Isabelle flips a fair coin and rells a fair six-sided dice.
Draw a sample space diagram to show all the possible outcomes.
Work out the probability that she gets an outcome of tails and 2.
Give your answer as a fraction in its simplest form.

Answer:

1. I'm $3 in debt, and I spend 4 more dollars. I am now 4 dollars more in debt than I was before.

2. I'm $3 in debt, and I pay back $2 of debt. I am now $1 in debt.

Step-by-step explanation:

-Hope this helped

x-3=0

so x = 3

-(y-2)=0

so y = 2

vertex = (3,2)

The ratio of 6 cups of sugar to pie that Quinn needs to make 12 potato pies will be 6 cups.

Ratio basically compares quantities, that shows value of one quantity with respect to other quantity.

If a and b are two values, there ratio will be a:b.

Given that,

For 3 potato pies required sugar is 3/2,

For 5 potato pies required sugar is 5/2,

for 9 potato pies required sugar is 9/2,

From the given information,

For 1 potato pies required sugar is 1/2

⇒For 12 potato pies required sugar=12×1/2=6

To make 12 potato pies,  required sugar will be 6.

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Answer: A

Step-by-step explanation :

HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )

When the the light's angle is 20° from perpendicular to the wall, and the light is rotating at an angular speed of one rotation in 2 seconds the rate the light projected onto the wall is moving is approximately 60.48 feet/s

Angular speed, ω, is the angle, θ, in radians rotated by a rotating object per second. The unit of angular speed is radians per second, rad/s.

Mathematically;

[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]

Where;

Δt = The time the object rotates through an angle of Δθ

The distance of the light from the wall, x = 17 feet

Time it takes the light to complete one rotation = 2 seconds

Angle the light makes with the perpendicular wall = 20°

[tex]tan(\theta) = \dfrac{y}{x}[/tex]

The distance the light has moved along the wall, y = x × tan(θ)

Therefore;

The y = 17 × tan(θ)

The angular velocity of the light, ω = θ/t

Therefore, θ = ω × t = ω·t

Which gives; y = 17 × tan(ω·t)

[tex]\omega = \dfrac{2\cdot \pi}{2}\ rad/s = \pi \ rad/s[/tex]

Therefore; x = 17 × tan(·t)

[tex]\dfrac{dy}{dt} = \dfrac{d}{dt} \left(17\times tan(\omega\cdot t)\right) = 17\cdot \omega\cdot sec^2(\omega \cdot t)[/tex]

ω = π rad/s (constant)

ω·t = θ

Therefore;

[tex]\dfrac{dy}{dt}= 17\cdot \omega\cdot sec^2(\theta)[/tex]

Rate the light is moving along the wall, dy/dt when θ = 20°, is therefore;

[tex]\dfrac{dy}{dt}= 17\times \pi\cdot sec^2(20^{\circ}) \approx 60.48[/tex]

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The equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].

According to the question,

We have the following information:

The square of a number is equal to the square root of that number.

Now, let's take this number to be x.

Now, square of this number will be [tex]x^{2}[/tex] and the square root of this number will be [tex]\sqrt{x}[/tex].

Now, according to the sentence, we will have the following expression:

[tex]x^{2} =\sqrt{x}[/tex]

Hence, the equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].

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Answer:

1). True

2). x = 16.4 m^2

3). A = 24, h = 4

4). A = 18.39

5). 162

Step-by-step explanation:

I took this quiz on K12 and got everything correct! Brainliest welcome! :)

Differentiation of f(x) is [tex]-8x^{3} sinx^{4}[/tex].

Given,

f(x) = [tex]cos2x^{4}[/tex]

Now, we will differentiate f(x) with respect to x,

[tex]\frac{d}{dx}cos2x^{4} = (\frac{d}{dx}cos2x^{4})(\frac{d}{dx}2x^{4} )[/tex]

              [tex]= (-sin2x^{4})(2*4x^{3})[/tex]

              [tex]= -8x^{3}sin2x^{4}[/tex]

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When only 17 posters have been printed, it will cost $ 5. 46to print 143 more.

A mathematical formula known as a cost function is used to visualise how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.

