Step 2 Using Proportional Relationships

Answer:

33.3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The mode is the number that appear most often

The number with the most dots is 2

The mode is 2

The mode in any data set is the number that gets represented the most.

As you can see on the plot, the number that gets represented the most is 2.

Best of Luck!

Answer:

see explanation

Step-by-step explanation:

The line x = - 2

Is a vertical line parallel to the y- axis

It passes through all points with an x- coordinate of - 2

Answer:

1/4 was eaten by mama and Baby also ate 1/4

Step-by-step explanation:

goldilocks got 0/4

if papa ate half and baby and mama each ate 1/4 they equal up to 2/4 which is 1/2

papa ate 1/2 and 1/2+1/2=1

Mama bear ate (1/4)a part of pie and the (1/8) fractional part was left for Goldilocks.

The fraction is a rational number that simply divides two numbers and is written in the form a/b where a is called the numerator and b is called the denominator.

Let the full part of the pie is a.

Papa bear ate 1/2 part of the pie.

Then papa bear ate = (1/2)a

rest of the pie is= a- (1/2)a= (1/2)a

Mama bear ate (1/2) of the rest of the pie.

so mama bear ate = (1/2)(1/2)a= (1/4)a part of pie
rest of pie after mama bear ate = (1/2)a- (1/4)a= (1/4)a

Then baby bear ate (1/2) of the rest of the pie.

so baby bear ate = (1/2)(1/4)a= (1/8)a part of pie
rest of pie after baby bear ate = (1/4)a- (1/8)a= (1/8)

The rest of the part was left for GoldLiocks.

Therefore mama bear ate (1/4)a part of pie and the (1/8) fractional part was left for Goldilocks.

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Answer:

∠RPS = 49º

Step-by-step explanation:

∠RPS + ∠QPR = 88º

(5x + 34) + (8x + 15) = 88

13x + 49 = 88

13x = 39

x = 3

plug x into equations:

∠RPS = 5(3) + 34

∠RPS = 15 + 34

∠RPS = 49º

check work:

∠QPR = 8(3) + 15

∠QPR = 24 + 15

∠QPR = 39

∠RPS + ∠QPR = 88º

49 + 39 = 88

Answer:

49

Step-by-step explanation:

(5x+34) + (8x+15)= 88

13x + 49 = 88

13x= 39

x=3

RPS= 5(3)+34

RPS= 15 +34

RPS= 49

Answer:

a(1) = 72

a(n) = a (n-1) - 18

Step-by-step explanation:

This is a simple series of multiplication of 18 . If we divide all the numbers by 18 we get

72/18, 54/18, 36/18. 18/18, 0/18

4      , 3      , 2     , 1 ,       0

So we can see that the numbers are in  decreasing order as the multiples of 18.

in other words the first term is a= 72

from which we subtract 18 and get 54 and so on.

So the general rule would be

a(1) = 72

a(n) = a (n-1) - 18

Where n and (n-1 ) are subscripts. We are just subtracting 18 from the number to get the answer.

72-18= 54

54-18= 36

36-18= 18

18-18=0

Answer:

998

Step-by-step explanation:

I haven't included the 1 or the 1000

Answer:

There are 200 numbers between 1 and 1000  that do not contain the digits 8, and 9.

Step-by-step explanation:

1-100

=(8,9,18,19,28,29,38,39,48,49,58,59,68,69,78,79,88,89,98,99)=20

101-200

=(108,109,118,119,128,129,138,139,148,149,158,159,168,169,178,179,188,189,198,199)=

201-300=20

.......

100*10=1000

20*10=200

Answer:

Solution: (-4,-3)

Step-by-step explanation:

We need to complete the solution set of given graph.

We are given two graph one straight line and one parabola. We can see in graph both intersect at two points.

At x=-4 and x=-1

We can easily find the value of y corresponding to the value of x using given graph.

At x=-4,

First we draw a vertical line at x=-4 and see where it cut graph. From that point draw a horizontal line and see where y-axis cut.

The value of at x=-4 would be -3

Please see the attachment and see the vertical and horizontal line.

Thus, The Solution is (-4,-3)

Answer:

3.14 units²

Step-by-step explanation:

The key realization here is that this shape is one quarter of a circle.

Therefore, it's area will be [tex]\frac{1}{4}[/tex] of the whole circle's area.

So, let's first find the area as if this were a whole circle.

The formula is [tex]\pi r^2[/tex], and we know that the radius, r, is 2. So:

[tex]\pi\cdot2^2\\\\\pi\cdot4\\\\3.14\cdot4\\\\12.56[/tex]

Now we need to find one fourth of this, we can do this by dividing by 4.

[tex]12.56\div4=3.14[/tex]

Hope this helped!

Answer:

pi units squared

Step-by-step explanation:

(cant find pi sign)

(pi times r^2)/4

4pi/4

pi

Answer:

70

80

Step-by-step explanation:

Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle___70____ more red bottles than plant A. Plant C would recycle_____80___________ more red bottles than plant D.

