Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. He wants to weigh 150 pounds. If p represents the number of pounds he wants to lose, write an equation to represent this situation.

Answer:

Start with equation,

         y''(x) = f(x) = 6y/(10x-x²)               about point x₀ = 5

Then,

       y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….

by inspection,

           y(5) = a₀      and       y'(5) = a₁

then,

y''(5) = 6a₀/(50-25) = 6a₀/25              

y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2

then,                      

                              y'''(5) = 6a₁/25 - 0 = 6a₁/25                

y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³

then,

    y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0

              = 48a₀/625

So,

y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …

                                                       or

y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...

                                                         or

y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....

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answer:

tell us why the other gardens are needed

Answer:

The choice B. 5°

Step-by-step explanation:

The angle in the figure is 90°

\(36 + (11x - 1) = 90 \\ 36 + 11x - 1 = 90 \\ 11x + 35 = 90 \\ 11x = 90 - 35 \\ 11x = 55 \\ \\ x = \frac{55}{11} \\ \\ x = 5\)

Answer:

Median 81

Mode 73, appeared 2 times

Range 24

Step-by-step explanation:

As performed by calculator.net:

Mean (Average) 82

Median 81

Range 24

Mode 73, appeared 2 times

Geometric Mean 81.633806378697

Largest 97

Smallest 73

Sum 574

Count 7

Answer:

1st option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3 , so

y = - 3x + c ← is the partial equation

To find c substitute (- 1, 6 ) into the partial equation

6 = 3 + c ⇒ c = 6 - 3 = 3

y = - 3x + 3 ← equation of line

Answer:

3 = 14 and 4 = 8

Step-by-step explanation:

The reason as to why this is, is because of the line going down the middle. If you were to open one of the lengths as a door starting from the middle line it would fit perfectly with the top one.

Answer:

t=5

Step-by-step explanation:

y represents height above the ground.

so when it touches the ground height above the ground =0

y=-16t²+80 t

it will hit the ground when y=0

-16t²+80t=0

-16t(t-5)=0

either t=0 or t-5=0

or t=5

t=0 gives initial value.(rejected)

t=5

To find the limit of cos(x)/(1-sin(x)) as x approaches (π/2)+, we can use l'Hospital's Rule.

First, we can take the derivative of both the numerator and denominator with respect to x: lim cos(x)/(1 − sin(x)) x → (π/2)+ = lim [-sin(x)/(cos(x))] / [-cos(x)] x → (π/2)+ = lim sin(x) / [cos(x) * cos(x)] x → (π/2)+

Now, plugging in (π/2)+ for x, we get: lim sin(π/2) / [cos(π/2) * cos(π/2)] x → (π/2)+ = 1 / (0 * 0) = undefined

Since the denominator approaches 0 as x approaches (π/2)+, and the numerator is bounded between -1 and 1, the limit does not exist.

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Answer:

\(\frac{5}{3}\)

Step-by-step explanation:

zero: Also known as a root, a zero is an  x  value at which the function of  x  is equal to  0.

\(3x-5=0\\x=\frac{5}{3}\)

.

8 divided by 5.2

that’s all it takes

Answer:

0.65

Step-by-step explanation:

Since we have given that

Cost of 8 pencils = 5.20

We need to find the cost of 1 pencil.

For this we'll use the unitary method,

5.20 divided by 8 = 0.65

Answer:

C

Step-by-step explanation:

Becuase 68 is closer to c than b

The solved logarithmic functions are log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet,  e. For example log 10 = 1 and e^2.

Solving the given expressions: y = 2x⁺⁴, y - 4x⁻¹ = 0

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take expression y = 2x⁺⁴

Applying log on both sides, we get,

log y = log (2x⁺⁴)

log y = log 2 + log x⁺⁴

log y = log 2 + 4 log x

To Check Results,

Taking exponential,

y = e^[log 2 + 4 log x]

y = e^(log 2) × e^[4 log (x)]

y = 2 × e^(log x⁴)

y = 2x⁴

Thus, the answer is verified.

Take expression y - 4x⁻¹ = 0

Applying log on both sides, we get,

log y = log (4x⁻¹)

log y = log 4 + log x⁻¹

log y = 2 log 2 - log x

To Check Results,

Taking exponential,

y = e^[2 log 2 - log x]

y = e^(2 log 2) × e^[-log (x)]

y = e^(log 4) × e^(log x⁻¹)

y = 4x⁻¹

y - 4 x⁻¹ = 0

Thus, the answer is verified.

