What is the slope formate!

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

B. negative

Step-by-step explanation:

it is on the negative side of the graph

Answer:

C.

Step-by-step explanation:

its c, undefined. remember that zero will be horizontal and undefined will be vertical like in this picture. hope this helped

\(\boxed{\sf ab+ac=a(b+c)}\)

\(\\ \rm\longmapsto (8\times 5)+(8\times 2)\)

\(\\ \rm\longmapsto 8(5+2)\)

\(\\ \rm\longmapsto 8(7)\)

\(\\ \rm\longmapsto 56\)

Given that

We have to find the inverse of a function and the function is

Explanation -

The steps to find the solution are -

(1). First, we will consider the function equal to y as

(2). Now from this, we will find the value of x in terms of y.

And we will take the base of the log as 2 because the x is in the power of 2. As an exponential function.

As

(3). Now from eq (i) we have

(4). At last, we will replace y with x. Then,

Final answer -

Answer:

0.859493

0.859

Hope This Helps!!!

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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If y and x vary directly, the value of y=2.6 then value of x is 1.14.

The tenths place is represented by the initial digit following the decimal. The hundredths place is denoted by the digit that followed the decimal. Up until there are no additional digits, the remaining ones keep the place values filled in the quantity.

For example, 2.84620364 can be round to two decimal places as 2.85, and 0.8035 can be round to two decimal places as 0.80.

Here x and y vary directly,

So , x/y = k

Therefore K is constant

For x = 3.2 and y = 1.4

Then x/y = k

3.2/1.4 = k

K = 1.6/0.7

If y = 2.6 what is x

y = 2.6 and k = 1.6/0.7

2.6/x = 1.6/0.7

1.6x = 18.2

X = 1.1375.

Hence, the Round to two decimal places of x is 1.14

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Answer

sum of all 3 digit even number = 247050

The series is 100 + 102 + 104 + .... + 998

which by using formula Sn = N/2 ( a + an)

where N = number of terms

a = first term = 100

an = last term = 998

Answer:

20\(c^{6}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × \(c^{(3+3)}\)

= 20\(c^{6}\)

Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

An equivalent ratio to the tape diagram shown is 1 to 2

From the tape diagram, we have:

Red = 2

Blue = 4

Express as a ratio

Red : Blue = 2 : 4

Divide by 2

Red : Blue = 1 : 2

Hence, an equivalent ratio to the tape diagram shown is 1 to 2

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Answer:

Yes

Step-by-step explanation:

Answer:

6 eggs and 2 cups of oil

Step-by-step explanation:

Answer:

if she wants to double the recipe multiply the ingredients by 2, making it 2 servings. so 6 eggs and 2 cups oil should make double the original recipe. hope this helps

Answer:

Angles in a triangle sum to 180.

So

x= 180 - 75 - 43

x=62°

Answer:

x=62°

Step-by-step explanation:

x= 180 - 75 - 43

Answer:

Step-by-step explanation:

Hello!

There are some values missing, so I'll find the probability distribution using others as example. Afterwards you can calculate the ones corresponding to this exercise following the same steps.

Considering there are 5000 undergraduates registered in the college.

465 are taking one course

658 are taking two courses

566 are taking three courses

1877 are taking four courses

1344 are taking five courses

90 are taking six courses

First you have to define the variable of interest. To identify it you have to ask yourself the following question: what is the characteristic of this population that is being measured?

The answer is "the number of courses an undergraduate is taking" and this will be the study variable X

X can take values from 1 to 6 courses.

To calculate the probability of each value of X, you have to divide the "number of students taking Xi courses" by "total number of students registered in the college"

For

X=1

P(1)= 465/5000= 0.093

X=2

P(2)= 658/5000= 0.1316

X=3

P(3)= 566/5000= 0.1132

X=4

P(4)= 1877/5000= 0.3754

X=5

P(5)= 1344/5000= 0.2688

X=6

P(6)= 90/5000= 0.018

For this to be a probability distribution the following condition should be met:

F(X)= ∑P(X) = 1

In this example: 0.093 + 0.1316 + 0.1132 + 0.3754 + 0.2688 + 0.018 = 1

I hope this helps!

Answer:

The question is not complete

area of circle:

π * radius²

π * 2²

4π in²

area of rectangle:

length * width

20 * 4

80 in²

total area:

4π in² + 80 in²

93 in²

area of triangular prism:

( base length * perpendicular height * length ) ÷ 2

( 12.6 * 1.6 * 10.75 ) ÷ 2

216.72 ÷ 2

108.36 mm³

Answer:

$840.77

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Answer will be D hope this helps ya :)

The function representing the number of bacteria present each day is

\(\rm f(t) = 2032(0.85)^{t}\) .

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

The set X is called the domain of the function and the set Y is called the codomain of the function

A bacteria population starts at 2032 and decrease by 15% everyday.

a function representing the number of bacteria present each day

\(\rm f(t) = 2032(1-.15)^{t}\)

\(\rm f(t) = 2032(0.85)^{t}\)

Therefore \(\rm f(t) = 2032(0.85)^{t}\) is the correct answer .

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The difference between 126 1/4 and 78 7/12 is 143/3 or 47 2/3.

To find the difference between the numbers simplify means;

to subtract 78 7/12 from 126 1/4 .

126 1/4 - 78 7/12

First, convert the mixed fractions into improper fractions.

( 126 × 4 + 1 )/4 - ( 78 × 12 + 7) /12

505/4 - 943/12

Multiply first term by 3/3 which is the same as 1.

( 505/4 × 3/3 ) - 943/12

1515/12 - 943/12

( 1515 - 943) / 12

572 / 12

143/3 or 47 2/3.

Therefore, the difference is 143/3 or 47 2/3.

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Answer:

C.

Step-by-step explanation:

So we have the equation:

\(y=\sqrt{x-3}\)

This is a square root equation.

For square root equations, the radicand(s) must be positive.

Therefore, to find the domain, set the radicand to be greater than or equal to 0:

\(x-3\geq 0\)

Solve for x. Add 3 to both sides:

\(x\geq 3\)

Therefore, our domain must be greater than or equal to 3.

In set notation, this is:

\(\{x:x\geq 3\}\)

Therefore, our answer is C.

All we need to do is solve for the 0 of the function.

Solution:

0 = √x-3

0^2 = x - 3

0 = x - 3

3 = x

The domain is greater than or equal to 3 and this can be written as x ≥ 3 or in other words, Option 3.

Best of Luck!

Answer:

1.56 seconds

Step-by-step explanation:

Once we make the product we get:

in this expression the constant term is 4, therefore the expression has one constant term.

The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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The most common bottom numbers are "4, 8, and 16". A further explanation is provided below.

The bottom numeral indicates the type of remark to measure. That seems to be, if whether measures should be counted as quarterly notes, 8th or 16th notes.

As nothing more than a result, the only quantities you'll see as the bottom amount relate to note value systems:

You could keep going with 32 or 64, although presumably, you won't have to because it becomes a little cumbersome after a time.

Thus the aforementioned response is appropriate.

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Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Answer:

A

Step-by-step explanation:

There is an x in all for terms that means that x = 0 is one of the factors and H is incorrect.

One of the remaining factors is x^2 - 9 which factors into (x - 3)(x + 3)

You are told that x = 1  is a zero which means x - 1 is a factor.

The answer is g(x) = x (x - 3)(x + 3) (x - 1) which is A

Answer:

No

Step-by-step explanation:

the graph fails the vertical line test