A daily workout plan involves a total of 40 minutes of running and swimming. Gregory burns 20 calories per minute of running (r) and 10 calories per minute of swimming (s). Create an equation to model this scenario. *

The electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.

The electric field is a vector field that represents the force experienced by a charged particle due to an electric charge distribution. It is a measure of the electric force per unit charge at a particular point in space. The electric field is defined as the negative gradient of the electric potential, which is the energy per unit charge that a charged particle would have at that point in space. The electric field can be used to calculate the force experienced by a charged particle in the presence of other charges, and is a fundamental concept in the study of electromagnetism.

The electric field force between two point charges is given by Coulomb's law:

F = k * (q₁ * q₂) / r²

where k is the Coulomb constant (8.99 x 10⁹ N m²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between the charges.

To calculate the work done by the electric field force, we need to find the force at the initial distance (0.30 m) and the final distance (1.05 m), and then subtract the work done at the initial distance from the work done at the final distance.

At a distance of 0.30 m, the force is:

F = k * (1.75 x 10⁻⁸ C)² / (0.30 m)² = 4.02 x 10⁻⁸ N

The work done at this distance is:

W = F * 0.30 m = 1.21 x 10⁻⁷ J

At a distance of 1.05 m, the force is:

F = k * (1.75 x 10⁻⁸ C)² / (1.05 m)² = 1.33 x 10⁻⁸ N

The work done at this distance is:

W = F * 1.05 m = 1.40 x 10⁻⁷ J

Finally, to find the total work done, we subtract the work done at the initial distance from the work done at the final distance:

W total = W final - W initial = 1.40 x 10⁻⁷ J - 1.21 x 10⁻⁷ J = 1.90 x 10⁻⁸ J.

Therefore, the electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.

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A prime number is defined as a natural number which is only and only divisible by 1 and itself.

Note that 72 and 106 are even numbers, so they will have at least one factor as 2, which is neither 1 nor the number itself. Therefore, 72 and 196 cannot be a prime number.

Now, consider that 141 has the sum of digits as 6 which is divisible by 3, so according to the divisible rule of 3, the number 141 is divisible by 3, which is neither 1 nor the number itself. Therefore, 141 cannot be a prime number.

The last choice 107 do not possess any factor other than 1 and 107, so the number 107 is referred as a prime number.

Thus, option D is the correct choice.

Answer: $15,000

Step-by-step explanation:

Given the following :

Percentage earned as commission = 20% of profit.

What is Graydon’s gross pay for the month.

Sales for the month = $350,000

Profit on sales for the month = $75,000

Graydon’s earning is 20% of the profit made :

Hence, Graydon's gross pay for the month :

20% of $75,000

= 0.2 × $75,000

= $15,000

Graydon’s gross pay for the month is $15,000

Answer:

  5π/6

Step-by-step explanation:

Subtract multiples of 2π until you find the angle in the desired range.

  41π/6 -36π/6 = 5π/6

The angle 5π/6 is co-terminal with 41π/6.

Answer:

43

Step-by-step explanation:

If X + 21 = 64

then subtract 64 by 21 and you get 43

Let x = number of weeks

Initial cost = $85

Cost per week = $18

Final cost = $155

An inequality that represents this situation is:

Then solve for x:

Answer: he needs to save 4 weeks to buy the skis

Answer:

25/4

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

-18 = -5x-(-2)

-18 = -5x+2

5x-18 = 2

5x = 2+18

5x = 20

\( \frac{5x}{5} = \frac{20}{5} \)

\(x = 4\)

Answer:

•They are congruent from what it looks like.

Congruent means that they are exactly of size and shape, and they show scale factors of 1.  

Hence the option A and C are correct.

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a. The distribution of X is a normal distribution.

b. The median giraffe height is also 19 feet.

c. The Z-score for a giraffe that is 22 foot tall is 3.

d. The probability that a randomly selected giraffe will be shorter than 18.9 feet tall is less than -0.1.

f. The 80th percentile represents the value below which 80% of the data falls.

a. The distribution of X is a normal distribution (or Gaussian distribution) with a mean of 19 feet and a standard deviation of 1 foot. This can be denoted as X ~ N(19, 1).

b. The median of a normal distribution is equal to its mean.

c. To find the Z-score for a giraffe that is 22 feet tall, we can use the formula: Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (22 - 19) / 1 = 3.

d. To find the probability that a randomly selected giraffe will be shorter than 18.9 feet tall, we need to calculate the area under the normal curve to the left of 18.9. This can be done using the Z-score and a standard normal distribution table or a calculator.

Alternatively, we can use the Z-score formula from the previous question. The Z-score for 18.9 feet can be calculated as Z = (18.9 - 19) / 1 = -0.1. We can then look up the corresponding probability in the standard normal distribution table or use a calculator to find the probability that Z is less than -0.1.

e. To find the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall, we need to calculate the area under the normal curve between these two values.

Again, we can use the Z-score formula to standardize the values and then find the corresponding probabilities using a standard normal distribution table or a calculator.

f. To find the height at the 80th percentile, we can use the standard normal distribution table or a calculator to find the Z-score that corresponds to the 80th percentile.

Once we have the Z-score, we can use the formula Z = (X - μ) / σ to solve for X. Rearranging the formula, we have X = Z * σ + μ. Plugging in the values for Z (obtained from the percentile) and μ (mean) and σ (standard deviation), we can calculate the height at the 80th percentile.

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Hello!

Let's solve:

 \(\dfrac{2}{5}(15x+40)} =6x+10\\\\\\\text{Multiply the '2/5' into the function inside the parentheses}\\\dfrac{2}{5} *15x + \dfrac{2}{5} *40=6x+10\\\\6x + 16 =6x+10\\\\\\\text{Subtract '6x' from both sides}\\6x + 16-6x=6x+10-6x\\16 = 10\)

Since 16 doesn't equal 10 ==> There are no solution

Hope that helps!

Answer:

alguien habla español

Step-by-step explanation:

Answer:

no i dont think so

Step-by-step explanation:

The probability of having at least 2 red balls in the 3 that I picked will be 1/3.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

I have 3 red balls, 3 blue balls, and 3 yellow balls in a crate. All out of 9 balls.

If the three balls are picked randomly, then the probability of having at least 2 red balls in the 3 that I picked will be given as,

P = 3/9

P = 1/3

The probability of having at least 2 red balls in the 3 that I picked will be 1/3.

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Answer:

the mode is 0.3

Step-by-step explanation:

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

hope this helps!!!!!!!!

Answer:

B. 1 inch = 0.5 miles

Step-by-step explanation:

trust

nằmbê nbdgghdbbfdgbffmythrgvfcbgfjhjgftry43rjfdgtrhbfregdbgfjh

Answer:

\(3x + y = - 17 - - - eqn(i) \\ 5x - 2y = 13 - - - eqn(ii) \\ by \: elimination \\ (2 \times eqn(i)) + eqn(ii) \\ (6 + 5)x + (2 - 2)y = ( - 34+ 13) \\ 11x = - 21\\ x = - \frac{21}{11} \\ substitute \: for \: x \: in \: eqn(i) \\ - \frac{ 63}{11} + y = - 7 \\ y = - 7 + \frac{63}{11} \\ y = - \frac{ 14}{11} \)

Answer:

area of triangle = 1/2 ×base×height

The reference angle for the angle with the measure 2x/3 is 54⁰

You should understand that a reference angle is the acute angle to a given angle.

The given angle is 2x/3

We should understand that since the angle has the variable x

= x + 2x/3 = 90⁰

Simplifying the fraction to have

(3x+2x)/3 = 90

Cross and multiply we have 5x=270⁰

Making x the subject

x= 270/5

x=54⁰

Therefore, the reference angle with the measure 2x/3 is = 54⁰

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Answer:

s

Step-by-step explanation:

First, calculate how many cents there are in 135 dollars by multiplying 135 by 100, and then divide that result by 5 cents to get the answer.

135 dollars x 100 cents

= 13,500 cents

13,500 cents / 5 cents

= 2,700 nickels

Answer:

65.44985

Step-by-step explanation:

V=πr2h 3=π·2.52·10  3≈65.44985

Answer:

The sequence is increasing by 5 at each step. So, we can write:

a1 = 30

a2 = 30 + 5 = 35

a3 = 30 + 25 = 40

a4 = 30 + 35 = 45

a5 = 30 + 4*5 = 50

We notice that the nth term is given by:

an = 30 + (n-1)5

So, the explicit formula for the nth term is:

an = 25n + 5

Answer:

f(1/3) = 9

Step-by-step explanation:

f(x) = 1/x + 2/x

f(1/3) = 1/(1/3) + 2/(1/3)

f(1/3) = 1(3) + 2(3)

f(1/3) = 3 + 6

f(1/3) = 9

Answer:

15

Step-by-step explanation:

Answer:

15 (this is an answer from maxcolon89)

Step-by-step explanation:

To give an explanation, divide 675/45 to get 15

Answer: 10

Step-by-step explanation: it is a 5+ 5 =

Remember! This is important!

(positive number, positive number) = quadrant 1 or quadrant I

(negative number, positive number) = quadrant 2 or quadrant II

(negative number, negative number) = quadrant 3 or quadrant III

(positive number, negative number) = quadrant 4 or quadrant IV

So the answer is quadrant 4 or quadrant IV.

Answer:

24 arrangements.

Step-by-step explanation:

ive done this before

Answer:

5

6

Step-by-step explanation:

To solve, collect like terms

x ≥ 2 + 21/2

x ≥ 4 1/2

the whole number that would be greater than 41/2 would be 5

2.  2.7 + 3.3  > x

6 > x