Help please, question attached

Sum of the first five terms of the geometric progression with a common ratio of 2 and whose last or 5th term is -48 is -62

What is sum of first n terms of a geometric progression?

The formula for calculation the sum of 1st to n term in a geometric progression is

\(S_n = \frac{a ( 1 - r^n) }{ (1 - r)}\) where n is number of terms in GP, r is common ratio and

a is first term in GP

According to the given question:

To find the sum of the first five terms of the geometric progression with a common ratio of 2 and whose last or 5th term is -48.

We have r = 2, n = 5 and I = -48

We can find first term using last term

\(I = ar^{n-1}\\-48 = a 2^{5-1}\)

∴ a = -3

Now we can find the sum by using the formula

\(S_5 = \frac{-3(1-2^5)}{1-2}\) = -62

Therefore sum of the first five terms of the geometric progression with a common ratio of 2 and whose last or 5th term is -48 is -62

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The following statement is true: strong winds occur where isobars are closely spaced.

Isobars are lines on a weather map that connect points of equal atmospheric pressure. The spacing between isobars provides information about the pressure gradient, which is the change in pressure over a given distance. When isobars are closely spaced, it indicates a steep pressure gradient, which in turn leads to strong winds.

This is because air moves from areas of high pressure to areas of low pressure, and the greater the pressure difference, the faster the air will flow. Therefore, when isobars are closely spaced, it suggests a rapid change in pressure over a short distance, creating strong winds.

Regarding the other options:

- Isobars on a surface map are not necessarily drawn at 8mb intervals. The spacing between isobars can vary depending on the map and the purpose for which it is created.

- Atmospheric pressure increases towards the center of a high-pressure system, not a low-pressure system. In a high-pressure system, air descends and compresses near the surface, leading to higher pressure at the center.

- Atmospheric pressure decreases towards the center of a low-pressure system. In a low-pressure system, air rises and expands, causing lower pressure at the center.

Therefore, the true statement is that strong winds occur where isobars are closely spaced.

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Answer:

1

Step-by-step explanation:

because if you do 1 1/2 - 1/2 = 1

The equation is solved and the graph is plotted

Given data ,

Let the equation be represented as A

Now , the value of A is

4e^ ( 0.1x ) = 60

On simplifying , we get

To solve the equation 4e^0.1x = 60 graphically, we can plot the graphs of y = 4e^0.1x and y = 60 on the same set of axes and find their point of intersection.

The point of intersection of these two graphs by looking for the point where they cross. From the graph, we can see that the point of intersection is P ( 27.081 , 60 )

Hence , the solution is P ( 27.081 , 60 )

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Answer:

ΔCBA ≅ ΔZYX

ΔBCA ≅ ΔYZX

BA ≅ YX

AC ≅ XZ

Step-by-step explanation:

Given the following functions:

to find f(g(4)), we can start by finding g(4) first:

now that we know that g(4) = 8, we can calculate the composition f(g(4)):

Answer:

f(g(4) ) = 31

Step-by-step explanation:

evaluate g(4) then substitute the value obtained into f(x)

g(4) = \(\frac{4^2}{2}\) = \(\frac{16}{2}\) = 8 , then

f(8) = 3(8) + 7 = 24 + 7 = 31

The expression, (5 > 57 % 8), evaluates to false.

To determine if the expression (5 > 57 % 8) evaluates to true or false, we need to first calculate the value of 57 % 8.

Step 1: Calculate 57 % 8, which represents the remainder when 57 is divided by 8.
57 % 8 = 1

Step 2: Compare 5 and the result from Step 1 using the '>' operator.
5 > 1

Step 3: Determine if the comparison in Step 2 is true or false.
Since 5 is greater than 1, the expression evaluates to true.

So, the expression (5 > 57 % 8) evaluates to true.

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Answer:

0.79

Hope this helps :)

Answer:

it is 0.79 that is less then 0.8

Answer:

60 ft

Step-by-step explanation:

a² + b² = c²

20² + 15² = c²

c = √625

c = 25

total distance = 20 ft + 15 ft + 25 ft = 60 ft

36.99. It says total and out of all those numbers I just added.

Answer:

36.99

Step-by-step explanation:

The vertex of the parabola y = f(x + 1) is (1, -1).

To find the vertex of the parabola given by the equation y = f(x + 1), we need to determine the effect of the transformation on the vertex coordinates.

The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

In the given equation, y = f(x + 1), we can see that the transformation is a horizontal shift of 1 unit to the left. This means that the new vertex will be located 1 unit to the left of the original vertex.

Given that the original vertex is (2, -1), shifting 1 unit to the left would result in a new x-coordinate of 2 - 1 = 1. The y-coordinate remains the same.

Therefore, the vertex of the parabola y = f(x + 1) is (1, -1).

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600 degrees is approximately equal to 10.47 radians or 10π / 3 radians when expressed in terms of π.

To convert 600 degrees to radians, we need to use the conversion formula: Radians = (Degrees * π) / 180.

Let's plug in the given value:

Radians = (600 * π) / 180

Simplifying the equation, we have:

Radians = 10π / 3

Now let's express this answer in terms of π and as a decimal rounded to the nearest hundredth.

In terms of π, the answer is 10π / 3 radians. This means that the measure is equal to 10 times the irrational number π divided by 3.

To find the decimal approximation, we substitute the value of π ≈ 3.14:

Radians ≈ (10 * 3.14) / 3

≈ 31.4 / 3

≈ 10.47

Therefore, when rounded to the nearest hundredth, 600 degrees is approximately equal to 10.47 radians or 10π / 3 radians when expressed in terms of π.

This conversion allows us to relate angles measured in degrees to their equivalent measures in radians, which is often useful in mathematical calculations involving trigonometric functions or circular motion.

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Answer:

Smaller number = 6

Larger number =  36

Step-by-step explanation:

Let the smaller number  be x

Larger number = 4x + 12

Sum of two numbers = 42

x + 4x + 12  = 42               {Add like terms}

    5x  + 12 = 42                {Subtract 12 from both sides}

             5x = 42 - 12

             5x = 30                   {Dive both sides by 5}

         5x/5 = 30/5

x = 6

Smaller number = 6

Larger number = 4*6 + 12 = 24 + 12 = 36

Answer:

35°

Step-by-step explanation:

The representation of D in the form D_x, D_y, where the x and y components are separated by a comma will be D[6.08,7.27]

Any vector oriented in two dimensions can be understood to have an impact in both directions. This implies that it may be divided into two halves. A component is a portion of a two-dimensional vector. The components of a vector assist to represent the vector's effect in a certain direction. The total impact of these two components is equivalent to the influence of the separate two-dimensional vectors. The two vector components can substitute the single two-dimensional vector.

Determine the x and y components for each vector A & B for vector A

Ax=sin (15) * 2=0.5176

Ay=cos (15) * 2=1.9318

for Vector B

Bx=cos (15) * 4=3.8637

By=sin (15)* 4=1.0352

The vector addition and scalar multiplication for x and y individually D=4.3 * A+B

Dx=4.3 *(sin (15) * 2)+cos (15) * 4

Dx=4.3 * 0.5176+3.8637

Dx=6.0893

Dy=4.3 *(cos (15) * 2)-sin (15) * 4

Dy=4.3 * 1.9318-1.0352

Dy=7.2715

D[6.08,7.27]

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The actual question may be:

Express D in the form D_x, D_y, where the x and y components are separated by a comma using two significant figures.

In this exercise, you’ll create a form that accepts one or more scores from the user. Each time a score is added, the score total, score count, and average score are calculated and displayed.

In order to achieve this, you will need to utilize HTML and JavaScript. First, create an HTML form that contains a text input field for the user to input a score and a button to add the score to a list. Then, create a JavaScript function that is triggered when the button is clicked.

To update these values, you will need to loop through the array of scores and calculate the total and count, and then divide the total by the count to get the average.

Finally, the function should display the updated values to the user. You can use HTML elements such as `` or `

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Answer:

Step-by-step explanation:

see the image below

Step-by-step explanation:

The side that is adjacent to 60 degree and 90 degree is the shortest side.

If u know the hypoutnese you can divide it by 2 to find the shortest side. for example if the hypotenuse is 10 then the shortest side is 5

If you know the other leg you can simply just remove the entire radical and just keep the whole number to find the length of the shortest side.

The side that his the adjacent to the 30 degree and 90 degree angle is the second longest side of the triangle.

If u know the shortest side, just multiply the radical

\( \sqrt{3} \)

to the whole number.

If you know the hypotunese, divide the hypotenuse by 2 and then multiply the radical to find the length of the second shortest side

Finally, the hypotunese is the largest side. It is the slanted side length that is adjacent to the 30 and 60 triangle.

If you know the shortest side, just multiply the side length by 2 to get the hypotenuse.

If you know the other leg, remove the radical and keep the who the number and multiply the whole number by 2.

E.x if the second longest side length is

\(5 \sqrt{3} \)

Remove the radical so it becomes

\(5\)

then multiply it by two to find the hypotunese.

\(5 \times 2 = 10\)

There exists an n × n matrix A with rational entries such that A^3 = A if and only if n is an even positive integer. Let's consider the case when n is an even positive integer.

We can construct a matrix A with rational entries that satisfies A^3 = A. One way to achieve this is by constructing a diagonal matrix with entries 1/2 on the main diagonal and 0 elsewhere.

Since the powers of a diagonal matrix are obtained by raising each diagonal entry to the corresponding power, we have (1/2)^3 = 1/8 on the main diagonal. Thus, A^3 = A.

Now, let's consider the case when n is an odd positive integer. In this case, it can be shown that there does not exist an n × n matrix A with rational entries that satisfies A^3 = A.

This can be proved using a technique called eigenvalues. If A^3 = A, then the eigenvalues of A must satisfy λ^3 = λ. However, the only rational solutions to this equation are 0, 1, and -1.

Therefore, the eigenvalues of A can only be 0, 1, or -1. However, it can be shown that an n × n matrix with rational entries cannot have eigenvalues 0, 1, and -1 simultaneously, which implies that such a matrix A does not exist when n is odd.

There exists an n × n matrix A with rational entries such that A^3 = A if and only if n is an even positive integer.

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Answer:

The side lengths of the larger polygon are;

15 cm

20.625 cm

16.875 cm

9.375 cm

13.125 cm

Step-by-step explanation:

Firstly, we need to calculate the perimeter of the first polygon

Mathematically, we can get this by adding the side lengths together

We have this as;

5 + 7 + 8 + 11 + 9

= 40 cm

so we have the ratio of the lengths of both as;

75 cm/40 cm = 1.875

Now, we simply will multiply the lengths of the smaller polygon by 1.875

So we have the side lengths of the bigger polygon as;

1.875 * 5 = 9.375 cm

1.875 * 7 = 13.125 cm

1.875 * 8 = 15 cm

1.875 * 9 = 16.875 cm

1.875 * 11 = 20.625 cm

The value of 60 percent of $600 will be $360.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, 60% of $600 will be illustrated thus:

= 60% × $600

= 60/100 × $600

= 0.6 × $600

= $360

Therefore, the value is $360.

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They are writing the values of the coins and the sum using their understanding of the computational language Python.

Python is a general-purpose, high-level programming language that is interpreted. Code readability is a priority in its design philosophy, which uses substantial indentation. Garbage collection and dynamic typing are features of Python.

Writing code in python      

quarters = int(input())

dimes = int(input())

nickels = int(input())

pennies = int(input())

cents = (quarters*25 + dimes*10 + nickels*5 + pennies)

#convert cents to dollars

# 1 dollar = 100 cents

# n cents = n/100 dollars

dollars = cents / 100.00

#Print the amount in dollars up to two decimal places

print("Amount: $"+"{:.2f}".format(dollars))

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I understand that the question you are looking for is:

In python 3.17 LAB: Convert to dollars

Given four values representing counts of quarters, dimes, nickels and pennies, output the total amount as dollars and cents

Output each floating-point value with two digits after the decimal point, which can be achieved as follows:

print(f'Amount: ${dollars:.2f}'

Ex: If the input is

4

3

2

1

where 4 is the number of quarters, 3 is the number of dimes, 2 is the number of nickels, and 1 is the number of pennies, the output is:

Amount: $1.41

For simplicity, assume input is non-negative

Answer:

4

Step-by-step explanation:

took the test and got it right!

The problem wants us to solve for the area of the window.

As we can see the window is in the form of a SQUARE shape with a measurement of 0.25 in for 1/2 the side of the window.

Since 1/2 of the side of the window is 0.25, the full measurement of its side is just times two of its half. Therefore:

Side = 0.25(2) = 0.5 in

And we can see at the bottom of the picture the word SCALE. The SCALE shows the relationship between the measurement of something (in our case a cabin) in a model to the measurement of that something in the real life.

In our case we have a scale of 1 in = 8 ft, it means that 1 inch in the paper is actually 8 feet in real life. Therefore the side of the window which measures 0.5 in. in the paper is actually 4 feet in real life. Because 0.5 inch is half of 1 inch and 4 feet is half of 8 feet. To show it mathematically we have:

Since we now have a side of 4 ft. We can now solve for the area of our SQUARE WINDOW, using the formula of the area of the sqaure which is Area = Side x Side.

Therefore the area of the window is 16 square feet. LETTER C.

Answer:

A unique triangle will be produced if you are given: all three sides (Side-Side-Side) two sides and the included angle (Side-Angle-Side) two angles and the included side (Angle-Side-Angle)

Step-by-step explanation:

oof sorry I barely realized that I was supposed to select a number....sorry, but hope this helps :)

1. The mean number of households that will have one or more cats is 15.

2. This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.

The mean number of households that will have one or more cats can be calculated as:

Mean = (30/100) x 50 = 15

Therefore, the mean number of households that will have one or more cats is 15.

The standard deviation can be calculated using the formula:

Standard deviation = \(\sqrt{(npq)}\)

where n is the sample size (50), p is the probability of success (30/100 = 0.3), and q is the probability of failure (1 - p = 0.7).

Standard deviation = sqrt(50 x 0.3 x 0.7) = 3.08

Rounding to 1 decimal place, the standard deviation is 3.1.

If 10 of the 50 random households had one or more cats, we can calculate the z-score as:

z = (x - μ) / σ

where x is the observed number of households with cats (10), μ is the mean (15), and σ is the standard deviation (3.1).

z = (10 - 15) / 3.1 = -1.61

Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score of -1.61 or lower is 0.053.

This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.

However, it is somewhat lower than the expected value of 15, which suggests that the sample may not be fully representative of the population.

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Answer:

56%

Step-by-step explanation:

We know that there are 6 groups of 6 and 4 groups of 5.

6x6 = 36

4x5 = 20

Add them up. 36 + 20 = 56.

Add the percent sign for 56%.

Answer:

56%

Step-by-step explanation: