Please help me I am really confused.

The values of the expressions are;

z³³

d⁻¹⁶

Note that index forms are described as forms used in the representation of numbers or variables too large or small.

Some rules of index forms are;

Then, from the information given, we have that;

(z⁻⁴/z⁶  × z⁵/z⁻⁶)⁻¹¹

Subtract the exponents, we have;

(z⁻² × z⁻¹)⁻¹¹

expand the bracket

z²² ⁺ ¹¹

z³³

(d⁴)⁻³/(d⁶)⁻²  ÷  (d⁴/d⁶)⁻⁸

expand the brackets

d⁻¹²/d¹²  ÷    (d⁻²)⁻⁸

subtract the exponents

d⁰  ÷  d¹⁶

d⁻¹⁶

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Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.

Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.

The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.

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Answer:

D

Step-by-step explanation:

Look at the y-values for both dots, the open circle is -7 and the closed circle is 5. The closed circle means y is going to be equal to, so the greater than sign is made to be equal.

Answer:

Equilateral triangle

Step-by-step explanation:

When all sides of a triangle are equal or all angles of the triangle are 60 degree then the triangle is called an equilateral triangle

Answer:

I have attached a really rough graph!!

Step-by-step explanation:

The point that does not fit in the proportional relationship is (6,2) when we plot the other three points and join the points they will give us a staright line but the point (6,2) isnt lying on that staright line.. Therefore, it does not fit in the proportional relationship!

Answer:

(6,2)

Step-by-step explanation:

Answer:

74 kilometers per hour.

Step-by-step explanation:

Let's call the speed of the faster car "x" (in kilometers per hour). Then, according to the problem, the speed of the slower car is "x - 12" (in kilometers per hour).

The two cars are traveling towards each other, so the distance between them decreases at a rate equal to the sum of their speeds. In other words, the relative speed between the two cars is:

x + (x - 12) = 2x - 12

According to the problem, they meet after 2 hours of travel, so the total distance they cover is:

distance = speed × time

For the faster car, the distance it covers is:

distance = x × 2

For the slower car, the distance it covers is:

distance = (x - 12) × 2

Since they are both traveling towards each other, the sum of the distances covered by both cars should be equal to the total distance between them at the start of the trip (320 kilometers):

x × 2 + (x - 12) × 2 = 320

Simplifying this equation:

2x + 2x - 24 = 320

4x = 344

x = 86

Therefore, the speed of the faster car is 86 kilometers per hour.

To find the speed of the slower car, we can use the expression we found earlier:

x - 12 = 86 - 12 = 74

Therefore, the speed of the slower car is 74 kilometers per hour.

The price of the refrigerators that is the median for the first half of the data is $498.

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

The prices arranged in ascending order is: $379, $498, $619, $777, $895, $1052, $1256

The first half of the prices are $379, $498, $619,

Median = $498

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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Answer:

\(\dfrac{dV}{dt}=502.65\ mm^3/s\)

Step-by-step explanation:

The volume of a sphere is given by :

\(V=\dfrac{4}{3}\pi r^3\)

The rate of change of volume means,

\(\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}\)

We have, \(\dfrac{dr}{dt}=2\ mm/s\ and\ r=40\ mm\)

So,

\(\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s\)

So, the volume is increasing at the rate of \(502.65\ mm^3/s\).

Answer:

4 is 20% of 20

Step-by-step explanation:

4/20 × 100

20%

Answer:

(5x-4)(x+1)

Step-by-step explanation:

Answer: To calculate the amount of pasta needed for eight servings, we need to multiply the original amount of pasta in the recipe by 8/6.

So, 1.75 cups * 8/6 = 2.3 cups of pasta.

Therefore, Rosa will use 2.3 cups or four and one quarter cups of pasta if she wants to make eight servings.

Step-by-step explanation:

Answer:

x=-3/4n

Step-by-step explanation:

first, remove the parenthesis.

-3(x + n) = x

-3x -3n = x

collect like terms.

-3x - x = 3n

divide both sides.

-4 = 3n

and therefore,

x= -3/4n

Answer:

inertia

equilibrium

free body diagram

net force

force

Step-by-step explanation:

Answer: yes

Step-by-step explanation:

By answering the presented question, we may conclude that Therefore, 1  expressions cm on the map corresponds to a real distance of 3.2 km. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Scale 1:

320000 means that 1 unit on the map represents his 320000 units in the real world.

To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.

1 kilometer = 100000 cm

So,

1 unit on the map = 320000 units in the real world

1 cm on the map = (1/100000) km in the real world

Multiplying both sides by 1 cm gives:

1 cm on the map = (1/100000) km * 320000

A simplification of this expression:

1 cm on the map = 3.2 km

Therefore, 1 cm on the map corresponds to a real distance of 3.2 km. 

