your grade in a class is determined by the average of three test scores. you scored 70 and 88 on the first two tests. to earn at least 76 for this course, how much do you have to score on the third test? let x be the score you will earn on the third test.

The variable b in terms of the variables a and c is b = ac/(a - c)

From the given formula expressed as

1/a + 1/b = 1/c

We want to express variable b in terms of the variables a and c. We would make variable b the subject of the formula.

Subtracting 1/a from the left hand side of the equation and the right hand side of the equation, it becomes

1/a - 1/a + 1/b = 1/c - 1/a

1/b = 1/c - 1/a

1/b = (a - c)/ac

Taking the reciprocal of the left hand side of the equation and the right hand side of the equation, it becomes

b = ac/(a - c)

Learn more about subject of formula at: https://brainly.com/question/21140562

#SPJ1

Luke was solving the equation √(3-x) = -16. He was about to square

each side, but then he realized he could give an answer without doing any algebra, here is explanation,

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Luke realized that squaring each side of the equation √(3-x) = -16 would lead to an extraneous solution. This happens because squaring each side of the equation changes the direction of the inequality, which may result in solutions that do not actually satisfy the original equation.

The square root of any positive number is always positive, so the left side of the equation is always non-negative. However, -16 is a negative number, so there is no real solution to the equation √(3-x) = -16.

Therefore, Luke realized that he could give an answer without doing any algebra and that the equation has no real solution.

To know more about Equation check:

https://brainly.com/question/1529522

#SPJ1

Answer:

2:3:7

Step-by-step explanation:

a/b = 2/3 and b/c = 3/7

a/b/c =2/3/7

The simplification steps are as follows:

(2³)(7.2³) = 2³+3 = 128

(5³)³ = 125

(1 + 3) = 4

72² = 5184

125 - 7 = 118

So, the simplified expression is:

118 (5xy³) (5184³) 2y

Properties of rational exponents are rules that dictate how to simplify expressions with fractional exponents. Some of the key properties are:

Fractional Exponent: a^(m/n) = (a^m)^(1/n)

These properties are used to simplify expressions with rational exponents, which are exponents that are in the form of a fraction.

learn more about rational exponents: https://brainly.com/question/20726608

#SPJ1

Answer:

(x + 10)(x - 4)

Step-by-step explanation:

x² + 6x - 40

consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term.

the factors are + 10 and - 4 , since

10 × - 4 = - 40 and 10 - 4 = + 6 , then

x² + 6x - 40 = (x + 10)(x - 4) ← in factored form

Answer:

Slope: y= 4/5x+21/8

The distance is 4 units up and 5 units to the right.

Step-by-step explanation:

As ΔABC ≅ ΔDEF, Using congruence properties the value of x= 5 and the value of y= 14.

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

Given that ΔABC ≅ ΔDEF, so that

AB ≅ DE

BC ≅ EF

AC ≅ DF

and AB = 8

BC = 19

AC = 14

EF = 4x-1

DE = y-6,

As AB ≅ DE

8 = y - 6

add 6 both sides we get

y = 8 + 6

y = 14

and BC ≅ EF

19 = 4x - 1

Add 1 both sides we get

4x = 19 + 1

4x = 20

divide both sides by 4 we get

x = 20/4

x = 5

To learn more about congruent triangles visit:

brainly.com/question/20521780

#SPJ1

Answer:

Last option: Stocks which drop from 5.25 by 1.35

Step-by-step explanation:

5.25 + (- 1.35) = 5.25 - 1.35

This represents a decrease in value of stock which starts at 5.25 and drops by 1.35.

The stock value at end of day = 5.25 - 1.35 = $3,9

So, approximately 2.28% of the observations are less than 140.

To find the percentage of observations that are less than 140, we need to find the standard score (z-score) that corresponds to 140, and then use a standard normal table to find the proportion of data that is less than that z-score.

The standard score is calculated as follows:

z = (140 - 130) / 5 = 2

Using a standard normal table, we can find the proportion of data that is less than 2 standard deviations from the mean. This proportion is approximately 0.0228 or 2.28%.

Mean is nothing but the average of data.

To know more about Standard deviation:

brainly.com/question/23907081

#SPJ4

The quantity of 68% hydrochloric acid solution must be mixed are;

94 ml of 68% Acid type I

1,535.33 ml 16.00% acid type II

The quantities and percentages given are;

Acid type I 68% ---------------- x liters

Acid type II 16% ------ 1629.33 - x liters

Mixture 19% ---------------- 1629.33

Thus, by combination of the values given we have;

68% x + 16%(1629.33 - x ) = 19% * 1629.33

Multiply through by 100 to get;

68x + 16(1629.33 - x ) = 30957.27

68x + 26069.28 - 16x = 30957.27

68x - 16 x = 30957.27 - 26069.28

52x = 4,887.99

x = 4,887.99/52

x = 94 ml of 68% Acid type I

Acid type II 16% ------ 1629.33 - 94

= 1,535.33 ml 16.00% acid type II

Read more about Algebra Word Problems at; https://brainly.com/question/21405634

#SPJ1

1 furlong, a unit used in horse racing, is equal to 40 rods and 10 chains, both units used in surveying and equal to 201.168 meters (660 feet).

A furlong is a unit of length used primarily in horse racing. It is equal to 201.168 meters (660 feet). A rod is a unit of length used in surveying and is equal to 5.5 yards (16.5 feet). A chain is also a unit of length used in surveying and is equal to 66 feet.

To calculate 1 furlong in rods, we multiply 1 furlong by the conversion factor of 40 rods per furlong:

1 furlong x 40 rods/furlong

= 40 rods

To calculate 1 furlong in chains, we multiply 1 furlong by the conversion factor of 10 chains per furlong:

1 furlong x 10 chains/furlong

= 10 chains

To convert from furlongs to rods, we multiply the number of furlongs by the conversion factor of 40 rods per furlong:

4.0 furlongs x 40 rods/furlong = 160 rods

And to convert from furlongs to chains, we multiply the number of furlongs by the conversion factor of 10 chains per furlong:

4.0 furlongs x 10 chains/furlong = 40 chains

Learn more about unit of length here:

https://brainly.com/question/27351903

#SPJ4

The inequality that represents the graph is y ≤ -x - 2.

In mathematics, inequality is a declaration of an order connection between two numbers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).

In the graph, we have

1. the line is going down (negative slope) so that's why u have the negative

2. it translated 2 units Downwards on the y-axis so that's why there is - 2

3. the line is Solid so it's going to have the equal sign under it, if the line was dashed it would just be a regular sign fr example (<)

4. the shading is below the line so that means it's going to be Less than or Equal to.

Learn more about Inequality:
https://brainly.com/question/28823603
#SPJ1

Answer:

96

Step-by-step explanation:

large rectangle area = 7* (4+3+5) =7*12 =84

top & bottom 2 little triangles:

look at the bottom one:

triangle area formula = 1/2 base * height

so it's a right angle triangle, so the height is 4, base is 3

so area = 1/2 * 3* 4 =6

you have another one on the top

so 12

total = 84+12 =96

The value of exterior angle is 108°.

What are exterior angles ?
An exterior angle is an angle which is formed by one of the sides of any closed shape structure such as polygon and the extension of its adjacent side.

Given:

Interior angles : (a+10)° and 44°

Thus , we know that

Exterior angle  = sum of interior opposite angles

Therefore , Exterior angle  = (a+10)° + 44°

or

2a° = (a+10)° + 44°

or

a = 54°

Therefore , exterior angle = 2a = 2*54° = 108°

Thus , the value of exterior angle is 108°.

Learn more about exterior angle at:

https://brainly.com/question/29389110

#SPJ1

The table that represents a linear relationship that is also proportional is; Table B

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and as such it can be modeled or represented by the following mathematical expression:

y = kx

Where:

x and y represents the variables.

k represents the constant of proportionality.

For us to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) using table B as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = -2/-1 = 2 or 2/1 = 2

Constant of proportionality (k) = 2

Thus, table B is correct.

Read more about Proportional relationship at; https://brainly.com/question/12242745

#SPJ1

Answer:

the second one....

x −1 0 1

y −2 −1 0

Step-by-step explanation:

12 ounces of cherries did Ms Winn buy.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Ms. Winn bought = 3/5 lb of grapes

Ms Winn bought = 5/8 lb of cherries.

As, there are 16 ounces in a pound then

= 3 pounds/4 x 16 ounces/pound

= 3 x 4

= 12 ounces

Hence, She buy 12 ounce of cherries.

Learn more about Unit conversion here:

https://brainly.com/question/8653845

#SPJ1

2.40.π is the  expression can be used to find the circumference of the skating rink.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that a circular skating rink has a radius of 40 feet.

Radius = 40 ft.

We need to find the  expression can be used to find the circumference of the skating rink.

The formula for circumference of circle is 2πr.

Circumference=2.40.π.

Hence, 2.40.π is the  expression which can be used to find the circumference of the skating rink.

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

Answer: 2 x 40 x pie

Step-by-step explanation:

The linear function that models the giraffe's height after x months is given as follows:

y = 6 + 0.5x.

The graph is given by the image presented at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 0.5x + 6.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

If a man has a garden and he divide them equally into minimum number of square plots , then length of each square plot is 28m  .

the length of the garden is = 84m  ;

the width of garden is = 56m ;

the man is dividing the garden into equally minimum number of square plots ,

then , Factors of Width = 2×2×2×2×7 = 2×28  ;

the Factors of Length is = 2×2×2×3×7 = 3×28  ;

So , we will notice with a side of 28 m each , we can make 2 squares along the width of the garden ;

Similarly , with the side = 28m each, we can make 3 squares along the length of the garden ;

That means , we can make 6 squares of 28m side.

Therefore , the minimum length of each square plot = 28 m.

Learn more about Square here

https://brainly.com/question/20386976

#SPJ4

Here are the simplified expressions for each equation:

(x⁵) * (x⁸) * (2x³)² * (x⁻³) * (x⁵) = (x⁵) * (x⁸) * (2x⁶) * (x⁻³) * (x⁵) =

2x⁽⁵⁺⁸⁺⁶⁻³⁺⁵⁾ = 2x²¹

(y⁶) * (y⁹) = y⁽⁶⁺⁹⁾ = y¹⁵

(3x)³ = 27x³

(y⁷) * (y⁻³) = y⁽⁷⁻³⁾= y⁴

(z⁻⁸) * (z³) = z⁽⁻⁸⁺³⁾ = z⁻⁵

(x⁻²) * (x^⁻⁶) * (x⁴) = x⁽⁻²⁻⁶⁺⁴⁾ = x⁻⁴

(x¹⁵) * (x¹⁰) = x⁽¹⁵⁺¹⁰⁾ = x²⁵

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

the simplified expressions for each equation is:

a) 2x²¹            b)  y¹⁵

c) 27x³           d)  y⁴

e) z⁻⁵              f)   x⁻⁴

g)  x²⁵

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation.

Addition, subtraction, multiplication, or division are all examples of math operations. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided.

An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

Here are the simplified expressions for each equation:

(x⁵) * (x⁸) * (2x³)² * (x⁻³) * (x⁵) = (x⁵) * (x⁸) * (2x⁶) * (x⁻³) * (x⁵) =

2x⁽⁵⁺⁸⁺⁶⁻³⁺⁵⁾ = 2x²¹

(y⁶) * (y⁹) = y⁽⁶⁺⁹⁾ = y¹⁵

(3x)³ = 27x³

(y⁷) * (y⁻³) = y⁽⁷⁻³⁾= y⁴

(z⁻⁸) * (z³) = z⁽⁻⁸⁺³⁾ = z⁻⁵

(x⁻²) * (x^⁻⁶) * (x⁴) = x⁽⁻²⁻⁶⁺⁴⁾ = x⁻⁴

(x¹⁵) * (x¹⁰) = x⁽¹⁵⁺¹⁰⁾ = x²⁵

To know more about expression,

brainly.com/question/30091997

#SPJ1

Yes, his pulse rate is in the normal range for children. His pulse rate was calculated to be 120 beats per minute, which falls within the range of 60-100 beats per minute.

The student took his resting pulse rate by counting the number of beats in 20 seconds. He then multiplied his result by three to calculate his pulse rate for a minute. To determine if his pulse rate was within the normal range for children, he compared his result to the data shown in the table. His pulse rate of 120 beats per minute was within the range of 60-100 beats per minute, so it was considered to be normal for children. To ensure accuracy, the student could have taken his pulse rate for a longer period of time, such as 30 or 60 seconds, before calculating his pulse rate for a minute. This would have given him a more accurate result.

Learn more about range here

https://brainly.com/question/20259728

#SPJ4

The linear equation that represents this situation will be y = 4x + 3.

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.

To ride go-carts at Rick's Play Zone costs $4 per ride plus $3 to rent a helmet.

Let 'y' be the total cost in dollars and 'x' be the number of times you ride the go-carts. Then the equation is given as,

y = 4x + 3

The equation that represents this situation will be y = 4x + 3.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ1

Answer:

B.

Step-by-step explanation:

i think 99.9% sure!

Answer:

he representation that is most appropriate to show the relationship between the number of chapters and the total pages of a book is given by:

Graph 3

How to choose the correct graph?

Before choosing the correct graph, we must classify the function as discrete or continuous, as follows:

Discrete function: the input values of the function are only certain values on an interval.

Continuous function: the input values of the function are all the real values in the interval.

Then the graph of each type of function is given as follows:

Discrete function: dots.

Continuous function: solid line.

The input and output variables in this problem are given as follows:

Input variable: number of chapters.

Output variable: number of pages.

The number of chapters assumes only integer values, hence the function has a discrete domain, meaning that the graph is composed by dots.

However, the first graph is correct, as the third graph has a range of input and output values that is not present on the table, while the range in the first graph is according to the table.

More can be learned about discrete and continuous variables at brainly.com/question/3130222

#SPJ1

Step-by-step explanation:

Answer:

(-2,2)

Step-by-step explanation:

First, let's look at the 2 inequalities:

y ≤ -x + 1

y > x

Just by looking at the second inequality, we can remove any ordered pairs where x is greater than or equal to y. This eliminated the ordered pairs (-1,-3) and (0,-1). Now, the answer has to be (-3,5) or (-2,2). Knowing this, we can plug x and y into the equation and see if either of the answers are true.

(-3,5):

x = -3

y = 5

y ≤ -x + 1

5 ≤ -(-3) + 1

5 ≤ 3 + 1

5 ≤ 4

NOT TRUE

(-2,2)

x = -2

y = 2

2 ≤ -(-2) + 1

2 ≤ 2 + 1

2 ≤ 3

TRUE

So, since plugging in the ordered pair (-2,2) into the inequality gives us a true answer while (-3,5) doesn't, the order pair (-2,2) must be out answer.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

The correlation between the two variables in the data set for 13 colonies of sparrowhawks is 0.5602.

This means that there is a moderate positive correlation between the two variables, indicating that when one variable increases, the other variable is likely to increase as well.

To calculate the correlation coefficient, we can use Pearson’s correlation coefficient equation:

r = (n * Σxiyi - Σxi * Σyi) / √[(n * Σxi2 - (Σxi)2) * (n * Σyi2 - (Σyi)2)]

Where: n = the number of observations Σxi = the sum of all x-values Σyi = the sum of all y-values Σxiyi = the sum of the products of each x-value and y-value Σxi2 = the sum of the squares of each x-value Σyi2 = the sum of the squares of each y-value

Plugging in the values for our data set, we get:

r = (13 * 0.5602 - (13 * 0.5602)) / √[(13 * 0.2532 - (13)2) * (13 * 0.2532 - (13)2)]

r = 0.5602

This means that there is a moderate positive correlation between the two variables in the data set, indicating that when one variable increases, the other variable is likely to increase as well.

Learn more about correlation :

https://brainly.com/question/4219149

#SPJ4

Answer: I think cash and checks??

Step-by-step explanation:

Sorry if I'm wrong

Answer:

6.00

Step-by-step explanation:

4r + g = 24

4r + 2g = 30       Subtract equation 2 from equation 1

     -g = -6

so g = cost of gravity = 6 dollars

The decimal number that corresponds to the binary number 11111111 is 255.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. A decimal number is made up of two parts: a whole number and a fractional component separated by a decimal point. The decimal point is the dot between the whole number and the fractions. 25.5, for example, is a decimal number.

Here,

In binary, each digit represents a power of 2, starting with the rightmost digit. The rightmost digit in 11111111 represents 2^0, the second digit from the right represents 2^1, and so on. To convert a binary number to decimal, you add up the value of each digit times the corresponding power of 2.

For 11111111, the calculation would be:

=1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1

=255

The decimal equivalent of the binary number 11111111 is 255.

To know more about decimal number,

https://brainly.com/question/4708407

#SPJ4

Answer:

assuming that it can be solved, then yes

Step-by-step explanation: