Name: Date: 6. A biased four-sided die is rolled. The following table gives the probability of each score. Score 1 21 3 Probability 0.28 k 0.15 0.3 a. Find the value of k. (2 marks) b. Calculate the e

\(\\ \sf\longmapsto \dfrac{x}{5}=\dfrac{16}{21}\)

\(\\ \sf\longmapsto 21x=16(5)\)

\(\\ \sf\longmapsto 21x=80\)

\(\\ \sf\longmapsto x=\dfrac{80}{21}\)

\(\\ \sf\longmapsto x=3.6\)

Step-by-step explanation:

\( \frac{x}{5} = \frac{16}{21} \\ by \: cross \: multiplication \\ x \times 21 = 5 \times 16 \\ 21x = 80 \\ x = \frac{80}{21} \\ x = 3.8\)

Answer:

Step-by-step explanation:

1) There exists a 3.82% probability that at least one right-handed student in this class is forced to utilize a seat designed for a left-hander.

2) There exists a 68.35% probability that at least one left-handed student in this class is forced to use a seat designed for a right-hander.

The binomial probability exists the probability of exactly x successes on n repeated trials, and X can only contain two outcomes.

\($P(X=x)=C_{n, x} \cdot \pi^x .(1-\pi)^{n-x}$$\)

In which \($C_{n, x}$\) exists the number of different combinations of x objects from a set of n elements, given by the following formula.

\($C_{n, x}=\frac{n !}{x !(n-x) !}\)

And π exists the probability of X happening.

Given: 13 % of the students are left-handed and 100 - 13 = 87 % are right handed.

There are 220 sets. Of them, 25 exists designed for left handers and 220-25 = 195 for right handers.

There are 215 students, so n = 215.

In this case, a success is a student being right-handed. So \($\pi=0.87$\).

There are 195 seats for right handed students. If there are 196 or more right handed students, they will have to use a seat designed for a left hander. We have to find \($P(X \geq 196)$\). Utilizing a binomial probability calculator, we find that \($P(X \geq 196)=0.0382$\)

So, there is a 3.82 % probability that at least one right-handed student in this class exists forced to utilize a seat designed for a left-hander.

There are 25 seats for left-handed students. If there exists 26 , or more, at least one exists going to be forced to utilize a seat designed for a right-hander.

In this case, a success is a student being left-handed. So \($\pi=0.13$\).

We have to find \($P(X \geq 26)$\).

Using a binomial probability calculator, we have that \($P(X \geq 26)=0.6835$\)

There exists a 68.35 % probability that at least one left-handed student in this class is forced to utilize a seat designed for a right-hander.

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Answer:

x = 55 degrees

Step-by-step explanation:

The sum of the internal angles of a triangle results in 180°

x + 50° + 75° = 180°

x + 125° =180°

x = 180° - 125°

x = 55°

Erika has 6.53 kilograms of apples, which is more than the 6 kilograms she needed for the recipe. Therefore, she has enough apples to make the recipe.

To determine if Erika has at least 6 kilograms of apples, we need to add the weight of all three bags of apples. The total weight of the apples is:

2.56 kg + 1.18 kg + 2.79 kg = 6.53 kg

Erika needs a certain amount of apples for a recipe, specifically 6 kilograms. She goes to the store and picks three different bags of apples - a 2.56-kilogram bag of red apples, a 1.18-kilogram bag of green apples, and a 2.79-kilogram bag of yellow apples. To determine if she has enough apples, she needs to add the weight of all three bags. The total weight of the apples comes out to be 6.53 kilograms. This means that Erika has more than the required 6 kilograms of apples and is sufficient to make the recipe. It's important to note that Erika has an excess of apples, which can be helpful in case she needs extra for the recipe or for future use. The combination of different types of apples can also add variety and flavor to the recipe.

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Answer:

Step-by-step explanation:

Sddviwedcbhbdciuasdlasadc

Answer:

142

Step-by-step explanation:

Okay look here, I'm not always accurate! But I am mature, I do algebra so I might be accurate, but I'm not always accurate.

The probability that X is greater than 3Y is 1/2, and the probability that X + Y is greater than 3 is 1/8.

To find P(X > 3Y), we need to integrate the joint probability density function over the region where X is greater than 3Y. We set up the integral as follows:

P(X > 3Y) = ∫∫[2(x^2)y/81] dy dx

The integration limits are determined by the condition X > 3Y. From 0 ≤ x ≤ 3, we have 0 ≤ 3Y ≤ x, which gives us 0 ≤ Y ≤ x/3. So, the integral becomes:

P(X > 3Y) = ∫[0 to 3] ∫[0 to x/3] [2(x^2)y/81] dy dx

Simplifying the integral, we get:

P(X > 3Y) = ∫[0 to 3] [(x^2)/27] dx

Evaluating the integral, we find P(X > 3Y) = 1/2.

To find P(X + Y > 3), we integrate the joint probability density function over the region where X + Y is greater than 3. We set up the integral as follows:

P(X + Y > 3) = ∫∫[2(x^2)y/81] dx dy

The integration limits are determined by the condition X + Y > 3. From 0 ≤ y ≤ 3, we have 3 - y ≤ X ≤ 3. So, the integral becomes:

P(X + Y > 3) = ∫[0 to 3] ∫[3-y to 3] [2(x^2)y/81] dx dy

Simplifying the integral, we get:

P(X + Y > 3) = ∫[0 to 3] [2y/27] dy

Evaluating the integral, we find P(X + Y > 3) = 1/8.

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There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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The normal curve to estimate the chance that the sum of the 36 draws is greater than 60. The z-score for 60 is 8.

To estimate the chance that the sum of the 36 draws is greater than 60, we need to make some assumptions about the distribution of the draws. Assuming that the draws are independent and identically distributed, we can use the Central Limit Theorem to approximate the distribution of the sum of the draws as a normal distribution with mean (mu) and standard deviation (sigma) given by:

mu = n \(\times\)ev

sigma = \(\sqrt{(n) }\)\(\times\) se

where n is the number of draws, ev is the expected value of each draw, and se is the standard error of each draw.

Without knowing the specifics of the distribution of the draws, we cannot calculate the exact values of mu and sigma. However, we can still use the normal distribution to make an estimate.

First, we need to convert the sum of the 36 draws, 60, to a z-score by subtracting the expected value and dividing by the standard error. Let's assume that the expected value of each draw is 1 and the standard error of each draw is 0.5 (these are just example values).

z = (x - mu) / sigma

z = (60 - 36) / (sqrt(36) * 0.5)

z = 8

So the z-score for 60 is 8.

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Answer: x = -8

Step-by-step explanation:

12 ( x + 10 ) = 24

First we divide the two sides of the exercise by 12.

\(\boldsymbol{\sf{x+10=\dfrac{24}{12} }}\)

We divide 24 by 12..

x + 10 = 2

Subtract 10 from both sides.

x = 2 - 10

Subtract 10 from 2 to get. Since the number 10 is greater than 2, the result will be negative.

x = -8

Answer:

\( \sf \: x = - 8\)

Step-by-step explanation:

Given equation,

→ 12(x + 10) = 24

Now the value of x will be,

→ 12(x + 10) = 24

→ 12(x) + 12(10) = 24

→ 12x + 120 = 24

→ 12x = 24 - 120

→ 12x = -96

→ x = -96 ÷ 12

→ [ x = -8 ]

Hence, the value of x is -8.

A price floor is a law that limits the minimum price at which a good, service, or factor of production can be sold while a price ceiling is a regulation that limits the maximum price at which a good, service, or factor of production can be sold

Price floors are commonly implemented to support producers, while price ceilings are typically put in place to protect consumers from higher prices that might result from shortages or monopolies.

Example of Price Floor:Agricultural subsidies are a common example of price floors. Government price floors ensure that farmers receive a minimum price for their crops.

If the market price of wheat falls below the government-established price floor, the government may buy the excess supply at the guaranteed price, ensuring that farmers are able to make a profit. If there is a price floor, the minimum price is set above the equilibrium price.

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The given rational expression is 4y + 16 y + 4. To find the restricted values of y, we need to identify any values of y that would make the expression undefined.

In this case, the expression is in the form of a sum, so we don't have any denominators that could lead to division by zero. Therefore, there are no restricted values of y for this rational expression.

The expression 4y + 16 y + 4 is defined for all real numbers. We can evaluate it for any value of y without encountering any restrictions.

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To graph the equation y = -1 1/3x + 10, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

In this case, the equation is already in slope-intercept form, where the slope is -1 1/3 and the y-intercept is 10. We can use these values to graph the line as follows:

Plot the y-intercept: The y-intercept is the point where the line crosses the y-axis, which is (0, 10). So, plot the point (0, 10) on the coordinate plane.

Use the slope to find other points: The slope of the line is -1 1/3, which means that for every 3 units we move horizontally (to the right), we move 4 units vertically (downwards). So, starting from the y-intercept (0, 10), we can use this ratio to find other points on the line.

For example, we can move 3 units to the right from the y-intercept to get to the point (3, 10 - 4) = (3, 6). We can also move 6 units to the right to get to the point (6, 10 - 8) = (6, 2). We can continue this process to find as many points on the line as we want.

Plot the points and draw the line: Once we have a few points on the line, we can plot them on the coordinate plane and draw a straight line through them. The line should extend indefinitely in both directions.

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Answer:

Mine is starburst

Step-by-step explanation:

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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The graph is attached. :D

Hope I helped you! The graph calculator is desmos. You can use it for these types of questions.

Stay safe and God bless!

- eli <3

Answer: for the whole test

1. C: x + y ≤ 8

2. C: third graph

3. A: first graph

4. D: fourth graph

5. D: last graph

6. D:0.85x + 1.29y < 5

7. B:6

8. B:3.2x + 0.8y ≤ 50

9. A: first graph

10. D: last graph

Step-by-step explanation:

how because i got an 100%

Answer:

74

10x7=70

10-6=4

70+4=74

The result of the given mathematical expression is 74.

