A group of 25 employees want to go out for a group dinner.
18 employees want to go to Restaurant A.
7 employees want to go to Restaurant B.

The statement (c) describes that the graph of f is shifted 5 units down to create the graph of g. The solution has been obtained using the concept of vertical translation.

What is translation?

Translation is the act of moving a shape or a figure from one position to another. It is classified into two types:

Now, for a function f(x) we define a vertical translation of N units as:

g(x) = f(x) + N

If N is positive, the translation is upwards.

if N is negative, the translation is downwards.

We are given g(x) = f(x) - 5

This shows that N is negative and therefore, there is translation of 5 units downwards.

Hence, the graph of f is shifted 5 units down to create

the graph of g.

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Answer:

multiple everything by three so say 3×-9x is -27x and 3 ×8 is 24 and you would then divide -27x by 24 and you would get -27x+24 I think

The total flops as a function of the number of equations n for the LU decomposition version of Gauss elimination is given by (n^3 + 3n^2)/3.

The LU decomposition version of Gauss elimination involves 3 phases which are :

The flops in decomposition phase is (n^3)/3, forward-substitution phase is n^2 and back-substitution phase is 2n^2. By adding all the flops for these 3 disinct phases we get (n^3 + 3n^2)/3 as total flops as a function of the number of equations n for the LU decomposition version of Gauss elimination.

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Step-by-step explanation:

x = my number

3(x + 21)

multiply sum of 21 and my number by 3

=

(2/3)x + 84

84 more than 2/3 of my number

3(x + 21) = (2/3)x + 84

9(x + 21) = 2x + 3×84 = 2x + 252

9x + 189 = 2x + 252

7x + 189 = 252

7x = 63

x = 9

my number is 9.

we determined median = 140 and lower quartile = 105.

Median is the middle value of a set of data. Median is determined by the formula, median = 2/4 (N+1)th term, where N is the number of data set.

Quartile is a statistics terms defines that a list of data is divided into four parts. There are three quartiles in the statistics data such as lower quartile, middle quartile and upper quartile.

lower quartile = 1/4(N+1)th term

upper quartile = 3/4(N+1)th term

the median is called the middle quartile.

From the histogram we obtain the data below

80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200

number of data, N = 13

median = 2/4 (N+1)th term= 1/2 ×14 = 7th term

we find 7th term is 140.

median = 140

lower quartile= 1/4× (N+1)th = 1/4 × 14 = 3.5 th term

that means average of 3 and 4th term.

lower quartile = (100 + 110) /2 = 105

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Jim spent a total of $125.15 for the 130 miles he traveled in one day at the $14.95 base fee.

A mathematical equation is a formula that connects two statements using the equal sign (=) to signify equivalence. A mathematical statement demonstrating the equality of two mathematical expressions is the definition of an equation in algebra. For instance, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematically, the connection between two phrases on either side of a letter is stated. The symbol doubles as the sole variable most of the time. for illustration, 2x - 4 = 2.

given

per mile the cost is $0.85

Base fee is 14.95

0.85x+14.95= 125.15

0.85x=125.15 - 14.95

0.85x = 110 . 92

x= 110 . 92 / 0.85

x= 130. 49

Jim spent a total of $125.15 for the 130 miles he traveled in one day at the $14.95 base fee.

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     (x-2)² + ( y + 1)² = 34 is the equation of the circle in standard form.

What is the short definition of a circle?

To put it simply, a circle is a spherical shape without any edges or line segments. In terms of geometry, it has the shape of a closed curve.

                                             The circle's points are set apart from the center by a predetermined amount.

The endpoints of the diameter (7,−4) and (−3,2)

the center of the circle is the midpoint of the diameter.

So, the coordinates of the center  

                      (h,k) = ( 7 + (-3)/2  , -4 +2/2)

                                = ( 4/2 , -1 )

                                 = ( 2 , -1 )

the radius of the circle is just half of the length of the diameter.

So,                 r = 1/2√(-3 -7 )² + ( 2 - (-4))²

                        = 1/2√(10)²  + ( 2 +4 )²

                        = 1/2√100 + 36

                        = 1/2√136

                         = √136/2

                        = 2√34/2

                         = √34

substitute the values of h, k, and r into the standard equation of the circle

                       ( x-h)² + ( y-k)² = r²

                      ( x - 2)² + ( y -(-1))² = (√34)²

                       (x-2)² + ( y + 1)² = 34

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14) Probability that exactly 5 of the students will graduate is 0.1636.

15) Probability that atleast 8 of the students will graduate is 0.2405.

We have , In a college,

The freshmen graduate enters = 64%

Probability of sucess , p = 64% = 0.64

Probability of failure , q = 1 - 0.64 = 0.36

Randomly selected entering = 10 , i.e, n = 10.

This follows a Binomial probability distribution with the parameters, n = 10 and p = 0.64.

Using Binomial probability formula,

P(X = x) = ⁿCₖ pᵏ (1 - p)ⁿ⁻ᵏ

(14) Probability that exactly 5 of the students will graduate = P(x = 5),

P( x = 5) = ¹⁰C ₅ (0.64⁵) (0.36⁵)

= 0.1636

15) Probability that at least 8 of the students will graduate, P(x ≥8) = P(X= 8) + P(X= 9) + P(X= 10)

= ¹⁰C₈ 0.64⁸ 0.36² + ¹⁰C₉ 0.64⁹ 0.36¹ + ¹⁰C₁₀ 0.64¹⁰ 0.36⁰ = 0.2405

Hence, the required probabilities are 0.1636 and 0.2405.

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The correct option is:

d) Median is a better measure of central tendency

When a graph of a distribution of data is symmetric, it means that the left and right sides of the graph are mirror images of each other. This indicates that the data is evenly distributed around the center and that there are no extreme outliers. In such cases, the median is the best measure of central tendency, because it is the middle value of the dataset and it represents the center of the data distribution. The median is not affected by outliers.

The mean, mode, and midrange are also measures of central tendency, but they may not be as representative of the center of the data distribution when the data is symmetric. The mean is sensitive to outliers, the mode is the value that appears most frequently in the data, and the midrange is the average of the maximum and minimum values.

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The vertices of the image after transformation is K(5,-2), L(-1,3) and M(4,-5)

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

According to the given question,

with respect to the mirror

the vertices of the image of the triangle is

J (2,-5) ---------->! (5,2)

K (-1, -3) --------> K'(-1,3 )

L (-4, 5) --------->"(4,-5 )

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In  linear equation, Length of each piece of fabric is 3/2  yards.

What in mathematics is a 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.

Number of pieces of fabric = 3

Total length of a fabric  = 2 1/4 yards

                                     = 9/4 yards

Therefore,

Length of each piece of fabric = 9/4 ÷ 3

                                             = 3/4 yards

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Answer:

≈[tex]4.4117647059\times10^{10}[/tex] computations in five minutes.

Step-by-step explanation:

[tex]\frac{5*60}{6.8\cdot10^{-9}}[/tex] = [tex]4.4117647059\times10^{10}[/tex].

Proof in the image.

Please mark brainliest so I can get to the expert rank (only 10 to go!)

Answer:

30%

Step-by-step explanation:

3 pizzas = 30 slices.  count yellow 1+6+2 = 9

9/30 = 30%

16 is the number  gives a result of −4 when 8 is subtracted from the quotient of the number and 4.

A division is a process of splitting a specific amount into equal parts.

If it gives a result of -4 then our equation will have ___ = -4

If we subtract 8 from the quotient of a number and 4 we have  x/4 - 8

Our equation is:

x/4 - 8 = -4    

Add 8 to both sides

x/4=-4+8

x/4=4

Multiply both sides by 4

x=16.

Hence, 16 is the number  gives a result of −4 when 8 is subtracted from the quotient of the number and 4.

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Answer:16.98$

Step-by-step explanation:

A pound of roast beef costs 8.49

2 pounds of roast cost?

2x8.49=16.98

Answer:

Step-by-step explanation:

9 7/12 - 5 4/12 = 4 3/12

The algebraic expression 15(2 + r) by the distributive property can be written as 30 + 15r.

This property states that multiplying the sum of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the algebraic expression is 15(2 + r). The expression by using the distributive property can be written as:-

E = 15(2 + r)

E = 30 + 15r

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Answer:

d

Step-by-step explanation:

Answer:

The answer is 20

Answer: 254 in^2

Step-by-step explanation:

A term that means the same as the term "variable" in an ANOVA procedure is a factor.

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.

Let us consider the number 8. 8 can be a product of 1 and 8, and 2 and 4. As a result, the factors of 8 are 1, 2, 4, and 8. Therefore, when finding or solving problems involving factors, only positive numbers, whole numbers, and non-fractional numbers are considered.

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Answer:

m∠1 = 64

m∠2 = 117

m∠3 = 117

Step-by-step explanation:

m∠1 = 64

m∠2 = x+64 = 180

        = x = 117

m∠2 = 117

m∠3 = 117

Answer:

I think A is the answer.

U're welcome amigo.

3.76 many times large is 7.9 x 10⁴ than 2.1 x 10³. This can be solved using scientific notation method.

A method of writing numbers that combines a power of 10 with a number between 1 and 10. Using scientific notation, one may express extremely big or extremely small values. Once a number between 1 and 10 has been multiplied by such a power of 10, it is then expressed in scientific notation. For instance, 6.9 × 10⁸ can be used to represent the number 690,000,000.

The main goal of scientific notation is to simplify computations using numbers that are abnormally big or tiny. When a number is written in scientific notation, all of the digits are important since zeros are no longer utilized to set the decimal point.

For: 7.9 x 10⁴

= (79/10) x 10⁴

= 79 x 10³

on the other hand for: 2.1 x 10³

Thus, 3.76 many times large is 7.9 x 10⁴ than 2.1 x 10³.

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Answer: In an experiment, if the probability that event A occurs is 0.2 and the probability that event B occurs is 0.5, then the probability that either event A or event B (or both) will occur is the sum of their individual probabilities, which is 0.2 + 0.5 = 0.7.

It should be noted that the sum of the individual probabilities of two events is less than or equal to 1. If the sum of the probabilities is greater than 1, it means that the events are not mutually exclusive and that means that they can happen at the same time.

It's important to mention that the above answer is based on the assumption that events A and B are mutually exclusive events, which means that they cannot happen at the same time. If they are not mutually exclusive, the probability of both occurring at the same time would have to be calculated using the formula P(A and B) = P(A) * P(B|A) where P(A) is the probability of event A occurring and P(B|A) is the probability of event B occurring given that event A has already occurred.

Step-by-step explanation:

The value of the evaluated iterated integral is = 0.002

As per the given data the iterated integral is, [tex]I[/tex] = [tex]\int\limits^1_0[/tex] [tex]\int\limits^s_0[/tex] cos ([tex]s^{6}[/tex] ) [tex]dt ds[/tex]

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as,

[tex]\int\limits^a_b f({x} )\, dx[/tex] = f(b) - f(a)

Where,

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, [tex]\int\limits^_[/tex] ab f(x) dx is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]I[/tex] = [tex]\int\limits^1_0[/tex] [tex]\int\limits^s_0[/tex] cos ([tex]s^{6}[/tex] ) [tex]dt ds[/tex]

Integrate the given iterated integral.

We get:

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) ([tex]\int\limits^5_0dt[/tex] ) ds

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) [t][tex]0 to s^{5}[/tex] ds

= [tex]\int\limits^1_0[/tex] cos ([tex]s^{6}[/tex] ) [tex](s^{5} -0)[/tex] ds

= [tex]\int\limits^1_0[/tex] [tex]s^{5}[/tex]cos ([tex]s^{6}[/tex] )ds

Then,

[tex]s^{6}[/tex] = t       when s = 0

[tex]\frac{dt}{ds}[/tex] = 6[tex]s^{5}[/tex]         t = 0  

[tex]\frac{dt}{6}[/tex] = [tex]s^{5}[/tex]  ds      when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

[tex]I[/tex] = [tex]\int\limits^1_0[/tex] cos(t) [tex]\frac{dt}{6}[/tex]

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [tex]\int\limits^1_0[/tex] cos(t) dt

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [sin(t)][tex]0to1[/tex]

[tex]I[/tex] = [tex]\frac{1}{6}[/tex] [ sin(1) - sin(0) ]

[tex]I[/tex] = [tex]\frac{sin(1)}{6}[/tex]

[tex]I[/tex] = 0.002

Therefore,

The value of the evaluated iterated integral is = 0.002

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Answer:

-87

Step-by-step explanation:

y=2

3y(2-7)-3(y-4)-63 
3(2)(2-7)-3(2-4)-63 

6(2-7)-3(2-4)-63

6(-5)-3(-2)-63

-30+6-63=-87

Note that where the following values are given: 0, 3, 4, 6, 9, 10, 11, 12, 16, the respective quartile values are:

The minimum = 0

The first quartile (Q₁) is = 3.5

The median (Q₂) = 9

The third quartile (Q₃) = 11.5

The maximum = 16

The IQR = 8 .

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory.

It is to be noted that sometimes referred to as "the middle" value in data collection.

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Answer:

(x+2)(4x-1)

For this problem, use the FOIL (first, outside, inside, last) method

You have x, 2, 4x, and -1. Start by multiplying x by 4x and -1. Then multiply 2 by 4x and -1. You should have four separate values to add together.

(x*4x)+(x*(-1))+(2*4x)+(2*(-1)) = 4x^2+(-x)+8x+(-2)

Once you have this, order each value by their exponents and combine like terms. The highest exponents always go to the left and lowest exponents go to the right.

4x^2+7x-2