The following equation, C'(x)=x-3/4, tells us the marginal cost (in dollars) of printing a poster after x posters have been printed.

The given equation is :C'(x)=x-3/4

The cost of printing 133 more posters when 17 have already been printed is given by;

applying the limitations we obtain and integrating both sides of the equation;

[tex]$$\int_a^b C^{\prime}(x) d x=\int_{17}^{133} x^{\frac{-3}{4}} d x$$[/tex]

As we know that [tex]$\int x^n d x=\frac{x^{n+1}}{n+1}$[/tex], so;

[tex]$&=4\left[x^{\frac{1}{4}}\right]_{17}^{133} \\[/tex]

[tex]$&=4\left[(133)^{\frac{1}{4}}-(17)^{\frac{1}{4}}\right] \\[/tex]

= $ 5.4616

Therefore When only 17 posters have been printed, it will cost $ 5. 46to print 143 more.

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Answer: 667

Step-by-step explanation:

14.50 x 46

The meaning of the expression x + 4 as required in the task content is; "four more than the number of questions on test".

It follows from the task content that the word phrase which best represent the algebraic expression; x + 4 is to be determined.

Given; x = the number of questions on test.

It therefore follows that the algebraic expression x + 4 can be interpreted as; "four more than the number of questions on test".

Hence, the meaning of the expression is; "four more than the number of questions on test".

PS: Just like word phrases can be accurately represented by algebraic expressions, the latter can be represented by the former too.

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The paper company can produce 25 notebooks for $285

From the question, the equation of the total cost is given as

Equation = 4x + 185

Rewrite as

Cost = 4x + 185

Express the equation as a cost function

So, we have the following representations

C(x) = 4x + 185

When the total cost is $285, we have

C(x) = 285

This gives

4x + 185 = 285

Subtract 185 from both sides

4x = 100

Divide by 4

x  = 25

Hence, the number of notebooks is 25

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If a claim will be made against such a policy and an average claim of $4900. the insurance company should make on average off of each policy holder is $683.5.

Using this formula to find the amount

Amount = [Percentage claim × ( Base price - Average claim)] + [(1 - percentage claim) × Base price]

Let plug in the formula

Amount = [0.085 × ($1,100 - $4,900)] + [(1-0.085) × $1,100]

Amount = [0.085 ×  (- $3,800)] + [(0.915 × $1,100]

Amount = -$325+ $1,006.5

Amount = $683.5

Therefore the insurance company will make the amount of $683.5.

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Answer:

yes if b is odd then b+6 is odd

Step-by-step explanation:

example

consider a odd number 1,3,5,7,and 9

1+6=7

3+6=9

5+6=11

7+6=13

9+6=15

all answers are odd number

Answer:

a )

[tex]6 ( ? ) = 27[/tex]

b )

? = The amount of rice in each container.

So, 1 container = ( ? ) ounce.

6 containers have = 6 x ( ? ) ounces.

We know that 6 containers have 27 ounces so...

[tex]6 ( ? ) = 27[/tex]

[tex]? = \frac{27}{6}[/tex]

[tex]? = 4.5[/tex]

Final Answer: 4.5 ounces in each container

Hope this helps! :)

Lester's final score from the two Judges is 7.6

The scores of the judges are in percentage and this will be converted to decimal by dividing by 100

impact (worth 40%) = 0.4

composition (worth 30%) = 0.3

lighting (worth 20%) = 0.2

color balance (worth 10%) = 0.1

Average score from the Judges will be used to multiply the percentages

Impact: 8 and 9

= 8.5 * 0.4 = 3.4

Composition: 7 and 7

= 7 * 0.3 = 2.1

Lighting: 8 and 7

= 7.5 * 0.2 = 1.5

Color balance: 5 and 7

= 6 * 0.1 = 0.6

sum of the scores gives Lester's final score as 7.6

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The expected mean for a sample of 150 women is 168.5 pounds.

Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.

The formula for expected mean is :

E ( X ) = μ = ∑ x P ( x )

Where:

x = values of the random variable X

P(x) = Corresponding probability

∑ =Sum of all products xP(x)

μ = mean

Therefore the expected mean is 168.5 pounds.

