2. In a random sample of 130 World Campus students, 92 were employed full-time.


We want use these data to construct a 95% confidence interval to estimate the proportion of all World Campus students who are employed full-time. Is it appropriate to use the normal approximation method? Show how you checked assumptions.

 -9.75 + 3.25x

= -3.25(3) + 3.25(x)

= -3.25(3)  -  -3.25(x)     notice they have the same factor of -3.25

= -3.25(3 - x)

Answer: A

Okay so fiquring out 1/2 of 1/4 is simple got to the third diagram since it has been cut to match the 1/2.  1/3 of 3/8 would be the first diagram since the squares have been sliced in half.

Remark

Question B is a bit of a guess, but A is pretty straight forward.

A

Let P = Platinum Gym's income (total)

Let M = Platinum Gym's Registration Fee.

Number of people who received free membership registrations = 50

The total income from anyone who had to register was

P = (124 - 50)*M

P = 74 * M

B

Monthly Fee = MF

n = number of months = 6

c = customer base  = 124

Equation

P = Registration Fee (found in A) + n * c * MF

Solution

P = 74*M + 6*124*MC

P = 74M + 744*MC

The question is, do you count the registration fee at the beginning or not? I would.

[tex]\dfrac{1}{2}x+2=1\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{2}x=-1\qquad\text{multiply both sides by 2}\\\\\boxed{x=-2}[/tex]

Let the width of rectangle= x centimeter

According to condition length =  (x+2) centimeter

As accoding to formula

perimeter of rectangle = 2( lenght +width)

so Perimeter = 2{(x+2) +(x)}     equation 1

Give perimeter = 60cm          equation 2

comparing  equation 1 and equation 2

2{(x+2) +(x)} = 60

Solving   2{2x+2} =60

4x+4 =60  

subtracting 4 both sides

4x= 56

dividing 4 both sides.

x=14  width of rectangle

AS we have assume length = x+2 ⇒ 14 +2

Length =16

Answer

83

Step-by-step explanation:

she had 90.

turned in to 78.

now she has  83

well I think it is 7.214  give me brainiest if i got it right plz

To divide a number by a 1-digit divisor, simply divide the number by the divisor. For example, 15 divided by 3 is 5, and 21 divided by 7 is 3. Practice makes perfect in this fundamental aspect of mathematics.

I understand you are trying to learn how to divide by 1-digit divisors. It is a fundamental topic in mathematics that you will use many times in the future.

Let's take the numbers 3 and 7 as examples. To divide by 3 or 7, simply take the number you are wanting to divide and divide it by either 3 or 7. For example, if we want to divide 15 by 3, you would simply perform 15 ÷ 3, which results in 5.

Now, if we want to divide 21 by 7, you would do 21 ÷ 7, which gives you a result of 3. It's that simple! Remember, the biggest key to success here is practice. The more you practice these divisions, the better you'll get at them.

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The inverse function is [tex]\( f^{-1}(x) = \frac{x + 7}{4} \)[/tex].

To find the inverse function of [tex]\( f(x) = 4x - 7 \)[/tex], we follow these steps:

1. Replace [tex]\( f(x) \) with \( y \): \( y = 4x - 7 \)[/tex].

2. Swap[tex]\( x \) and \( y \): \( x = 4y - 7 \)[/tex].

3. Solve this equation for [tex]\( y \)[/tex].

So, let's solve for [tex]\( y \)[/tex]:

[tex]\[ x = 4y - 7 \][/tex]

Add 7 to both sides:

[tex]\[ x + 7 = 4y \][/tex]

Divide both sides by 4:

[tex]\[ \frac{x + 7}{4} = y \][/tex]

Thus, the inverse function of [tex]\( f(x) = 4x - 7 \)[/tex] is:

[tex]\[ f^{-1}(x) = \frac{x + 7}{4} \][/tex]

Transformations of the graph y = x^3 to y=2x^3, y=(2x)^3, and y=(0.2x)^3 include a vertical stretch by a factor of 2, a horizontal compression by a factor of 2, and a horizontal stretch by a factor of 5 respectively.

The transformation of the graph of y = x^3 to the graphs of the equations: 1) y=2x^3, 2) y=(2x)^3, and 3) y=(0.2x)^3, is based on changes in scaling and stretching.

These transformations are characterized as vertically stretched, horizontally compressed, and horizontally stretched respectively.

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What even is this ???

16)

15x + 7y = -5    ⇒  -10(15x + 7y = -5)   ⇒   -150x - 70y =   50

11x + 10y = -28 ⇒    7(11x + 10y = -28)  ⇒     77x + 70y = -196

                                                                    -73x           = -146

                                                                                   x = 2

11x + 10y = -28

11(2) + 10y = -28

 22 + 10y = -28

         10y = -50

             y = -5

Answer: x = 2, y = -5

18)

7x - 4y =  1     ⇒   1(7x - 4y =  1)   ⇒    7x  -  4y =  1

5x + 2y = -9   ⇒ 2(5x + 2y = -9)  ⇒ 10x  + 4y = -18

                                                          17x          = -17

                                                                      x = -1

 7x - 4y =  1

7(-1) - 4y =  1

 -7  - 4y = 1

       -4y = 8

          y = -2

Answer: x = -1, y = -2

Wx + yz = h

yz = h - wx

z = (h - wx) / y

Answer

z = (h - wx) / y

a 1.25L Coca Cola that cost $1.29

Unit rate means we need to find the rate of 1 liter of Coca Cola

1.25 L Coca Cola =  $1.29

1 L of Coca Cola = ?

To find 1 liter of Coca cola divide the cost by liter, so we divide 1.29 by 1.25

[tex]\frac{1.29}{1.25}[/tex]

1.032

So the cost of 1 liter of Coco Cola = $1.032

Answer:

The number of melon was 3 and the number of apples was 45.

Step-by-step explanation:

1. Melons cost $20 per crate and apples cost $8 per create. If the total was 48 crates for $420, you can make the following system of equations, where [tex]x[/tex] is the number of melons and [tex]y[/tex] is the number of apples:

[tex]\left \{ {{x+y=48} \atop {20x+8y=420}} \right.[/tex]

2. By applying the Method of substitution, you can solve for [tex]y[/tex] in the first equation and substitute it into the second one to find [tex]x[/tex]. Then, you can substitute the value of [tex]x[/tex] into the first equation to find [tex]y[/tex]:

[tex]y=48-x[/tex]

[tex]20x+8(48-x)=420\\20x+384-8x=420\\12x=36\\x=3[/tex]

[tex]3+y=48\\y=45[/tex]

Final answer:

The order consisted of 3 crates of melons and 45 crates of apples.

Explanation:

To solve the problem of determining the number of crates of melons and apples based on the total cost and quantity, we can use a system of linear equations.

Given that melons cost $20 per crate and apples cost $8 per crate, with a total order of 48 crates for $420, we can set up the following equations:

Solving this system of equations:

Thus, the order consisted of 3 crates of melons and 45 crates of apples.

The product for these two fractions is equal to 12/55

Answer:

PAST

Step-by-step explanation:

the words "taught" and "yesterday" are in the past tense.

Solution: The function that represents the Grace earning each week is defined as [tex]e(h)=9h[/tex], where [tex]e(h)[/tex] is in dollar and [tex]h[/tex] is the time in hours. domain of the function [tex]e(h)=9h[/tex] is [10,20].

Explanation:

Let, Grace works for h hours per week.

For one hour she get $9.

For h hours she get [tex]\$(9\times h)=\$9h[/tex].

So, the function that represents the Grace earning each week is defined as [tex]e(h)=9h[/tex].

It is given that she works from 10 to 20 hours per week, therefore the value of h lies between 10 to 20. Hence the Grace's earnings for each week is defined as [tex]e(h)=9h[/tex] and the domain of the function [tex]e(h)=9h[/tex] is [10,20].

Answer:

21

Step-by-step explanation:

There are two parallel lines given.

Two transversals cut them.

Here m and n are parallel.

Two transversals cut them so that a triangle is formed.

Let us use the property that sum of angles of a triangle = 180

Bottom angle of triangle = 39 (vertically opposite angles)

Top left angle = 4x+3 (vertically opposite angles)

Top right angle = 180-6x (linear pair property)

Now add these 3 and equate to 180

39+4x+3+180-6x = 180

2x = 42

Or x = 21

Hey mate!!

Answer

4/7 and 8/14 are equivalent fractions, because they are both equal to 4/7 when they are simplified.

Correct answer is D. 8/14

Hope it helps you!

Answer:

a. $36

b. $336

Step-by-step explanation:

The simple interest on a amount is:

A=P(1+rt)

A is the amount after interest, P is the amount before interest, r is the rate of interest and t is the time in years.

a.

We can use the formula:

The interest earned is the amount after interest minus the original amount before interest:

$36 of interest was earned

b.

The balance of the account is $336 worked out in a

To order the numbers from least to greatest: -2.8, -1.25 (-5/4), -1.17 (-7/6), 1.3, 1.33 (4/3). Decimal conversion helps compare their values, with negative numbers being smaller than positive ones.

To order the numbers from least to greatest, we need to compare their values. Negative numbers are less than positive numbers, and among negative numbers, the one with the smaller absolute value is greater. We can convert the fractions to decimals to make it easier to compare all the numbers:

Now we order them from least to greatest:

[tex]3\frac{3}{8} = \frac{8(3) + 3}{8} = \frac{27}{8}[/tex]

[tex]5\frac{1}{4} = \frac{4(5) + 1}{4} = \frac{21}{4}[/tex]

[tex]\frac{21 (miles)}{4}[/tex] ÷ [tex]\frac{27 (miles)}{8 (hour)}[/tex]

= [tex]\frac{21 (miles)}{4} * \frac{8 (hours)}{27 (miles)} = \frac{21(8)hours}{4(27)} = \frac{42}{27}hours[/tex]

[tex]\frac{42}{27} hours[/tex] = [tex]\frac{14}{9}= 1\frac{14-9}{9} hours = 1\frac{5}{9}hours[/tex]

Answer:  [tex]1\frac{5}{9}hours[/tex]

B. This is because falling represents negatives, or subtracting. 3-5 is -2.

Answer:

A. 5

Step-by-step explanation:

Let n = number

(3n)+6 = 5n-4

Subtract 3n from each side

(3n)-3n+6 = 5n-3n-4

6 = 2n-4

Add 4 to each side

6+4 = 2n -4+4

10 = 2n

Divide by 2

10/2 = 2n/2

5 =n

Answer-

The abs. minimum value of the given function was found to be 3.

Solution-

Here, the given function is,

[tex]f(x)=x^4-x^2-2x+5[/tex]

Then, calculating its first derivative,

[tex]{f}'(x)=4x^3-2x-2[/tex]

Then, calculating its second derivative,

[tex]{f}''(x)=12x^2-2[/tex]

Then, calculating all the critical values of the given function by equating the first derivative to 0,

[tex]\Rightarrow {f}'(x)=0[/tex]

[tex]\Rightarrow 4x^3-2x-2=0[/tex]

[tex]\Rightarrow 2x^3-x-1=0[/tex]

[tex]\Rightarrow 2x^3-x-1=0[/tex]

[tex]\Rightarrow 2x^3-2x+x-1=0[/tex]

[tex]\Rightarrow 2x(x^2-1)+(x-1)=0[/tex]

[tex]\Rightarrow 2x(x+1)(x-1)+(x-1)=0[/tex]

[tex]\Rightarrow (x-1)(2x(x+1)+1)=0[/tex]

[tex]\Rightarrow (x-1)(2x^2+2x+1)=0[/tex]

[tex]\Rightarrow (x-1)=0[/tex]    ( ∵ ignoring the imaginary roots)

[tex]\Rightarrow x=1[/tex]

Putting the value of x, in the second derivative,

[tex]{f}''(1)=12(1)^2-2=10[/tex]

As, the value of f"(x) is positive, the function attains its minimum value at x=1.

So, f(1) will give the absolute minimum value of the function,

[tex]f(1)=(1)^4-(1)^2-2(1)+5=3[/tex]

∴ The abs. minimum value of the given function is 3.

The series is A.P. with first term = 44 and common difference = 39-44=-5 = 34- 39

Sum of A.P. is S = n/2(2a+ (n-1)d)

Where a is first term ,d is common difference and n no. Of terms

Here a = 44 ,d= -5 and n = 23

S = 23 /2(2×44+ (23-1)(-5))

S=23/2(88-110)

S = 23/ 2(-22)

S = 23×-11

S = -253

25% is the same is 1/4 of something. So you have to find what 1/4th of 48 is. To do that, just divide 48 by 4. and you get 12.

A 25% payment on a CD player that costs $48 would be $12. Hope that helps!

We are given that

a line is perpendicular bisector on line between point (4,1) and (2,-5)

So, line intersect at mid-point between (4,1) and (2,-5)

so, firstly we will find mid-point

[tex](a,b)=(\frac{4+2}{2},\frac{1-5}{2})[/tex]

[tex](a,b)=(3,-2)[/tex]

now, we will find slope between (4,1) and (2,-5)

x1=4 , y1=1

x2=2 , y2=-5

slope is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

now, we can plug values

[tex]m=\frac{-5-1}{2-4}[/tex]

[tex]m=3[/tex]

now, our required line is perpendicular to this line

so, slope of required line is -1/m

so, we get slope

[tex]m'=\frac{-1}{3}[/tex]

we have a point as (3 ,-2)

we can use point slope form of line

[tex]y-y_1=m'(x-x_1)[/tex]

we can plug values

[tex]y+2=-\frac{1}{3}(x-3)[/tex]

now, we can solve for y

[tex]y=-\frac{1}{3}x-1[/tex]................Answer

The three consecutive odd integers are 23, 25,27

What is Algebraic expression ?

Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables.

Let the three consecutive odd integers be x , x + 2 , x+ 4 then,

the sum of these three odd integers is 17 less than four times the smallest integer that is :

x + (x+2) + (x+4) = 4x -17

3x + 6 = 4x -17

4x - 3x  = 6 + 17

x = 23

x + 2 = 25

x +  4 = 27

Therefore, the three consecutive odd integers are 23, 25,27

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