if range of the function f(x) = 3x+2 is {5,8,11,14}, find the domain of the function

Therefore, Chase ran 49/8 miles each day.

To find out how many miles Chase ran each day, we need to divide the total distance he ran (36 3/4 miles) by the number of days (6 days).

First, let's convert the mixed number into an improper fraction. 36 3/4 is equal to (4 * 36 + 3)/4 = 147/4.

Now, we can divide 147/4 by 6 to find the distance he ran each day:

(147/4) / 6 = 147/4 * 1/6 = (147 * 1) / (4 * 6) = 147/24.

Therefore, Chase ran 147/24 miles each day.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 147 and 24 is 3.

So, dividing 147 and 24 by 3, we get:

147/3 / 24/3 = 49/8.

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Chase ran a total of 36 3/4 miles over six days. To find out how many miles he ran each day, simply divide the total distance (36.75 miles) by the number of days (6). The result is approximately 6.125 miles per day.

To solve this problem, you simply need to divide the total number of miles Chase ran by the total number of days. In this case, Chase ran 36 3/4 miles over six days. To express 36 3/4 as a decimal, convert 3/4 to .75. So, 36 3/4 becomes 36.75 miles.

Now, we can divide the total distance by the total number of days:

36.75 miles ÷ 6 days = 6.125 miles per day. So, Chase ran about 6.125 miles each day.

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Answer:

255,000,000m^2

Step-by-step explanation:

Let 5:12:17:25 be 5x, 12x, 17 x, 25x respectively

So

Perimeter of quadrilateral=5x+12x+17x+25x

590m=59x

590m/59=x

10m=x

So now value

5x= 5*10 =50

12x= 12*10 =120

17x= 17*10 =170

25x= 25*10 =250

Now

Area of quadrilateral=50m*120m* 170m* 250m

=255,000,000m^2

Step-by-step explanation:

if I understand you correctly the sides are in a

5 : 12 : 17 : 25 ratio.

a ratio is basically a fraction. but instead of the denominator telling us the structure of the whole (e.g. 2/5 tells us that the whole is split into 5 equal parts), a ratio tells us this by the sum of its elements :

5 : 12 : 17 : 25

means that the whole perimeter of the quadrilateral has

5 + 12 + 17 + 25 = 59 equal parts.

since the perimeter is 590 m, we know with 59 equal parts, that one part is 590/59 = 10 m.

so, the sides are

50 m, 120 m, 170 m, 250 m

but for the area of the quadrilateral there is at least the information of one angle missing.

to have just the 4 side lengths is not enough. these sides can still have all kinds of angles between them, which creates different areas.

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

probability that a player wins after playing the game once = 5/9

Step-by-step explanation:

To solve this, we will find the probability of the opposite event which in this case, it's probability of not winning and subtract it from 1.

Since, we are told that there are 2 fair six sided die thrown at the same time and that he receives a five or a one on either die ;

Probability of not winning, P(not win) = 4/6.

Thus;

P(winning) = 1 - ((4/6) × (4/6))

P(winning) = 1 - 4/9 = 5/9

Answer:

Let B = the brothers age now

Let L = Lisa's age now

Then today:

L = 7B

And three years from now, Lisa's current age plus 3 equals 4 times the brothers age plus 3 represented by the following formula

L+3 = 4(B+3)

Now we can substitute the value of L in the first formula for L in the second formula

7B + 3 = 4(B+3)

So the answer is C

Step-by-step explanation:

Answer:

hope it helped you

Step-by-step explanation:

in image

Determine the sum of each geometric series.

Thus sums can be arranges from smallest to largest as,

Answer:

1) the first choice

2) the first choice

Step-by-step explanation:

1) "<" means less than, so if she wants to spend less than $300 that's your answer

2) "5x" means 5 times however many hours she chooses to have her carpet cleaned, so this is correct as well as the less than 300.

hope this helps <3

Answer:

Would you mind including the ratios in the comments?

You didn't post any material to solve.

Answer:

4 IS THE ANSWER MATE

Step-by-step explanation:

Absolutely, I can do that!

Let's take a look at each statement:

1) f(x) has a y-intercept at (0,2)

To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:

f(0) = -log(0+4) + 2

f(0) = -log(4) + 2

f(0) = -0.602 + 2

f(0) = 1.398

Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.

2) The function -f(x) has a y-intercept at (0,2)

Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.

3) As x approaches positive infinity, the function f(x) approaches negative infinity.

The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.

4) As x approaches -4 from the right, the function f(x) approaches negative infinity.

As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.

In summary, statements (1) and (2) are false, while statements (3) and (4) are true.

