Carol has 1\frac{5}{8} cups of yogurt to make smoothies. Each smoothie uses \frac{1}{3} cup of yogurt.

What is the maximum number of smoothies that Carol can make with yogurt?

Possible outcomes are Head, Middle, and Tail.

Since all outcomes are equally likely, the probability of each event is same, therefore

P(Head) = P(Middle) = P(Tail)

= 1/3

P(B|A) is 1/3

P(C|A) is 2/3

A and B are independent

A and C are not independent

Part a

Finding the sample space, S

S = { (HH), (HM), (HT), (MH), (MM), (MT), (TH), (TM), (TT) }

Part b

Finding  P(B|A) and P(C|A):

n(B and A) = no. of outcomes in which the first toss is Middle and second toss is Tail = 1

n(A) = Total no. of events in which the first toss is Middle = 3

Therefore, P(B|A) = 1/3

n(C and A) = no. of outcomes in which the first toss is Middle and total no. of heads is zero = 2

n(A) = Total no. of events in which the first toss is Middle = 3

Therefore, P(C|A) = 2/3

Part c

Finding if A and B are independent, or if A and C are independent

Two events A and B are said to be independent when the occurrence of one event does not affect the occurrence of the other event and vice versa. In case of independent events,

P(A) = P(first toss is Middle) = 3/9 =1/3

P(B) = P(second toss is Tail) = 3/9 = 1/3

P(A and B) = P(first toss is Middle and second toss is Tail) = 1/9

P(A)*P(B) = (1/3)*(1/3)

= 1/9 = P(A and B)

Hence, we can say that events A and B are independent.

For A and C, we have,

P(A) = P(first toss is Middle) = 3/9

P(C) = P(total no. of Heads is 0) = 4/9

P(A and C) = P(first toss is Middle and total no. of heads is 0) = 2/9

P(A)*P(C) = (3/9)*(4/9)

= 4/27 P(A and C)

Hence, events A and C are not independent.

The question was incomplete, the complete question is:

(Extra Credit) Suppose you have a well-balanced "super coin" with three sides or outcomes equally likely: Head, Middle, and Tail. (the super coin is a die with opposite faces showing Head, Middle, and Tail) You tossed this super coin two times

a) Describe the sample space using the notation HM for example, if the results are Head first, and Middle second.

Let;

A = event the first toss is Middle,

B = event the second toss is Tail, and

C = event the total number of Heads is 0.

b) Find

P(B|A)

P(C|A)

c) Are A and B independent? YES, NO, Why?

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Answer:

answer is D prettyy sure

Answer:

Time since the person starts walking is the input

t represents the input

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The Elephant Building is 335 feet high. A real Asian elephant is 12 feet tall. If 29 real elephants could stand on top of each other, would they reach the top of the building?

They are asking if 29 12' elephants are as tall as as a 335' building:

29 × 12' = 348' elephant stack

because 348' is taller than 335' building then yes, 29 staked elephant would reach and pass the top of a 335' building.  

The Venus is at a distance of [tex]1.5876 * 10^8[/tex] further away from the earth than the moon

We have given that

The Distance of moon from the earth(in miles)= a=  [tex]2.4 * 10^5[/tex] miles

The Distance of venus from the earth(in miles)= b =   [tex]1.59 * 10^8[/tex] miles

The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects.

Now,

Let the distance from which venus is further away from the earth than the moon be x

So, x = b - a

x = [tex]1.59 * 10^8-2.4 * 10^5[/tex]

x = [tex]1590 * 10^5 - 2.4*10^5[/tex]

x = [tex](1590 - 2.4)*10^5[/tex]

x = [tex]1587.6*10^5[/tex]

x = [tex]1.5876 * 10^8[/tex]

Therefore, venus is at a distance of  [tex]1.5876 * 10^8[/tex] further away from the earth than the moon.

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Answer:

3x + 4

.................

The factor 3x + 4 have common in both the given expressions.

A whole number that is a factor of two or more numbers is referred to as a common factor. The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).

The given expressions are,

[tex]9x^2 + 24x + 16, 9x^2 - 16[/tex]

The expression [tex]9x^2 + 24x + 16[/tex] is of the form [tex](a + b)^2[/tex]

where [tex]a = 3x , b = 4[/tex]

Therefore,   [tex]9x^2 + 24x + 16 = (3x + 4)^2.[/tex]

The expression [tex]9x^2 - 16[/tex]   is of the form [tex]a^2 - b^2[/tex].

It can be written as, [tex]a^2 - b^2 = (a - b)(a + b)[/tex]

Here, [tex]a = 3x , b = 4[/tex]

Therefore,

[tex]9x^2 - 16 = (3x - 4)(3x + 4)[/tex]

So, in both the expressions the factor (3x + 4) is common.

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In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.

Given that,

In the picture there are 2 problems.

We have to find the difference and similarities of question in the picture.

The similarities are they 2 are word problems.

Another similarity is they two have to find 2 question.

1. How much money for 10 days and How many days to collect the money $1.05?

2.How much gallon of water need for 50 minutes and How much time take to fill the pool?

Another similarity is they two have to justified the answer in a mathematical model.

Now,

The difference is,

First question has given sisters and money problem where as the second has given pool and gallon water problem.

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Answer:

I think this is correct.

Step-by-step explanation:

The numeric values for the given functions are as follows:

1. g(-4) = -21.

2. f(-1) = 3.

To find the numeric value of a function at input x = a, we replace each instance of the variable x in the function by the desired value of a.

For item 1, function g(x) is defined as follows:

g(x) = -x² - 5.

We want to find the numeric value at x = -4, hence the lone instance of x is replaced by -4 as is shown below:

g(-4) = -(-4)² - 5 = -16 - 5 = -21.

Hence g(-4) = -21 is the numeric value.

For item 2, the function f(x) is given as follows:

f(x) = -3(1 - x - 3x²).

To find the numeric value at x = -1, both instances of x have their values replaced by -1, hence the numeric value will be given as follows:

f(-1) = -3(1 - (-1) - 3(-1)²) = -3(1 + 1 - 3) = 3.

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Answer: a = 6 and 1/4

Step-by-step explanation:

you subtract the 1/4 to the other side and theres your answer

Answer:

A square pyramid is composed of an eight-sided square base, four triangular sides, five vertices, and five vertices. This pyramid has a square base with a peak at the top. The fact that a square pyramid is a polyhedron was noted.

Step-by-step explanation:

The three-dimensional geometric shape of a square pyramid has a square base and four triangular sides that are joined at the vertex. Five facets make up its polyhedron shape (pentahedron). Four triangles joined at the vertex and a square base make up a square pyramid. Three sides, a square base, and a central vertex characterize the triangle side faces. The tallest point of the pyramid is known as its "apex." The base is represented by the bottom square. Faces are the three triangular vertices of the triangle. When viewed from the bottom up, a pentahedron is a five-sided, three-dimensional shape that resembles a square pyramid.

Answer:

0.29761904761

Step-by-step explanation:

Brainlest, Please!

Answer:

25/84

Step-by-step explanation:

1. 2 1/10 is mixed number fraction so convert it into an improper fraction.

~ Multiply whole number and denominator and add the numerator of 1

~ Improper fraction: 21/10

2. So, new equation is (5/8) / (21/10)

3. Use the Keep, Change, Flip method:

~ Keep the 5/8

~ Change division to multiplication

~ Flip the improper fraction to 10/21

4. Solve the equation:

~ (5/8) x (10/21) = 50/ 168

5. Reduce fraction:

~ By 2

~ 25/84

The least common multiple of 32, 48, and 16 is 96

The first step is to get the prime factors of each number

The prime factors of 32 are 2, 2, 2, 2 and 2.