A = We first multiply 150 x 2.333 (2 1/3)  = 350 tbottles 60 x 2.333 = 140

B = Then multiply  350/200  = 200 x 1.75 350 tbottles  RED = 120 x 1.75=210

First answer = 210-140 = B recycles 70 more than A

C = We first multiply 175 x 2 = 350 tbottles  RED = 110 x 2 = 220

D = We first find LCM of 180 and 350

Then find 18x now equals 1/10 x 35x tbottles RED = 72 / 18 = 4  then 4 x 35 = 140

Second answer = 220-140 = C recycles 80 more than D.

Answer:

Plant B would recycle 60 more red bottles than plant A. Plant C would recycle 38 more red bottles than plant D.

Hope this helps!

Sorry for answering so late!

Answer:

4

Step-by-step explanation:

factoring , using square roots , completing the square and the quadratic formular

Answer:

See below.

Step-by-step explanation:

The four main ways to solve a quadratic equation are:

1) Factoring, 2) Completing the Square, 3) Graphing, and 4) Quadratic Formula.

Each method has it's own pros and cons.

1) Factoring. You should factor when the given equation is easily factor-able or already factored. For instance:

[tex]0=x^2-4x-12\\0=(x+7)(x-1)[/tex]

These problems are easily factored so factoring is preferred here. However, factoring will not always work.

2) Completing the Square. You complete the square if you are able to complete the perfect square trinomial with only integers. For instance:

[tex]x^2-2x-7=0\\(x^2-2x+1)-7-1=0\\(x-2)^2-8=0[/tex]

However, you wound't use completing the square if:

[tex]x^2-3x+2=0\\(x^2-3x+9/4)+2-9/4=0[/tex]

The perfect square trinomial includes fractions so you would use alternative methods here (and factoring works here!).

Despite the complexity of completing the square, if done correctly, it works every time. However, sometimes, it can be time-consuming.

3) Graphing. Graphing (if on paper) is time-consuming. You would only use graphing when you only need an approximation. Unless directed to, you probably won't need to use graphing.

However, if you have a graphing calculator, graphing the equation can allow you to check your answer. So, graphing won't get you precise answer, but it will allow you to check your answer is necessary.

4) Quadratic Formula. Use the quadratic formula if the equation isn't factor-able and completing the square is too tedious. For instance:

[tex]4.1x^2-3x-7=0\\[/tex]

This doesn't seem factor-able and completing the square will take a while. Graphing won't get the exact answer, so the quadratic formula is the only avenue left.

The quadratic method, like completing the square, will always work.

Only con is that you need to memorize the formula.

Answer:

80

Step-by-step explanation:

0,   3,   8,   15,   24,  35,   48,   63,  80 which is the nth term

first step you have to find how many steps the sequence was going with.

examples= from 0 to 3 the steps were 3

                =from 3 to 8 the steps were 5

                = from 8 to 15 the steps were 7

you will recognize that the steps the sequence is going with is odd numbers.

so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.

Answer:

80

Step-by-step explanation:

Answer:

1st circle: 1.25

Second circle: 2

Step-by-step explanation:

We can use the cross product property here to find the value of what's in the circles.

Let's first look at the first two fractions.

[tex]\frac{x}{5} = \frac{1}{4}[/tex]

We can multiply the cross values and divide by the number that is diagonal to the variable.

[tex]5\cdot1 = 5\\5\div4 = 1.25[/tex]

So 1.25 goes in the first circle.

Now let's look at the last two circles and use the same property to find the missing value.

[tex]\frac{1}{4} = \frac{0.5}{x}\\ 4\cdot0.5 = 2\\2\div1 = 2[/tex]

So 2 goes in the second circle.

Hope this helped!

Answer:

x = 5/4

Step-by-step explanation:

Use the variable 'x' instead of 'the circle.'  Then:

 x         1

----- = ------

 5         4

Cross-multiplying, we get

4x = 5, and so x = 5/4

Answer:

6/7

Step-by-step explanation:

First, find two points that fall on the line and are coordinates on the graph.

The two points I found were (3,5) and (10,11).

Use the slope formula to come up with the slope.

[tex]slope = \frac{change in y}{change in x}[/tex]  

slope = [tex]\frac{11-5}{10-3}[/tex] = [tex]\frac{6}{7}[/tex]

Answer:

option (c)

Step-by-step explanation:

g.f= g(f(x))

= g(x2 -3)

= (x2 -3)+1

=x2 -2

The composite function g.f is option c) x² - 2.

Functions which are formed by composing two or more functions in a way that one's output is another's input are called composite functions. They are also called function of functions.

Given: f(x) = x² - 3 and g(x)= x+1

The composite of the function;

g.f= g(f(x))

= g(x²-3)

= (x² -3)+1

= x² -2

Thus, The composite function g.f is option c) x² - 2.

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I am sure the answer is D

Answer:

D 100

Step-by-step explanation:

60% = 60/100

70% =70/100

Answer:

1

Step-by-step explanation:

(-3 + 3) + (-2 + 3) =

= 0 + 1

= 1

Answer:

A=[tex]\frac{a+b}{2} (h)[/tex]

Step-by-step explanation:

Option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.

It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.

The options are:

We have a formula for finding the area of the trapezoid:

[tex]\rm A= \dfrac{1}{2}h(b_1+b_2)[/tex]

Make a subject h and solve for h:

[tex]\rm \dfrac{2A}{(b_1+b_2)}= h[/tex]

or

[tex]\rm h = \dfrac{2A}{(b_1+b_2)}[/tex]

[tex]\rm b_2 = \dfrac{2A}{h}- b_1[/tex]

[tex]\rm b_1 = \dfrac{2A}{h}- b_2[/tex]

Thus, option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.

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Answer:

c

Step-by-step explanation:

the correct answer is c

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Answer:

[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]

Step-by-step explanation:

Let x be the amount of dough required for small pizza, y be the amount of dough required for medium pizza and z be the amount of dough required for large pizza.

As per the question , we have

[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]

Hence, the equation for the question with the variable representing the amount of dough needed for small pizza.

[tex]y=\dfrac{3}{2}x\ ...(i)\\\\ z=\dfrac{5}{2}x\ ...(ii)\\\\ z=x+y\ ....(iii)[/tex]

Answer:

Hey there!

This would be a 2.5% increase in salary.

Using the percent increase formula we find the answer to be a 2.5% increase.

Let me know if this helps :)

Answer:

2.5%

Step-by-step explanation:

((new - original) / original) * 100

328-320 = 8/320 = 0.025

0.025 * 100 = 2.5

Answer:

[tex]\large \boxed{\mathrm{2 \ meters}}[/tex]

Step-by-step explanation:

The triangle formed is a right triangle.

We can use trig functions to solve.

The maximum length of the seesaw is the length of the hypotenuse of the triangle.

sin θ = opp/hyp

Let x be the hypotenuse length.

sin 30 = 1/x

x = 1/sin30

x = 2

The maximum length of the seesaw is 2 meters.

Answer:

2

Step-by-step explanation:

Take the right triangle formed by the seesaw.

Let x be the maximum heigth that we are looking for

● sin 30° = 1/x

Switch x and sin 30°

● x = 1 /(1/2)

● x = 1 ×(2/1)

● x= 1×2

● x = 2

the above photos is the solution

Answer:

No 1 would be 500 + 2400*30/100 = 500 + 720 = 1220

No 2 would be 500 + x*30/100

Step-by-step explanation:

Answer:

$1200 and 500+ .3x

Step-by-step explanation:

Use this equation: 500+ .3x and insert in 1200.

Made equation by taking garented amount, $500, and have that be added.  Sense you get 30 percent of of x (the amount of sales), have x be multiplied by .3 to get 30 percent.

Answer:

[tex]\boxed{x=1}[/tex]

Step-by-step explanation:

[tex]2(10-2x) = 4(3x + 1)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]20 - 4x = 12x + 4[/tex]

[tex]\sf Subtract \ 12x \ and \ 20 \ from \ both \ sides.[/tex]

[tex]20 - 4x - 12x - 20 = 12x + 4 - 12x - 20[/tex]

[tex]-16x = -16[/tex]

[tex]\sf Divide \ both \ sides \ by \ -16.[/tex]

[tex]\displaystyle \frac{-16x}{-16} =\frac{-16}{-16}[/tex]

[tex]x=1[/tex]

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▹ Answer

x = 1

▹ Step-by-Step Explanation

2(10 - 2x) = 4(3x + 1)

Simple terms are written last:

2(-2x + 10) = 4(3x + 1)

Distributive Property:

-2 * 2x + 2 * 10 = 4 * 3x + 4

x = 1

Hope this helps!

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Answer:

10.5% compounded quarterly will be worth more at the end of 7 years.

Step-by-step explanation:

Investment 1:

Principal=$1,000

t=7 years

n=12 months

r=9%=0.09

FV=PV(1+r/n)^nt

Where,

FV=future value

PV=present value

r=interest rate

t=time (years)

n=number of periods

FV=PV(1+r/n)^nt

=1000(1+0.09/12)^12*7

=1000(1+0.0075)^84

=1000(1.0075)^84

=1000(1.8732)

=1,873.2

FV=$1,873.2

Investment 2:

Principal=$1,000

t=7 years

r=10.5%=0.105

n=4

FV=PV(1+r/n)^nt

=1000(1+0.105/4)^4*7

=1000(1+0.02625)^28

=1000(1.02625)^28

=1000(2.0658)

=2,065.8

FV=$2,065.8

10.5% compounded quarterly will be worth more at the end of 7 years.

Answer:

6/8 of a mile,

Step-by-step explanation:

if one furlong is 1/8 of a mile, the 6 shall be 1/8 added to itself 6 times, therefore it shall be 6/8.

Answer:

3/4 of a mile

Step-by-step explanation:

1 furlong = 1/8 mile

========     ====

6 forlongs = x

cross multiply

1*x = 6 * (1/8)

x = 6/8

reduce 6/8. Divide top and bottom by 2

x = 3/4

Answer:

its

1/7

step by step

Answer:

The answer is H because there are 7 balls in total and two of which is red so the possiblity of getting the red ball is 2/7

Answer:

D

Step-by-step explanation: