For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables).If it does, find the constant of variation and write it in simplest form.3r - 81 = -7O Direct variation ( K =__)O Not direct variation10y = -5xO Direct variation ( K =__)O Not direct variation-Picture included-

The next two terms in the sequence,  -13, 8, -5, 3,-2 is 1 and -1.

The mathematical operations that would be used to determine the next two terms are addition and subtraction. Addition is used to determine the sum of two or more numbers. Subtraction is used to determine the difference between two or more numbers.

The first step is to determine the relationship between the numbers in the sequence. Looking at the numbers, it can be seen that the the difference between the first number and the second number gives the third number.

-13 + 8 = -5

-5 + 3 = -2

3 - 2 = 1

-2 + 1 = -1

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Answer:

A is 729,2187,6561 and it would be geometric

B is 46,55,64 and is arithmetic

C is 32,36,40 and is arithmetic

If the probability of being dealt this type of hand is 7654/133,784,560. the probability of not being dealt this type of hand is:  0.999944..

Probability of complement of the event A =P (Ac) = 1- P(A)

A = event of the particular type of hand

Probability of A :

P(A) = n (A) / n(S)

P(A) = 7480 / 133,784,560​

Ac = event of not being dealt of this type of hand

Probability of Ac:

P (Ac) = 1- P(A)

P (Ac) = 1- 7480 / 133,784,560​

P (Ac) = 133, 777,080 / 133,784,560

P (Ac) = 0.999944

Therefore the probability of not being dealt this type of hand is 0.999944.

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The complete question is :

In 7 card poker,played with a standard 52 card deck 52C7 or 133,784,560 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 133,784,560. The probability of being dealt this type of hand is 7654/133,784,560. Find the probability of not being dealt this type of hand.

The value of x in the equation x⁵ + 64x² = 0 is x = 0 or  x = -8 after taking common.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the polynomial equation is:

x⁵ + 64x² = 0

x²(x³ + 64) = 0

x² = 0    or  x³ + 64 = 0

x = 0   or    x³ = -64

x = 0 or    x = -8

Thus, the value of x in the equation x⁵ + 64x² = 0 is x = 0 or  x = -8 after taking common.

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in this case we have that it is growth formula, so we have that r= 0.05 and a =5500. Therefore the formula is

we only need to replace t by 20 and calculate

so after 20 years we hace $14593.13 in our bank account

The amount of direct materials cost in the unfinished job would be $97600.

The price of direct materials is directly related to the unit of production and is immediately identifiable. For instance, the price of glass is a direct material expense in the production of light bulbs. The primary component needed for the production of commodities or products was material. Costs of raw materials or components used directly in the production of goods are referred to as direct material costs. For instance, if Company A manufactures toys, the cost of the plastic used to build the toys would be an example of a direct material cost.

Given Data

Work in Process inventory account was credited for $120,500.

charged with $9,600 of applied overhead cost.

Direct material cost = Work in progress - Overhead cost - Direct labor

Direct labor = 9600 ×[tex]\frac{100}{75}[/tex]

Direct labor = 12800

Direct material cost =  120000 - 9600-12800

Direct material cost = 97600

The amount of direct materials cost in the unfinished job would be $97600.

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The total finance charge on the computer purchased on finance by Gary is $58.00

What is finance charge?

The finance charge on the computer purchase is the excess of the total payments over the principal of the loan, where the principal is the purchase price of $1,250 minus the down payment of $150

principal=purchase price-down payment

principal=$1,250-$150

principal=$1,100

total payments=monthly payment*number of months in 2 years

total payments=$48.25

total payments=$48.25*24

total payments=$1,158.00

total finance charge=total payments-principal

total finance charge=$1,158.00-$1,100.00

total finance charge=$58.00

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Answer:

Proportion: 22.80/2=x/3

x= 34.20

Step-by-step explanation:

First find what the value of one scarf is:

22.80/2=11.40

Then multiple by 3 to get $34.20

Answer:

Proportion : 1 scarf = $11.40

Cost of 3 scarves = $34.20

Step-by-step explanation:

GIVEN: 2 SCARVES = 22.80

LET X = # OF SCARVES

2X=22.80

X=$11.40

$11.40(3) = cost of 3 scarves

$34.20 = cost of 3 scarves

Answer:

Explanation:

A die has 6 faces numbered 1 to 6.

