Carlos ran 25 miles in 5 days. He ran the same distance each day. Write and solve an equation to determine the number of miles he ran each day. O 5x = 25 --> x = 5 miles each day O 25 + 5 = x --> X = 30 miles each day O x + 5 = 25 --> X = 20 miles each day 0 25x = 5 --> X = 1/5 mile each day

Answer:

Step-by-step explanation:

A = l*w

13.5 * 10.67 = 144.045 or 144

Hope that helps!

133.24 ____ 133.25

133.24 stands for one hundred and thirty three two tenth and four hundredth

133.25 stands for one hundred and thirty three two tenth and five hundredth

five hundredth is greater than four hundredth

133.24 < 133.25

Answer:

the point of view is known as compromise D

Answer:

An agreement that is halfway between two opposing points of view is known as: D. Compromise

To find the sale price of a bottle of perfume after a 13.4% discount, we need to first calculate the amount of the discount, and then subtract that amount from the original price.

The discount rate is 13.4%, which can be written as a decimal as 0.134. To calculate the amount of the discount, we can multiply the original price by the decimal equivalent of the discount rate:

Discount amount = 0.134 x $72.45

Discount amount = $9.72

This means that the discount on the bottle of perfume is $9.72. To find the sale price of the perfume, we can subtract this amount from the original price:

Sale price = $72.45 - $9.72

Sale price = $62.73

Therefore, the sale price of the bottle of perfume is $62.73. This is the amount that customers would need to pay during the clearance sale, after the 13.4% discount has been applied.

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Answer:

1.2

Step-by-step explanation:

Output of f, which also means f(x), when x = -6 is 1.2.

Using the graph given, this implies that, when x = -6, the corresponding value of f(x) will give us 1.2.

Thus:

f(-6) = 1.2 =>> (-6, 1.2).

Hello,

2 points of the line: (2,0) and (0,3)

\(\Delta\ y=3-0=3\\\Delta\ x=0-2=-2\\\dfrac{\Delta\ y}{\Delta\ x} =\dfrac{-3}{2} \\\\y-0=\dfrac{-3}{2}*(x-2)\\\\\boxed{y=-\dfrac{3x}{2}+3}\\\)

Hey there!

The formula to find the perimeter of a rectangle is "P=2(l+w)".

Hope this helps!

Have a great day! :)

Answer:

formula to find the perimeter of rectangle is

hope it helps

stay safe healthy and happy.

Answer:

The answer is below

Step-by-step explanation:

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 270 minutes and a standard deviation of 50 minutes. a) What is the probability that a battery lasts more than four hours b) What are the quartiles (the 25% and 75% values) of batterylife? c) c) What value of life in minutes is exceeded with 95% probability? (Roundthe answer to the nearest integer.)

Solution:

The z score is used to determine by how many standard deviations the mean is above or below the raw score. If the z score is positive then the raw score is above the mean while if the z score is negative then the raw score is below the mean. The z score is given by:

\(z=\frac{x-\mu}{\sigma}\\ \\\mu=mean, \sigma=standard\ deviation\)

Given μ = 270 minutes, σ = 50 minutes

a)

P(x > 4 hours) = P(x > 240 minutes)

\(z=\frac{x-\mu}{\sigma}\\ \\z=\frac{240-270}{50} =-0.6\)

From the distribution table, P(x > 240) = P(z > -0.6) = 1- P(z < 0.6) = 1 - 0.2743 = 0.7257

c)  P(z > z*) = 0.95

1 - P(z < z*) = 0.95

P(z < z*) = 0.05

This corresponds to a z score of -1.645

\(z=\frac{x-\mu}{\sigma}\\ \\-1.645=\frac{x-270}{50} \\\\x=187.75 \ minutes\)

For 75%, P(z < z*) = 0.75

This corresponds to a z score of 0.68

\(z=\frac{x-\mu}{\sigma}\\ \\0.68=\frac{x-270}{50} \\\\x=304 \ minutes\)

c) For 25%, P(z < z*) = 0.25

This corresponds to a z score of -0.67

\(z=\frac{x-\mu}{\sigma}\\ \\-0.67=\frac{x-270}{50} \\\\x=236.5 \ minutes\)

Answer:

56 minute 40 seconds

Explanation:

unit rate: 6 meters per minute

The elevator starts from 20 m below ground level.

So, in total have to cover distance = 20 + 320 = 340 meter

Time taken = distance/speed

                   = 340/6

                   = 56.67 minute

                   ≈ 56 minute 40 seconds

The Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.

A polynomial is  described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:

We get the derivatives :

pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....

f(x) = cos(x)

f'(x) = -sin(x)

f''(x) = -cos(x)

f'''(x) = sin(x)

We the  evaluate these derivatives at x = pi/2:

f(pi/2) = cos(pi/2) = 0

f'(pi/2) = -sin(pi/2) = -1

f''(pi/2) = -cos(pi/2) = 0

f'''(pi/2) = sin(pi/2) = 1

We substitute  these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:

the Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.

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Answer: 51 yards

Step-by-step explanation:

To know how far the football kicked, you would need to know when it hits the ground, meaning the height, y=0. You would find the roots of the equation.

y=-0.03x²+1.53x

0=-0.03x²+1.53x

This equation is hard to factor, but when you plug it into the quadratic equation, you would get x=0 and x=51. The problem states that x is the horizontal distance in yards. Therefore, the football was kicked 51 yards.

Answer:

51 yards

Step-by-step explanation:

Answer: In that picture the slope is increasing

Step-by-step explanation: positive rise and positive run (uphill from left to right)

Check the picture below.

notice, sides are equal, opposite sides are perpendicular to their counterparts.

The value for each greatest integer function is:

[55.9] = 55

[55.001] = 55

[0.65] = 0

[-34.11] = -35

[16(3/14)] = [227/14] = [16.214] = 16

[-8.21] = -9

[19] = 19

[-0.45] = -1

[-8(1/2)] =[-8.05] = -9

[2/3] = [0.67] = 0

We have,

The greatest integer function, denoted as [x] gives the largest integer that is less than or equal to x.

So,

We can create the inequalities as:

55 ≤ 55.9 ≤ 56

[55.9] = 55

55 ≤ 55.001 ≤ 56

[55.001] = 55

0 ≤ 0.65 ≤ 1

[0.65] = 0

-35 ≤ -34.11 ≤ -33

[-34.11] = -35

16 ≤ 16.214 ≤ 17

[16(3/14)] = [227/14] = [16.214] = 16

Similarly,

[-8.21] = -9

[19] = 19

[-0.45] = -1

[-8(1/2)] =[-8.05] = -9

[2/3] = [0.67] = 0

Thus,

The value for each greatest integer function is given above.

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Answer:

30 60 90

Step-by-step explanation:

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.

To find out how many months it takes to pay off the credit card and the total amount paid including interest, we can use the following steps:

Step 1: Calculate the monthly interest rate

Divide the annual percentage rate (APR) by 12 to get the monthly interest rate.

Monthly interest rate = 14.5% / 12 = 0.145 / 12 = 0.01208 (rounded to 5 decimal places)

Step 2: Set up the equation for the number of months

Let's denote the number of months it takes to pay off the card as 'n'. The monthly payment is $1,200.00, and the initial balance is $3,287.90. The monthly interest rate is 0.01208. The equation for the number of months can be written as:

(1) $3,287.90 ×\((1 + 0.01208)^n\) - $1,200.00 ×\([(1 + 0.01208)^n\) - 1] = 0

Step 3: Solve the equation

To find the value of 'n', we need to solve equation (1). However, solving it algebraically can be complex. Instead, we can use numerical methods like trial and error, or we can use a spreadsheet or a calculator to find the solution.

Using a spreadsheet or a calculator, we can input the values and increment 'n' until we find the point where the equation equals zero.

After performing the calculations, it is determined that it takes approximately 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.

Therefore, the answer to the original question is that it takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.

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As per the unitary method, each piece is 3.25 meters long by dividing the total length of the ribbon by the number of pieces.

Larry has cut a ribbon into 8 equal pieces. The total length of the ribbon is 26 m. We need to find out the length of each piece of the ribbon.

To do this, we can use the unitary method. We know that the ribbon is divided into 8 equal pieces, so each piece is 1/8th of the total length of the ribbon.

Therefore, we can find the length of each piece by dividing the total length of the ribbon by 8:

Length of each piece = Total length of ribbon / Number of pieces

Length of each piece = 26 m / 8

Length of each piece = 3.25 m

So, each piece of the ribbon is 3.25 meters long.

We used the unitary method by finding the value of one unit (1/8th of the ribbon) and then using it to calculate the value of other units (the length of each piece).

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Answer:

-42/11

Step-by-step explanation:

x = y - 8

5x = 6 - 6y

So now solve the system of equations, divide everything in the second equation by 5 to get it to x = 6/5 - 6y/5

Now...

x = y - 8

x = 6/5 - 6y/5

Now substitute first equation into the second and x is gonna be -42/11 or the first number

Answer:

x = 27 , ∠ EAF = 27°

Step-by-step explanation:

∠ GAF = 90° , then

∠ GAC + ∠ CAF = ∠ GAF , that is

x + 63 = 90 ( subtract 63 from both sides )

x = 27

∠ DAE = 90°

since CD is a straight angle of 180° , then

∠ CAE = 90° , so

∠ CAF + ∠ EAF = ∠ CAE , that is

63° + ∠ EAF = 90° ( subtract 63° from both sides )

∠ EAF = 27°

Answer:131290

Step-by-step explanation:13129*100/10=131290

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

12.87, 12.5  is closer to 13

12.08, 12.13  is closer to 12

Step-by-step explanation:

Least to Greatest:

12

13

Answer:

400 miles each day

Step-by-step explanation:

You have 1600 miles divided into four days.

1600 / 4

We can use the basic fact that multiplying a number by ten simply means shifting everything to the left, for example 2 x 10 = 20, we just shifted 2 to the left and inserted a 0.

So for this problem, we can do the same. Divide 1600 by 100, or 10 x 10, then divide by 4.

1600/16 = 100

16/4 = 4.

Now, since we divided by ten twice before, we can get the right answer by multiplying by ten twice.

4 x 10 = 40

40 x 10 = 400

Answer:

The circumference of a circle is calculated using the formula: C = πd, where C represents the circumference and d represents the diameter of the circle.

In this case, the diameter of the circle is given as 24 inches.

Using the formula, we can substitute the values:

C = πd

C = 3.14 * 24

C ≈ 75.36 inches

Therefore, the circumference of a circle with a diameter of 24 inches (and using π = 3.14) is approximately 75.36 inches.

Step-by-step explanation:

Answer:

Step-by-step explanation:

- A cylindrical fish tank can hold approximately 502.40

cubic inches of water. If the height of the fish tank is

10 inches, what is the radius of the tank? Use 3.14 for

the answer, 6.86

The correct answer is (a). P′(2005) represents the growth rate (in people per year) of the population in 2005.

This is because P′(t) is the derivative of P(t), which measures the rate of change of P(t) concerning t.

In other words, P′(t) tells us how fast the population is changing at a given year t.

The units of P′(t) are the same as the units of P(t) divided by the units of t, which are millions of people per year.

Therefore, P′(2005) gives the number of millions of people by which the population changed in 2005. To find the actual number of people, we would have to multiply P′(2005) by one million.

The derivative can help us analyze the behavior of the population function, such as it's increasing or decreasing intervals, its maximum or minimum values, and its concavity or inflection points. The derivative can also help us model and predict the future trends of the population based on the current data and assumptions.

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The steps peter could use in solving the quadratic equation is by applying the quadratic formula; x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

8x² + 16x + 3 = 0

using Quadratic formula

The following steps are involved

\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

\(x = \frac{ -16 \pm \sqrt{16^2 - 4(8)(3)}}{ 2(8) }\)

\(x = \frac{ -16 \pm \sqrt{256 - 96}}{ 16 }\)

\(x = \frac{ -16 \pm \sqrt{160}}{ 16 }\)

\(x = \frac{ -16 \pm 4\sqrt{10}\, }{ 16 }\)

\(x = \frac{ -16 }{ 16 } \pm \frac{4\sqrt{10}\, }{ 16 }\)

\(x = -1 \pm \frac{ \sqrt{10}\, }{ 4 }\)

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

\(x = -0.209431\)

or

\(x = -1.79057\)

Therefore, the steps peter could follow will give the result

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

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Answer: (4, 3)

Step-by-step explanation:

To solve the system of equations using elimination, we can manipulate the equations to eliminate one variable and solve for the other.

Let's start with the given system of equations:

Equation 1: 4x + 4y = 28

Equation 2: 3x + y = 15

To eliminate the y variable, we can multiply Equation 2 by 4 to make the coefficients of y in both equations the same:

4 * (3x + y) = 4 * 15

12x + 4y = 60

Now we have two equations with the same coefficient for y:

Equation 1: 4x + 4y = 28

Equation 3: 12x + 4y = 60

We can subtract Equation 1 from Equation 3 to eliminate the y variable:

Equation 3 - Equation 1:

(12x + 4y) - (4x + 4y) = 60 - 28

12x - 4x = 32

8x = 32

x = 4

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use Equation 2:

3x + y = 15

3(4) + y = 15

12 + y = 15

y = 15 - 12

y = 3

Therefore, the solution to the system of equations is x = 4 and y = 3. So the answer is (4, 3).

Answer:

(4, 3)

Step-by-step explanation:

i got it right on my quiz