HELP PLS !! WORTH 62 PTS !!!
Find P (Sophomore Girl)
Hint:P(A and B) / P(B)
Classroom of Students:
Boys Girls
Freshman: 4 boys,4 girls =8
Sophomore: 5 boys,7 girls =12
Junior: 2 boys,3 girls =5
Senior: 1 boy, 4 girls =5
12 boys total & 18 girls total
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.

The general solution to the differential equation is y = [-(1/4)x^2 - (1/3)x + (C/4)]^(1/3).

To solve 2yy' + x^2 + y^2 + x = 0 using an appropriate substitution, we can substitute u = y^2. Taking the derivative of u with respect to x, we get du/dx = 2yy'. We can then rewrite the original equation as 2(u^(1/2))(du/dx) + x^2 + u + x = 0.

This is now a separable differential equation, where we can move the u term to the right side and the x terms to the left side: 2(u^(1/2))du/u = -(x^2 + x)dx. Integrating both sides, we get 4/3u^(3/2) = -(1/3)x^3 - 1/2x^2 + C, where C is the constant of integration.

Substituting back u = y^2, we get 4/3y^3 = -(1/3)x^3 - 1/2x^2 + C.

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To determine if a misspelled name is repeated throughout a dataset, a data analyst can use the COUNT function. This function counts the number of occurrences of a value in a range of cells.

Alternatively, the data analyst could use the COUNTA function, which counts the number of cells in a range that contain data (including text and numbers, but not empty or blank cells). The COUNTA function would also count the number of occurrences of the misspelled name in the dataset.

What is a dataset, using an example?

A collection of numbers or values pertaining to one subject constitutes a data set. An example of a data set might be each student's test scores for a certain class. The amount of fish that each dolphin eats in an aquarium is a data set.

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Answer:

B) all real numbers.

Step-by-step explanation:

From Algebra we know that polynomials, including the quadratic function presented on statement, are continuous in every part of real number set, which means the existence of images for every element of domain. Hence, the domain of the quadratic function is all real numbers. (Answer: B)

To find the radius and interval of convergence for a series, use the ratio test. Determine absolute convergence by finding values of x for which the series converges regardless of an's sign, and conditional convergence by considering the sign of an.

To find the radius and interval of convergence for a series, we can use the ratio test. Let's denote the given series as ∑(an * x^n).

(a) To find the series' radius of convergence, we apply the ratio test: lim┬(n→∞)⁡(a_(n+1) * x^(n+1)|/|a_n * x^n).

If the limit is less than 1, the series converges absolutely. If the limit is greater than 1, the series diverges. If the limit is equal to 1, the test is inconclusive.

(b) For absolute convergence, we need to find the values of x for which the series converges regardless of the sign of an. Once we find the interval of convergence, we need to check the endpoints to see if the series converges at those points.

(c) For conditional convergence, we need to find the values of x for which the series converges when the sign of an is considered. In other words, the series converges conditionally if it converges but not absolutely.

Unfortunately, you have not provided the specific series for which you want to find the radius and interval of convergence. Please provide the series, and I will be able to assist you further.

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The correct answer is i. For sufficiently large samples, regardless of the population distribution of variable X itself.

According to the central limit theorem, when we take a sufficiently large sample size from any population, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. This is true as long as the sample size is large enough, typically considered to be greater than or equal to 30.

Therefore, the central limit theorem states that the distribution of sample means approaches a normal distribution, regardless of the population distribution, as the sample size increases. This is a fundamental concept in statistics and allows us to make inferences about population parameters based on sample data.

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Answer:

(

y

−

4

)

=

2

⋅

(

x

+

3

)

y

−

4

=

2

x

+

6

y

=

2

x

+

6

+

4

We get the equation of the line as :

y

=

2

x

+

10

The graph will look like this:

graph{y=2x+10 [-10, 10, -5, 5]

Step-by-step explanation:

The LP problem is to maximize the objective function 10x+15y subject to the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. By graphing the constraints and identifying the feasible region, we can determine the optimal solution.

To find the optimal solution for the LP problem, we first graph the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. These constraints represent the inequalities that the variables x and y must satisfy. We plot the lines 2x+5y = 40 and 6x+3y = 48 on a graph and shade the region that satisfies both constraints.

The feasible region is the area where the shaded regions of both inequalities overlap. We then identify the corner points of the feasible region, which represent the extreme points where the objective function can be maximized.

Next, we evaluate the objective function 10x+15y at each corner point of the feasible region. The point that gives the highest value for the objective function is the optimal solution.