A mathematical expression consists of numbers, variables, and common mathematical operations such as addition, subtraction, multiplication, division, and more.

The given expression is:

{10 x 7} + (10 - 6)

= 70 + 4

= 74

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Answer:

8r

Step-by-step explanation:

(6r - 1)(-8r - 3)

(6r - 8r)( -1 - 3)

-2r(-4)

8r

Pls consider marking me as Brainliest! It would mean a lot!

Answer:

305

Step-by-step explanation:

61 x 5 = 305

Given:

Jimmy done the subtraction directly without changing the mixed fraction to improper fraction and didn't took the LCM.

Answer:17/18

Step-by-step explanation:

Answer:

the first one is (6.5,13)

the second one is (4,4)

Step-by-step explanation:

-2x-0=-13    

-2x=-13 divide -2 by -13

x=6.5

-2(0)-1y=-13

0-1y=-13

-1y=-13

13

so that gives you (6.5,13)

2x+2(0)=8

2x+0=8

2x=8 divide two by eight

x=4

2(0)+2y=8

0+2y=8

2y=8 divide two by eight

y=8

Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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Answer:

Step-by-step explanation:

Elimination sounds the easiest for y:

\(I - 2II: 2x+3y -2x -2y = 15-12 \rightarrow y= 3\)

Now we got one value, let's replace in one of the two and find the second

\(II: x+(3)=6 \rightarrow x=3\)

Answer:

\(2x + 3y = 15...(1) \\ x + y = 6...(2) \\ 2 \times (2) \\ 2x + 2y = 12...(3) \\ (1) - (3) \\ 0 + 3y - 2y = 15 - 12 \\ \color{red} \boxed{ y = 3 }\\ sub \: in \: (2) \\ x + 3 = 6 \rightarrow \: x = 6 - 3 \\ \color{green} \boxed{ x = 3 }\)

\(\bf Step-by-step~explanation:\)

Remember: A coefficient is usually a constant quantity placed before multiplying in algebra. They are usually just numbers.

Since 19 in 19 - 3x is the number here, the coefficient is 19.

\(\large\boxed {\bf Our~final~answer:~19}\)

Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

Step-by-step explanation:

54+90+5×+6=360

so add like terms

54+90+6=150

150+5×=360

5×=360-150

5×=210

--- ----

5 5

×=42

Step-by-step explanation:

90+54+(5x+6)=180...(sum of angles of a triangle)

144+5x+6=180

The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

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The process of writing a = lu is known as the LU decomposition of a matrix.

A matrix A can be decomposed into a lower triangular matrix L and an upper triangular matrix U, such that A=LU. This is called the LU decomposition of a matrix. The lower triangular matrix L has ones on the diagonal, and the upper triangular matrix U has nonzero elements on the diagonal. Here's how you can find the LU decomposition of a matrix:

Step 1: Write the matrix A in the form of an augmented matrix, with an identity matrix on the right-hand side.

Step 2: Use Gaussian elimination to reduce the matrix A to an upper triangular matrix U.

Step 3: The lower triangular matrix L is obtained from the elementary row operations performed on the identity matrix during the Gaussian elimination process.

Step 4: Write the matrix A as the product of the lower triangular matrix L and the upper triangular matrix U.

For example, let's find the LU decomposition of the matrix

                                      \(A = \begin{pmatrix} 2 & 1 & -1 \\ 4 & 2 & 0 \\ -2 & -3 & 8 \end{pmatrix}\)

Step 1: Write the matrix A in the form of an augmented matrix:

                                     \(\begin{pmatrix} 2 & 1 & -1 & 1 & 0 & 0 \\ 4 & 2 & 0 & 0 & 1 & 0 \\ -2 & -3 & 8 & 0 & 0 & 1 \end{pmatrix}\)

Step 2: Use Gaussian elimination to reduce the matrix A to an upper triangular matrix U:

                                    \(\begin{pmatrix} 2 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 2 & -2 & 1 & 0 \\ 0 & 0 & 6 & 2 & 0 & 1 \end{pmatrix}\)

Step 3: The lower triangular matrix L is obtained from the elementary row operations performed on the identity matrix:

                                    \(L = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -1 & 3 & 1 \end{pmatrix}\)

Step 4: Write the matrix A as the product of the lower triangular matrix L and the upper triangular matrix U:

                         \(A = LU = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -1 & 3 & 1 \end{pmatrix} \begin{pmatrix} 2 & 1 & -1 \\ 0 & 0 & 2 \\ 0 & 0 & 6 \end{pmatrix}\)

Therefore, the LU decomposition of the matrix A is:

                                         \(L = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -1 & 3 & 1 \end{pmatrix}\)

                                        \(U = \begin{pmatrix} 2 & 1 & -1 \\ 0 & 0 & 2 \\ 0 & 0 & 6 \end{pmatrix}\)

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