The sample space when a die is rolled is:

Thus, the number of odd number outcomes when a die is rolled is:

Answer:

-4

Step-by-step explanation:

Given:

To Find:

Concept used:

For the given equation, we have

a = 3, b = -12 and c = 108

So, Slope of line perpendicular to given line = -12/3 = -4

So, the slope of required line is -4.

The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

3x - 12y = - 108

Convert the equation into a slope intercept, then we have

3x - 12y = - 108

12y = 3x + 108

y = (1/4)x + 9

The product of the slopes of the perpendicular line will be a negative one. Then we have

(1/4)m = -1

m = - 4

The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.

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NSWER

EXPLANATION

In a isometry the distances between points are conserved, so the image of segment PQ has to have the same length as segment PQ.

When we have a translation defined by a vector the x-coordinate of the vector tells the horizontal translation and the y-coordinate the vertical translation.

For this problem, if the vector is <3, 5>, we have to translate each point 3 units to the right and 5 units up.

The endpoints of the image segment are Q'(1, 3) and P'(-1, 1)

====================================================

Work Shown:

(2.50 dollars)/(8 juice boxes) = (x dollars)/(24 juice boxes)

2.50/8 = x/24

2.50*24 = 8x

60 = 8x

8x = 60

x = 60/8

x = 7.50

----------------

Another approach:

She paid $2.50 for 8 juice boxes. The unit price is 2.50/8 = 0.3125 dollars per juice box. Multiply this by 24 to get 24*0.3125 = 7.50

----------------

Yet another method:

We know the cost for 8 juice boxes is $2.50

We want to know the cost for 24 juice boxes.

The jump from 8 to 24 is "times 3". So we'll multiply the $2.50 cost by 3 to get 3*2.50 = 7.50

We can think of it like this

[tex]\frac{2.50 \ \text{dollars}}{8 \ \text{juice boxes}}=\frac{3*2.50 \ \text{dollars}}{3*8 \ \text{juice boxes}}=\frac{7.50 \ \text{dollars}}{24 \ \text{juice boxes}}[/tex]

The 2000th digit after the decimal point is 5. See the explanation below.

First, we divide the fraction to get the decimal number.

2/13 = 0.15384615384

Paying close attention, you'd notice that after the 6th number forms the decimal point, the number forms a loop that repeats again. That is:

0.153846 153846 154...

Hence, to detect the 2000th number,

we divide 2000/6

we are left with 2

(that is 333 x 6 = 1998)

Hence we count two from the decimal and that gives us the 2000th digit.

That is: 5

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Full Question:

[tex]When $\dfrac{2}{13}$ is written as a decimal, what is the $2000^\text{th}$ digit after the decimal point?[/tex]

Solution:

Given that a sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at shore for awhile, then returns to the open sea.

This implies that that:

On solving the equation z-a = z/b if b≠1   , for z we get z=ab/(b-1)    .

in the question ,

the equation is given as

z-a = z/b

adding "a" to both the sides

we get

z-a+a = z/b + a

z = z/b + a

subtracting z/b from both the sides , we get

z - z/b [tex]=[/tex] z/b - z/b + a

z - z/b = a

taking z common

z(1-1/b) = a

taking LCM as b and solving further , we get

z (b-1)/b = a

on cross multiplication we get

z = ab/(b-1)

Therefore , on solving the equation z-a = z/b if b≠1   , for z we get z = ab/(b-1)  .

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Given:

Number of appetizers offered = 8

Number of appetizers customer is to select = 6

Number of main courses offered = 9

Number of main courses customer is to select = 6

Number of desserts offered = 3

Number of desserts the customer is to select = 2

Let's determine how many ways this can be done.

This is a combination problem.

To determine the number of ways this can be selected, apply the combination formula below:

Thus, we have:

Solving further, let's apply the formula and combine:

Solving further:

herefore, there are

The given polynomial is:

Substitute x = -2/5 into the expression:

Therefore by the remainder theorem x = -2/5 is a root.

Hence, the factor is

5x + 2

A

Answer:

A

Step-by-step explanation:

[tex]{ \tt{ {30x}^{3} - {13x}^{2} - 40x - 12}}[/tex]

- For a value to be a factor of a function, the function range must be zero if the factor is substituted into it.

Testing with 5x+2

[tex]{ \tt{5x + 2 = 0}} \\ { \tt{x = - \frac{2}{5} }}[/tex]

Therefore;

[tex]{ \tt{ = 30( - \frac{2}{5}) {}^{3} - 13( - \frac{2}{5} ) {}^{2} - 40( - \frac{2}{5}) - 12 }} \\ \\ = { \tt{0}}[/tex]

hence 5x + 2 is a factor

Given

mean = 185 mg/dL

standard deviation = 29

Required: The percent of adults that have cholesterol levels over 190 mg/dL

Step 1: Find the z-score for the given cholesterol level using the formula:

Substituting the given values:

Step 2: Using a normal distribution table, find the probability of a random value greater than 0.1724

Step 3: Convert to percent by multiplying by 100%

Hence, the percent of adults that should have a cholesterol level greater than 190 mg/dL is 43,2%

It should be emphasized that a connection is proportional if its graph is a line that passes through its origin.

If the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to achieve this, the ratio is not proportional.

The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.

If the graph of a connection is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional.

Additionally, if anything is not linear, it is not proportional.

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When there are 3 women to to 5 men and there is a total of 224 people, the number of men will be 140 men.

From the information, it was stated that there are 3 women to to 5 men and a total of 224 people.

Therefore, it should be noted that the fraction for men that illustrates the information will be:

= 5/(3 + 5) × 224

= 5/8 × 224

= 5 × 28

= 140

Therefore, the number of men is 140 men.

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The radius of the cylindrical bucket which contains 314 cubic inches of water and 4 inch height of water is 5 inches.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

To determine the radius r, plug the given values into the volume formula above and solve r.

V = π × r² × h

314 in³ = 3.14 × r² × 4

314 in³ = r² × 12.56 in

Divide both sides by 12.56 in

r² = 314 in³ / 12.56 in

r² = 25 in²

Take the square root of both sides

r = √( 25 in² )

Radius r = 5 in

Therefore, the radius r of the cylindrical bucket is 5 inches.

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NSWER

140 Ffeet

EXPLANATION

istance is an absolute value wquantity, so it is expressed either as a positive value or an absolute value of a negative number.

Explanation

We are given the following equation:

We are required to determine the solution of the given equation.

This is achieved thus:

The only solution to this equation involves complex numbers. So, there is no real solution.

Hence, the answer is:

Question 1Step 1: Problem

Step 2: Concept

Factor the highest common factor out.

Step 3: Method

Step 4: Final answer

4mn(2n + 3)

Question 2

Step 1: Question

Step 2: Concept

Apply laws of exponent

Step 3: Method

Step 4: Final answer

Option D is the correct answer

ANSWER

Infinitely many solutions (0 = 0)

EXPLANATION

We have the two equations and we are to solve them simultaneously.

We have:

y = 5x + 2 ___(1)

10y - 50x = 20 ___(2)

Put (1) in (2):

We have that:

10(5x + 2) - 50x = 20

50x + 20 - 50x = 20

=> 50x - 50x = 20 - 20

=> 0 = 0

This kind of solution implies that there are infinitely many solutions to this equation.

Answer:

213

Step-by-step explanation:

First we decide how many ounces 12 has in 32 (2.6)

Then we multiply 2.6 to 80 calories and get 213 calories

Brian likes the feeling of owning his own car. He takes good care of it and doesn't like changing cars often is whom a car loan would be a better option than a car lease and is denoted as option B.

This is referred to as the total money borrowed which is used in the purchase of a car while on the other hand car lease involves the vehicle being made available to be driven for  certain period of time or limit.

Since Brian likes the feeling of owning his own car and doesn't change cars often, then the car loan is best for him as it becomes his after the money or amount to be repaid is completed.

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