The mean of Fred’s grades on five tests was 75.2. The grades on the first 4 of these tests were 87, 84, 88, and 45. Find the grade on his fifth test.

Let's call the speed of the river "r". The speed of the current in the downstream direction is 9 + r mph, and the speed of the current in the upstream direction is 9 - r mph. The time it takes to travel downstream and return upstream is the same, so we can set up the following equation:

(32 miles) / (9 + r mph) + (32 miles) / (9 - r mph) = 9 hours

We can simplify this equation by converting hours to minutes and miles to feet, and then simplify further by multiplying both sides of the equation by the denominators:

32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 9 * 60 * (9 + r) * (9 - r)

Expanding the right side of the equation and simplifying:

32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 810 * (9 + r) * (9 - r)

Expanding the left side of the equation and simplifying:

32 * 60 * 9 + 32 * 60 * r + 32 * 60 * 9 - 32 * 60 * r = 810 * (9 + r) * (9 - r)

Combining like terms and solving for r:

32 * 60 * 9 * 2 = 810 * (9 + r) * (9 - r)

96720 = 810 * (9 + r) * (9 - r)

Dividing both sides by 810:

119 = (9 + r) * (9 - r)

Expanding the right side of the equation:

119 = 81 - r^2

Adding r^2 to both sides of the equation:

119 + r^2 = 81

Subtracting 81 from both sides of the equation:

38 + r^2 = 0

Taking the square root of both sides of the equation:

r = ± sqrt(38)

Since r is the speed of the current, it must be a positive value, so we take the positive square root:

r = sqrt(38) mph

The speed of the river (current speed) is approximately 6.17 mph.

To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

For more such question on coins

https://brainly.in/question/26939811

#SPJ8

The measure of the exterior angle is 139 degrees.

The sum of the interior angle of a triangle is 180 degree.

The sum of angles on a straight line is 180 degrees.

From the diagram;

First, we determine the third interior angle of the triangle.

Angle 1 + Angle 2 + Angle 3 = 180

64 + 75 + Angle 3 = 180

139 + Angle 3 = 180

Angle 3 = 180 - 139

Angle 3 = 41 degrees

Now, angle 3 and the exterior angle forms a angle on a straight line.

Hence;

Angle 3 + Exterior angle = 180

41 +  Exterior angle = 180

Exterior angle = 180 - 41

Exterior angle = 139 degrees.

Therefore, 139 degrees is the exterior angle.

Learn more about triangles here: https://brainly.com/question/27490624

#SPJ1

Answer:

x = 11.5

Step-by-step explanation:

using the sine ratio in the right triangle

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{23}\) ( multiply both sides by 23 )

23 × sin30° = x , then

x = 11.5

Answer:

I personally would use cm (centimeters)

Step-by-step explanation:

Meters is pretty long (kilometers being even longer) and millimeters is pretty small. Centimeters is a good medium distance, about 1/3 of an inch

Hope this helps, good luck and have a nice day :D

Answer:

Step-by-step explanation:

$314.50

Answeri

dont

Step-by-step explanation:

i dont becaus i work

Me! I love playing games they are just so fun

Explanation

Step 1

apply common factor

Step 2

divide both sides by (2+6z)

I hope this helps you

The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

The system of equations is given as

2x - y + 2z = -6

-3y + z = -2

2x - 3z = -4

Subtract 2x - 3z = -4 from 2x - y + 2z = -6

This is represented as

(2x - y + 2z = -6) - (2x - 3z = -4)

This gives

- y + 5z = -2

Multiply - y + 5z = -2 by 3

-3y + 15z = -6

Subtract -3y + 15z = -6 from -3y + z = -2

This is represented as

(-3y + z = -2) - (-3y + 15z = -6)

This gives

-14z = 4

Divide by -14

z = -2/7

Substitute z = -2/7 in - y + 5z = -2

- y - 5 * 2/7 = -2

This gives

- y - 10/7 = -2

Rewrite as:

y = 2 - 10/7

Evaluate

y = 4/7

Substitute z = -2/7 in 2x - 3z = -4

2x - 3 * 4/7 = -4

This gives

2x - 12/7 = -4

So, we have:

2x = 12/7 - 4

Evaluate

2x = -16/7

Divide by 2

x = -8/7

Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

Answer:

B

Step-by-step explanation:

Answer:

B. relative minimum

Step-by-step explanation:

This is because a relative minimum is a point where decreasing turns to increasing, but an ABSOLUTE minimum is a point where the line cannot go any lower, whatsoever.

Answer:

a = 38⁰

b = 54⁰

c = 54⁰

Step-by-step explanation:

a + 142⁰ = 180⁰ because a straight line = 180⁰

b + 38⁰ + 88⁰ = 180⁰ because the angles of a triangle equal 180⁰, and the missing measurement = 38⁰ because it is a vertical angle to angle a

c + 88⁰ = 142⁰ because the angles are corresponding angles

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

6561/256

Step-by-step explanation:

You can notice that each term is equal to the previous term multiplied by 3/2. This means that it is a geometric series. The formula to find the nth term is as follows:

\(a_{n}= a_{1} *(r)^{n-1}\)

The first term, a1, is 1 and r, the common ratio is 3/2 because that is what you are multiplying by. We can also substitute in n as 9 because we are looking for the ninth term:

\(a_{9} = 1 *(\frac{3}{2} )^{9-1}\\\\a_{9} = (\frac{3}{2})^{8}\\\\a_{9} =\frac{3^8}{2^8} \\\\a_{9} =\frac{6561}{256}\)

Answer:

4xy ×3xy -2xy

12xy-2xy

10xy

Hello!

4 + (6/10) + (7/100)

= 4 + 0.6 + 0.07

= 4.67

Answer:

2,240

Step-by-step explanation:

13*12=156

156*5=280

280*8=2,240

If my math is correct

Answer:

a) area = side²

225 in² = side²

side = √225 = 15 inches

b) 15 inches per side x 4 sides x $1.35 per inch = $81.00

Step-by-step explanation:

The equation of the line with a slope of 2/3 passing through (-4, 1) is y = (2/3)x + 11/3

An equation is an expression relating two or more numbers and variables.

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The equation of a line passing through (x₁, y₁) with a slope of m is given by:

y - y₁ = m(x - x₁)

The line has a slope of 2/3 and pass through point (-4, 1). Hence:

y - 1 = (2/3)(x - (-4))

y - 1 = (2/3)(x + 4)

y = (2/3)x + 11/3

The equation of the line is y = (2/3)x + 11/3

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

y = sec(x) has a range of f(x) ≤ -1 and f(x) ≥ 1

Thus does not include zero in the range scale.

Extra's:

y = cos(x) has a range of -1 ≤ f(x) ≤ 1

y = cot(x) has infinity range

y = tan(x) has infinity range.

Answer:

sec x

Step-by-step explanation:

Let's set each function equal to zero to see if they have zero in their function.

If there is no solution, then we no solution of zero.

\( \cos(x) = 0\)

\(x = \frac{\pi}{2} + 2\pi(n)\)

So there is a solution of zero.

\( \cot(x) = 0\)

\( \frac{ \cos(x) }{ \sin(x) } = 0\)

There answer here is

\(x = \frac{\pi}{2} + 2\pi(n)\)

So there is a solution. of zero here

If cot x=0, has a solution of zero, then tan x does as well. Since we can use

\( \frac{ \sin(x) }{ \cos(x) } = \tan(x) \)

\( \frac{ \sin(x) }{ \cos(x) } = 0\)

The answer here will be

\(0 + 2\pi(n)\)

So that leaves sec x.

Proof:

\( \sec(x) = \frac{1}{ \cos(x) } \)

1 divided by any number won't equal zero, so the solution will never be 0.

Answer: 132.5 or 85 degree

Step-by-step explanation:

Answer:

55

Explanation, when 2 angles are bisected, they are even

(Angle DBF is 35 degrees with that logic)

All triangles add up to 180 degrees

(Angle is 55 degrees because of that)

I might be incorrect, but I think its 55

The probability that the sum of the pips selected that is at least 11 would be = 1/12.

To determine the probability of the selected events, the formula for problem should be used which is given below;

Probability = possible outcome/sample space

Possible outcome = at least 11 = (5,6),(6,5),(6,6)

= 3

Sample space = 36

Probability = 3/36 = 1/12

Learn more about probability here:

https://brainly.com/question/31123570

#SPJ1

The length of the other two sides are 4m and 5m

Using the Pythagorean theorem, we have that the square of the hypotenuse sides is equal to the sum of the squares of the other two sides of the triangle

This is represented as;

x² = y² + z²

From the information given, we have that;

z = 3m

x = x + 1

y = x

Substitute the values, we get

(x + 1)² = x² + 3²

Find the squares

(x + 1) ² = 9 + x²

expand the bracket

(x + 1) ( x + 1) - x² = 9

x² + x + x + 1 - x² = 9

collect like terms

2x = 8

x = 4

Then,

x + 1 = 5

x = 4

Hence, the values are 4m and 5m

Learn about triangles on:

https://brainly.com/question/14285697

#SPJ1

The expression that is equal to the given Polynomial expression is (x^3-4)(2x+5).

The polynomial expression given is 2x^4+5x^3-8x-20. We have to identify the expression that is equal to this given polynomial expression.

We will factor the given polynomial expression to determine the equivalent expression. We can use factorization by grouping to factor the expression completely and determine the equivalent expression .

Factorization by grouping:

We can group the first two terms 2x^4 and 5x^3 together and factor out x^3 from them. We can also group the last two terms -8x and -20 together and factor out -4 from them.

This gives us;2x^4+5x^3-8x-20= x^3(2x+5)-4(2x+5) =(x^3-4)(2x+5)

Therefore, the expression that is equal to the given polynomial expression is (x^3-4)(2x+5).

For more questions on Polynomial .

https://brainly.com/question/4142886

#SPJ8

Answer:

1.having less value.EXAMPLE: 4 is less than 12

2.having greater value.EXAMPLE: 6 is greater than five

3.having the same or less value.EXAMPLE: 13 is less than or equal to 13

4.having the same or greater value.EXAMPLE: 14 is greater than or equal to 7

Step-by-step explanation:

Answer:

M = the mean/slope b = y intercept hope this helps :)

Step-by-step explanation:

Answer:

A change from 45 to 60 represents a positive change (increase) of 33.3333333333%

Step-by-step explanation:

Percent change = 60 - 45

45

× 100 = 33.333333333333 % (increase)

Answer:

33.3% increase

Step-by-step explanation:

Percent of Change =

\( \frac{change}{original} \)

The change would be 15:

60 - 45 = 15

So the percent of change would be:

15/45 = 1/3 = 33.3% increase

Hope this helps! Brainliest would be appreciated!

Answer:

The 2nd answer

Step-by-step explanation:

because the light figure had more mature in the materials