9 Decide whether the function f(x)=x² is a probability density function on [-1, 1]. If not, tell why. Is the function a probability density function on [-1, 1]? OA. No, because dx # 1. B. Yes, the fu

The Policeman’s rate of change is $10 per hour and the firefighter's rate of change is $10 per hour

The Policeman’s rate of change

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

The graph

On the line of the policeman, we have the following point

(x, y) = (4, 40)

So, the rate of change is

Rate = y/x

This gives

Rate = 40/4

Evaluate

Rate = 10

The firefighter's rate of change

On the line of the firefighters, we have the following point

(x, y) = (4, 60)

So, the rate of change is

Rate = y/x

This gives

Rate = 60/4

Evaluate

Rate = 15

Hence, the rate is $15 per hour

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Given that events A and B are independent, with P(A) = 0.2 and P(B) = 0.7, we can determine the probability of their intersection using the formula   P(A ∩ B) = P(A) * P(B).

When two events, A and B, are independent, the occurrence of one event does not affect the probability of the other event occurring. In this case, the probability of event A, denoted as P(A), is 0.2, and the probability of event B, denoted as P(B), is 0.7.

To find the probability of the intersection of events A and B, denoted as P(A ∩ B), we can use the formula for independent events: P(A ∩ B) = P(A) * P(B). By substituting the given probabilities into the formula, we have P(A ∩ B) = 0.2 * 0.7 = 0.14.

Therefore, the probability of events A and B both occurring, given that they are independent, is 0.14, or 14%. This means that there is a 14% chance of both events A and B happening simultaneously.

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Step-by-step explanation:

Try factoring. If you cannot find the pair of numbers, it is best to use the quadratic formula, unless you need something like the turning point, then you should use completing the square

Answer:

Interest rate formula

I = PRT

where,

I = simple interest

P= principle

R= annual interest

T= relevant time period

I= PRT

I=500×15/100×2

I=150

total amount formula,

A=P+PRT

where,

A=total amount

A=P+PRT

A=500+150

A=650

answer,

interest amount=$150

total amount = $650

Using relations in a right triangle, it is found that the approximate angle made by the stairway with the ground is given by:

D. 43.76.

The relations in a right triangle are given as follows:

This situation can be modeled by a right triangle described as follows:

Hence the angle is found as follows:

\(\cos{\theta} = \frac{13}{18}\)

\(\theta = \arccos{\left(\frac{13}{18}\right)}\)

\(\theta = 43.76^\circ\)

Hence option D is correct.

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Answer:

46.24

Step-by-step explanation:

:)

Answer:

t= -105

Step-by-step explanation:

To solve the equation, we want to find out what t is. In order to do this, we have to get t by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

-1/15t=7

t is being multiplied by -1/15. The opposite of multiplication is division. Divide both sides by -1/15.

-1/15t/-1/15=7/ -1/15

t=7/ -1/15

Instead of dividing a number by a fraction, you can multiply the number by the reciprocal of the fraction.

To find the reciprocal, flip the numerator (top number) and denominator (bottom number).

-1/15--flip--> -15/1=-15

Substitute -15 in for -1/15, and switch the division sign to a multiplication sign.

t= 7* -15

t=-105

Let's check out solution. Plug -105 back in for t in the original equation.

-1/15t=7

-1/15*-105=7

7=7

Both sides are the same, so we know that t=-105.

Answer:

t=-105

Step-by-step explanation:

\(-\frac{1}{15} t =7\)

What we need to do here is to isolate t.

Let's multiply both sides by -15.

\(-\frac{1}{15}t * -15 = 1t\)

7*-15= -105

t=-105

Answer:

The answer is 5

Step-by-step explanation:

hope this helped you

Today Britney beat 5 levels of a video game if she played at the same playing proportion with time as yesterday.

proportion or rate of work done is the ratio of the total work done in a given time divided by the given time. It is the measure of the proportion of doing work per unit time.

proportion of work done = Total work done / Given time

Yesterday ,Britney played 3 levels in time  27 minutes

Work done(levels cleared) = 3 levels

Time taken  = 27 minutes

Yesterday the proportion or rate of playing game = 3 levels / 27 minutes = ( 1/ 9) levels/ min

Today, Britney is allowed to play  for 45 minutes at the same proportion rate she played yesterday

