capacity measures how much a liquid weighs

Answer:

y=1/2x-5/4

Step-by-step explanation:

y=2x+5/2

x=2y+5/2

2y=x-5/2

y=1/2x-(5/2)/2

y=1/2x-(5/2)(1/2)

y=1/2x-5/4

Answer:

C. $68,395.76

Step-by-step explanation:

ED2020

Final answer:

Will would have saved approximately $9,420.12 in 10 years by contributing 9% of his $41,000 salary annually, with a 3% employer match and a 7.13% interest rate.

Explanation:

To calculate how much Will would have saved in 10 years, we need to consider both his salary contribution and the employer's matching contribution. Will saves 9% of his $41,000 salary every year, which comes out to $3,690. The employer matches his contribution up to 3%, so the employer would contribute an additional $1,230 (3% of $41,000) every year.

To calculate the total savings after 10 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt). In this case, the principal P is the total annual contributions, the interest rate r is 7.13%, and n is the number of times interest is compounded per year, which we will assume to be once per year.

Using the formula, we can calculate:

A = ($3,690 + $1,230)(1 + 0.0713/1)^(1*10)

A = $5,920 * 1.0713^10

A = $9,420.123296

Rounding to the nearest cent, Will would have saved approximately $9,420.12 in 10 years.

Answer:

The answer can be calculated by doing the following steps;

Step-by-step explanation:

The Reminder is 0 and (x -2) is the factor of polynomial p(x).

Polynomials are mathematical articulations that comprise of factors and coefficients. In other cases, variables are referred to as indeterminates. We can perform math activities like expansion, deduction, increase, and furthermore sure number types for polynomial articulations yet not division by factor.

Given polynomials p(x) = -4x⁴ + 6x³ + 8x² - 6x - 4

to divide by (x - 2)

We choose long division and look for what will multiply with (x-2) to make the polynomial

(x - 2)(-4x³) = -4x⁴ + 8x³

We subtract this from the original -4x⁴ + 6x³ + 8x² - 6x - 4 - (-4x⁴ + 8x³)

this leaves -2x³ + 8x² - 6x - 4

repeat the same process

(x - 2)(-2x²) = -2x³ + 4x²

subtract this from -2x³ + 8x² - 6x - 4 we get

-2x³ + 8x² - 6x - 4  - (-2x³ + 4x²) = 4x² - 6x - 4

again repeat the process

(x - 2)(4x) = 4x² - 8x

subtract this from 4x² - 6x - 4 we get

4x² - 6x - 4 - (4x² - 8x) = 2x - 4

repeat again

(x - 2)(2) = 2x - 4

subtract this from 2x - 4 we get

2x - 4  - (2x - 4) = 0

Hence the reminder of  polynomials p(x) = -4x⁴ + 6x³ + 8x² - 6x - 4 is 0 and (x - 2) is factor of p(x).

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Answer:

Adverage of 20 mph

30 1/5 = 30.2

2/3 = .6667

30.2 x .6667 = 20.13

Answer:

45.3 miles/hour

Step-by-step explanation:

the information we have is:

distance:

[tex]d=30\frac{1}{5}miles=30.2miles[/tex]

time:

[tex]t=\frac{2}{3} hour[/tex]

the formula for the average speed is:

[tex]v=\frac{distance}{time} =\frac{d}{t}[/tex]

substituting all the known values we get:

[tex]v=\frac{30.2miles}{2/3hour} =\frac{3(30.2miles)}{2hour}= 45.3miles/hour[/tex]

the average speed in miles per hour is: 45.3

Answer:

x-intercept - x = 1/2y - 3.15

y-intercept - y = 2x + 6.3

Step-by-step explanation:

For x,

-6x + 3y = 18.9

-6x = -3y + 18.9

x = -3y/-6 + 18.9/-6

x = 1/2y - 3.15

For y,

-6x + 3y = 18.9

3y = 6x + 18.9

y = 6x/3 + 18.9/3

y = 2x + 6.3

The range of (u circle v) (x) is (negative infinity, 0).

To find the range of (u circle v) (x), we need to substitute v(x) into u(x), which means replacing x in u(x) with v(x).

u(x) = -2x²

So, (u circle v) (x) = -2(v(x))² = -2(1/x)² = -2/x²

The range of (u circle v) (x) is (negative infinity, 0) because as x approaches 0 from the right, (-2/x²) approaches negative infinity, and as x approaches 0 from the left, (-2/x²) approaches positive infinity.

The equation which is equivalent to [tex]\log _{x} 36=2[/tex] is [tex]x^{2}=36[/tex] or x = 6 ([tex]\log _{6} 36=2[/tex]).

Step-by-step explanation:

Given Equation:

           [tex]\log _{x} 36=2[/tex]

As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:

           [tex]b^{y}=a[/tex]

Then, the base b logarithm of x is equal to y

           [tex]\log _{b}(x)=y[/tex]

Now, use the logarithmic rule for the given equation by comparing with above equation. We get b = x, y = 2, and x = 36. Apply this in equation,

            [tex]b^{y}=a[/tex]

            [tex]x^{2}=36[/tex]

When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as [tex]\log _{6} 36=2[/tex]

Answer:D

Step-by-step explanation:

i got it right

From 2 hours to 4 hours she traveled 7 miles.

7 miles  / 2 hours = 3.5 miles per hour.

The slope is 3.5 , which is 3.5 miles per hour, which is how fast she is walking.

Answer:

The number of each coin she have are 17 dimes and 14 nickels.

Step-by-step explanation:

Given:

A coin collector has 31 dimes and nickels with a total face value of $2.40.

Now, to find each does she have.

Let the number of dimes be [tex]x[/tex].

Let the number of nickels be [tex]y[/tex].

So, total number of coins are:

[tex]x+y=31[/tex]

[tex]x=31-y.............(1)[/tex]

Value of a dime = 10 cents

Value of a nickel = 5 cents

Total face value = 240 cents

(1$ = 100 cents.  $2.40×100 =240 cents)

Now, total value of coins:

[tex]10x+5y=240[/tex]

Putting the equation (1) in the place of [tex]x[/tex]:

[tex]10(31-y)+5y=240[/tex]

[tex]310-10y+5y=240[/tex]

[tex]310-5y=240[/tex]

Moving variables on one side and the numbers on other:

[tex]310-240=5y[/tex]

[tex]70=5y[/tex]

Dividing both sides by 5 we get:

[tex]14=y[/tex]

The number of nickels = 14.

Now, putting the value of [tex]y[/tex] in equation (1) we get:

[tex]x+y=31[/tex]

[tex]x+14=31[/tex]

Subtracting both sides by 14 we get:

[tex]x=17.[/tex]

The number of dimes = 17.

Therefore, the number of each coin she have are 17 dimes and 14 nickels.

Answer:

32 cars

Step-by-step explanation:

we know that he can paint 12 cars in 3 weeks.

that means that he can paint 4 cars per week.

4cars x 8weeks = 32 cars in 8 weeks

Answer:

Step-by-step explanation:

12 cars in 3weeks

Then in 1week he will paint= 12/3 car

= 4 cars

so in 8weeks = 4 × 8 cars

= 32cars

Answer:

26.5%

Step-by-step explanation:

Increasing  Percentages

When sequential percentages increasing are computed, each increase applies to the previous result, instead of the first quantity. That is why sometimes the final results may be confusing. For example, increasing 10% and then 15% will not be the same as increasing a total of 25%.