To determine the probabilities, we need to consider the number of favorable outcomes for each situation divided by the total number of possible outcomes.

1.Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)

2. Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7%

3. Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)

4.Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)

1. Salmon chooses a composite number, a cool color (G, B, I, or V), and an A:

a) Composite numbers between 1 and 100: There are 57 composite numbers in this range.

b) Cool colors (G, B, I, or V): There are 4 cool colors.

c) The letter A: There is 1 A in "INDIANA."

Total favorable outcomes: 57 (composite numbers) * 4 (cool colors) * 1 (A) = 228

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 1 (possible letter) = 700

Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)

2. Federico chooses a prime number, a color starting with a vowel (E or I), and a consonant:

a) Prime numbers between 1 and 100: There are 25 prime numbers in this range.

b) Colors starting with a vowel (E or I): There are 2 colors starting with a vowel.

c) Consonants in "INDIANA": There are 4 consonants.

Total favorable outcomes: 25 (prime numbers) * 2 (vowel colors) * 4 (consonants) = 200

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 5 (possible letters) = 3500

Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7% (rounded to one decimal place)

3. Either chooses a number divisible by 7 or 8, any color, and a vowel:

a) Numbers divisible by 7 or 8: There are 24 numbers divisible by 7 or 8 in the range of 1 to 100.

b) Any color: There are 7 possible colors.

c) Vowels in "INDIANA": There are 3 vowels.

Total favorable outcomes: 24 (divisible numbers) * 7 (possible colors) * 3 (vowels) = 504

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 3 (possible letters) = 2100

Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)

4. Either chooses a number divisible by 5 or 4, blue or green, and L or N:

a) Numbers divisible by 5 or 4: There are 45 numbers divisible by 5 or 4 in the range of 1 to 100.

b) Blue or green colors: There are 2 possible colors (blue or green).

c) L or N in "INDIANA": There are 2 letters (L or N).

Total favorable outcomes: 45 (divisible numbers) * 2 (possible colors) * 2 (letters) = 180

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 2 (possible letters) = 1400

Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)

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Approximately 0.456 hours (or about 27.36 minutes) elapsed before the body was found.

To solve this problem, we can use Newton's Law of Cooling, which states that the rate of change of temperature of an object is proportional to the difference between its temperature and the surrounding temperature.

Let's denote T(t) as the core temperature of the body at time t, and T_s as the surrounding temperature (which is 70 F in this case).

According to the problem, at time t = 0, the core temperature of the body is T(0) = 98.6 F. One hour later, at t = 1, the core temperature is T(1) = 80 F.

Using Newton's Law of Cooling, we can set up the differential equation:

dT/dt = k(T - T_s)

where k is the proportionality constant.

Substituting the given values at t = 0 and t = 1, we can find the specific value of k.

At t = 0: dT/dt = k(98.6 - 70)

At t = 1: dT/dt = k(80 - 70)

Integrating both sides of the equation, we get:

∫ dT/(T - T_s) = ∫ k dt

Applying the natural logarithm, we have:

ln|T - T_s| = kt + C

Simplifying the equation, we get:

T - T_s = Ce^(kt)

Substituting the values at t = 0, we have:

98.6 - 70 = Ce^(k * 0)

Solving for C, we get:

C = 28.6

Now we can rewrite the equation as:

T - 70 = 28.6e^(kt)

At t = 1, we have:

80 - 70 = 28.6e^(k * 1)

Simplifying the equation, we get:

10 = 28.6e^k

Dividing both sides by 28.6, we have:

e^k = 10/28.6

Taking the natural logarithm of both sides, we get:

k = ln(10/28.6)

Now, we can use this value of k to determine how many hours elapsed before the body was found.

We want to find the value of t when T(t) = 85. Substituting this value into our equation, we have:

85 - 70 = 28.6e^(ln(10/28.6) * t)

15 = 28.6(10/28.6)^t

Dividing both sides by 28.6, we get:

15/28.6 = (10/28.6)^t

Taking the natural logarithm of both sides, we have:

ln(15/28.6) = t * ln(10/28.6)

Dividing both sides by ln(10/28.6), we can solve for t:

t = ln(15/28.6) / ln(10/28.6)

Calculating this expression, we find:

t ≈ 0.456 hours

Therefore, approximately 0.456 hours (or about 27.36 minutes) elapsed before the body was found.

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The solutions to the given quadratic equation are x=[5+13i]/14 or x=[5-13i]/14.

Given that, the quadratic formula is x= [-(-5)±√((-5)²-4×7×7)]/2×7.

