The sum of two numbers is 60 and the difference is 4. What are the numbers?​

The probability that Lamont reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie is 1/15

The probability can be calculated as follows:

P(peanut butter cookie) = 5/25 = 1/5

P(oatmeal cookie) = 8/24 = 1/3

P(peanut butter cookie and oatmeal cookie) = P(peanut butter cookie) x P(oatmeal cookie)

P(peanut butter cookie and oatmeal cookie) = (1/5) x (1/3)

P(peanut butter cookie and oatmeal cookie) = 1/15

Therefore, the probability that Lamont reaches back in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie is 1/15.

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Answer:

This is your answer ☺️☺️☺️

The baker will need 3600g of sugar to bake 12 cakes of half a kilogram each.

To find out how much sugar the baker will need to bake 12 cakes, we need to multiply the amount of sugar he uses for one cake by the number of cakes he wants to bake.

Here is the step-by-step explanation:
Step 1: Determine the amount of sugar the baker uses for one cake: 300g
Step 2: Determine the number of cakes the baker wants to bake: 12
Step 3: Multiply the amount of sugar for one cake by the number of cakes: 300g x 12 = 3600g

Therefore, the baker will need 3600g of sugar to bake 12 cakes of half a kg each.

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Answer:

B

Step-by-step explanation:

With answer B, x is marked 4 on the x-axis and because there was no given y-intercept, the line must be vertical.

For the two triangles, the appropriate option is D) The triangles aren't similar.

When on comparing the properties of two triangles and a common relations hold, then the triangles are said to be similar. The sides of the similar triangles will have a representative fraction.

Representative fraction is the ration that shows how the corresponding sides of two triangles relate.

In the given triangle on comparing their sides, we have;

KP/ KN = KL/ KM

12/ 15 = 8/ 10

But,

12/ 15 ≠ 8/ 10

Therefore the triangles are not similar. Thus option D) The triangles aren't similar.

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Answer:

missing length is 8

Step-by-step explanation:

17^2 - 15^2 = 64

square root of 64 is 8

Answer:

8 inches

Step-by-step explanation:

Use the Pythagorean Theorem:

a²+b²=c²

15²+b²=17²

225+b²=289

b²=64

b=8

Therefore, the missing side is 8 inches long.

As you consider the various factors involved in starting a group, the most important factor you have to judge is the group's purpose or goal.

Step 1: Identify the group's purpose or goal - This is crucial because it will guide all other decisions, including membership criteria, communication methods, and meeting schedules.

Step 2: Assess the needs and resources of potential members - This will help you understand their motivations and ensure the group can support their needs while accomplishing its goal.

Step 3: Establish clear membership criteria and expectations - This will ensure that everyone in the group is on the same page and committed to the same goals.

Step 4: Choose an appropriate communication method - This will facilitate smooth and efficient communication among group members.

Step 5: Develop a meeting schedule that works for all members - Regular meetings help keep the group on track and provide opportunities for collaboration and feedback.

By focusing on the group's purpose or goal, you can create a solid foundation for a successful and productive group.

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Answer:

x = 122°

Step-by-step explanation:

There is remote angle( non- adjecent angle) and their sum equal to the exterior angle .

Exterior angle is an angle formed from one side of the polygone and the extended side so

<A and <B are remot angle and <BCD is exterior angle .

And we write the equetion as

<A + <B = <BCD

58° + 64° = x°

122° = X°

so the exterior angle ( x ) measures 122° .

Answer:

∠M ≅ ∠G

Step-by-step explanation:

Given:

This means that triangle MTD is congruent to triangle GLS.

Two triangles are said to be congruent if:

Therefore:

Similarly:

Therefore, the true statement is ∠M ≅ ∠G.

Answer:

Slope is 5

Step-by-step explanation:

if line is parallel to 5x + 10

then the slope has to be equal

y= mx+ b

m = 5

Answer:

yes of course it exists until to you practice a little bit hard. so let's. try

The condition for a portfolio to be self-financing in the Black-Scholes model is that the portfolio's value does not change due to trading (buying or selling) costs or external cash flows. In other words, the portfolio's value remains constant over time, excluding the effects of the underlying assets' price changes.

For the given portfolio, a = -t (units of the stock) and b = S_t (units of the savings account). To determine if this portfolio is self-financing, we need to check if its value remains constant over time. Using Ito's lemma, we can express the value of the portfolio as:

d(Vt) = a_t * d(St) + b_t * d(Ct)

Substituting the values of a and b, we have:

d(Vt) = -t * (2St * dt + 4St * dBt) + S_t * d(t)

Simplifying this expression, we get:

d(Vt) = -2tSt * dt - 4tSt * dBt + S_t * dt

The portfolio is self-financing if d(Vt) = 0. However, in this case, we can see that the terms involving dBt do not cancel out, indicating that the portfolio is not self-financing.

Girsanov's theorem states that under certain conditions, it is possible to transform a Brownian motion under the real-world measure into a Brownian motion under an equivalent martingale measure (EMM). The EMM is a probability measure under which the discounted asset prices are martingales. By applying Girsanov's theorem or alternative techniques, we can derive the expression for St, the stock price, under the EMM. Unfortunately, without further information or specifications, it is not possible to provide the specific expression in this case.

To determine the price Ct of the call option on the stock at time t ≤ 2, with an exercise price K = 1 and expiration date T = 2, additional information or an appropriate result is required. Without specific details, such as the volatility of the stock or the risk-free interest rate, it is not possible to provide an expression for Ct.

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To evaluate a function with a specific value in the domain you susbtitute in the equation of the function the independient variable (x) for the value in domain.

For x = -1 (a number n powered to a negative number (m) n^-m is equal to 1/n^m

For x=0 (any number powered to 0 is equal to 1)

For x = 1

For x = 2

Answer:

Step-by-step explanation:

trapezoid's S1 = 20m

                  S2 = 18m

distance between the sides, i.e. height of the trapezoid, h = 25m

1.

area of the garden = area of a trapezoid =

(S1 + S2) / 2 * h

2.

area of a garden is asked which is in the shape of a trapezoid so we have to calculate the area of a trapezoid.

3.

the given facts are the length of two sides as well as the distance between the sides which will be considered as the height.

4.

formula to find the area of a trapezoid, = (a+b) / 2 * h

where a, b are the two sides and h is the height

5.

number sentence = (20 + 18) / 2 * 25

                             = 38 / 2 * 25

                             = 19 * 25

6.

answer is 475 m²

The general rule for each sum is that when you add the tenth term together we will get ten which will make the value an integer. The whole sum is equals to eleven.

Let's sum the decimal numbers to know the general rule,

Therefore,

3.7 + 7.3 = 11.0

6.4 + 4.6 = 11.0

9.1 + 1.9 = 11.0

5.5 + 5.5 = 11.0

Therefore, the  values added are the reverse of the decimals. example is 3.7 and 7.3 or 6.4 and 4.6.

When you add the tenth term together we will get ten which will make the value an integer

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The sample is a stratified sample.

A stratified sample is a sampling method in which a population is separated into distinct, non-overlapping subpopulations, or strata, and a random sample is taken from each stratum.

This is frequently utilized when the population contains subpopulations with distinct characteristics, and the researcher wants to guarantee that these subpopulations are adequately represented in the sample.

Likewise, in the provided scenario of the electronics store, the store will first separate the customers who purchased a computer over the past two years and then take 100 receipts through a random number generator to question customers about high-speed Internet rates.

This way, it can ensure that all customers are adequately represented in the sample and the information it receives is not biased.

A stratified sample is a sampling technique used in statistics and research to ensure that the sample accurately represents the different subgroups or strata within a population. It involves dividing the population into distinct subgroups or strata based on certain characteristics or variables and then selecting a sample from each stratum.

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Answer:

d is correct

Step-by-step explanation:

Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.

Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

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Answer:

(15squrt3)/2

Step-by-step explanation:

cos30=x/15

The ratios of online sales to shop sales of A jewelery shop which sold 240 necklaces in a month is equals to the 3:1.

We have a jewelery shop and they sold there necklaces to the different shops.

Total number of sold necklaces in a month = 240

Number of online sold necklaces in a month = 180

Total online sales of jewelery shop = 180

and rest of necklaces were sold in a high street shop. So, the number of sold necklaces in high street shop during a month = total number of sold necklaces - online sold necklaces

= 240 - 180 = 60

Total shop sales jewelery shop = 60 necklaces

Ratio is used to determine the relationship between two or more things ( like size, quantity, etc.). It is represented by a/b or a : b ( read as a ratio b). Here, we have to calculate the ratios of online sales to shop sales. So, the ratio of online sales to shop sales = 180 : 60 or 180/60

Simplify the expression,

=> 180/60 = 3

Hence, required ratio is 3: 1.

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After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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Recall that a reflection over a line y=k transforms the point (x,y) into:

Therefore the given sequence of transformations will change point (x,y) into:

Answer:

Since the original coordinates are P(-4,3), Q(0,3), and B(-3,-1), the coordinates of image 2 are:

The minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

Given: To find the minimum sample size, confidence level = 99%, standard deviation = 13.8, and one unit population mean. [Normally distributed]

Solving the given question:

We know that the formula for Margin of error is:

Margin of error = z-score * (standard deviation) / root (sample size)

E = z * σ / √(n), where

E = Margin of error

z = z-score

n = Sample size

σ = standard deviation

Therefore, sample size = ( z – score * standard deviation / margin of error)²

n = ( z * σ / E )²

First, calculate the z-score for the 99% confidence level.

From the normal distribution curve, the area under 99% confidence level is given as:

Area under 99% confidence level = (1 + confidence level) / 2 = (1 + 0.99) / 2 = 0.995

From the z-score table, we find the value of z with the corresponding area of 0.995

We find the value of the z-score corresponding to 0.995 is 2.58

Also given sample mean is one unit of the population. So the margin of error is 1

E = 1

And given Standard deviation = 13.8

σ = 13.8

Putting the values in the given formula of sample size n =

n = (2.58 * 13.8 / 1 )²

n = 1267.64

n = 1268

Hence the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

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Disclaimer: Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and G = 13.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed )

The surface area of the cylinder is 118.76 square inches if the height is 8 inches and base radius is 4 inches.

A cylinder is defined as a solid geometric figure with straight parallel sides and a circular or oval cross section.

Surface area is the amount of space covering the outside of a three-dimensional shape.

Surface area  of the cylinder is calculated as  : - 2πr² + 2πrh

We have:

Height of the cylinder h = 8 inches

The radius r = 4 inches

π = 3.14

Surface Area  = 2(3.14)(4)² + 2(3.14)(4)(8)

surface Area = 2x 3.14 x 16 + 18.28

surface Area = 100.48 + 18.28

surface Area = 118.76 square inches

Therefore , the surface area of the cylinder is 118.76 square inches if the height is 8 inches and base radius is 4 inches.

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Answer:

Step-by-step explanation:

You want the image coordinates for P(2, 2), N(3, -1), and B(-1, -2) after translation by (x, y) ⇒ (x, y-1) and reflection over x = 2.

Reflection over x=2 is the transformation ...

  (x, y) ⇒ (4 -x, y)

When the reflection occurs after the given translation, the composite transformation is ...

  (x, y) ⇒ (4 -x, y -1)

Then the image points are ...

  P(2, 2) ⇒ P''(4 -2, 2 -1) = P''(2, 1)

  N(3, -1) ⇒ N''(4 -3, -1 -1) = N''(1, -2)

  B(-1, -2) ⇒ B''(4 -(-1), -2 -1) = B''(5, -3)

The transformed coordinates are ...

__

Additional comment

Reflection over x=a has the transformation (x, y) ⇒ (2a -x, y). Similarly, the reflection over y=a has the transformation (x, y) ⇒ (x, 2a -y).

Note that point P lies on the line of reflection, so its x-coordinate is unchanged.

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Answer:

A≈263.89

Step-by-step explanation:

Solution

A=2πrh+2πr2=2·π·3·11+2·π·32≈263.89378

(a) To find the joint probability density function f(x, y), we multiply the marginal probability density functions fX(x) and fY(y):

f(x, y) = fX(x) * fY(y)

From the given information:

fX(x) = 1, for x > 0

fY(y) = y * exp(-y), for y > 0

Therefore, the joint probability density function is:

f(x, y) = fX(x) * fY(y) = 1 * (y * exp(-y)) = y * exp(-y), for x > 0 and y > 0.

(b) To find the marginal probability density function of X, we integrate the joint probability density function f(x, y) over all possible values of y:

fX(x) = ∫[0, ∞] (y * exp(-y)) dy

Integrating by parts, we have:

fX(x) = -y * exp(-y) |[0, ∞] + ∫[0, ∞] exp(-y) dy

      = 0 + 1

      = 1, for x > 0.

Therefore, the marginal probability density function of X is fX(x) = 1, for x > 0.

(c) To find the conditional probability density function fY|X=z, we use the formula:

fY|X(z) = f(x, y) / fX(z)

From part (a), we know that f(x, y) = y * exp(-y) for x > 0 and y > 0. And from part (b), we know that fX(z) = 1 for z > 0. Therefore, the conditional probability density function is:

fY|X(z) = (y * exp(-y)) / 1 = y * exp(-y), for z > 0 and y > 0.

This is the same as the joint probability density function f(x, y) obtained in part (a).

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