the table below lists probabilities for the corresponding number of girls in three live births. what is the random variable, what are its possible values, and are its values all numerical?

Answer:352

Step-by-step explanation:

Answer:

Step-by-step explanation:

The number of hours it is suggested to study is 8.5 hours using the concept of the equation.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. LHS = RHS (left-hand side = right-hand side) appears in all mathematical equations. The value of an unknown variable, or unknown quantity, can be determined by solving equations.

Given,

The given linear equation P = 6.31H + 41.5, is used to predict the points earned P.

Also P = 95,

Now, we will find the value of H by using LHS=RHS

95 = 6.31H+41.5

Subtract 41.5 from both sides,

53.5 = 6.31H

Now, divide both sides by 6.31,

8.5 = H

Therefore, the number of hours it is suggested to study is 8.5 hours.

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The number problems solved by the little Monsters  of Beast Academy in March's meet is 15.

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

let the number of questions solved by little Monsters  of Beast Academy in

In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems = y/5

In March's Math Meet, they solved $\frac23$ of the problems = 2x/3

Hence:

y/5 + 2x/3 = 12

x + y = 30

solving the equation gives

x = y = 15

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Answer:

Step-by-step explanation:

y = ¼x + (-7/4) is the standard form for the line that passes through (3, −1) and (−5, −3)

What is Slope intercept form?

y=mx=c is the slope intercept form of a line, m is the slope.

We need to find equation of line passing through (3, −1) and (−5, −3)

First we need to calculate slope 'm'.

slope m = y2- y1 / x2-x1

y2=-3, y1=-1, x2=-5, x1=3

m= -3 - (-1)/(-5)-3 = -2/-8=1/4

Equation of line, y=mx+c

find C in the equation (y=mx+c)

C = y-mx

C = -1-1/4(3)= -7/4

now replace the values you find in the equation (y=Mx+C)

y =1/4x-7/4

Hence y =1/4x-7/4 is the equation of line  passes through (3, −1) and (−5, −3).

[tex]{ \pink{ \boxed{ \blue{ \sf{x = 2}}}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \sf{3x + 4x - 2 = 12}}}[/tex]

[tex]{ \red{ \sf{7x = 12 + 2}}}[/tex]

[tex]{ \red{ \sf{7x = 14}}}[/tex]

[tex]{ \red{ \sf{x = \frac{14}{7}}}} [/tex]

[tex]{ \blue{ \boxed{ \green{ \sf{x = 2}}}}}[/tex]

The value of the equation g(x+1) is -2x²-x

Given equation,

g(x) = -2x²+3x-1

Replacing x in the equation by x+1

g(x+1) = -2(x+1)² +3(x+1) -1

g(x+1) = -2(x²+1+2x) +3x +3 -1

g(x+1) = -2x² -2 -4x +3x +3 -1

g(x+1) = -2x²- x

Hence the final answer is g(x+1) = -2x²-x

Since this, the question says to find the value g(x+1) we need to replace the value of x in the given equation g(x) by x+1 to find value. After replacing we get -2(x+1)² +3(x+1) -1. Next, we need to solve the bracket (x+1)² which will give us x²+1+2x. We will multiply this by -2, which will give us -2x² -2 - 4x. Next, we will solve 3(x+1) which will give us 3x+3. Finally, we need to solve the whole equation to get the answer -2x²- x

I hope this answer helps.

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The probability is 0.6 that if randomly choosen none of them are senior.

acc to our question-

Hence,the probability is 0.6 that if randomly choosen none of them are senior.

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Step-by-step explanation:

the slow of a line is the factor of x in a "y = ..." firm of equation.

the line going through (1, 5) has a slope of 3 (when x increases by +1, then y increases by +3, so the slope y/x = 3).

(B) and (C) are out, because there is no line with slope 3 (only -3).

the line going through (-2, 9) has a slope of -2 (when x increases by 1, y decreases by 2, so the slope y/x = -2/1 = -2).

(A) is out, as there is no line with the slope -2 (only +2).

so, (D) is the correct answer.

From the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).

As given in the question,

Table which represents the system of linear function are as follow:

table 1:

x:      -4       -2        0       2

y:     26       18       10     2

table 2:

x:      -4       -2        0       2

y:     14       8         2      -4

For table1 :

System of linear function:

(x₁ , y₁) = (0,10)

(x₂ , y₂) = (2, 2)

Equation of linear function:

(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)

⇒(y -10)/ (x-0) =(2-10)/(2-0)

⇒y-10 =-4(x)

⇒ y = -4x +10     __(1)

For table2 :

System of linear function:

(x₁ , y₁) = (0,2)

(x₂ , y₂) = (2, -4)

Equation of linear function:

(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)

⇒(y -2)/ (x-0) =(-4-2)/(2-0)

⇒y-2 =-3(x)

⇒ y = -3x +2     __(2)

Solve system of linear function (1) and (2) we get,

-4x +10 = -3x +2

⇒4x -3x =10 -2

⇒x =8

⇒y = -4(8) +10

     = -22

(x, y) = (8 ,-22)

Therefore, from the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).

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Answer:

D

Step-by-step explanation:

trust

Answer:

 50 people

Step-by-step explanation:

Solution

25% as a fraction is 25/100 which reduces down to 1/4. What this tells you is that 1/4 of the people asked want the hotel

1/4 * 200 = 50

50 people want the hotel.

The "Poisson distribution" is the probability distribution that comes the closest to accurately describing that many dog bite patients visit this hospital across any given day.

For the given data of,

An average of two dog bite victims show up at Carver Memorial Hospital each day.

A probability distribution that most accurately predicts the number of dog bite victims who visit this hospital on any given day is characterized as the "Poisson distribution."

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There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.

In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:

x + 2 · y + 8 = 0

2 · y = - x - 8

y = - (1 / 2) · x - 4

Then, the resulting line has a slope of - 1 / 2.

Second, determine the intercept of the resulting line:

y = m · x + b

b = y - m · x

b = - 3 - (- 1 / 2) · (- 2)

b = - 3 - 1

b = - 4

The intercept of the resulting line is - 4.

Third, transform the equation of the resulting line into standard form:

y = - (1 / 2) · x - 4

- 2 · y = x + 8

x + 2 · y + 8 = 0

There is no parallel line for the point (x, y) = (- 2, 3).

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The relation accepts reflexive, symmetry, and transitive.

Recall that a relation R is reflexive if the element (x, x) belongs to R for all elements X in the domain of R.

If (x, y) belongs to R, then follows that (y, x) must likewise belong to R, making the situation symmetric.

And it is transitive if (x, y) and (y, z) belongs to R necessarily implies that (x, z) belongs to R.

Given r is a relation on the set of all nonnegative integers R(a,b)

Reflexive - YES. A given number a will always have the same remainder when divided by 5.

Symmetric - YES. If a and b have the same remainder when divided by 5, then b and a are the same pair, so again they will have the same remainder.

Transitive - YES. If a and b as well as b and c have the same remainder when divided by 5, this is possible if both a and c also have the same remainder when divided by 5.

Therefore the relation accepts reflexive, symmetry, and transitive.

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The answer to this question is provided in main body.The equation will be as,

What is equation?

an equation could be a formula that uses the sign to attach 2 expressions to indicate that they're equal.

Main Body:

given : points (5,1) and (3,5).

Since slope of line passing through two points

(x₁,y₁ ) and (x ₂ ,y₂​ ) is m= (x₂​ −x₁)/(y₂​ −y₁)

​We now find the slope of the line passing through the points (5,1) and (3,5) as shown below:

⇒m= (5-1)/(3-5)

⇒m= 4/-2

⇒m= -2

Therefore, the slope of the line is  -2

Now use the slope and point (5,1) to find the y-intercept.

y= mx+b

⇒1= -2(5) +b

⇒1= -10 + b

⇒b= -11

Write the equation in slope intercept form as:

y= mx+b

y = -2x -11

Hence the equation of line is, 2x + y= -11.

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The value of the expression -5(-6k-6)-(-9k-10) in simplest terms is 39k + 40

An algebraic expression can be described as an expression that is made up of terms, variables, coefficients, factors and constants.

These expressions are also known to be composed of certain mathematical operations, such as;

We have the expression;

-5(-6k-6)-(-9k-10)

expand the bracket

-5(-6k - 6) + 9k + 10

collect like terms

30k + 30 + 9k + 10

Add the like terms

39k + 40

Hence, the value is 39k + 40

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The monthly payment for the first condition is $1750.11 and the total number of payments is 156.

What is the monthly payment?

Monthly payment is defined as the amount paid every month depending on the terms of the mortgage loan. This includes the principal, which is the actual balance on the loan, and the interest on the loan.

The formula for monthly payments on the mortgage is given:

                                [tex]MP = \frac{P(\frac{r}{n}) }{1- (1+\frac{r}{n})^{-nt} }[/tex]

where, MP = monthly payment

            P = principal amount

             r = rate of interest

             n = number of payments per year

              t = number of years

Given, a couple buys a house for $290000 and makes a down payment of 15%

Down payment = 0.15*290000 = $ 43500

First condition,

Present value of loan (P) = $290000 - $43500 = $246500

rate of interest (r) = 3.4% = 0.034

number of payments per year (n) = 12

number of years (t) = 15 years

Then, the monthly payment is calculated by:

             [tex]MP = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*15} } = 1750.11[/tex]

Therefore, monthly payment = $1750.11

Second condition,

monthly payment (MP) = $1950

Present value of loan (P) = $290000 - $43500 = $246500

rate of interest (r) = 3.4% = 0.034

number of payments per year (n) = 12

time in years (t) = x years

Then,

or,  [tex]1950 = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*x} }[/tex]

or, [tex]x = 13.06 = 13[/tex]

So, the total number of payments =  13*12 = 156

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Answer:

0.64 feet

Step-by-step explanation:

make h the subject of this expression

[tex]t = \sqrt{ \frac{h}{16} } [/tex]

[tex] {t}^{2} = \frac{h}{16} [/tex]

[tex]h = 16 {t}^{2} [/tex]

then substitute in the value of t=0.2 into the equation of h:

h = 16 × (0.2)² = 0.64 feet(answer)

Answer:

Step-by-step explanation:

One example is a=-6 and b=3

-6/3=-2

-6*3=-18

-2 is greater than -18; the quotient is greater than the product in this case.

Another example is a=6 and b=3

6/3=2

6*3=18

2 is smaller than 18; the quotient is smaller than the product in this case.

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Using the general addition rule, p(F or G) = 0.667.

What is sample space?

In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.

Let,

S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

F = {8, 9, 10, 11, 12, 13}

G = {12, 13, 14, 15}

n(S) = number of elements in set S are 12.

n(F) = 6

n(G) = 4

n(F and G) = common elements in F and G = 2

n(F or G) = n(F) + n(G) - (F and G)

n(F or G) = 6 + 4 - 2

n(F or G) = 8

Now, using the general addition rule,

P(F or G) = P(F) + P(G) - P(F and G)

Here,

P(F) = n(F)/n(S) = 6/12 = 1/2

P(G) = n(G)/n(S) = 4/12 = 1/3

P(F and G) = n(F and G)/n(S) = 2/12 = 1/6

⇒ P(F or G) = 1/2 + 1/3 - 1/6

                   = 5/6 - 1/6

                   = 4/6

⇒ P(F or G) = 0.667

Hence, using the general addition rule, P(F or G) = 0.667.

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Answer:A=72

B=108

Step-by-step explanation:

The solution is, angle a = 72 & b = 108

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

given that,

from the given figure we get,

∠ABC = 180

∠BCD = 180

so, we have,

∠ABC + ∠BCD = 180 + 180

ABE + EBC + a + b = 360

again, we know that,

EBC + a = 180 - 38 = 142

[we know, from property of triangle's angle]

now, we get,

ABE + 142 + b = 360

or, 110 + 142 + b = 360

or, b = 108

so, we get,

a = 180 - 108 = 72

Hence, The solution is, angle a = 72 & b = 108.

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Amoli is Correct, where distributive property is used to multiply two expressions.

What is Distributive property?

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

What is Associative property?

A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.

Step-by-step explanation:

According to distributive property:

= (125 * (1/2y)) +( y * (1/2y))

= 125/2y + 1/2

Here, Associative property does not held.

Hence, Distributive property should be used.

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Answer:

Step-by-step explanation:

Dibuja una diagrama de cinta dividido en 3 y pinta 2 de los espacios

De nada :>

The number of combinations of random samples of 5 students can be 792.

Given, 12 groups of students

We have to select random samples of 5 students,

Here we will use the combination formula,

Cₙ,ₓ = n! / x! (n - x)!

Here n=12 and x=5

Cₙ,ₓ = 12! / 5! (7!)

Cₙ,ₓ = 479,001,600 / (120) × (5040)

Cₙ,ₓ = 792

Therefore the possible ways of selecting the random samples of 5 students are 792.

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The rationalization of the denominator of the given fraction gives 8 -2√3

From the question, we are to rationalize the denominator of the given fraction

The given fraction is

26 / (4+√3)

To rationalize the given expression, we will multiply both the numerator and the denominator of the fraction by the conjugate of the denominator.

The denominator is 4+√3

Thus,

The conjugate of the denominator is 4-√3

Now, multiply the numerator and the denominator by the conjugate.

That is,

(26 × (4-√3)) / ((4+√3) × (4-√3))

(104 - 26√3) / (16 - 3)

(104 - 26√3) / 13

= 104/13 - (26√3)/13

= 8 - 2√3

Hence,

The result of rationalizing is 8 -2√3

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The Maximum and Minimum values of x is  = (3,30)

The maximum of a quadratic function occurs at

x = − b/2a

If  a is negative, the maximum value of the function is

f ( − b/2a).

f max x  =ax^2+bx+c occurs at

x = −b/2a

Finding the value of

x = −b/2a

Substitute in the values of a and b.

x = − 18/2(3)

Simplify

x = -3

Replace the variable x with -3 in the expression

f (-3) = -3(-3)^2+18(-3)+3

f(-3) = - 27 +54 +3

f(-3) = -30

f(3) = 30

The maximum   of -3x^2+18x+3 = (3,30)

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The diagramfull decision tree for the parity function of four boolean attributes, a, b, c, and d is shown below picture and  it is possible to simplify the tree.

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Step-by-step explanation:

that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.

finally we use one of the original equations to solve for the second variable.

4x + y = 19

so, that gives us

y = 19 - 4x

we use that now in the second equation :

6x + 7(19 - 4x) = 1

6x + 133 - 28x = 1

-22x + 133 = 1

-22x = -132

22x = 132

x = 6

now, let's use e.g.

4x + y = 19

4×6 + y = 19

24 + y = 19

y = -5

Answer:

  (4)  5 m

Step-by-step explanation:

You want the length of side x of a right triangular prism with base edge lengths of 2.5 m and 2 m, and a volume of 12.5 m³.

The volume of the prism is given by the formula ...

  V = Bh

where B is the area of the base:

  B = 1/2bh . . . . where b and h are the leg dimensions of the right triangle

Using these formulas together, we have ...

  V = 1/2(2.5 m)(2 m)x

  12.5 m³ = 2.5x m²

Dividing by 2.5 m², we find x to be ...

  (12.5 m³)/(2.5 m²) = x = 5 m

The dimension labeled x has length 5 meters.