What is the decimal equivalent of 5/7 (Round to the nearest hundredth)

The circumference of the circle is given by C = 2 * π * r, where r is the radius. In this case, the circumference of the circle is 2 * π * 14 = 88 cm.

Let's call the linear speed of the object v. Then, in 20 seconds, the object travels a distance of v * 20. This distance is equal to the arc length of the central angle of 1/2 radian:

v * 20 = (1/2) * (C/2π) = (1/2) * (88/2π) = 22/π cm

Solving for v, we get:

v = (22/π) / 20 = 22 / (20π) cm/s

The angular speed ω can be found by dividing the central angle by the time it took to travel that angle:

ω = 1/2 / 20 = 1/40 rad/s

So the linear speed of the object is v = 22 / (20π) cm/s, and the angular speed is ω = 1/40 rad/s.

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Answer:

86

Step-by-step explanation:

I just subtracted 198 and 112

The volume of the tank can be found using the given information as:\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

Assuming that the area bounded is given by a function f(x), the volume of the oil storage tank can be calculated using the formula for the volume of a solid of revolution:

\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

where a and b are the limits of integration. In this case, the axis of revolution is the x-axis, so we are revolving the area about the x-axis.

Therefore, the volume of the tank can be found using the given information as:

\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

We need more information about the function f(x) or a curve that bounds the area in order to find the limits of integration and calculate the volume.

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Answer:

As Per Given Information

Area of Trapezoid is 27cm²

base ,b1 = 13

base , b2 = 5

we have to find the height of trapezoid .

Let the height of trapezoid be h cm .

Area of Trapezoid = ½ ( b1 + b2) × h

On Putting the value we obtain

↝ 27 = ½ ( 13+5) × h

↝ 27 × 2 = 18 × h

↝ 54 = 18 × h

↝ 54/18 = h

↝ 3cm = h

So , the height of trapezoid is 3 cm.

Answer:

$3,700

Step-by-step explanation:

16% of 2500=400

400×3(years)=1,200

2500+1200=3700

The required width of the river is 70 meter

Trigonometric function are sine, cosine, tangent,etc. here we will use tangent function to find the width of the river.

We have given,

distance(d) that she walk along the river = 100m

The angle from her bascline to the tree = 35°

Let we consider width of the river is y,

We know that,

tanθ = y/d

y=dtanθ = (100)tan(35°)= 100×0.7 = 70m

Thus, the width of the river is 70 meter.

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Complete question:

A surveyor measures the distance across a straight river by the following method (Fig. above). Starting directly across from a tree on the opposite bank, she walks  d=100m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is θ=35.0 . How wide is the river?

When using a frequency distribution to identify the interval containing the median, the most useful column is the cumulative frequencies (option d).

The cumulative frequencies provide the running total of the frequencies as you move through the intervals. The median is the middle value of a dataset, and it divides the data into two equal halves. By examining the cumulative frequencies, you can determine the interval that contains the median value.

The cumulative frequencies allow you to track the progression of frequencies as you move through the intervals. When the cumulative frequency exceeds half of the total number of observations (n/2), you have found the interval containing the median.

The cumulative frequencies help you identify this interval by showing you the point at which the cumulative frequency crosses or exceeds the halfway mark. By examining the interval associated with that cumulative frequency, you can determine the interval containing the median value.

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A distribution of the means of two independent groups serves as the comparison distribution for an independent-samples t-test.

By using the one-sample t-test formula

If s is the sample standard deviation, n is the sample size, and x is the sample mean, is the population mean.

The between-groups variance measures the variability of the group means, whereas the within-groups variance measures the variability of the individual scores within the groups. This is a key distinction between variance terms for between-groups and within-groups.

By using the formula,

df = (n1 - 1) + (n2 - 1) (n2 - 1)

where the sample sizes for the two groups are n1 and n2.

The mean of the differences between the scores in the two groups can be used to compute the mean of the difference scores for the original data. The mean of the difference scores would be determined as follows, for instance, if the first group has scores of 3, 5, and 7, while the second group has scores of 4, 6, and 8.

\(\frac{(3 - 4) + (5 - 6) + (7 - 8)}{3}\)

= \(\frac{(-1 + -1 + -1)}{3}\)

= \(\frac{- 3}{3}\)

= -1

The name of the statistical test, the sample sizes, the averages and standard deviations of the groups, the estimated t-value and degrees of freedom, and the p-value would all be included in a report of statistical results that follows proper APA format. The research question and hypothesis being examined should be stated clearly in the report, together with a discussion of the findings and their implications.

The standard error of the difference scores for the provided data can be calculated as

SE = \(((\frac{s12}{n1}) + (\frac{s22}{n2}))\)

where n1 and n2 are the sample sizes, s1 and s2 are the standard deviations of the two groups, and

Calculating the t-value and comparing it to the critical value of t from the appropriate degrees of freedom in the t-distribution is the fifth step in performing a single-sample t-test. The null hypothesis can be rejected if the estimated t-value is greater than the critical value since it shows that the observed differences between the sample and the population are statistically significant.

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As per the given options, the uniform probability distribution can be defined as the probabilities of drawing any individual card in a deck with one draw.

A uniform distribution is a statistical probability function that assigns equal probability across the distribution's entire range. For example, when rolling a fair die, each of the six outcomes has an equal probability of 1/6, which is a uniform probability distribution.

The formula for a Uniform Distribution.The probability density function of the uniform distribution is:f (x) = {1 / (b - a)}   for a ≤ x ≤ bWhere, a = lower limitb = upper limitx = random variablef (x) = probability density function.

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Answer:

37

Step-by-step explanation:

Given :

Sample size, n = 128

Mean, μ = 18

Standard deviation, σ = 5.4

Number of people who lost atleast 15 pounds :

The Zscore = (x - μ) / (σ)

Zscore = (15 - 18) / 5.4

Zscore = - 3 / 5.4

Zscore = - 0.5555

P(Z < - 0.555) = 0.28945

Number of people who lost atleast 15 pounds :

0.28945 * 128 = 37.0496

= 37 people

Answer:

Property of Symmetry

Step-by-step explanation:

The symmetric property of equality tells us that both sides of an equal sign are equal no matter which side of the equal sign they are on. Remember it states that if x = y, then y = x.

Answer:9

Step-by-step explanation:

We'll assume the quadratic equation has real coefficients

Answer:

The other solution is x=1-8i.

Step-by-step explanation:

The Complex Conjugate Root Theorem

if P(x) is a polynomial in x with real coefficients, and a + bi is a root of P(x) with a and b real numbers, then its complex conjugate a − bi is also a root of P(x).

The question does not specify if the quadratic equation has real coefficients, but we will assume that.

Given x=1+8i is one solution of the equation, the complex conjugate root theorem guarantees that the other solution must be x=1-8i.

Answer:

the answer would be x= 1-8i

Step-by-step explanation:

plato said so

Answer:

he included four and does not belong in the quotient

Step-by-step explanation:

i took the test ;)

Answer:

y = -2/3x + 16/3

Step-by-step explanation:

y = -2/3x + b

4 = -2/3(2) + b

4 = -4/3 + b

16/3 = b

The highest frequency of any score in the histogram would be 5/20 = 0.25.

The score that has the highest frequency is 8. This is determined by counting the number of bars corresponding to each score. In this histogram, there are 5 bars corresponding to the score 8, which is the highest number compared to any other score.

Formulaically, we can calculate the frequency for each score by dividing the number of observations for that score by the total number of observations. For the score 8, this would be 5/20 = 0.25. This is the highest frequency of any score in the histogram.

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Answer:7/8

Step-by-step explanation:your mom

Answer:

Area of a cricle:  \(A = \pi r^2\)

Subject of the formula for radius is:

\(r= \sqrt{ \frac{A}{\pi }}\)

Now replacing these values for circle 1, we get:

\(r= \sqrt{ \frac{490.63}{\pi }} = 12.5ft\)

Similar for circle 2:

\(r= \sqrt{ \frac{219.45}{\pi }} = 8.36 in\)

Answer:

please see detailed answers below

Step-by-step explanation:

Area of circle = π r ²

Circumference = π X D (D = diameter = 2 X radius)

1st circle:

Area of circle = π r ²

490.63 = π r ²

r ² = 490.63/π

r = ± √( 490.63/π )  ...... we only need the + (positive result since this is a length).

r = 12.5 feet. Diameter = 2r = 2(12.5) = 25 feet.

