PLZ HURRY IT'S URGENT!!
The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 12 square inches. What are the length and width?

Which equation models this problem?


w – (4 + w) = 12


w + (4 + w) = 12


w(4 + w) = 12


4 • w = 12

Answer:  [tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given : An opaque bag contains 5 green marbles, 3 blue marbles and 2 red marbles.

Total marbles = 5+3+2=10

Now, if it given that the a red marble is already drawn, then the total marbles left in the bag = 10-1=9

But the number of blue marbles remains the same.

Now, the probability of drawing a blue marble given the first marble was red :-

[tex]=\dfrac{\text{Number of blue marbles}}{\text{Total marbles left}}\\\\=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

Hence, the required probability = [tex]\dfrac{1}{3}[/tex]

Answer:

100 dollar rebate

Step-by-step explanation:

ok so since you have to find which deal takes off more money from the initial price you have to start by doing 479.99 times 20% or .2 which gives you 95.998 which is already lower than 100 buuuut just in case you want to check if you subtract 100 and 95.998 from 479.99 then inevitably the 100 dollars ends up being more money off from the initial price

(sorry about my last answer, hope this ones better ^-^)

Answer:

100 dollar rebate

Step-by-step explanation:

Answer:

481 / 2142 = 22.46%

A pie chart is also commonly used to illustrate it.

Step-by-step explanation:

We can get the sample proportion of every case, applying the following relations:

1288 / 2142 (60.13%) answered "no"

481 / 2142 (22.46%) answered "yes"

373 / 2142 (17.41%) had no opinion

where 2142 (1288 + 481 + 373 = 2142) is the total of adults who were asked.

Answer:

Function [tex]sin(60^o)\,\,s=h[/tex]

Height of an equilateral angle of side length 88m: [tex]76.21\,m=h[/tex]

Step-by-step explanation:

An equilateral triangle has 3 equal sides and 3 equal angles. The height of the triangle could be expressed as:

[tex]sin(\theta)=\frac{O}{H}[/tex]

[tex]sin(60^o)=\frac{h}{s}[/tex]

Moving s to the other side we find the function for the height:

[tex]sin(60^o)\,\,s=h[/tex]

As we know that s=88m we have

[tex]sin(60^o)\,\,88m=h[/tex][tex]\frac{\sqrt{3}}{2}88m=h[/tex]

[tex]44\sqrt3 \,m=h[/tex]

[tex]76.21\,m=h[/tex]

Explanation of the height of an equilateral triangle as a function of its side length and calculation for a triangle with a side length of 88m.

Justify that the triangles are similar: Equilateral triangles have all sides equal and all angles equal, therefore they are similar.

Write an equation that relates the sides of the triangles using words to describe the quantities: The height h of an equilateral triangle is equal to √3/2 times the side length s.

Rewrite your equation using your symbols: h = √3/2 * s

Algebraically isolate the unknown quantity: Given s = 88 m, plug it into the formula h = √3/2 * s to find the height h.

Plug-in numbers and calculate answer: h = √3/2 * 88 m ≈ 76.12 m

Check answer: The calculated height of approximately 76.12 m seems reasonable for an equilateral triangle with a side length of 88 m.

125 liters of pure peroxide should be added to the 500 liters of the 10% solution to produce a new product that is 28% peroxide.

The concentration C of the new mixture is given by the formula:

C = (x + 0.1 * 500) / (x + 500)

We want to find out how many liters of pure peroxide (100% peroxide) should be added to produce a new product that is 28% peroxide.

In other words, we want to find the value of x that makes C equal to 0.28 (28%).

So, we set up the equation:

0.28 = (x + 0.1 * 500) / (x + 500)

Now, we can solve for x:

0.28(x + 500) = x + 0.1 * 500

Distribute 0.28 on the left side:

0.28x + 0.28 * 500 = x + 0.1 * 500

Simplify:

0.28x + 140 = x + 50

Subtract x from both sides:

0.28x - x + 140 = 50

-0.72x + 140 = 50

Subtract 140 from both sides:

-0.72x = -90

Divide by -0.72:

x = 125

So, 125 liters of pure peroxide should be added to the 500 liters of the 10% solution to produce a new product that is 28% peroxide.

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Final answer:

To achieve a 28% peroxide concentration, approximately 125 liters of pure peroxide should be added to the existing 500-liter, 10% peroxide solution.

Explanation:

The question asks how many liters of pure peroxide (x liters) must be added to a 500-liter solution with a 10% peroxide concentration to produce a new product that is 28% peroxide. To solve this, we'll set up the equation:

C = (x+0.1(500)) / (x+500) where C = 0.28 (the target concentration). So,

0.28 = (x + 50)/(x + 500)

Multiply both sides by (x + 500) to get 0.28(x + 500) = x + 50

Distribute 0.28 to get 0.28x + 140 = x + 50

Subtract 0.28x from both sides to isolate x on one side: 140 = 0.72x + 50

Subtract 50 from both sides: 90 = 0.72x

Divide both sides by 0.72 to solve for x: x ≈ 125 liters

Therefore, approximately 125 liters of pure peroxide should be added to the 500-liter solution to achieve a 28% peroxide concentration.

So Julia... 6 miles in 30 minutes. Let's find out how much she travelled in 1 hour. Multiply it by 2, since 30 x 2 = 60 mins = 1 hour, you get 12 miles per hour for Julia.

For Alex... 2 miles in 12 minutes. Multiply it by 5, as 12 x 5 = 60 mins = 1 hour, you get 10 miles per hour for Alex.

Julia travelled faster. She travelled 12 miles per hour while Alex travelled 10 miles per hour.

Julia travelled at a greater speed at 12 miles per hour.

Unitary method is a mathematical way of first deriving the value of a single unit and then deriving the required unit by multiplying with it.

According to the given question Julia rode a bicycle 6 miles in 30 minutes.

∴  In 60 minutes Julia rode (6×60)/30 miles which is

= 12 miles per hour.

Alex rode his skateboard 2 miles in 12 minutes.

So, In 60 minutes he rode (60×2)/12 miles which is

= 10 miles per hour.

Therefore the average speed of Julia is more by 2 miles per hour.

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The money that club make $ 639.75.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The Spanish club began the year with $15.00 in its account.

At the end the club had = $654. 75

so, the Club earned

= 654. 75- 15

= 639.75

Hence, the money club make $ 639.75

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Answer:

Discrepancy = 665,15 L

Step-by-step explanation:

Data: 1 Apple Barrel: 7056 cubic inches

         1 Cranberry Barrel: 5826 cubic inches

The merchant sells 33 cranberry barrels, so we need to find out the total volume of that. So we multiply our cranberry volume (data) 33 times:

33 x 5826 cubic inches = 192258 cubic inches

Now, the customer thinks that he is receiveing apple barrels. To calculate this volume, we need to multiply the apple volume (data) 33 times:

33 x 7056 cubic inches = 232848 cubic inches

(You can see that 33 apple barrels have more volume that 33 cranberry barrels, so the customer will receive less volume than he is expecting)

The problem is asking the discrepancy in the shipment in liters (L). First we calculate the discrepancy (difference) in cubic inches.

Discrepancy (cubic inches) = 232848 cubic inches - 192258 cubic inches = 40590 cubic inches

Finally we need to transform the units. As a general rule, we know that:

1 litre (L) = 61,0237 cubic inches. Using a simple rule of three we can solve it:

Discrepancy (L) = [tex]\frac{40590 cubic inches}{61,0237 cubic inches\\}[/tex] x 1 L

Discrepancy (L) = 665,15 L

Answer:

x>[tex]\frac{16}{-9}[/tex] and x ≤[tex]\frac{-19}{13}[/tex].

Step-by-step explanation:

Given  : −9x+2>18 AND 13x+15≤−4.

To find : Solve.

Solution : We have given  −9x+2>18 AND 13x+15≤−4.

For  −9x + 2 > 18 .

On subtracting both sides by 2

- 9x > 18-2

- 9x > 16.

On dividing both sides by -9.

x>[tex]\frac{16}{-9}[/tex].

For  13x + 15 ≤ −4.

On subtracting both sides by 15.

13 x ≤  -4 - 15.

13 x ≤ -19.

On dividing both sides by 13.

x ≤ [tex]\frac{-19}{13}[/tex].

Therefore, x>[tex]\frac{16}{-9}[/tex] and x≤[tex]\frac{-19}{13}[/tex].

Answer:

B. x < -16/9

Step-by-step explanation:

I got it right on Kahn Academy

Answer:

It is a structured, orderly process for conducting a research study.

Step-by-step explanation:

The main steps of the scientific method are:

1) make an observation describing the problem

2) creating and then testing a hypothesis

3) drawing conclusions and refine the hypothesis.

The scientific method is a standard way of making observations and gathering data, forming theories based on the data, finally testing and interpreting results.

So, the answer here is option A. It is a structured, orderly process for conducting a research study.

Answer:

1/4

decimal- 0.25

percent- 25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Answer:

a) r = 6

b) r = 0

Step-by-step explanation:

See it in the pic.

Answer:

a)r=6  b)r=0

Step-by-step explanation:

Before to get started, Let's to express each number in base r.

We should take in account that it process is similar to express numbers in  decimal base, except that in this case [tex]10^{n}[/tex] is  replaced by [tex]r^{n}[/tex].

a) 14=1x[tex]1*r^{1} +4*r^{0}  =r+4\\[/tex]

  [tex]2=2*r^{0} \\[/tex]

  [tex]5=5*r^{0}[/tex]

Replacing each number in base r  on the equalitie a.

[tex]\frac{r+4}{2} =5[/tex]

Solving this equation

[tex](r+4)=10\\r=6[/tex]

b) [tex]54=5*r^{1} +4*r^{0} =5r+4\\4=4*r^{0} \\1=1*r^{0}[/tex]

Replacing each number in base r  on the equalitie b.

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

Solving this equation:

[tex]5r+4=4\\r=0[/tex]

Answer:

Step-by-step explanation:

Given that When n is divided by 21, the remainder is an odd number.

i.e. [tex]n=21m+k[/tex] where m is an integer and k a positive integer <21

When n is divided by 28, the remainder is 3

[tex]n=28c+3[/tex], where c is a positive integer

This can be written as

[tex]n=4(7c)+3\\n=7(4c)+3[/tex]

Since n is giving odd remainder when divided by 21,

we get r =3 as n is a multiple of 7 +3

Answer:

Variance = 4.68

Step-by-step explanation:

The formula for the variance is:

[tex]\sigma^{2} =\frac{\Sigma(X- \mu)^{2}}{N} \\or \\ \sigma^{2} =\frac{\Sigma(X)^{2}}{N} -\mu^{2} \\[/tex]

Where:

[tex]X: Values \\\mu: Mean \\N: Number\ of\ values[/tex]

The mean can be calculated as each value multiplied by its probability

[tex]\mu = 0*0.4 + 1*0.3 + 2*0.1+3*0.15+ 4*0.05=1.15[/tex]

[tex]\frac{\Sigma (X)^{2}}{N} =\frac{(0^{2}+1^{2}+2^{2}+3^{2}+4^{2})}{5} =6[/tex]

Replacing the mean and the summatory of X:

[tex]\sigma^{2} = \frac{\Sigma(X)^{2}}{N} -\mu^{2} \\= 6 - 1.15^{2}\\= 4.6775[/tex]

Answer:

The answer to your question is:  The last option is correct

Step-by-step explanation:

Just remember thta when we divide by a negative number, the inequality changes, then,

                            - 125 ≥ -135      divide by -5

                              25  ≤ 27

Answer:

25 < 27 not 25 ≤ 27

Step-by-step explanation:

-125 ≥ -135

on the number, you count through -125 before -135, so -125 is greater but not equal to -135.

-125/ -5  > -135/ -5

= 25 < 27

25 is less than 27. They are not equal.

Answer:

Slope: 6

y-intercept: 8

x-intercept: -4/3

Step-by-step explanation:

Isolate the y. Note the equal sign, what you do to one side, you do to the other. First, divide 2 from both sides:

(2y - 6x - 8)/2 = (0)/2

y - 6x - 8 = 0

Isolate the variable, y. Add 6x and 8 to both sides:

y -6x (+6x) - 8 (+8) = 0 (+6x) (+8)

y = 0 + 6x + 8

y = 6x + 8

The slope intercept form is: y = mx + b, in which m = slope, and b = y-intercept.

Slope: 6

y-intercept: 8

To find the x-intercept, plug in 0 for y in the equation:

y = 6x + 8

0 = 6x + 8

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 8 from both sides:

0 (-8) = 6x + 8 (-8)

-8 = 6x

Isolate the variable, x. Divide 6 from both sides:

(-8)/6 = (6x)/6

x = -8/6

x = -4/3

x-intercept: -4/3

~

The values for x and y are as follows: ( x = 25 ) feet and ( y = 15 ) feet.

To find the values of x and y, we can set up a system of equations based on the given information. Let( x ) be the side length of the large square and ( y ) be the side length of the small square. The perimeter of the entire fence is given by ( 4x + 4y = 350) feet, and the total area enclosed by the fence is( xy + xy = 2xy = 6125 ) square feet.

First, we solve the perimeter equation for  x

4x + 4y = 350

[tex]\[ x + y = \frac{350}{4} \][/tex]

x + y = 87.5

Now, we have two equations:

x + y = 87.5

2xy = 6125

We can substitute the value of ( x + y ) from the first equation into the second equation:

2xy = 6125

2(87.5 - y)y = 6125

175y - 2y² = 6125

y² - 87.5y + 3062.5 = 0

Solving the quadratic equation, we find two possible values for  y  However, since the side length cannot be negative, we discard the smaller value, leaving us with y = 15  feet. Substituting this into the first equation, we find x = 25feet.

Therefore, the final answer is x = 25 feet and  y = 15  feet.

Answer:

1) [tex]2.406e^{-4}[/tex]

2) [tex]-5.618e^{-19}[/tex]

3) [tex]-2.14275e^{-16}[/tex]

Step-by-step explanation:

1) First you need to reorder the terms, to do a simple sum:

  (61 x 10⁻⁷) + (2.25 x 10⁻⁵) + (212.0 x 10⁻⁶) =

  [tex]6.1e^{-6} + 22.5e^{-6} + 212e^{-6}=[/tex]

Now you can simply sum each term, because the exponential is the same:

 [tex]240.6e^{-6}=\\ 2.406e^{-4}[/tex]

2) First you need to reorder the terms, to do a simple sum:

  ( ― 54 x 10⁻²⁰ ) + ( ― 2.18 x 10⁻¹⁸ ) =

  [tex]-5.4e^{-19} - 0.218e^{-19}=[/tex]

Now you can simply sum each term, because the exponential is the same:

[tex]-5.618e^{-19}[/tex]

3) First you need to reorder the terms, to do a simple sum:

 ( ― 21.46 x 10⁻¹⁷ ) ― ( ― 3,250 x 10⁻¹⁹ ) =

[tex]-21.46e^{-17} + 0.0325e^{-17}=[/tex]

Now you can simply sum each term, because the exponential is the same:

[tex]-21.4275e^{-17}=\\-2.14275e^{-16}[/tex]

Answer:  20

Step-by-step explanation:

Given : Angel can choose from 4 different types of chocolate and 5 different flavors of gum.

By the fundamental counting principle , the total number of outcomes is the product of the number of outcomes for each event.

i.e. The number of different types of grab bags can she put together if she puts one chocolate and one flavor of gum in each bag will be :_

[tex]4\times5=20[/tex]

Hence, The number of different types of grab bags can she put together if she puts one chocolate and one flavor of gum in each bag =20

Answer: x=30

Step-by-step explanation:

The sum of the angles must be 360.

4x+3x+3x+2x = 12x

12x = 360

x =360/12 = 30

Answer:

The answer to your question is:

mABC = 120°               mBCD = 90°        mCDA = 60°          mDAB = 90°

Step-by-step explanation:

To solve this problem, we remember that the sum of the angles in a quadrilateral = 360°.

Then

360° = mABC +  mBCD + mCDA  + mDAB

360 = 3x + 4x + 3x + 2x                   substitution

360 = 12x                                         simplifying

x = 360/12

x = 30                                          

Now, we find the values of each angle

mABC = 4(30) = 120°         mBCD = 3(30) = 90°       mCDA = 2(30) = 60°

mDAB = 3(30) = 90°

Because there are 4 inside angles the sum of the four angles must equal 360 degrees.

