a paddling canoeist took 2 h to travel 12 km down a river, with the current. It took 4 h to do the return trip up the river, against the current. What was the speed of the current

Answer:

[tex]\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}[/tex] [tex]=\frac{81m^{2}n^{5}}{8}[/tex]

Step-by-step explanation:

[tex]\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}[/tex]

[tex]=\frac{(3^4m^{-4}n^8)}{2^3m^{-6}n^3}[/tex]

[tex]=\frac{(3^4m^{-4+6}n^{8-3})}{2^3}[/tex]

[tex]=\frac{3^4m^{2}n^{5}}{2^3}[/tex]

[tex]=\frac{81m^{2}n^{5}}{8}[/tex]

Answer: The five exponent properties are

Product of Powers: When you are multiplying like terms with exponents, use the product of powers rule as a shortcut to finding the answer. It states that when you are multiplying two terms that have the same base, just add their exponents to find your answer.

Power to a Power.: When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. ... Then multiply the two expressions together. You get to see multiplying exponents (raising a power to a power) and adding exponents (multiplying same bases).

Quotient of Powers.:  When you are dividing like terms with exponents, use the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer. The key is to only subtract those exponents whose bases are the same.

Power of a Product: The Power of a Product rule is another way to simplify exponents. ... When you have a number or variable raised to a power, it is called the base, while the superscript number, or the number after the '^' mark, is called the exponent or power.

Power of a Quotient.: The Power of a Quotient rule is another way you can simplify an algebraic expression with exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent or power

You can use these any way you want to rewrite an equation.

Hope this helped

:D

The properties of exponents are rules to simplify expressions with powers, which include adding exponents when multiplying like bases, multiplying exponents when raising powers to powers, and subtracting exponents when dividing like bases.

The properties of exponents are mathematical rules used to rewrite expressions involving powers in simpler or alternative forms. These properties are essential for performing operations with exponents and include rules for multiplying, dividing, and raising powers to powers.

Examples of Exponent Properties

Multiplying Powers with the Same Base: 10³ × 10² = 10³+2 = 10µ.

Raising a Power to a Power: (5³)⁴ = 5³×4 = 5¹², or 5 multiplied by itself 12 times.

Negative Exponents: 2.4 x 10⁻² tells you to move the decimal point to the left twice, which equals 0.024.

Application of Exponent Properties

To apply these properties, you would systematically use the appropriate rule based on the operation you're performing. For multiplication, add the exponents when the bases are the same. For powers, multiply the exponents. For division, subtract the exponents when the bases are the same. Using these rules simplifies complex expressions and makes it easier to work with exponents in algebra and science.

Answer:

see here our answer is 60 degrees now how I will tell u see u know the sum of triangle that is 180 degrees now add up. y +y + 60 = 180 and solve it u will get ur correct answer

comment if u have doubt

Answer:

60

Step-by-step explanation:

Because you would 180/3 and will get 60

Answer:

R' (-4,1)

Step-by-step explanation:

Since the current coordinates is (-1, -4) and when rotating clock wise it would put into the second quadrant, which would mean the points would flip and the sign for the Y coordinate would change.

Answer:

i think the answer is A R' (4, -1)

Answer:

Step-by-step explanation:

-0.5(3x + 5)   and   -1.5x + 2.5

-0.5(3x + 5)...distribute the -0.5 thru the parenthesis

-1.5x - 2.5

no, these are not equivalent.... one is -1.5x + 2.5 and the other is -1.5x - 2.5....not the same

Answer:

Both expressions are not equal

Step-by-step explanation:

First expression is

-0.5(3x + 5)

By multiplying

-1.5x - 2.5

2nd expression is

-1.5x + 2.5

Only Sign is different with 2.5 in both cases

Answer:

305.12 square inches

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The area of the window is equal to the area of a rectangle, plus the area of two quarter circles plus the area of the smaller square between the two upper corners

so

Find the area of rectangle

[tex]A=(12)(26-4)=264\ in^2[/tex]

Find the area of the two quarter circle

[tex]A=2[\frac{1}{4}(3.14)(4^2)][/tex]

[tex]A=25.12\ in^2[/tex]

Find the area of the smaller square between the two upper corners

[tex]A=(12-8)(4)=4^2=16\ in^2[/tex]

The total area is equal to

[tex]A=264+25.12+16=305.12\ in^2[/tex]

Jaylon's stained-glass window consists of two quarter circles with a radius of 4 inches each and a rectangle with dimensions 4 inches (height) by approximately 25.12 inches (width). The total area of the stained-glass window is approximately 125.6 square inches.

To find the area of the stained-glass window that Jaylon created, we'll break it down into its constituent shapes: two quarter circles and a rectangle.

Quarter Circles:

Each quarter circle has a radius of 4 inches.

The formula for the area of a quarter circle is (1/4) * π * r^2, where r is the radius.

For each quarter circle:

Area = (1/4) * π * (4)^2

≈ (1/4) * 3.14 * 16

≈ 12.56 square inches (rounded to two decimal places).

Since there are two quarter circles, the total area contributed by the quarter circles is:

Total Area of Quarter Circles = 2 * 12.56

≈ 25.12 square inches.

Rectangle:

The rectangle's height is the same as the radius of the quarter circles, which is 4 inches.

The width of the rectangle can be found by calculating the circumference of a circle with a radius of 4 inches (since it will form the other two sides of the rectangle).

The circumference of a circle is given by 2 * π * r.

So, the width of the rectangle is:

Width = 2 * π * 4

≈ 25.12 inches.

Area of the rectangle:

Area = length * width

≈ 4 * 25.12

≈ 100.48 square inches.

Total Area:

The total area of the stained-glass window is the sum of the areas of the quarter circles and the rectangle:

Total Area = Area of Quarter Circles + Area of Rectangle

≈ 25.12 + 100.48

≈ 125.6 square inches.

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Answer:

1. This equation of m<a + m<c = m<b - m<c wouldn't be correct unless the measure of angle c was 0. So technically there is no statment to make that equation true.

2. Angle addition postulate.

3. Transitive property of equality.  

4. Substitution property.

Step-by-step explanation:

You might want to recheck and see if these are the correct answer they seem to be to me. Im only in 10th grade so i kind of just learned this.

If you have any questions feel free to ask in the comments - Mark

Also when you have the chance please mark me brainliest.

GF = 11, GE = 28, HF = 14, [tex]DG=5\sqrt3[/tex]

Solution:

Given data:

DE = 11, GH = 14

In rectangle, opposite sides are equal.

DE = GF

GF = 11

Property of a rectangle:

The diagonals of a rectangle are equal in length and they bisect each other.

Half of diagonal GE = GH = 14

GE = 2 × GH

     = 2 × 14

GE = 28

HF is also a half of the diagonal DF.

By property of a rectangle, GH = HF

HF = 14

Diagonal of a rectangle formula:

[tex]D=\sqrt{\text{length}^2+\text{breadth}^2}[/tex]

[tex]14=\sqrt{DG^2+11^2}[/tex]

Squaring on both sides, we get

[tex]196={DG^2+121}[/tex]

[tex]{DG^2=196-121}[/tex]

[tex]{DG^2=75}[/tex]

Taking square root on both sides, we get

[tex]DG=5\sqrt3[/tex]

Hence GF = 11, GE = 28, HF = 14, [tex]DG=5\sqrt3[/tex].

The unit price per pound is $4.91.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

A 13 ounce box of cereal cost $3.99.

Also, 0.8125 pound of cereal cost $3.99.

So, the unit price

= 3.99 / 0.8125

=  $4.91

Thus, the unit price is $4.91.

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Final answer:

To calculate the unit price per pound of a 13-ounce box of cereal costing $3.99, convert ounces to pounds and divide the cost by the weight in pounds, resulting in approximately $4.91 per pound.

Explanation:

To calculate the unit price per pound of a cereal box that weighs 13 ounces and costs $3.99, first convert the weight from ounces to pounds. Since there are 16 ounces in a pound, we calculate the weight of the cereal in pounds by dividing 13 ounces by 16 ounces/pound, which gives us 0.8125 pounds.

Next, we find the unit price per pound by dividing the total cost by the weight of the cereal in pounds. Therefore, the unit price is $3.99 divided by 0.8125 pounds which equals approximately $4.91 per pound (when rounded to two decimal places).

Answer:

y>- 22/63

Step-by-step explanation

-65y+19<-2y+41

-65y+2y<41-19

-63y<22

y>-22/63

The solution to the inequality is y > -22/63.

To solve the inequality -65y + 19 < -2y + 41 for y, we'll follow these steps:

-65y + 19 < -2y + 41

First, we'll combine like terms by moving the terms with y to the left side and the constant terms to the right side:

-65y + 2y < 41 - 19

-63y < 22

Next, we'll isolate y by dividing both sides of the inequality by -63. Remember that when we divide by a negative number, the inequality sign flips:

y > 22 / -63

Simplifying the fraction:

y > -22/63

Therefore, the solution to the inequality is y > -22/63.

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Answer:

slope is -1

Step-by-step explanation:

y1-y2/ x1-x2

= -3 - 7 / 8 - (-2)

= -10/ 10

= -1

Answer:

it is B 2.5

Step-by-step explanation:

The height of the pan that he should use for the batter to completely fill the pan is 2.5 inches.

From this interactive, formula for volume is V = l w h (volume equals length times width times height) and can also be written V = B h (volume equals the area of the base times the height).

The volume is equal to the product of the area and height of the shape. Volume = Base Area x Height.

Given:

Base Area= 45 sq. inches

Volume= 112.5 cubic inches

So,

Volume= Base Area x Height

112.5 = 45 x Height

Height= 112.5 / 45

Height =  2.5 inches

Hence, the height of the pan that he should use for the batter to completely fill the pan is 2.5 inches.

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Answer:

[6 , +∞[

Step-by-step explanation:

Domain of g is all x≥4

domain of f is all real numbers

domain of goh is all real numbers x that verify 2x-8≥4 ⇒ x≥6

The restriction on the domain of goh is x ≥ 4.

To find the restrictions on the domain of goh, we need to consider the compositions of the two functions g(x) and h(x).

It is important to note that the square root function √x has a restriction on its domain. The expression inside the square root must be greater than or equal to zero. So, for g(x), we have x - 4 ≥ 0. Solving for x, we find that x ≥ 4.

Now, let's consider the composition goh(x). We substitute h(x) into g(x) as follows: goh(x) = g(h(x)) = g(2x-8).

The domain of h(x) is all real numbers, so we don't have any restriction for h(x). However, when we substitute h(x) into g(x), we must make sure that the resulting expression is within the domain of g(x), which is x ≥ 4. Therefore, the restriction on the domain of goh is x ≥ 4.

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Answer:

d

Step-by-step explanation:

Answer: 36

Step-by-step explanation:

120 students is the same as 100%, so you would divide 120 by 100 and your quotient would be 1.2 Then you multiply 30 by 1.2, since you would multiply 100 by 1.2 to get 120. 30×1.2=36. So 36 seventh graders have completed their science project.

Cameron should buy 7 cans of wet food to feed his cat for a week.

To calculate the number of cans of wet food Cameron should buy to feed his cat for a week, we need to first determine the amount of dry food and wet food consumed daily. Cameron's cat eats 4 ounces of dry food and 3 ounces of wet food twice a day, so it consumes a total of 8 ounces of dry food and 6 ounces of wet food per day.

Next, we need to calculate the total amount of wet food consumed in a week. Since there are 7 days in a week, the cat would consume 7 times 6 ounces, which is 42 ounces of wet food in a week.

Now, we need to determine how many cans of wet food Cameron should buy. Each can of wet food contains 6 ounces, so to find the number of cans, we divide the total amount of wet food (42 ounces) by the weight of each can (6 ounces). Therefore, Cameron should buy 7 cans of wet food to feed his cat for a week.

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Answer:

Step-by-step explanation:

The volume formula for a cylinder is B*h

B : the area of the base

h : the height

Cylinder 1

The volume is 8pi

Cylinder 2

The volume is 32pi

Cylinder 3

The volume is 72pi

Answer:

Cylinder 1:  V = 8π

Cylinder 2:  V = 32π

Cylinder 3:  V = 72π

Step-by-step explanation:

The volume of the cylinder of radius r and height h is calculated using the form:  V = π r² h

Cylinder 1:  r = 1 cm  and  h = 8 cm

Volume of Cylinder 1 = π r² h = π 1² * 8 = 8π

Cylinder 2:  r = 2 cm  and  h = 8 cm

Volume of Cylinder 2 = π r² h = π 2² * 8 =  π * 4 * 8 = 32π

Cylinder 3:  r = 3 cm  and  h = 8 cm

Volume of Cylinder 1 = π r² h = π 3² * 8 = π * 9 * 8 = 72π

Answer:

r > -178

Step-by-step explanation:

Solving the equations means to find what "r" can be for the equation to be true.

If the sign < confuses you, you can always write = then change it back.

To find "r", we need to isolate it. To do this, we move "r" to the left side, and every other number to the right side. When you move something to the other side, remember you need to do the reverse operation on both sides.

I want to move -195 first. The opposite is +195.

-17 < -195 - r

-17 + 195< -195 + 195- r    Add 195 to both sides. 195 cancels out on the right

-17 + 195 < -r           Simplify left right by add 195 to -17

178 < -r             The opposite of multiply by -1 is divide by -1.

178/-1 < -r/-1          Divide both sides by -1.

178/-1 < r          "r" is isolated now. Simplify left side

-178 < r          Answer is found. Put variable on left side. Remember the keep the open side of the symbol facing "r".

r > -178         The solution is when "r" is greater than -178.

Answer:

$72 earned on monday

Step-by-step explanation:

Delta pays Pete Rose $360 per day in the maintenance department at air port. Pete became I'll Monday and went home after 1/5 of a day

Delta works for only 1/5 of the day

To get the amount earn , multiply the work done by the rate

[tex]\frac{1}{5} \cdot 360 =72[/tex]

So $72 earned on monday

Pete Rose earns $360 per full day of work. On Monday, he worked for 1/5 of the day before becoming ill. By calculating 1/5 of his daily rate, we find that Pete earned $72 for that day.

The student's question is about calculating Pete's earnings for the part of the day he worked before he became ill. Since Pete earns $360 for a full day, we want to find out what he earns for 1/5 of that day, as 1/5 of the day is the amount of time he worked before going home.

Therefore, on Monday, Pete earned $72.

Option C

Math teacher would need to buy 130 prizes

Solution:

Given that,

Math teacher currently has 109 students and the box has 88 prizes in it

The math teacher likes to keep at least twice as many prizes in the box as she has students

So, she wants the number of prizes to be twice the number of students

Therefore,

number of prizes = 2 x 109 students

number of prizes = 2 x 109 = 218 prizes

The box has 88 prizes in it

Therefore, number of prizes she would need to buy is:

⇒ 218 - 88 = 130

Thus she would need to buy 130 prizes

Answer:

3x - 4y

Step-by-step explanation:

sum means addition so:

(2x - 5y) + (x + y) =

2x + x = 3x

-5y + y = -4y

put those two answers together and you get 3x - 4y

Answer:

(A) 3x - 4y

Step-by-step explanation:

A. There are 33 special characters.

B. The probability of guessing the password under the given circumstances is 1 out of 858 combinations.

Step-by-step explanation:

Step 1; First we need to determine all the possible values that can come in each space of the password.

From 0 to 9, there are a total of 10 values.

For uppercase letters, there are a total of 26 values from A, B, C, D ...Z

For lower case letters, there are also a total of 26 values from a, b, c, d ...z.

So out of these three characters, we have a total of 10 × 26 × 26 = 6,760 different combinations.

If there are 223,080 password combinations we need to divide this by 6,760 to calculate the possible values of the special characters.

6,760 × Number of possible special characters = 223,080,

Number of special characters = [tex]\frac{223,080}{6,760}[/tex] = 33. So there are 33 special characters.

Step 2; If the number and uppercase values are known then the  various lowercase letters and special characters are the unknown values.

The number of possible combinations = number of lowercase letters × number of special characters = 26 × 33 = 858.

So the probability of guessing the password is 1 out of 858 combinations.

(a) There are 216,320 special characters in the password combinations.

(b) The probability of guessing the account password with knowledge of the number and uppercase letter, but not the rest, is [tex]\(\frac{320}{11}\)[/tex].

Let's solve each part of the problem:

(a) Number of Special Characters:

Given that there are 223,080 password combinations and the special character comes last, it means there are 10 possible numbers (0-9), 26 possible uppercase letters, and 26 possible lowercase letters, leaving the remaining positions for special characters. Therefore, the number of special characters is:

[tex]\[ \text{Number of special characters} = 223,080 - (10 \times 26 \times 26) = 223,080 - 6760 = {216,320} \][/tex]word:

If you know the number and uppercase letter but forget the rest, you only need to guess the lowercase letter and special character. The total number of possible lowercase letters is 26, and the total number of possible special characters is 216,320 (calculated in part a).

Therefore, the probability of guessing the account password is:

[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{26 \times 216,320}{223,080} \]\[ \text{Probability} = \frac{6,387,520}{223,080}[/tex]

=320/11

Step-by-step explanation:

Equation of line in slope point form is given as:

[tex]y-y_1 =m(x-x_1) \\ \\ \therefore \: y - ( - 4) = - \frac{1}{2} (x - 2) \\ \\ \therefore \: y + 4= - \frac{1}{2} x + \frac{1}{2} \times 2 \\ \\ \therefore \: y + 4= - \frac{1}{2} x + 1 \\ \\ \therefore \: y + 4 - 1= - \frac{1}{2} x \\ \\ \therefore \: y + 3= - \frac{1}{2} x \\ \\ \therefore \: 2y + 6= - x \\ \\ \huge \purple{ \boxed{\therefore \: x + 2y + 6= 0}} \\ is \: the \: required \: equation \: of \: line.[/tex]

Answer: x=−3 or x=−5

Step-by-step explanation:

Step 1: Factor left side of equation.

(x+3)(x+5)=0

Step 2: Set factors equal to 0.

x+3=0 or x+5=0

x=−3 or x=−5

Answer:

These are the answers

Step-by-step explanation:

Answer:

Scientific Notation:

4.2 × 10^-3

E-Notation:

4.2e-3

Engineering Notation:

4.2 × 10^-3

Real Number:

0.0042

______________________________

6120

Step-by-step explanation:

Answer:

34 for one ticket

Step-by-step explanation:

374 ÷ 11 = 34

divide by the amount of tickets they bought by the amount of money spent

Answer:

Step-by-step explanation:

Yo sup??

Since you haven't mentioned the reference potential therefore we will consider it to be ground.

Since just before hitting the ground there is negligible amount of kinetic energy and also the velocity is very high hence we can say that it will have more kinetic energy than potential energy.

Hope this helps.

Answer:

Y=-5x+32

Step-by-step explanation:

So you would plug in (7,-3) into y=mx+b. Solve the problem and you get -3=-35+b. So b would equal 32 because -35+32 is -3

Answer:8:24

Step-by-step explanation:

So since it is 1:3 and 2 dozen is 24 so 24 divided by 3 = 8 so now it’s 8:24