Alex is 6 years older than Frank. The sum of their ages is 50. Find Alex's age and
Frank's age.
HELP

To check our answer, we can verify that the number of quarters is 1.7 times the number of dimes, which would be 102. And the total value of her dimes and quarters would be:  $31.50

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's start by using algebra to solve the problem.

Let x be the number of dimes that Carol has saved.

According to the problem, there are 70% more quarters than dimes. We can express the number of quarters in terms of x as 1.7x, since 1.7 times the number of dimes is equal to the number of quarters.

We also know that the combined value of her quarters and dimes is $31.50. We can express this as an equation:

0.10x + 0.25(1.7x) = 31.50

Simplifying and solving for x, we get:

0.10x + 0.425x = 31.50

0.525x = 31.50

x = 60

Therefore, Carol has 60 dimes.

Therefore, To check our answer, we can verify that the number of quarters is 1.7 times the number of dimes, which would be 102. And the total value of her dimes and quarters would be:

60 * $0.10 (dimes) + 102 * $0.25 (quarters) = $31.50

which matches the information given in the problem.

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Answer:

1) \(16\frac{2}{3}\)% or 20%

Step-by-step explanation:

Given that:

An experiment which is carried out by flipping a coin and rolling six sided die.

The outcomes can be:

{H1, H2, H3, H5, H6, T1, T1, T2, T3, T5}

As per question statement:

Number of outcomes having tails and an odd number greater than one is 2 (i.e. T3 and T5)

Total number of outcomes here is 10.

Therefore, to find the percentage, we use the following formula:

\(\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\times 100\)

\(\Rightarrow \dfrac{2}{10}\times 100 = 20\%\)

As per question statement, the answer is 20%.

If we consider all the outcomes, i.e.

{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

Total number of outcomes = 12

The percentage will come out be :

\(\Rightarrow \dfrac{2}{12}\times 100 = 16\frac{2}{3}\%\)

The form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

Given:

A carnival has a game where players can win stuffed animals. the rules allow for players to win no more than 10 small animals, no more than 6 large animals, and no more than 12 total animals.

x be the number of small animals and y be the number of large animals

The number of small animals = 10x

Number of large animals = 6y

The equation:

= 10x + 6y = 12.

Therefore the form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.


A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.

Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.

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Answer:

39.3078

Step-by-step explanation:

i am not for sure but i belive this is correct:)

Answer:

C. 244,596 gal

Step-by-step explanation:

To determine the number of gallons of water that a swimming pool holds, you can use the following formula:

gallons = cubic feet * 7.48

Plugging in the given volume of 32,700 cubic feet, you get:

gallons = 32,700 cubic feet * 7.48

= 244,596 gal

Therefore, the swimming pool holds approximately 244,596 gallons of water.

The value of integer k is -5.

Polynomial equations formed with variables, exponents and coefficients .

Since the polynomial has three integer roots, we can express it as:

(x - r1)(x - r2)(x - r3) = 0

where r1, r2, and r3 are the three integer roots.

Expanding the left-hand side, we get:

x^3 - (r1 + r2 + r3)x^2 + (r1r2 + r1r3 + r2r3)x - r1r2r3 = 0

Comparing this with the given polynomial, we see that:

r1 + r2 + r3 = 1

r1r2 + r1r3 + r2r3 = k

r1r2r3 = 3

First we need to find the value of k. From the first equation, we see that one of the roots must be 1, since the sum of three integers that are not 1 cannot be 1. Without loss of generality, assume that r1 = 1. Then we have:

r2 + r3 = 0

r2r3 = 3

Since the roots are integers, the only possibility is r2 = -3 and r3 = 1.

Therefore, we have:

k = r1r2 + r1r3 + r2r3 = 1(-3) + 1(1) + (-3)(1) = -5

Therefore, the value of integer k is -5.

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The work done to lift the bucket out of the well is:

Work = 103 pounds × 60 feet = 6180 foot-pounds.

To find the average value of the function f(x) = √x on the interval [3.14/4], we need to evaluate the definite integral of the function over that interval and divide it by the length of the interval.

The average value of f(x) on the interval [a, b] is given by:

Avg = (1/(b - a)) * ∫[a to b] f(x) dx

In this case, the interval is [3.14/4]. Evaluating the integral, we have:

Avg = (1/(3.14/4 - 3.14/4)) * ∫[(3.14/4) to (3.14/4)] √x dx

   = (1/(0)) * 0

   = undefined

Since the length of the interval is zero, the average value of the function on this interval is undefined.

Regarding the work done to lift the 70 pound bucket of water up a 60-foot deep well using a chain that weighs 0.55 pounds per foot, we can calculate it using the formula:

Work = Force × Distance

The force required to lift the bucket is the weight of the bucket plus the weight of the chain. The weight of the bucket is 70 pounds, and the weight of the chain is given by:

Weight of chain = (0.55 pounds/foot) × (60 feet) = 33 pounds

Therefore, the total force is 70 pounds + 33 pounds = 103 pounds.

The distance over which the force is applied is the depth of the well, which is 60 feet.

