Find the area of the shaded region.
y=7e^x y=7xe^x^2

There are 13 diamonds in the deck (as well as other colors). Since there are 52 cards, the probability of getting a diamond on the first draw is 13/52. After the first card is drawn, all that's left are his 12 diamonds. Therefore, the probability of drawing a diamond is 12/51 (note that he has only 51 cards left after pulling/removing the first card since there are no replacement cards). The overall probability is the product of two possibilities. The odds of drawing diamonds from the original deck are 13/52 times the odds of drawing diamonds from his remaining 51 cards. Assuming the first card drawn is a diamond, 12/51.

P=13/52*12/51=1/4*4/17=1/17.

More problems related to a similar concept are solved in the link below.

https://brainly.com/question/11234923?referrer=searchResults

#SPJ4

Answer:

T (2, 2)

U (4 , 0)

V (1, -2)

Step-by-step explanation:

The translation is (x + 5, y), meaning 5 is being added to the X-values and Y stays the same.

Jada can buy approx. 4 bags of chips if each bag costs $0.99 and she also buys a bottle of soda.

Given, Jada has $6. She goes to the store and buys one bottle of soda for $1.20.

Each bag of chips cost $0.99

We have to find the number of chips bags she can buy,

as, she has $6 from which she spent $1.20 for a bottle of soda.

now she left with,

= 6 - 1.20

= $ 4.8

Now, as each chips bag is of $0.99

so, the number of chips bags she can buy are

= 4.8/0.99

= 4.84

So, she can buy approx. 4 bags of chips.

Hence, she can buy approx. 4 bags of chips if each bag costs $0.99 and she also buys a bottle of soda.

Learn more about Unitary Method here https://brainly.com/question/28627316

#SPJ4

A cat weighing 5 lb and fed at a rate of 40 calories/lb/day should be fed a certain number of cups of commercial cat food at each meal if fed twice a day. We need to calculate this based on the given information that the cat food has 120 kcal/cup.

To determine the amount of cat food to be fed at each meal, we can follow these steps:

1. Calculate the total daily caloric intake for the cat:

  Total Calories = Weight (lb) * Calories per lb per day

                 = 5 lb * 40 calories/lb/day

                 = 200 calories/day

2. Determine the caloric content per meal:

  Since the cat is fed twice a day, divide the total daily caloric intake by 2:

  Caloric Content per Meal = Total Calories / Number of Meals per Day

                          = 200 calories/day / 2 meals

                          = 100 calories/meal

3. Find the number of cups needed per meal:

  Caloric Content per Meal = Calories per Cup * Cups per Meal

  Cups per Meal = Caloric Content per Meal / Calories per Cup

                = 100 calories/meal / 120 calories/cup

                ≈ 0.833 cups/meal

Therefore, the cat should be fed approximately 0.833 cups of commercial cat food at each meal if fed twice a day.

To learn more about number  Click Here: brainly.com/question/3589540

#SPJ11

The value of x is obtained as follows:

128º.

The measure of angle A is given as follows:

m < A = 132º.

For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:

5x - 508 = x + 4.

4x = 512

x = 512/4

x = 128.

Then the measure of angle A is given as follows:

m < A = 5(128) - 508

m < A = 132º.

More can be learned about angle measures at https://brainly.com/question/25716982

#SPJ1

Answer:

60

Step-by-step explanation:

straight lines are 180

since all lines are parallel

180 - 120 = 60

For the given set of parallel lines measurement of angle 2 is equals to 60degrees.

" Parallel lines are defined as coplanar lines which do not intersect in the same plane. They are equidistant from each other in the same plane."

According to the question,

Given,

Line 'n' is parallel to line 'm'

Line 's' is parallel to line 't'

As diagram drawn we have,

AB is a part of line 'n'

BC is a part of line 't'

CD is a part of line 'm'

DA is a part of line 's'

From this we get,

AB parallel to CD

BC parallel to DA

Therefore,

ABCD is a parallelogram.

Opposite angles in a parallelogram are congruent we have,

∠1 ≅∠3 = 120°

∠2 and ∠3 are supplementary angles.

⇒∠2 + ∠3 = 180°

⇒∠2 + 120° = 180°

⇒∠2 = 180° - 120°

⇒∠2 = 60°

Hence, for given parallel lines measure of angle2 is equals to 60degrees.

Learn more about parallel lines here

https://brainly.com/question/16701300

#SPJ2

To find the expected number of times Joan rolls a 3, we use the formula for mean of a binomial distribution.

The correct option is, option (C) 6.

The probability of rolling a number 3 on any given roll is 1/4

If Joan rolls the die 20 times, the number of times she rolls a 3 will follow a binomial distribution with n = 20 (number of trials) and p = 1/4 (probability of success).

The formula for the probability mass function of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (the number of times Joan rolls a 3), k is the number of successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can calculate the probability of rolling a 3 exactly k times out of 20 rolls:

P(X=k) = (20 choose k) * (1/4)^k * (3/4)^(20-k)

To find the expected number of times Joan rolls a 3, we can use the formula for the mean of a binomial distribution:

E(X) = n * p

In this case, E(X) = 20 * 1/4 = 5

Therefore, the expected number of times Joan rolls a 3 is 5.

Since the possible answers are integers, the closest answer to 5 is 6. Therefore, the answer is (C) 6.

Know more about binomial distribution here:

https://brainly.com/question/29163389

#SPJ11

If the surface area of a sphere is 1, then its radius is √(1/4π) = 0.2821 (approximate to four decimal places).

The surface area of a hemisphere with the same radius is half that of the sphere since it only covers half of the surface area.

So, the surface area (including the base area) of the hemisphere would be:

2π(0.2821)^2 + π(0.2821)^2 = 0.5 + 0.25π = 0.7854 (approximate to four decimal places).

Therefore, the surface area (including the base area) of the hemisphere with the same radius is approximately 0.7854 square units.
Hi! To find the surface area of a hemisphere with the same radius as a sphere, we'll first determine the radius using the sphere's surface area formula, and then apply the hemisphere's surface area formula.

1. Sphere's surface area formula: A = 4πr²
Given surface area A = 1, we'll solve for radius r:

1 = 4πr²
Divide both sides by 4π:
1 / 4π = r²

2. Find r:
r = √(1 / 4π)

3. Hemisphere's surface area formula (including base area): A_hemisphere = 3πr²
Substitute r with the value we found:

A_hemisphere = 3π(√(1 / 4π))²

4. Simplify the expression:
A_hemisphere = 3π(1 / 4π)
A_hemisphere = (3/4)π

So, the surface area (including the base area) of the hemisphere with the same radius as the given sphere is (3/4)π.

know more

https://brainly.com/question/31464920

#SPJ11

The standard deviation for the total portfolio returns can be calculated using the weighted average of the standard deviations of the index fund and the risk-free asset. The standard deviation for the total portfolio returns is 10.5%.


The standard deviation of a portfolio measures the variability or risk associated with the portfolio's returns. In this case, the portfolio is 70% invested in an index fund (with a standard deviation of returns of 15%) and 30% invested in a risk-free asset.

To calculate the standard deviation of the total portfolio returns, we use the weighted average formula:

Standard deviation of portfolio returns = √[(Weight of index fund * Standard deviation of index fund)^2 + (Weight of risk-free asset * Standard deviation of risk-free asset)^2 + 2 * (Weight of index fund * Weight of risk-free asset * 1Covariance  between index fund and risk-free asset)]

Since the risk-free asset has a standard deviation of zero (as it is risk-free), the second term in the formula becomes zero. Additionally, the covariance between the index fund and the risk-free asset is also zero because they are independent. Therefore, the formula simplifies to:

Standard deviation of portfolio returns = Weight of index fund * Standard deviation of index fund

Plugging in the values, we get:

Standard deviation of portfolio returns = 0.70 * 15% = 10.5%

Hence, the standard deviation for the total portfolio returns is 10.5%. This means that the total portfolio's returns are expected to have a variability or risk represented by this standard deviation.

Learn more about standard deviation here : brainly.com/question/13498201

#SPJ11

Answer:

D. 54 degrees

Step-by-step explanation:

subtract 72 from 180 and divide by 2

The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4)

What is center of dilation?

A dilation's center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure.

The center of dilation is the origin, so to find the new coordinates of each vertex, we need to multiply the original coordinates by the scale factor of 2.

A(2, 2) becomes A'(2 * 2, 2 * 2) = A'(4, 4)

B(4, 4) becomes B'(4 * 2, 4 * 2) = B'(8, 8)

C(-4, 2) becomes C'(-4 * 2, 2 * 2) = C'(-8, 4)

So, The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4).

To know more about center of dilation visit,

https://brainly.com/question/13173812

#SPJ1

The given vectors are: u = (20 + i, i, 2)v = (1 + i, 2, 41)The dot product of u and v is:u.v = (20 + i)(1 + i) + (i)(2) + (2)(41 - 1)= 20 + 20i + i + i² + 2i + 80= 101 + 22i

To find the imaginary part of u.v, we can simply extract the coefficient of i, which is 22. Hence, the imaginary part of u.v is 22. Therefore, the answer is rounded off to 22.00.

A quantity or phenomenon with two distinct properties is known as a vector. magnitude and course. The mathematical or geometrical representation of such a quantity is also referred to by this term. In nature, velocity, momentum, force, electromagnetic fields, and weight are all examples of vectors.

A movement from one point to another is described by a vector. Direction and magnitude (size) are both properties of a vector quantity. A scalar amount has just greatness. An arrow-labeled line segment can be used to represent a vector. The following describes a vector between two points A and B: A B → , or .

Learn more about vectors:

https://brainly.com/question/24256726

#SPJ11

Answer:

-1

Step-by-step explanation:

In order to find the perimeter of the polygon we need to find the measure of each side

We have the next sides

s1=18.4

s2=21.9

s3=20.5

s4=?

we need to find s4 with the fact that two tangents from the same vertex have equal measurements

then we sum all the sides in order to find the perimeter

The perimeter is P=77.8

a) Solve the first equation for \(x\).

\(x + 3y = 7 \impiles x = 7 - 3y\)

Substitute this into the second equation and solve for \(y\).

\(2x + 4y = 12 \implies 2(7 - 3y) + 4y = 12 \\\\ \implies 14 - 6y + 4y = 12 \\\\ \implies -2y = -2 \\\\ \implies \boxed{y=1}\)

Solve for \(x\).

\(x = 7 - 3y \implies x = 7-3\times1 \\\\ \implies \boxed{x = 4}\)

b) Eliminate \(y\) by combining the two equations in appropriate parts, namely

\(2 (2x - y) + (3x + 2y) = 2\times3 + (-3)\)

and solve for \(x\).

\(2 (2x - y) + (3x + 2y) = 2\times3 + (-3) \implies 4x - 2y + 3x + 2y = 6 - 3 \\\\ \implies 7x = 3 \\\\ \implies \boxed{x = \dfrac37}\)

Solve for \(y\).

\(2x - y = 3 \implies 2\times\dfrac37 - y = 3 \\\\ \implies \dfrac67 - y = 3 \\\\ \implies -y = \dfrac{15}7 \\\\ \implies \boxed{y = -\dfrac{15}7}\)

"The median and the 50th percentile rank score will always have the same value". The statement is false, so the correct option is b.

The median and the 50th percentile rank score do not always have the same value. While they are related concepts, they are not identical.

The median is the middle value in a dataset when it is arranged in ascending or descending order. It divides the dataset into two equal halves, where 50% of the data points are below the median and 50% are above it. It is a specific value within the dataset.

On the other hand, the 50th percentile rank score represents the value below which 50% of the data falls. It is a measure of relative position within the dataset. The 50th percentile rank score can correspond to a value that is not necessarily the same as the median.

In cases where the dataset has repeated values, the 50th percentile rank score could refer to a value that lies between two data points, rather than an actual data point.

Therefore, the median and the 50th percentile rank score are not always equal, making the statement false.

Visit here to learn more about median:

brainly.com/question/26177250

#SPJ11

Answer:

10 + 2y

Step-by-step explanation:

2(5+y)

Distribute

10 + 2y

Answer:

2y + 10

Step-by-step explanation:

2(5(2) + y(2))

2 x 5 = 10

y x 2 = 2y

2y + 10

Answer:

I got you, The rectangle on the left is 1.62 and the rectangle on the right is 0.432 :)

Step-by-step explanation:

Answer:

ok

Step-by-step explanation:

11.36

Answer:

41/7+11/2=82+77/14=159/14=11.36

Answer:

for me the good one is black with 18 speed

Answer:

Black with 18 speeds

Step-by-step explanation:

's' and 't' represent free parameters that can take on any real values.

In the given system of equations:

x1 - x2 + 4x3 = -4

6x1 - 5x2 + 7x3 = -5

3x1 - 39x3 = 45

To solve this system, we can use the method of Gaussian elimination or matrix operations. Let's use Gaussian elimination:

Step 1: Write the augmented matrix for the system:

[1 -1 4 | -4]

[6 -5 7 | -5]

[3 0 -39 | 45]

Step 2: Perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 6R1

R3 = R3 - 3R1

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 3 -51 | 57]

Step 3: Perform additional row operations to further simplify the matrix:

R3 = R3 - 3R2

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 0 0 | 0]

Step 4: Write the system of equations corresponding to the row-echelon form:

x1 - x2 + 4x3 = -4

x2 - 17x3 = 19

0 = 0

Step 5: Express the variables in terms of a parameter:

x1 = s

x2 = 19 + 17s

x3 = t

where s and t are parameters.

Therefore, the solution to the system is:

[x1] = [s]

[x2] = [19 + 17s]

[x3] = [t]

In the provided solution format:

[x1] = [s] []

[x2] = [19 + 17s] + s []

[x3] = [t] [__]

Here, 's' and 't' represent free parameters that can take on any real values.

Know more about the row-echelon form click here:

https://brainly.com/question/30403280

#SPJ11

Let x be the number of large frames and y be the number of small frames that a woman bought from the closeout sale.Therefore, the two equations that we can use to solve the problem are:

x + y = 27 ...(1)and19x + 9y = 343 ...(2)Multiplying equation (1) by 9 and subtracting it from equation (2), we get:19x + 9y = 343  ...(2)- (9x + 9y = 243) ...(3)10x = 100x = 10Thus, the woman bought 10 large frames

.Substituting x = 10 in equation (1), we get:10 + y = 27y = 27 - 10y = 17Thus, the woman bought 17 small frames. Therefore, the woman bought 10 large frames and 17 small frames.

To Know more about Substituting visit:

brainly.com/question/29383142

#SPJ11

Answer:

hope it helps

stay safe healthy and happy.

Using the substitution method, we will see that the solution is (2, 3).

Here we have the following system of equations:

y = -2x + 7

y = 5x - 7

To solve it we can use the substitution method, y is isolated in both equations, so we can substitute y on the second equation by the right side of the first equation:

-2x+ 7 = 5x - 7

Now we can solve this for x.

-2x + 7 = 5x - 7

7 + 7 = 5x + 2x

14 = 7x

14/7 = x

2 = x

Now we can evaluate any of the two lines in x = 2 to get the y-value.

y = 5*2 - 7

y = 10 - 7

y = 3

The solution to the system is (2, 3).

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

It will take approx. 8.3 weeks to completely pay the remaining amount after the down payment.

Given, Leonardo put a $600 ring on layaway by making a 10% down payment and agreeing to pay $65 a week.

So, he made a down payment of 10% of $600 i.e. $60

remaining amount to pay be,

600 - 60 = 540

Let he will take x weeks to pay the remaining amount.

Now, if he pay $65 per week

then, 65x = 540

x = 540/65

x = 8.31

So, it will take approx. 8 - 9 weeks to completely pay the remaining amount after the down payment.

Hence, it will take approx. 8.3 weeks to completely pay the remaining amount after the down payment.

Learn more about Unitary Method here https://brainly.com/question/28627316

#SPJ4

Answer:

9 weeks

Step by step explanation:

It’s right.

The total cost functions associated with the two different methods for wrecking cars are as follows: 1. Method 1 (Hydraulic Car Crusher):

Total Cost = $2000 + $10 * Number of Cars

2. Method 2 (Fancy Shovel and Scoop):

Total Cost = $100 + $50 * Number of Cars

The average cost of each method can be calculated by dividing the total cost by the number of cars. For Method 1, the average cost is $10 per car ($2000 divided by the number of cars). For Method 2, the average cost is $50 per car ($100 + $50 per car).

The marginal cost represents the additional cost incurred by producing one more unit (car) using each method. In Method 1, the marginal cost is a constant $10 per car, as each additional car adds the same cost of $10. In Method 2, the marginal cost is $50 per car, as each additional car requires the payment of $50 to Rex's brother, Scoop.

To determine which method minimizes the cost of wrecking k cars per year, we need to compare the average cost for each method. If k is less than 40, Method 1 (Hydraulic Car Crusher) will have a lower average cost of $10 per car. If k is greater than or equal to 40, Method 2 (Fancy Shovel and Scoop) will have a lower average cost of $50 per car.

If the price for wrecking cars is $100 per car, the profit per car is given by the price minus the average total cost (ATC). For Rex, if p > ATC, which is $10, he will have a positive profit. Therefore, for Rex to have a positive profit, p must be greater than $10. Similarly, for Scoop, if p > ATC, which is $50, he will have a positive profit. Therefore, for Scoop to have a positive profit, p must be greater than $50.

In summary, if the number of cars wrecked per year (k) is less than 40, Rex should use Method 1 (Hydraulic Car Crusher) as it has a lower average cost. If k is greater than or equal to 40, Rex should use Method 2 (Fancy Shovel and Scoop) as it has a lower average cost. If the price for wrecking cars (p) is greater than $10, Rex will have a positive profit, and if the price is greater than $50, Scoop will have a positive profit.

Learn more about cost functions here:

https://brainly.com/question/31777035

#SPJ11

Opportunity cost is the price of giving up an option. An opportunity cost is the price you pay for selecting a particular option over another. Opportunity cost is the benefits you lose by choosing one alternative over another one.”

The value of the next-highest-valued alternative use of a resource is what economists mean when they talk about its "opportunity cost." You cannot, for instance, read a book at home during the time you would have spent seeing a movie and spend the money you would have spent on something else.

Opportunity cost is frequently referred to as the second-best option. The loss of benefit that would have been realized if a different option had been taken is sometimes referred to as the alternative cost. The loss of advantage as a result of a change in decision is another way to explain it.

Learn more about opportunity costs  to visit this link

https://brainly.com/question/13036997

#SPJ4

last one is the answer:D. X=12 and X=1

step by step:

d=b2-4ac=169-48=121

x1=(-b+√d)2a=(13+11)2=12

x2=(-b-√d)2a=(13-11)/2=1

X1=12 and X2=1

please give me brainlest❤️

The time complexity functions and big-O notations of the program is O(log n)

Let's analyze the time complexity of the code using mathematical terms.

The outer loop runs log n times, where n is the input size, because i doubles in each iteration until it reaches n. Therefore, the time complexity of the outer loop is O(log n).

For each iteration of the outer loop, the inner loop runs log i times. Since i doubles in each iteration of the outer loop, the number of iterations of the inner loop is 1, 2, 4, 8, ..., i.

The total number of iterations of the inner loop is the sum of the geometric series 1 + 2 + 4 + ... + n/2 + n. This series sums up to 2n - 1, which is O(n).

Therefore, the overall time complexity of the code is the product of the time complexity of the outer and inner loops, which is O(n log n).

To know more about big-O notations here.

https://brainly.com/question/27985749

#SPJ4