Then, the  work done or level beat today = rate of playing game × time

                                                                    = (1/9)×45 = 5 games

Therefore, Britney cleared 5 games today if she played at same rate as she did yesterday

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Answer:

\(\huge\colorbox{pink}{✏﹏ \: Inertia \: }\)

➳ Inertia refers to the tendency to do nothing or to remain unchanged in its state of motion or rest unless an external unbalanced force acts on it (Newton's third law of motion - also known as the Law of Inertia)

Answer:

its A -0.75

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

i got it right on edge unit review

Answer:

You have to first figure out how many different possibilities there are, here there are 10. And they're asking for the chance that one option will be chosen

Therefore it is 1/10

I'm new to the app, hope that helped

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

  All apply

Step-by-step explanation:

Complementary angles are ones that total 90°. Here, we have two pairs of congruent angles such that each pair totals 90°. We can mix and match to find pairs of complementary angles.

  less than 45°: BGC and EGF

  more than 45°: AGB and DGE

A complementary pair will consist of one angle from the first list and one angle from the second list. There are 4 possible pairings, and all are shown as answer choices.

All of the choices apply.

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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- - - - - - - - - - - - - - - - - -

Let's try to divide 1,772 and see how much math we need to do...

1,772 / 90 = 19.6888888889

Well, clearly we need more than 1,772!

- - - - - - - - - - - - - - - - - -

Now, play around with adding numbers.

(I'm gonna skip all the experimenting, here's the closest # available for easy division!)

⇣

1,800 / 90 = 20

1,800

hope this helps

The required variance for the question is var (x - y) is 2.

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Andrew is correct because 60 is the highest whole number that can round to 60. Any number higher than 60 will round up to a higher number. For example, 61 will round up to 70, and 62 will round up to 70. Therefore, 60 is the greatest whole number that rounds to 60.

The highest whole number is infinity, as there is no limit to how high a number can be. Whole numbers are all the numbers that are greater than or equal to 0, including 0 itself. The highest whole number is therefore infinity, as this is the highest possible number.

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Answer:

130 ft

Step-by-step explanation:

The distance across the canyon is 130 feet.

When Christian moved 100 feet from the tree on his side, the angle formed by the tree on his side and the tree on the other side was 70°. This means that the distance across the canyon is the length of the opposite side of the right triangle formed by Christian's position, the tree on his side, and the tree on the other side.

To find the length of the opposite side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the distance across the canyon, and the other two sides are 100 feet and the length of the opposite side of the triangle.

We can write this as an equation: (distance across the canyon)^2 = (100 feet)^2 + (opposite side of the triangle)^2.

To solve for the distance across the canyon, we can take the square root of both sides of the equation: distance across the canyon = √((100 feet)^2 + (opposite side of the triangle)^2).

Since the length of the opposite side of the triangle is equal to the length of the adjacent side (100 feet) divided by the tangent of the angle formed by the tree on his side and the tree on the other side, we can substitute this value into the equation above: distance across the canyon = √((100 feet)^2 + (100 feet / tan 70°)^2).

To calculate the value of tan 70°, we can use a calculator or look up the value in a table of trigonometric functions. The value of tan 70° is approximately 1.73. We can substitute this value into the equation above to get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2).

We can now use a calculator to evaluate this expression and find the distance across the canyon. When we do this, we get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2) ≈ 130 feet.

Therefore, the distance across the canyon is approximately 130 feet.

The correct option is A) 5 – 1 ≠ 1 – 5  shows why the commutative property doesn't work under subtraction

The commutative property works for addition and multiplication. It says that when adding or multiplying, you can switch the order of the numbers around and still get the same answer.

For instance, in simple terms, the commutative property of addition states that changing the order of the addends will not change the sum. That is, a + b = b + a.

Similarly, the commutative property of multiplication states that changing the order of the factors will not change the product. That is, a × b = b × a.

However, the commutative property does not work for subtraction and division. You cannot change the order of numbers around and still get the same answer when you're subtracting or dividing. In other words, the order of the numbers matters in these cases.

That is, a - b ≠ b - a; a / b ≠ b / a.Here, the options C and D are not valid since they both represent addition operations, whereas the question demands subtraction. Between options A and B, A represents the subtraction operation and the result for this option is not the same as the result for the reverse subtraction operation which is why A is the right option.

