Write an equation for nth 45, 30, 15, 0 sequences and series

Answer: The square root of 96 in simplified form is 4√6.

Have a great day !

The number of plants 3 : 8 have if 3:7 has 10 plants is 11 plants.

Ratio refers to a number representing a comparison between two named things. It is also the relative magnitudes of two quantities usually expressed as a quotient.

So,

3 : 7

= 3 + 7

= 10 plants

Then,

3 : 8

= 3 + 8

= 11 plants

In conclusion, 3 ratio 8 has 11 plants.

Read more on ratio:

https://brainly.com/question/2328454

#SPJ1

Answer:

-2x-2

Step-by-step explanation:

(−4x+3)−(−2x+5)

To find the opposite of −2x+5, find the opposite of each term.

−4x+3−(−2x)−5

The opposite of −2x is 2x.

−4x+3+2x−5

Combine −4x and 2x to get −2x.

−2x+3−5

Subtract 5 from 3 to get −2.

−2x−2

Answer:  The top graph.

Step-by-step explanation:  The inflection is at x = 0, since the absolute value of x starts becoming greater as x decreases.  E.g., at x = -2,

f(x) = |x| - 4

f(x) = |-2| - 4

f(x) = 2 - 4

f(x) = - 2

At x = -4

f(x) = |x| - 4

f(x) = |-4| - 4

f(x) = 4 - 4

f(x) = 0

Answer:

7.5

Step-by-step explanation:

Answer: The volume is 3 3/4 cm^3   or  3.75 cm^3

Step-by-step explanation:

If each grid is 1/2 and there are 5 grids for the length, 2 grids for the with and 3  grids for the height, then we will multiply one-half by the number of grids to find real lengths.

Length:   1/2 *  5 =  5/2

Width:  1/2 * 2 = 1  

Height :   1/2 * 3 = 3/2  

Now find the volume by multiply the length by the width by the height

V = 5/2 * 1 * 3/2

V = 2.5 * 1 * 1.5

v = 3.75  

Answer:

h.

Step-by-step explanation:

11 / 232 = 0.047

0.047 x 100% = 4.7%

Answer:

1523

Step-by-step explanation:

10-9+1522

First, find 10-9.

10-9=1

Add the difference of 10-9 (1) to 1522.

1+1522=1523

The sum is equal to 37/22.

To find the sum: 10 - 9 + 15/22, we need to convert all the terms to a common denominator.

The denominators we have are 1, 1, and 22. To find the least common denominator (LCD), we need to find the least common multiple (LCM) of these numbers.

The LCM of 1, 1, and 22 is 22.

Now, let's rewrite each term with the common denominator of 22:

10 - 9 + 15/22 = (10 * 22/22) - (9 * 22/22) + 15/22

               = 220/22 - 198/22 + 15/22

Next, we can combine the numerators:

220/22 - 198/22 + 15/22 = (220 - 198 + 15)/22

                        = 37/22

Therefore, the sum 10 - 9 + 15/22 is equal to 37/22.

Learn more about arithmetic operations

brainly.com/question/30553381

#SPJ11

Answer:

Magnitude and Direction is 928 and 44

Step-by-step explanation:

For a Vector w = (x)i+(y)j

The Magnitude of w \(=\sqrt{x^{2} +y^{2} }\)

and the Direction of w \(=tan^{-1}(\frac{y}{x} )\)

So for our Question , w = - 168i - 160j

Then -4w = -4 (- 168i - 160j) = (-4*-168)i +(-4*-160)j = 672i + 640j

Then the Magnitude of -4w = \(\sqrt{672^{2} +640^{2} } =928\)

and the Direction of -4w = \(tan^{-1}(\frac{640}{672} )=tan^{-1}(\frac{20}{21} )=44\) ( to the nearest whole number)

Hope it Helps:)

The additive counterpart of given expressions are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

When two numbers may be added together or multiplied, regardless of the order in which they are entered, the result is said to be commutative. There are different formulas available for the conversion of multiplicative expressions to their additive counterparts.

a) The first expression is a²b³. This expression is written as aabbb. This is of the form ab and its corresponding additive counterpart is of the form a+b.

Then, a+a+b+b+b=2a+3b.

b) The second expression is a⁻²(b⁻¹c)². This expression is of the form a⁻¹ and its corresponding additive counterpart is of the form -a.

Then,

\(\begin{aligned}a^{-2}(b^{-1}c)^2&=a^{-1}a^{-1}(b^{-1}c)(b^{-1}c)\\&=-a-a-b+c-b+c\\&=-2a+2(-b+c)\end{aligned}\)

c) The third expression is (ab²)⁻³c²=e. This expression is first expanded as, (ab²)⁻¹(ab²)⁻¹(ab²)⁻¹c²=e. Using property, (xy)⁻¹=y⁻¹x⁻¹.

Then,

\(\begin{aligned}((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})c^2&=e\\(b^{-2}a^{-1})(b^{-2}a^{-1})(b^{-2}a^{-1})c^2&=e\end{aligned}\)

Also, the additive identity to e is zero. And, aⁿ=na.

Then,

(-2b-a)+(-2b-a)+(-2b-a)+2c=0

Simplifying we get,

-3(a+2b)+2c=0.

The answers are  (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

The complete question is -

Translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative

a. a²b³

b. a⁻²(b⁻¹c)²

c. (ab²)⁻³c²=e

To know more about commutative:

https://brainly.com/question/778086

#SPJ4

Answer:

the Riemann Sum for $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points is $\frac{15}{2}$.

Step-by-step explanation:

To evaluate the Riemann Sum for the function $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points, we first need to determine the width of each subinterval. Since we have four subintervals to cover the interval $[0, 2]$, each subinterval has a width of $\Delta x = \frac{2-0}{4} = \frac{1}{2}$.

Next, we need to choose a sample point from each subinterval to evaluate the function. Since we are using right-hand endpoints as the sample points, we choose the endpoint of each subinterval as the sample point. The four subintervals are:

$[0, \frac{1}{2}]$, with sample point $x_1 = \frac{1}{2}$

$[\frac{1}{2}, 1]$, with sample point $x_2 = 1$

$[1, \frac{3}{2}]$, with sample point $x_3 = \frac{3}{2}$

$[\frac{3}{2}, 2]$, with sample point $x_4 = 2$

The Riemann Sum is then given by:

∑i=14f(xi)Δx=f(x1)Δx+f(x2)Δx+f(x3)Δx+f(x4)Δx=2(12)2⋅12+2(1)2⋅12+2(32)2⋅12+2(2)2⋅12=12+2+92+4=152i=1∑4​f(xi​)Δx​=f(x1​)Δx+f(x2​)Δx+f(x3​)Δx+f(x4​)Δx=2(21​)2⋅21​+2(1)2⋅21​+2(23​)2⋅21​+2(2)2⋅21​=21​+2+29​+4=215​​

Therefore, the Riemann Sum for $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points is $\frac{15}{2}$.

The Riemann Sum is 15/2 or 7.5.

To evaluate the Riemann Sum for the function f(x) = 2x^2 on the interval [0, 2] using 4 equal subintervals and right-hand endpoints, follow these steps:

1. Determine the width of each subinterval:
  Δx = (b - a) / n = (2 - 0) / 4 = 0.5

2. Identify the right-hand endpoints of each subinterval:
  x1 = 0.5, x2 = 1, x3 = 1.5, x4 = 2

3. Evaluate the function at each right-hand endpoint:
  f(x1) = 2(0.5)^2 = 0.5
  f(x2) = 2(1)^2 = 2
  f(x3) = 2(1.5)^2 = 4.5
  f(x4) = 2(2)^2 = 8

4. Calculate the Riemann Sum using these values:
  Riemann Sum = Δx * (f(x1) + f(x2) + f(x3) + f(x4))
  Riemann Sum = 0.5 * (0.5 + 2 + 4.5 + 8)
  Riemann Sum = 0.5 * (15)
  Riemann Sum = 7.5

The Riemann Sum for the given function using 4 equal subintervals and right-hand endpoints is 7.5, which is not among the provided options. However, the closest answer choice would be 15/2 or 7.5.

visit here to learn more about Riemann Sum:

brainly.com/question/30404402

#SPJ11

We know that the surface area of cuboid with sides L, B and H is given by,

S = 2 (LB + BH + LH)

Given that the sides of cuboid are x cm, 5 cm and 7 cm.

So L = x cm and B = 5 cm and H = 7 cm.

Given that the surface area of the cuboid is 142 square cm.

According to information the suitable equation for this is:

2(5x+7*5+7x) = 142

Now solving the equation we get,

5x+35+7x = 142/2 = 71

12x+35 = 71

12x = 71-35

12x = 36

x = 36/12

x = 3

Hence the value of x is 3 cm.

To know more about Cuboid refer to:

https://brainly.com/question/26403859

#SPJ9

Answer:

72°

Step-by-step explanation:

Hello There!

Complementary angles have a sum of 90 degrees

So to find the missing angle we subtract the measure of the given angle (18 in this case) from 90

90 - 18 = 72

so your answer will be 72°

Answer:

B. 5626.9

Step-by-step explanation:

• volume of cylinder= pi(r)2h

• plug in the values into the equation

• pi(8)2(28)

pi=3.14 so 3.14(8)2(28)

• multiply all the values

• you get 5629. 73

• b is the closest the that answer since it says approximate

The distance between the lines AB and CD is √46/√14 units. The distance between two skew lines is given by the scalar projection of the vector between the position vectors of the lines onto the unit normal vector.

To find the distance between two skew lines (lines that do not intersect), we can use the vector projection method. Let's solve it step by step:

1. Find the direction vectors: The direction vector of line AB is obtained by subtracting the coordinates of A and B.

  AB = B - A = (-4 - 1, 2 - (-3), -3 - 7) = (-5, 5, -10).

  Similarly, the direction vector of line CD is obtained by subtracting the coordinates of C and D.

  CD = D - C = (11 - 2, 0 - 3, -3 - 0) = (9, -3, -3).

2. Find the normal vector: The normal vector to both lines can be obtained by taking the cross product of the direction vectors AB and CD.

  AB × CD = (-5, 5, -10) × (9, -3, -3) = (-35, -55, -20).

  Let's normalize the vector by dividing it by its magnitude to obtain the unit normal vector.

  N = (-35, -55, -20) / √((-35)^2 + (-55)^2 + (-20)^2) = (-35, -55, -20) / √(4620) = (-35, -55, -20) / √(4 * 1155).

  Simplifying, we get N = (-35, -55, -20) / (2√1155).

3. Find the position vector: To find the position vector of one of the lines, we can choose A or C.

  Let's use A as the position vector for line AB.

  A = (1, -3, 7).

4. Calculate the distance: The distance between two skew lines is given by the scalar projection of the vector between the position vectors of the lines onto the unit normal vector.

  Distance = |AC · N| = |(C - A) · N| = |(2 - 1, 3 - (-3), 0 - 7) · N| = |(1, 6, -7) · (-35, -55, -20) / (2√1155)|.

  Simplifying, we get |(1, 6, -7) · (-35, -55, -20) / (2√1155)| = |(-35 - 330 + 140) / (2√1155)| = √46/√14.

  Therefore, the distance between the lines AB and CD is √46/√14 units.

Learn more about vectors here:

brainly.com/question/24256726

#SPJ11

Answer:

sure whats the problem

Step-by-step explanation:

Answer:

O

Step-by-step explanation:

Answer:

O 0.0000186 mi/s

Step-by-step explanation:

Answer:

No.

First, multiply 6 x 4 ($4 is the amount of money he makes from each sale).

6 x 4 = $24

If Lin's goal is $32, and he sells 6 boxes of popcorn for only $24, then he will not reach his goal in that specified range.

The First World War was a global conflict that took place from 1914 to 1918. It was sparked by the assassination of Archduke Franz Ferdinand of Austria-Hungary by a Serbian nationalist in 1914, but the underlying causes of the war were more complex and multifaceted.

Some of the main causes of the First World War include:

The effects of the First World War were far-reaching and had a profound impact on the world. Some of the main effects of the war include:

Learn more about First World War at

https://brainly.com/question/1027241?referrer=searchResults

#SPJ4

Hello !

Answer:

\(\boxed{\sf C\approx62.8 ft}\)

Step-by-step explanation:

To find the circumference of a circle with its radius, we will apply the following formula:

\(\sf C=2\pi r\)

Where r is the radius of the circle.

Given :

We know that the diameter is equal to two times the radius, so \(r=10\) ft.

Let's substitute our value into the formula :

\(\sf C=2\times \pi\times 10\\\boxed{\sf C\approx62.8 ft}\)

Have a nice day !

Answer:

Step-by-step explanation:

We know that

So,

→ R = 20/2

→ R = 10

Now,

We know that,

Circumference of circle = 2πr

→ 2 × 22/7 × 10

→ 440/7

→ 62.8 ft

Hence ,

The change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.

Nominal exchange rate is the price of one currency in terms of another currency. It represents the number of units of one currency that can be purchased with a single unit of another currency. In Canada's perspective, a change in nominal exchange rate means the value of the Canadian dollar in US dollars. So, to calculate the change in nominal exchange rate from Canada's perspective.

Nominal Exchange Rate = Real Exchange Rate x (1 + Inflation of Canada) / (1 + Inflation of US) Given, Real Exchange Rate of Canada

= 4.9% Inflation of Canada

= 8.5% Inflation of US

= 3.8%  Nominal Exchange Rate

= 4.9% x (1 + 8.5%) / (1 + 3.8%) Nominal Exchange Rate

= 4.9% x 1.085 / 1.038 Nominal Exchange Rate

= 5.3099 / 1.038 Nominal Exchange Rate

= 5.11 (rounded to two decimal places)

This means that if there were no inflation, the nominal exchange rate from Canada's perspective would have been 5.11 Canadian dollars per US dollar. But due to inflation, the Canadian dollar depreciated by 2.76% (calculated as (5.11 - 4.97) / 5.11 x 100%). Therefore, the change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.

To know more about nominal, visit:

https://brainly.com/question/27994820

#SPJ11

-19

1) Let's evaluate that

-9-16-12+18 Add the negative ones

-25 -12+18

-25+6

-19

2) Hence, the answer is -19

The correct answer is: D.

The system has only one solution, and it is viable because it results in positive side lengths.

Let x be the shorter leg of the triangle, and y be the area. The longer leg is 4 + 6x, and the area of the triangle is y = (1/2) * x * (4 + 6x).

For the rectangle, the width is 5 + x, the length is 3, and its area is also y = (5 + x) * 3.

The system of equations is:

y = (1/2) * x * (4 + 6x)

y = (5 + x) * 3

Substitute equation (2) into equation (1) and solve for x:

(5 + x) * 3 = (1/2) * x * (4 + 6x)

30 + 6x = 4x + 6x^2

6x^2 - 2x - 30 = 0

Using the quadratic formula, we find two solutions for x:

x1 ≈ 2.62

x2 ≈ -1.95

Since x represents the length of the shorter leg, we discard the negative solution. Thus, there is only one viable solution for x: x ≈ 2.62. Now find y using equation (2): y ≈ 22.86.

Read more about equations here:

https://brainly.com/question/22688504

#SPJ1

A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is 4 inches more than six times the shorter leg.

The second template will be in the shape of a rectangle, where the width is 5 inches more than the triangle’s shorter leg, and the length is 3 inches.

The carpenter needs the areas of the two templates to be the same. Write a system of equations to represent this situation, where y is the area, and x is the length of the shorter leg of the triangle. Which statement describes the number and viability of the system’s solutions?

A.

The system has two solutions, but only one is viable because the other results in negative side lengths.

B.

The system has two solutions, and both are viable because they result in positive side lengths.

C.

The system has only one solution, but it is not viable because it results in negative side lengths.

D.

The system has only one solution, and it is viable because it results in positive side lengths.

Answer:

3 gallons i believe

Step-by-step explanation:

3 gals in 48 cups

Answer:

it helps by finding out how you got it

Step-by-step explanation:

Answer:The solution is in the attached file

Step-by-step explanation:

Averages are a useful tool for summarizing data and providing a general idea of the central tendency of a dataset. However, it is important to recognize that averages can have drawbacks and should not always be taken literally.

One of the main drawbacks of using averages is that they can be heavily influenced by outliers or extreme values in the dataset. These outliers can skew the average, making it a poor representation of the typical or average value in the dataset. For example, if a dataset includes a few very large values, the average may be much higher than what is typical for the majority of the data.

Another drawback of using averages is that they can mask important variation or patterns in the data. Averages provide a summary of the data, but they do not provide any information about the distribution or spread of the data. For example, two datasets with the same average may have very different distributions, one with a narrow range of values and the other with a wide range of values. Therefore, relying solely on averages can obscure important information about the data.

My understanding and perception of averages has changed as I have learned more about statistics and data analysis. While averages are still a useful tool for summarizing data, I now recognize the importance of considering other measures of central tendency and variability, as well as visualizing the data through graphs or charts. I also appreciate the importance of understanding the context and limitations of the data when interpreting averages. Overall, I have come to recognize that averages are just one tool in the data analyst's toolbox and should be used in conjunction with other techniques to gain a more complete understanding of the data.

Learn more about average here: brainly.com/question/130657

#SPJ4

It will take 13 minutes and 30 seconds for the tanks to have an equal amount of water.

Since Louis is filling two tanks of water in his home, and Tank A currently contains 27 gallons and has a hose filling it at a rate of 3 gallons per minute, while the other tank, Tank B, has 38 gallons and is being filled at a rate of 2 gallons per minute, to determine how many minutes will it take for the tanks to have an equal amount of water, the following calculation must be made:

Therefore, it will take 13 minutes and 30 seconds for the tanks to have an equal amount of water.

Learn more about quantities in https://brainly.com/question/25831031

The equation that represents the number of the bucket filled, y, after x hours is y = (2/5)Cx, where C represents the total capacity of the bucket.

To write an equation that represents the number of the bucket filled, we can use the information given. Let's break it down step by step:

1. In half an hour, the bucket was 1/5 of the way full.

  This means that after 30 minutes (0.5 hours), the bucket was 1/5 filled. We can represent this as follows:

  The amount of the bucket filled, y, after 0.5 hours is equal to 1/5 of the total capacity of the bucket.

2. Let's assume the total capacity of the bucket is C (in some unit of measurement, like liters or gallons).

  Since the bucket was 1/5 full after 0.5 hours, we can express it as:

  y = (1/5)C

3. Now, we need to find an equation that represents the number of the bucket filled, y, after x hours.

  We know that the bucket fills up at a constant rate over time, so we can set up a proportion to relate the time and the amount filled:

  (0.5 hours) / (1/5)C = x hours / y

  Solving the proportion, we can cross-multiply:

  (0.5 hours) * y = (1/5)C * x

  Simplifying further:

  0.5y = (1/5)Cx

  Dividing both sides by 0.5:

  y = (1/5)Cx / 0.5

  Simplifying once more:

  y = (2/5)Cx

Therefore, the equation that represents the number of the bucket filled, y, after x hours is y = (2/5)Cx, where C represents the total capacity of the bucket.

Learn more about time and work:

brainly.com/question/19382734

#SPJ11