how many different ways can you write the number 8 as a power​

(a)  (1203)4 is equal to 99 in decimal and 12 in hexadecimal.

(b)  (5243)8 is equal to 2211 in decimal and 1523 in hexadecimal.

To convert numbers from different bases to decimal using the direct method, we multiply each digit of the number by the corresponding power of the base and sum the results. To convert to hexadecimal using the intermediary binary conversion method, we first convert the number to binary and then group the binary digits into groups of 4, starting from the rightmost digit, and convert each group to its hexadecimal equivalent.

(a) Converting (1203)4 to decimal:

(1203)4 = 1 * 4³ + 2 * 4² + 0 * 4¹ + 3 * 4⁰

= 64 + 32 + 0 + 3

= 99

Converting (1203)4 to hexadecimal:

First, convert (1203)4 to binary:

(1203)4 = (10010)2

Next, group the binary digits into groups of 4:

(10010)2 = (0001 0010)2

Finally, convert each group to its hexadecimal equivalent:

(0001 0010)2 = (12)16

Therefore, (1203)4 is equal to 99 in decimal and 12 in hexadecimal.

(b) Converting (5243)8 to decimal:

(5243)8 = 5 * 8³ + 2 * 8² + 4 * 8¹ + 3 * 8⁰

= 2048 + 128 + 32 + 3

= 2211

Converting (5243)8 to hexadecimal:

First, convert (5243)8 to binary:

(5243)8 = (101 010 100 011)2

Next, group the binary digits into groups of 4:

(101 010 100 011)2 = (0001 0101 0010 0011)2

Finally, convert each group to its hexadecimal equivalent:

(0001 0101 0010 0011)2 = (1523)16

Therefore, (5243)8 is equal to 2211 in decimal and 1523 in hexadecimal.

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Answer:

12.9 cm

Step-by-step explanation:

area of full circle = 2 X 65.8 = 131.6cm².

131.6 = π r² = (3.14r²)

r² = 131.6/3.14 = 41.9108....

r = 6.47.

diameter = 2r = 12.94 = 12.9 cm to nearest tenth

Answer:

Ok, here is the answers! brainliest pleaseee :D

Step-by-step explanation:

13. - 0.624 kg.   (Explanation: 104 grams per one pack of pop-tarts. 104 g x 6 packs of pop-tarts equal 624 grams in total. 624 grams to kilograms is 0.624 kg.)

14. - No. The tablecloth is 155 cm long. It needs to cover a table that is 1.6 meters long. 155 cm to meters is 1.55 meters. The tablecloth is 0.05 to short to cover the table. 1.6 meters - 1.55 meters = 0.005.

15 - Alex's sister rode the farthest. She rode 1,000 meters farther than Alex. 2 kilometers in meters is 2,000 meters. His sister rode 1,000 meters more than that, 3,000.

Answer:

1.71 pounds of sugar per dollar.

Step-by-step explanation:

To calculate how many pounds of sugar Keisha got per dollar, we divide the total amount of sugar by the total amount of money spent. In this case, she bought 12 pounds of sugar for $7, so we divide 12 by 7:

12 ÷ 7 = 1.71

So, Keisha got 1.71 pounds of sugar per dollar.

Answer:

onse sec and ill help

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because it is an open circle and x has to be greater that 7 so therefore the numberlike is pointing to the numbers that are greater!

To solve the equation 9²y = 66, we need to isolate the variable y.  First, let's simplify 9², which is equal to 81. So, the equation becomes 81y = 66.

To solve for y, we divide both sides of the equation by 81: y = 66/81. Rounding to the nearest ten-thousandth, we can divide 66 by 81 and obtain y ≈ 0.8148. To check our answer, we substitute y = 0.8148 back into the original equation: 9²(0.8148) = 66. Evaluating the left side, we have 81(0.8148) ≈ 65.9928, which rounds to 66 when rounded to the nearest whole number.