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The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

Answer:

24 pencils

Step-by-step explanation:

Let's call total number of pencils T.

she gave 1/2 to friends. Now she has (1/2)T.

she then used 3/4 of those, leaving her with only 1/4 of what she had AFTER giving them to friends. That is 1/2 X 1/4 = 1/8.

She now has 3 pencils. 3 pencils = 1/8.

Multiply both sides by 8 to get 24 pencils = 1 (whole ie T).

Total number of pencils, T, bought in August is 24.

According to the given image, x is the radius of the circle.

So, we can find x using Pythagorean's Theorem in the following right triangle.

Where x is the hypothenuse.

Answer:

0 gallon

Step-by-step explanation:

Given: 1 gallon per mile

total amount = 3000 gallons

capacity of truck = 1000 gallons

total number of trips = 3000/1000 = 3

total oil to reach the destination = 3000-3000=0

I hope this helps.

The maximum gallons of oil that can reach the destination when taking into account the truck consumption equals to zeroes.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is 3000 gallons of oil are to be transported to a destination 1000 miles away. The only delivery truck available has a load capacity of 1000 gallons max. Additionally the truck consumes 1 gallon per mile from its load.

The maximum number of gallons of oil that can reach the destination when taking into account the truck consumption can be calculated as follows.

In one trip of 1000 miles, The amount of oil transferred will be -

1000 - 1 x 1000

0 Gallons.

Similarly, in all the trips the total gallons of oil reaching the destination will be zero.

Therefore, the maximum gallons of oil that can reach the destination when taking into account the truck consumption equals to zero gallons.

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Answer:

The greatest possible distance between two points on the walls in the room is 17 feet.

Step-by-step explanation:

The room can be modelled as a rectangular prism with the following dimensions:

The greatest possible distance between two points on the walls in the room is the line between diagonally opposite corners. This is marked as the blue line (x) on the attached 3D diagram.

This distance is the hypotenuse of a right triangle with a base of the diagonal of the floor and a height of the height of the room.

The diagonal of the floor (marked "y" on the attached diagram) is the hypotenuse of a right triangle with legs of the width and length of the room.  To calculate the diagonal of the floor, use Pythagoras Theorem.

\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)

Substitute a = 8, b = 12 and c = y into the formula and solve for y:

\(\implies 8^2+12^2=y^2\)

\(\implies 64+144=y^2\)

\(\implies y^2=208\)

\(\implies y=\sqrt{208}\; \sf ft\)

Therefore, the diagonal of the floor (y) is √(208) feet in length.

We can now use Pythagoras Theorem again to find the length x.

Substitute a = y, b = 9 and c = x into the formula:

\(\implies y^2+9^2=x^2\)

Substitute the found value of y and solve for x:

\(\implies (\sqrt{208})^2+9^2=x^2\)

\(\implies 208+81=x^2\)

\(\implies 289=x^2\)

\(\implies x=\sqrt{289}\)

\(\implies x=17 \sf \; ft\)

Therefore, the greatest possible distance between two points on the walls in the room is 17 feet.

Answer:

===========================

Twice a number n is no less than 10 units from −1:

The inequality becomes an absolute value and translates as:

The speed of light is 1.08 x 10⁹ k/h Express this in SI units is 3 x 10⁸ m/s and in millimeters per nanosecond​ is  0.3 mm/ns.

(a) To express the speed of light in SI units, we can convert kilometers to meters and hours to seconds.

1 km = 1000 m

1 h = 3600 s

Therefore,

1.08 x 10⁹ k/h = (1.08 x 10⁹) x (1000 m/km) / (3600 s/h) = 3 x 10⁸ m/s

So the speed of light in SI units is 3 x 10⁸ m/s.

(b) To express the speed of light in millimeters per nanosecond, we need to convert meters per second to millimeters per nanosecond.

1 m = 10⁶ mm

1 s = 10⁹ ns

Therefore,

3 x 10⁸ m/s = (3 x 10⁸) x (10⁶ mm/m) / (10⁹ ns/s) = 0.3 mm/ns

So the speed of light in millimeters per nanosecond is 0.3 mm/ns.

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Answer:

33 , 39

Step-by-step explanation:

given

9 , 15 , 21 , 27

there is a common difference between consecutive terms, that is

15 - 9 = 21 - 15 = 27 - 21 = 6

to obtain terms in the sequence add 6 to the preceding term

27 + 6 = 33

33 + 6 = 39

the next two terms are 33 and 39

Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation: