Kyle buys $50,000 of company XYZ's shares, at a share price of
$100. A year later, XYZ's share price is $110, and Kyle sells all his
shares. How many dollars did Kyle's investment gain?

The solution of the expressions are

(a) (30+10 ÷ 2)-5-10 = 20

(d) 30+ (10 ÷ 2·5)-10 = 24

What is meaning of expressions?

An expression is a combination of operations, variables, and numbers.

What is BODMAS rule?

According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right.

Given expression is

(30+10 ÷ 2)-5-10

Applying BODMAS rule:

= (30 + 5) - 5 - 10

= 35 - 5 - 10

= 30 - 10

=40

Second expression is:

30+ (10 ÷ 2·5)-10

= 30 + (10 ÷ 10) - 10

= 30 + 1 - 10

= 31 -10

= 21

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Answer:

1.5x = 30 - 1.5

Step-by-step explanation:

30 grams minus the weight of the bag 1.5

1.5x x is the number of marbles and the bag so take 1 out and you have an answer which is 28.5 19 marbles

The three ordered pairs that could be added to the set so that f remains a function is D) (-3, -2), (1, 6), and (2, 3)

We are told that the displayed set of ordered pairs represents a function f.

{(-5,3),(4,9),(3,-2),(0,6)}

We must determine which three ordered pairs can be added to the set while the function remains unchanged. It is a mapping between elements of two sets A and B, with each element of set A uniquely mapped to each element of set B.

Alternatively, we can say that each element has only one image. For D,(-3,-2),(1,6) and (2,3) (2,3)

The image of f -3 is -2.

The image of one is six.

3 is the image of 2

It is correct because each element has a unique image while maintaining the same function.

As a result, option D is correct.

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Complete question

The set of ordered pairs shown represents a function f. {(-5, 3), (4, 9), (3, -2), (0, 6)} Which three ordered pairs could be added to the set so that f remains a function? a. (-3, -2), (4, 0), and (0, -1) B) (1, 6), (2, 3), and (-5, 9) C) (4, 0), (0, -1), and (-5, 9) D) (-3, -2), (1, 6), and (2, 3)

Answer:

b)  64 to 76 inches.

Step-by-step explanation:

In a normal distribution, 95% of the population is within 2 standard deviations of the mean.

Given values:

Given that the mean height is 70 inches and the standard deviation is 3 inches:

[tex]\implies \mu -2 \sigma = 70-2(3)=64[/tex]

[tex]\implies \mu+2 \sigma = 70+2(3)=76[/tex]

Therefore, an appropriate height range for 95% of all people in the sample would be:

Answer:

the length of WZ is 10

Step-by-step explanation:

The correct strategy between Pedro and Rebecca trying to solve the quadratic equation: 0.1x^2 - 0.7x + 1.2 = 0 is A - Only Pedro's

The given function is a quadratic function which is solved by several method including the method both Pedro and Rebecca are trying to use

Pedro's method is the factorization method and the steps mentioned are correct

However Rebecca's method has some error

The equation is: 0.1x^2 - 0.7x + 1.2 = 0

factor of the leading coefficient a is 0.1, Rebecca is using 0.11

The error of using 0.11 instead of 0.1 will make the method ineffective

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Answer: y = -9/8 + 7

Step-by-step explanation:

point a = (0,7), point b = (8,-2)

y = mx + b

b = 7

y = mx + 7

-2 = 8m + 7

-9 = 8m

m = -9/8

y = -9/8 + 7

Answer:

y= -9/8x+7

Step-by-step explanation:

find the slope

y2-y1/x2-x1

-2-7/8-0

-9/8

y=mx+b

m=slope

b=y intercept

y=  - 9/8x + b

y= -9/8x+7

Answer:

The new value is $292,110

Step-by-step explanation:

321,000 - (1 - 0.09) = 292,110

The rate of libraries per 100000 is 88.05   .

In the question ,

it is given that ,

the number of public libraries in New York City = 207 libraries

the population of the New York City = 8.805 million

we have to find the rate of libraries per 100000  .

for this we first have to express the population in numbers .

the population 8.805 million expressed in numbers is 8805000 ,

the rate of libraries per 100000 is

= 8805000/100000

On further simplification ,

we get ,

= 88.05

Therefore , The rate of libraries per 100000 is 88.05   .

