At 1:00 the water level in a pool is 13 inches. At 2:30 the water level is 28 inches what is the rate of change?
A: 15/90
B: 1/10
C: 10/1

Answer:

See below. The result using the binomial theorem  is 1049.8560 compared with 1049.8573 using a calculator.

Step-by-step explanation:

Binomial theorem:-

( a + x)^n  =   a^n + nC1 a^(n-1) x + nC2 a^(n - 2)x^2 +  .......

(4 + 0.02)^5 = 4^5  + 5C1* 4^4 *0.02 + 5C2* 4^3* 0.02^2 +  5C3*4^2*0.02^3

+ 5C4 * 4 * 0.02^4 + 0.02^5

= 1024 +  5*4^4*0.02 + 10*4^3*0.02^2 + 10*4^2*0.02^3 + 5*4*0.02^4 + 0.02^5

= 1024 + 25.6 + 0.256 + 0.0000032

Answer:

Keisha's Response: The 4th term is almost 0, so the 5th and 6th terms are also close to 0. Add the terms shown to approximate 4.025:  1024 + 25.6 + 0.256 + 0.001 = 1049.857.

Step-by-step explanation:

EDGINUITY

Answer:

[tex](x-1)^2+(y+5)^2=100[/tex]

Step-by-step explanation:

The equation of a circle has the following form:

[tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center of a circle with radius r.

Our equation center is (1.-5) and radius is 10.

[tex](x-1)^2+(y--5)^2=10^2[/tex]

[tex](x-1)^2+(y+5)^2=100[/tex]

Answer:

We need to sell the nuts at 35 dollars to make $20 profit

Step-by-step explanation:

Profit = Selling price - cost

We know we want a 20 dollar profit

The cost of the nuts is 15 dollar

Substitute this in

20 = Selling price -15

Add 15 to each side

20+15 = Selling price -15+15

35 = Selling price

We need to sell the nuts at 35 dollars to make $20 profit

Answer:

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

Answer:

The simplified version of this would be (63 - 19x)/2

Step-by-step explanation:

In order to find this, we first distribute the numbers outside of the parenthesis.

13(11-3x)-5(16-4x)/2

143 - 39x - 80 + 20x/2

Then we combine like terms

(63 - 19x)/2

Answer:

see explanation

Step-by-step explanation:

(a)

1.2² = 1.2 × 1.2 = 1.44

(b)

2³ + 17 - 3 × 4 ← evaluate exponent and multiplication before adding/subtracting

= 8 + 17 - 12 = 25 - 12 = 13

(c)

9² ÷ 3³ ← evaluate exponents before dividing

= 81 ÷ 27 = 3

Answer:

a = 1.44

b = 21.6

c = 3

Step-by-step explanation:

a is 1.44 because 1.2 × 1.2 = 1.44

b is 21.6 because 2 × 2 × 2 = 8 so it is 8 + 17 - 3.4 which is 21.6

c is 3 because 9 × 9 = 81 and 3 × 3 × 3 = 27 so 81 ÷ 27 = 3

Answer:

Step-by-step explanation:

The population density is the ration between the population and the area covered. So, the population density of Marble City

[tex]M=\frac{52348}{125}\approx418.78[/tex]

If both cities have the same population density, this can be used to find the dimension of Pebble City:

[tex]P=\frac{85312}{A}\\ 418.78=\frac{85312}{A}\\A=\frac{85312}{418.78}\approx 203.72[/tex]

Now, knowing the area of Pebble City, we can find its length

[tex]A=(length)(width)\\203.72=l(11.8)\\l=\frac{203.72}{11.8}\approx 17[/tex]

Therefore, the length of Pebble City has a length of 17 miles, approximately.

Answer: y = 2x^4

The graph represents a parabolic-looking shape so it's either a quadratic or some even degree polynomial. This rules out y = -2x^3 and y = 2x^3 as they are cubics with odd degrees

The degree of a polynomial is the largest exponent. It determines the end behavior. In this case, both ends are rising upward together. Because they are rising up in the positive y direction, this means that we cannot have y = -2x^4 as the answer. For example, if x = 2 then y = -2*x^4 = -2*2^4 = -32, but the point (x,y) = (2,-32) isn't on the blue curve. So we can rule y = -2x^4 out.

The fact that y = 2x^4 has a positive leading coefficient tells us that the endpoints point upward.  

Answer:

25/2

Step-by-step explanation:

Answer:

a= 1/2m+25

Step-by-step explanation:

As the statement says that Sophie pays for one half of the cost of the car rental (m) and that she spent $25 on gasoline, the expression that could be used to determine the amount that she spent would be equal to the sum of one half of the cost of the car rental plus 25:

a= 1/2m+25

a= amount Sophie spent

m= cost of the car rental

Answer:

Let charge per day be $x  and charge per mile be $y  

then:

as per the given condition we have;

3x + 300y =159          .....[1]

5x + 600y = 289       .....[2]

Multiply equation [1] both sides by 5 we get;

[tex]5(3x+300y) = 5 \cdot 159[/tex]

Using distributive property: [tex]a \cdot(b+c) = a\cdot b+ a\cdot c[/tex]

15x+1500y = 795                 .....[3]

Multiply equation [2] by 3 both sides we get;

[tex]3(5x+600y) = 3 \cdot 289[/tex]

Using distributive property: [tex]a \cdot(b+c) = a\cdot b+ a\cdot c[/tex]

15x+1800y = 867                    .....[4]

Subtract equation [3] from [4] to eliminate x and solve for y;

15x+1800y-15x-1500y = 867 -795

Combined like terms;

300y = 72

Divide both sides by 300 we get;

[tex]y = \frac{72}{300}=0.24[/tex]

⇒  y =$0.24 per mile.

Now substitute this value y in equation [1] to solve for x;

3x + 300(0.24) =159

3x + 72 =159

Subtract 72 both sides we get;

3x + 72 -72 = 159 -72

Simplify:

3x = 87

Divide both sides by 3 we get;

[tex]x = \frac{87}{3} = 29[/tex]

Therefore, the best rental charges per day is, $ 29 and the charges per mile is, $0.24

The problem can be solved by setting up a system of linear equations from the given information. Then, solving these equations will yield the daily fee and mileage fee that Best Rental charges.

To solve this problem, we can create a system of linear equations. Let's denote the daily fee as 'd' and the mileage fee as 'm'

From Barney's rental, we know that 3d + 300m = 159.

From Mary's rental, we know that 5d + 600m = 289.

We solve these two equations to find the values of 'd' and 'm'. This is an application of algebra in solving real-world problems

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Answer:

I'mma be honest someone else asked the same question and this is the answer they gotten They gotten 4 and 5 and 4.1 but in my opinion I say the answer should be 4

Step-by-step explanation:

Best estimate would be B, because the answer is 4.1067 and you would round down

For [tex]\( n = 0, 1, \) and \( 2 \)[/tex], the inequality [tex]\( 3n < 18 \)[/tex] holds true. These are the values that satisfy the inequality.

To solve the inequality 3n < 18, we need to find values for ( n ) that make the inequality true. Here are three such values:

n = 0 , n = 1 , n = 2

Let's go through the detailed calculation step-by-step:

Starting with  n = 0:

Plug  n = 0  into the inequality:

[tex]\( 3(0) < 18 \)[/tex]

Simplify:

[tex]\( 0 < 18 \)[/tex]

Since ( 0 ) is less than ( 18 ), this statement is true.

Next,  n = 1 :

Plug  n = 1 into the inequality:

[tex]\( 3(1) < 18 \)[/tex]

Simplify:

[tex]\( 3 < 18 \)[/tex]

Again, this statement is true.

Finally, [tex]\( n = 2 \)[/tex]:

Plug [tex]\( n = 2 \)[/tex] into the inequality:

[tex]\( 3(2) < 18 \)[/tex]

Simplify:

[tex]\( 6 < 18 \)[/tex]

This statement is also true.

Therefore, for [tex]\( n = 0, 1, \) and \( 2 \)[/tex], the inequality [tex]\( 3n < 18 \)[/tex] holds true. These are the values that satisfy the inequality.

Answer:

Yee it's the second one I took the edge test don't worry I"m right even tho I have wrong grammar

Step-by-step explanation:

Answer:

slope = -1/2

Step-by-step explanation:

To find the slope, we can use the formula

m = (y2-y1)/(x2-x1)

   = (4-3)/(-2-0)

   = 1 /-2

   = -1/2

The slope is -1/2

Answer:

x = 387

Step-by-step explanation:

The wind acts in the opposite direction to the plane when the time is longer.

The wind acts in the same direction as the plane when the time is shorter.

Equation

d = r*t

Givens

Substitution

Since the two distances are the same, you can equate the right hand sides.

Now use one of the given equations with the distance

Hello from MrBillDoesMath!

Answer:

Choice B (176)

Discussion:

Volume of a box = (area of base) * height.    

In our case this  becomes

"2 of the boxes have a height of 3"      + "and one box has a height of 5"

16 * 3  + 16 * 3                                         + 16 * 5 =

48 + 48 + 80  =

96 + 80 =

176

which is choice B

Thank you,

MrB

Answer:

option B

Step-by-step explanation:

9/10 + 6/5 + 3/2...........

We find the difference between the terms

[tex]\frac{6}{5} - \frac{9}{10}[/tex]

[tex]\frac{12}{10} - \frac{9}{10} = \frac{3}{10}[/tex]

We will get the same difference when we subtract consecutive terms.

so , d= 3/10, a= 9/10

we find the formula for nth term

a_n = a+(n-1) d

[tex]a_n = \frac{9}{10} + (n-1)\frac{3}{10}[/tex]

[tex]a_n = \frac{9}{10} +\frac{3}{10}n-\frac{3}{10}[/tex]

[tex]a_n = \frac{6}{10} +\frac{3}{10}n[/tex]

[tex]a_n = \frac{3}{5} +\frac{3}{10}n[/tex]

we need to find eighth partial sum so we  take n=1 to 8

sum of 8 terms ([tex]\frac{3}{5} +\frac{3}{10}n[/tex])

So option B is correct

The eighth partial sum of a series, denoted as S8, sums up the first 8 terms in the series. In summation notation, it can be expressed as S8 = Σ_[k=1]^8 a_k.

In mathematics, specifically in series and sequences, the notation for the eighth partial sum of a series is denoted by S8. Here the numeral 8 indicates the number of terms in that partial sum which is 8 in this case. The general formula for the sum of an arithmetic series is S_n = n/2 * (a + l) where n is the number of terms, a is the first term, and l is the last term.

If the terms of the series are denoted by a_k where k=1,2,3,... is the index of the term, the eighth partial sum of a series can be written in summation notation as:

 S8 = Σ_[k=1]^8 a_k

This means that the eighth partial sum is the sum of the first 8 terms of the series.

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Answer: g(x) is the image of f(x)

Step-by-step explanation:

multiplying the x value by -1 means you reflect that point across y-axis, therefore, g(x) is the reflection of f(x) across y-axis.

Multiplying the x value by -1 means you reflect that point across y-axis,

therefore, g(x) is the reflection of f(x) across y-axis.

You are basically assigning the same y-value to the opposite x-values to make g(x). So, for the point (x, 31), on f(x), x is -2, but on g(x), x is 2. Thinking about this visually, you can imagine that this represents a reflection of f across the y-axis.

Here is the general rule for reflection across the y-axis: Given an equation y=f(x) y = f ( x ) , the new reflection equation of the reflected graph will be y=f(−x) y = f ( − x ).

The relationship between the graphs is Option 3 . they are reflection of each other across the y axis.

The reflection vector is generated by applying the equation R = U − 2NT(U · N), where N is the vertex normal transformed into eye space. The reflection equation used is the standard for computing the reflection vector given a surface normal and incident vector.

The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.

Learn more about reflection equation, refer

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Answer:

Annalisa uses 7/6 cups altogether.

Step-by-step explanation:

First you find common denominators for both fractions, which is 6, then convert the fractions to the denominator 6.

You get 3/6+4/6.

The answer is 7/6!

Answer:

p= 2l+2b

Step-by-step explanation:

distribution

Answer:

P = 2 * 1 + 2 * B

Step-by-step explanation:

This equation needs to be written using the distributive property:

A (B + C) = A * B + A * C

Put in the numbers:

P = 2 (1 + B)

=

P = 2 * 1 + 2 * B

Best Of Luck,

- I.A. -

Answer: The number of pounds each camel have to carry=44 pounds

The pounds of goods left=3 pounds

Step-by-step explanation:

The total pounds of goods the merchant have=[tex]269+167+51[/tex]

=487 pounds

The total number of camels the merchant have = 11

If each camel carry same weight of goods, then we divide total weight by 11, we get

487÷11=44.27

The number of pounds each camel have to carry=44 pounds

The pounds of goods left=487-44×11=487-484=3 pounds

The standard form of speed of light is 300000 kilometers per second

Here the standard form means converting the given expression to the simple expression .

So, 3x10^5 can be written as 3 x 100000

By multiplying we get 300000

So, the standard form of speed of light is 300000 kilometers per second

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[tex]Use\ (a^n)^m=a^{nm}\ and\ a^3-b^3=(a-b)(a^2+ab+b^2).\\\\m^{15}=m^{5\cdot3}=(m^5)^3\\\\m^{15}-1,000=(m^5)^3-10^3=(m^5-10)[(m^5)^2+(m^5)(10)+10^2]\\\\=(m^5-10)(m^{10}+10m^5+100)\\\\Answer:\ \boxed{m^5-10}[/tex]

Final answer:

The binomial factor in the factorization of [tex]m^{15}[/tex] - 1,000 is [tex]m^{5}[/tex] - 10

Explanation:

To find the binomial factor in the factorization of [tex]m^{15}[/tex] - 1,000, we should recognize this expression as a difference of two powers. Both [tex]m^{15}[/tex] and 1,000 (which is the cube of 10, or 103), can be written as a power of their respective bases. We can factor this expression using the difference of cubes formula, which states that [tex]a^{3}[/tex] - [tex]b^{3}[/tex] = (a - b)([tex]a^{2}[/tex] + ab + [tex]b^{2}[/tex]). Applying this formula, we look for a cube of m that matches one of the options provided. The closest match here is [tex](m^{5})^3[/tex] [tex]-10^{3}[/tex], which gives us the factor of ([tex]m^{5}[/tex] - 10). Therefore, the binomial factor is [tex]m^{5}[/tex] - 10.

The total is $21 + $6 or $27.

There are 3 students.

Let p = how much each student will pay

p = $27 ÷ 3 students

p = $9

Each student will pay $9.

The answer is $9 each

Answer:-70

Step-by-step explanation:

Answer:-70

Step-by-step explanation:

−3.5

0.05

=−70

Answer:

-8\3

Hope That Helps!

4 rectangles are 3 in x 2 in = 6 square inches each.

4 * 6 = 24 square inches.

2 squares are 3 in x 3 in = 9 square inches each

2 * 9 = 18 square inches.

Total area = 24 + 18 = 42 square inches.

Answer:

J. $638.14

Step-by-step explanation:

We will use compound interest formula to solve our given problem.

[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,

A=Final amount after T years.

P= Principal amount.

r= Interest rate in decimal form.

n= Period of compounding.

T= Time in years.

Let us convert our given interest rate in decimal form.

[tex]5\%=\frac{5}{100}=0.05[/tex]

Let us substitute our given values in above formula.

[tex]A=500*(1+\frac{0.05}{1})^{1*5}[/tex]

[tex]A=500*(1+0.05)^{5}[/tex]

[tex]A=500*(1.05)^{5}[/tex]

[tex]A=500*1.2762815625[/tex]

[tex]A=638.14078125\approx 638.14[/tex]

Therefore, we will have an amount of $638.14 after 5 years and option J is the correct choice.

The balance in your account after depositing $500 with an annual compound interest rate of 5% for 5 years would be $638.14, according to the formula for compound interest.

To calculate the balance in an account after a certain period of time, we would use the formula for compound interest. This formula is

, where 'A' is the amount of money accumulated after n years, taking into account interest. 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal), 'n' is the number of times that interest is compounded per year, and 't' is the time the money is invested for in years.

Here, P = $500, r = 5/100 = 0.05 (because the rate was given in percentage), n = 1 (because the interest is compounded annually), and t = 5 years. Inserting these values into the formula gives us

which simplifies to A = $638.14. So, the balance in your account after 5 years would be $638.14, rounded to the nearest cent.

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Answer:

D

Step-by-step explanation:

5+7(8r-2)

5+56r-14

-9+56r=56r-9

d

Answer:

D) 56r - 9

Step by Step Explanation:

Answer:

$53,700

Step-by-step explanation:

If we have 537 people coming and paying $100 each, we multiply 537  and $100

537 * $100

$53,700