The prime factors of 48 are  2, 2, 2, 2 and 3

The prime factors of 16 are 2,2,2 and 2

The least common multiple of 32, 48 and 16 can be calculated as follows

2 × 2 × 2 × 2 × 2 × 3

= 32 × 3

= 96

Hence the least common multiple of 32, 48, and 16 is 96

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Answer:

7.071068 ≈ 7.07

Step-by-step explanation:

The distance, d,  between 2 points (x1, y1) and (x2, y2) is given by the formula

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

The two points as determined from the graph are (1, 5) and (2, -2)

[tex]d = \sqrt {(2 - 1)^2 + (-2 - 5)^2}[/tex]

[tex]d = \sqrt {(1)^2 + (-7)^2}[/tex]

[tex]d = \sqrt {{1} + {49}}[/tex]

[tex]d = \sqrt {50}[/tex]

[tex]d = 7.071068[/tex]

The only student with the correct claim about the given quadratic equation is; Neil: The vertex is at (2, -9)

We are given the quadratic function;

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

1) The x-intercepts of the quadratic function are simply the roots of the quadratic function. Now, the roots are at; (5, 0) and (-1, 0). Thus, Annie's claim is not correct.

2) The y-intercept is the point at which x = 0. Thus;

f(0) = (0 - 5)(0 + 1)

f(0) = -5

y-intercept is at; (0, -5)

Thus, Jacob is wrong.

3) The x-coordinate of the vertex is;

x = -b/2a

The equation is; x² - 4x - 5

Vertex = -(-4)/(2 * 1) = 2

y-coordinate is;

y = 2² - 4(2) - 5

y = -9

Thus, Jacob is correct

4) Zoey is incorrect because she didn't properly find the midpoint of the x-intercepts.

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Step-by-step explanation:

For Arithmetic Sequence

Tn = a + (n -- 1)d

Where Tn = the no of nth term

a = First number

n = nth term

d = common difference

a = --27, T2 = --21

d = second term -- first term

d = --27 -- (--21)

d = --27 + 21 = --6

a = --27, n = 62, d = --6, T62 = ?

Tn = a + (n -- 1)d

T62 = --27 + (62 -- 1)×--6

T62 = --27 + (61 × --6)

T62 = --27 + (--366)

T62 = --27 -- 366

T62 = --393

Answer: top: x= 2   bottom: x= -5

Step-by-step explanation: First you need to get rid of everything on the x side, so for example on the top one you would do 9-9 to get 0 so that x is by itself and then you also have to 11-9 because whatever you do to one side you have to do to the other. And then 11-9=2 so you are left with x= 2.

Answer:

y=8

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

3x + 2 = 11

3x = 11 - 2

3x = 9

x = 9/3

x = 3

Answer:

Separate the x and the numbers on each side and solve.

3x + 2 = 11

3x = 9

x = 3

Si definimos N como el nuevo número de esferas en la urna, entonces la expresión algebraica será:

N = x - 3.

Sabemos que tenemos una urna con x esferas, donde x representa un numero entero.

Sabemos que 3 esferas se extraen de la urna, es decir, el número total de esferas en la urna decrese en 3 unidades.

Entonces podemos escribir la expresión algebraica como:

N = x - 3

Donde definimos N como el nuevo número de esferas en la urna.

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Answer:

 x = 5.33333333333

Step-by-step explanation:

3x-5=11

   +5   +5

3x= 16

3      3      

u need to separate the 3x

so u use the opposite operation on - 5

add +5 on both sides

-5 plus 5 cancel each other

add 11 to 5 and that is 16

bring them down and divide both by 3

and ur 3 cancel each other,

now divide 16 by 3

and u get  x = 5.33333333333

The total cost of painting per cm will be 45.2% i.e. option(d).

Total cost of painting = Rate × Surface area of sphere

We know the radius is increases by 10%.

Thus, the Surface area will change by 21%

using formula a + b + (a × b)/ 100

The total change in cost of painting will be

= 20+21 +(20x21)/100

= 45.2%.

What is surface area?

The total area of all faces (or surfaces) on a 3D form is the surface area. For example:

There are six rectangular faces of a cuboid.

Add the areas of each of the cuboid's six faces to determine its surface area.

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The speed of the walker is 16.67 miles per hour.

The speed of the cyclist is 25 miles per hour.

Let the speed of a walker = x

Biker's speed = 1.5x

Their relative speed will be:

= 1.5x - x = 0.5x

Distance between them = 12.5 miles

Time taken = 1.5 hours.

It should be noted that distance will be:

= Speed × Time

12.5 = 1.5 × 0.5x

Divide through to get x

12.5 = 0.75x

x = 16.67 miles per hour.

Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.

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Hence the angle theta is 70.5°

What is angle?

The space between two lines or surface that meet  measured in degrees.

As per the given question a ladder 3.5 m long leaning against the wall of a house reaches a height of 3.3 m we have to find what ladder make the ground.

Sol-

Let the angle is theta

Length of the ladder is 3.5m

Height of the ladder is 3.3 m

Sin= 3.5/3.3

      =0.942

Sin =sin 70.5°

Theta = 70.5°

Hence the angle is theta =70.5°

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[tex]\displaystyle\\Answer:\ \frac{7}{5}x +\frac{34}{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\(-7,-3)\ \ \ \ (-2,4)\\\\\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=-7\ \ \ \ \ x_2=-2\ \ \ \ y_1=-3\ \ \ \ \ y_2=4\\\\\frac{x-(-7)}{-2-(-7)} =\frac{y-(-3)}{4-(-3)}\\\\\frac{x+7}{-2+7}=\frac{y+3}{4+3} \\\\\frac{x+7}{5} =\frac{y+3}{7} \\\\[/tex]

Multiply both parts of the equation by 7:

[tex]\displaystyle\\7(\frac{x+7}{5} )=y+3\\\\7(\frac{1}{5} x+\frac{7}{5} )=y+3\\\\\frac{7}{5}x +\frac{49}{5} =y+3\\\\\frac{7}{5}x +\frac{49}{5} -3=y+3-3\\\\\frac{7}{5}x +\frac{49}{5}-3=y\\\\\frac{7}{5}x +\frac{49-3(5)}{5} =y\\\\\frac{7}{5}x +\frac{49-15}{5} =y\\\\\frac{7}{5}x +\frac{34}{5} =y\\\\So,\ y=\frac{7}{5}x +\frac{34}{5}[/tex]

Step-by-step explanation:

what do you need to do ?

the only thing we can do here without any further information is simplification if the expression:

-23x² + x² - 6x + 10 + 2x²

now we group ask the terms of the same variable exponents :

-23x² + x² + 2x² - 6x + 10

-20x² -6x + 10

we could do

2×(-10x² - 3x + 5)

but I personally don't find this more simplified that the previous form.

Answer:

-1

Step-by-step explanation:

First combine like terms on the right side (5x-10x) to get -5x +4

6-3x=-5x+4

then move the -5x over to get 2x because you would add the -5x to the -3x.

6+2x= 4

then subtract 6 on both sides.

2x=-2

to make your final answer -1.

Answer:

f(g(x) ) = x² + 2

Step-by-step explanation:

to find f(g(x) ) substitute x = g(x) into f(x)

f(g(x) )

= f(x²)

= x² + 2

The statement that explains why one source is the most reliable is D. The Local Reader article is the most reliable source because the author offers a neutral reporting of facts.

Reliable sources are necessary for reliable information. A trustworthy source will offer a "complete, well-reasoned hypothesis, argument, etc. based on substantial evidence," according to UGA Libraries.

Scholarly, peer-reviewed articles and books are examples of widely regarded sources. trade publications, professional books, etc.

It should be noted that a reliable source should be based in facts and should not be biased.

Therefore, the correct option is D.

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