graph g(t) = 4 sin t +2

2x-3y=6

You have to pass the y term to the other side of the equation

2x=6+3y

Then divide by 2 to get the expression for x

RANGE

The range of a given data is the difference between the largest and smallest numbers.

Steps for solving range:

Step 1: Arrange the data values in ascending order

Step 2: Identify the largest and smallest numbers

Step 3: Calculate the difference between the numbers.

The range is 70.

MIDRANGE

The midrange of a given set of data is the average of the largest and smallest number.

Steps for solving midrange:

Step 1: Arrange the data values in ascending order

Step 2: Identify the largest and smallest numbers

Step 3: Calculate the average of the numbers.

The midrange is 35.

ANSWER:

The correct option is OPTION B.

The speed of the car associated with a braking distance of 12 feet is approximately equal to 14.697 miles per hour.

In this problem we find a radical equation that describes the speed (s), in miles per hour, and the braking distance (d), in miles. If we know that d = 12 ft, then the initial speed of the car is:

s = √(18 · d)

s = √[18 · (12)]

s = 6√6 ft

s ≈ 14.697 mi / h

The initial speed of the car is approximately 14.697 miles per hour.

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The semicircle's arc measures five units. In order to get 15.7 units, we could also multiply 5 by 3.14.

a symmetrical, curved structure that spans an aperture and often bears the weight of a wall, roof, or bridge.

A semicircle is the circumference or half of a circle.

The circle's radius is r=d+h=s22h+h2. The length of the entire arc is equal to the angle of the half-arc, which is equal to arc sin(s/r) or, alternatively, arctan(s/d). Multiply this angle (in radians! ), by 2r.

The half of a circle is called a semicircle.

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The recursive formula of the arithmetic sequence is

Where d is the common difference between each 2 consecutive terms

The explicit form of the arithmetic sequence is

a is the first term

d is the common difference

Since the given explicit form of the sequence is

Then

a = 13

d = 6

The recursive form of the sequence should be

The missing number is 6

The answer is D

The linear equation with a slope of -5 and that passese through (-1, -6) is:

y = -5*x - 11

A general linear equation is of the form:

y = a*x +b

Where a is the slope and b is the y-intercept, here we know taht the slope is -5, then:

y = -5*x + b

Now we also know that the line passes through (-1, -6), then we can replace that to get:

-6 = -5*-1 + b

-6 = 5 + b

-6 - 5 = b

-11 = b

Then the linear equation is:

y = -5*x - 11

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In this case, x represents the amount that has increased year after year.

The monetary value of an asset or service is the amount that would be paid in cash if it were sold to a third party. Tangible property, intangible property, labor, and commodities, for example, are priced at their monetary value.

Given,

Belinda wishes to invest $1,000. The table below shows the value of her investment for three different years under two different scenarios:

The number of years is 1 2 3

Option 1 (dollar amount) 1100 1200 1300

Option 2 (dollar amount) 1100 1210 1331

Part A: Using options 1 and 2, linear and exponential functions can be used to describe the value of an investment after a set number of years.

In the case of Option 1, the linear function can be used to describe the investment's value after a set number of years. This is due to the fact that in Option One, the amount increases by a fixed amount each year.

In the case of option 2, the exponential function can be used to calculate the value of the investment after a specified number of years. This is because the amount increase in Option 2 is greater than last year.

Part B: (n=n+100) and (n=n+100x) are functions for each option that describe the monetary value of the investment f(n) after n years.

Option 1's function is n = n + 100.

Option 2's function is n = n + 100 x.

In this case, x represents the amount that has increased year after year.

Part C: Yes, the value of Belinda's investment after 20 years will differ by 1900 if she chooses Option 2 over Option 1.

After 20 years, the option 1 amount would be 3000, and the option 2 amount would be 4900. As a result, there is a difference of 1900.

The complete question is:

Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:

Number of years 1 2 3

Option 1 (amount in dollars) 1100 1200 1300

Option 2 (amount in dollars) 1100 1210 1331

Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)

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Part a: The correct solution was found by Justin as b = -1.

Part b: The mistake made by the Christian was taking negative value as positive.

For the following question,

The solution found by Justin is b = 1.

The solution found by Christian is b = -1.

The equation is given as;

10(1 + 3b) = -20

To find the solution, use distributive property.

10×1 + 10×3b = -20

30b = - 20 - 10

30b = -30

b = -1

Part a: The correct solution was found by Justin as b = -1.

Part b: The mistake made by the Christian can be that he did not consider the right hand value as negative and put it as positive value.

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Given:

1) The equation is,

To solve this equation,

using synthetic division,

Now solving further,

Hence, the solution of given equation is,

2) the equation is,

Now, factor the equation,

Hence, the solution of above equation is x= -2/9 , i , -i.

The binary connective of implication ⇒ is defined as (A ⇒ B) ⇔ ((¬ A) ∨ B). It can be read « A implies B », « A is a sufficient condition for B », or « B is a necessary condition for A ».

What is connective?

Connective is function, or the symbol representing a function, which corresponds to English conjunctions such as "and," "or," "not," etc. that takes one or more truth values as input and returns a single truth value as output.

What is logical connective?

A Logical Connective is a symbol which is used to connect two or more propositional or predicate logics in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.

Generally there are five connectives which are −

OR (∨)

AND (∧)

Negation/ NOT (¬)

Implication / if-then (→)

If and only if (⇔).

connective of implication ⇒ is defined as (A ⇒ B) ⇔ ((¬ A) ∨ B).

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Answer:

students that are in middle school

Step-by-step explanation:

i took the test and got it correct.

The category with the greatest marginal frequency is students who chose playing sports. The correct option is C.

There are 16 students who chose playing sports in middle school and 11 students who chose playing sports in high school, for a total of 27 students who chose playing sports. This is the greatest marginal frequency of all the categories.

The marginal frequency for high school students who chose playing sports is 11.

The marginal frequency for middle school students who chose watching movies/TV is 21.

The marginal frequency for students who chose playing sports is 27.

The marginal frequency for students that are in middle school is 21.

Therefore, the answer is (C) Students who chose playing sports.

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10 m

Explanation:

Data:

Second side : x

Third side : four times the second side : 4*x

The other side : 5 m longer than the second side : 5 + x

Perimeter of the triangle : 65 m

Formula:

Perimeter of a triangle = one side + second side + third side

Solution:

65 = 5 + x + x + 4 * x

65 = 5 + 6 * x

65 - 5 = 5 + 6 * x - 5

60 = 6 * x

60 / 6 = 6 * x / 6

10 = x

Answer: $25.44

Step-by-step explanation:

Multiply 24 by 0.06.

You get 1.44

Add 1.44 + 24 = 25.44

In a case whereby Sarah used 3.5 cups of cheese in a dish that serves 10 people the constant of proportionality that  relates the number of servings to cups of cheese is  0.35.

We were told that Sarah used 3.5 cups of cheese with 10 people, this can be written as :

let the c= the cups of cheese which is 3.5 cups of cheese

let n = number of the people that is been served

Then the equation can be written as :

c∝n

then we can bring in the proportionality constant sign as ;

then c=kn

then we can introduce the given figures into the equation as ;

3.5=k *10

the we can determine the value of the constant as :

k=3.5/10 = 0.35

Therefore, option A is correct.

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Answer:

Any answer greater than 10 seems to work.

Step-by-step explanation:

This question is not that specific, but 5*2 is 10, so anything more than 10 would be more than double the quantity.

The inequality is c-7≥-30. The c value we get has inequality c≥-23.

Given that,

The inequality is c-7≥-30.

We have to solve the inequality c.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. When two values are not equal, we typically use the "not equal symbol (≠)". However, a number of inequalities are used to compare the numbers and determine whether one is greater than the other.

When the symbols  “>”, “<”, “≥”, “≤” are used to connect two real numbers or algebraic expressions, the relationship is referred to as an inequality.

Take the inequality,

c-7≥-30

c≥-30+7

c≥-23

Therefore, The c value we get has c≥-23.

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As given by the question

There are given that the graph of line.

Now,

For find the slope, first select point from the graph of line.

So,

The point is:

Then,

From the formula of slope:

Then,

Hence, the slope of the line is 1.

We need to know about percentage to solve the given problem. The amount of money that Kelly has in dollars is approximately $24.

Percentage is a number or ratio expressed as a ratio or fraction of 100. If for example we have to find out one-fourth of a quantity then we can say that we need to find 25% of the quantity. In the given question we know that Maria has $40 which is 170% of the money that Kelly has, we need to find out the amount of money that Kelly has.

170/100x a=40

a=40x100/170=23.5

Therefore the amount that Kelly has in dollars is $23.5 approximately $24.

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2 orders of bacon and eggs cost: 2*$3.99 = $7.98

an order of pancakes cost: $2.55

3 glasses of milk cost: 3*$0.95 = $2.85

Total bill: $7.98 + $2.55 + $2.85 = $13.38

Each person pays $13.38/3 = $4.46

The number of significant digits that the product have is 3.

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures.

Rules for determining Significant Numbers,

Given Numbers are  [tex]5.2187 * 10^{-3}, 2.05 *10^{7} and 3.40 * 10^{3}[/tex]

Now, Multiplying the given numbers,

[tex]5.2187 * 10^{-3}* 2.05 *10^{7} * 3.40 * 10^{3} =3.64 *10^{8}[/tex]

So, In 3.64 *10^8, The number of significant digits is 3.

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Answer:

answer is 3

Step-by-step explanation:

Given the equation of the function:

The graph of the function will be as shown in the following picture:

As shown in the figure:

The amplitude = 1

The period = 2π

The phase shift = π/4

We know that each pack has 6 bowls and we need 40 bowls. Let x be the number of packs, then we can write:

If we move the coefficient of x to the right hand side, we get

which gives x= 6.666.

However, the number of packs are integer numbers, so we must round up to the nearest integer. Hence, the answer is 7 packs.

Answer:

200 millimeters

Step-by-step explanation:

The radius is the distance from the center outwards.  The diameter goes straight across the circle through the center, and is therefore twice the radius.

Answer:

4

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x+7-(23)=0

Pull out like factors :

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.

                     4x - 16  =   4 • (x - 4) = 0

                      x-4 = 0

Add  4  to both sides of the equation :

therefore, x = 4

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m∠C = (16x - 7 )° because ∠A ≅ ∠C

When two angles add up to 180 degrees, they are referred to as supplementary angles because they combine to make a linear angle. The opposite is true if the total of two angles is 90 degrees; in this case, they are considered to be complementary angles and together they create a right angle.

When two angles sum up to 180 degrees, they are referred to as supplementary angles in geometry. A and B are referred to as supplementary angles, for instance, if A + B = 180°. When supplementary angles are combined, they always create a straight angle (180 degrees).

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Winning the jackpot in a certain lottery requires you to pick two correct numbers between 1 and 59, and in a separate drawing, you also have a 7.32397915e-8 chance of winning when you also pick one correct number between 1 and 30.

A number of ways to select r items from n, nCr = n!/(r! x (n - r)!)

Number of possible methods to choose 4 winning numbers from 59 = 59C4

= 59!/(55! x 4!)

= 455,126

The number of possible ways to choose a single accurate number from 30 = 30.

The odds of winning the jackpot are 1/(probability) (Number of ways in which 4 winning numbers can be selected from 59 x Number of ways in which the correct single number can be selected from 30)

= 1/(455,126 x 30)

= 1/13653780

= [tex]7.32397915^{8}[/tex]

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Answer:

10 & 12

Step-by-step explanation:

First, we set up equations:

x - y = 2

2(y) = x + 8

Then, we solve for the variable of our choice (x) in one equation:

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

Then, we substitute it for the variable (x) in the other equation:

(2y = x + 8) = (2y = (y + 2) + 8)

Then, we solve for the remaining variable (y):

(2y = (y + 2) + 8) = (2y = y + 10) = (y = 10)

Finally, we can plug the value that variable (y) into the initial equations:

(x - (10) = 2) = (x = 12)

(2(10) = x + 8) = (x = 12)

Now, we have the value of both variables:

y = 10 & x = 12

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The equation of a direct proportion is A. y=8x.

It should be noted that a direct proportion is also a direct variation. It is one when the relation between the two quantities have a value that's constant.

In this case, it's illustrated as y = 8x.

Let's say x = 1 y will be = (8 × 1) = 8

When x = 2, y = (8 × 2) = 16

In this case, it should be noted that the constant of 8 is illustrated.

In conclusion, the correct option is A.

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Answer:

See below

Step-by-step explanation:

x^2 -6x   = - 4    

     take 1/2 of the x  coefficient, square it , and add to both sides

x^2 - 6x  + 9   = -4 + 9

(x-3)^2   = 5      now sqrt both sides

x-3 =  +- √5

  x = 3 ± √5

Answer:

xπg73 xueu iwkwbsjdhhsd