Only #1 and 5 please show work THANK YOU

Using the combination formula, the number of ways to order the pizzas in each case is given as follows:

a) 638 ways if Grogg must order at least five toppings.

b) 937,024 ways if each pizza must have at least three toppings.

c) 1024 ways if Lizzie's pizza must have at least four toppings and Grogg's must have at least one topping.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.

[tex]C(n,x) = \frac{n!}{x!(n-x)!}[/tex]

For this problem, the order of the toppings is not important, which is why the combination formula is used.

Hence the numbers of pizzas from 0 to 10 toppings are given as follows:

In item a, Greg must order at least five, hence the number of ways is:

252 + 210 + 120 + 45 + 10 + 1 = 638 ways.

In item b, each must have at least three toppings, hence the number of ways for each is:

120 + 210 + 252 + 210 + 120 + 45 + 10 + 1 = 968 ways.

968 ways for each, two people, hence, by the Fundamental Counting Theorem, the number of ways is:

968² = 937,024 ways.

In item c, the number of ways is the sum of all the possible toppings, except zero, from the conditions given, hence:

1 + 10 + 45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 + 1 = 1024 ways.

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Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-2)}{2-0}[/tex] = [tex]\frac{-1+2}{2}[/tex] = [tex]\frac{1}{2}[/tex]

The cumulative grade point average of Hung Lee is 2.5.

It is given in the question that:-

A = 4

B = 3

C = 2

Grade received in Accounting = A

Grade received in History = C

Grade received in Psychology = C

Grade received in Algebra = C

We have to find her cumulative grade point average.

We know that:-

The cumulative grade point average of Hung Lee will be:-

Sum of grade point averages in the all the courses/Total number of courses

Hence, we can write,

The cumulative grade point average of Hung Lee is given by:-

(4+2+2+2)/4 = 2.5

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Answer:

Divide both sides by -2

Step-by-step explanation:

-2(c+8) = -8

-2(c+8) / -2 = -8/-2

c + 8 = 4

c = -4

Answer:

{x ∈ R: x ≠ -5 and x ≠ 1}.

Step-by-step explanation:

x^2+8/x^2+4x-5

= x^2+8 / (x - 1)(x + 5)

The denominator is zero when x = 1 or x = -5

So:

Domain is:

{x ∈ R : x ≠ -5 and x ≠ 1}.

Riley bought  2 boxes of  thank you cards and 3 boxes of get well cards.

What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let Riley have bought x boxes of  thank you cards and y boxes of get well cards.

Therefore according to the question,
x + y = 5.......(1)
9x + 4y = 30........(2)

Multiplying equation 1  with 4 we get.
4x + 4y = 20.......(a)
Subtracting (a) form (2) we get:
5x = 10
=> x = 2
Putting the value of in (1) we get y= 3

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Using the number line to find the coordinate of P that represents the weighted average of the set of points we see that the value of 6 represents the weighted average of the coordinates.

The ordinary arithmetic mean is comparable to a weighted arithmetic mean. The primary difference between the two is that the weighted arithmetic mean takes into account the fact that not all of the data points contribute the same amount to the overall average; rather, some data points contribute more than others.

Generally, the equation for Average weight is mathematically given as

[tex]Av=\frac{ (3 * 2 + 8 * 3)}{(2 + 3)}[/tex]

Consider the quotient in question.

Average weight = 6

As a direct result of this, the value 6 was determined to be the weighted average of the coordinates.

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The probability that in a given year it will not snow on January 1st in that town is 0.572.

It should be noted that from the information, the meteorological records illustrates that the probability that it will snow in a certain town on January 1st is 0.428.

Therefore, the probability that in a given year it will not snow on January 1st in that town will be:

= 1 - 0.428

= 0.572

The probability is 0.572.

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From the scrabble information given above, the odds in favor of selecting E is given as 0.073 while the odds against selecting an E is 13.667.

The odds are defined as the chance of the event occurring divided by the probability of the event not occurring. If the chance of an event happening is Y, the probability of it not happening is 1-Y.

Given:

Total number of tiles = 100

Number of E tiles = 12 [See attached image]

The odds in favor of selecting E =

= no of cases in favor of E / no of cases against E

= 12 / ( 100 - 12)

= 6 / 82

= 0.0731707317

[tex]\approx[/tex] 0.073

Given the above,

The odds against selecting E = 82/6

= 13.6666666667

[tex]\approx[/tex] 13.667

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Answer:

Below in bold.

Step-by-step explanation:

< 1 = 122 degrees     (alternate angles)

< 2 = 180 - 122

     = 58 degrees        (adjacent angles)

The graph of the linear function y = 2/3x + 1 is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For this problem, the function is given as follows:

y = 2/3x + 1.

From this, we have that:

From the slope, when x changes by 3, y changes by 2, hence:

Thus the linear function also passes through point (3,3), and it's graph is sketched at the end of the answer.

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Table b. doesn't show y as a function of x as is has to two x values for a same y value '100'.

A function, as used in mathematics, is an expression that depicts the relationship between an independent variable (input) and a dependent variable (output), where only one output is possible for each input. In daily life and many professions, functions are useful.

For instance, assuming a constant stride length, a person's distance traveled in an hour is dependent on the number of steps taken. The same individual can extend their walking distance by merely changing the number of steps taken.

Similar to this, the quantity of goods sold may affect the amount of profit a bakery makes. The bakery will generate more revenue by offering more items. The function form of both of these examples is writable. In mathematics, function notation is used to express functions. Such as, f(x) = 3x+ 2

The meaning of y as a function of x is x is y is directly varied with x  that is  y = ax + b, so for every different x there is a unique y too,

But in Table b. there are two y whose values are 100 but the x are different

which is not possible.

Therefore, Table b. doesn't show y as a function of x as is has to two x values for a same y value '100'.

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Given:

Surfacea area of cylinder is 82π square meter.

The objective is to find the new surfacea area if dimensions are tripled.

Consider the radius of cylinder as r, height of the cylinder as h.

The formula to find the surfacea area is,

It is given that the dimensions are tripled. Then, the formula will become.

Now, substitute the given value of surface area in the above equation.

Thus, the new surfacea area is 738π square meter.

Hence, option (C) is the correct answer.

The probability of selecting a three both times is 0.2

Probability:

Probability is a measure of the likelihood of an event to occur.

Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes / Total Number of outcomes

Given,

you randomly select an integer from 0 to 9 (inclusively) and then randomly select an integer from 0 to 4 (inclusively).

Here we need to find the  probability of selecting a three both times.

Here we need to find the individual probabilities for both,

So, the probability of getting 3 in 0 - 9 is

=> 1/10

And the probability of getting 3 in 0 -4  is

=> 1/5

So, in both times

=> (1/10)/(1/5)

=> 1/10 x 5

=> 0.2

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The number of hits the baseball player should expect is 14 hits

A proportion an be defined as a mathematical comparison of two numbers.

The numbers mostly represent a comparison between events, people, elements or things.

It is also described as an equation having two ratios that are set equal to each other.

The arithmetic operations involved in proportion includes;

From the information given, we have that;

If 7 hits is equivalent = 8 times

Then x hits is equivalent = 16

cross multiply

8x = 112

Make 'x' the subject of formula by dividing both sides by 8

x = 112/8

x = 14 hits

Hence, the number is 14 hits

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After a certain time of n hours, the number of bacteria inside the lab will be, 300 ( 1 + 1/5n ) ^ n.

This is a problem with compound interest calculation. Here we have to calculate the number of bacteria present at the center of disease control and prevention after a certain time of n hours.

We can solve this using a few steps.

Let's assume that,

As we all know the formula for compound interest is,

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

Where,

A = final amount

P = initial principal number =  300 bacteria

r = growth rate = 20% = 20/100

n = number of times growth applied per period

t = number of periods elapsed = 1 hour

So,

A = 300 ( 1 + 20/ 100n ) ^ n = 300 ( 1 + 1/5n ) ^ n

Hence we can conclude that after n hours the number of bacteria inside the lab will be, 300 ( 1 + 1/5n ) ^ n.

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Correct question :

A researcher at the center for disease control and prevention is studying the growth of a certain bacteria he starts his experiment with 300 bacteria that grow at a rate of 20% per hour. After n hours, what will be the number?

If the pattern (see attachment) below was tripled, the ratio of black squares to gray squares would be equal to 1:2.

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented by the following equation:

y = kx

Where:

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

For this exercise, the ratio of black square to gray squares is given by:

B:G = 1:2

Tripling the pattern, we would multiply by three (3) as follows:

B:G = [1:2] × 3

B:G = 3:6

Dividing all through by 3, we have:

B:G = [3:6]/3

B:G = 3/3 : 6/3

B:G = 1:2.

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Answer:

second and fourth are correct

Step-by-step explanation:

remembering the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m +n)}[/tex]

then

- 7x²(4x³ + 2) = - 28[tex]x^{5}[/tex] - 14x² ≠ - 28[tex]x^{6}[/tex] - 14x²

- 2b³(6b² + 5) = - 12[tex]b^{5}[/tex] - 10b³ ← correct

- 3[tex]y^{4}[/tex] (5y² + 2) = - 15[tex]y^{6}[/tex] - 3[tex]y^{4}[/tex] ≠ - 15[tex]y^{8}[/tex] - 6[tex]y^{4}[/tex]

- 5d³ (3d² + 4) = - 15[tex]d^{5}[/tex] - 20d³ ← correct

As x approach to +∞ function y approaches -∞

And as x approach to -∞ function y approaches -∞

A coordinate plane is a two-dimensional surface created when two number lines are combined. When a horizontal line crosses the origin, which is the location where the X and Y axes meet, it is generated. A coordinate grid's integers are used to locate points. A coordinate plane can be used to graph points, lines, and a variety of other objects. It functions as a map and offers straightforward directions between two sites.

F(x)=[tex]x^{2} +2x^{2} -4x^{2}[/tex]

F(x)=-[tex]x^{2}[/tex]

if x =0 then y = 0

if x = 1 then y = -1

End behavior

As x approach to +∞ function y approaches -∞

And as x approach to -∞ function y approaches -∞

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Answer:

36000 inches

Step-by-step explanation:

the equivalent ratios will be 1 : 2 and 4 : 8.

We are given that:

Colton mowed 3 lawns in 6 hours.

We are also given the table:

Lawns   Hours

____         2

    3            6

    4         ____

We need to fill the table with the equivalent ratios.

We get the ratio between lawns: hours as = 3 : 6

= 1 : 2

So, for 2 hours, it will be 1 lawn

and for 4 lawns, it will be:

= 4 : 8

So, we get the table as:

Lawns   Hours

    1            2

   3            6

   4            8

Therefore, we get that, the equivalent ratios will be 1 : 2 and 4 : 8.

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The rational roots of the equation is x=0, x=-1.

What is a rational number?

A rational number in mathematics is one that can be stated as the quotient or fraction p/q of two numbers, p and q, with p being the numerator and q being the denominator. For instance, every integer and 3/7 are rational numbers. Boldface Q is typically used to represent the set of all rational numbers, commonly known as "the rationals," the field of rationals, or the field of rational numbers.

The rational roots of the equation is x=0, x=-1.

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ANSWER:

C.

STEP-BY-STEP EXPLANATION:

We have that the population is the following:

A group of individuals under consideration is known as polulation.

The sample would be a subset of the population.

From the information provided, we have that the weights of the golden retrevier dogs are normally distributed. This means that the study population follows a normal distribution.

Therefore, if the original population has a normal distribution, the sample means will also be normally distributed regardless of the sample size.

Therefore, the correct option is C.

A path bounds a circular lawn at a park. if the inner edge of the path is 132 ft. around, Approximate the amount of area of the lawn inside a circular path​ ?

CIRCULAR LAWN

Inner edge Perimeter = 132 feet

2 x pi x r = 132

2 x 22/ 7 x r = 132

r = 132 / ( 2 x 22/ 7 )

r = 132 x 7 / 44

r = 924 / 24

r

we know that

the coordinates of point A are (0,1) and point C(3,3)

Applying the formula to calculate the distance between two points

therefore

Using equation, the number of children and adult tickets sold are 33 and 78 respectively

111 people attend the concert and tickets for adults cost $3.5 while tickets for children cost $2.25 and total receipts for the concert was $347.25.

Therefore, the number of ticket sold for adult and children can be calculated as follows :

let

x = number of children ticket sold

y = number of adult tickets sold.

Therefore, the equation that represent the situation is as follows:

2.25x + 3.5y = 347.25

x  + y = 111

multiply equation(ii) by 3.5

2.25x + 3.5y = 347.25

3.5x + 3.5y = 388.5

subtract equation(i) from equation(ii)

1.25x = 41.25

divide both sides by 1.25

x = 41.25 / 1.25

x = 33

Hence,

y = 111 - 33

y = 78

Therefore,

number of children ticket = 33

number of adult ticket = 78

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After evaluating the limit we have came to find that the limit of    [tex]\lim_{x\rightarrow \infty }-\frac{3x^4}{3x^2\ +4}[/tex] as x approaches ∞ is -∞

A limit in mathematics is the value that a function, sequence, or index approaches as an input, or that an index approaches as an index. Limits are required in the definitions of continuity, derivatives, and integrals, which are basic to calculus and mathematical analysis.

The concept of a sequence limit is further generalised to encompass the concept of a topological network limit, as well as being strongly related to the concepts of limit and direct limit in category theory.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow \infty }-\frac{3x^4}{3x^2\ +4}[/tex]

⇒ [tex]\lim_{x\rightarrow \infty }\frac{-12x^3}{6x + 0}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{-12x^3}{6x }[/tex]

Evalúe ∞ as x

⇒ [tex]\frac{-12(\infty)^3}{6(\infty)} }[/tex]

⇒ -2 × ∞

⇒ -∞

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The simplified expression of (4²) x (4³) is 4⁵

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(4²) x (4³)

The base of the above expression are the same

i.e. Base = 4

This means that we can apply the law of indices

When the law of indices is applied, we have the following equation:

(4²) x (4³) = 4²+³

Evaluate the sum in the above equation

So, we have

(4²) x (4³) = 4⁵

Hence, the simplified expression of the expression given as (4²) x (4³) is 4⁵

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Possible question

Simplify the expression.

(4²) x (4³)