Hence, the work done to lift the bucket out of the well is:

Work = 103 pounds × 60 feet = 6180 foot-pounds.

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Answer:

It's B

Step-by-step explanation:

Given that we have the graph of f(x), we want to see which one is the graph of its inverse. i just had that question and i got a 100 on it

The probability that exactly two of the students are juniors is given as follows:

0.270 = 27%.

The mass probability formula is presented as follows:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

The values of these parameters for this problem are given as follows:

\(N = 60, n = 4, k = 18\)

Hence the probability that exactly two of the students are juniors is calculated as follows:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,60,4,18) = \frac{C_{18,2}C_{42,2}}{C_{60,4}} = 0.270\)

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Answer:

50*

Step-by-step explanation:

1a) Complementary solution: y(t) = c₁ + c₂e^t + c₃e^(-t) + c₄cos(t) + c₅sin(t)

1b) Particular solutions:

(i) yp(t) = (1/2)e^t

(ii) yp(t) = (1/5)t^2 + (2/15)

(iii) yp(t) = [(3/20)t^2 + (1/4)t + C₁]cos(2t) - [(3/40)t^3 + (1/8)t^2 + C₂]sin(2t)

2) Linear differential equation: y''(x) + 4y'(x) + 5y(x) = 0

1a) To find the complementary solution of y(5) - y(3) = f(t), we need to find the homogeneous solution of the differential equation y(5) - y(3) = 0. We assume that y(t) = e^(rt) and substitute it into the differential equation to obtain the characteristic equation:

r^5 - r^3 = 0

r = 0, ±1

Since there are three distinct roots, the complementary solution is of the form:

y(t) = c₁ + c₂e^t + c₃e^(-t) + c₄cos(t) + c₅sin(t)

where c₁, c₂, c₃, c₄, and c₅ are constants.

1b) Using the method of undetermined coefficients, we can determine the particular solution of y(5) - y(3) = f(t) for each of the given functions f(t):

(i) f(t) = e^t

Assuming yp(t) = Ae^t, we obtain:

A(e^(5t) - e^(3t)) = e^t

A = 1/2

yp(t) = (1/2)e^t

(ii) f(t) = 2t^2

2A(t^5 - t^3) + 6B(t^3 - t) + 6C(t^2 - 1) = 2t^2

A = 1/5, B = 0, C = 2/15

yp(t) = (1/5)t^2 + (2/15)

(iii) f(t) = (3t+2)cos(2t)

A''(t)cos(2t) + B''(t)sin(2t) + 4A'(t)sin(2t) - 4B'(t)cos(2t) = (3t+2)cos(2t)

A(t) = (3/20)t^2 + (1/4)t + C₁

B(t) = -(3/40)t^3 + (1/8)t^2 + C₂

yp(t) = [(3/20)t^2 + (1/4)t + C₁]cos(2t) - [(3/40)t^3 + (1/8)t^2 + C₂]sin(2t)

2) The given general solution is:

y(x) = C₁e^x + C₂xe^x + C₃e^(-x)cos(2x) + C₄e^(-x)sin(2x)

y'(x) = C₁e^x + C₂(e^x + xe^x) - C₃e^(-x)sin(2x) + C₄e^(-x)cos(2x)

y''(x) = C₁e^x + C₂(2e^x + xe^x) + C₃e^(-x)cos(2x) - C₄e^(-x)sin(2x)

(C₁ + C₂ + C₃ + C₄)e^x + (2C₂ + C₂x - C₃sin(2x) + C₄cos(2x))e^x + (-C₁ + 2C₂ - C₃cos(2x) - C₄sin(2x))e^(-x) = 0

Since this equation must hold for all values of x, we obtain the following system of equations:

C₁ + C₂ + C₃ + C₄ = 0

2C₂ - C₁ - C₃cos(2x) - C₄sin(2x) = 0

C₂x - C

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Tthe population of the colony after 2 hours is 64a

From the question, we have the following parameters that can be used in our computation:

Rate = doubles every 20 minutes

Represent the initial population with a

So, we have the following representation

f(t) = a(2)^t

Where t is the number of 20 minutes in the time

The time is given as 2 hours

So, we have

t = 2 hours/20 minutes

Evaluate

t = 6

The function becomes

f(t) = a(2)^6

Evaluate

f(t) = 64a

hence, the population is 64a

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Answer:

2x-2  -2 is the y intercept and the 2x is the rate of change its easy lol

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

The inequality can be used to determine the number is 0.4x > x/2 - 15

The term inequality means the unequal relationship between the two or more expressions.

Here we have given that Forty percent of a number is greater than one-half the number decreased by 15.

And we need to find the number that is used to determine the inequality.

While we looking into the given question, let us consider x be that unknown  number.

Then based on the given statement, we have divide it into two parts.

First, forty percent of the number and it can be written as 40%x or 0.4x.

Next is one-half the number is 1/2 x or x/2

When we combine the whole statement,

Then we get the inequality,

=> 0.4x > x/2 - 15

Therefore option (c) is correct.

