117/4

Terms:

*denominators - the bottom number of a fraction

Hope this helped,

Kavitha Banarjee

What is the product? 2x+8 x2 + 3x-4 x(x-4)(x-1) 20x+4) 2 (x+4)(x-4) 2x(x-1) 2x(x+4)

Answers

The products of the given expressions are:

$(2x + 8) * (x^2 + 3x - 4) = 2x^3 + 14x^2 + 16x - 32\n(x - 4)(x - 1)(20x + 4) = 20x^3 - 96x^2 + 60x + 16\n2(x + 4)(x - 4) = 2x^2 - 32\n2x(x - 1) = 2x^2 - 2x\n2x(x + 4) = 2x^2 + 8x$

Here, we have to find the product of the expressions given,

let's multiply them step by step:

$(2x + 8) * (x^2 + 3x - 4):$

First, apply the distributive property:

$(2x + 8) * x^2 = 2x^3 + 8x^2\n(2x + 8) * 3x = 6x^2 + 24x\n(2x + 8) * (-4) = -8x - 32$

Now, add the results:

Product of (2x + 8) and $(x^2 + 3x - 4) = 2x^3 + 8x^2 + 6x^2 + 24x - 8x - 32$

Combine like terms:

Product = $2x^3 + (8x^2 + 6x^2) + (24x - 8x) - 32$

Product = $2x^3 + 14x^2 + 16x - 32$

(x - 4)(x - 1)(20x + 4):

First, apply the distributive property:

$(x - 4)(x - 1) = x^2 - x - 4x + 4 = x^2 - 5x + 4$

Now, multiply the result with (20x + 4):

$(x^2 - 5x + 4)(20x + 4) = 20x^3 + 4x^2 - 100x^2 - 20x + 80x + 16$

Combine like terms:

Product = $20x^3 + (4x^2 - 100x^2) + (-20x + 80x) + 16$

Product = $20x^3 - 96x^2 + 60x + 16$

2(x + 4)(x - 4):

First, apply the distributive property:

2(x + 4) = 2x + 8

Now, multiply the result with (x - 4):

$(2x + 8)(x - 4) = 2x^2 + 8x - 8x - 32$

Combine like terms:

Product = $2x^2 + (8x - 8x) - 32$

Product = $2x^2 - 32$

2x(x - 1):

Apply the distributive property:

$2x * x = 2x^2$

2x * (-1) = -2x

Combine the terms:

Product = $2x^2 - 2x$

2x(x + 4):

Apply the distributive property:

$2x * x = 2x^2$

2x * 4 = 8x

Combine the terms:

Product = $2x^2 + 8x$

So, the products of the given expressions are:

$(2x + 8) * (x^2 + 3x - 4) = 2x^3 + 14x^2 + 16x - 32\n(x - 4)(x - 1)(20x + 4) = 20x^3 - 96x^2 + 60x + 16\n2(x + 4)(x - 4) = 2x^2 - 32\n2x(x - 1) = 2x^2 - 2x\n2x(x + 4) = 2x^2 + 8x$

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=−640x10+1280x9+19904x8−40728x7−144488x6+323904x5−162304x4+1024x3+2048x2

step by step

(2x+8x2+3x−4x(x−4)(x−1)(20)x+4)(2)(x+4)(x−4)(2)x(x−1)(2)x(x+4)

=((2x+8x2+3x−4x(x−4)(x−1)(20)x+4)(2)(x+4)(x−4)(2)x(x−1)(2)x)(x+4)

=((2x+8x2+3x−4x(x−4)(x−1)(20)x+4)(2)(x+4)(x−4)(2)x(x−1)(2)x)(x)+((2x+8x2+3x−4x(x−4)(x−1)(20)x+4)(2)(x+4)(x−4)(2)x(x−1)(2)x)(4)

=−640x10+3840x9+4544x8−58904x7+91128x6−40608x5+128x4+512x3−2560x9+15360x8+18176x7−235616x6+364512x5−162432x4+512x3+2048x2

=−640x10+1280x9+19904x8−40728x7−144488x6+323904x5−162304x4+1024x3+2048x2

-1 7/9 is the same as them sum of -2 5/6 and 1/3 times a number. what is the number?

Answers

-1 7/9= -2 5/6 + 1/3x
+2 5/6 to each side
-1 7/9 + 2 5/6 = 1 1/18

1 1/18 = 1/3x
Divide each side by 1/3

Answer is 3 1/6

Give two examples of addition of two mixed numbers with different denominators
SHOW ALL STEPS

Answers

Answer:

First Example: 3 1/2 + 4 3/4, Second Example: 6 3/8 + 7 9/15

Extra Example: 8 4/20 + 3 5/10

Step-by-step explanation:

First Example:

1/2 + 3/4

1/2 is equal to 2/4 so it is now compatible to be added to 3/4.

2/4 + 3/4

= 5/4

Now for the mixed numbers since its 3 and 4, 3 + 4 = 7.

Final answer is 7 5/4.

Second Example:

3/8 + 9/15

9/15 can be reduced to 3/5

Now the equation is 3/8 + 3/5

= 15/40 + 24/40 is an equivalent equation

15/40 + 24/40

= 39/40

Now for the mixed numbers since its 6 and 7, 6 + 7 = 13

Final answer is 13 39/40.

I am going to include one last example just in case you need one:

Third Example:

4/20 + 5/10

We can reduce these to

1/5 + 1/2

= 2/10 + 5/10 is the equivalent equation

2/10 + 5/10

= 7/10

Now for the mixed numbers since its 8 and 3, 8 + 3 = 11.

Final answer is 11 7/10.

I Hope this helps!

What does the expression (8x)2 represent

Answers

Option D is correct.

We have an expression that is used to calculate the area of a square - $s^(2)$ , where s is the side of the square.

We have to estimate the value of the expression $(8x)^(2)$

What is the area and perimeter of a square of side 'a' ?

The area of a square is - Area = $a^(2)$ and the perimeter is - P = 4a.

In the question, we have to estimate the value of the expression $(8x)^(2)$ .

Let f(x) = $(8x)^(2)$

The expression given to us is $s^(2)$ .

Let f(s) = $s^(2)$

Compare f(s) and f(x), you will get -

s = 8x

Hence, the expression $(8x)^(2)$ represents the area of square with side length of 8x.

Hence, Option D is correct.

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Answer:

option d

Step-by-step explanation:

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A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean

Answers

Answer:

The minimum sample size needed is $n = ((1.96√(\sigma))/(4))^2$ . If n is a decimal number, it is rounded up to the next integer. $\sigma$ is the standard deviation of the population.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1 - 0.9)/(2) = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = z(\sigma)/(√(n))$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean?

A sample of n is needed, and n is found when M = 4. So

$M = z(\sigma)/(√(n))$

$4 = 1.96(\sigma)/(√(n))$

$4√(n) = 1.96√(\sigma)$

$√(n) = (1.96√(\sigma))/(4)$

$(√(n))^2 = ((1.96√(\sigma))/(4))^2$

$n = ((1.96√(\sigma))/(4))^2$

The minimum sample size needed is $n = ((1.96√(\sigma))/(4))^2$ . If n is a decimal number, it is rounded up to the next integer. $\sigma$ is the standard deviation of the population.

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