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Answer:

6x^2-17x+12

Step-by-step explanation:

Distribute

2x^2-3x+1+x^2-2x+2(-2x+3)^2

Square (2x+3)

(-2x+3)(-2x+3)

FOIL

4x^2-6x-6x+9

Combine like terms

4x^2-12x+9

re-write equation

2x^2-3x+1+x^2-2x+2+4x^2-12x+9

Combine like terms

6x^2-17x+12

The probability that the proportion of surgeons will differ from the population proportion by greater than 6%-22.22%

P of 6%

= P (p > 0.06)

we would have to use the formula that is given below

[tex]P[z > \frac{p-P}{\sqrt{} \frac{PQ}{n} }[/tex]

where we have n = 465

p = 6%

P = 0.57

Q = 1 - 0.57 = 0.43

We would have to put the values into the equation that we have here as:

0.06 - 0.057 = -0.51

0.57 x 0.43 / 465 = 0.000527

√0.000527 = 0.022956

The probability =  -0.51 /  0.022956

= -22.22%

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The total distance traveled by the patient in 1 hour and 10 minutes is 10.6 kilometers.

The distance is the length from one point to the end.

For our purpose, distance represents the product of speed and time.

Diameter of the bicycle's wheel = 590 mm

Speed (Revolutions) per minute = 82 rpm

Time riding the bicycle = 1 hr and 10 minutes = 70 minutes

1 Kilometer = 1,000,000 Millimeters

Distance per rotation = pi x diameter

= 3.14 x 590

= 1,852.6 mm/minute

Total distance traveled in kilometers = (1,852.6 x 82 x 70) ÷ 1,000,000

= 10,633,924 ÷ 1,000,000

= 10.6 kilometers

Thus, we can conclude that the patient traveled 10.6 kilometers by bicycling for one hour and 10 minutes.

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The point estimate of the population mean  is 22 and margin of error for the confidence interval is 3.

1. Point estimate

Point estimate = Upper bound+ Lower bound/2

Point estimate = (25+19) /2

Point estimate = 44/2

Point estimate = 22

2. Margin error

Margin error = Upper bound  - Lower bound/2

Margin error = ( 25-19) /2

Margin error = 6 /2

Margin error = 3

Therefore the point estimate is 22.

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Answer:

394,200

Step-by-step explanation:

You have to multiply the house value by 1.08 or 108%

365,000*1.08=394,200

The Sample space for number greater than 3= {4, 5, 6}

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

A number cube with faces labeled from 1 to 6 will be rolled once.

so, Sample Space = { 1, 2, 3, 4, 5, 6}

sample space for number greater than 3= {4, 5, 6}

Thus, the probability is 3/6 or 1/2.

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If Tater and Pepper incurred $14.4 million in depreciation expense and paid $30.5 million in taxes on EBIT in 2021. The EBIT is $93.3 million.

First step is to find the operating cash flow

Operating cash flow =$47.1 million + $30.1 million

Operating cash flow = $77.1 million

Now let find the EBIT

EBIT = Operating cash flow + Depreciation expenses - taxes

EBIT = $77.1 million + ($30.5 million - $14.4 million)

EBIT = $93.3 million

Therefore the EBIT is $93.3 million.

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The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.

Given,

The cost for one calendar = $8

The cost for one coffee mug = $12

Dominique must sell at least $800 of merchandise and it should include at least 60 coffee mugs.

Here,

x be the number of calendars and y be the number of coffee mugs;

We have to find an inequality which represents the given situation;

So,

The inequality be;

8x + 12y ≥ 800 and x ≥ 60

That is,

The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.

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Answer:

Step-by-step explanation:

We know that the exterior angle of a triangle is the sum of remote interior angles.

If the triangle is equilateral then the sum of any two interior angles is same otherwise, with any isosceles triangle, we get different sums and therefore the friend is wrong.

Answer:

No.

Step-by-step explanation:

An isosceles triangle has two sides of equal length.  Therefore, only two of its interior angles are congruent.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles).  Therefore, as not all of the three interior angles of an isosceles triangle are congruent, all the exterior angles will also not be congruent.

50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies​.

How to solve equations in word problems?

Let x be the number of bags she bought:

50 + 20x ≥ 250

3x ≥ 200

x ≥ 200/3

x ≥ 66.67

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[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2 - 9\qquad \textit{we also know that} \begin{cases} x=2\\ y=-7 \end{cases} \\\\\\ -7=a(2-1)^2-9\implies 2=a(1)^2\implies 2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 -9 \end{array}} ~\hfill[/tex]

The dimensions of the playground are;

Width = 60 feet

Length = 160 feet

The formula for calculating perimeter of a rectangle is expressed as;

Perimeter = 2( l + w)

Where;

We have the values as;

Perimeter = 440 feet

Length = 3w - 20

Width = w

Now, substitute the values into the formula, we have;

440 = 2( 3w - 20 + w)

expand the bracket

440 = 2( 4w - 20)

440 = 8w - 40

collect like terms

8w = 480

Make 'w' the subject of formula

w = 60 feet

Length = 3(60) - 20

Length = 180 - 20

Length = 160 feet

Hence, the values are 60feet and 160 feet

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Answer:

7.25 %

Step-by-step explanation:

58 out of 800g  is    58 / 800 = .0725    which is  7.25 %

Answer:

Step-by-step explanation:

You want to know whether the pairs of equations describe lines that are parallel, perpendicular, or neither.

