Find the common difference of the arithmetic sequence -13, -22, -31,.

Function A has a rate of change of 5 & function B has a rate of change of -4.5. so, function A has a greater rate of change.

What is the rate of change?

The rate at which a variable changes over a given time period. It is frequently used when discussing momentum, and it can be expressed as a ratio of a change in one variable to a corresponding change in another. This ratio is represented graphically by the slope of a line.

For the first function, we can use the equation of the slope

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

take any two points,

m = (25-15)/5.5-3.5 = 10/2 = 5

The general equation of a straight line is;

y = mx + c

where m is the slope

Therefore, in the case of the second equation, -4.5 is the slope

Hence, function A has a rate of change of 5 & function B has a rate of change of -4.5. so, function A has a greater rate of change.

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After evaluating the integral is [tex]69x^{6}/2 + 23x^{3} +C[/tex].

Given:

(3x3+1)69x2 dx

= 69[tex]x^{2}[/tex]*3[tex]x^{3}[/tex] + [tex]69x^{2}[/tex]

= 207[tex]x^{5}[/tex] + [tex]69x^{2}[/tex]

apply integration

= ∫ 207[tex]x^{5}[/tex] + [tex]69x^{2}[/tex]

= 207∫[tex]x^{5}[/tex] + 69∫[tex]x^{2}[/tex]

= 207*[tex]x^{6} /6[/tex] + 69*[tex]x^{3} /3[/tex]

= 69[tex]x^{6} /2[/tex] + [tex]23x^{3}[/tex] + C

Therefore After evaluating the integral is [tex]69x^{6}/2 + 23x^{3} +C[/tex].

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The state income tax that should be paid by Emmet Michael's is $1,336.50.

Given,

In the question:

Emmet Michael's gross pay is $31,700.

He takes a single exemption of $2,000.

and, His state income tax rate is 4. 5%.

To find the how much will he pay in state income tax?

Now, According to the question;

The calculation of the state income tax paid by Emmet Michael is as follows:

= (Gross pay - exemption amount) × income tax rate

= ($31,700 - $2,000) × 4.5%

= $29,700 × 4.5%

= $1,336.50

Hence, we can conclude that the state income tax that should be paid by Emmet Michael's is $1,336.50.

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The required ratio for the burger is 3:6:9 and the ratio for the hot dog is 5:10:15.

Let the missing ratio in Burger be x and the ratio in the Hot dogs be y,

Now,

According to the question,

3 / 5 = x / 10

x = 6

Now,

x / 10 = 9  / y

Substitute the value of x,

6 / 10 = 9 / y

y = 90 / 6

y = 15

Thus, the required ratio for the burger is 3;6:9 and the ratio for the hot dog is 5:10:15.

In mathematics, a ratio suggests how commonly one variety consists of another. for example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to 6 (this is, eight:6, that's equal to the ratio four:3). similarly, the ratio of lemons to oranges is 6: 8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7).

The numbers in a ratio may be quantities of any kind, consisting of counts of human beings or items, or which include measurements of lengths, weights, time, and many others. In maximum contexts, each number is constrained to be advantageous.

A ratio may be specified either by way of giving each constituting number, written as "a to b" or "a: b", or through giving simply the price of their quotient a/b. identical quotients correspond to the same ratios.

Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number inside the numerator and the second one in the denominator, or as the price denoted by using this fraction. Ratios of counts, given via (non-zero) herbal numbers, are rational numbers, and might occasionally be natural numbers. while portions are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of quantities that are measured with distinct devices is referred to as a rate.

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Answer: -14

Step-by-step explanation:

Answer:

x+y=73, 1.5x+2y=1−8

lazyuser30

Area of the triangle in R² using determinant for the given vertices (-4, -4) , (0,-2) and (-2,4) is equal to 14 square units.

As given in the question,

Vertices of the triangle are given by:

( x₁ , y₁ ) = (-4,-4)

(x₂ , y₂) = (0, -2)

( x₃ , y₃) = (-2, 4)

Area of triangle using determinant is given by

= [tex]\frac{1}{2} \left|\begin{array}{ccc}-4&-4&1\\0&-2&1\\-2&4&1\end{array}\right|[/tex]

= (1/2) [-4(-2 -4) + 4(0+2) +1(0-4)]

=(1/2) ( 24 + 8 - 4)

= (1/2) ( 28)

= 14

Therefore, area of the triangle in R² using determinant for the given vertices (-4, -4) , (0,-2) and (-2,4) is equal to 14 square units.

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Answer:

point C

Step-by-step explanation:

The mathematical expression is 3/5b -7 = a.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

7 less than three fifths of b is a

So, the mathematical expression for the above statement is

(3/5)b - 7 = a

3b - 35 = 5a

3b- 5a= 35

Hence, the mathematical expression is 3/5b -7 = a.

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The number remaining for 19.35 to get to 25 is 5.65.

Expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both

In this case, the number remaining for 19.35 to get to 25 will be:

= New number - Old number

= 25 - 19.35

= 5.65

The number is 5.65.

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Answer:

a if both are right triangle

Step-by-step explanation:

if both are right triangles is the correct answer. Three sides and three angles together create a triangle. Here, Ryan and Kathy drew triangles with the same angle. We can say that two triangles are similarly based on certain rules.Ma

Answer:

x+a= b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these can/may vary.

Step-by-step explanation:

x+a= b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these can/may vary.

Answer: 3 is less than 7, the absolute value of 3 is less than the absolute value of 7

Step-by-step explanation: Absolute value is how far a number is from 0. the best way to show absolute value is to test how far away the number is from 0 by using a number line. For example, the absolute value of -9 would be 9, or the absolute value of 5 would be 5. Absolute value is the amount of distance between the number and 0.

Hope this helps!

The equation represents the price of a pumpkin is p = 5 + 0.35x

The cost of each pumpkin = $5.00

The cost of the pumpkin per pound = $0.35

Consider the price of the pumpkin = p

Consider the number of pounds = x

The equation is the mathematical statement that shows the relationship between two expression with an equal sign. In equation the inequality will not be a part. The expression is the combination of two expression and an equal sign

Then the equation will be

p = 5  + 0.35x

Hence, the equation represents the price of a pumpkin is p = 5 + 0.35x

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Answer: Yes

Step-by-step explanation:

Add all of their best times.

11.9 + 12.6 + 12.52 + 11.95 = 48.97

48.97 < 49.6

Answer:

6:8:10, 9:12:15

Answer:

HL

Step-by-step explanation:

Since the two triangles are right triangles and have 2 sets of congruent sides, you can use the HL congruence theorem to prove that they are congruent.

**HL only works with right triangles

Answer:

a. parallel    b. neither      c. neither      d. perpendicular

Step-by-step explanation:

Find the gradient of the line in the graph

Choose 2 coordinates, I choose (0,1) and (3,3)

Use the formula

(y2 - y1)/(x2 - x1)

(3 - 1) / (3 - 0)

2/3

Gradient of a parallel line is the same

Gradient of a perpendicular line formula m1m2 = -1

(2/3)m2 = -1

m2 = -3/2

The gradient of the perpendicular line will be -3/2

The gradient of the parallel line will be 2/3

Any other gradient will be neither parallel nor perpendicular.

The probability that the person is over 40 years of age is 32/51 or 62.75%.

(the table is attached as image)

We know that,

The ratio of the size of the event space to the size of the sample space is the probability of an event.

The total number of possible outcomes is the size of the sample space.

The number of outcomes in the event you are interested in is called the event space.

Using the formula,

P = size of the event space/size of the sample space

⇒The probability that the person is older than 40,

sample size=255

size of the event space=85

P=85/255------> P=1/3

⇒the probability that the person drinks root beer,

sample size=255

size of the event space=75

P=75/255------> P=5/17

⇒the probability that the person is older than 40 of age or that they drink root beer,

P=(1/3)+(5/17)-----> P=(17*1+3*5)/51------> P=32/51-----> 0.6275----> 62.75%

therefore,

the answer is

32/51 or 62.75%

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(complete question)

if one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.

Answer:

Set the two functions equal to each other to find the point where they intersect:

[tex]x+2=2x+1\\\\x-2x=1-2\\\\-x=-1\\\\x=1[/tex]

Plug the x-value in to find the corresponding y-value. It should be the same for both functions:

[tex]y=x+2=1+2=3\\\\y=2x+1=2(1)+1=2+1=3[/tex]

So, they intersect on (1, 3), as shown on the graph below.

The domain and range of the relation shown in the table include the following: A. domain:{−3, −1, 2, 4}, range:{0, 2, 4}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined.

This ultimately implies that, a domain is the set of all possible input values (x-values) to a relation, and the domain of a graph comprises all the input values which are located on the x-coordinate from the least to the greatest.

Additionally, a range is the set of all real numbers that is associated with the elements of a domain i.e all of the y-values shown on the y-coordinate of the graph of a relation, from the least to the greatest.

By critically observing the table of this relation shown, we can reasonably infer and logically deduce the following:

Domain = {−3, −1, 2, 4}.

Range = {0, 2, 4}.

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Answer:

las fórmulas de 3 dividir por r te va a dar igual a 1.862

Answer: i think this is the same thing https://brainly.com/question/28965695?referrer=searchResults

if it is then theres ur answer

Step-by-step explanation:

The comparison of the linear functions to line A are given as follows:

A linear function is defined as follows:

y = mx + b.

In which the coefficients are listed as follows:

The slope determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, the function is:

y = 4x - 6.

Hence the slope is of:

m = 4.

Then the functions, relative to y = 4x - 6, are classified as follows:

The problem gives three lines with different slopes, and you have to define if they are parallel, perpendicular or neither parallel nor perpendicular.

The intercepts are not relevant and I couldn't find the problem on the internet, hence I say that they are constants.

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Using the Sample size formula , the sample manufactuer of paints observations or sample size is 22 ton .

Sample size: It is defined as the number of participants or total observations in a study of sample.

we have provided that,

standard deviations of sample (σ)= 3 tons

mean of sample ( X) = 70 tons

confidence level = 98% = 0.98

Margin of error (M.E) = 1 ton

Using the sample size formula,

n = z²(σ)(1-σ) /( M.E)²[1+σ (1-σ)z²/(M.E)²X]

where, X---> population size

s.d --> standard deviations

M.E ---> margin of error

Z-value for confidence level

so, z-value corresponding to 98% of confidence level is 2.32 ..

putting all the values in above formula we get, n = (2.32)²(2)3/(1)²(1+ (2.32)²(6)70×1)

=> n= 32.29/(1+(0.46))= 32.29/ 0.46

= 22.1 ~ 22

Hence, sample size is 22 ton .

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The amount of water that Neil uses is 7.22 gallons

From the information, Melissa uses 3/5 as much water as Neil to water her plants and Melissa uses 4 and 1/3 gallons of water.

Let Neil be illustrated as x

Therefore, 3/5 × x = 4 1/3

0.6x = 4 1/3

0.6x = 4.33

Divide

x = 4.33 / 0.6

x = 7.22 gallons

Neil used 7.22 gallons.

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The distance from an angle of depression to the boat at 21° to angle of depression of 50° is 112 feet

Information from the question

A boat is heading towards a lighthouse, where Yaritza is watching from a vertical distance of 139 feet

Yaritza measures an angle of depression to the boat at point AA to be 21°

Yaritza takes another measurement and finds the angle of depression to the boat (now at point BB) to be 50°

the distance from point AA to point BB = ?

The direction of movements describes a right triangle of

opposite =  ?

adjacent = 139 feet

The distance is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

for x = 21 point AA is solved

tan 21 = ? / 139

? = 139 * tan 21

? = 53.357

for x = 50 point BB is solved

? = 139 * tan 50

? = 165.654

the distance from point AA to point BB

= 165.654 - 53.357

= 112.297

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Answer:

You will have 4 dollars left

Step-by-step explanation:

Assuming from the question, you start with 10 dollars. You lose 75 cents for each games. If you play 8 games, you multiply 0.75 by 8 to get 6. Then you subtract 6 from 10 to get your remaining money, which is 4 dollars