Consider a situation where P(A) = 4/5 and P(A and B) = 1/2. If the events are independent, then what is P(B)?

Answer:

x is the input, or independent variable and f(x) is the output, or dependent variable or quantity. f(2) represents the output (y-value) when x = 2. The value of f(2) is 2.

Step-by-step explanation:

If the values of a variable depends on the other variable, then it called dependent variable.

If the value of a variable does not depend on the other, then it is called independent variable.

If a function is f(x)=x, then x is an independent variable and f(x) is a dependent variable.

The given function is

[tex]f(x)=10-x^3[/tex]

Here, x is the input, or independent variable and f(x) is the output, or dependent variable or quantity.

The notation f(a) represents the output (y-value) when x = a. So, f(2) represents the output (y-value) when x = 2.

Substitute x=2 in the given function.

[tex]f(2)=10-(2)^3[/tex]

[tex]f(2)=10-8[/tex]

[tex]f(2)=2[/tex]

The value of f(2) is 2.

For a function y = f(x) we define x as the independent variable and y as the dependent variable. y = f(x) means that "y depends on x in a given way, defined by f(x)".

Here we know that:

f(x) = 10 - x^3

1) What is the input, or independent variable?

The independent variable is the one inside the function, in this case, is x.

2) What is the output, or dependent variable or quantity?

in this case, the output is f(x), the value of the whole function evaluated in x.

(note that we do not have y = f(x), so y can't be the output, as we can't invent a variable and add it there.)

3) What does f(2) mean?

This means that we need to replace all the "x's" in the function by 2, we get:

f(2) = 10 - 2^3 = 2

so f(2) is the output when x = 2.

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QUESTION 1

The given polynomial function is [tex]y=4x^2-3x+7[/tex]

The degree of the polynomial is the exponent on the leading term of the polynomial after the polynomial has been written in descending powers of [tex]x[/tex].

The leading term is [tex]4x^2[/tex] the exponent of [tex]x[/tex] in this term is [tex]2[/tex], hence the degree is 2.

The coefficient of this term is the leading coefficient which is [tex]4[/tex].

The correct answer is B.

QUESTION 2

The function graphed has two x intercepts.

The first x intercept has a multiplicity that is even. The least positive even integer is 2.

The second x intercept has a multiplicity that is odd.

The least positive odd integer is 1.

Therefore the lowest degree  is the sum of the two least values which is

[tex]2+1=3[/tex]

The correct answer is C

QUESTION 3

The given polynomial function is [tex]y=ax^5+cx^2+f[/tex], where [tex]a,c[/tex] and [tex]f[/tex] are real numbers.

The x intercepts are the roots of the polynomial and we know the maximum number of real roots a polynomial of degree 5 can have is 5.

The maximum number of the x-intercepts of the polynomial is therefore 5.

The correct answer is D

QUESTION 4

To find the y-intercept, we substitute [tex]x=0[/tex] into each polynomial function.

The first function is [tex]y=2x^4+x^2-3[/tex]

When [tex]x=0[/tex], [tex]y=2(0)^4+(0)^2-3=-3[/tex]

The y-intercept is -3

The second function is [tex]y=3x^2+4[/tex].

When [tex]x=0[/tex], [tex]y=3(0)^2+4=4[/tex].

The y-intercept is 4

The third function is [tex]y=-4x^7-5x+3[/tex], when [tex]x=0[/tex],

[tex]y=-4(0)^7-5(0)+3=3[/tex]

The y-intercept is 3

The fourth function is [tex]y=9x^3+3x^2[/tex]

When [tex]x=0[/tex], [tex]y=9(0)^3+3(0)^2=0[/tex]

The y-intercept is 0

The correct answer is C.

QUESTION 5

The given polynomial function is [tex]y=-2x^{13}+25x^8-3[/tex].

This is already in standard form.

The degree of the polynomial is 13, which is odd.

The graph of the polynomial will rise at one end and fall at the other end.

The leading coefficient is negative, so the graph rises on the left and falls on the right.

Therefore as x approaches infinity, y will be approaching negative infinity.

The correct answer is D

The answers to the questions are as follows:

1. The correct option is B. degree=2 leading coefficient=4.

2. The correct option is c. 3. The lowest degree of the function graphed here is 3.

3.The correct option is D. 5.

4. The correct option is C. [tex]\( y = -4x^7 - 5x + 3 \).[/tex]

5.The correct option is d. [tex]\( y \)[/tex] approaches negative infinity.

1. The degree and leading coefficient of the function [tex]\( y = 4x^2 - 3x + 7 \)[/tex]are:

 - Degree = 2

 - Leading coefficient = 4

 Therefore, the correct option is B. degree=2 leading coefficient=4.

The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] that appears in the polynomial with a non-zero coefficient. In the given function, the highest power of [tex]\( x \)[/tex] is 2 (in the term [tex]\( 4x^2 \))[/tex], so the degree is 2. The leading coefficient is the coefficient of the term with the highest power, which is 4 in this case.

2. The function graphed has two x intercepts.

The correct answer is C

3. The maximum number of x-intercepts that can be found on a graph with the equation [tex]\( y = ax^5 + cx^2 + f \)[/tex] is:

 - A. 2

 - B. 3

 - C. 4

 - D. 5

The correct option is D. 5.

The degree of the polynomial [tex]\( y = ax^5 + cx^2 + f \)[/tex] is 5, which means it is a fifth-degree polynomial. The maximum number of x-intercepts (real roots) for a polynomial is equal to its degree, provided that the roots are counted with multiplicity and include complex roots. Since we are looking for the maximum number of x-intercepts, we consider the degree of the polynomial, which is 5.

4. The polynomial function that has a y-intercept of 3 is:

 - A. [tex]\( y = 2x^4 + x^2 - 3 \)[/tex]

 - B. [tex]\( y = 3x^2 + 4 \)[/tex]

 - C. [tex]\( y = -4x^7 - 5x + 3 \)[/tex]

 - D. [tex]\( y = 9x^3 + 3x^2 \)[/tex]

 The correct option is C. [tex]\( y = -4x^7 - 5x + 3 \).[/tex]

5. The end behavior of the function [tex]\( y = -2x^{13} + 25x^8 - 3 \) as \( x \)[/tex] approaches infinity is:

 - a. [tex]\( y = -3 \)[/tex]

 - b. [tex]\( y = 13 \)[/tex]

 - c. [tex]\( y \)[/tex] approaches infinity

 - d. [tex]\( y \)[/tex] approaches negative infinity

 The correct option is d. [tex]\( y \)[/tex] approaches negative infinity.

There are 10 students in a class: 5 boys and 5 girls then the probability that everyone in the group is a boy is 1/12.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.  

P(E) = Number of favorable outcomes / total number of outcomes  

It is given that the Total number of students = 10

Number of boys = 5

Number of girls= 5

The number of ways to choose 5 students from 10 is ₁₀C₅.  

= 9! / 5! 5!      

= 252

The number of ways to choose 5 students from 10 is ₁₀C₅.  

The number of ways to choose 5 students from 7 girls is ₇C₅.

=  6! / 5! 2!    

= 21

Then the probability that everyone in the group is a boy

P(E) = Number of favorable outcomes / total number of outcomes        

     = 21/252

     = 1/12.

Thus, the probability that everyone in the group is a boy is  1/12.

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Answer:

The measure of angle 1 is 55.

Step-by-step explanation:

The top angle= 75 because of the vertical angle theorem

The right angle= 50 because of the alternate exterior angle theorem

75+50=125

There are 180 degrees in a triangle so the angle has to equal 55

Answer:

a=5, b=10, c=11

Step-by-step explanation:

a= shortest side

b= "third" side

c= longest side

Equations:

c=6+a

b=2a

a+b+c=26

so we can see there is a in all of the equations, so we can plug all of them into the equation for the perimeter

a+(2a)+(6+a)=26-->4a=20-->a=5

with a, we can plug that into the equations to get b and c

c=6+a-->6+(5)-->c=11

b=2a-->b=2(5)--> b=10

3/17 = x/544

If x=96 then there are 96 grams of zinc.

The amount of zinc that contains in the jar will be 96 grams based on the given ratio.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Suppose the amount of zinc is Z while the copper is C.

The ratio Z/C = 3/17

And, C = 544

Z/544 = 3/17

Z = (3/17)544 = 96 grams.

Hence "The amount of zinc that contains in the jar will be 96 grams based on the given ratio".

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point-slope form: y-y1 = m(x-x1)

given m, (x1, y1)

m = 5

x1 = 1

y1 = 9

y - 9 = 5(x - 1)

aka: choice C

Answer:

your answer is C or number three (3)

-9=5(x-1)

i hope this helps ya out

Answer:

the first option

Step-by-step explanation:

Answer:

[tex]\displaystyle B.g(2)[/tex]

Step-by-step explanation:

we are given f(x) and the graph of g(x)

to figure out which function has the greatest value we need to figure out g(x) function first

the given graph is a parabola so g(x) has to be quadratic function

both vertex and y-intercept of the function is (0,-1)

remember,[tex]\sf \displaystyle Q_{\text{vertex}}=g(x)=a(x-h)^2+k[/tex]

vertex:(h,k)

we got from the graph (h,k)=(0,-1)

substitute the value of h and k to the vertex form:

[tex]\displaystyle g(x)=a(x-0)^2+( - 1)[/tex]

simplify:

[tex]\displaystyle g(x)=ax^2- 1[/tex]

now we need to know figure out a

to do so take (-4,-5) coordinate pair which means if x=-4 then g(x)=-5

it is helpful to figure out a

substitute the value -4 for x and -5 for g(x):

[tex]\displaystyle - 5=a( - 4)^2- 1[/tex]

simplify square:

[tex]\displaystyle - 5=16a- 1[/tex]

add 1 to both sides:

[tex]\displaystyle - 4=16a[/tex]

divide both sides by 16:

[tex]\displaystyle a = - \frac{1}{4} [/tex]

our quadratic function is

[tex]\displaystyle g(x)= - \frac{1}{4} x^2- 1[/tex]

for f(x) and g(x) substitute the values 6,0 and 2,-4 to determine which function has the greatest value

let's work with f(x)

when x is 6 then f(x)

[tex] \displaystyle \: f(6) = \frac{2}{3} \times 6 - 8[/tex]

simplify multiplication:

[tex] \displaystyle \: f(6) = 2\times 2- 8[/tex]

simplify:

[tex] \displaystyle \: f(6) = 4- 8[/tex]

simplify substraction:

[tex] \displaystyle \: f(6) = - 4[/tex]

when x is 0 then f(x)

[tex] \displaystyle \: f(0) = \frac{2}{3} \times 0 - 8[/tex]

simplify multiplication:

[tex] \displaystyle \: f(0) = - 8[/tex]

let's work with g(x) now

when x is 2 then g(x)

[tex]\displaystyle g(2)= - \frac{1}{4} \times 2^2- 1[/tex]

simplify square:

[tex]\displaystyle g(2)= - \frac{1}{4} \times 4- 1[/tex]

simplify:

[tex]\displaystyle g(2)= - 1- 1[/tex]

simplify substraction:

[tex]\displaystyle g(2)= -2[/tex]

when x is -4 then g(x)

[tex]\displaystyle g( - 4)= - \frac{1}{4} (- 4)^2- 1[/tex]

simplify square:

[tex]\displaystyle g( - 4)= - \frac{1}{4} \times 16- 1[/tex]

simplify;

[tex]\displaystyle g( - 4)= - 1 \times 4- 1[/tex]

simplify multiplication:

[tex]\displaystyle g( - 4)= - 4- 1[/tex]

simplify subtraction:

[tex]\displaystyle g( - 4)= - 5[/tex]

so

[tex] \begin{array}{c c c} g(2) > f( 6) > g( - 4) > f(0)\\ - 2 > - 4 > - 5> - 8 \end{array}[/tex]

hence,

our answer choice is [tex]\displaystyle B.g(2)[/tex]

To determine which function has the greatest value, value of f(x) was calculated at given points. Without knowing the form of g(x), we can't calculate values g(2) and g(-4). Comparing calculated values of f(6) and f(0), f(6) has the greater value.

In order to answer this question, you should first calculate the value of the function f(x) at the given points. The function f(x) is given as f(x) = 2/3x − 8.

For f(6), substitute x = 6 into your function: f(6) = 2/3 * 6 - 8 = 4. For f(0), substitute x = 0: f(0) = 2/3 * 0 - 8 = -8.

Since we don't know the explicit form of function g(x), we can't calculate g(2) and g(-4). They could be any value depending on the form and graph of g(x), which is not provided. Therefore, we can only compare f(6) and f(0). Between these two, f(6) has the greater value.

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Answer:

Commutative property of algebra.

Step-by-step explanation:

We have been given two expressions:

2x+6=10

And 6+2x=10

This is the commutative property  of algebra

which is:  a+b=c  implies b+a=c

Here, a=2x ,b=6 and c=10

On Comparing the two equations with general form of commutative property we get the required result.

[tex]x^2+2x+1=x^2+x+x+1=x(x+1)+1(x+1)=(x+1)(x+1)\\----------------------\\2x+2=2(x+1)\\----------------------\\\\\dfrac{2x+2}{x^2+2x+1}=\dfrac{2(x+1)}{(x+1)(x+1)}\\\\\text{Canceled}\ (x+1)\\\\=\boxed{\dfrac{2}{x+1}}[/tex]

Answer:

DC = 55

Step-by-step explanation:

Since this is a parallelogram, opposite sides are congruent.  WE need to find the value of y from AD = BC

AD = BC

6y+40 = 9y+10

Subtract 6y from each side

6y-6y+40 = 9y-6y+10

40 = 3y+10

Subtract 10 from each side

40-10 = 3y+10-10

30 = 3y

Divide each side by 3y

30/3 = 3y/3

10 =y

Since opposite sides are congruent

DC = AB

DC = .5y + 50

   = .5 (10) +50

    =5 + 50

   = 55

DC =55

Answer:

x=5

Step-by-step explanation:

5x=7x-10

First get the variables on one side, and numbers on the other

-2x=10

Therefore,

x=5

Answer:

6 cup of milk

Step-by-step explanation:

From question

         for 11 cookies → [tex]\frac{2}{3}[/tex] of a cup of milk required

         Now,

                  for 99 cookies

          we multiply both sides by 9.

                        11 × 9 = [tex]\frac{2}{3}[/tex] × 9

                  for 99 cookies = 6 cup of milk

Answer:

Yes he will not have any left over

Step-by-step explanation:

because 64 / 6 = 10.666666..

Answer:

The measure of angle CAD is 83 degrees.

Step-by-step explanation:

Given information: ABCD is a parallelogram, AC is a diagonal, [tex]\angle ABC=40^{\circ}[/tex] and  [tex]\angle ACD=57^{\circ}[/tex].

The opposite sides of parallelogram are congruent.

The diagonal AC divides the parallelogram in two congruent triangles.

In triangle ABC and ADC,

[tex]AB\cong CD[/tex]                                     (Opposite sides of parallelogram)

[tex]\angle ABC\cong \angle ADC[/tex]         (Opposite angles of parallelogram)

[tex]BC\cong DA[/tex]                                     (Opposite sides of parallelogram)

By SAS postulate,

[tex]\triangle ABC\cong \triangle CDA[/tex]

Since we know that opposite angles of parallelogram are equal, therefore

[tex]\angle ABC\cong \angle ADC[/tex]

[tex]\angle ADC=40^{\circ}[/tex]

According to the angle sum property the sum of interior angles of a triangle is 180 degrees.

[tex]\angle CAD+\angle ACD+\angle ADC=180^{\circ}[/tex]

[tex]\angle CAD+57^{\circ}+40^{\circ}=180^{\circ}[/tex]

[tex]\angle CAD=83^{\circ}[/tex]

Therefore the measure of angle CAD is 83 degrees.

Reference angle is angle C

AT is the opposite side as this leg is not adjacent to angle C (or put another way, point C is nowhere to be found in AT)

AC is the adjacent leg because angle C is part of this segment. It is next to or touching the segment, hence the name "adjacent"

side note: CT is the hypotenuse and always the longest side of the right triangle. It is opposite the largest angle (90 degrees) of this triangle.

Answer:

24 balloons

Step-by-step explanation:

1 hour= 60 min

60 min/ 5 min= 12 min

12 min* 2 balloons= 24 balloons per hour

Answer:

The correct answer is A

Sorry if this is late but hope it helps however finds it

Answer:

1) 2.71%

2) $38.32

Step-by-step explanation:

Opening balance = $1220

Balance after 10 days (after expense) = $1690

Balance after 10 days(after payment) = $1340

APR = 33%

1) Periodic interest rate = APR × [tex]\frac{No. of days in a billing cycle}{365}[/tex]

                                  =  33%× 30/365

                                  = 2.71%

2) Interest charged for first 10 days = [tex]\frac{1220*2.71*\frac{10}{30} }{100}[/tex]

                                                              = $11.02

Interst charged for the next 10 days = [tex]\frac{1690*2.71*\frac{10}{30} }{100}[/tex]

                                                            = $15.2

Interest charged for the next 10 days = [tex]\frac{1340*2.71*\frac{10}{30} }{100}[/tex]

                                                           = $12.10

Total interest for 30 days = 11.02+15.2+12.10

                                          = $38.32

Answer:

Choice A) 50 inches

Step-by-step explanation:

The stem is the value on the left side of the vertical bar (5, 6, and 7 in that first column). The leaf is a single digit on the right side that pairs up with the stem to form the whole value. In the first row, the stem of 5 pairs up with the 0 to get 50. The next value is 51 because the stem 5 pairs up with the 1 after the 0. Then the value after that is 51 again. Repeated values are allowed.

The entire first row of values is: 50, 51, 51, 53, 56

The second row is: 62, 69

The third row is: 71, 71, 73, 75, 77

We see that only 50 is listed in the four answer choices and no other value.

✿ The Quantity best expressed as -3.2 is a Withdrawal of $3.20

Because :

[tex]\heartsuit[/tex]  The Value which is expressed above sea level should be Positive.

[tex]\heartsuit[/tex]  Profit is always a Positive

[tex]\heartsuit[/tex]  Withdrawal's are Negative

✿ The Quantity best expressed as +5.1 is 5.1 feet above sea level

Because :

[tex]\heartsuit[/tex]  The Value which is expressed above sea level should be Positive.

[tex]\heartsuit[/tex]  Debt and Withdrawals are always Negative

Answer:

first part : a withdrawal of 3.20

second part : 5.1 feet above sea level

Step-by-step explanation:

Answer:

27 muffins.

Step-by-step explanation:

We have been given that a baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold.

To find the number of muffins sold by noon let us find 45% of 60.

[tex]\text{The number of muffins sold by noon}=\frac{45}{100}\times 60[/tex]

[tex]\text{The number of muffins sold by noon}=0.45\times 60[/tex]

[tex]\text{The number of muffins sold by noon}=27[/tex]

Therefore, 27 muffins were sold by noon.

Answer:

Proportion states that the two fractions or ratios are equal.

As per the given statement: A leaky faucet is losing water and is filling a 8-gallon bucket every 25 hours.

Let x represents the number of gallons of water that faucet leak in 13 hours.

then by definition of proportion;

[tex]\frac{8}{25} =\frac{x}{13}[/tex]

By cross multiply we get;

[tex]13 \times 8 = 25x[/tex]

Simplify:

[tex]104 = 25x[/tex]

Divide both sides by 25 we get;

[tex]x = \frac{104}{25}[/tex]

Simplify:

x = 4.16

Therefore, 4.16 number of gallons of water will the faucet leak in 13 hours

Answer:

V≈ 904.78in³

Step-by-step explanation:

V= 4/3 π r cubed

diameter= 12 cm

radius= 1/2 diameter= 6 cm

3.14= pi

V= 4/3 * 3.14 * 6 cubed

V= 4/3 * 3.14 * 216

V= 1.33 * 3.14 * 216

V= 902.06

As given, the current height of Bobby is = 61 inches

Bobby hopes to be taller than 70 inches.

Let the number of inches Bobby needs to grow to reach 70 be = x

So, he needs to grow

[tex]x+61=70[/tex]

Hence, x=9 inches

So, Bobby needs to grow 9 inches to reach a height of 70 inches and more than 9 if he wants to be taller than 70 inches.

Answer:

The correct option is 1.

Step-by-step explanation:

Statement                                          Reasons

1.   AB is parallel to DC and         Definition of parallelogram

    AD is parallel to BC

2.   angle 1 = angle 2,                   If two parallel lines are cut by a

    angle 3 = angle 4                    transversal then the alternate

                                                      interior angles are congruent

3.    BD = BD                                   Reflexive Property

4.    [tex]\triangle ADB\cong \triangle CBD[/tex]                 ASA postulate

5.   AB = DC, AD = BC                  (CPCTC)

If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.

According to alternate interior angles theorem, two parallel lines are cut by a transversal then the alternate interior angles are congruent.

Therefore option 1 is correct.

Answer:

21:38

Step-by-step explanation:

The answer you get is 42:76, but if you simplify it, it's 21:38 by dividing the ratio by 2.

Answer:

The answer is D)

Step-by-step explanation: