Suppose a bag of colored marbles contains 33 marbles numbered 1 to 33. If you draw one marble at a time from the bag, without replacement, how many different ways can you draw all of the marbles from the bag? Remember that "without replacement" means that the marbles are not returned to the bag after they are chosen. Write your answer in factorial notation.

The average daily balance on the June 5 bill is $1,037.32, including the finance charge.

The average daily balance is the total balance divided by the number of days in the billing cycle.

May has a 31-day billing cycle.

The average daily balance determines the finance charge, which is a product of the monthly interest rate (MPR) and the ending average daily balance.

                                                       Daily Balance

May 5 Credit card balance $939    $11,260 ($939 x 12)

May 17 Purchase                    216     $4,620 ($1,155 x 4)

May 20 Payment                  -100   $15,825 ($1,055 x 15)

Total daily balances                       $31,705

Average daily balance                   $1,023 ($31,705 ÷ 31)

Interest rate per month = 1.4%

Finance charge for the month = $14.32 ($1,023 x 1.4%)

June 5 balance = $1,037.32 ($1,023 + $14.32)

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The solution for the given system of equation is (x,y,z) is = (0 , (3-4t) , t) .

In the question ,

it is given that the system of equations are ,

3x + 3y + 12z = 9

x + y + 4z = 3

2x + 5y + 20z = 15

-x + 2y + 8z = 6

we have to solve the equations for x, y , z.

writing the given equations in augmented matrix form ,

we get ,

[tex]\left[\begin{array}{ccc}3&3&12\\1&1&4\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}9\\3\\15\\6\end{array}\right][/tex]

Applying the operation , R₁/3 ⇒ R₁

[tex]\left[\begin{array}{ccc}1&1&4\\1&1&4\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\3\\15\\6\end{array}\right][/tex]

Applying the row operation , R₂ - R₁ ⇒ R₂  .

[tex]\left[\begin{array}{ccc}1&1&4\\0&0&0\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\0\\15\\6\end{array}\right][/tex]

After applying more row operations , in the above matrix ,

to make the lower triangle matrix 0 ,

we get ,

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&4\\0&0&0\\0&0&0\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}0\\3\\0\\0\end{array}\right][/tex]

The above result can be expressed as x = 0,

and y + 4z = 3 .

So , the system of equations have infinite solutions .

So , the solution x, y, and z expressed in terms of the parameter t is

(0 , (3-4t) , t)  .

Therefore , the solution is (x,y,z) is = (0 , (3-4t) , t) .

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(a) 15⁶ many distinct pizza varieties are there.

(b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, 8108520 many different sorts of pizza are possible.

Given that,

A brand-new pizza restaurant offers 15 topping choices and consistent cost, allowing customers to select any six of them. For instance, a customer can choose 4 mushrooms and 2 olives if they just want mushrooms and olives on their pizza.

We have to find

a) How many distinct pizza varieties are there.

b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, how many different sorts of pizza are possible.

We know that,

(a) we have 6 places to fill form 15 options.

So, each place has 15 choice

Type of pizza possible=15⁶.

(b) No jalapeno used = 14⁶

1 jalapeno used = 14⁵

2 jalapeno used = 14⁴

3 jalapeno used = 14³

Total pizza = 14³+14⁴+14⁵+14⁶

Total pizza = 14³(1+14+14²+14³)

Total pizza = 8108520

Therefore,

(a) 15⁶ many distinct pizza varieties are there.

(b) Given that we are heat-sensitive and that there can be no more than three types of jalapeno, 8108520 many different sorts of pizza are possible.

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Answer: She had 167.57 remaining in her account

Step-by-step explanation:

You add all her expenses and then subtract it from the beginning balance

By the information provided in the question, we can say that , Power is the measure of how much work can be done in a given amount of time.

Work in physics is the energy that is transferred to or from an item when a force is applied along a displacement. In its simplest form, it equals the product of the force's magnitude and the distance travelled for a constant force directed in the direction of motion.

Power measures how quickly labor is completed or energy is used. It is equal to the work completed divided by the time required to do the task. The Watt (W), which is a unit of power, is equivalent to a Joule per second (J/s).

Power is the measure of how much work can be done in a given length of time.

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Answer:

Step-by-step explanation:

Find the corner points of X (x,y) and Y(x,y)

Answer:

D)8.00

σ = √64

= 8

Among the following relations, the Function is option D,{1,2,2,3,3,4,4,5}.

In simple words, a function is a relationship between inputs where each input is related to exactly one output.  Functions are often defined by a formula that describes a combination of arithmetic operations

A function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. To identify a function from a relation, we just have to see if any 'x' values are being repeated, if not, it is a function. If x values are repeated, and y values are different, then we have a relationship and not a function.

