there are 15 different colored marbles in a bag and you have one six-sided die. if you roll the die and choose a marble, how many possible combinations of marble color and die number are possible?

The exponential function in the graph can be written as:

h(x) = 3*2^x

We can see that h(x) is an exponential function, so we can write this in a general form as:

h(x) = a*b^x

Where a is the initial value and b is the base of the exponential.

First, we can see that it passes through the ponit (0, 3), replacing these values we will get:

3 = a*b^0

3 = a

So the equation is:

h(x) = 3*b^x

We also can see that it passes through (1, 6), replacing these values we will geT:

6 = 3*b^1

6 = 3*b

6/3 = b

2 =b

The exponential function is:

h(x) =3*2^x

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Both Option C. 5k+5 and Option D. 5(k+1) are equivalent expressions to 2k+2+k+3+2k.

To simplify the expression 2k+2+k+3+2k, we can combine like terms, as follows:

2k + k + 2k + 2 + 3 = 5k + 5

Therefore, the expression 2k+2+k+3+2k is equivalent to 5k+5. We can also write this expression as 5(k+1), since we can factor out the common factor of 5 from both terms:

5(k+1)

Therefore, both Option C. 5k+5 and Option D. 5(k+1) are equivalent expressions to 2k+2+k+3+2k.

Option A, [tex]5k^5[/tex], is not equivalent to the given expression, as it contains an exponent of 5, which is not present in the original expression.

Option B, [tex]5+k^5[/tex], is also not equivalent to the given expression, as it contains a term k^5, which is not present in the original expression.

Option C, 5k+5, is equivalent to the given expression, as shown above.

Option D, 5(k+1), is also equivalent to the given expression, as shown above.

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The complete question is :

Select all expressions that are equivalent to 2k+2+k+3+2k.

A. [tex]5k^5[/tex]

B. [tex]5+k^5[/tex]

C. [tex]5k+5[/tex]

D. [tex]5(k+1)[/tex]

Answer:

Step-by-step explanation:

The required larger and smaller number is 7 and 3 respectively.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

Let the larger number be x and smaller number be y,

According to the question,

the sum of the larger and twice the smaller is equal to 13.

x + 2y = 13 - - - -(1)

And, twice their positive difference is equal to eight.

2(x - y) = 8

x - y = 4 - - - -(2)

Subtracting equation 1 by 2

3y = 9

y = 3

Now,

x - y =4

x -3 = 4

x = 7

Thus, the required larger and smaller number is 7 and 3 respectively.

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There are 7 students who are studying both programming languages in the given class of 55 freshman.

This can be determined using a Venn diagram.

A Venn diagram is a graphical representation of sets or classes. The diagram shows sets, their elements, and the union, intersection, and complement of these sets.

A set is a collection of distinct objects, considered as an object in its own right. The elements of a set are frequently things of a similar nature, and sets are characterized by a distinctive property.

The size of a set is represented by the number of elements it contains. Let's use the following symbols to represent sets:

A={Elements in set A}

B={Elements in set B}

The intersection of sets A and B is the set of elements that are in both sets A and B. This can be expressed in the following way

n(A∪B) = n(A) + n(B) - n(A⋂B) where n(A⋂B) is known as intersection

The number of students studying both programming languages can be calculated by taking the intersection of the two sets.

We can use this formula to calculate the number of students studying both programming languages

:|A∩B|=|A|+|B|-|A∪B|

Where |A| denotes the number of elements in set  A studying C programming

|B| denotes the number of elements in set B studying Java

|A∪B| denotes the number of elements in the union of sets A and B (total students)

Now we can substitute the given values into the formula as follows

|A∩B|=38+24−55=7

Therefore, there are 7 students studying both programming languages.

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The number of sacks of trash that Jorge's brother picked up is given as follows:

3.75 sacks.

The number of sacks of trash that Jorge's brother picked up is obtained applying the proportions in the context of the problem.

Jorge picks up 2 1/2 sacks of trash, which is a mixed number, hence the decimal number that represents this amount is given as follows:

2 + 1/2 = 2 + 0.5 = 2.5 sacks.

His brother picks up 1 1/2 times as much as Jorge, which is 1 + 1/2 = 1.5 times the amount picked by Jorge, hence the number of sacks of trash that Jorge's brother picked up is obtained as follows:

2.5 x 1.5 = 3.75 sacks.

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If 3x is the cost of x notebooks, we can find the cost of 24 notebooks by substituting x = 24:

3(24) = 72

Therefore, the cost of 24 notebooks is $72.

Answer:

here ya go, i didnt really feel like tpoing so its in the picture

Step-by-step explanation:

Answer: y = x + 6

Step-by-step explanation:

         For every unit moved right, the next point is one unit up. This gives us a slope of 1, which we can simplify to just x in the final equation.

[tex]\frac{rise}{run} =\frac{1}{1}=1[/tex]

         We see that the graph intersects the y-axis at (0, 6), giving us a y-intercept of + 6.

         Lastly, we will write the equation.

y = x + 6

         Try it without the 1. Usually we simplify as anything multiplied by 1 is itself.

Answer:

[tex]x = \frac{5}{p - 1} [/tex]

p ≠ 1

Step-by-step explanation:

20 = 4x (p - 1)

20 = 4xp - 4x

4xp - 4x = 20

(4p - 4)x = 20 / : (4p - 4)

[tex]x = \frac{20}{4p - 4} = \frac{20}{4(p - 1)} = \frac{5}{p - 1} [/tex]

we determine the scope of the definition:

4p - 4 ≠ 0

4p ≠ 4 / : 4

p ≠ 1

Answer:

Let x be Taub and y for Chloe

y-x=1. since their ages are consecutive

y-1=x

xy=12.…..... eq 1

(y-1)y=12....... eq 2

y²-y-12=0

y=4 or y=-3

since age can never be a negative, we choose y=4 and substitute in eq 1

4x=12

x=12/4=3

Taub is 3 years old

The sample mean for the given data set is 3.044 miles.

Let's use the given data to calculate the sample mean. We have the distances in miles that 10 visitors live from the library: 0.5, 0.8, 0.8, 1.5, 1.8, 3.5, 4.8, 6.2, and 8.3.

To find the sample mean, we first add up all the distances:

0.5 + 0.8 + 0.8 + 1.5 + 1.8 + 3.5 + 4.8 + 6.2 + 8.3 = 27.4

Next, we divide the sum by the total number of distances, which is 9 (since we have data for 10 visitors):

27.4 / 9 = 3.044 (rounded to three decimal places)

This means that, on average, the visitors to the library live about 3.044 miles away from the library.

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Answer:

C

Step-by-step explanation:

P and N are a linear pair and sum to 180° , that is

P + 67° = 180° ( subtract 67° from both sides )

P = 113°

Answer:

True

Step-by-step explanation:

A vertical number line is line that runs vertically, or up and down. Starting from 0, it has positive numbers moving up and negative numbers moving down.

Based on what we know, positive numbers move up on a vertical number line and move to the right on a horizontal number line. Negative numbers move down on a vertical number line and to the left on a horizontal number line.

So, because 14 is negative, and it's on a vertical number line, it would be below any positive number such as 7.

In short, the answer is true because negative numbers are below or behind positive numbers.

Answer:-72x

Step-by-step explanation:

V = πr^2h

V1 = π14/2^2•9
V1 = π7^2•9

V1 = π49•9

V1 = 1,385.442360233099

V2 = π6/2^2•9

V2 = π3^2•9

V2 = π9•9

V2 = 254.4690049407733

V = V1 - V2

V = 1,385.442360233099 - 254.4690049407733

V = 1,130.973355292326 or 1,130.97

Thus, the volume of the cylinder is 1,130.97cm^3.

The non - markup price of the pair of shoes is $103. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

It is believed that the four fundamental operations, often known as "arithmetic operations," adequately explain all real numbers. After division, multiplication, addition, and subtraction in mathematics are the operations quotient, product, sum, and difference.

We are given that the store sells the shoes for $193.21 which includes the 87% markup.

So, using the subtraction operation, we get

⇒ Non - markup price = ($193.21 * 100) ÷ 187

⇒ Non - markup price = $19321 ÷ 187

⇒ Non - markup price = $103.3208

Hence, the non - markup price of the pair of shoes is $103.

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The independent variable in a study is the one that can be controlled or manipulated, and in this case, it is the number of hours of overtime assigned at the facility.

To better understand the relationship between the two variables, we can use mathematical terms. Let's consider X as the independent variable, which represents the number of overtime hours assigned, and Y as the dependent variable, which represents the number of defects in the product. In this case, we can express the relationship between X and Y as:

Y = f(X)

This means that the value of Y is a function of the value of X. In other words, the number of defects in the product depends on the number of overtime hours assigned.

To determine the nature of the relationship between X and Y, we can plot a graph with X on the horizontal axis and Y on the vertical axis. If the graph shows a positive correlation, it means that an increase in X leads to an increase in Y, and vice versa. On the other hand, if the graph shows a negative correlation, it means that an increase in X leads to a decrease in Y, and vice versa.

Finally, if there is no correlation, it means that there is no relationship between X and Y.

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The linear equation to represent the cost, correct answer is A) C = 0.04z.

What is equation?

An equation is a mathematical statement that shows the equality of two expressions. It consists of two parts, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).

To find the cost per zinnia plant, we can first find the cost per plant for each order separately, and then take the average.

For the first order of 200 zinnia plants at a cost of $23, the cost per plant is:

$23 ÷ 200 = $0.115

For the second order of 500 zinnia plants at a cost of $35, the cost per plant is:

$35 ÷ 500 = $0.07

To find the average cost per plant, we can take the total cost and divide by the total number of plants:

($23 + $35) ÷ (200 + 500) = $0.067

So the cost per zinnia plant is $0.067.

Now we can write the linear equation to represent the cost, C, to purchase z number of zinnia plants:

C = 0.067z

Therefore, the correct answer is A) C = 0.04z.

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the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

To describe the end behavior of a polynomial function, we need to examine the degree and leading coefficient of the function. In the polynomial function f(x) =[tex]2x^3 + 5x^2 - 2x - 3[/tex], the degree is 3 and the leading coefficient is 2.

The end behavior of the polynomial function f(x) is determined by the behavior of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the leading term dominates the behavior of the function. Since the leading coefficient is positive and the degree is odd, the function will increase without bound, or approach positive infinity. In other words, as x becomes very large and positive, the function will also become very large and positive.

As x approaches negative infinity, the leading term also dominates the behavior of the function. However, since the degree is odd, the function will decrease without bound, or approach negative infinity. In other words, as x becomes very large and negative, the function will also become very large and negative.

Therefore, the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

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The probability that p falls between 0 and 0.06 is 0.00000205.

How to calculate the probability

Based on the information, to calculate the probability that p falls between 0 and 0.06, we need to first calculate the standard error (SE) of the sample proportion, which can be calculated as:

SE = ✓[ p * (1-p) / N ]

where p is the sample proportion and N is the sample size.

In this case, we have:

p = 25/85 = 0.2941

N = 85

SE = ✓[ 0.2941 * (1-0.2941) / 85 ] = 0.0545

Next, we need to calculate the z-score corresponding to the upper limit of the interval (0.06). This can be calculated as:

z = (0.06 - p) / SE = (0.06 - 0.2941) / 0.0545 = -4.4702

Using the dCMP normal distribution tool, we can find the probability that a standard normal random variable falls below this z-score as:

P(z < -4.4702) = 0.00000205

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Answer:

Step-by-step explanation:

Answer:

1.28*10^6

Step-by-step explanation:

It is up to you whether you convert 1400000 into scientific notation or convert 1.2*10^5 into decimal notation, subtract, and then convert once more into scientific notation for your final answer.

Either way, it will come out to be 1.28*10^6

Work is below:

1.2*10^5 = 120,000

1400000 - 120000 = 1280000

= 1.28*10^6 (remember it is every number behind the decimal)

An expression for the number of bracelets of n beads, where rotations.

Whats an expression for the bracelets?

In mathematics, the term "bracelets" can refer to a type of combinatorial object, specifically, a set of beads arranged in a circular pattern. An expression for the number of bracelets of n beads, where rotations and reflections are considered identical, can be given as follows:

B(n) = (1/n) * (2raise to the power (n-1) + Σ(d|n, d<n) μ((n/d)) * 2 raise to the power ((n/d)-1))

Here, B(n) represents the number of distinct bracelets of n beads, Σ denotes the summation, d|n denotes "d divides n", and μ is the Möbius function.

The first term in the expression, (1/n) * (2 raise to the power (n-1)), represents the number of bracelets that are invariant under rotation. The second term takes into account the bracelets that are not invariant under rotation, but are invariant under reflection, and involves the Möbius function.

This expression can be used to calculate the number of bracelets for any value of n, by plugging in the value of n and evaluating the expression.

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Answer:

360∘

The sum of the exterior angles of a polygon is always 360∘ . Therefore, the sum of the exterior angles of a 25-gon is 360∘ .

Answer:

41 chickens and 9 cows

Step-by-step explanation:

Chickens have 2 legs each.

Cows have 4 legs each.

There are 50 animals total.

There are 118 legs total.

You can set up a system to represent this situation.

Let x represent the number of chickens and y represent the number of cows.

x + y  = 50

2x + 4y = 118

Multiply the first equation by 2 and subract it from the second equation.

    2x + 4y = 118

-    2x + 2y = 100

_____________

2y = 18

y = 9

So there are 9 cows. There are 50 animals total so there must be 41 chickens.

There is a total of 50 chickens and cows.

Chickens have 2 legs each. Cows have 4 legs each.

There are 118 legs in total. We are focusing on how much chickens there are.

CHICKENS=50-COWS.

2CHICKENS+4COWS=118

2(50-COWS)+4COWS=118

100-2COWS+4COWS=118

2COWS=118-100

2COWS=18

C0WS=18/2

COWS=9

CHICKENS+9=50

CHICKENS=50-9

CHICKENS=41

PROOF:

2*41+4*9=118

82+36=118

118=118

This is a bit long and confusing but I hope this helps!

The probability that a basketball player makes all four of his free throws when the probability of making one is 80% is 0.4096.

This is calculated using the binomial probability formula, which states that the probability of k successes in n trials is given by the following:

P(k successes in n trials) = [tex](n!/(k!(n-k)!))\timespk(1-p)(n-k)[/tex]

In this case, the probability of making a single free throw is 80% (0.8),

so we can plug this into the formula.

We know that the player is taking 4 free throws, so k is 4 and n is also 4.

Plugging these values into the formula, we get:

P(4 successes in 4 trials) = [tex](4!/(4!(4-4)!))\times 0.84(1-0.8)(4-4) = 0.4096[/tex]

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Answer:

3/4.

Step-by-step explanation:

y = x^1/2

dy/dx = 1/2 x^-1/2

dy/dt = dy/dx * dx/dt

        =  1/2 x^-1/2 * 3

         = 3/2 x^-1/2

When x = 4:

dy/dt = 3/2 * 4 ^-1/2

         = 3/2* 1/ √4

         = 3/2 * 1/2

         = 3/4.