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answer :138

x/3=46

x=46*3

x=138

The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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Answer:

a. The probability of guessing correctly for any individual question is 1/4, since there are four response choices and only one of them is correct.

b. On average, a student would answer 8 questions correctly for the entire test by guessing. This is because there are 32 questions and each question has a 1/4 chance of being answered correctly, so 32 x 1/4 = 8.

c.To calculate the probability of a student getting more than 12 answers correct simply by guessing, we need to use the binomial distribution formula. The formula is:

P(X > k) = 1 - Σ P(X = i), i = 0 to k

where P(X > k) is the probability of getting more than k correct answers, P(X = i) is the probability of getting exactly i correct answers, and Σ represents the sum from i = 0 to k.

In this case, k = 12, since we want to find the probability of getting more than 12 correct answers. The probability of getting exactly i correct answers can be calculated using the binomial distribution formula:

P(X = i) = C(32, i) * (1/4)^i * (3/4)^(32-i)where C(32, i) is the number of ways to choose i correct answers out of 32 questions.

By plugging in the values into the first formula, we can find that the probability of a student getting more than 12 answers correct simply by guessing is approximately 0.097 or 9.7%. This means that a student has a relatively low chance of getting more than 12 answers correct by simply guessing on the test.

\(\{2,3\}\) is a set containing two elements - numbers 2 and 3

\(\{\{2,3\}\}\) is a set containing one element - a set \(\{2,3\}\)

The number of people who waited at least 6 minutes is given as follows:

50 people.

The height of each bin of the histogram represents the number of observations of the data-set in the desired interval.

The desired outcomes for this problem are given as follows:

Hence the number of people who waited at least 6 minutes is given as follows:

20 + 15 + 10 + 5 = 50 people.

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Part A:The sample space contains 20 possible outcomes.

Part B :there are 3 favorable outcomes.

Part C:The probability of selecting 2 cards that are consonants is 3/20.

The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.

Part A:  When two cards are selected from the pile, the set of all possible outcomes known as the sample space is created. Since one of the five cards has already been selected, there are five choices for the first card and four for the second.

As a result, the sample space contains 20 possible outcomes, or 5 x 4.

Part B: There are 3 consonants in the arrangement of cards: R, S, and T, so the number of ways to choose two consonants from the set of three is one of the favorable outcomes. The following combination formula can be used to find this:

f = (number of ways to choose 2 consonants from 3)

= C(3,2)

= 3

So there are 3 favorable outcomes.

Part C: The probability of selecting two consonant-containing cards in the sample space is the product of the number of favorable outcomes and the number of possible outcomes.

P(selecting two consonants) = f / n,

where n is the number of possible outcomes in the sample space and f is the number of favorable outcomes.

Substituting the values we found in parts A and B, we get:

P(selecting 2 consonants) = 3 / 20

Therefore, the probability of selecting 2 cards that are consonants is 3/20.

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Answer:

50% decrease

Step-by-step explanation:

it would be a 50% decrease because half of 8 is 4 and 1/2 is 50 %.

If 4/7 of the puffs that Mr. Tan made were curry puffs and he made 32 curry puffs, then the total number of puffs that he make in all is 56 puffs

The fraction of curry puffs made by Mr. Tan = 4/7

Total number of curry puffs made by Mr. Tan = 32 curry puffs

The rest of the puffs were sardine puffs

Consider the total number of puffs he made as x

Then the equation will be

x × 4/7 = 32

Move 4/7 to the right hand side of the equation

x = 32 ÷ 4/7

x = 32 × 7/4

Divide the terms

x = 32 × 1.75

multiply the terms

x = 56

Therefore, he made 56 puffs in total

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Answer:

22b - 15

Step-by-step explanation:

add the dependent variable together

Answer: 23b- 15

Explation:

Answer:

Ben ate 1 1/2 more chocolate than Alice

Step-by-step explanation:

2 5/8 - 1 1/8 = 1 4/8

Simplify: 1 1/2

Ben ate 1 1/2 more chocolate than Alice.

C. May or may not increase in size even if the added variable has statistical significance.

The R-squared value measures the proportion of variance in the dependent variable that is explained by the model, including the independent variable.

Therefore, if an independent variable is added to the model and it is statistically significant, then it will increase the R-squared value. However, if the variable added is not statistically significant, then it will not have an effect on the R-squared value.

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The correlation between variables x and y is 0.50 . The true option is option (c) .

that's the regression coefficient is positive for given bivariata.

Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The

sample correlation coefficient r quantifies the strength of the relationship.

Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.

Here:

Pearson's correlation coefficient is denoted by "r" and is

r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)

We have given that correlation between x and y is 0.50.

cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2

=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)

Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.

Symbolically it can be expressed as:

bₓᵧ= r σ ₓ /σ ᵧ

where x and y are correlated

σ ₓ --> standard deviation of X

σᵧ ---> standard deviation of y

We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.

Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.

Hence, Regression cofficient is positive.

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Answer:

1 button.

Step-by-step explanation:

Total buttons = 40

Total red buttons = 6

Total Buttons removed =25

Buttons left = 40–25 = 15

Let the red buttons left = x

1.)Then, the probability of red buttons after removing 25 buttons = x/15 outcome / Total outcome)

2.)Probability of red buttons in the bag after removing 25 buttons is 1/3 (As given in the question)

Comparing Statement 1.) & 2.) , We get

x/15 = 1/3

x = 5

So the red buttons left = 5

Total red buttons= 6

Red buttons removed = 6–5= 1

Hence, only 1 button was red in the 25 removed buttons

There is only one red button in the removed buttons if it has a chance of drawing a red button from the bag after removing 25 buttons from the bag with 14 blue, 6 red, 12 green, and 8 purple buttons is 1/3. This is obtained by equating the probability of getting red buttons from the bag after removing 25 buttons with the given probability of red buttons.

Probability is the measure of the likelihood of an event occurring.

Probability is given by the ratio of the number of favorable outcomes with respect to an event to the total number of possible outcomes.

\(p(A) = \frac{n(A)}{n(S)}\)

p(A) is the probability of event A

n(A) is the number of outcomes with respect to A

n(S) is the total number of possible outcomes

Given that a bag contains 14 blue, 6 red, 12 green, and 8 purple buttons.

So the total number of buttons in the bag = 40

It is given that 25 buttons are removed from the bag randomly

thus, the remaining buttons in the bag = 40 - 25 = 15

It is given that the probability of drawing a red button from the bag after removing 25 buttons is 1/3

So, for finding the number of red buttons in the bag after removing we can write,

n(A) = p(A) × n(S)

here, A is the event of drawing the number of red buttons and p(A) = 1/3 and  n(s) = 15 (after removing)

Thus, the number of red buttons in the bag after removing = \(\frac{1}{3}\) × 15 = 5

So, the number of red buttons left in the bag = 5

then, the red buttons removed from the bag = 6 - 5 = 1

Therefore, only 1 red button is removed from the bag.

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The rank of A is at most n-1 and John is correct. Mary's claim is incorrect

Let A = a(i,j) = min(i,j) be an x n matrix. John and Mary were asked to find the rank of A. John claimed that rank r of A should be less than or equal to n/2, whereas Mary said n/2.

We need to check whether these claims are right or wrong.

Now, to find the rank of the given matrix A, we need to reduce it to the row-echelon form.

Consider the matrix below: A=begin{bmatrix} 0 & 0 & 0 &dots&0  1 & 1 & 1 &dots&12 & 2 & 2 & dots &2 3 & 3 & 3 & dots & 3 vdots & vdot s &v dots dots & vdots  n-1 & n-1 & n-1 & dots & n-1   end {bmatrix}

This is the row-echelon form of the matrix A. Here, we have n rows and n-1 columns.

We can obtain this by subtracting first row from the second row, second row from the third row and so on. Let's analyze this matrix to get the rank of A.

The first row of the matrix A has only zeros, which means the first column of the matrix A is a zero column.

Hence, we can eliminate this column from the matrix A and the remaining matrix will have n-1 columns. Therefore, the rank of A is at most n-1.

Now, n-1 is less than or equal to n/2, which means John is correct. Mary's claim that the rank of A is n/2 is incorrect. Therefore, John's claim is true and Mary's claim is incorrect.

Hence, the correct option is "John is correct. Mary's claim is incorrect".

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The probability of losing less than $72 in total is 0.68.

To find the probability of losing less than $72 in total, we need to first calculate the expected loss for each game and then use the law of total probability to find the overall probability.

First, let's calculate the expected loss for each game. The expected loss for the first game is 36 * -2 = -72, and the expected loss for the second game is 50 * -1.5 = -75.

Now, we need to use the law of total probability to find the overall probability of losing less than $72 in total. The law of total probability states that the probability of an event occurring is the sum of the probabilities of the event occurring under each possible condition. In this case, the possible conditions are losing less than $72 in the first game and losing less than $72 in the second game.

So the overall probability of losing less than $72 in total is:

P(losing less than $72) = P(losing less than $72 in first game) + P(losing less than $72 in second game) - P(losing less than $72 in both games)
= (36/100) + (50/100) - (36/100) * (50/100)
= 0.36 + 0.5 - 0.18
= 0.68

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Answer:

i think there both obtuse

Answer:

y int = -1 x= 1/4

Step-by-step explanation:

the y int is always the number after x in slope format to find x int

subtract 4x both sides and y both sides then divide by 4 all sides so x int = 1/4

The appropriate answer is B: There's not enough evidence to decide whether the distribution is skewed or roughly symmetric.

a. The quartiles divide the data into four equal parts. Q1 (the first quartile) is the median of the lower half of the data, Q3 (the third quartile) is the median of the upper half of the data. In this case, Q1 is 71 pounds, which means that 25% of the high school female athletes had a maximum bench press less than or equal to 71 pounds. Q3 is 91 pounds, indicating that 75% of the athletes had a maximum bench press less than or equal to 91 pounds.

b. Based on the given information, we can make an educated guess about the distribution's symmetry. The median (81 pounds) is equal to the mean, which suggests a roughly symmetric distribution. Additionally, the values of Q1 (71 pounds) and Q3 (91 pounds) are symmetrically distributed around the median. However, without additional information or a graphical representation of the data, we cannot definitively determine the distribution's skewness.

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Answer:

The expression to find the perimeter is 12x² - 6, and the perimeter when x= 1.5 is 21

Step-by-step explanation:

The perimeter is the sum of all side lengths for a 2d shape, such as this triangle. Our perimeter is thus

4x² - 3 + 4x² - 2 + 4x² - 1

We can then separate our variables and constants to make it

4x² + 4x² + 4x² - 3 - 2 - 1

Add the constants to get

4x²+4x²+4x²  - 6

To add variables, we must first make sure that they are the same variable/letter as well as to the same degree. The coefficient only affects the result. Because all of our variables are the same letter (x) and are all to the second degree, we can add them. To do this, we simply add the coefficients together to make one big coefficient, and multiply that by the variable. Thus,

4x² + 4x² + 4x² = (4+4+4)x² = 12x²

4x²+4x²+4x²  - 6 = 12x² - 6

Another way of looking at it is that 4x² = 4(x²) = x²+x²+x²+x²

Therefore, the expression to find the perimeter is 12x² - 6, and the perimeter when x= 1.5 is 12 * 1.5² - 6 = 21

Answer:

I got the one above it: L=\(\frac{P}{2}\)-w

Step-by-step explanation:

To solve "P= 2(L+W)" , first distribute:

P= 2L+2W

Then get "2L" alone (by subtracting 2W from both sides):

P-2W= 2L-------- 2L= P-2W

Then divide by two to get just "L":

L= \(\frac{P}{2}\)-W

Hope this helps!

Answer:

\(8b+56\)

Step-by-step explanation:

Given the following question:

\(8(b+7)\)

To rewrite any expression using the distributive property we have to multiply the number outside of the paratheses to the numbers/variables within the paratheses.

\(8(b+7)\)
\(8\times b=8b\)
\(7\times8=56\)
\(8b+56\)

Your answer is "8b + 56."

Hope this helps.

Answer:

Pick any point that has x and y together.

For example,   3               4

                         2                7

                         1                 6

Here the two points which you will be picking is either 3 and 4, or 2 and 7 or 1 and 6.

Once you pick, use the formula: rise/run (which means y/x)

Using the same example above, let's just say that you picked 1 and 6. (remember the first column always represents x values whereas the second column always represent y values). You get the slope by 6/1 = 6.  

Hope that helped!!

Mark brainliest!!

Answer:

SEE BELOW

Step-by-step explanation:

INTERRIOR ANGLES

3.

∠A + ∠B + ∠C = 180

(180 - 103) + (3x - 14) + (3x + 9) = 180

6x = 180 - 77 + 14 - 9

x = 108 / 6

x = 18

m∠ACB = (3x - 14)

             = 3(18) - 14

             = 40

m∠ABC = (3x + 9)

              = 3(18) + 9

              = 63

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

INTERRIOR ANGLES

4.

∠A + ∠B + ∠C = 180

(180 - 97) + (2x + 2) + (14x - 1) = 180

16x = 180 - 83 - 2 + 1

x = 96 / 16

x = 6

m∠BCA = 2x + 2

             = 2(6) + 2

             = 14

m∠ABC = 14x - 1

             = 14(6) - 1

             = 83

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

EXTERIOR ANGLES

5.

∠B

180 - 15x + 20

15x = 180 + 20

   x = 200/15

   x = 13.33

∠C

180 - 9x + 10  

9x = 190

 x = 190/9

 x = 21.11

∠E

180 - 17x + 2

17x = 182

  x = 182/17

  x = 10.706

m∠BEF = 17x + 2

             = 17 (10.706) + 2

             = 184

m∠ABC = 15x + 20

             = 15(15.33) + 20

             = 220

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

EXTERIOR ANGLES

6.

first solve x by adding all the interior angles = 180

∠B + ∠E + ∠C = 180

2x + x + 93 = 180

3x = 180 - 93

x = 87/2

x = 43.5

m∠BEC = 360 - x

             = 360 - 43.5

             = 316.5

m∠ABC = 180 - 2x

             = 180 - 2(43.5)

             = 93

Set up an IVP for the equation of motion of a mass attached to a spring in a medium with damping force, where the damping force is numerically equal to twice the velocity of the mass. The spring is initially displaced below equilibrium and released from rest.

Let's denote the displacement of the mass from its equilibrium position as x(t) and the velocity as v(t). Since the spring is initially stretched to a position 0.1 meters below equilibrium, we have x(0) = -0.1. The equation of motion for the mass-spring system can be written as m * x''(t) = -k * x(t) - b * v(t), where m is the mass, k is the spring constant, and b is the damping coefficient. In this problem, the damping force is given as 2 * m * v(t), so we have b * v(t) = 2 * m * v(t). Substituting these values into the equation of motion, we get m * x''(t) = -k * x(t) - 2 * m * v(t). To fully set up the IVP, we need to specify the initial conditions for the displacement and velocity. Since the mass is released from rest, we have x'(0) = v(0) = 0. To solve this IVP and obtain the equation of motion for z(t), further calculations and analysis are required.

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The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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Answer:

Step-by-step explanation:

6). Since, m∠JMN = 90° [Given]

    And m∠JMK + m∠NMK = m∠JMN

    m∠JMK = m∠JMN - m∠NMK

                  = 90° - 28°

                  = 62°

    From the other figure,

    m∠STR + m∠STP = 180° [Linear pair of angles]

    m∠STR = 180° - m∠STP

                  = 180° - 118°

                  = 62°

    Therefore, mJMK = m∠STR = 62°

    And m∠JMK ≅ m∠STR

8). Since, BF is the angle bisector of ∠AFC,

    ∠AFB ≅ ∠BFC [By angle bisector theorem]

    ∠CFD ≅ ∠BFC [Given]

    Therefore, ∠AFB ≅ ∠CFD [Transitive property of equality]

9). AG is the bisector of CD,

    Therefore, CE ≅ DE ------- (1)

    IJ is the bisector of CE,

    Therefore, CK ≅ KE ---------(2)

    BH is the bisector of ED,

    Therefore, EF ≅ FD -------(3)

    Since, CE ≅ DE [Given as (1)]

    (CK + KE) ≅ (EF + FD)

    2(KE) ≅ 2(EF) [Given in properties (2) and (3)]

     KE ≅ EF

Answer:

$1,843.63

Step-by-step explanation:

\((1+0.11)^{8}\) · 800 = $1,843.63