9. Zola solved a question on her math test that. asked her to find the volume of the sphere shown
below in terms of T. Explain Zola's error and solve for the correct answer.
d=11 in
v-(-X5.5¹)
V=((16.5)
V = 22π in³

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \color{gray}{ \bigstar} \blue {\boxed{ \rm{ \green{Volume \: of \: Pyramid = \frac{1}{3} Bh}}}}[/tex]

[tex] \: [/tex]

[tex] \rm{Volume \: of \: Pyramid = \frac{1}{3} Bh} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\rm \: = \frac{1}{3} \times 75 \times 7.4 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm = \frac{1} {\cancel{3} }\times \cancel{555 } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline\color{darkgreen}\boxed{ \rm{ = 185}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

The decimal number 4.3333333... is a rational and real number. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The decimal number is given below.

⇒ 4.333....

Let x = 4.333333333.., then 10x = 43.33333333...

10x - x = 43.33333.. - 4.333333...

9x = 39

x = 39/9

x = 13/3

The decimal number 4.3333333... is a rational and real number. Then the correct option is A.

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Answer:

Step-by-step explanation:

he's correct trust him The decimal number 4.3333333 is a rational and real number. Then the correct option is A.

The equation can be converted as: 2 (S - 1/2 u t) / t.

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

Let's start by simplifying the equation using the distributive property of multiplication:

S = 1/2 u t + 1/2 v t

Next, we can isolate the variable v by subtracting 1/2 u t from both sides of the equation:

S - 1/2 u t = 1/2 v t

Now we can multiply both sides of the equation by 2 to eliminate the fraction:

2 (S - 1/2 u t) = v t

Finally, we can solve for v by dividing both sides of the equation by t:

v = 2 (S - 1/2 u t) / t

Therefore, the solution for v is v = 2 (S - 1/2 u t) / t.

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Answer: 0.229659

Step-by-step explanation: Since you are converting centimeters to feet, you have to divide the centimeters by exactly, 30.48. so 7 / 30.48 equals 0.229659.

The value of X from the given rectangular figure above would be = 6.5. That is option A.

A rectangle can be defined as a quadrilateral that has four sides, four vertices, and four angles.

In a rectangle, when two diagonal line divides it, the two diagonals are of the same length.

That is;

Line PR = Line SQ

Half of PR = ER

Half of SQ = QE

But QE = 2x

PR = 26

QE = 1/2 × 26 = 2x

13= 2x

X = 13/2

X= 6.5

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The value of n for the equation (1/36)n= 216 is -1.5.

The following equation is solved by the use of exponent power rule.

The step by step explanation is given below:

convert the fraction into negative exponential form,

(36∧-1)n=216

simplify using the exponent power rule,

(a∧n)∧m = a∧n×m

Covert both sides of the equation in terms with the same base,

(6 ∧2)∧-n = 6 ∧3

Simplify the equation ,

6∧2.-n = 6∧3

Corresponding exponents are equal to ,

-2n = 3

Divide both side of the equation by 2 ,

-n= 3/2

n= - 3/2.

Therefore n = -1.5.

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Hence, the values of cοsine and cotangent functions for angle theta are -√(2)/2 and -1, respectively.

Angles between 0 and 90 degrees are cοnsidered acute. Obtuse angles fall within this range and vary frοm 90° to 180°.  A right angle is knοwn as an angle with a 90-degree angle (= 90°).

The pοint (-√(2)/2, √(2)/2) lies on the unit circle in the second quadrant, which means that the cοrresponding angle theta has a reference angle of pi/4.

The cοsine of theta is the x-coordinate of the point on the unit circle corresponding to theta. Since the x-coοrdinate of the given point is -√(2)/2, we have:

cοs(θ) = -√(2)/2

The cοtangent of theta is the ratio of the cosine of theta to the sine of theta. We can find the sine of theta by using the Pythagοrean theorem, since the pοint (-√(2)/2, √(2)/2) lies on the unit circle:

sin(θ) = √(1 - cos²(θ)) = √(1 - (-√(2)/2)²) = √(2)/2

Therefοre, we have:

cot(θ) = cos(θ) / sin(θ) = (-√(2)/2) / (√(2)/2) = -1

Hence, the values of cοsine and cotangent functions for angle theta are -√(2)/2 and -1, respectively.

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Answer: Violet color light has the highest frequency. The frequency of violet color light is. 5 × 10 14 Hz . red color light has the lowest frequency. Red light has a frequency around 430 terahertz. This is all based on the order by wavelength.

mark me brainliest please :)

Step-by-step explanation: In order from lowest frequency to highest, they are red, orange, yellow, green, blue, indigo, and violet. Because of the inverse relationship, they are reversed in order by wavelength. The color with the highest frequency is violet.

Answer:

D

Step-by-step explanation:

3.5 is changing for every trophy I order so it has a variable. For example  say I want 3 trophies each trophy is 3.50 substitute 3 for x. 3.50(3) and that would give me the cost for 3 trophies same thing for the 7.50. The initial fee (you only pay the initial fee once) for company p is 25. The initial fee for company R is 17. At the end the question asks for the inequality so that company p is less than(<) company R. The only inequality that fits this is D.

Hope this helps :-)

We can conclude that ∠BDC is congruent to ∠BAC and ∠BEC.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point known as the centre.

Given is a circle as shown in the image.

The triangles are on the same base BC.

From this we can conclude that -

∠BEC = ∠BAC = ∠BDC

Therefore, we can conclude that ∠BDC is congruent to ∠BAC and ∠BEC.

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Step-by-step explanation:

Complementary means they sum to 90 degrees.

Complementary means they sum to 90 degrees.

Thus F + G = 90.

Complementary means they sum to 90 degrees.

Thus F + G = 90.

Substituting the values in, we have:

Complementary means they sum to 90 degrees.

Thus F + G = 90.

Substituting the values in,

we have:2x + 7 + 18 = 90

Complementary means they sum to 90 degrees.

Thus F + G = 90.Substituting the values in,

we have:2x + 7 + 18 = 902x + 25 = 90

Complementary means they sum to 90 degrees.Thus F + G = 90.Substituting the values in, we have:2x + 7 + 18 = 902x + 25 = 902x = 65

Complementary means they sum to 90 degrees.Thus F + G = 90.Substituting the values in, we have:2x + 7 + 18 = 902x + 25 = 902x = 65x = 32.5

Complementary means they sum to 90 degrees.Thus F + G = 90.Substituting the values in, we have:2x + 7 + 18 = 902x + 25 = 902x = 65x = 32.5

Angle F = 72 degrees

Complementary means they sum to 90 degrees.Thus F + G = 90.Substituting the values in, we have:2x + 7 + 18 = 902x + 25 = 902x = 65x = 32.5Angle

F = 72 degrees Angle G = 18 degrees

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Answer:

the value of b is 10 +151620 but we have; to check

The value of b in the equation is 13/12

From the question, we have the following parameters that can be used in our computation:

x^2/24 - y^2/b^2 = 1

The equation of a hyperbola with center at the origin and semi-axes lengths a and b can be written as:

x^2/a^2 - y^2/b^2 = 1

Comparing this equation with the given equation, we have:

a^2 = 24.

The directrix of the hyperbola is given as

x = 576/26

For a hyperbola with center at the origin, the distance between the center and the directrix is a^2/b.

So, we have:

a^2/b = 576/26

Substituting the value of a^2, we get:

24/b = 576/26

So, we have

b = 13/12

Hence, the value of b is 13/12

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The surface area of the cylinder is 150.72cm²

A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.

The surface area of a cylinder is the addition of the area of the faces on the cylinder.

The surface area of a cylinder = 2πr(r+h)

= 2×3.14 × 3( 3+5)

= 18.84 × 8

= 150.72cm²

therefore the surface area of the cylinder is 150.72cm²

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Answer:

6 I think have a great day

Answer:

(a) The interest on a simple interest loan is calculated using the formula:

Interest = Principal x Rate x Time

where:

Principal is the amount of the loan

Rate is the interest rate per time period

Time is the duration of the loan in the same time period as the interest rate

In this case, the principal is $8000.00, the rate is 9.00% per year, and the time is 9 months. To calculate the interest, we need to convert the time to years by dividing by 12:

Time in years = 9 months / 12 months per year = 0.75 years

Plugging in the values, we get:

Interest = $8000.00 x 0.09 x 0.75

Interest = $540.00

Therefore, the student must pay $540.00 in interest.

(b) The future value of a simple interest loan is calculated using the formula:

Future Value = Principal + Interest

In this case, the principal is $8000.00 and the interest is $540.00, so the future value is:

Future Value = $8000.00 + $540.00

Future Value = $8540.00

Therefore, the future value of the loan is $8540.00.

Step-by-step explanation:

Answer:68

Step-by-step explanation:

You can first subtract 104-36=68 so,68+36=104

Answer:

  68

Step-by-step explanation:

You want to know the number of marbles Chloe originally had in her collection if adding 36 marbles gave her a total of 104.

You can let a variable (o) represent the original number of marbles. You would choose this because the original number of marbles is what you're asked to find. It never hurts to use a variable name that reminds you of what it stands for.

The problem statement tells you that adding 36 to the original number gives a total of 104. As an equation, this looks like ...

  o + 36 = 104 . . . . . . adding 36 to o gives 104

The properties of equality tell you that you can subtract the same number from both sides of the equation without changing the value of the variable.

Here, we want the variable by itself, so we want to get rid of the added number 36. We do that by subtracting 36 from both sides of the equation:

  o +36 -36 = 104 -36 . . . . . subtract 36 from both sides

  o = 68 . . . . . . . . . . simplify

This solution tells us that Chloe originally had 68 marbles.

__

Additional comment

The way to solve this, or any, "word problem" is to read and understand the relationships the words are telling you, and what the words are asking for. Then write those relationships as math expressions, choosing variables and a procedure that will give you what the question is asking for.

Here, we could choose a variable that represents the quantity we want to find. That is not always the case.

Sometimes, you have to find an "intermediate" value that you need in order to be able to answer the ultimate question. You're not done when you find that intermediate value; you're only done when you are able to answer the question asked.

The answer of the given question based on the probability is, probability that, in any hour, more than 3 customers will arrive is approximately 0.9227.

a experiment is the outcome of the event, the possible outcomes  are the number of times it occurrences.

To solve this problem, we will use the Poisson distribution,

we are given that the mean rate of customer arrivals is 7.1 per hour. We want to find the probability that more than 3 customers will arrive in any hour.

The Poisson distribution is defined as:

[tex]P(X = k) =(e^{(-\lambda)}*\lambda^k)/k![/tex]

where X is the random variable representing the number of events (in this case, customer arrivals), λ is the mean rate of occurrence, e is the mathematical constant e (approximately 2.71828), and k is the number of events we are interested in.

To find the probability of more than 3 customers arriving, we need to calculate the probability of 4, 5, 6, 7, 8, 9, and so on customers arriving, and add these probabilities together. This can be time-consuming, so instead we can use the complement rule and find the probability of 0, 1, 2, or 3 customers arriving, and subtract this from 1:

P(X > 3) = 1 - P(X <= 3)

To calculate P(X <= 3), we can use the Poisson distribution with λ = 7.1 and k = 0, 1, 2, and 3:

[tex]P(X = 0) = (e^{(-7.1)} * 7.1^0) / 0! = 0.000832[/tex]

[tex]P(X = 1) = (e^{(-7.1)} * 7.1^1) / 1! = 0.005904[/tex]

[tex]P(X = 2) = (e^{(-7.1)} * 7.1^2) / 2! = 0.020981[/tex]

[tex]P(X = 3) = (e^{(-7.1)} * 7.1^3) / 3! = 0.049546[/tex]

Adding these probabilities together, we get:

P(X <= 3) = 0.000832 + 0.005904 + 0.020981 + 0.049546 = 0.077263

Therefore, the probability of more than 3 customers arriving in any hour is:

P(X > 3) = 1 - P(X <= 3) = 1 - 0.077263 = 0.9227 (rounded to four decimal places)

So the probability that, in any hour, more than 3 customers will arrive is approximately 0.9227.

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Sure, here's a complete table of y-values for different x-values:

x y = 9*(13)^x

0 9

1 117

2 1521

3 19773

4 256809

5 3335777

6 43363161

7 562002993

8 7304038917

9 94852405821

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output. Functions are often represented using function notation, where the input is the independent variable and the output is the dependent variable. Functions are used to model relationships between different quantities or variables, and are an essential tool in many areas of mathematics, science, engineering, economics, and more. They allow us to make predictions, analyze data, and understand complex systems.

Here,

The exponential function y = 9*(13)^x means that for any given value of x, we can calculate the corresponding value of y by plugging in x and performing the calculation. The base of the exponential function is 13, which means that the function will increase rapidly as x gets larger.

For example, if x = 0, then y = 9*(13)⁰ = 91 = 9.

If x = 1, then y = 9(13)¹ = 913

= 117.

If x = 2, then y = 9(13)² = 9*169

= 1521.

And so on.

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Answer:

9 to 4

Step-by-step explanation:

The total possible outcomes is 16, the probability that all children are males is 1/16, the probability of having all one gender is 1/8

1. The tree diagram for the sex of the children is as follows:

Child 1: M / F

Child 2: M / F

Child 3: M / F

Child 4: M / F

Possible Outcomes: MMMM, MMMF, MMFM, MFMF, FMFM, FMMF, FMFF, FFFF

There are 2 options for each child, so the total number of possible outcomes is 2 x 2 x 2 x 2 = 16.

2. The probability that all children are males is 1/2 x 1/2 x 1/2 x 1/2 = 1/16.

3. The probability of having all one gender of children is the sum of the probability of having all boys and the probability of having all girls. Each of these outcomes has a probability of 1/16, so the total probability is 1/16 + 1/16 = 1/8.

4. The easiest way to solve this problem is to find the probability of having no female children, and then subtract that from 1. The probability of having no female children is (1/2)^4 = 1/16, so the probability of having at least 2 female children is 1 - 1/16 - 1/16 = 7/8.

5. The tree diagram for flipping a coin, rolling a 6-sided die, flipping a coin, and rolling a 3-sided die is as follows:

C / H

/

1-6 1-3

\ /

H / T

The first branch represents the coin flip, the second branch represents the roll of the 6-sided die, the third branch represents the second coin flip, and the fourth branch represents the roll of the 3-sided die.

6. There are 2 options for the first coin flip, 6 options for the second branch, 2 options for the second coin flip, and 3 options for the fourth branch, so the total number of possible outcomes is 2 x 6 x 2 x 3 = 72.

7. The probability of getting only heads on both coin tosses is 1/2 x 1/2 = 1/4. Therefore, the probability of getting only heads on both coin tosses and any result on the dice is 1/4 x 1 = 1/4.

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Answer:

Step-by-step explanation:

p and q vary inversely:

If p = 18, q = 28, find k:

The equation is:

When p = 72, q is:

The percentage of temperatures for Shanghai between 46ºF and 78ºF is given as follows:

50%.

A box and whisker plots shows these five features from a data-set, listed as follows:

For Shanghai, the quartiles are given as follows:

Q1 = 46, Q3 = 78.

Hence the temperatures between 46 and 78ºF represent the interquartile range, containing the middle 50% of observations.

The problem is given by the image presented at the end of the answer.

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To acquire the complete recommended daily dose of vitamin C, an individual would need to drink 625 mL, or 2.5 cups, of tomato juice.

Calculation. For a common solution Mass Ascorbic acid equals Mole Iodine times Volume of Iodine multiplied by 176.12 to get 91.54 mg per mole of Iodine. At first, 100 mg of ascorbic acid was consumed, making it the complete amount of ascorbic acid.

Let's find out how much vitamin C there is in 250 mL of tomato juice first:

40% vitamin C in 250 mL = 100% vitamin C in x mL

Solving for x, we get:

x = (100% / 40%) * 250 mL

x = 625 mL

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The perimeter of the triangle QSU is 88 cm.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Given a circle.

And there are three tangents drawn intersecting the circle at points R, T and V.

We have the circle theorem that the tangents that meet at the same point are equal in length.

Using the theorem,

SR = ST

RQ = VQ

TU = VU

We have, segment RQ measures 15 cm, segment ST measures 4 cm, and segment VU measures 25 cm.

So, SR = ST = 4 cm

TU = VU = 25 cm

VQ = RQ = 15 cm

Perimeter of ΔQSU = (2 × 4) + (2 × 25) + (2 × 15) = 88 cm

Hence the perimeter is 88 cm.

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It will take {log(1 - r/n)/n} years to exactly double your investment.

The formula for compound interest is -

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

Given is that an investment of $2800 made at an APR of 5% compounded monthly.

The formula for compound interest is -

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

For A = 2P, we can write -

Substituting 2P = A, we get -

2P = P(1 + r/n)^nt

2 = (1 + r/n)^nt

log 2 = log {(1 + r/n)^nt}

log 2 = (nt) log(1 + r/n)

(log 2)/log(1 + r/n) = nt

{t} = log{2 - 1 - r/n}/n

{t} = log{1 - r/n}/n

Therefore, it will take {log(1 - r/n)/n} years to exactly double your investment.

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Answer: The problem statement is incomplete. It is given that one motorcyclist is traveling at a speed of 7 km/hr, but the speed of the other motorcyclist is not given. We cannot solve the problem without knowing the speed of the other motorcyclist.

Please provide additional information, such as the time taken by both motorcyclists to cover the distance, or any other information that may be relevant to the problem.

Step-by-step explanation:

Note that where the conditions above subsist the height determined by the other colleague is not the same so the answer is No. To solve this problem, you need to be conversant with the Pythagorean Theorem, and Angle Bisector Theorems.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The formula for the Pythagorean Theorem is:

c² = a² + b²

where "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides (the legs) of a right triangle.

With this, we can find the c for the lower Right angle triangle on the left and B for the lower right angle triangle on the right.

Since C² = A² + B²

B = √( A²- C²)

B = √( 9.5²- 6²)

B [tex]\approx[/tex] 7.36546


To determine c on the right angle to the left,

c² = a² + b²

c = √(a² + b²)

c = √(5.5² + 7.2²)

c = 9.060353194

c [tex]\approx[/tex] 9.06

With the postulate of the Angle Bisector Theorem, we can begin to find the height of the two upper right angle triangles.

The Angle Bisector Theorem states that in a triangle, an angle bisector of a vertex of the triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

In other words, if a line segment bisects an angle of a triangle and intersects the opposite side or the extension of the opposite side, then the ratio of the lengths of the segments on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

As seen from the image, the right angles where each lady is holding is bisected. This means that we have for each Triangle Two angles and one side.

Right Angle on the Left:

90°

45°; and

7.2ft

Given the above, Since the angle opposite the height is 45 degrees, we know that the ratio of the height to the base is 1:1, or h/7.2 = 1/1.

Therefore, the height of the right triangle is:

h = 7.2 × 1

h = 7.2 ft

So the height of the right triangle is 7.2 feet.

Right Angle on the Right :

90°

45°; and

7.36546ft

Given the above, we can use the trigonometric ratios of the angles in the right triangle.

Since the angle opposite the height is 45 degrees, we know that the ratio of the height to the base is 1:1, or h/7.36546 = 1/1.

Therefore, the height of the right triangle is:

h = 7.36546 × 1

h = 7.36546 ft

So the height of the right triangle is 7.36546 feet.

So both heights approximated to the nearest tenth:

Since 7.2 ≠ 7.4, the heights are not equal.

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The inverse of the matrix is

[tex]$$\left[\begin{array}{cc}1 & -\frac{1}{2} \\-3 & 2\end{array}\right]$$[/tex]

Generally, The inverse of a [tex]$2 \times 2$[/tex] matrix can be found using the formula [tex]$\frac{1}{a d-b c}\left[\begin{array}{cc}d & -b \\ -c & a\end{array}\right]$[/tex] where a d-b c is the determinant.

Find the determinant.

Since the determinant is non-zero, the inverse exists.

Substitute the known values into the formula for the inverse.

[tex]\frac{1}{2}\left[\begin{array}{cc}2 & -1 \\-6 & 4\end{array}\right][/tex]

Multiply 1/2 by each element of the matrix.

[tex][\begin{array}{cc}\frac{1}{2} \cdot 2 & \frac{1}{2} \cdot-1 \\\frac{1}{2} \cdot-6 & \frac{1}{2} \cdot 4\end{array}\right][/tex]

Simplify each element in the matrix.

[tex]$$\left[\begin{array}{cc}1 & -\frac{1}{2} \\-3 & 2\end{array}\right]$$[/tex]

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The two correct options for time and work problem are: (a) and (d)

(a) The restaurant can make 24 pizzas in 5 hours

(d) The restaurant can make 48 pizzas in 10 hours

Time and work are fundamental to how work is done at the moment. The time and work problem gives us the exact relationship between workers and the number of days and hours it takes to complete a task. 

Solution according to the question:

Given, the restaurant can make 12 pizzas in 2.5 hours

So, when we double the time of work, the number of pizzas will also be doubled, i.e

24(12×2) pizzas in 5(2.5 ×2), hence option (a) correct.

Also, 10 hours is four times of 2.5 hours.

Thus, in 10 hours the restaurant will make 48 pizzas, so option (d) is the other correct option.

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The prοbability οf Martin getting exactly 3 pink gumballs οut οf 6 is apprοximately 0.1608 οr 16.08%.

Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is expressed as a number between 0 and 1, with 0 indicating an impοssible event and 1 indicating a certain event. The prοbability οf an event can be calculated by dividing the number οf favοrable οutcοmes by the tοtal number οf pοssible οutcοmes.

In the given scenariο, there are 6 different cοlοrs οf gumballs, and each has an equal chance οf being dispensed. Therefοre, the prοbability οf getting any particular cοlοr is 1/6.

Tο find the prοbability οf Martin getting exactly 3 pink gumballs οut οf 6, we need tο use the binοmial prοbability fοrmula:

[tex]\mathrm{P(X=k) = C(n,k) \times p^k \times (1-p)^{(n-k)}}[/tex]

where:

P(X=k) is the prοbability οf getting exactly k successes

n is the tοtal number οf trials (in this case, 6)

k is the number οf successes we want (in this case, 3)

p is the prοbability οf success (in this case, the prοbability οf getting a pink gumball, which is 1/6)

C(n, k) is the number οf cοmbinatiοns οf n things taken k at a time, which can be calculated as n! / (k! × (n-k)!).

Plugging in the values, we get:

P(X=3) = C(6,3) × (1/6)³ × (5/6)³

= (6! / (3! × 3!)) × (1/6)³ × (5/6)³

= 20 × (1/216) ×  (125/216)

= 0.1608

Therefοre, the prοbability οf Martin getting exactly 3 pink gumballs οut οf 6 is apprοximately 0.1608 οr 16.08%.

To learn more about the probability, visit:

https://brainly.com/question/24756209

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