Since both sides of the equation are equal when y ≈ 0.8148, we can conclude that the solution is correct. The solution to the equation 9²y = 66, rounded to the nearest ten-thousandth, is y ≈ 0.8148. This solution satisfies the original equation when substituted back in.

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Answer:

For the column "Slope Intercept", the graph is displaying y = -7/2x + 3. Because the line is going down 7 units and to the right 2 units, and the 3 is the point in which the line crosses the y-axis.

For the "Standard" column, it will be

7x + 2y = 6, because that's what it would look like in standard form. (To turn it from standard to slope intercept form, remember you must first subtract 7x on both sides to get 2y = -7x + 6, and then divide by 2 on both sides to get

y = -7/2x + 3.)

For column "Point Slope", I just realized you are supposed to pick a point on the line and plug the coordinates into this formula:⤵⤵⤵

This is the point-slope formula.⤵⤵⤵

\(y - y _{1} = m(x - x _{1})\)

For example we'll use point (2,-4). Also, remember that coordinates are written as (x,y), and that m represents slope.

So we have: y - (-4) = -7/2(x-2).

In other words, "Point Slope" would be

y + 4 = -7/2(x-2).

By the way, sorry this is a bit long, and took a while to complete. I had to re-educate myself on point-slope. Anyways hope this helps, I tried :)

Answer:

5.19

Step-by-step explanation:

23/62 = x/14

Cross multiply

322 = 62x

x = 5.1935

x = 5.19

Thus, the Taylor polynomial of degree two that approximates the function f(x) = 1/x centered at the point a = 1 is P2(x) = 1 - (x-1) + (x-1)^2/2.

The Taylor polynomial of degree two for the function f(x) = 1/x centered at the point a = 1 can be found using the Taylor series formula.

The formula for the nth degree Taylor polynomial is:
Pn(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + ... + (fn(a)/n!)(x-a)^n

Using this formula and plugging in the values for f(x) and a, we get:
P2(x) = 1 + (-1/x^2)(x-1) + (-2/x^3)(x-1)^2/2

Simplifying this expression, we get:
P2(x) = 1 - (x-1) + (x-1)^2/2

Therefore, the Taylor polynomial of degree two that approximates the function f(x) = 1/x centered at the point a = 1 is P2(x) = 1 - (x-1) + (x-1)^2/2.

This polynomial gives a good approximation of the function near x = 1, but may not be as accurate for values far away from the center point.

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Answer:

966 calories

Step-by-step explanation:

644 / 6 = 107.333

107.333 * 9 = 966

If a group consists of 3 men and 2 women, what is the probability that all the men end up sitting next to each other is 60%.

The first step in understanding the probability that the set of 3 men will end up sitting next to each other, we have to determine the number of seating arrangements and divide by the likely number of seating arrangements. Like this:

Then, based on this data, we can build our permutation, which will be:

Therefore, the probability found for the set of men to sit next to each other is 0.6 or 60%.

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To plot the function f(x) = -4x^2 + sin(5x) and its derivative, and to save the results in a file named "results.txt" with 2 decimal places.

You can use the following MATLAB code:

```matlab

x = -10:0.5:10; % Generate x values

f = -4*x.^2 + sin(5*x); % Calculate f(x)

df_dx = -8*x + 5*pi*cos(5*x); % Calculate the derivative

% Saving results to file

output = [x', f', df_dx'];

dlmwrite('results.txt', output, 'delimiter', '\t', 'precision', '%.2f');

1. First, we define the range of x values using the vector `-10:0.5:10` to cover the desired interval with a step size of 0.5.

2. Next, we calculate the values of f(x) and its derivative using the defined mathematical expressions.

3. We then plot the function and its derivative using the `plot` function. The red dashed line represents f(x), and the blue solid line represents its derivative.

4. To save the results, we create a matrix `output` that concatenates the x values, f(x), and the derivative column-wise.

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Easy claps

Answer: slope=3 and point is (5,6)

Step-by-step explanation: It's just basic prealgebra!

Answer:

a. 65

b. D

Step-by-step explanation:

The question asks for an expression that solves for the profit that the company will make from each phone. The expression would be 65x, where 65 represents $65 profit from each phone, since $50 is spent and $115 is made, 115-50 gives you the profit, $65

D is the answer because the question asks for the expression that shows the earnings, or how much is made from each phone

The normal distribution that best approximates X is N(42, 21).

In an accounting college class, 50% of students receive a B or above on the final exam. 84 students are randomly selected from an accounting class at a local college. Let X be the number of students who received a B or above on the final exam. The normal distribution that best approximates X is a normal distribution with mean µ = np and variance σ^2 = np(1 - p).

In this case, n = 84 and p = 0.5 since 50% of the students receive a B or above on the final exam, and we want to find the distribution of the number of students who receive a B or above on the final exam.X ~ N(µ, σ^2) = N(np, np(1 - p)) = N(84(0.5), 84(0.5)(0.5)) = N(42, 21)

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The predicted response value for x = 90 is approximately 177.0 (rounded to one decimal place).

The given regression equation is y = 1.674x + 28.269. This means that for every one unit increase in x, the predicted value of y will increase by 1.674 units. The intercept of 28.269 represents the predicted value of y when x=0.

To predict the value of y for x = 90, we can simply substitute x = 90 into the regression equation and solve for y:

y = 1.674(90) + 28.269

y = 176.97

Therefore, the predicted response value for x = 90 is approximately 177.0 (rounded to one decimal place). This means that, on average, we expect the response variable to have a value of 177.0 when the explanatory variable has a value of 90.

It's important to note that this prediction is based on the assumption that the relationship between x and y is linear and that the data used to develop the regression equation are representative of the population of interest. Additionally, there may be other variables that affect the response variable that are not included in the analysis, so caution should be taken when interpreting the results of any regression analysis.

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The correct answer is c. Learning curves are important for estimating performance improvement as workers become experienced.

Learning curves are often used in project management to estimating the time, effort, and resources required to complete a task or project. They help to estimate how long it will take for a worker or team to become proficient at a task or process, based on the amount of time and effort that they have put into it.

This can be helpful in estimating performance improvement as workers become more experienced and efficient in their work. The concept of a learning curve is a curved line that represents the rate of improvement over time, which is why the term "curve" is relevant. While learning curves do involve some math, they are not primarily focused on helping new PMs understand required math, nor are they used for visualization of curved mechanical parts or estimating cost improvement as parts become "broken in."
Learning curves are important for:
c. estimating performance improvement as workers become experienced.
Learning curves represent the progress made in a skill or job over time, whereas a curve illustrates the relationship between experience and efficiency. As workers become more experienced, their performance typically improves, which can be estimated using a learning curve in various industries and tasks.

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The standard error of the mean is 2.

n =  64

X = 152

s = 16

Standard error: 5/\(\sqrt{x}\)

= 16/\(\sqrt{64}\)

=2

what is standard error?

The statistical standard error (SE) is the approximate standard deviation of a statistical sample population.

Standard error is a statistical term that uses standard deviation to measure how well a sampling distribution represents a population. In statistics, the sample mean is different from the actual mean of the population. This deviation is the standard error of the mean.

Therefore, The standard error of the mean is 2.

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Answer:

30 cm

Step-by-step explanation:

Make sure all units are the same!

P = Perimeter

A = Area

Formula used for similar figures:

\(\frac{A_{1}}{A_{2}} = (\frac{l_{1}}{l_{2}})^{2}\) —- eq(i)

\(\frac{P_{1}}{P_{2}} = \frac{l_{1}}{l_{2}}\) ———— eq(ii)

Applying eq(ii):

∴\(\frac{25}{P_{2}} = \frac{10}{12}\)

Cross-multiplication is applied:

\((25)(12) = 10P_{2}\)

\(300 = 10P_{2}\)

\(P_{2}\) has to be isolated and made the subject of the equation:

\(P_{2} = \frac{300}{10}\)

∴Perimeter of second figure = 30 cm

Step-by-step explanation:

12x^2 + 8x

4x ( 3x + 2)

2x^2 - 16x

2x ( x - 8)

Answer:

horizontal lines of symmetry

Step-by-step explanation:

In 90 minutes, she would have created 36 drawings.

The first step is to establish a pattern between time and the number of drawing that Frankita creates.

When the question is studied, it can be deduced that every 15 minutes the rate of increase in drawing is (previous drawing + (1 + rate of increase of previous drawing.

Drawing created in 30 minutes = 15 + 2 = 17

Drawing created in 45 minutes = 17 + ( 1 + 2) = 20

Drawing created in 60 minutes = 20 + (3 + 1 ) = 24

Drawing created in 75 minutes = 24 + (4 + 1) = 30

Drawing created in 90 minutes = 30 + (5 + 1) = 36

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Using the equation y = 12.4/20, the amount of time it would take to read a book that has 424 pages is: A. 262.88 min.

The equation, y = kx, represents a proportional relationship where the value of k is the unit rate of the relationship between the two variables, x and y.

In the scenario given:

To find how long it will take to read a book with 424 pages, substitute x = 424 into the equation y = 12.4/20x:

y = 12.4/20(424)

y = 262.88 minutes.

To read 424 pages, it will take: A. 262.88 min.

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The  value of n, to the nearest tenth, is 1.5.

What is Logarithm?

A logarithm is a mathematical function that represents the exponent to which a base number must be raised to obtain a given number. In other words, it is the inverse operation of exponentiation. The logarithm of a number y to a given base b is denoted as log base b of y, or simply logby.

To solve the equation \(1/3 log(Vx) + log(x^3) = n log(x),\) we can use logarithmic properties to simplify it.

Let's start by applying the power rule of logarithms, which states that \(log(a^b) = b log(a\)). We can rewrite the equation as follows:

\(log(Vx)^(1/3) + log(x^3) = n log(x)\)

Next, we'll use the sum rule of logarithms, which states that log(a) + log(b) = log(a * b). Applying this rule, we get:

\(log((Vx)^(1/3) * x^3) = n log(x)\)

Using the property log(a * b) = log(a) + log(b), we can further simplify:

\(log((Vx * x^9)^(1/3)) = n log(x)\)

Now, applying the power rule again, we have:

\(log((Vx * x^9)^(1/3)) = log(x^n)\)

Since the logarithms on both sides are equal, we can equate their arguments:

\((Vx * x^9)^(1/3) = x^n\)

Now, we can remove the cube root by raising both sides to the power of 3:

\(Vx * x^9 = x^(3n)\)

Simplifying further:

\(V * x^(9/2) = x^(3n)\)

Now, we can equate the exponents:

9/2 = 3n

To solve for n, divide both sides by 3:

n = (9/2) / 3

n = 9/6

n = 1.5

Therefore, the value of n, to the nearest tenth, is 1.5.

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The probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

Assuming that each die is fair and that the outcome of rolling one die does not affect the outcome of rolling the others, the probability of rolling a 6 with the red die is 1/6, the probability of rolling a 5 with the green die is also 1/6, and the probability of rolling a 4 with the blue die is 1/6.

Since the three events of rolling each die are independent of each other, we can multiply their probabilities to get the probability of all three events happening at the same time, i.e., rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die:

Probability of rolling 6 with the red die = 1/6

Probability of rolling 5 with the green die = 1/6

Probability of rolling 4 with the blue die = 1/6

Probability of rolling 6 (R), 5 (G), 4 (B) at the same time = Probability of rolling R and G and B together = Probability of R × Probability of G × Probability of B

= 1/6 × 1/6 × 1/6 = 1/216

Therefore, the probability of rolling a 6 with the red die, a 5 with the green die, and a 4 with the blue die at the same time is 1/216, or approximately 0.46%.

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You have three dice: one red (R), one green (G), and one blue (B). When all three dice are rolled at the same time, calculate the probability of the following outcome: 6 (R), 5 (G), 4 (B)?