Here, x= [5±√(25-196)]/14

x= [5±√(-171)]/14

x=[5±13i]/14

x=[5+13i]/14 or x=[5-13i]/14

Now, (x-(5+13i)/14) (x-(5-13i)/14)=0

Therefore, the solutions to the given quadratic equation are x=[5+13i]/14 or x=[5-13i]/14.

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Answer

35 (3 + x)

Step-by-step explanation:

Answer:

(D) \(3 \pm i\sqrt{3}\)

Step-by-step explanation:

We can solve this using the quadratic formula, where a is 1, b is -6, and c is 12.

\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\frac{-(-6)\pm\sqrt{6^2-4\cdot1\cdot12}}{2\cdot1}\\\\\frac{6\pm\sqrt{36-48}}{2}\\\\\frac{6\pm\sqrt{-12}}{2}\\\\\frac{6\pm i\sqrt{12}}{2}\\\\3\pm i\sqrt{3}\\\\\)

Hope this helped!

Answer:

its the fourth graph (i took the test)

Answer:

FV= $1,545

Step-by-step explanation:

Giving the following information:

Elena deposits $1,500 in a savings account that earns 3.0% simple interest per year.

To calculate the nominal value of the account after one year, we need to use the following formula:

FV= (P*r*t) + P

FV= future value

P= principal

r= interest rate

t= 1

FV= (1,500*0.03*1) + 1,500

FV= $1,545

Answer:The answer is below

Step-by-step explanation:

The bottom of a river makes a V-shape that can be modeled with the absolute value function, d(h) = ⅕ ⎜h − 240⎟ − 48, where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet). A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 20 feet below the surface. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed

Answer:

To solve the problem, the depth of the water would be equated to the position of the river bottom.

h is=380 or h=100

Step-by-step explanation:

Answer:

73 numbers

Step-by-step explanation:

36²

=36 × 36

=1,296

37²

=37 × 37

=1,369

The total number that lies between 36² and 37² = 37² - 36²

=1,369 - 1,296

= 73 numbers

This is to say that, there are 73 numbers between 36² (1,296 ) and 37² ( 1,369)

Let's denote the price of a student ticket as "s" and the price of an adult ticket as "a".

From the information given, we can set up the following system of equations:

Equation 1: 10s + 20a = 200 (from the first event)

Equation 2: 20s + 25a = 280 (from the second event)

To solve this system of equations, we can use any method, such as substitution or elimination. In this case, let's use the elimination method.

Multiply Equation 1 by 2 to make the coefficients of "s" in both equations equal:

20s + 40a = 400

Now, subtract Equation 2 from this new equation:

(20s + 40a) - (20s + 25a) = 400 - 280

15a = 120

Divide both sides of the equation by 15:

a = 120/15

a = 8

Now, substitute the value of "a" back into Equation 1 to solve for "s":

10s + 20(8) = 200

10s + 160 = 200

10s = 200 - 160

10s = 40

s = 40/10

s = 4

Therefore, the price of one student ticket is $4, and the price of one adult ticket is $8.

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its lonmg.answer

Step-by-step explanation:

Answer:

A quadratic equation is an equation of the second degree.

Step-by-step explanation:

The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

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The number of cows needed to satisfy the beef appetite would be 5263

With an average yield of 570 pounds (258.1 Kg.) of prepared beef per cow, we need to determine how many people can be fed from this amount. The number of people fed per cow can vary depending on various factors such as portion sizes and individual dietary preferences. Assuming a reasonable estimate, let's consider that one pound (0.45 Kg.) of prepared beef can feed about three people.

To find the number of cows needed to satisfy the beef appetite for New York City's population of approximately 9,000,000 people, we divide the population by the number of people fed by one cow. Thus, the calculation becomes 9,000,000 / (570 pounds x 3 people/pound).

After simplifying the equation, we get 9,000,000 / 1710 people, which equals approximately 5,263 cows. However, it's important to note that this is a rough estimate and does not consider factors such as variations in consumption patterns, distribution logistics, or other sources of meat supply. Additionally, individual dietary choices and preferences may result in different consumption rates. Therefore, this estimate serves as a general indication of the number of cows needed to satisfy the beef appetite for New York City's population.

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The balance in Adam's account at the end of June which has the credit card with an apr of 14.63% is $627.27.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

The Adam’s credit card has an Apr of 14.63%,The table below shows his use of that credit card over three months.

For the purchase add the previous balance and for payment subtract the previous balance. I have mentioned another column for remaining balance in the above table.

The total of this transaction when multiplied with number of days, we get the total balance, 56498.48.

Now the monthly average balance is,

\(m=\dfrac{56498.48}{90}\\m=627.76\)

Thus, the balance in Adam's account at the end of June which has the credit card with an Apr of 14.63% is near to $627.27.