In the question, we can see that values 2,3, and 4 are repeating. This specifies that they are a function.

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A local minimum or a local maximum are both examples of local extremums.

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We don't have claim to strength of composite B is smaller than the strength of composite B by at least 2 [N].

From the given data we calculate μ₁s₁ and μ₂s₂ mean and standard deviation of samples A and B respectively.

μ₁ = 464.7, s₁ = 13.42 composite A

μ₂ = 479.49, s₂ = 13.38 composite B

n₁ : n₂ < 30 then we will use t-table.

Null hypothesis  H₀:μ₂-μ₁ ≥ 2

Alternative hypothesis Hₐ : μ₂ - μ₁ < 2

assuming CI 95%

α = 5% = 0.05

and degree of freedom is n₁ + n₂ - 2 = 9 + 9 - 2 = 16

then for the one tail t(c) = 1.746  

now we will compute t(s),

t(s) = (μ₂ - μ₁ - 2)/ sp×√1/n₁ + 1/n₂

sp²= (n₁ - 1) × s₁² + (n₂ - 1) × s₂² / n₁ + n₂ - 2

    = 8 × (13.42)² + 8 × (13.38)²/ 16

     = (8 × 180.1 + 8 × 179) / 16

sp² = 179.55

sp = 13.40

Therefore

t(s) = (479.49 - 464.7 - 2)/ 13.40 ×√1/9+1/9

     = 12.79 / 13.40 × 0.4714

     = 12.79 / 6.32

t(s) = 2.02

t(s) > t(c)

t(s) is rejection region.

Therefore we reject H₀

so we don't have evidence to claim to strength pf composite B is smaller than the strength of composite B at least 2 [N].

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The cost of the task, given the perimeter of the figure, and the cost of feets of fence, is $ 5.17

First, find the perimeter of the figure which is just the distance around the shape:

= 4 + 2 + 6 + 3

= 15 cm

The fence needs 5 % more :

= 15 x ( 1 + 5%)

= 15.75 cm

This distance in feet is :

= 15 . 75 / 30.48 cm per feet

= 0. 5167 feet

The cost of the task is therefore:

= 0. 5167 x 30 / 3 feet

= $ 5.17

In conclusion, the cost of the entire task after accounting for the various costs, is $ 5.17.

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The values of the expression (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

The given parameters that will help us to calculate the values are

r(x) = x+5

s(x) = 4x +2

(1)  r*s(x) will be

(x+5)(4x+2)

Opening the brackets we have

4x²+2x+20x+10

= 4x²+22x+10

(2) (r-5)(x)

Putting the values of r and s

(x+5)- (4x+2)

Open the brackets to have

x+5-4x-2

Collecting like terms to get

-3x+3

(3) (r+s)(x)

By substitution we have

x+5+4x+2

⇒5x +7

In conclusion the values of the expressions are (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

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The sum of the series is 25/3

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

5, 2, 4/5, ....

The sum of the series to infinity is

Sum = First term/1 - common ratio

In this, we have

First term = 5

common ratio = 2/5

So, we have

Sum = 5/(1 - 2/5)

Evaluate

Sum = 25/3

Here, we have

Initial population, a = 79000

Rate = 5%

An exponential function is represented as

P(x) = a *(1 + r)^x

So, we have

P(x) = 79000 *(1 + 5%)^x

In 2003. we have

x = 2003 - 1990 = 13

So, we have

P(13) = 79000 *(1 + 5%)^13

Evaluate

P(13) =148966

This means that

P(x) = 3a

So, we have

3a = a *(1 + 5%)^x

This gives

3 = (1 + 5%)^x

Take the logarithm of both sides

x = log(3)/log(1 + 5%)

Evaluate

x = 23

So, the year is

Year = 1990 + 23 = 2013

Hence, the year is 2013

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The value of x for an equation

1)  2x - 4 = 4x + 4 is x = -4

2) 6(x - 2) = 36 - 10x   is x = 3

3) 3(x-2) = 2x + 6 is x = 12

In this question, we have been given an equation.

we need to find the value of x in the equation 2x - 4 = 4x + 4;

6(x - 2) = 36 - 10x

and 3(x-2)=2x+6;

1) consider an equation 2x - 4 = 4x + 4

2x - 4x - 4 = 4x + 4 - 4x

-2x - 4 + 4 = 4 + 4

-2x = 8

x = -4

2)  consider an equation, 6(x - 2) = 36 - 10x

6x - 12 = 36 - 10x

6x + 10x = 36 + 12

16x = 48

x = 48/16

x = 3

3) consider an equation 3(x - 2) = 2x + 6

3x - 6 = 2x + 6

3x - 2x = 6 + 6

x = 12

Therefore, the value of x for

a)  2x - 4 = 4x + 4 is x = -4

b) 6(x - 2) = 36 - 10x   is x = 3

c) 3(x-2) = 2x + 6 is x = 12

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Answer:

A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

Answer:

minus 5 times x and the quantity x squared minus 1.

