The first term of an arithmetic sequence is -140 and the 90th term is 483. What is the value of the 55th term?

Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

Answer:

Para despejar la variable x de la ecuación x - 2y = -10, podemos seguir los siguientes pasos:

Sumar 2y a ambos lados de la ecuación para eliminar el término -2y en el lado izquierdo:

x - 2y + 2y = -10 + 2y

x = -10 + 2y

Por lo tanto, la variable x se puede despejar como x = -10 + 2y.

The amount $500 invested at 8% interest compounded annually be worth after 3 years is $ 629.86

Since we have $500 invested at 8% interest compounded annually, we need to find the worth after 3 years.

Using the compound interest formula, the amount

A = P(1 + r)ⁿ where

Given that

So, substituting the values of the variables into the equation, we have that

A = P(1 + r)ⁿ

A = $500(1 + 0.08)³

A = $500(1.08)³

A = $500 × 1.259712

A = $ 629.856

A ≅ $ 629.86

So, the amount is $ 629.86

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Therefore , the solution of the given problem of trigonometry comes out to be -1 is the simplified formula.

Some claim that the fusion of various fields contributed to the development of astrophysics. With the aid of precise mathematical methods, many metric issues can be resolved or the output of a computation can be determined. The scientific investigation of all six fundamental geometric calculations is known as trigonometry. They are known by a number of names and abbreviations, such as sine, variance, angle, and others. (csc).

Here,

Let's first use trigonometric identities to separately simplify each term:

=> cos(x - 90°) equals sin(x)

=>  cos(x - 180°) = -cos(x)

=> tan(x) = cos(x) / sin(x)(x)

=>  x(cos(-)) = x(x)

=> (180° + x) sin = -sin(x)

When we replace the equation with these simplifications, we get:

=> cos(x) * sin(180° plus x) * cos(x) * (-cos(x)) + (sin(x) / cos(x))

=>  sin(180° plus x) * sin(-cos2(x))

=>  -cos²(x) - sin(x)*sin(180° + x) (using the equation sin(x)*sin(x)) = -sin^2(x))

Using the identity sin2(x) +cos2(x) = 1, we get = -1.

Consequently, -1 is the simplified formula.

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When graphing frequency distributions, bar charts are most commonly used to depict simple descriptions of categories for a single variable.

Bar charts provide a visual representation of the frequencies or counts of different categories or classes of a variable.

A bar chart consists of a series of rectangular bars, where the length or height of each bar represents the frequency or count of the corresponding category. The categories are displayed on the horizontal axis, while the frequency or count is shown on the vertical axis. Each bar is separate and distinct, allowing for easy comparison between categories.

The use of bar charts is particularly effective when working with categorical or discrete variables. Categorical variables represent data that can be divided into distinct groups or categories, such as colors, types of animals, or levels of satisfaction. By using a bar chart, we can clearly visualize the distribution of data across these categories.

Bar charts have several advantages that make them suitable for displaying frequency distributions. Firstly, they are easy to understand and interpret. The length or height of each bar directly corresponds to the frequency or count, making it straightforward to identify the relative magnitudes of the categories. Additionally, the spacing between the bars allows for clear differentiation between categories, enhancing readability.

Furthermore, bar charts facilitate the comparison of frequencies or counts across different categories. By aligning the bars side by side, we can easily assess the differences in frequencies or counts between categories. This visual comparison is especially useful for identifying dominant or minority categories, patterns, or trends within the data.

Bar charts also allow for additional visual enhancements to convey additional information. For example, different colors can be used to represent different categories, making it easier to distinguish between them. Labels can be added to the bars or axes to provide further context or explanation. These visual cues help in enhancing the overall clarity and communicability of the graph.

It is worth noting that bar charts are most appropriate when dealing with discrete or categorical variables. For continuous variables, a histogram is commonly used to depict the frequency distribution. Histograms are similar to bar charts, but the bars are connected to form a continuous distribution to represent the frequency or count of data within specific intervals or bins.

In conclusion, when graphing frequency distributions, bar charts are the most commonly used method to depict simple descriptions of categories for a single variable. Bar charts provide a clear and intuitive visual representation of the frequencies or counts of different categories, facilitating easy comparison and interpretation of the data. Their simplicity and versatility make them a valuable tool in data analysis and visualization.

