Please helppp meeeeee

The  product of the given matrices is [tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

Matrix multiplication is a binary operation that produces a matrix from two matricesThe given matrices are [tex]A=\left[\begin{array}{ccc}1\\2\end{array}\right][/tex] and [tex]B=\left[\begin{array}{ccc}4&5\end{array}\right][/tex]

To perform product of two matrices, we should make sure that the number of columns in the 1st matrix is equal to the rows in the 2nd matrix

AB=[tex]\left[\begin{array}{ccc}1\\2\end{array}\right].\left[\begin{array}{ccc}4&5\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}4+5\\8+10\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

Hence, the  product of the given matrices is [tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

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The slope of the line that represent this relationship is 3.75.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about the charges by this amusement park, we have the following system of equations;

51.25 = 7m + c  ....equation 1.

70 = 12m + c    ......equation 2.

By solving equation 1 and equation 2 simultaneously, we have the following:

70 = 12m + 51.25 - 7m

70 - 51.25 = 5m

18.75 = 5m

Slope, m = 18.75/5

Slope, m = 3.75

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The value of the line integral is (-16/3)cos(6) + (16/9)sin(6). Evaluating this integral, you will get the value of the line integral for the given curve.

To evaluate the line integral ∫c x sin yds, where C is the line segment from (0,3) to (4,6), we first need to parameterize the curve. We can do this by letting x = t and y = 3 + (3/4)t, where t goes from 0 to 4. This gives us the parametric equations x = t and y = (3/4)t + 3.

Next, we need to find ds, the length of the curve element. We can use the formula ds = sqrt(dx^2 + dy^2) to get ds = sqrt(1 + (3/4)^2)dt = sqrt(25/16)dt = (5/4)dt.

Now we can substitute in our parameterization and ds into the line integral to get ∫c x sin yds = ∫0^4 t sin((3/4)t + 3) (5/4)dt.

We can evaluate this integral using integration by parts. Let u = t and dv = sin((3/4)t + 3) (5/4)dt, then du/dt = 1 and v = (-4/3)cos((3/4)t + 3). The integral becomes:

∫0^4 t sin((3/4)t + 3) (5/4)dt = uv|0^4 - ∫0^4 v du/dt dt
= (-4/3)t cos((3/4)t + 3)|0^4 - ∫0^4 (-4/3)cos((3/4)t + 3) dt
= (-4/3)t cos((3/4)t + 3) + (16/9)sin((3/4)t + 3)|0^4
= (-16/3)cos(6) + (16/9)sin(6)

Therefore, the value of the line integral is (-16/3)cos(6) + (16/9)sin(6).

To evaluate the line integral ∫c x sin y ds, where C is the line segment from (0, 3) to (4, 6), you first need to parameterize the curve C.

A possible parameterization is r(t) = (1-t)(0, 3) + t(4, 6) = (4t, 3+3t), with t ∈ [0, 1]. Then, compute the derivative dr/dt = (4, 3).

Now, find the integrand by replacing x and y with the parameterized curve components: x sin y = (4t) sin(3 + 3t).

Next, find the magnitude of the derivative: |dr/dt| = √(4² + 3²) = 5.

Finally, compute the integral:

∫[0, 1] (4t sin(3 + 3t))(5) dt.

Evaluating this integral, you will get the value of the line integral for the given curve.

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the only critical number of g(y) is -1/4.

To find the critical numbers of the function g(y) = y - 2y^2 - 2y + 4, we need to find its derivative and set it equal to zero.

g'(y) = 1 - 4y - 2

Setting g'(y) = 0, we get:

1 - 4y - 2 = 0

-4y - 1 = 0

y = -1/4

what is number?

A number is a mathematical object used to represent a quantity or value. Numbers can be classified into different types based on their properties and the set of numbers they belong to. Some common types of numbers include:

Natural numbers: These are the counting numbers, such as 1, 2, 3, and so on.

Whole numbers: These are the natural numbers plus zero, such as 0, 1, 2, 3, and so on.

Integers: These are the whole numbers plus their negative counterparts, such as -3, -2, -1, 0, 1, 2, 3, and so on.

Rational numbers: These are numbers that can be expressed as a ratio of two integers, such as 1/2, 0.75, or -3/4.

Irrational numbers: These are numbers that cannot be expressed as a ratio of two integers, such as pi (3.14159...) or the square root of 2 (1.41421...).

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The correct explanation about the rectangle is No, the adjacent sides are not perpendicular. Option D

A rectangle is defined as a quadrilateral with four right angles (90 degrees).

The shape provided in the diagram is not a rectangle because its four sides are not right angles.

Given that the coordinates for each point is a (3.9, -1)  b(2, 4)  c. (-2, -2)  d. (-1, -3).

Slope of AB = (4 - (-1)) / (2 - 3.9) = 5 / (-1.9) =-2.63

Slope of BC = (4 - 2) / (2 - (-2)) = 2 / 4 = 0.5

Slope of CD = (-2 - (-3)) / (-2 - (-1)) = 1 / -1 = -1

Slope of DA = (-1 - (-2)) / (3.9 - (-1)) = 1 / 4.9 = 0.20

The slopes of AB and CD are not equal, and the slopes of BC and DA are not equal either. Therefore, the opposite sides are not parallel.

the product of the slopes of adjacent sides (AB and BC) is not -1, which indicates that the angle between them is not a right angle

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Answer:

x + y = 22

3x + 5 = 35

3x = 30, so x = 10 and y = 12.

The sum of the measures of the exterior angles of the 14 sides polygon shown is 360 degrees.

The sum of the measures of the exterior angles of any polygon is always equal to 360 degrees.

This means that the exterior angles for the sides of this 14 sided polygon would be:

= 360 / 14

= 25. 71 degrees

Regardless of the polygon, so long as it is a regular polygon, the exterior angles will always add up to 360 degrees so the sum of exterior angles here is the same measure of 360 degrees.

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By using the formula of final amount, The future value is,

Future value = 29,640

We have to given that;

Present value = 12,000

Time = 8 years

And, interest rate = 12%

Now, For Calculate a future value for present value of 12,000 term of 8 years interest rate 12%, we can use the formula for present amount.

Since, We know that;

Future value = P (1 + r)ⁿ

Where, P is present amount.

r is interest rate.

n is number of years.

Hence, We can substitute all the given values, we get;

Future value = P (1 + r)ⁿ

Future value = 12,000 (1 + 12%)⁸

Future value = 12,000 (1 + 0.12)⁸

Future value = 12,000 (1.12)⁸

Future value = 12,000 x 2.47

Future value = 29,640

Therefore, The future value for present value of 12,000 term of 8 years interest rate 12% is,

Future value = 29,640

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After the given sequence of operations, the parent node of element 1 is the node representing the set {1,5,6,7}.

The sequence of operations given involves the Union-Find algorithm, which is used for disjoint set data structure. In this algorithm, each element is represented by a node, and each node is initially considered as a parent node. Union operation is used to combine two sets, and Find operation is used to determine which set an element belongs to.
In the given sequence of operations, the sets {1,5,6,7} and {2,3,4,8} are formed by performing union operations. Now, to determine the parent node of element 1, we need to perform a Find operation on it. Since element 1 is part of the set {1,5,6,7}, we need to find the parent node of any element from this set.
By following the sequence of operations, we can see that union(1,5) combines the sets {1} and {5} into one set {1,5}. Similarly, union(5,6) combines sets {1,5} and {6} into one set {1,5,6}. Finally, union(1,7) combines sets {1,5,6} and {7} into one set {1,5,6,7}. Therefore, the parent node of element 1 is the node representing the set {1,5,6,7}.
In conclusion, after the given sequence of operations, the parent node of element 1 is the node representing the set {1,5,6,7}.

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Answer:

Let's denote the number of people in Team A as a, and the number of people in Team B as b. From the problem, we know that:

a/b = 3/4

Now, we also know that 4/5 of Team A and 24% (or 24/100 = 6/25) of Team B work full time. So, the number of people working full time from Team A is 4a/5 and from Team B is 6b/25.

The total number of people working for the company is a + b, and the total number of people working full time is 4a/5 + 6b/25.

We are asked to find the fraction of people working full time, which can be represented as:

(4a/5 + 6b/25) / (a + b)

Firstly, we need to have a common denominator for the fractions, so we can express 4a/5 as 20a/25:

[tex](20a/25 + 6b/25) / (a + b)[/tex]

Simplifying, we can write this as:

[tex](20a + 6b) / (25(a + b))[/tex]

Now, since we know a/b = 3/4, we can substitute a = 3b/4 in the above expression:

[tex](20*(3b/4) + 6b) / (25((3b/4) + b))[/tex]

Simplifying the above, we get:

[tex](15b + 6b) / (25((3b/4) + b)) = 21b / 25b[/tex]

So, the fraction of people working full time is 21/25.

Answer:

The length of the hypotenuse is 13 cm, so the area of the missing square is 13^2 = 169 cm.

Answer:

(-5, 2)

Step-by-step explanation:

2x + 3y = -4

x + 9y = 13

We can solve this by substituting or using elimination.

Substituting:

2x + 3y = -4

-2x     = -2x     Subtract 2 from both sides.

3y = -2x - 4

3    =   3              Divide both sides by 3.

y = -2/3x - 4/3

x + 9(-2/3x - 4/3) = 13  Replace the y with -2/3x - 4/3.

x - 6x - 12 = 13     use the distributive property.

-5x - 12 = 13

     +12 = + 12           Add 12 to both sides.

-5x = 25

-5  = -5                  Divide both sides by -5.

x = -5

Now that we know what x is, we substitute -5 for the variable x in any of the two equations.

x + 9y = 13

-5 + 9y = 13  Replaced x with -5

+5       = +5   Add 5 to both sides.

9y = 18

Divide both sides by 9 to get:

y = 2

The other way to solve:

Elimination:

2x + 3y = -4

x + 9y = 13

Make the variable y cancel out.

-3(2x + 3y = -4)  use the distributive property.

-6x - 9y = 12

-6x - 9y = 12

x + 9y = 13

Add the equation.

-5x = 25

Divide both sides by -5.

x = -5

Plug in -5 for x.

2(-5) + 3y = -4

-10 + 3y = -4

+10     = +10   Add 10 to both sides.

3y = 6

Divide both sides by 3:

y = 2

We get the same answer in both strategies, you could use either one.

The factors of the given polynomial 18m²-8 are 2, (3m+2) and (3m-2).

The factors are the polynomials which are multiplied to produce the original polynomial.

Use the identity (a²-b²)=(a+b)(a-b)

1) 2a²-2b²

= 2(a²-b²)

= 2(a+b)(a-b)

2) 6x²-6y²

= 6(x²-y²)

= 6(x+y)(x-y)

3) 4x² - 4

= 4(x²-1)

= 4(x+1)(x-1)

4) ax²-ay²

= a(x²-y²)

= a(x+y)(x-y)

5) cm²-cn²

= c(m²-n²)

= c(m+n)(m-n)

6) st²-s

= s(t²-1)

= s(t+1)(t-1)

7) 2x²-18

= 2(x²-9)

= 2(x²-3²)

= 2(x+3)(x-3)

8) 2x²-32

= 2(x²-16)

= 2(x²-4²)

= 2(x-4)(x+4)

9) 3x²-27y²

= 3(x²-9y²)

= 3(x²-(3y)²)

= 3(x+3y)(x-3y)

10) 18m²-8

= 2(9m²-4)

= 2((3m)²-(2)²)

= 2(3m+2)(3m-2)

Therefore, the factors of the given polynomial 18m²-8 are 2, (3m+2) and (3m-2).

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The probability that a randomly selected adult consumes more than 40.0 hamburgers in a year is approximately 0.85.

In order to find the probability that randomly selected adult eats more than 40.0 hamburgers in a year, we use the normal distribution and z-scores.

First, we need to standardize the value of 40.0 using the formula : z = (x - μ)/σ,

Where : x = value we want to standardize (40.0 hamburgers), μ = mean number of hamburgers eaten (48.5 hamburgers), σ = standard-deviation (8.3 hamburgers),

Substituting the values,

We get:

z = (40.0 - 48.5)/8.3,

z = -1.024

Next, we find the area under the normal-curve to the right of z = -1.024. This represents the probability of randomly selecting an adult who eats more than 40.0 hamburgers.

We know that area to left of z = -1.024 is approximately 0.15. We need the area to right, so, we subtract this value from 1,

P(x > 40.0) = 1 - P(x ≤ 40.0)

P(x > 40.0) = 1 - 0.15

P(x > 40.0) ≈ 0.85,

Therefore, the required probability is 0.85.

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Answer:

Step-by-step explanation:

0.9411764706 since you would just divide 16/17.

Answer:0.94

Step-by-step explanation:

You can put 16/17 into the calculator and you will get 0.941176471, so you just round to the nearest hundredths, like it asks ,and there you go.

False. It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are

While the information states that there is a moderate positive correlation between the speed of the motor vehicle and the severity of injuries, correlation does not imply causation. Therefore, it cannot be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are. Correlation simply indicates that there is a relationship between the two variables, but other factors may also be influencing the severity of injuries.