Parallel lines have the same slope. When the equations are written in slope-intercept form, the coefficients of x are identical.

Perpendicular lines have opposite reciprocal slopes. When the equations are written in slope-intercept form, the product of the x-coefficients is -1.

Solving the first equation for y gives ...

  y = 2x +2

The x-coefficients are 2 and -2, so the lines are neither parallel nor perpendicular.

Solving the first equation for y gives ...

  y = 2/4x -1 = 1/2x -1

The x-coefficients are 1/2 and -2, which have a product of -1. These lines are perpendicular.

Solving the second equation for y gives ...

  y = 2x -7/2

The x-coefficients are 2 and 2, which are identical. These lines are parallel.

The solution to the expression is -31.5

An algebraic expression in mathematical is statement that comprises of  numbers, variables, symbols and mathematical operators.

Given, when a= 0.25 and b = -1

Step 1: Substitute the given into the expression 36a + 42b - 18a +6

we have;  36(0.25) + 42(-1) - 18(0.25) +6

= 9 - 42 - 4.5 +6

Step 2; use BODMAS  to evaluate

we have; 9 - 42 - 4.5 +6= -31.5

Therefore the solution to the expression is -31.5

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The pitcher that has the lowest number of runs allowed per inning is Randy.

In order to determine the pitcher with the lowest number of runs per innings, divide the number of runs of each player by the number of innings of that player.

Division is the process of determining the quotient of two or more numbers. It is the process of putting a number into equal groups using another number.

Number of runs per innings = number of runs / number of innings

Number of runs per innings for Randy : 2 / 3 = 0.667

Number of runs per innings for Felix : 4 / 5 = 0.80

Number of runs per innings for Johan: 5 / 7= 0.714

Here is the complete question:

A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.

Which pitcher has the lowest number of runs allowed per inning?

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Answer:

A 35%

Step-by-step explanation:

take the higher number (27) and subtract the smaller number (20) from it. there's your difference. afterwards, take the difference (7) and divide it by the smaller number (20). this gives you .35. convert it into percentage move the decimal point to the right two spots and slap a percentage sign onto it (shift+3). giving you 35%, or A.

Answer:

a) 35%

Step-by-step explanation:

Given information,

→ 20 guests attended the 1st party, and 27 guests attended the 2nd party.

Now we have to,

→ find the % increase of number of guests from first party to second party.

Let's solve the problem,

→ ((27 - 20)/20) × 100

→ (7/20) × 100

→ 0.35 × 100

→ 35%

Hence, the answer is 35%.

Answer:

2 1/5

Step-by-step explanation:

8 4/5=44/5

(44/5)/(4)=(44/5)*(1/4)

(44/5)*(1/4)=44/20

44/20=2 1/5

Given graph represent the graph of  g(x) = [tex]-x^{2} (x -2)[/tex]

Given,

In the question;

The equation is:

g(x) = - [tex]x^{2} (x -2)[/tex] or h(x) = [tex]x^{2} (x -2)[/tex]

To find the is this the graph of g(x) or h(x).

Graph is given in the figure.

Now, According to the question;

g(x) = [tex]-x^{2} (x -2)[/tex]        and      h(x) = [tex]x^{2} (x -2)[/tex]

g(x) = 0                                    h(x) = 0

[tex]-x^{2} (x -2) = 0[/tex]                         [tex]x^{2} (x -2)[/tex] = 0

x = 0, 2                                    x = 0, 2

If we put x = 1 then,

g(1) = [tex]-(-1)^2(1-2)[/tex]     and   h(1) = [tex](1)^2(1-2)[/tex]

g(1)  =  -1 (-1)                          h(1) = 1(-1)

g(1)   = 1                                 h(1) = -1

But as shown in graph, graph take positive value at x = 1

∴Given graph is the graph of g(x) = [tex]-x^{2} (x -2)[/tex]

Hence, Given graph represent the graph of  g(x) = [tex]-x^{2} (x -2)[/tex]

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