The magnitude and direction of two forces acting on an object are 100 pounds, S80°E, and 90 pounds, N55°E,
respectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth
of a degree, of the resultant force.
The magnitude is approximately ? pounds.
(Do not round until the final answer. Then round to the nearest hundredth as needed.)

The time it will take for him to have enough money for the project is given as follows:

t = 8.5 years.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 4000, r = 0.062, n = 2, A(t) = 6720.

Hence the time needed is obtained as follows:

[tex]4000\left(1 + \frac{0.062}{2}\right)^{2t} = 6720[/tex]

(1.031)^2t = 672/400

(1.031)^2t = 1.68

2tlog(1.031) = log(1.68)

t = log(1.68)/[2 x log(1.031)]

t = 8.5 years.

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Answer:

[tex]\huge\boxed{\sf 1}[/tex]

Step-by-step explanation:

= [tex]\displaystyle (\frac{1}{4} )^0[/tex]

Using exponent rule:

So,

[tex]\displaystyle (\frac{1}{4} )^0=1[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

see attatched picture

Step-by-step explanation:

Yes , Han is correct as the a circle with a longer arc length has a larger central angle

Given data ,

Let the arc length of the circle A = 6π units

Let the radius of the circle A = 15 units

Let the arc length of circle B = 2π units

Let the radius of the circle B = 5 units

Now , The length of an arc in a circle is determined by both the radius of the circle and the central angle that subtends the arc. The formula for calculating the length of an arc in a circle is given by:

Arc length = (Central angle / 360 degrees) x (2πr)

Though two circles' radii differ, they may nevertheless have distinct arc lengths even though their centre angles are the same. Similar to this, if the radii of two circles are adjusted properly, two circles with differing central angles can nevertheless have the same arc length.

Hence , the central angle is solved

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a) To calculate SSTr, we need to first find the overall mean of the samples and then use it to calculate the sum of squares due to treatments (SSTr).

The overall mean of the samples can be found by adding up all the sample means and dividing by the number of samples:

Overall mean = (650 + 750 + 700 + 650) / 4 = 687.5

Next, we can calculate SSTr using the formula:

SSTr = n * (sample mean - overall mean)^2

where n is the number of observations in each sample. In this case, n = 5 for each sample.

So for the first sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5

For the second sample, SSTr = 5 * (750 - 687.5)^2 = 14062.5

For the third sample, SSTr = 5 * (700 - 687.5)^2 = 3062.5

For the fourth sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5

Therefore, the total SSTr is:

SSTr = 5362.5 + 14062.5 + 3062.5 + 5362.5 = 27750

b) The degrees of freedom (df) for SSTr is k-1 where k is the number of groups/populations, and df for SSE is N-k where N is the total number of observations.

df(SSTr) = k - 1 = 5 - 1 = 4

df(SSE) = N - k = 20 - 5 = 15

The mean square for treatments (MSTr) is calculated as:

MSTr = SSTr / df(SSTr) = 12 / 4 = 3

The mean square for error (MSE) is calculated as:

MSE = SSE / df(SSE) = (20 - 5) / 15 = 1

Finally, we can calculate the F-test statistic as:

F = MSTr / MSE = 3 / 1 = 3

Therefore, the MSTr is 3, the MSE is 1, and the F-test statistic is 3.

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There are 6 such paths, so there are 6 outcomes in the sample space that show Casey winning.

We can use a tree diagram to visualize the different outcomes of Casey's rolls:

Each branch of the tree represents one roll of the number cube.

The first two rolls are independent and equally likely to be any of the six numbers.

If the first two rolls are the same number, then Casey gets to roll again. If the third roll is a 6, she wins.

We can count the number of outcomes in the sample space that show Casey winning by counting the number of paths in the tree that lead to a 6 on the third roll.

These are:

1-1-6

2-2-6

3-3-6

4-4-6

5-5-6

6-6 (rolls again)-6

Therefore, the answer is 6.

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Answer:

(x + 4)/x^2 - 8x)

Step-by-step explanation:

The measures of the three angles are 30°, 86° and 64°.

Given that, in a triangle the sum of the measures of the second and third angles is five times the measure of the first angle.

The third angle is 22 more than the second.

If x, y, and z represent the measures of the first, second, and third angles, respectively, we need to find the measure of the angles.

So,

y + z = 5x...........(i)

z - y = 22...........(ii)

x + y + z = 180...........(iii)

Use eq(i) in eq(ii)

x + 5x = 180

6x = 180

x = 30°

Put x = 30 in eq(iii)

z + y = 150.......(iv)

add eq(ii) and eq(iv)

2z = 172

z = 86°

Put the values of z and x in eq(iii)

30° + 86° + y = 180°

y = 64°

Hence, the measures of the three angles are 30°, 86° and 64°.

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Answer:

Sidama Cofee Football Team, the Ethiopian premier league club in Yiregalem, plays 70 percent of their games at night and 30 percent during the day. The team wins 50 percent of their night games and 90 percent of their day games. According to today’s news, they won yesterday. What is the probability the game was played at night?

The possible shapes of the fencing are a parallelogram and a rectangle.

Given that, a worker fences in a construction site using four pieces of fencing that have lengths of 20, yards 16, yards, 20 yards, and 16 yards.

We need to tell possible four-sided shapes that the worker can enclose with the fencing.

So, we can see that, the pair of sides are equal,

Which is condition in a parallelogram and a rectangle.

Hence, the possible shapes of the fencing are a parallelogram and a rectangle.

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Answer:

D

Step-by-step explanation:

The pattern that the scatterplot would suggest, given that they have an exponential relationship is :

A function expressed as y = ab^x or y = a × e^(kx), where a, b, and k are constants represents an exponential relationship between two variables. Exponential functions demonstrate continuous increase or decrease throughout their entire domain; they do not alter direction.

In the event that the base 'b' is greater than 1, or if 'k' is positive, the function increases its output, otherwise, it will decrease when either or both conditions apply ('b' being between zero and one, or 'k' being negative). The concavity of a function is determined by the second derivative which takes on the form of an exponential function for all exponential functions, producing unchanged concavity throughout its entire domain.

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Answer:

(a) Area of the big circle

= π(9^2) = 81π square cm

(b) Area of both little circles

= 2π(4.5^2) = 40.5π square cm

= 81π/2 square cm

(c) Area of the blue section

= 81π - 40.5π = 40.5π square cm

= 81π/2 square cm

After the vertical stretch by factor 3 the function becomes g(x)=3x².

The given function is f(x)=x² is vertically stretched by the factor 3.

When we stretch a function vertically, we multiply the base function by its scale factor. Hence, we have g(x) = 3·f(x). Let’s make sure to distribute 3 to each of the term in f(x).

Here, g(x)=3×x²

g(x)=3x²

Therefore, after the vertical stretch by factor 3 the function becomes g(x)=3x².

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Answer: It's 30.

Step-by-step explanation: The dot at 200 on "Amount Spent" is also right between 20 and 40. Which is 30, your answer.

Answer:

r 0.6 kWh to run for 30 minutes.

Answer:

ok so it takes 1200 watts for a hair dryer to run for a full hour, that means it takes 600 watts, or 600 Wh, or 0.6 kWh to run for 30 minutes

Step-by-step explanation:

Answer:

  (b)  The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.

Step-by-step explanation:

You want the best description of the spread of data shown in the histogram.

The least data value that can be represented on the chart is 6. The greatest value the chart can represent is 25. This means the possible range of data values is ...

  range = max - min = 25 -6 = 19

This possible spread of 19 might mean there is a large difference in the number of trips taken by students, choice B.

__

Additional comment

The range must be at least 21 -10 = 11 trips, not an answer choice. The most common number appears to be in the range 16-20, so will likely not be 10. (This is referred to as the "mode range", as we cannot tell from the grouped data what the actual mode is.)

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After 20 years, the initial investment of $650 will have grown to $2,386.10

Now, let's consider the problem at hand: a $650 investment at 6.5% interest compounded continuously for 20 years. To calculate the final amount of the investment, we can use the formula:

A = P[tex]e^{rt}[/tex]

where A is the final amount, P is the initial investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time (in years).

Plugging in the values given in the problem, we get:

A = 650 x [tex]e^{0.065 \times 20}[/tex]

Simplifying this expression, we get:

A = 650 x [tex]e^{1.3}[/tex]

Using a calculator, we can find that  [tex]e^{1.3}[/tex] is approximately 3.6693. Therefore, the final amount of the investment is:

A = 650 x 3.6693

A = $2,386.10

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The value of function (f - g)(x) will be; 2x² - 3x

Since Function is a type of relation, or rule, that maps one input to specific single output. A Linear function is a function whose graph is a straight line

We are given that the function;

f(x)=-2x²-2x+1

g(x)=x+1

(f - g)(x) = f(x) - g(x)

(f - g)(x) =2x²-2x+1  - (x+1)

(f - g)(x) = 2x²-2x+1  - x - 1

(f - g)(x) = 2x² - 3x

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The expression that can be represented by product (50)*(-5) is 250

Any number that can be expressed as the product of 50 and -5 can be represented using the expression (50)*(-5).

For example, if we multiply 50 and -5, we get -250. Therefore, -250 can be represented using the expression (50)*(-5).

Similarly, if we multiply 50 and -5 by any other number, we can represent the product using the expression (50)*(-5).

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The measure of angle ABC is 30 degrees. Option B

It is important to note the properties of a circle, they include;

Also note that the measure of the angle at the circumference is half to twice the measure of the angle at the center.

From the information given, we have that;

<ADC = 60 degrees

This is the angle at the circle

Then,

<ABC is the angle at the circumference

<ABC = <ADC/2 = 60/2 = 30 degrees

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In conclusion 1324 base 5 = 326 base 8.

To convert the number 1324 in base 5 to base 8, you can follow these steps:

Step 1: Write the given number in expanded form with powers of 5.

1324 base 5 = 1 × 5² + 3 × 5¹ + 2 × 5⁰ + 4 × 5⁻¹

Step 2: Simplify the expression to obtain the decimal equivalent.

1324 base 5 = 25 + 15 + 2 + 0.4 = 42.4

Step 3: Convert the decimal equivalent to base 8 by successive multiplication by 8.

0.4 × 8 = 3.2 (0)

0.2 × 8 = 1.6 (1)

0.6 × 8 = 4.8 (4)

0.8 × 8 = 6.4 (6)

0.4 × 8 = 3.2 (3)

0.2 × 8 = 1.6 (1)

The integer parts obtained in order give the equivalent representation of the number in base 8.

Therefore, 1324 base 5 = 42163 base 8.

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complete question:

How can I convert the number 1324 in base 5 to its equivalent representation in base 8?

The function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2

Given that, a candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour.

We need find function to determine the length of the candle, y, after burning for x number of hours.

Since, the melting rate of the candle is 1/2 per hour,

So, the function will be =

y = 9-x/2

Hence, the function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2

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As our determined t-score (2.77) is larger than the critical t-value (2.262), we disregard the null hypothesis in favor of the alternative one

Given data:

The 1980 mean weight (μ) was 180.4 pounds, while the 2023 sample mean weight (x) was 197.9 pounds;

additionally, the sample size (n) was 10 and the sample standard deviation (σ) was 20 pounds.

At a significance level of 0.05, we calculate the t-score by first dividing (x-μ)/(σ/sqrt(n)).

This gives us the value 17.5/6.32 or 2.77 for the t-score.

Afterward, it is necessary to find the critical t-value with a two-tailed test at a significance level α=0.05 in respect to having 9 degrees of freedom (df = n – 1 = 10 – 1 = 9).

This can be located through either a t-distribution table or an online calculator; the result displays the calculated critical t-value being approximately ±2.262.

As our determined t-score (2.77) is larger than the critical t-value (2.262), we disregard the null hypothesis in favor of the alternative one, signifying there is a glaringly significant disparity between the average mass of grown male adults from 1980 and 2023 which upholds the researcher's statement that since 1980, males in the U.S. have gotten heavier.

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The insurance will pay toward Bob's expenses: $10,000.00.

The insurance will pay toward the wife and daughter's expenses: $11,000.00.

John will be responsible for paying the remaining amount, which is $3,000.00.

The insurance coverage of 10/20 means that the insurance company will pay up to $10,000.00 per person and up to a total of $20,000.00 for the entire accident.

The insurance will pay toward Bob's expenses: $10,000.00 (maximum coverage for one person).

The insurance will pay toward the wife and daughter's expenses: $11,000.00 ($8,000.00 for Mrs. Brownlee and $3,000.00 for the daughter).

John will be responsible for paying the remaining amount, which is $3,000.00 ($12,000.00 + $8,000.00 + $3,000.00 - $20,000.00 insurance coverage).

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Answer:

The insurance will pay toward Bob's expenses: $10,000.00.

The insurance will pay toward the wife and daughter's expenses: $11,000.00.

John will be responsible for paying the remaining amount, which is $3,000.00.

Step-by-step explanation:

The solution to the system of equations is (d) More than 1 solution

From the question, we have the following parameters that can be used in our computation:

3y-12x=18

2y-8x=12

Using the graphing function on a calculator, we have the solution to be

Infinite many solutions

This is so because the equations 3y-12x=18 and 2y-8x=12 are equivalent equations

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The correct fraction that goes in the blank seven over eight > _____> three over five are,

⇒ 2 / 3

We have to given that;

The expression is,

⇒  seven over eight > _____> three over five

Now, We can write as;

⇒ seven over eight > _____> three over five

⇒ 7 / 8 > ___ > 3 / 5

Now, We can fill with fraction as;

⇒ 7 / 8 > 2 / 3 > 3 / 5

Thus, The correct fraction that goes in the blank seven over eight > _____> three over five are,

⇒ 2 / 3

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Statement " There will be 5 dots above 7" is true. Therefore, option D is the correct answer.

A line plot is an effective way to visualize and compare data in a table. In this case, the line plot would show the total number of people on each team, with dots representing the values.

The greatest value in the table is 11, but this would not be represented with a dot in the line plot. There will be 11 dots in total, representing the 11 teams listed in the table.

There will be 4 more dots above 7 than above 8, since there are 4 teams with 7 people on each team and only 3 teams with 8 people on each team.

Finally, there will be 5 dots above 7, since there are 5 teams with 7 or more people on each team.

Therefore, option D is the correct answer.

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Answer:

Step-by-step explanation:

...Negative.

Answer:

Negative

Step-by-step explanation:

A type of association that is seen between the age and height of the children include the following: C. positive linear association.

In Mathematics and Statistics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Therefore, when one variable increases, the other variable generally increases, as well.

By critically observing the scatter plot shown in the image attached above, we can reasonably infer and logically deduce that there is a positive correlation between the x-values (age) and y-values (height) because they both increase simultaneously.

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