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The given system of equations is a set of differential equations, where the variables x and y are functions of time t. The equations can be interpreted as describing the rate of change of x and y with respect to time, based on their current values.

To solve this system of equations, we can use techniques such as separation of variables or substitution. However, finding an analytical solution may not be possible in all cases. The condition (x,y)>0 means that both x and y are positive, which restricts the possible solutions of the system.  In general, the behavior of the system depends on the initial conditions, i.e., the values of x and y at a given time t=0. Depending on the initial values, the system may have equilibrium points, periodic solutions, or chaotic behavior. Finding the exact behavior of the system requires numerical methods or graphical analysis. For example, we can use software tools such as MATLAB or Wolfram Mathematica to plot the trajectories of the system and study their properties.

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Answer:

625

Step-by-step explanation:

5*5*5*5

Answer:

625

Step-by-step explanation:

Because the exponent means you would multiply 5 by itself 5 times

so 5 times 5 = 25

25 times 5 and on and on.

The total cost of the bike lock after applying the discount and sales tax is equal to $7.49.

Original price of the bike lock = $8.75

Discount percent on original price = 20%

The bike lock was marked down 20% from an original price of $8.75, This implies,

The discounted price is equal to,

= original price - 20% of original price

= $8.75 - 0.20($8.75)

= $8.75 - $1.75

= $7.00

The sales tax in Brookfield is 7%, so the additional tax Janet had to pay is,

= 7% of $7.00

= ( 7 / 100 ) × ($7.00)

= 0.07 × ($7.00)

= $0.49

This implies,

The total cost of the bike lock is equal to,

= $7.00 + $0.49

= $7.49

Therefore, the total cost of the bike lock was $7.49.

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Assuming max value is an integer. int max(int x, int y) { if (x > y){ return x; } else { return y; } }.The function call max(4, 7) is a valid function call.

A valid function call for the given function would be:
max(4, 7)
Here's the step-by-step explanation:
1. The function definition is:
int max(int x, int y) {
 if (x > y){
   return x;
 } else {
   return y;
 }
}
2. In the function call, we need to provide two integer values as arguments to the function. For example, max(4, 7).
3. In this case, the first argument is 4 and the second argument is 7.
4. The function compares the two arguments using the if statement. Since 4 is greater than 7, the condition x > y is true.
5. As a result, the function returns the value of x, which is 4.
Therefore, the function call max(4, 7) is a valid function call.

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Answer:

5.603 ounces

Step-by-step explanation:

From the information given, you know the ounces of orange juice included in a bottle and the ounces of mixed fruit juice that the bottle has. So, to be able to determine how much of the bottle of mixed fruit juice is not orange juice​, you have to subtract the ounces of orange juice in the bottle from the ounces of mixed fruit juice that it has:

6.85-1.247=5.603

According to this, the answer is that the bottle of mixed fruit juice has 5.603 ounces that are not of orange juice.

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Answer:

it would be in the fourth quadrant, directly underneath where it is now. the base would be c and d

Step-by-step explanation:

Looks like it's a scale factor?

The base of the small one is 5ft and the base of the large is 45ft. If we divide

45/5 = 9

Since the height of the small is 40ft, we can multiply by 9, the number we just found, to find the value of X.

40 x 9 = 360ft

In the coordinate plane, the unit circle is a circle with a radius of 1 centered at the origin. When we refer to the terminal side of an angle in standard position, we mean the side that ends at a point on the unit circle.

Quadrant IV is the bottom-right quadrant of the coordinate plane, where both the x-coordinate and the y-coordinate are positive.

Therefore, a point on the unit circle lying on the terminal side of an angle in standard position in Quadrant IV would have positive x and y coordinates. This is because both coordinates are positive in Quadrant IV.

It is important to note that the x-coordinate of the point corresponds to the cosine of the angle, and the y-coordinate corresponds to the sine of the angle. In Quadrant IV, the cosine is positive, while the sine is positive.

By understanding the properties of the unit circle and the characteristics of each quadrant, we can determine the correct completion of the statement: A point on the unit circle lies on the terminal side of an angle in standard position in Quadrant IV when both the x-coordinate and the y-coordinate are positive.

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