2nd circle:

Area of circle = π r ²

219.45 =  π r ²

r² = 219.45/π

r = √(219.45/π )

= 8.36 inches. diameter = 2r = 16.7 inches.

The combination formula can be used to calculate the number of ways that a group of people can be divided into teams of a certain size. In this case, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.

To find out how many ways 18 people can be divided into 2 teams of 9 people, we need to use the combination formula. The formula for combination is nCr = n!/r!(n-r)!, where n is the total number of people and r is the number of people in each team.
In this case, n=18 and r=9. Plugging in the values into the formula, we get:
18C9 = 18!/9!(18-9)! = (18x17x16x15x14x13x12x11x10)/(9x8x7x6x5x4x3x2x1)
Simplifying the expression, we get:
18C9 = 48,620
Therefore, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.
It is important to note that the order of the teams does not matter. For example, team A consisting of 9 people and team B consisting of the remaining 9 people is the same as team B consisting of 9 people and team A consisting of the remaining 9 people.
In conclusion, the combination formula can be used to calculate the number of ways that a group of people can be divided into teams of a certain size. In this case, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.

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Rounding to the nearest hour, it would take the rocket approximately 8 hours to travel to the moon at a speed of 500 miles per minute.

The amount of time it takes a rocket to travel to the moon, we need to divide,

the distance between the earth and the moon (239,000 miles) by the speed of the rocket (500 miles per minute).
So, the calculation would be:

239,000 miles ÷ 500 miles per minute = 478 minutes
To convert this into hours, we need to divide by 60:
478 minutes ÷ 60 = 7.97 hours

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Answer:

-1.25

Step-by-step explanation:

When -8 is divided by 6.4 we get -1.25.

Use the concept of division defined as:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groupings. When dividing numbers, we divide a bigger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

Here we have to find the number when,

-8 divided by 6.4

It can be written as,

-8/6.4

Multiply and divide 10 on both the numerator and denominator,

-80/64

Now divide 80 by 64 then attach the negative sign in the quotient.

The division is attached below.

Hence,

The required number is -1.25.

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Answer:

8m = d

Step-by-step explanation:

Answer:

y²(y + 3)(5y - 3)

Step-by-step explanation:

Given

5\(y^{4}\) + 12y³ - 9y² ← factor out y² from each term

= y²(5y² + 12y - 9) ← factor the quadratic

Consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y- term

product = 5 × - 9 = - 45 and sum = + 12

The factors are + 15 and - 3

Use these factors to split the y- term

5y² + 15y - 3y - 9 ( factor the first/second and third/fourth terms )

= 5y(y + 3) - 3(y + 3) ← factor out (y + 3) from each term

= (y + 3)(5y - 3), so

5y² + 12y - 9 = (y + 3)(5y - 3)

Then

5\(y^{4}\) + 12y³ - 9y² = y²(y + 3)(5y - 3) ← in factored form

Gaussian elimination with partial pivoting can fail due to rounding errors or when a pivot element is very close to zero.

Without knowing the specific system of equations, it is not possible to determine at what point the Gaussian elimination process with partial pivoting would fail using exact arithmetic.

In the latter case, the algorithm can fail to find a suitable pivot and the elimination process can become unstable. This is known as a singularity or numerical instability.

To prevent this, in practice, pivoting strategies are used to avoid dividing by small or zero pivot elements. Additionally, high-precision arithmetic can be used to reduce the impact of rounding errors.

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To find positive numbers x and y that satisfy the given condition, we need to minimize the sum x + y while keeping the product xy constant. We can use the Arithmetic Mean-Geometric Mean (AM-GM) Inequality for this problem. The AM-GM inequality states that the arithmetic mean of a set of non-negative numbers is always greater than or equal to the geometric mean of the same numbers.

In this case, we have two numbers, x and y. The arithmetic mean of x and y is (x + y)/2, and the geometric mean is √(xy). According to the AM-GM inequality, we have:

(x + y)/2 ≥ √(xy)

Multiplying both sides by 2, we get:

x + y ≥ 2√(xy)

Now, we want to minimize the sum x + y, which means we need to find the minimum value for the right-hand side of the inequality. The minimum value occurs when the inequality becomes an equality:

x + y = 2√(xy)

To achieve this equality, x must be equal to y (x = y). This is because the arithmetic mean and geometric mean are equal only when all the numbers in the set are equal. Therefore, x = y and the product xy will have the minimum sum. The exact values of x and y will depend on the given constraint for the product xy.

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To find the determinant of a matrix using row reduction to echelon form, you can follow these steps:

1. Start with the given matrix.

2. Apply row operations to convert the matrix into echelon form. Row operations include multiplying a row by a nonzero scalar, adding a multiple of one row to another, and swapping two rows.

3. Continue performing row operations until you reach the echelon form, where all leading coefficients (the leftmost nonzero entry in each row) are 1 and the entries below leading coefficients are all zeros.

4. Once you have the matrix in echelon form, the determinant can be calculated by multiplying the leading coefficients of each row.

5. If you perform any row swaps during the row reduction process, keep track of the number of swaps. If the number of swaps is odd, multiply the determinant by -1.

Let's look at an example to illustrate these steps. Suppose we have the following 3x3 matrix:

| 2  1  3 |
| 1 -2 -4 |
| 3  0  1 |

Step 1: Start with the given matrix.

Step 2: Apply row operations to convert the matrix into echelon form.

First, we can multiply the first row by -1/2 and add it to the second row, resulting in:

| 2   1   3  |
| 0  -5/2 -5/2|
| 3   0    1  |

Next, multiply the first row by -3/2 and add it to the third row, giving us:

| 2   1   3  |
| 0  -5/2 -5/2|
| 0  -3/2 -8/2|

Finally, multiply the second row by -2/5 to get a leading coefficient of 1:

| 2   1   3  |
| 0   1    1 |
| 0  -3/2 -8/2|

Step 3: The matrix is now in echelon form.

Step 4: Calculate the determinant by multiplying the leading coefficients of each row:

2 * 1 * (-8/2) = -8

Step 5: Since no row swaps were performed, we don't need to multiply the determinant by -1.

Therefore, the determinant of the given matrix is -8.

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The real number √21 is an example of an irrational number. (Correct choice: C)

According to number theory, real numbers are formed by the following sets:

Then, by direct inspection we get the following conclusions:

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The correct graph that models this exponential decay would show a decreasing trend as x (the number of years) increases. we need to consider the information given regarding its decrease in value.

The piece of machinery decreases in value by 22.5% each year. This means that its value after one year is \(100\% - 22.5\% = 77.5\%\) of its original value. In other words, its value is 0.775 times its original value.

To model the value of the machinery after x years, we need to consider the exponential decay function. The general form of an exponential decay function is:

y = \(a(1 - r)^x\)

Where:

- y represents the value after x years.

- a represents the initial value.

- r represents the decay rate (expressed as a decimal).

In this case, the initial value (a) is $150,000 and the decay rate (r) is 22.5% or 0.225.

Therefore, the equation representing the value of the piece of machinery after x years would be:

y = \(\$150,000 * (1 - 0.225)^x\)

Simplifying the equation further, we have:

y = \(\$150,000 * (0.775)^x\)

From this equation, we can see that the value of the machinery decreases exponentially over time. The correct graph that models this exponential decay would show a decreasing trend as x (the number of years) increases.

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x = 3 , y = −4 , and z = −6

z-2xy =

Substitute the value of x,y and z in the expression.

-6-2(3)(-4)

-6-2(-12)

-6+24

18

Answer:

k - 2n = x

Step-by-step explanation:

4^n = 2 ^ 2n

2^k/2^2n = 2^(k-2n) = 2^x

k - 2n = x

Thanks

Answer:

x = k - 2n

Step-by-step explanation:

The main exponent properties

\(a^{m}\) × \(a^{n}\) = \(a^{m+n}\)         ........ (1)

\(\frac{a^{m} }{a^{n} }\) = \(a^{m}\) ÷ \(a^{n}\) = \(a^{m-n}\) ........ (2)

\((a^{m} )^{n}\) = \(a^{m*n}\) = \(a^{mn}\)   ........ (3)

~~~~~~~~~~~~~~~~~~

\(\frac{2^{k} }{4^{n} }\) = \(2^{x}\)

Let apply (3) and (2) exponent properties

L.H. = \(\frac{2^{k} }{(2^2 )^{n} }\) = \(\frac{2^{k} }{2^{2n} }\) = \(2^{k-2n}\)

\(2^{k-2n}\) = \(2^{x}\)  ⇒  x = k - 2n