Hence, the solved expression is log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.

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If August 17 is a Sunday, then the first of September will be a Monday.

First, we need to count the number of days between Agust 17 and September 1.

We know that August has 31 days, so between Agust 17 and September 1 there are:

31 - 17 = 14

And adding the other day until September 1, we have 15 days.

So there are 15 days between August 17 and September 1, and we know that the days have a pattern in a period of 7 days.

So, 7 days after August 17, is Sunday again.

Another 7 days (for a total of 14) Is Sunday again.

Adding the last day (total of 15) is Monday.

So we conclude that the first of September will be a Monday.

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8/36 = 2/9 represents the likelihood that the sum of the two rolled numbers is a perfect square.

 A fraction is a piece of the entire. The quantity is represented as a quotient by dividing the numerator by the denominator. Both are integers in a straightforward fraction. A fraction appears in a complex fraction's numerator or denominator. The numerator of a valid fraction is smaller than the denominator. Six times six is equal to 36 possible outcomes when two dice are rolled. Only 8 of these 36 possible outcomes—the result of two diced integers producing a perfect square—are beneficial for the occurrence of the essential occurrences. The six diagonal elements (a, a) from the sample space are shown here, along with two additional elements (1, 4) and (4, 1). probabilities are 8/36, or 2/9.

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Given,

ΔABC and ΔDEF are similar triangles.

AB = 6 feet, BC = 4 feet, AC = 7 feet

Let the shortest side of ΔDEF be  EF = 12 feet.

Let DE = x and DF = y

Since,  ΔABC and ΔDEF are similar,

\(\frac{BC}{EF}\)  = \(\frac{AB}{DE} = \frac{AC}{DF}\)

⇒ \(\frac{4}{12} = \frac{6}{x} =\frac{5}{y}\)

On Solving,

x = 18 feet and y = 15 feet

We know,

Perimeter of a triangle = sum of all three sides

Hence, perimeter of ΔDEF = DE + EF + DF = 18 + 15 + 12 = 45 feet.

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Answer:

See below for all answers and explanations

Step-by-step explanation:

Problem A

\(\displaystyle S_n=\frac{n}{2}(a_1+a_n)=\frac{25}{2}(4+100)=12.5(104)=1300\)

Problem B

\(a_n=a_1+(n-1)d\\52=132+(n-1)(-4)\\52=132-4n+4\\52=136-4n\\-84=-4n\\n=21\\\\\displaystyle S_n=\frac{n}{2}(a_1+a_n)=\frac{21}{2}(132+52)=10.5(184)=1932\)

Problem C

\(a_n=a_1+(n-1)d\\a_n=4+(n-1)(6)\\a_n=4+6n-6\\a_n=6n-2\\106=6n-2\\108=6n\\n=18\\\\\displaystyle S_n=\frac{n}{2}(a_1+a_n)=\frac{18}{2}(4+106)=9(110)=990\)

Problem D

\(\displaystyle S_n=\frac{n}{2}(a_1+a_n)\\\\108=\frac{n}{2}(3+24)\\\\108=\frac{n}{2}(27)\\\\216=27n\\\\n=8\\\\\\a_n=a_1+(n-1)d\\24=3+(8-1)d\\21=7d\\d=3\\\\\\a_n=3+(n-1)(3)\\a_n=3+3n-3\\a_n=3n\\\\a_1=3 \leftarrow \text{First Term}\\a_2=3(2)=6\leftarrow \text{Second Term}\\a_3=3(3)=9\leftarrow \text{Third Term}\)

I hope this was all helpful! Please let me know if anything is confusing to you and I'll try to clarify.

Answer:

\(c^6h^3\)

Step-by-step explanation:

         \(hhh=h^3\\c^3c^2h^3c\\c^3c^2c\\ccc = c^3\\=c^{3 \cdot 2}\\=c^6\\=c^6h^3\)

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

Answer:

In 2007 it was 450 and 2011 it was 300

Step-by-step explanation:

So the change was 300 I think this correct

Answer:

Y=3x-13

Step-by-step explanation:

y = 2x - 13

It's not 3x - 13

Step-by-step explanation:

-21 -40 -61 -85

because negative numbers are the same as positive numbers. imagine it like this

-3 -2 -1, 0, 1, 2, 3

Answer: B

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

180 * .2 = 36

20% is the same thing as 1/5 of something, so read the question again,

"36 is 1/5 of what number?"

Multiply 36 by 5 to get 180

Double check yourself by finding 20% of 180

180 * .2 = 36

Hope this helped, queen!

To sanitize a hot tub in a hotel sauna, dilution of 2 cups of chlorine for every gallon of water. If 120 gallons of water are used, the total amount of fluid in the hot tub will be 120 gallons.

According to the manufacturer's recommendation, a dilution of 2 cups of chlorine is required for every gallon of water. Since 120 gallons of water are used in the hot tub, we can calculate the total amount of fluid in the hot tub by adding the water and chlorine together.

To determine the amount of chlorine needed, we need to convert the cups into gallons. There are 16 cups in a gallon, so 2 cups of chlorine is equivalent to 2/16 = 1/8 of a gallon.

Now, we can add the amount of water and chlorine together to find the total fluid volume in the hot tub. The amount of water is given as 120 gallons, and we need to add 1/8 of a gallon of chlorine to it.

Therefore, the total amount of fluid in the hot tub will be 120 + 1/8 = 120.125 gallons. Since we generally round off measurements, the total fluid volume in the hot tub would be approximately 120 gallons.

In summary, if 120 gallons of water is used in the hot tub, the total amount of fluid, including the recommended chlorine dilution, would be approximately 120 gallons.

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The proof by mathematical induction shows that the statement 1^3 + 2^3 + 3^3 + n^3 = (n^2(n+1)^2)/4 holds for all positive integers n. The base case n = 1 is true, and assuming the statement is true for n = k, we can prove it is true for n = k+1 by substituting k+1 for n and simplifying the expression.

To prove the statement 1^3 + 2^3 + 3^3 + ... + n^3 = (n^2(n+1)^2)/4 for all natural numbers n using mathematical induction, we proceed as follows:

Base case: Let n = 1. Then 1^3 = (1^2(1+1)^2)/4 = 1, which is true.

Inductive step: Assume the statement is true for some arbitrary value k, i.e., 1^3 + 2^3 + 3^3 + ... + k^3 = (k^2(k+1)^2)/4.

We need to show that the statement is also true for n = k+1, i.e., 1^3 + 2^3 + 3^3 + ... + (k+1)^3 = ((k+1)^2(k+2)^2)/4.

Starting with the left-hand side of the equation, we have:

1^3 + 2^3 + 3^3 + ... + (k+1)^3

= (1^3 + 2^3 + 3^3 + ... + k^3) + (k+1)^3 // regrouping the last term

= (k^2(k+1)^2)/4 + (k+1)^3 // using the induction hypothesis

= (k+1)^2(k^2+4k+4)/4 // factoring out (k+1)^2

= ((k+1)^2(k+2)^2)/4 // simplifying the expression

Therefore, the statement is true for n = k+1, and by mathematical induction, the statement is true for all natural numbers n.

Hence, we have proven that 1^3 + 2^3 + 3^3 + ... + n^3 = (n^2(n+1)^2)/4 for all natural numbers n.

Your question is incomplete.

Complete question may be:

Use mathematical induction to prove that statement 1^3 + 2^3 + 3^3 + n^3 = (n^2(n+1)^2)/4 , ∀n∈N

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The Law of Large Numbers, which states that as the number of trials increases, the observed probability will get closer and closer to the expected probability.

This is an example of the Law of Large Numbers. The Law of Large Numbers states that as the number of trials (in this case, the number of coin flips) increases, the observed probability (in this case, the probability that the next coin flip will be heads) will get closer and closer to the expected probability (in this case, 50%). The formula for this is P(n) = P(1) + (P(n) - P(1))/n, where n is the number of trials and P(1) is the probability of the first trial.

For example, if the first coin flip results in heads (P(1) = 1), the probability of the 5th coin flip being heads is P(5) = 1 + (0.5 - 1) / 5 = 0.2. This means that the probability of the 6th coin flip being heads is 0.2 + (0.5 - 0.2) / 6 = 0.3125, or 1/64.

This is an example of the Law of Large Numbers, which states that as the number of trials increases, the observed probability will get closer and closer to the expected probability.

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Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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