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In linear equation., 33 far will the ball have traveled when it hits the ground for the fourth time.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

in order to calculate the distance of the ball taht would have traveled when it hits the ground for the fourth time is to list the height everytime it bounces. We calculate as follows:

12+6+6+3+3+1.5+1.5 = 33 feet

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Answer:

52

Step-by-step explanation:

\(r^{2} -14+8p\)

Substitute values given:

\((8)^{2} -14+8(\frac{1}{4} )\)

Simplify:

64-14+2

50+2

52

Therefore 52 is our answer

Answer:

56

Step-by-step explanation:

if r = 8 than r to the second power is 8 to the second power (or 8x8) which equals 64

64 - 14 + 8p

If p + 1/4 = 2

64 - 14 + 2

54 + 2

56

Answer: can you show us the graph?

Step-by-step explanation:

The probability that both of his kids are boys are 1/3.

If a man has 2 kids, the possible combinations of kids are:

There are 4 possible combinations of the sexes of the two kids.

The fourth possibility is impossible, because one of the kids is a boy. So it can't be both girls. Then the possible combinations are:

The number of combinations of the both kids are boys = 1

The number of combinations that minimum one kid is boy = 3

Then the probability that both of kids are boys are:

\(P_{both boy}=\frac{both boy}{minimal one boy} \\P_{both boy}=\frac{1}{3} \\\)

So the probability both of kids are boy is 1/3.

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Answer:

12cos59, about 6.18

Step-by-step explanation:

cos59 = x/12

(adjacent/hypotenuse)

x = 12cos59

plugging this into a calculator gets you about 6.18

Answer:

5.8 lemme know if im wrong :)

Step-by-step explanation:

Answer:

5 4/5. ( decimal 5.8)

Step-by-step explanation:

21 1/2 -15 7/10

= 43/2 - 15 17/10

=43/2 - 157/10

=29/5

= 5 4/5

To prove the property ez2 = ez2 . 5, we first used the definition of the complex exponential function to express ez and ez2 in terms of x and y. Next, we substituted z = x + iy and z/2 = x/2 + i(y/2) to simplify the expressions. Finally, we showed that ez2 and ez2.5 are equal by multiplying ez2.5 by itself and obtaining the same result as ez2.

To prove the property ez2 = ez2 . 5, we can start by using the definition of the complex exponential function:

ez = e^(x+iy) = e^x * e^(iy) = e^x * (cos(y) + i*sin(y))

Then, we can square this expression:

ez2 = (e^x * (cos(y) + i*sin(y)))^2
   = e^(2x) * (cos^2(y) - sin^2(y) + 2i*sin(y)*cos(y))

Next, we can substitute z = x + iy, and z/2 = x/2 + i(y/2):

ez2 = e^(2z) = e^(2(x+iy)) = e^(2x) * e^(2iy)
   = e^(2x) * (cos(2y) + i*sin(2y))

And:

ez2.5 = e^(2z/2) = e^(z) = e^(x+iy) = e^x * e^(iy)
     = e^x * (cos(y) + i*sin(y))

Now, we can see that:

ez2 = e^(2x) * (cos^2(y) - sin^2(y) + 2i*sin(y)*cos(y))
   = e^(2x) * (cos(2y) + i*sin(2y))

And:

ez2.5 = e^x * (cos(y) + i*sin(y))

If we multiply ez2.5 by itself, we get:

(ez2.5)^2 = e^(2x) * (cos^2(y) + sin^2(y) + 2i*sin(y)*cos(y))
         = e^(2x) * (cos(2y) + i*sin(2y))

Which is exactly the same as ez2. Therefore, we have proven that ez2 = ez2 . 5.

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Answer:

ok, here is your answer

Step-by-step explanation:

The answer is (d) 258.000 g and 2.58×10^-2g.Both numbers have the same number of significant figures, which is six.The first number, 258.000 g, has three significant figures after the decimal point, and three before the decimal point. The zeros after the decimal point are significant because they are part of a measured quantity.The second number, 2.58×10^-2g, is written in scientific notation. It also has six significant figures because the number 2.58 has three significant figures, and the exponent -2 has two significant figures.-

A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. A base can be any whole number greater than 0. The most commonly used number system is the decimal system, commonly known as base 10. ... Binary is the most commonly used non-base 10 system.

Step-by-step explanation:

hope it helps ☺️

Answer:

B

Step-by-step explanation:

if two minutes at the time was 100percent,

then X=5percent

x=2×5/100=10/100=0.01 longer

so

0.01+2=2.01

Answer:

\(x\le \:-1\)

Step-by-step explanation:

\(3\left(x-1\right)\le \frac{1}{2}\left(x+1\right)-6\)

\(3x-3\le \:-\frac{11}{2}+\frac{1}{2}x\)

\(3x\le \:-\frac{5}{2}+\frac{1}{2}x\\\)

\(\frac{5}{2}x\le \:-\frac{5}{2}\)

\(5x\le \:-5\)

\(x\le \:-1\)

x = -1

3(-2) ≤ ½(0) - 6

-6 ≤ 0 - 6

-6 ≤ -6

This is true.

x = -2

3(-3) ≤ ½(-1) - 6

-9 ≤ -½ - 6

-9 ≤ \(-\frac{13}{2}\)

This is also true.

Therefore, x ≤ -1.

To determine a reasonable range for the function h(t) = -16t^2 + 48t + 36, we need to consider the physical context of the problem.

Since the function represents the height of a ball thrown into the air, the range of the function should be the set of all possible heights that the ball can reach. In this case, the ball is thrown upward and then falls back down due to gravity.

The vertex of the parabolic function can give us some insights. The vertex of the parabola h(t) = -16t^2 + 48t + 36 occurs at the value of t = -b/2a = -48 / (2 * -16) = 1.5 seconds. Plugging this value into the function, we find h(1.5) = 54 feet.

Therefore, a reasonable range for the function is all heights from 0 feet up to a maximum height of 54 feet. In interval notation, the range can be expressed as [0, 54].

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The surface area of the given object is 20 square yards

The question asks for the surface area of an object, but it does not provide any specific information about the object itself. Without knowing the shape or dimensions of the object, it is not possible to determine its surface area.

In order to calculate the surface area of a shape, we need to know its specific measurements, such as length, width, and height. Additionally, different shapes have different formulas to calculate their surface areas. For example, the surface area of a cube is given by the formula 6s^2, where s represents the length of a side. The surface area of a rectangular prism is calculated using the formula 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height, respectively.

Therefore, without further information about the shape or measurements of the object, it is not possible to determine its surface area. The given answer options of 20, 16, 20, 24, and 23 square yards are unrelated to the question and cannot be used to determine the correct surface area.

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Cars with exactly two options = Total cars - Cars with none or one option - Cars with all three options. 8 cars had exactly two of the given options during the month of July.

To determine the number of cars that had exactly two of the given options (air conditioning, automatic transmission, and power steering), we can follow these steps:

1. Find the total number of cars sold in July.
2. Subtract the number of cars with none, one, or all three options to get the number of cars with exactly two options.

Step 1: Find the total number of cars sold in July
- 24 cars had none of the extras
- 24 cars had only air conditioning
- 64 cars had only automatic transmission
- 35 cars had only power steering
- 8 cars had all three extras
Total cars = 24 + 24 + 64 + 35 + 8 = 155 cars

Step 2: Subtract the number of cars with one or all three options
- 87 cars had air conditioning
- 99 cars had an automatic transmission
- 73 cars had power steering
- 8 cars had all three extras

Total cars with at least one option = 87 + 99 + 73 - 8 = 251 cars

Now, subtract the number of cars with none or one option from the total number of cars to find the number of cars with exactly two options:

Cars with exactly two options = Total cars - Cars with none or one option - Cars with all three options
Cars with exactly two options = 155 - (24 + 24 + 64 + 35) - 8 = 155 - 147 = 8 cars
Therefore, 8 cars had exactly two of the given options during the month of July.

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Answer:

see explanation

Step-by-step explanation:

Given

5y + 4 = 10 ( subtract 4 from both sides )

5y = 10 - 4 , that is

5y = 6

Thus 5y + 4 = 10 is equivalent to 5y = 6

Answer: y=  9x+6y=15

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The mean of the deviation scores in any data distribution is also known by research scientists as the mean deviation or the average deviation. It is a measure of the average distance of each data point from the mean of the distribution.

The mean deviation is calculated by finding the absolute difference between each data point and the mean, adding up these differences, and dividing by the number of data points. Unlike the standard deviation, the mean deviation gives equal weight to each data point and is less affected by outliers.

However, it is not as commonly used as the standard deviation because it does not have the same statistical properties and is not as easily interpreted in terms of probability distributions.

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To solve the given differential equation using Laplace transformation, we'll follow these steps:

Step 1: Apply the Laplace transformation to both sides of the equation.

Taking the Laplace transform of the equation, we have:

L{du(t)/dt} + 2L{dy(t)/dt} + 17L{y(t)} = -10L{dt/dt}

Using the properties of the Laplace transform, we get:

sU(s) - u(0) + 2sY(s) - y(0) + 17Y(s) = -10/s

Step 2: Apply the initial conditions.

Since we have the initial condition dy(0)/dt = 0, and y(0) = 0, we can substitute these values into the equation:

sU(s) - u(0) + 2sY(s) - 0 + 17Y(s) = -10/s

sU(s) + 2sY(s) + 17Y(s) = -10/s

Step 3: Solve for Y(s).

Rearranging the equation to isolate Y(s), we have:

Y(s)(2s + 17) = -10/s - sU(s)

Y(s) = (-10 - sU(s))/s(2s + 17)

Step 4: Take the inverse Laplace transform.

To find the solution y(t), we need to take the inverse Laplace transform of Y(s). However, the given u(t) = e is not in Laplace transform form. Please provide the correct Laplace transform expression for u(t) so that we can proceed with finding the inverse Laplace transform and the solution to the differential equation.

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The expression in scientific notation is given as follows:

3.5 x 10³.

A number in scientific notation is given by:

\(a \times 10^b\)

With the base being \(a \in [1, 10)\).

For this problem, the expression is given by:

\(\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3}\)

When two factors of a multiplication have the same base and different exponent, we keep the base and add the exponents, hence:

\(10^2 \times 10^4 = 10^6\)

5 x 4.2 = 21, hence the expression is:

\(\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3} = \frac{21 \times 10^6}{6 \times 10^3}\)

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

\(\frac{21 \times 10^6}{6 \times 10^3} = 3.5 \times 10^3\)

Which is the simplified expression.

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The sets of transformations that result in the same image when performed in any order are:

Translation, dilation with center (0,0)

Two translations

In mathematics, a transformation refers to a process that changes the size, shape, position, or orientation of a geometric figure or an object in a coordinate plane or space. There are several types of transformations, such as translation, rotation, reflection, and dilation, which are used to alter the original figure to create a new one that is similar or congruent to the original. Transformations are used in geometry, algebra, and other branches of mathematics to study and understand various properties of geometric shapes and objects.

Here,

For the first set, if we perform a translation followed by a dilation with center (0,0), the result will be the same as if we perform the dilation first followed by the translation. This is because the dilation does not change the direction of the translation, and the center of dilation is at the origin, so the translation is unaffected.

For the second set, any two translations can be combined to form a single translation, so the order in which they are performed does not matter.

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Answer:

\(C = 36.0\)

\(B = 46.2\)

\(A = 97.8\)

Step-by-step explanation:

Given

\(\triangle ABC\)

\(AC = 4.3\)

\(BC = 5.9\)

\(BA = 3.5\)

Required

List the angles from smallest to largest

The given parameters is illustrated with the attached image.

\(AC = 4.3\) -- b

\(BC = 5.9\) --- a

\(BA = 3.5\) --- c

This question will be solved using cosine rule

To calculate A, we have:

\(a^2 = b^2 + c^2 -2bc\ cos(A)\)

So, we have:

\(5.9^2 = 4.3^2 + 3.5^2 - 2 * 4.3 * 3.5 * \cos(A)\)

\(34.81 = 18.49+ 12.25 - 30.10* \cos(A)\)

Collect like terms

\(34.81 - 18.49- 12.25 = - 30.10* \cos(A)\)

\(4.07 = - 30.10* \cos(A)\)

Make cos(A) the subject

\(\cos(A) = -\frac{4.07}{30.10}\)

\(\cos(A) = -0.1352\)

Take arccos of both sides

\(A = cos^{-1}(-0.1352)\)

\(A = 97.8\)

Solving for B, we have:

\(b^2 = a^2 + c^2 -2ac\ cos(B)\)

This gives:

\(4.3^2 = 5.9^2 + 3.5^2 -2*5.9*3.5\ cos(B)\)

\(18.49 = 34.81+ 12.25 -41.30 *\cos(B)\)

Collect like terms

\(18.49 - 34.81 - 12.25 = -41.30 *\cos(B)\)

\(-28.57 = -41.30 *\cos(B)\)

Solve for cos(B)

\(\cos(B) = \frac{-28.57}{-41.30}\)

\(\cos(B) = 0.6918\)

Take arccos of both sides

\(B = cos^{-1}(0.6918)\)

\(B = 46.2\)

To solve for C, we make use of:

\(A + B + C = 180\) --- angles in a triangle

\(97.8 + 46.2 + C = 180\)

Collect like terms

\(C = - 97.8 - 46.2 + 180\)

\(C = 36.0\)

So, we have:

\(C = 36.0\)

\(B = 46.2\)

\(A = 97.8\)