By solving the LP problem graphically, we can determine the corner point that maximizes the objective function. The optimal solution will have specific values for x and y that satisfy the constraints and maximize the objective function 10x+15y.

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(a) The fraction of books that are fiction is 2/3.

(b) The fraction of books that are non-fiction is 1/3.

To find the fraction of fiction and non-fiction books on a bookshelf:

Given: A bookshelf has 96 books. 64 of the books are fiction and the rest are non-fiction books. (a)Fraction of fiction books =?

(b)Fraction of non-fiction books =?

Now,

As given, we have,

The total number of books on a bookshelf = 96

Out of 96, the total number of fiction books = 64

So,

The remaining number of books = non-fiction books = 96-64 = 32

(a) Fraction of fiction books = fiction books/total books

= 64/96

On simplification,

= 2/3

(b) Fraction of non-fiction books = non-fiction books/total books

= 32/96

= 1/3

Therefore, the fraction of fiction and non-fiction books is 2/3 and 1/3 respectively.

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By Lagrange's Theorem, the order of any subgroup of a group must divide the order of the group. Therefore, any subgroup of order 5 in a group of order 20 must be a cyclic subgroup generated by an element of order 5.

There are four elements of order 5 in a group of order 20, and each generates a unique cyclic subgroup of order 5. Therefore, there are four subgroups of order 5 in a group of order 20.
There are 4 subgroups of order 5 in a group of order 20. This is because the number of subgroups of a given order can be found using the formula n(G)/n(H), where n(G) is the order of the group and n(H) is the order of the subgroup. In this case, n(G) = 20 and n(H) = 5, so the number of subgroups is 20/5 = 4.

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Answer: A

Step-by-step explanation: This sign should be shown one-half a mile before the working area, just in case they have to detour to another route.

Based on the information given, the correct option is D since all the options given are correct.

Given,

Motorist entering a work zone .

Construction sites are dangerous as there are numerous hazards there, that's why the construction site safety signs are put in place in order to minimize the risk of injuries and accidents.

Some of the shapes or signs that are used in construction sites in order to prevent accidents include:

• the presence of a flagger.

• orange and diamond shaped work signs.

• a sign with an arrow flashing panel.

It should be noted that the reason why orange color is used is to ensure visibility, that's why a bright color is used in order to prevent accidents. Some of the signs can be shown in a picture or through written words that shows that there's road work ahead.

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The equation of the line of best fit for the data is given as follows:

y = 2.1x - 7.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

(as there are multiple types of regression).

From the text in this problem, the points of the data-set are given as follows:

(0, -8), (1, -5), (2, -1), (3,-1), (5, 2), (6,5), (7,8).

Inserting these points into the linear regression calculator, the equation is defined as follows:

y = 2.1x - 7.

(rounding the slope to the nearest tenth and the y-intercept to the nearest integer.).

The slope for the line is of 2.1 and the intercept is of -7, following the slope-intercept definition of a linear function.

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Answer:

15.4z-12

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

Answer:

x³ - x² - 6x + 60

Step-by-step explanation:

you can write the polinom in this form: (x+2) × (x-3) × (x-10)

(x+2 = 0 => x = -2) same for other two zeros

(x² -3x +2x -6) × (x - 10) =

(x³ - 10x - 3x² + 30x + 2x² - 20x - 6x + 60) =

x³ - x² - 6x + 60

The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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The required three equivalent forms of 6.375. is 6 3/8, 637.5%, 51/8. Option D is correct.

Given that,
The three equivalent forms of the 6.375 is to be determined for the given options.

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Here,
The given number is 6.375

6.375 can be written as,
1)  6.375 = 637.5 / 100 = 637.5%
2) 6.375 = 6 + 0.375 = 6 + 3 / 8 = 6 3/8
3) 6.375 = 63705 / 1000 = 51 / 8

Thus, the required three equivalent forms of 6.375. is 6 3/8, 637.5%, 51/8. Option D is correct.

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Method of predicting a continuous dependent variable on the basis of two or more independent variables. The correct answer is (b)

Multiple regression is a statistical technique used to examine the relationship between a single dependent variable and multiple independent variables.

It is a type of regression analysis that can help to identify which independent variables are related to the dependent variable and to what extent.

The goal of multiple regression is to create a model that can be used to predict the value of the dependent variable based on the values of the independent variables.

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Answer:

A =(Composite number Less than 10)

Answer: (1,8) and (10,1)

Step-by-step explanation:

To find the line of best fit, we need to find the line that comes closest to passing through all the data points. One way to do this is to find the two points that are farthest away from each other and draw a line through them.

By looking at the four options, we can see that the points (1,8) and (10,1) are the farthest away from each other. Therefore, a line passing through these two points would be the line of best fit for the given data.

Answer:

(6, 4) and (9, 1) (3, 5) and (10, 1) (1, 8) and (10, 1) (1, 5) and (7, 3)

Step-by-step explanation:

Answer: -3/2x + 3 ⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀

Answer:

10

Step-by-step explanation:

sqrt root (x2-x1)^2 + (y2-y1)^2

Answer:

top left questions answer is B

the area of the triangle is A

Volume of the cylinder is B

The area of the triangle for q 17 is A

Answer:

1. b

2.a

17.c

Step-by-step explanation:

The total cost of the dinner is given by the equation A = $ 161.19

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of the dinner be represented as A

Now , the equation will be

The cost of the dinner without tax and tip = $ 128.95

The sales tax percentage = 7.5 %

So , the sales tax amount = ( 7.5 % ) x cost of the dinner without tax and tip

Substituting the values in the equation , we get

The sales tax amount = ( 7.5/100 ) x 128.95

The sales tax amount = $ 9.0265

Now , the percentage of tip = 18 %

So , the tip amount = ( 18 % ) x 128.95

The tip amount = $ 23.211

And , the total cost of the dinner A = cost of the dinner without tax and tip + sales tax amount + tip amount

On simplifying the equation , we get

The total cost of the dinner A = $ 128.95 + $ 9.0265 + $ 23.211

The total cost of the dinner A = $ 161.1875

Hence , the total amount of dinner is $ 161.19

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Answer:

-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2

Step-by-step explanation:

-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2

The number of water stations there are along the 13 1/2 miles long road race according to the task content is; Choice C; 18 water stations.

It follows from the task content that the number of water stations can be determined as follows;

13 1/2 ÷ 3/4

= 27/2 × 4/3

= 18 water stations.

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Step-by-step explanation:

l = length

w = width

we know, the perimeter of our rectangle is

2×l + 2×w = 600

and that tells us

l + w = 300

l = 300 - w

the area of the rectangle is

A = l × w

so, we use the previous equation in this one :

A = (300 - w) × w = -w² + 300w

this is a quadratic equation that is opening down (negative initial factor).

so the vertex of this parabola is the maximum.

the x (or in our case w) coordinate of the vertex is

-b / 2a

a = -1

b = 300

so,

w = -300 / (2×-1) = -300/-2 = 150 ft

and l × w = 300

l = 300 - w = 300 - 150 = 150 ft.

the maximum area for 600 ft fence is a square with 150 ft side length.

Answer:

The formula is \(a_n = 3n-2\)

The 14th term is 40, in other words, \(a_{14} = 40\)

========================================================

Explanation:

The given sequence is 1, 4, 7, 10, ...

Subtract each adjacent term:

This shows that each term is increasing by 3. This is the common difference, so d = 3.

The first term is \(a_1 = 1\)

The nth term of the arithmetic sequence is...

\(a_n = a_1 + d(n-1)\\\\a_n = 1 + 3(n-1)\\\\a_n = 1 + 3n-3\\\\a_n = 3n-2\\\\\)

As a check, let's plug in say n = 3 to find that:

\(a_n = 3n-2\\\\a_3 = 3(3)-2\\\\a_3 = 9-2\\\\a_3 = 7\\\\\)

The third term is 7, which matches with the sequence given to us. I'll let you confirm the other values.

-----------

We'll repeat this idea but now for n = 14 to find the 14th term of the sequence.

\(a_n = 3n-2\\\\a_{14} = 3(14)-2\\\\a_{14} = 42-2\\\\a_{14} = 40\\\\\)

The 14th term is 40.

You can make a table of values to help confirm the answer. In the first column you'll have the values of n (1,2,3,...) all the way up to 14. The second column will consist of the sequence 1, 4, 7, 10, ... each time going up by 3 until you reach the 14th term of 40.

Answer:

5000

Step-by-step explanation:

100/52=?

?x2600=5000

Answer:

x=5000

Step-by-step explanation:

100%=5000

branliest

Answer:

336.

Step-by-step explanation:

8P3 = 8! / (8 - 3)!

       = 8*7*6*5*4*3*2*1 / 5*4*3*2*1

       = 8*7*6

       = 336