Add the angles to equal 360:

4x + 3x + 2x + 3x = 360

Simplify:

12x = 360

Solve for x by dividing both sides by 12:

x = 360 /12

x = 30

Now you have x, solve for each angle:

ABC = 4x = 4 x 30 = 120 degrees.

BCD = 3x = 3 x 30 = 90 degrees.

CDA = 2x = 2x 30 = 60 degrees.

DAB = 3x = 3 x 30 = 90 degrees.

C. It's important to know that a four sides figure needs the inside angles when added together need to equal 360 degrees.

Good morning ☕️

____________________

Step-by-step explanation:

Look at the photo below for the answer.

:)

Answer:

  2.2 m/s²

Step-by-step explanation:

Fill in the given values and solve for the unknown variable.

  F = m·a

  7.92 = 3.6·a

  7.92/3.6 = a = 2.2 . . . . . . divide by the coefficient of "a"

The units of this answer are Newtons/kilogram = meters/second/second. We abbreviate those units as m/s².

The acceleration is 2.2 m/s².

Answer:

  117

Step-by-step explanation:

Put the numbers where the corresponding variables are and do the arithmetic.

  3·4² 5·3·4 +3² = 48 +60 +9 = 117

Answer:  c. 7,999,999 phone numbers

A can be any digit 2-9, then there are 8 possible numbers.

B can be any digit 0-9, then there are 10 possible numbers.

C can be any digit 0-9, then there are 10 possible numbers.

X can be any digit 0-9, then there are 10 possible numbers.

X can be any digit 0-9, then there are 10 possible numbers.

X can be any digit 0-9, then there are 10 possible numbers.

X can be any digit 0-9, then there are 10 possible numbers.

Then are possible: 8·10·10·10·10·10·10 = 8·10⁶ = 8,000,000 phone numbers

But the number 867-5309 is not used then 8,000,000 - 1 = 7,999,999 possible phone numbers.

Answer: c. 7,999,999 phone numbers

[tex]\textit{\textbf{Spymore}}[/tex]  

Answer:

Step-by-step explanation:

You know that 3 pennies are involved, because $0.68 cannot be made without them.

Then 6 coins must make up 65¢. If 1 is a quarter, then the remaining 40¢ must be made using 5 coins. 4 dimes is too few, and 8 nickels is too many. However 3 dimes and 2 nickels is just right.

Bobby gave the cashier 1 quarter, 3 dimes, 2 nickels, 3 pennies.

Answer:

The answer to your question is: 16x + 3

Step-by-step explanation:

Step 1 :      f(x) = 8x² + 3x

                f(x +h) =  8(x + h)² + 3( x + h)

                f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

                f (x + h) = 8x² + 16xh + 8h² + 3x + 3h

Step 2 f(x+h) - f(x) =  8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

                              = 8x² + 16xh + 8h² + 3x + 3h - 8x² -3x

                              = 16xh + 8h² + 3 h

Step 3 f(x + h) - f(x)/ h = h(16x + 8h + 3) /h

                                    = 16x + 8h + 3

Step 4 lim  f(x + h) - f(x)/ h = lim 16x + 8h + 3  = lim 16x + 8(0) + 3 = 16x + 3

        h ⇒0                           h ⇒0                     h ⇒0

Here, we are required to find the slope of the tangent line to the graph of the given function at any point.

The correct answer is 16x + 3.

The four step process to find the slope of the tangent line to the graph at any point is as follows;

First step (1):

f(x +h) = 8(x + h)² + 3( x + h) and yields;

f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

and, f (x + h) = 8x² + 16xh + 8h² + 3x + 3h.

Second step(2):

F(x+h) - f(x) = 8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

and, F(x+h) - f(x) = 16xh + 8h² + 3 h

Third step (3):

{F(x+h) - f(x)} / h = (16xh)/h + (8h²)/h + (3 h)/h

This in turn yields;

{F(x+h) - f(x)} / h = 16x + 8h + 3.

Fourth step(4):

lim f(x + h) - f(x)/ h =

h=>0

lim 16x + 8h + 3 = lim 16x + 8(0) + 3 = 16x + 3

h=>0. h=>0

Therefore, the slope of the tangent line to the graph of the given function at any point is;

16x + 3.

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