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Answer:

B

Step-by-step explanation:

Combine 2x^2 and 3x^2 to get 5x^2.

Combine x and 2x to get 3x.

Add 3 and 1 to get 4.

Using the monthly payment formula, it is found that:

A. You can afford a car at a price of $13,742.36.

B. The monthly payments are of $109.15.

The monthly payments are given by the equation presented as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

The variables involved in the equation are listed and explained as follows:

For item a, the parameters are given as follows:

A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60

Hence the maximum value of the car is obtained as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]

0.0181919241P = 250

P = 250/0.0181919241

P = $13,742.36

For item b, the parameters are given as follows:

P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60

(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).

Hence the monthly payments are given as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]

A = 6000 x 0.0181919241

A = $109.15.

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Answer:

New: $44,840 Original: 47,200

Step-by-step explanation:

You have to multiply 47,200 by 95% or 0.95

Answer:

[tex]y-7=-\frac{4}{3}(x+7)[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{-9-7}{5-(-7)}=-\frac{4}{3}[/tex].

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex], so the equation is [tex]y-7=-\frac{4}{3}(x+7)[/tex].

P(A∪B)=24/35 when A and B are independent and P(A)=2/5,P(B)=2/7

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty. The greater the likelihood of an occurrence, the more likely it will occur.

Probability theory, which is widely used in domains such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these concepts axiomatic mathematical formalization.

Given,

P(A)=2/5

P(A)=2/7

P(A∪B)=?

And also given that A and B are independent then,

P(A∩B)=0

P(A∪B)=P(A)+P(B)-P(A∩B)

P(A∪B)=(2/5)+(2/7)-0

P(A∪B)=(14+10)/35

P(A∪B)=24/35

Therefore, P(A∪B)=24/35 when A and B are independent.

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The correct strategy between Pedro and Rebecca trying to solve the quadratic equation: 0.1x^2 - 0.7x + 1.2 = 0 is A - Only Pedro's

The given function is a quadratic function which is solved by several method including the method both Pedro and Rebecca are trying to use

Pedro's method is the factorization method and the steps mentioned are correct

However Rebecca's method has some error

The equation is: 0.1x^2 - 0.7x + 1.2 = 0

factor of the leading coefficient a is 0.1, Rebecca is using 0.11

The error of using 0.11 instead of 0.1 will make the method ineffective

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Answer:4/5 : 1/3=4/5 x 3/1=12/5

Step-by-step explanation:

Answer:

12/5

Step-by-step explanation:

If you set it in the calculator 4/5 ÷ 1/3 you get = 12/5

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The required value of x is 3 in the given equilateral triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The triangle given in the figure is an equilateral triangle.

We know that all sides are equal in the equilateral triangle.

As per the given figure,

side AB = side AC

6x - 3 = 3x + 6

6x - 3x = 6 + 3

Apply the arithmetic operation,

3x = 9

x = 9/3

x = 3

Therefore, the required value of x is 3 in the given equilateral triangle.

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The Probability of P(B│A) is 0.77

Independent events are those events whose occurrence is independent on any other event. For example, if we flip a coin in the air and get the outcome as tail, then again if we flip the coin but this time we get the outcome as Head, In both cases, the occurrence of both events is independent of each other. It is a type of events in probability.

If A is the event that even number will appear when a die is rolled and B is when 4 or 6 appears

P(A)= 3/6 = 1/2 and P(B) = 2/6 = 1/3

Also A and B is the event ‘the number appearing is even and a multiple of 4 or 6 so that

P(A ∩ B) = 1/6

P(B│A) = P(A ∩ B)/ P(A)

= 1/6 /1/2= 1/3 = P(B)

Therefore P(B│A) = P(B)

if A= 0.15 and P(B)= 0.77

P(B│A) = 0.77

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589 in base five is  [tex]4324_{5}[/tex].

Given number:

589

converting to [tex]589_{5}[/tex].

⇒ 5|589

⇒ 5|117|4

⇒ 5|23|2

⇒ 5|4|3

⇒ 5|4|4

Now we write the last digit from last number to first that is,

= [tex]4324_{5}[/tex].

Hence 589 in base five is  [tex]4324_{5}[/tex].

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