Mr. Gordon has 13 girls and 14 boys in his fourth period algebra class. One person is chosen at random.
What is the probability that the person chosen is a boy?
A. 1/14
B. 1/27
C. 13/14
D. 13/27
E. 14/27

Answer:

6x^2

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

thats math

Answer:

5 hours

Step-by-step explanation:

227.5+97.5=325

325/65=5

Answer:

The probability that neither player gets on base is 0.4824

Step-by-step explanation:

1. Both players get to base. Just multiply the two probabilities together:

= (probability first batter gets on base) x (probability second batter gets on base, if the first batter gets on base)

= 0.23 x 0.38

= 0.0874

2. One player gets to base. The formula here is P(A+B) =P(A) + P(B) - P(A) x P(B)

= (probability first batter gets on base) + (probability second batter gets on base, if the first batter does not) - (0.23 x 0.26)

= 0.23 + 0.26 - (0.23 x 0.26)

= 0.49 - 0.0598

= 0.4302

3. Neither player gets to base = 1 - addition of the previous two cases.

= 1 - (0.0874 + 0.4302)

= 1 - 0.5176

= 0.4824

Answer:

[tex]b = 12\,m[/tex] and [tex]h = 12\,m[/tex]

Step-by-step explanation:

The formula of the area for a triangle is:

[tex]A = \frac{1}{2}\cdot b\cdot h[/tex]

Where:

[tex]b[/tex] - Base

[tex]h[/tex] - Height

But [tex]b = h[/tex], then, the formula is simplified into this form:

[tex]A = \frac{1}{2}\cdot b^{2}[/tex]

Now, all known variables are substituted and the base is:

[tex]b = \sqrt{2\cdot A}[/tex]

[tex]b = \sqrt{2\cdot (72\,m^{2})}[/tex]

[tex]b = \sqrt{144\,m^{2}}[/tex]

[tex]b = 12\,m[/tex]

And the height is:

[tex]h = 12\,m[/tex]

The base and height of the triangle, both having equal measures, are found to be 12 meters each by using the formula for the area of a triangle and quadratic equations.

The subject of this problem is triangle geometry within Mathematics. The area of a triangle is calculated using the formula A = 1/2 * base * height. Since we know that the base is equal to the height, we can say that base = height, and hence we can modify the formula to become A = 1/2 * base². Given that the area A is 72 square meters, we substitute this value back into the equation to calculate it as follows:

72 = 1/2 * base².

Solving for base (and consequently, height due to its equal measure), we get base = height = √(72 * 2) = √144 = 12 meters.

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Answer:

Step-by-step explanation:

The amount Gia got for her car was ...

  1800/3000 × 100% = 60%

of the amount it is worth. This percentage is less than the 70% Gia wanted as a minimum. She did not get what she wanted.

Answer:

There are 4 desired outcomes.

Step-by-step explanation:

You want to select a white ball from a bag of balls. So the number of desired outcomes is the number of white balls in the bag.

In this problem:

Ball being drawn from a bag containing 4 white balls, 3 black balls, and 5 red balls

4 white balls

So there are 4 desired outcomes.

Answer:

$5336.90

Step-by-step explanation:

First step is to filter through what is given And to deduce the important information....

Kindly go through the attached file for further comprehension and a detailed solution.

To determine the average annual income difference between individuals with a 4-year degree and those with a 2-year degree, multiply the education coefficient (2668.45) by 2, resulting in an approximate difference of $5336.90.

Based on the regression analysis provided, the variable coefficient for education is 2668.45. This coefficient represents the average change in annual income associated with an additional year of formal education. If we want to compare the annual earnings of individuals with a 4-year college degree to those with a 2-year degree, we calculate the difference by multiplying the coefficient by the difference in years of education (4 years - 2 years = 2 years).

To find the increase in annual income for those with a 4-year degree compared to a 2-year degree, we perform the following calculation:
2668.45 × 2 = 5336.90.

Therefore, on average, people with a 4-year college degree earn approximately $5336.90 more annually than those with only a 2-year degree, according to this model.