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Adam’s balance at the end of June is $629.42.

The adjusted balance method is an accounting method that bases finance charges on the amount(s) owed at the end of the current billing cycle after credits and payments post to the account.

Balance at the end of April = 626.45 + 37.41 + 44.50 = $708.36

Interest levied on $708.36= 708.36* (14.63/12) * 1/100

Interest levied on $708.36 = $8.64

So, balance on May 1st= 708.36+ 8.64 = $717

Balance at the end of May = 717-65.50+24.89-104.77 = $571.62

Interest levied on $571.62 = $571.62 * (14.63/12) * 1/100

Interest levied on  $571.62=$6.97

So, balance on June 1st = $578.59

Balance at the end of June = 578.59-23.60 + 15+51.85 = $621.84

Interest levied on $621.84 = $621.84* (14.63/12) * 1/100

Interest levied on $621.84 =$ 7.58

So balance at the end of the june = 621.84 + 7.58 = $629.42

Therefore, Adam’s balance at the end of June is $629.42.

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The area of the surface generated by rotating the parametric curve about the x-axis is π/8.

To find the area of the surface generated by rotating the parametric curve about the x-axis, we can use the formula for the surface area of revolution:

\(A = \int\limits^a_b {2\pi y} \sqrt{(\frac{dx}{d\theta})^2+ (\frac{dy}{d\theta})^2} \, dx\)

In this case, the given parametric equations are:

\(x = cos^3\theta\\\\y = sin^3\theta\)

Let's calculate the derivatives of x and y with respect to θ:

\(\frac{dx}{d\theta} = -3cos^2\theta sin\theta\\\\\frac{dy}{d\theta} = 3sin^2\theta cos\theta\\\)

Now we can substitute these values into the surface area formula:

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{(-3cos^2\theta sin\theta)^2+ (3sin^2\theta cos\theta)^2} \, d\theta\)

Simplifying the expression inside the square root:

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^4\theta sin^2\theta+ 9sin^4\theta cos^2\theta} \, d\theta\)

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^2\theta sin^2\theta(cos^2\theta +sin^2\theta)} \, d\theta\)

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \sqrt{9cos^2\theta sin^2\theta} \, d\theta\)

\(A = \int_{0}^{\pi /2} {2\pi sin^3\theta} \quad 3cos^2\theta sin^2\theta \, d\theta\)

\(A = 6\pi \int_{0}^{\pi /2} {sin^4\theta} \quad cos^2\theta d\theta\)

Now, we can use a trigonometric identity to simplify the integral. The identity is:

\(Sin^2\theta = \frac{1-cos2\theta}{2}\)

Using this identity, we can rewrite the integral as:

\(A = 6\pi \int_{0}^{\pi /2} {(\frac{1-cos2\theta}{2})^2 } \quad cos^2\theta d\theta\)

Simplifying further:

\(A = 6\pi \int_{0}^{\pi /2} {(\frac{1+cos^22\theta-2cos2\theta}{4}) } \quad cos^2\theta d\theta\)

\(A = 3\pi /2\int_{0}^{\pi /2} {cos\theta-2cos2\theta cos\theta+\frac{1}{4} cos^3\theta} d\theta\)

Evaluating the limits of integration:

\(A = 3\pi /2[\frac{1}{2} sin\theta-\frac{1}{3} cos^3\theta+\frac{1}{12} cos^32\theta]^{\pi /2}_0\)

Evaluating =

A = π/8

Therefore, the area of the surface generated by rotating the parametric curve about the x-axis is π/8.

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Answer:

Approximately 16.67 liters concentration of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

Step-by-step explanation:

Let's denote the amount of the 6% solution as x liters and the amount of the 15% solution as y liters. We need to find the values of x and y that satisfy the conditions.

Since we want to make 30 liters of a 10% solution, we can set up the following equations:

Equation 1: x + y = 30 (total volume equation)

Equation 2: (0.06x + 0.15y) / 30 = 0.10 (concentration equation)

From Equation 1, we have x = 30 - y. Substituting this into Equation 2, we get:

(0.06(30 - y) + 0.15y) / 30 = 0.10

Simplifying the equation gives:

(1.8 - 0.06y + 0.15y) / 30 = 0.10

1.8 + 0.09y = 3

0.09y = 1.2

y ≈ 13.33

Substituting y back into Equation 1, we find:

x + 13.33 = 30

x ≈ 16.67

Therefore, approximately 16.67 liters of the 6% solution and approximately 13.33 liters of the 15% solution are required to make 30 liters of a 10% solution.

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Answer:

y=2/3x-2

Step-by-step explanation: