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From simplification of the given algebra, the correct answers are as shown below.

1) (a² - b)/(a³b²)

This reduces to;

(a²/(a³b²)) - b/(a³b²)

⇒ a/(ab²) - 1/(a³b)

2) The algebraic expression is;

(b - a)/a³b³

⇒ b/a³b³ - a/a³b³

⇒ 1/a³b² - 1/a²b³

3) The algebraic expression is;

(2 - ab²)/(a²b³)

⇒ (2/(a²b³)) - (ab²)/(a²b³)

⇒ 2/(a²b³)) - 1/(ab)

4) The algebraic expression is;

(2 - ab²)/(a²b³)

⇒ 2/(a²b³) - 1/ab

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The 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is option B. 0.62 plus-or-minus 1.96 start root start fraction 0.62 (1 minus 0.62) over 100 end fraction end root .

Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.

Confidence interval for the population proportion can be calculated as,

p ± z × [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

Here, p is the sample proportion and n is the sample size.

z value for 95% confidence interval is 1.96.

Here, n = 100,

p = [tex]\frac{62}{100}[/tex] = 0.62

Substituting the values, confidence interval of true proportion is,

0.62 ± 1.96 × [tex]\sqrt{\frac{0.62(1-0.62)}{100} }[/tex]

Hence the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is 0.62 ± 1.96 × [tex]\sqrt{\frac{0.62(1-0.62)}{100} }[/tex].

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The rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute

From the question, we are to determine the rate which is equivalent to the rate Paula walked

Using the formula,

[tex]Rate = \frac{Distance}{Time}[/tex]

From the given information,

Distance = 1/12 mile

Time = 5/3 minutes

Putting the parameters into the formula, we get

[tex]Rate =\frac{\frac{1}{12} }{\frac{5}{3} }[/tex]

[tex]Rate = \frac{1}{12} \div \frac{5}{3}[/tex]

[tex]Rate = \frac{1}{12} \times \frac{3}{5}[/tex]

[tex]Rate = \frac{3}{60}[/tex]

[tex]Rate = \frac{1}{20}[/tex] mile/minute

Hence, the rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute

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Answer:

68077

Step-by-step explanation:

he had spent 68077 because by 59425+8652 makes 68077

Trapezoid and kite make up the first split of quadrilaterals on the quadrilateral hierarchy

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilateral are square, kite, trapezoid, rectangle, rhombus and so on.

A quadrilateral hierarchy is a graphical way of representing the different types of quadrilaterals.

Trapezoid and kite make up the first split of quadrilaterals on the quadrilateral hierarchy

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Answer with step-by-step explanation:

1) 4x - 24 = 1000

Add 24 to both sides.

4x = 1024

Divide both sides by 4.

x = 256

2) 7x = 343

Divide both sides by 7.

x = 49

3) x⁴ = 4096

Find 4th root of both sides.

x = 8

Answer:

23cm

Step-by-step explanation:

If you multiply like terms you will get the answers. Then you add last to get 23cm

The required length ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).

Given that,
Package that had a length of 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3.

How much ribbon would be needed to go around the package in centimeters is to be determined.

Perimeter is the measure of the figure on its circumference.

The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.

Quantity of ribbon = perimeter of the rectangular package
                            = 2 * length + 2* width
                            = 2 * (2x^2+3x-5/x^2+x-3) + 2(x^2-x-5/x^2+x-3)
                            = 2 (3x^2 + 2x -10) / (x^2 + x - 3)

Thus, the required length of  ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).

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Using it's concept, it is found that the probability of tossing heads and rolling a number less than 3 is given by:

C. 1/6

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there were 12 trials. Of those, 2 are H1 and H2, which are heads and a number less than 3, hence the probability is given by:

p = 2/12 = 1/6.

Which means that option C is correct.

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Answer:

first ans =x-7

second ans= x+y/x-y

Step-by-step explanation:

I think you would get it and it doesn't need explanation.

Answer:

x = -9 and 16

Step-by-step explanation:

1. Separate in two cases:

(a) -2x + 7 = 25          and          (b) -2x + 7 = -25

(a) -2x + 7 = 25  ⇒ subtract 7 from both sides

     -2x = 18 ⇒ divide both sides by -2

      x = -9

(b) -2x + 7 = -25 ⇒ subtract 7 to both sides

    -2x = -32 ⇒ divide both sides by -2

     x = 16

Solutions: x = -9, 16

Hope this helps!

Answer:

45

Step-by-step explanation:

perimeter is the sum of all sides

for rectangle, it's (length + width) x 2

so do the reverse: 146/ 2 = l + w

73-45 = 30 this means the longer side is 45

=> length is 45

Answer:c

Step-by-step explanation:just took the test

Answer:

He could work 10 hours as a lifeguard, and 5 hours as a tutor

Step-by-step explanation:

If he makes $16 an hour as a lifeguard

            and $18 an hour as a tutor,

He could work 10 times $16, to make $160 for 10 hours.

Now we subtract this from $250, this makes $90.

We know need to find out how many times 18 goes into 90, 5 times.

So we know that he could work 10 hours as a lifeguard and 5 hours as a tutor.

I hope this is right.

I hope this helps too, have a nice day!

Answer:

6x-6x56 =-2016

Step-by-step explanation:

You have to subtract, then multiply by 56 to get -2016, as it shows a negative.

Answer:

19 nickels, 57 dimes, and 114 quarters

Step-by-step explanation:

57/3 = 19

1 × 19 = 19

3 × 19 = 57

6 × 19 = 114

Answer:

The car would have traveled 25 km.

Step-by-step explanation:

Set up the Proportion [tex]\frac{50}{60} = \frac{x}{30}[/tex]. Solving that proportion gets you an answer of 25, getting you the answer 25 km in 30 minutes. I hope this helps! :)

No it can't be factored , whenever there is addition between two squares , the expression can't be factored

Answer:

c. diameter

because when a line intersects the center and even touches the centre is called a diameter

hope it helps.

Answer:

C

Step-by-step explanation:

Diameter

Answer:

135

Step-by-step explanation:

every njmber is divided by 3

If 135 is divised by 3 it becomes 45

Hi student, let me help you out! :)

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We are asked to fill in the missing number in the following sequence:

[tex]\pmb{(~~~),45,15,5}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Since every number here is divided by 3, the common ratio is 3.

To find the missing number, we should multiply 45 times the common ratio, 3:

[tex]\star~\mathrm{\overline{\underline{\overline{\underline{135}}}}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

100cm²

Step-by-step explanation:

The notepad is square.

The area of a square = length X width.

All the sides of a square are the same length.

Therefore, the area of the notepad = 10 X 10 which equals 100.

Don't forget the units!

The units for area is cm².

The units for volume is cm³.

This is area so your answer is 100cm².

Hope this helped, have a nice day!

The amount of pot holders Brent sold for 58 weeks is 3016

He sells 52 pot holders each week.

This means for every week, he sold 52 pot holders. Therefore, the amount of pot holders he sold for 58 weeks can be solved as follows:

1 week = 52 pot holders

58 weeks  = ?

cross multiply

number of pot sold for 58 weeks = 58 × 52

number of pot sold for 58 weeks = 3016

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Answer:

15days.

Step-by-step explanation:

total amount=$85

renting amount=$10

amount per day=$5

to find the number of days the trimmer was rented it will be;

total amount-renting amount ÷$5

$85-$10÷$5

$75÷$5

=15days

Answer:

$25 - $10f

Step-by-step explanation:

Fishie's name is fishy.  

We know Mr. Fishie spent $15 on a tank.  His 10 fish cost 10*$f.  His total is:

Total =15 + 10*f

His change after 2 $20 would be:

$40 - ($15 - $10f), or

$25 - $10f

Answer:

first line: 0, 4

explanation: middle of -12 and 12 is 0, then 12/3 = 4

second line: -9, 6

explanation: split into 4 sections per each 12 so 12/4 is 3 and the location of the first unknown point is one section away from 12 so we know the distance between there is 3, leaving -12+3 = -9. Then two sections less than 12 is 12-6 = 6

third line: -12, 4

explanation: 24/6 = 4, -24 + 12 = -12 so 4 units each sections 0 + 4 = 4

Answer:

Option 1 -----> -10

Step-by-step explanation:

Substitute a and b into the equation :

-{a-b} =  

-{7-(-3)} =

-{7+3} =

-{10} =

-10 ---> Option 1

Hoep this helped and brainliest please

Answer:

None of these answers are correct

Step-by-step explanation:

neither of them are rays.

a ray goes from the center to the edge of a circle.

Answer:

C

Step-by-step explanation:

since ∠ m ≅ ∠ p , then

9x - 2 = 4x + 18 ( subtract 4x from both sides )

5x - 2 = 18 ( add 2 to both sides )

5x = 20 ( divide both sides by 5 )

x = 4

then

∠ p = 4x + 8 = 4(4) + 18 = 16 + 18 = 34°