Answer:

[tex] X+Y \sim N(\mu_X +\mu_Y , \sqrt{\sigma^2_X +\sigma^2_Y})[/tex]

The mean is given by:

[tex] \mu = 3.8+2.9= 6.7[/tex]

And the standard deviation would be:

[tex] \sigma =\sqrt{1.2^2 + 1.7^2} = 2.08[/tex]

And the distribution for X+Y would be:

[tex] X+Y \sim N(6.7 , 2.08) [/tex]

And the best answer would be:

D.) Mean, 6.7; standard deviation, 2.08

Step-by-step explanation:

Let X the random variable who represent the AP Art History exam we know that the distribution for X is given by:

[tex] X \sim N(3.8, 1.2)[/tex]

Let Y the random variable who represent the AP English exam we know that the distribution for X is given by:

[tex] X \sim N(2.9, 1.7)[/tex]

We want to find the distribution for X+Y. Assuming independence between the two distributions we have:

[tex] X+Y \sim N(\mu_X +\mu_Y , \sqrt{\sigma^2_X +\sigma^2_Y})[/tex]

The mean is given by:

[tex] \mu = 3.8+2.9= 6.7[/tex]

And the standard deviation would be:

[tex] \sigma =\sqrt{1.2^2 + 1.7^2} = 2.08[/tex]

And the distribution for X+Y would be:

[tex] X+Y \sim N(6.7 , 2.08) [/tex]

And the best answer would be:

D.) Mean, 6.7; standard deviation, 2.08

To find the combined mean and standard deviation, use weighted average for means and formula for standard deviation of two independent variables.

To find the combined mean and standard deviation for the AP Art History and AP English exams, we need to use the formulas for combining means and standard deviations when the two sets of data are independent. The combined mean can be found by taking the weighted average of the two means, where the weights are the number of observations in each dataset.

The combined standard deviation can be found using the formula for the standard deviation of the sum of two independent variables. After calculating, the combined mean is 3.35 and the combined standard deviation is 2.08.

So the correct answer is D) Mean, 3.35; standard deviation, 2.08.

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Answer:

Find the arc length.

532.95863765

Step-by-step explanation:

Answer:

15 players played in the chess tournament.

Step-by-step explanation:

When there are 15 players, the first player plays 14 games and step aside.

remaining 14 player

next player plays 13 games. steps aside

remaining 13 players

next player plays 12 games. steps aside

remaining 12 players

next player plays 11 games. steps aside

remaining 11 players

.

.

.

.

Last player plays 1 game and steps aside

remaining 1 player who will not play against himself.

∴ Sum of all games played

= 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105 games played

Answer:

Step-by-step explanation:

Let be the number of players. There was a game for every pair of players, so there must be 105 pairs of players.

(−1)/2=105.

should be easy to solve after that.

Answer:

all work is shown and pictured

Answer:

A. a circle, B. an octagon, E. a decagon, F. a triangle

Step-by-step explanation:

Squares and rectangles can be made by slicing a cube.

Answer:

A

a circle

B

an octagon

E

a decagon

Step-by-step explanation:

I had this question on my math test and these are correct

Answer:

[tex]a_{n} = 32(\frac{1}{4})^{n-1}[/tex]

Step-by-step explanation:

The nth term of a geometric sequence is given by the following equation.

[tex]a_{n+1} = ra_{n}[/tex]

In which r is the common ratio.

This can be expanded for the nth term in the following way:

[tex]a_{n} = a_{1}r^{n-1}[/tex]

In which [tex]a_{1}[/tex] is the first term.

This means that for example:

[tex]a_{3} = a_{1}r^{3-1}[/tex]

So

[tex]a_{3} = a_{1}r^{2}[/tex]

[tex]2 = a_{1}(\frac{1}{4})^{2}[/tex]

[tex]2 = \frac{a_{1}}{16}[/tex]

[tex]a_{1} = 32[/tex]

Then

[tex]a_{n} = 32(\frac{1}{4})^{n-1}[/tex]

Answer:

=2(4+9w)

=2(4) 2(+9w)

=8 +18w

=18w+8

Step-by-step explanation:

Answer:

Hence P values of beta becomes smaller(< 0.0001). and doest affect the mean response

Step-by-step explanation:

Given:

AS Predictor  become more highly correlated .

To find:

Descriptive  Nature of high correlated Predictor .

Solution:

A predictor is high correlated means:

1)It means that the two variables are strongly related to each other.

2)This is also called as problem of multicollinearity when two variables are

in Regression.

Effects when predictor are highly correlated ;

In short ,Mulitcollinearity does not affect the mean response and  new response of the model.

Hence P values of beta becomes smaller(< 0.0001). and doest affect the mean response

Answer:

A Dot Plot, also called a dot chart or strip plot, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete bins (categories). ... A dot plot is a graphical display of data using dots

Answer:

60% or 3/5

Step-by-step explanation:

Tails was the result 3 times.

There were 5 trials.

The probability is 3/5.

Answer:$6250

Step-by-step explanation:

selling price(sp)=12000

Original price(op)=?

sp+500=2 x op

12000+500=2 x op

12500=2 x op

Divide both sides by 2

12500/2=(2 x op)/2

6250=op

Therefore original price is $6250

To find the original price of the car, set up an equation with the given information and solve for X. The original price of the car was $6,250.

To find the original price of the car, we need to set up an equation based on the given information. Let's assume the original price of the car is X. According to the question, the selling price of the car is $12,000, which is $500 less than two times its original price. So, we can write the equation as:

2X - $500 = $12,000

To solve the equation, we add $500 to both sides:

2X = $12,500

Finally, we divide both sides by 2 to find the original price of the car:

X = $6,250

Therefore, the original price of the car was $6,250.

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Answer:

a)Null hypothesis:- H₀: μ> 500

  Alternative hypothesis:-H₁ : μ< 500

b) (5211.05 , 5411.7)

95% lower confidence bound on the mean.

c) The test of hypothesis t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Step-by-step explanation:

Step :-1

Given  a random sample of 15 devices is selected in the laboratory.

size of the small sample 'n' = 15

An average life of 5311.4 hours and a sample standard deviation of 220.7 hours.

Average of sample mean (x⁻) =  5311.4 hours

sample standard deviation (S) = 220.7 hours.

Step :- 2

a) Null hypothesis:- H₀: μ> 500

Alternative hypothesis:-H₁ : μ< 500

Level of significance :- α = 0.95 or 0.05

b) The test statistic

[tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n-1} } }[/tex]

[tex]t = \frac{5311.4 - 500}{\frac{220.7}{\sqrt{15-1} } }[/tex]

t = 5.826

The degrees of freedom γ= n-1 = 15-1 =14

tabulated value t =1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

calculated value t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Null hypothesis is rejected at  95% confidence on the mean.

C) The 95% of confidence limits

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } ,x^{-} + t_{0.05}\frac{S}{\sqrt{n} } )[/tex]

substitute values and simplification , we get

[tex](5311.4 - 1.761 \frac{220.7}{\sqrt{15} } ,5311.4 +1.761\frac{220.7}{\sqrt{15} } )[/tex]

(5211.05 , 5411.7)

95% lower confidence bound on the mean.

The correct answer is 27√​3

Answer: The area or "the answer" will be 27√​3

Step-by-step explanation:

(Please vote me Brainliest if this helped!)

A reflection across the line x=-3 is achieved by subtracting each x-coordinate from -6, resulting in a new point of (-6 - x, y). The y-coordinate remains unchanged in the reflection.

In mathematics, a reflection is a transformation that uses a line of reflection to create a mirror image of the original figure. In this case, the line of reflection is x = -3.

To reflect a point across this line, we modify only the x-coordinate of each vertex. The rule for a reflection over the line x = -3 is to take each x-coordinate and subtract it from -6 (which is the double of -3). So, if we have a point (x, y), after the reflection the new point would be (-6 - x, y). This results in a new x-coordinate that is the mirror image around the line x = -3, while the y-coordinate remains unchanged.

For example, if we have a vertex at (2, 5), after the reflection, it would be at (-6 - 2, 5), or (-8, 5).

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Answer:

a.

[tex]\vec{u}=\frac{\bigtriangledown F(-3,3)}{|\bigtriangledown F(-3,3)|}=\frac{1}{\sqrt{2}}[\hat{i}-\hat{j}][/tex] (ascent)

[tex]\vec{u}=-\frac{\bigtriangledown F(-3,3)}{|\bigtriangledown F(-3,3)|}=-\frac{1}{\sqrt{2}}[\hat{i}-\hat{j}][/tex]  (descent)

b.

[tex]\vec{v}=\frac{1}{\sqrt{2}}[\hat{i}+\hat{j}][/tex]

Step-by-step explanation:

a. The function is given by:

[tex]F(x,y)=e^{-(x^2/6+y^2/6)}[/tex]

the point is P(-3,3)

a. The unit vector that gives the direction of the steepest ascent is necessary to compute the gradient of F(x,y):

[tex]\bigtriangledown F(x,y)=e^{-(x^2/6+y^2/6)}(-\frac{x}{3})\hat{i}+e^{-(x^2/6+y^2/6)}(-\frac{y}{3})\hat{j}\\\\\bigtriangledown F(x,y)=-\frac{1}{3}e^{-(x^2/6+y^2/6)}[x\hat{i}+y\hat{j}][/tex]

The, it is necessary to evaluate in the point P, and to compute the norm of the vector in order to get the unit vector:

[tex]\bigtriangledown F(-3,3)=-\frac{1}{3}e^{-(\frac{9}{6}+\frac{9}{6})}[-3\hat{i}+3\hat{j}]\\\\\bigtriangledown F(-3,3)=e^{-3}[\hat{i}-\hat{j}]\\\\|\bigtriangledown F(-3,3)|=\sqrt{(e^{-3})^2+(e^{-3})^2}=\sqrt{2}e^{-3}\\\\\vec{u}=\frac{\bigtriangledown F(-3,3)}{|\bigtriangledown F(-3,3)|}=\frac{1}{\sqrt{2}}[\hat{i}-\hat{j}][/tex]   (ascent)

for the steepest descend you have

[tex]\vec{u}=-\frac{\bigtriangledown F(-3,3)}{|\bigtriangledown F(-3,3)|}=-\frac{1}{\sqrt{2}}[\hat{i}-\hat{j}][/tex]

b.

the vector with the direction of no change is a vector perpendicular to grad(F):

[tex]\bigtriangledown F(-3,3)\cdot \vec{v}=0\\\\e^{-3}v_1-e^{-3}v_2=0\\\\v_1=v_2[/tex]

furthermore, v is an unit vector:

[tex]\sqrt{v_1^2+v_2^2}=1\\\\v_1 ^2+v_1^2=1\\\\2v_1^2=1\\\\v_1=\frac{1}{\sqrt{2}}=v_2[/tex]

then, the vector is:

[tex]\vec{v}=\frac{1}{\sqrt{2}}[\hat{i}+\hat{j}][/tex]

The probability that a randomly selected airfare between Boston and Orlando will be less than $300 is approximately 10.04%.

To find the probability that a randomly selected airfare between Boston and Orlando will be less than $300, we need to calculate the z-score and use the standard normal distribution table.

Therefore, the probability that a randomly selected airfare between Boston and Orlando will be less than $300 is approximately 0.10035, or 10.04%.

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Final answer:

To find the lower quartile of a data set, sort the data in ascending order and find the median of the lower half.

Explanation:

To calculate the lower quartile of a data set, you need to find the median of the lower half of the data. In this case, we have 10 blood glucose readings. To find the lower quartile:

First, sort the data in ascending order: 88, 97, 101, 104, 104, 107, 109, 117, 121, 147.

Since we have an even number of values (10), the lower half has 10/2 = 5 values.

The median of the lower half of the data is the average of the two middle values: 104 and 104. So, the lower quartile is 104.

Answer:

Bottling plant B (with 175,000 sports drinks per day), because the daily mean will be closer to 21 fluid ounces with more sports drinks in the sample.

Given Information:

Mean volume = μ = 20 fl oz

Sampling size of plant A = n₁ = 50,000 drinks/day

Sampling size of plant B = n₂ = 175,000 drinks/day

Required Information:

Which bottling plant is less likely to record a mean volume of 21 fl oz ?

Answer:

Plant B is less likely to record a mean volume of 21 fl oz

Step-by-step explanation:

The standard deviation of the plant A is given by

σa = σ/√n₁

The standard deviation of the plant B is given by

σb = σ/√n₂

Where σ is standard deviation for the mean volume of 20 fl oz and it is fixed.

As you can notice in the above relation, the standard deviation of the plants depend upon the number of samples (n). As the number of sample increases, the standard deviation of samples decreases which means that the mean of the samples will be closer to the actual mean (that is 20 fl oz).

Since the plant B has more samples (n₂ = 175,000) then its standard deviation (σb) will be less and the mean will be closer to 20 fl oz therefore, it is less likely that it will record a mean of 21 fl oz.

Plant A is more likely to record a mean volume of 21 fl oz

Answer:

There will be required 590 repair persons.

Step-by-step explanation:

Lets count the amount of minutes that are going to be used per week repairing. The amount of minutes of repair work required per week is

100*23 + 100*42+ 100*19 + 150*27 + 150*35 = 17700.

Each worker works 6 hours per day in average and 5 times per week. This means that each worker will do 30 hours of work each week. Therefore, we will need 17700/30 = 590 workers (In practice you should contract a few more, like 600, just in case).

Answer:

Is there a picture of the table I will try and solve but I'm not sure if I can

Answer:

0,3,7/4

Step-by-step explanation: In the equation,x-1/4 means 1/4 is subtracted from x to find each value of y,we need to take each value of x and subtract 1/4 for example: when x = 1/4: y = 1/4 - 1/4 , y = 0

Answer:

139 boys

Step-by-step explanation:

Using the given information, we can set up a system of equations.

Let the number of girls in the class be x and let the number of boys in the class be y.

x + y = 351

x = y + 73

Solving this system of equations would tell you that there are 139 boys in this graduating class.

Leave a comment if you want me to be a bit more in-depth.

Answer:

that is the solution to the question

The percentage change to 2 decimal places when a price of £60 is increased to £89.99 is 49.98%.

Given that, a price of £60 is increased to £89.99.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, old price =£60 and new price =£89.99

Change in price = 89.99-60

= 29.99

Percentage = Change in price/Old price ×100

= 29.99/60 ×100

= 0.4998 ×100

= 49.98%

Therefore, the percentage change to 2 decimal places when a price of £60 is increased to £89.99 is 49.98%.

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