The average test scores of RSM students first increased by 10%. It means that some quantity C increased by

[tex]10C/100=0.1C[/tex]

Now the average test scores are

[tex]C+0.1C=1.1C[/tex]

A new increasing occurred by 15%, and the previous quantity must be multiplied by 1.15, so the final average test scores are

[tex]1.15(1.1C)=1.265C[/tex]

It means that the total increasing was [tex]100(1.265-1)=26.5\%[/tex]

Answer:

26.5%

Step-by-step explanation:

IM SMART! :D

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Given the first equation:

[tex]y=- 6x - 2[/tex]

You can identify that:

[tex]m=-6\\b=-2[/tex]

 By definition, the line intersects the x-axis when [tex]y=0[/tex]. Then, subsituting this value into the equation and solving for "x", you get that the x-intercept is:

[tex]0=- 6x - 2\\\\2=-6x\\\\x=-\frac{1}{3}\\\\x=-0.333[/tex]

Now you can graph it.

Solve for "y" from the second equation:

[tex]y +2=- 6x\\\\y=-6x-2[/tex]

 You can identify that:

[tex]m=-6\\b=-2[/tex]

Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations  has Infinitely many solutions.

See the graph attached.

Answer:

405.224

Step-by-step explanation:

The student is probably asking about the cube root function multiplied by 3, which is an increasing function and is defined for all real numbers, including negative values.

The phrase 'f(x)=3 square root x' seems to be a typo. Assuming this refers to the cube root function, such as 'f(x) = 3 √x,' then this function represents the cube root of 'x' multiplied by 3. To graph this function, start by plotting points, taking the cube root of various values of 'x' and scaling these by 3.

The graph will pass through the origin and rise less steeply than a linear function; it will be an increasing function for all 'x' as the cube root of a real number is always real. This also means that the function will be defined for all real numbers, including negatives, as cubing can produce both positive and negative results.

Answer:

x= -15

Step-by-step explanation:

3x+10=2x-5

3(-15)+10=2(-15)-5

-45+10=-30-5

-35=-35

Each side of the angle is equal, that's how i knew the two were supposed to be equal. <3 Hope this helps!

(I found the picture.)

Answer:

17

Step-by-step explanation:

L 3x + 10 5875 =90 2x - 5 x=_17 5 5 - x =17 Use the image to answer questions 6-7. 125 Given that Xll Y use the figure below to answer questions 8 - 11. -40-40 normal Unit 2: Equations & Exponents Directions: 1. Solve each problem.

Answer:

$210

Step-by-step explanation:

1 ticket= 30

7 tickets = 7*30=$210

Answer:

The net pay of her will be $4702.21

Step-by-step explanation:

The State Tax plus Social Security Taxes plus Medicare takes (3 + 6.2 + 1.45) = 10.65% from Jessica's monthly gross pay.

If the gross pay is $5660 then the after the above deduction the remaining pay will be [tex]5660(1 - \frac{10.65}{100}) = 5057.21[/tex] dollars.

Now, again there is a deduction of $355 from her payment each month.

Therefore, the net pay of her will be = $(5057.21 - 355) = $4702.21 (Answer)

Answer:

Exponential Decay

Step-by-step explanation:

It's exponential growth when your base value is > 1. Example:

1.3ˣ, 2ˣ, 7ˣ, 999ˣ

It's exponential decay when the base value is < 1. Example:

0.9ˣ, 0.45ˣ, (1/2)ˣ, 0.79ˣ, .999ˣ

It's neither when the base value = 1. Example:

1ˣ

Answer:

Ic² + b²l = 13 units.

Step-by-step explanation:

We have to evaluate the expression Ic² + b²l with unknowns b and c and having the values of b and c respectively - 3 and - 2.

Now, Ic² + b²l

= I(- 2)² + (- 3)²l {Putting the values of b and c}

= I4 + 9l  

= I13l

= 13 units.

Therefore, Ic² + b²l = 13 units. (Answer)

Answer:

4/15 cocoa would be left if we made cookies

Step-by-step explanation:

4/6- 2/5

= 4(5)- 2(6)/30

= 20-12/30

=8/30

=4/15

After making the cookies using 2/5 cup of cocoa from the initial 4/6 cup, you would subtract 12/30 cup from 20/30 cup to find that you would have 4/15 cup of cocoa left.

To determine how much cocoa you would have left after making the cookies using 4/6 cup of cocoa and using 2/5 cup for the recipe, you would need to subtract the amount used from the initial amount. To perform the subtraction, you first need to have the quantities expressed with a common denominator. The least common denominator for 6 and 5 is 30.

Convert 4/6 cup to an equivalent fraction with a denominator of 30: (4 × 5) / (6 × 5) = 20/30 cup.

Convert 2/5 cup to an equivalent fraction with a denominator of 30: (2 × 6) / (5 × 6) = 12/30 cup.

Now you can subtract the amount of cocoa used for the cookies from the total amount you have:

Remaining cocoa = Initial amount - Amount used = 20/30 cup - 12/30 cup.

Remaining cocoa = (20 - 12) / 30 = 8/30 cup of cocoa.

To simplify this, divide both the numerator and denominator by their greatest common divisor, which is 2:

Remaining cocoa = 4/15 cup. So you would have 4/15 cup of cocoa left after making the cookies.

Answer:

Step-by-step explanation:

143.17

round the bill to the nearest $ 10..

that would make it $ 140

a 10% tip......its the same thing as multiplying by 0.1

and when u multiply any number by 0.1 ur actually starting at the decimal ( or the end of the number) and move one space to the left.

examples :

10% of 245 = 24.5

10% of 5010 = 501

10% of 76 = 7.6

10% of 88.5 = 8.85 .....if there is a decimal, start at the decimal

so.....10% of 140

start at the end of the number and move 1 space to the left...

ur answer is 14 <==

Answer:

Step-by-step explanation:

[tex]-2\\(-2)(-2)=4\\(-2)(4)=-8\\(-2)(-8)=16\\-----------------\\(-2)(16)=-32\\(-2)(-32)=64\\\vdots[/tex]

Each next term is created by multiplying the previous term by (-2).

Answer:

It's the geometric sequence so the following numbers are:

-32,64

d= -2(multiplication number)

Answer: i did not fully understand,since there are two similar answer options(it's wether A or B)

Good luck!

Intelligent Muslim,

From Uzbekistan.

The solution for y in 2x − 5y ≤ 15  is [tex]y \geq \frac{2x}{5} - 3[/tex]

Solution:

Given that we have to find solution for given inequality for y

2x − 5y ≤ 15

Let us solve above equation for "y"

[tex]2x - 5y \leq 15[/tex]

Add -2x on both sides

[tex]-2x + 2x - 5y\leq 15 - 2x\\\\-5y \leq 15 - 2x[/tex]

Divide by -5 on both sides

Remember that You can perform on operations on both sides of inequality, and have its truth value unchanged

But if we multiply or divide by a negative number, we must flip the sign

[tex]\frac{-5y}{-5} \geq \frac{15}{-5} - \frac{2x}{-5}\\\\y \geq -3 + \frac{2x}{5}\\\\y \geq \frac{2x}{5} - 3[/tex]

Thus solution for "y" is found

Answer:

121x2 + 36y2

Step-by-step explanation:

= (4x + 4)(x + 1)

= 4(x + 1)(x + 1)

= 4(x + 1)2 and is hence the fully factored form

not sure bout the rest though...... it may have mistakes in the question forms.

Polynomials given to us can be factored except 121x² + 36y²,

so we can say that 121x² + 36y² is factored completely.

Factorization of a polynomial is the method by which we write the given polynomial as a product of two or more factors, which when multiplied gives back the same Polynomial.

We will analyze all the given polynomial.

∴ After checking all the options, we can say that 121x² + 36y² was completely factored.

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Answer:

None. Wanda's work is correct.

Step-by-step explanation:

The first is correct.

Answer:

Wanda converted the percent to a decimal incorrectly. It should be 0.73

Step-by-step explanation:

It has to be move two decimal place.

Answer:

2^3

Step-by-step explanation:

2^-5×2^8=2^(-5+8)

= 2^3

Answer:

2³

Step-by-step explanation:

Written in numerical form:

2⁻⁵ · 2⁸

Since both exponents have the same base, one of the exponent rules apply. When multiplying exponents with the same base, you add the exponents.

xᵃ · xᵇ = xᵃ⁺ᵇ

2⁻⁵ · 2⁸

= 2⁽⁻⁵⁾ ⁺ ⁸

= 2³   Simplified exponent form

= 8    Most simplified form

Final answer:

Malory catches up to Dori 25 minutes after starting her walk. Since Malory started at 12:20 pm, she catches up to Dori at 12:45 pm by walking at a faster pace.

Explanation:

To determine what time Malory caught up to Dori, we can set up an equation based on the distance each has traveled. Since distance equals speed multiplied by time, and steps per minute can be considered as speed, we need to find a point at which they have both covered the same distance.

Dori started walking at 12:00 pm and Malory started at 12:20 pm, so Malory starts walking 20 minutes later. We'll use t to represent the time in minutes that Malory has been walking when she catches up to Dori.

Thus, Dori has been walking for t + 20 minutes by the time Malory catches up.

We set up the following equation to find t:
Dori's distance = Malory's distance
50 steps/minute × (t + 20) = 90 steps/minute × t

Solving for t gives us:
50t + 1000 = 90t
1000 = 40t
t = 25 minutes

Therefore, Malory catches up to Dori 25 minutes after Malory started walking. Since Malory started walking at 12:20 pm, we add 25 minutes to this time to find out the catch up time is 12:45 pm.

Answer:

6 1/2

Step-by-step explanation:

So basically 8 2/3 is equally to 26/3 so 45 minutes is 45/60.

45/60=3/4

26/3*3/4=6 1/2

Jordan, with a speed of 8 2/3 miles per hour, will cover a distance of 6.5 miles in a 45 minute bike ride.

First, we need to understand that Jordan is biking at a speed of 8 2/3 miles per hour. This means in 1 hour, or 60 minutes, he covers that distance. If we want to know how much he covers in a different timeframe - 45 minutes in this case - we have to adjust proportionally.

As a step-by-step calculation, first change 8 2/3 to a decimal, which equal to 8.67.

To find out how far Jordan bikes in 45 minutes, you need to multiply his speed (8.67 mph) by the time in hours. Since 45 minutes is 0.75 of an hour (45/60), the mathematical calculation will be:

Distance = Speed x Time = 8.67 miles/hour x 0.75 hour = 6.5 miles

Therefore, Jordan will bike 6.5 miles in 45 minutes.

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The expected value of purchasing a raffle ticket is -0.647.

The expected value is derived in probability analysis by the multiplication of each of the potential possibilities by the likelihood that each result will occur and then adding all of those values together.

Using the formula below, we can calculate the expected value as follows:

[tex]\mathbf{ E(X)= \sum^{n}_{i=1}X_i P(X_i)}[/tex]

However, the probability (Pr) of each event can be categorized as follows:

Thus;

[tex]\mathbf{E(X) = 70(\dfrac{20}{5500} \times 25 ((\dfrac{20}{5500} )- 1(\dfrac{5460}{5500} )}[/tex]

[tex]\mathbf{E(X) =-0.647}[/tex]

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Answer:

The number of weeks Marla will take to paint all the pots is  5 weeks and 3 days .

Step-by-step explanation:

Given as :

The number of pots Marla will paint = 48 pots

The number of pots she plans to paint each week = 9 pots

Let The number of weeks Marla needs to paints all pots = n weeks

Now, According to question

The number of weeks = [tex]\dfrac{number of pots Marla will paints}{\textrm The number of pots Marla will paints each week}[/tex]

Or , n = [tex]\dfrac{48}{9}[/tex]

∴ n = 5.3

So The number of weeks =  n = 5 weeks and 3 days

Hence The number of weeks Marla will take to paint all the pots is  5 weeks and 3 days . Answer