A coin and a die are tossed simultaneously.

a) What is the probability that the result is tails and an odd number?
b) What is the probability of getting tails or an odd number?
c) What are the probabilities of getting tails, or of getting an odd number, but not both simultaneously?

Inverse of the given function y= 4x² +12x + 9 is given by x=(1/2) (√y -3).

Restricted domain is required to make function one -one so that its inverse exist.

Domain of the inverse function is y ≥ 0.

As given in the question,

Given function is equal to :

y = 4x² +12x + 9

Inverse of the function exist if and only if it is one to one.

x₁ ≠ x₂

⇒2x₁ +3  ≠ 2x₂ + 3

⇒f(x₁) ≠ f(x₂)

It is one -one. Inverse exist.

y = (2x +3)²

⇒ 2x + 3 = √y

⇒x = (1/2) ( √y -3)

Restricted domain of the inverse of the function is y ≥0.

Therefore, Inverse of the given function y = 4x² +12x + 9 is given by

x = (1/2) (√y -3)

Restricted domain is required to make function one -one so that its inverse exist.

Domain of the inverse function is y ≥ 0.

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After factoring the given expression [tex]12y^2-17y-5[/tex], we get (4y+1)(3y-5).

The breakdown of a thing into a product of other objects, or factors, which when multiplied together provide the original, is known as factorization or factoring in mathematics. Factorization can be done using middle term splitting method in which the middle term of the expression is broken down to factor.

Factoring the given expression by splitting the middle term -17y to -3y and 20y as product of 12 and 5 is 60 and also the product of 3 and 20 is 60.

[tex]12y^2-17y-5=12y^2+3y-20y-5\\=3y(4y+1)-5(4y+1)\\[/tex]

Now, factoring out [tex](4y+1)[/tex],

[tex]=(4y+1)(3y-5)[/tex]

Therefore, After factoring the given expression, we get [tex](4y+1)(3y-5)[/tex].

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Answer: D

Step-by-step explanation:

The square root of 50 is less than 8.34, the square root of 15 is less than the absolute value of 4.32, 2.3x10^1 is greater than 2 2/5.

The absolute value of 5.43 is less than 2.1x10^1.

Answer:

2.25 cups of sugar per dozen cookies

Step-by-step explanation:

8 - 1.25 = 6.75

6.75 ÷ 3 = 2.25

Answer:

y = 7 + 2√2, y = 7 - 2√2

Step-by-step explanation:

We need to solve for y to find the solutions of the quadratic equation:

3(y-7)^2 = 24

(y-7)^2 = 8

y-7 = ±√8 = ±√(4*2) = ±2√2

y = 7 + 2√2

y = 7 - 2√2

2√2 is the simplified radical form because 4 is the highest factor of 8 that is a perfect square.

The inequality that describes the relationship between the maximum amount Herman wants to spend and the total golf costs for the season is 450 + 18x ≤ 1000.

Herman can play for a maximum of 30 rounds, which will cost $990 in total.

Herman decides to take up golf. His golf club membership will cost $450 for the season, and he will be charged $18 for each round of golf that he plays. Herman has decided not to spend more than $1000 on golf for the season.

Let the number of rounds of golf Herman plays be represented by the variable "x". We can write the inequality as given below.

450 + 18x ≤ 1000

We can further simplify and solve this inequality.

18x ≤ 1000 - 450

18x ≤ 550

x ≤ 30.56

Hence, the maximum number of rounds of golf is 30. The total cost is calculated below.

C = $450 + $18*30

C = $450 + $540

C = $990

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Answer:

[tex]x^{2} +12x+35[/tex]

Step-by-step explanation:

Distribute

(X+7)(X+5)

x^2+5x+7x+35

X^2+12x+35

Hopes this helps please mark brainliest

Answer:

x^2 + 12x + 35

Step-by-step explanation:

Hi! I solved this using the FOIL, or firsts, outsides, insides, and lasts, to simplify:

The firsts, or F, would be: x*x which equals x squared (x^2)

The outsides, or O, would be: x*5 which equals 5x

The insides, or I, would be 7*x which equals 7x

The lasts, or L, would be 7*5 which equals 35

Then, the FOIL method says to add up all the answers you got together:

x^2+5x+7x+35

and then you simplify and get:

x^2+12x+35

I hope this made sense! :)

Two angles A and B are supplementary when the value of x is 36°.

Two angles are said to be supplementary if their sum is 180°.

Two angles are said to be complementary if their sum is 90°.

Given, m∠A = (2x − 27)° and m∠B = (3x + 27)° are supplimentary to each other.

∴ (2x - 27)° + (3x + 27) = 180°.

2x + 3x - 27 + 27 = 180°.

5x = 180°.

x = 36°.

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The explicit function of the packages is f(x) = a +(n-1)d.

What is explicit function?

An explicit function is a function in algebra in which the output variable (dependent variable) can be explicitly written only in terms of the input variable (independent variable). An explicit function usually involves two variables - dependent and independent variables.

the given numbers are 110,88,66,44,22.

This is an AP (arithmetic progression)

f(x) = a +(n-1)d

were,

a is the first term, n is the number of terms, d is the difference.

n= 5, d = 22, a =110

f(x) = 110 +(5-1)22

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The differentiation of the function  f(x) = sin⁻¹(3x⁵) is  [tex]15x^4/\sqrt{1-9x^{10}}[/tex].

Function is a combination of different types of variable and constants.

A function is denoted by f(x).

The given function is,

f(x) = sin⁻¹(3x⁵)

Differentiate the given function with respect to x

f'(x) = d/dx(sin⁻¹(3x⁵))

The differentiation of sin⁻¹x is  [tex]1/\sqrt{1-x^2}[/tex],

f'(x) =[tex]1/\sqrt{1-(3x^5)^2}\cdot d/dx(3x^5)[/tex]

     = [tex]1/\sqrt{1-9x^{10}}\cdot 15x^4[/tex]

     = [tex]15x^4/\sqrt{1-9x^{10}}[/tex]

The differentiation of f(x) = sin⁻¹(3x⁵) is  [tex]15x^4/\sqrt{1-9x^{10}}[/tex].

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Answer:

part A=329.99=25.72+23.50x

part B=12.95=13 weeks

Step-by-step explanation:

need=329.99

have=25.72

save=23.50 per week

329.99=25.72+23.50x

23.50x=(329.99-25.72)

23.50x=304.24

x=12.95

=x =13

Answer: B

Step-by-step explanation:

B

You could buy 1 box, 14 bags and 4 single marbles and you could buy 2 box, 4 bags and 14 single marbles.

What is fundamental operation?

The fundamental operations are expressed in an order. Generally, the order will be in the format of “DMAS” where “D” stands for “Division”, “M” stands for “Multiplication”, “A” stands for “Addition”, “S” stands for “Subtraction”. This order is considered and sequentially performed from left to right.

Given, 1 box contains 10 bags of marbles

1 bag contains 10 marbles

Hence, 1 box contains 10 × 10 = 100 marbles.

Total numbers of marbles = 254

First condition is,

you can buy one box of marble = 1× 100 = 100

4 single marbles,

To find the number of bags, let x be the number of bag and one box contains 10 marbles,

therefore, x bags contains 10x marbles.

According to question,

100 + 4 +10x =254

104 +10x = 254

10x = 254- 104

10x = 150

x = 150÷10

= 15

Similarly in case of second condition,

2 boxes = 100×2 = 200

4 bags = 10× 4 = 40

Single marbles =?

200 + 40 +? =254

the single marble = 14

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The volume of premium antifreeze to be used is 60 gallons.

The volume of water to be used is 120 gallons

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Let the volume of 60% pure antifreeze be used to make 20% pure antifreeze.

= x gallons  

The volume of 20% pure antifreeze = 180 gallons

For 60% pure antifreeze:

C₁ = 60% , V₁ = x gallons

For 20% pure antifreeze :

C₂ = 20% , V₂ = 180  gallons

Applying,

C₁V₁ = C₂V₂

60 × x = 20 × 180

x = 60 gallons

The volume of 60% pure antifreeze used = 60 gallons.

The volume of water to be used.

= 180 - 60 gallons

= 120 gallons

Thus,

The volume of premium antifreeze to be used is 60 gallons.

The volume of water to be used is 120 gallons

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Answer:

you cannot factor it anymore

therefore, there is no solution

Answer:

0.64

Step-by-step explanation:

9/14 is 0.642

rounding that decimal to the nearest hundredth would get you 0.64 because the 2 next to the 4 is below 5 so it would keep it the same.

Answer:

57°

Step-by-step explanation:

Vertical angels are congruent.  They have the same measurements.

Answer:

57

Step-by-step explanation:

<PQS and <RQN are vertical angles and thus are congruent by the Vertical Angles Theorem. If m<PQS = 57, then m<RQN = 57.

Answer:

Step-by-step explanation:

x=3.5 and y=2.5

First, combine the equations in such a way that you can eliminate a variable. Then solve for the variable. Insert this value into one of the original equations and solve for the unknown variable.

See details:

Answer:

I c Phil and the way u are u 3AM u are u and tahsin will u be happy so we will be crazy for a different time to kick in hamtramck tomorrow so we will have

The completion of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:

                           Ratio      Amount

Department A     0.25       $15,000

Department B     0.75      $45,000

The ratio is the proportion of the whole shared by two or more numbers.

Ratios are fractional values like proportions.

Ratios, depicted in fractions, decimals, and percentages, show how much a value or variable is contained in another.

Total distributable overhead = $60,000

Ratios = 10,000:30,000

= 1:3

Sum of Ratios = 4

OR

= 0.25:0.75

Sum of Ratios = 1

Department   Square Feet  Ratio    Amount of Overhead Allocated

Dept. A            10,000         A = 1      B = $15,000 ($60,000 x 0.25)

Dept. B            30,000        C = 3     D = $45,000 ($60,000 x 0.75)

Thus, based on the cost driver ratios, Department A bears $15,000, while Department B will be allocated $45,000 of the distributable overheads.

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Answer:

d=3

Step-by-step explanation:

because

8-5=3

5-2=3

2--1=3

-1--4=3

The total amount that Ms. Henderson must pay, given the penalty and the amount of taxes is $1, 478.75

First, find the total penalty on the taxes, to Ms. Henderson.

= Tax amount x Penalty percentage

= 1, 400 x 11 ¹ / ₄%

= $157.50

Because she paid in 6 months, but the penalty is for a year, Ms. Henderson's tax penalty is:

= 157.50 / 2

= $78.75

The total amount to be paid is:

= Taxes owed + Penalty

= 1, 400 + 78. 75

= $1, 478.75

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Answer:

3.75%

Step-by-step explanation:

800+3.75%=830

The values of the composite functions f(g(x)) and g(f(x)) are (x/4) and (4x - 9),respectively.

We are given two functions, f(x) and g(x). The function f(x) is defined as 1/(x - 3). The function g(x) is defined as (4/x) + 3. A function connects an input to an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. We need to find the composition of the functions.

The first composition is f(g(x)). The composite function is solved below.

f(g(x)) = f((4/x) + 3)

f(g(x)) = 1/([(4/x) + 3] - 3)

f(g(x)) = 1/(4/x)

f(g(x)) = x/4

The second composition is g(f(x)). The composite function is solved below.

g(f(x)) = g(1/(x - 3))

g(f(x)) = (4/[1/(x - 3)]) + 3

g(f(x)) = 4(x - 3) + 3

g(f(x)) = 4x - 12 + 3

g(f(x)) = 4x - 9

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The rocket reaches its maximum height at 1.25 second(s) after launch

The maximum height reached by the object is 32 feet.

The function is given as

h(t) = -16t² + 40t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 40

Set to 0

-32t + 40 = 0

So, we have

32t = 40

Divide by 32

t = 1.25

Hence, the time is 1.25 seconds

In (a), we have

t = 1.25

Substitute t = 1.25 in h(t) = -16t² + 40t + 7

h(1.25) = -16(1.25)² + 40(1.25) + 7

Evaluate

h(1.25) = 32

Hence, the maximum height is 32 feet

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Answer:

29/400

Step-by-step explanation:

Answer:

x = - 4

Step-by-step explanation:

6x + 2 = 2x - 14 ( subtract 2x from both sides )

4x + 2 = - 14 ( subtract 2 from both sides )

4x = - 16 ( divide both sides by 4 )

x = - 4

We move all terms to the left:

We get rid of the parentheses.

We add all the numbers and all the variables.

We move all terms containing x to the left hand side, all other terms to the right hand side

1)1000

2) 4.4%

3) 4.4

4) 9%

5)4.4%

6) 0.6%

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Answer:

3.2

Step-by-step explanation:

8(4-a)=2a

32-8a=2a

collect like terms

32=2a+8a

32=10a

divide both sides by 10

a=3.2

Your solution is correct