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We can conclude  that there is a segment of the questioned population that values outdoor recreation and has children. The percentage of persons who belong to this subset is shown by the overlap percentage 15%.

29% of individuals say they have children and 52% say they like outdoor activities. 15% of respondents also mention having children and enjoying outdoor activities.

This evidence leads us to the conclusion that there is a correlation between those who prefer outdoor activities and those who are parents. There are people in the poll who fit into both categories as seen by the 15% of respondents who say they like outdoor activities and have children.

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A distance-time graph below shows a car travelling then the Speed of the car is 8.88 miles per hour

Speed is the time rate at which an object is moving along a path,

A distance-time graph below shows a car travelling

We know that speed is distance by time

From the graph the distance is 80 and time is 9

Speed= 80/9

=8.88 miles per hour

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The length of side x in the right triangle is approximately 38.2 units.

It looks like you have a right triangle problem where you need to solve for side x. The given information is the hypotenuse (Z) with a length of 56 units, an angle (M) of 43°, and side x which is opposite to angle M.
To solve for x, we can use the sine function in the context of the right triangle. The sine function is defined as:
sin(M) = opposite side (x) / hypotenuse (Z)
We are given the values for angle M (43°) and the hypotenuse (Z = 56 units). Plugging these values into the equation, we get:
sin(43°) = x / 56
Now, to solve for x, we will multiply both sides of the equation by 56:
x = 56 * sin(43°)
Next, use a calculator or trigonometric table to find the sine of 43°:
sin(43°) ≈ 0.682
Now, multiply this value by 56:
x ≈ 56 * 0.682
x ≈ 38.192
Finally, round your answer to the nearest tenth:
x ≈ 38.2
So, the length of side x in the right triangle is approximately 38.2 units.

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A. The x-intercepts of the graph represent a zero profit and $8 profit respectively, while the maximum value of the graph represents the maximum profit.

The interval over which the function is increasing is [0, 4] and the interval over which the function is decreasing is [4, 8]

With respect to the sale and profit, it means that the profit increases until it reaches the maximum profit of $270 and decreases after the vertex (4, 270).

B. An approximate average rate of change of the graph from x = 1 to x = 4 is $50 per unit sale.

C. The constraints of the domain is x > 0.

By critically observing the graph shown above, the x-intercepts are (0, 0) and (8, 0) while the maximum value of the graph is located at the vertex and it represent the maximum profit of $270.

Furthermore, the interval over which this quadratic function is increasing is [0, 4] and the interval over which the quadratic function is decreasing is [4, 8].

Part B.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function g(t) over the interval [1, 4]:

a = 1; f(a) = 120

b = 4; f(b) = 270

By substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (270 - 120)/(4 - 1)

Average rate of change = 150/3

Average rate of change = 50

Therefore, the average rate of change from x = 1 to x = 4 represent a profit of $50 per unit sale.

Part C.

In conclusion, the constraints of the domain is x > 0 or [1, 8] because the company cannot sell zero erasers and make profit.

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Complete Question;

The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent?

Part C: Describe the constraints of the domain.

The graph of the absolute function, p(x) = |x - 1|, has a minimum point (1, 0), and the points (-6, 7), and (6, 5), on the graph

Please find attached the graph of the absolute function created with MS Excel.

An absolute function is a function that nests an algebraic expression within an absolute value symbol.

The specified absolute function, p(x) = |x - 1|, indicates that the minimum value of the function, occurs where; p(x) = 0 = |x - 1|

Therefore; |x - 1| = 0, x = 1

When x = -6, we get; p(-6) = |(-6) - 1| = 7

When x = 6, we get; p(6) = |6 - 1| = 5

Therefore, the points on the graph are;

(-6, 7), (1, 0), and (6, 5)

Please find attached the graph of the absolute function created with MS Excel

The possible question, includes graph with the attached four options

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The correct solution to the inequality x^2 - 9x < -18 is x < 3 or x > 6.

To solve the inequality x^2 - 9x < -18, you can follow these steps:

Move all terms to one side of the inequality to form a quadratic expression: x^2 - 9x + 18 < 0.

Factorize the quadratic expression: (x - 6)(x - 3) < 0.

Determine the sign of the expression for different intervals of x. To do this, you can create a sign chart:

Interval | (x - 6) | (x - 3) | (x - 6)(x - 3) |

x < 3 | - | - | + |

3 < x < 6 | - | + | - |

x > 6 | + | + | + |

Analyze the sign chart to determine when the expression (x - 6)(x - 3) is less than zero (negative).

The expression is negative when x is between 3 and 6, i.e., 3 < x < 6.

Write the solution in interval notation:

x < 3 or x > 6

Therefore, the correct solution to the inequality x^2 - 9x < -18 is x < 3 or x > 6.

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The volume of the hemisphere is 261.8 cubic feet

We can easily find the volume of the hemisphere since the base of the sphere is circular. The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr³ cubic units.

In this problem, we simply substitute the values into the formula and then solve for the volume.

v = 2/3πr³

radius(r) = diameter(d) / 2

r = 10 /2

r = 5ft

Substituting the values;

v = 2/3π(5)³

v = 261.8ft³

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A) Yes, we can conclude that △ABD≅△ACD .

B) Rob says AB = AC and BD = CD. I agree.

C) The expression for the distance around the kite (perimeter) in centimeters is 4x + 30.

A) According to the principles of geometry, when two angles are marked alike, it means that they are equal.

Thus, ∠BAD ≅ ∠CAD; and

∠BDA ≅∠ADC

Since ∠BDA ≅∠ADC and

AD = DA (Based on the Reflexive postulate,

Then on the basis of the Angle  - Side - Angle theorem, △ABD≅△ACD.

B) AB = AC and BD = CD

This is because we have already proven that △ABD≅△ACD on the basis of A-S-A theorem.

C) Since both triangles are equal, the expression for their perimeter =

x + 15 + x + x + 15 + x

= 4x + 30

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Therefore, the degrees of freedom for the treatment source of variation is 3.

In ANOVA (Analysis of Variance), the total variability of a dataset is divided into different sources of variation, such as treatment, error, and total. The treatment source of variation represents the differences between the means of the groups being compared. The degrees of freedom for the treatment source of variation refer to the number of independent pieces of information used to estimate the variability due to treatment. It is calculated as the number of groups minus one. In this case, with four groups, the degrees of freedom for the treatment source of variation is 3. This value is used in calculating the F-statistic and determining if there are significant differences between the group means.

The degrees of freedom for the treatment source of variation can be calculated using the formula:

Degrees of freedom (treatment) = number of groups - 1

In this case, there are 4 groups, so the degrees of freedom for the treatment source of variation would be:

Degrees of freedom (treatment) = 4 - 1 = 3

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The combination formula  C(8, 5) is calculated as: 56

Combinations in probability theory and even other areas of mathematics tell us about a sequence of outcomes where the order does not matter. For example, when we order a pizza, it doesn't matter whether we order it with ham, mushrooms, and olives or olives, mushrooms, and ham.

Now, we want to find the combination given as C(8, 5)

The formula for combination is:

nCr = n!/(r!(n - r)!)

Thus;

8C5 = 8!/(5!(8 - 5)!)

= 56

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Converting 4315425 quinary number into a decimal number​ results in 73,240.

A quinary number is a number that is in base 5.

A decimal number is a number in base 10.

The powers of 5 include (1, 5, 25, 125, 625, and so on).  We write these powers of 5 beside the quinary digits written from bottom to top and then multiply each digit by its associated power.

The sum of the products gives the decimal number of the quinary number.

Digit         Power       Multiplication

5                 1                  5 (5 x 1)

2                 5               10 (2 x 5)

4               25            100 (4 x 25)

1              125             125 (1 x 125)

5            625          3,125 (5 x 625)

3          3,125         9,375 (3 x 3,125)

4       15,625       62,500 (4 x 15,625)

Total                   73,240

Thus, 4315425 quinary is equal to 73,240 decimal.

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The equation that shows how to find p, the total amount of Alex's paycheck, is:

35/p = 70/100.

This equation represents the fact that 70% of Alex's paycheck (0.7p) was automatically deposited into her savings account, and that amount is given as $35. To solve for p, we can divide both sides of the equation by 0.7:

p = 35 / 0.7

p = 35/70 x 1/100

35/p = 70/100.

Therefore, the total amount of Alex's paycheck this week is $50.

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Answer: What is the least number of gumballs jack has to buy to be certain he gets 6 gumballs of the same color?

Step-by-step explanation:

To be certain he gets 6 gumballs of the same color, Jack must buy at least 16 gumballs.

This is because he could buy 5 gumballs of each color (for a total of 15 gumballs) and still not have 6 gumballs of the same color. However, if he buys one more gumball, he will have at least 6 gumballs of one color.

Therefore, the least number of gumballs Jack has to buy to be certain he gets 6 gumballs of the same color is 16.

{Hope This Helps! :)}