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Step-by-step explanation:

let the three numbers be

(a-d) ,(a) and (a+d)

so we have the sum as

a-d+a+a+d=21

3a=21

a=7..............(1)

we have d product as

(a-d)(a)(a+d)=231

(a²-d²)(a)=231

a³-ad²=231..........(2)

subtitue (1) in (2)

we have

(7)³-(7)d²=231

343-7d²=231

343-231=7d²

112=7d²

d²=112/7

d²=16

d=±4

when d=-4

the first number is

a-d=7-(-4)=7+4=11

second number is

a=7

third number

a+d=7+(-4)=7-4=3

when d=4

the first number is

a-d=7-4=3

the second number is

a=7

the third number is

a+d=7+4=11

As per the trigonometric substitution the value of the integrals are

a) ∫ x² + 4 / x² dx is 2 tan θ

b) ∫ (16 - 9x²) / x² dx is (4/3) sec θ

c) ∫ (5x² - 3) / x² dx is (1/√3)tanθ

Let's take a look at the given integrals:

a) ∫ x² + 4 / x² dx

For this integral, we can use the trigonometric substitution x = 2tanθ. This substitution simplifies the integral and allows us to solve it using trigonometric identities.

b) ∫ (16 - 9x²) / x² dx

To solve this integral, we can use the trigonometric substitution x = (4/3)secθ. This substitution simplifies the expression under the integral sign and allows us to use trigonometric identities to solve the integral.

c) ∫ (5x² - 3) / x² dx

For this integral, we can use the trigonometric substitution x = (1/√3)tanθ. This substitution simplifies the integral and allows us to use trigonometric identities to solve it.

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Answer:

9x^3/y^3

Step-by-step explanation:

Hope this helps!

Answer:

measure the area inside of the shapes, and multiply it. online answers better than me sorry.

Step-by-step explanation:

Answer: Ask teacher

Step-by-step explanation:

Answer:

Don't want any but here's your answer

Step-by-step explanation:

He spends $165 on 20 gallons

Answer:14

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

60+72+55+80=267

267+58=325

325/5=65

Alejandro has completed the greatest portion of the race (65%).

The friend who has completed the greatest portion of the race is Alejandro, with 65% of the race completed. This is because 65% is greater than the other portions completed by the other friends: 3/5 (or 60%), 0.7 (or 70%), and 18/25 (or 72%). Therefore, Alejandro has completed the greatest portion of the race.

A portion of a race can refer to different distances depending on the race. For example, a marathon race is typically 26.2 miles long and can be divided into several different portions, such as the first 5 miles, the middle 8 miles, and the last 13.1 miles. In a shorter race such as a 5K or 10K, the portions may be shorter and more specific, such as the first quarter-mile or the second lap of the course.

Portions of a race are often used as checkpoints to help runners stay on pace and measure their progress during the race.

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Answer:

I think the answer is no because none of these are divisible by any of the numbers

The general solution of the given differential equation is

cos(x) y = [y ln|sec(x) + tan(x)| - C] x.

Therefore, we do not have any transient terms in the general solution

cos(x) dy dx (sin(x))y = 1.

Note: A transient solution is a solution of a differential equation that goes to zero as time goes to infinity.

The given differential equation is

cos(x) dy dx (sin(x))y = 1.

Here, the independent variable is x, and the dependent variable is y.To determine whether there are any transient terms in the general solution

cos(x) dy dx (sin(x))y = 1,

we need to find its general solution as follows:Integrating the given differential equation, we have:

∫(sin(x))y dy = ∫sec(x) dx

On integrating the above expression, we get:

(cos(x)/y) + C = ln|sec(x) + tan(x)|

Here, C is the constant of integration.

Now, we can express the general solution of the given differential equation as follows:

cos(x) y = [y ln|sec(x) + tan(x)| - C] x  

(multiplying both sides by x)

Therefore, the general solution of the given differential equation is

cos(x) y = [y ln|sec(x) + tan(x)| - C] x.

Therefore, we do not have any transient terms in the general solution

cos(x) dy dx (sin(x))y = 1.

Note: A transient solution is a solution of a differential equation that goes to zero as time goes to infinity.

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Answer:

V = 50.3 in ^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the radius is 2 and the height is 4

V = (3.14) * (2)^2 * 4

V =50.24

Rounding to the nearest tenth

V = 50.3 in ^2

Answer:

x = 9.27 cm

Volume = 289.2 cm³

Step-by-step explanation:

SA = Surface Area

SA = 229.2 cm²

P = Perimeter of Base

P = 3(6)

P = 18 cm

H = Height of Solid

H = x

A = Area of Base(Equilateral Triangle)

A = 6²√3 / 4

A = 36√3 / 4

A = 9√3

A = 9(1.732)

A = 31.176

A = 31.2 cm²

SA = Surface Area

SA = PH + 2A

229.2 = 18x + 2(31.2)

229.2 = 18x + 62.4

229.2 - 62.4 = 18x

166.8 = 18x

9.266 = x

9.27 = x

x = 9.27 cm

V = Volume

V = AH

V = 31.2(9.27)

V = 289.224

V = 289.2 cm³