Step-by-step explanation:

The error step in the problem of finding an inverse is Step 4.  

What is an inverse function?

In relation to the original function f, the inverse function is denoted by the symbol [tex]f^{-1}[/tex], and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively.

Given, based on the inverse function

Step 1: y = 6x - 11        (Given equation)

Step 2: x = 6y - 11       (Exchange of variables x and y with each other                 respectively)

Step 3: x + 11 = 6y      (Adding 11 on both sides)

Step 4: x/6 +11 = y      Error step ( because dividing both sides by 6 will give x/6 + 11/6 = y)

Hence, the error step in the problem of finding an inverse is Step 4.  

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Using the t-distribution, the 99% confidence intervals for the given standard deviation are given as follows: (5053.39 , 4126.61)

Given that,

Number of college students = 23

A simple random sample with a mean = $4590

A simple random sample with a standard deviation = $860

The t distributions is wide (has thicker tailed) for smaller sample sizes, reflecting that s can be smaller than σ. The thick tails ensure that the 80%, 95%, 99% confidence intervals are wider than those of a standard normal distribution (so are better for capturing the population mean).

The confidence interval is:

= μ ± [tex]t\frac{s}{\sqrt{n} }[/tex]

In which:

μ is the sample mean.

t is the critical value.

n is the sample size.

s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 23 - 1 = 22 df,

Upon using a t -table or a calculator, we see that the critical t -value for this 99% confidence interval is t0.005=2.581

The parameters are:

μ = $4590

n = 23

Hence, with s = 860, the bounds of the interval are:

= μ ± [tex]t\frac{s}{\sqrt{n} }[/tex]

= 4590 ± 2.581 [tex]\frac{860}{\sqrt{23} }[/tex]

= 4590 ± 2.581 [tex]\frac{860}{4.79}[/tex]

= 4590 ± 2.581 (179.54)

= 4590 ± 463.39

Then,

= 4590 + 463.39   ,      4590 - 463.39

= 5053.39              ,       4126.61

Therefore,

Using the t-distribution, the 99% confidence intervals for the given standard deviation are given as follows: (5053.39 , 4126.61)

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Six (6) confidence intervals or hypothesis tests would need to be done to make significant statements for each pair-wise comparison.

In an ANOVA F test, the null hypothesis is that the means of all the treatments are equal, and the alternative hypothesis is that at least two of the means are different. If the null hypothesis is rejected at the 5% significance level, this means that the differences between the means are statistically significant and the treatments can be considered different.

Since there are four treatments, there are 6 possible pairs of treatments. These tests would determine whether the means of each pair of treatments are significantly different from each other.

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Answer:  

The value of x that satisfies the equation 81 = 8(2x + 8) + x is x = 1.125.

Step-by-step explanation:

To solve for x in the equation 81 = 8(2x + 8) + x, you can first distribute the 8 on the right side of the equation to obtain 81 = 16x + 64 + x. Then, you can combine like terms on the right side of the equation by adding the two x terms and the constants to get 82 = 16x + 64. Next, you can subtract 64 from both sides of the equation to isolate the x term, which gives 18 = 16x. Finally, you can divide both sides of the equation by 16 to solve for x, resulting in x = 1.125.

Answer:

98.53

Step-by-step explanation:

[tex]100 \times 5 = 1500 \\ 1500 - 22 = 1478 \\ 1478 \div 15 = 98.53[/tex]

The weight of clothing is the ratio of weight to dye is different from the other ratios is B. 42 pounds.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

It should be noted that from the information given, others have a ratio of 1:7. This is different for 42 pounds since the ratio is:

= 42/9

= 14:3

In conclusion, the correct option is B.

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The total shipment amount of $ 33,066 must be paid back in order to receive a cash reimbursement for the $20,040 in goods that were returned.

When describing a singular noun that CANNOT be measured, you should use the word amount. – When discussing a singular, plural, or countable noun, the word number should be used. – Any single or plural noun that can be counted or measured should be referred to as having a certain quantity.

1/10 n (unclear) indicates that the consumer settled their debts within 10 days and was entitled to a 1% sales discount.

Therefore, the consumer should receive a refund equal to what they paid, which is 1% less than the total amount.

Using that as a basis, the calculation is,

Amount owed * (1-discount rate)

= $ 33,400 * ( 1 - 0.01)

= $ 33,066

$ 33,066 is is the sum that must be reimbursed.

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Answer:

[tex]6g=900[/tex]

Step-by-step explanation:

The number of calories in one bar multiplied by six is the number of calories in six bars. This is given to be equal to 900.

Answer: D) Two sides are congruent

Step-by-step explanation:

Option c 0.932 is the correct option of the given statement.

Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the pooled estimate overbar(p)

n1 = 100 n2 = 100

x1 = 42 x2 = 45

On a linear scale from 0 (impossibility) to 1 (certainty), or as a percentage between 0 and 100%, the word "probability" is commonly used to refer to the likelihood that a specific event (or group of events) will take place. Statistics describes the examination of events subject to probability.

The proportion of favorable outcomes to all possible outcomes serves as the basis for the formula used to determine an event's probability. Always between 0 and 1 are the possible outcomes. Probability = Number of Favorable Outcomes / Total Number of Outcomes is a general form of the probability formula.

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For the given matrix A ,(a) the eigen values are 0 and -3 . and the eigen vectors corresponding to the given eigen vectors are   [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex]  and  [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .

In the question ,

it is given that ,

the matrix A is = [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex]

Part(a)

the eigen values of the matrix A can be found by the characteristic equation ,

|A - λI | = [tex]\left|\begin{array}{ccc}-6-\lambda &6\\-3&3-\lambda\\\end{array}\right|[/tex] = 0 ;

= -(6 + λ)(3 - λ) + 18

= λ² - 3λ + 6λ = 0

= λ² + 3λ = 0

So , λ = 0 and λ = -3 .

the eigen values are 0 and -3 .

Part(b)

for finding the eigen vectors ,

For eigen value λ = 0  , [A - λI]*X = 0

on solving [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}x_{1} \\x_{2} \\\end{array}\right][/tex] = 0 ,

we get x₁ = 1 and x₂ = 1 ,

the eigen vector corresponding to eigen value 0 is [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex] .

Similarly solving for eigen value λ = -3 ,

[tex]\left[\begin{array}{ccc}-3&6\\-3&6\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}x_{1} \\x_{2} \\\end{array}\right][/tex] = 0 ,

Solving further ,

we get , x₁ = 2 and x₂ = 1 ,

the eigen vector corresponding to eigen value -3 is [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .

Therefore , (a) the eigen values are 0 and -3 .

(b) the eigen vectors are  [tex]\left[\begin{array}{ccc}1 \\1 \\\end{array}\right][/tex]  and  [tex]\left[\begin{array}{ccc}2 \\1 \\\end{array}\right][/tex] .

The given question is incomplete , the complete question is

The matrix is A = [tex]\left[\begin{array}{ccc}-6&6\\-3&3\\\end{array}\right][/tex] ,

(a) Find the eigenvalues of Matrix A .

(b) Find corresponding eigenvector for each of eigenvalues found in (a).

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The correct sentences here are n = 5, l = 2, ml = -2 , -1, 0 , +1 , +2. The 5 integer values for ml signify that there are 5 5d orbitals.

In the given question we have to list the quantum numbers associated with all of the 5d orbitals, and indicate how many 5d orbitals exist in the sentences below.

As we know that;

Quantum numbers are the collection of numbers used to represent the location and energy of an electron in an atom. The primary, azimuthal, magnetic, and spin quantum numbers are the four types of quantum numbers.

There are four different quantum numbers , principal , azimuthal , magnetic and magnetic spin quantum numbers . The correct sentences here are :

n = 5

l = 2

ml = -2 , -1, 0 , +1 , +2

The 5 integer values for ml signify that there are 5 5d orbitals.

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The time taken by A over the course is 109.3 s

The given parameters that will help us to solve the problem is  

A beats B by 60m in 7s

Length of track = 1km

Distance by which A beats B = 60m

And the time by which A beats B is 7 seconds

Time taken by A over the course according to the problem is

A covers 60m in 7 secs

Let us consider the formula,

Speed = Distance / Time

The Speed of B= 60/7 m/s = 8.6 m/s

This implies that Time taken by B over the course = Distance / Speed

= 1000/8.6 = 116.3 s

According to the problem, if A reaches earlier , then time taken by A = (116.3 - 7) s = 109.3 s

In conclusion time taken by A over the course is 109.3 s .

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