Use the formula to multiply:
8 x 2/3

Answer:

i) 32100 people

ii) 674100

iii) 5%

Step-by-step explanation:

The population in 2009 was : 642,000

The percent increase was by : 5%

This means the population in 2010 will be :

105/100 * 642000 = 674,100

i) Increase in population is ;  674,100 - 642,000 = 32100 people

ii) The population in 2010 was : 674,100

iii) Population of 2009 = 642000

   Population of 2010 = 674,100

   Increase in population = 674,100 - 642000 = 32100

   Percent increase = increase/ original population * 100

   Percent of increase = 32100/642000 * 100 = 5%

Question: It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

The probability that 2 students do not have the same birthday when 3 students are chosen is given as 0.992.Probability of two students not having the same birthday = 0.992

We need to find the probability that 2 students have the same birthday when 3 students are chosen.

Let's represent the probability that two students have the same birthday by p.

Since the number of possible outcomes when 3 students are chosen from 365 days in a year is 365^3.

Now, we can use the complement rule to find p.

Probability of 2 students having the same birthday

p = 1 - Probability of 2 students not having the same birthday p = 1 - 0.992p = 0.008

Thus, the probability that the 2 students have the same birthday is 0.008.

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Answer:

F(n) =-3n+24

Step-by-step explanation:

Answer:

x = 233.4 feet

y = 318.3 feet

z = 233.4 feet

Step-by-step explanation:

To find side x, we need angle (a) or angle (b) of the right triangle. In this case it is 45 degrees. We also need the hypotenuse and in this case it is 330 feet.

x = 233.35 feet, rounded to x = 233.4 feet

Side (z) is equal to side (x) because both angles (a) and (b) are 45 degrees.

z = 233.35 feet, rounded to z = 233.4 feet

The value of (a) for the top triangle is 84.93 and the value of (x) is 233.35

84.93+233.35 = 318.28

y = 318.3 feet

a) To evaluate the integral ∭f(x²y + 3xyz) dxdydz over the region G, we will apply the given transformation u = x, v = xy, and w = 3z.

The Jacobian matrix of the transformation is:

J = {{∂u/∂x, ∂u/∂y, ∂u/∂z},

{∂v/∂x, ∂v/∂y, ∂v/∂z},

{∂w/∂x, ∂w/∂y, ∂w/∂z}}

Calculating the partial derivatives, we have:

J = {{1, 0, 0},

{y, x, 0},

{0, 0, 3}}

The absolute value of the determinant of the Jacobian matrix is |J| = 3x.

Now we need to express the integral in terms of the new variables:

∭f(x²y + 3xyz) dxdydz = ∭f(u²v + 3uvw) |J| dudvdw.

The new limits of integration are obtained by transforming the limits of the region G:

1 ≤ x ≤ 2 --> 1 ≤ u ≤ 2

0 ≤ xy ≤ 2 --> 0 ≤ v ≤ 2

0 ≤ z ≤ 1 --> 0 ≤ w ≤ 3.

Substituting all the values, the integral becomes:

∭f(u²v + 3uvw) |J| dudvdw = ∭f(u²v + 3uvw) (3x) dudvdw.

Using Mathematica or any other software, you can compute this integralover the new region with the given expression. The result will depend on the specific function f(x, y, z).

b) To evaluate the integral [xy dx + (x+y)dy] along the curve y = x² from (-1,1) to (2,4), we parameterize the curve as follows:

r(t) = ti + t²j, where -1 ≤ t ≤ 2.

The integral becomes:

∫[xy dx + (x+y)dy] = ∫[xt dx + (x+x²)dy].

Now we substitute x = t and y = t² into the integrand:

∫[xt dx + (x+x²)dy] = ∫[t(t) dt + (t+t²)(2t) dt] from -1 to 2.

Simplifying, we have:

∫[xt dx + (x+x²)dy] = ∫[(t² + 2t³) dt] from -1 to 2.

Evaluate this integral using Mathematica or any other software to obtain the result.

c) To evaluate the integral √√(x² + y²) ds along the curve r(t) = (4cost)i + (4sint)j + 3tk, -27 ≤ t ≤ 27, we need to find the derivative of the curve and calculate the magnitude.

The derivative of r(t) is:r'(t) = (-4sint)i + (4cost)j + 3k.

The magnitude of r'(t) is:

|r'(t)| = √((-4sint)² + (4cost)² + 3²) = √(16sin²t + 16cos²t + 9) = √(25) = 5.

Now, we evaluate the integral:

∫√√(x² + y²) ds = ∫√√(x² + y²) |r'(t)| dt from -27 to 27.

Substitute x = 4cost, y = 4sint, and ds = |r'(t)| dt into the integrand:

∫√√(x² + y²) ds = ∫√√(16cos²t + 16sin²t) (5) dt from -27 to 27.

Simplify and evaluate this integral using Mathematica or any other software.

d) To integrate f(x, y, z) = -√√(x² + z²) over the circle r(t) = (acost)j + (asint)k, 0 ≤ t ≤ 27, we need to parameterize the circle.

The parameterization is:

x = 0

y = acos(t)

z = asin(t)

The integral becomes:

∫f(x, y, z) ds = ∫-√√(x² + z²) |r'(t)| dt from 0 to 27.

Substitute x = 0, y = acos(t), z = asin(t), and ds = |r'(t)| dt into the integrand:

∫-√√(x² + z²) ds = ∫-√√(0² + (asint)²) |r'(t)| dt from 0 to 27.

Simplify and evaluate this integral using mathematical methods or any other software.

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The median of the given set of science test scores is 73. Therefore, none of the options provided (A. 68, B. 88, C. 78, D. 58) matches the calculated median of 73.

To determine the median of the given set of science test scores, we need to first arrange the scores in ascending order: 58, 68, 78, 88. The median is the middle value in a dataset when it is sorted in ascending order.

In this case, we have an even number of scores, so we need to find the average of the two middle values. The middle values are 68 and 78. To find the average, we add the two numbers and divide by 2: (68 + 78) / 2 = 146 / 2 = 73.

It seems there may be an error either in the options or in the given set of scores. It's essential to verify the information provided to ensure accurate results.

If the set of scores or the options are incorrect, it may be necessary to obtain the correct information or consult the relevant source to find the accurate median of the science test scores.

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Answer:

Median

Step-by-step explanation:

I took the test myself.

The vector d is approximately |d| = 23.283 at an angle of -10.09 degrees.To find the sum of the vectors analytically, you can add their corresponding components together.

Given: |a| = 8.9 at 26.6 degrees,|b| = 14.1 at 172.9 degrees ,|c| = 6.1 at -80.5 degrees. The x-component of vector d is the sum of the x-components of vectors a, b, and c:

d_x = a_x + b_x + c_x,d_x = 7.958 + 13.96 + 1.007

d_x = 22.925

The y-component of vector d is the sum of the y-components of vectors a, b, and c:

d_y = a_y + b_y + c_y

d_y = 3.958 + (-1.987) + (-6.016)

d_y = -4.045

Therefore, vector d = 22.925 at an angle of arctan(d_y / d_x) degrees.

The magnitude of vector d, |d|, can be calculated using the Pythagorean theorem:

|d| = \(sqrt(d_x^2 + d_y^2)\)

|d| = \(sqrt((22.925)^2 + (-4.045)^2)\)

|d| = sqrt(525.664025 + 16.363025)

|d| = \(sqrt(542.02705)\)

|d| ≈ 23.283

The angle of vector d can be calculated using the inverse tangent (arctan) function: angle_d = arctan(d_y / d_x)

angle_d = arctan(-4.045 / 22.925)

angle_d ≈ -10.09 degrees (approximately)

Therefore, the vector d is approximately |d| = 23.283 at an angle of -10.09 degrees.

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Answer:

189$

Step-by-step explanation:

25 times 5 = 125

0.20 times 320 = 64

125 + 64 = 189

Answer: $189

Step-by-step explanation: So, first of all Alex rents the car for 5 days and then it costs $25 per day. So since he needs it for 5 days you do $25 x 5 and that is equal to $125 dollars. So the next part is his miles. It costs $0.20 so he drove 320 miles. You do $0.20 miles X 320 miles. That is $64. So add $125 + $64 that is equals to $189.

~~~~Inuola1234

To find the longest side of an obtuse triangle, measure all three sides and compare them to determine which one is the longest.

To find the longest side of an obtuse triangle, start by measuring each side of the triangle. Use a measuring tape or ruler to measure the length of each side. Compare the three measurements, and the side with the longest measurement will be the longest side of the triangle. It is important to note that an obtuse triangle is a triangle that has one angle greater than 90 degrees, so it is important to be aware of this when measuring the angles. Once you have the measurements, compare them to determine which one is the longest. The side with the longest measurement will be the longest side of the triangle.

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The correct answer is c. Yhat = 51.39 + 0.4924x1 + 0.2425x2 - 0.2019x3.

Based on the given information, the regression equation for forecasting the value of each lot is:

c. Yhat = 51.39 + 0.4924x1 + 0.2425x2 - 0.2019x3

In this equation, Yhat represents the forecasted value of the lot. The variables x1, x2, and x3 represent the size of the lot, the number of mature trees, and the distance to the lake, respectively. The coefficients 0.4924, 0.2425, and -0.2019 indicate the impact of each variable on the forecasted value.

To estimate the value of a specific lot, the developer would plug in the corresponding values for size, number of mature trees, and distance to the lake into the regression equation. The resulting Yhat would provide an estimate of the lot's value based on the given factors.

It is important to note that the regression equation is based on the gathered data from the nearby area and the assumption that the relationship between the variables in that area holds true for the lots in question. The accuracy of the regression equation's predictions relies on the quality and representativeness of the data used for its development.

Therefore, the correct answer is c. Yhat = 51.39 + 0.4924x1 + 0.2425x2 - 0.2019x3.

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The eigenvalues of matrix a are λ1 = 17 + 3i and λ2 = 17 - 3i, and the corresponding eigenspaces are spanned by the bases {(13/14-3i), 1} and {(13/14+3i), 1}, respectively.

What are complex numbers?

Complex numbers are numbers that consist of a real part and an imaginary part. They are represented in the form a+bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

To find the eigenvalues of matrix a, we need to solve the characteristic equation det(a-λI) = 0, where I is the identity matrix and det is the determinant.

a = 31 -13

-1 3

The characteristic equation is:

det(a-λI) =

|31-λ -13|

|-1 3-λ| = 0

Expanding the determinant, we get:

(31-λ)(3-λ) - (-13)(-1) = 0

(31-λ)(3-λ) + 13 = 0

λ^2 - 34λ + 190 = 0

Using the quadratic formula, we get:

λ1 = 17 + 3i

λ2 = 17 - 3i

To find the eigenvectors corresponding to each eigenvalue, we need to solve the system of equations (a-λI)x = 0, where x is the eigenvector.

For λ1 = 17 + 3i:

(a-λ1I)x =

|31-(17+3i) -13|

|-1 3-(17+3i)|x = 0

Simplifying, we get:

|14-3i -13| |x1| |0|

|-1 -14-3i| * |x2| = 0

From the first row, we get:

(14-3i)x1 - 13x2 = 0

x1 = (13/14-3i)x2

Substituting into the second row, we get:

-x2 - (14+3i)(13/14-3i)x2 = 0

x2 = -(14+3i)(13/14-3i)x2

Thus, a basis for the eigenspace corresponding to λ1 is:

{(13/14-3i), 1}

For λ2 = 17 - 3i:

(a-λ2I)x =

|31-(17-3i) -13|

|-1 3-(17-3i)|x = 0

Simplifying, we get:

|14+3i -13| |x1| |0|

|-1 -14+3i| * |x2| = 0

Following the same steps as for λ1, we obtain a basis for the eigenspace corresponding to λ2:

{(13/14+3i), 1}

Therefore, the eigenvalues of matrix a are λ1 = 17 + 3i and λ2 = 17 - 3i, and the corresponding eigenspaces are spanned by the bases {(13/14-3i), 1} and {(13/14+3i), 1}, respectively.

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For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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The average increase in flower count is 42.

The average is the ratio created by dividing the total number of figures in a set by the number of elements

Fowers pollinated in this instance is f(x), where x is the number of days. The nunumber of figures.The number of flmber of flowers that were pollinated between days 4 and 10 as well as on those days must first be determined.

F(4) = 3(4^2) = 3*16 = 48

F(5) = 3(5^2) = 3*25 = 75

F(6) = 3(6^2) = 3*36 = 108

F(7) = 3(7^2) = 3*49 = 147

F(8) = 3(8^2) = 3*64 = 192

F(9) = 3(9^2) = 3*81 = 243

F(10) = 3(10^2) = 3*100 = 300

The average of the day-to-day variations will be

[(75-48)+(108-75)+(147-108)+(192-147)+(243-192)+(300-243] in order to obtain the average increase.

=(27+33+39+45+51+57)/6=42

There the average increase in the number of flowers pollinated per day is 42

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Each side of cube is 100 cm.

In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

Given that,

Volume of cube = 1 cubic meter

We know that,

1 m = 100 cm

Also  volume of cube = \(a^{3}\)

Then,

Volume of cube = 1000000 cm

                   \(a^{3}\)  = \(100^{3}\)

                   a = 100 cm

Hence, Each side of cube is 100 cm.

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Answer: Red ribbon.

Step-by-step explanation:

When it comes to fractions, if all the fractions being compared have the same numerator, the fraction with the smallest denominator is the largest.

In this question, all the fractions have a numerator of 1 so the longest one will be the one with the smallest denominator which is 1/3. The red ribbon is the longest.

Another way is to convert them to percentages:

1/6 * 100% = 16.7%

1/3 * 100% = 33.3%

1/4 * 100% = 25%

Red ribbon is again the largest.

Answer:

301.7 cm

Step-by-step explanation:

Given,

Height of cone (h)=8cm

base radius (r)=6cm

Volume of the cone (V)=

3

1

πr

2

h

=

3

1

×

7

22

×6×6×8

=

7

2112

=301.7cm

3

Hence, volume of the cone =301.7cm

3

Answer:

402.1402.1 cm

Step-by-step explanation

height = 6cm

Radius= 8cm

After 7 days, there is $78 left in Xavier's account with a lunch food budget of $120per month by spending an average of $6 per day

An average value, also known as the mean, is a numerical value that summarizes a set of data. It represents the central tendency of a data set and provides a general sense of what is typical or a typical value in the data.

It is calculated by summing up all the values in a data set and then dividing the sum by the number of values in the set. The result is a single value that summarizes the data set as a whole.

For example, if  a set of test scores are {80, 75, 90, 85, 95}, the average value would be calculated as follows:

(80 + 75 + 90 + 85 + 95) / 5 = 425 / 5 = 85

So, in this case, the average value is 85, which provides a general sense of the typical performance of the group.

Assume the amount of money left in Xavier's account after x days "f(x)".

Since Xavier has a lunch food budget of $120 per month, and he spends an average of $6 per day on lunch, write the function f(x) as follows:

f(x) = 120 - 6x

To find the amount of money left in Xavier's account after 7 days, plug in

x = 7 into the function:

f(7) = 120 - 6 * 7 = 120 - 42 = 78

So, after 7 days, there is $78 left in Xavier's account.

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The angles involved are acute angles, which means that 3θ+10° < 90°. Using the identity that sin x = cos (90°-x), we can write: sin(θ-40°) = cos(80°-3θ)θ-40° = 80°-3θ4θ = 120°θ = 30°.Therefore, θ = 30°.

tan(2B-29°) = cot(4B+5°)B = 42°We need to find the value of B.

We can do this by using the identity that says tan x = cot (90°-x).

Let's start by substituting the angles into the equation.

tan(2B-29°) = cot(4B+5°)tan(2B-29°) = tan(90°- (4B+5°))

The angles involved are acute angles, which means that 4B+5° < 90°. Using the identity that tan x = cot (90°-x), we can write:

tan(2B-29°)

= tan(85°-4B)2B - 29°

= 85° - 4B6B = 114°B

= 19°.

Therefore, B = 19°.2. sin(θ-40°) = cos(3θ+10°)We need to find the value of θ.

We can use the identity sin x = cos (90°-x) to solve this equation.

Let's begin by substituting the angles into the equation.

sin(θ-40°) = cos(3θ+10°)sin(θ-40°) = sin(90°- (3θ+10°))

The angles involved are acute angles, which means that 3θ+10° < 90°.

Using the identity that sin x = cos (90°-x), we can write: sin(θ-40°) = cos(80°-3θ)θ-40° = 80°-3θ4θ = 120°θ = 30°.Therefore, θ = 30°.

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Amani earns 59 dollars in a week if she sells 18 books.

Amani earns a base amount of $41 per week for working part-time at the bookstore. In addition to that, she earns an extra dollar for each book she sells. The equation A = 41 + b represents her total earnings, where A represents the amount she earns and b represents the number of books she sells.

To find out how much Amani earns in a week if she sells 18 books, we substitute the value of b (18) into the equation:

A = 41 + 18

This simplifies to:

A = 59

Therefore, if Amani sells 18 books in a week, she will earn $59.

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An inverse variatiοn includes the pοints (8, 3) and (2, n), the value οf n is 12.

Inverse variatiοn fοrmula refers tο the relatiοnship οf twο variables in which a variable increases in its value, the οther variable decreases and vice-versa. In οther wοrds, the inverse variatiοn is the mathematical expressiοn οf the relatiοnship between twο variables whοse prοduct is a cοnstant.

Using the given pοints, we can set up a prοpοrtiοn tο find k:

8 * 3 = k

2 * n = k

Setting the twο expressiοns fοr k equal tο each οther, we get:

8 * 3 = 2 * n

24 = 2n

Dividing bοth sides by 2, we get:

n = 12

Therefοre, the value οf n is 12.

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Answer:

y=1/2x+6

Step-by-step explanation:

Change to slope intercept form: y=1/2x-2

Take out the b term

Plug in point (-8, 2)

Get b as 6

Plug in b

Get y=1/2x+6

The empirical (68-95-99.7) rule, also known as the three-sigma rule or the standard deviation rule, applies to the bell-shaped distribution. we can estimate that the percentage of 1-mile-long roadways with potholes numbering between 32 and 65 is approximately 95%. is the answer.

The 68-95-99.7 rule gives a rough approximation of the percentage of data values that fall within certain distances from the mean. It states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations of the mean. In this question, the mean of the distribution is 43 and the standard deviation is 11.

To find the percentage of 1-mile-long roadways with potholes numbering between 32 and 65, we first need to determine how many standard deviations away from the mean these values are.

Using the formula for z-score (z = (x - µ) / σ), where x is the data value, µ is the mean, and σ is the standard deviation, we get: z for 32 = (32 - 43) / 11 = -1z for 65 = (65 - 43) / 11 = 2

Therefore, 32 is one standard deviation below the mean and 65 is two standard deviations above the mean.

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% falls within two standard deviations.

Since 32 is within one standard deviation below the mean and 65 is within two standard deviations above the mean, we can estimate that the percentage of 1-mile-long roadways with potholes numbering between 32 and 65 is approximately 68% + 95% = 163%.

However, since the values are outside the normal range, we cannot use the empirical rule to get an accurate percentage.

Therefore, we can estimate that the percentage of 1-mile-long roadways with potholes numbering between 32 and 65 is approximately 95%.

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There are 15 blue counters in the bag.

Two quantities are compared to form a ratio. An equality of two ratios is a proportion.

We know that the initial ratio of red counters to blue counters was 4:5. Therefore, we can write:

4x : 5x

We also know that 10 more red counters were added to the bag. Therefore, the new number of red counters in the bag is:

4x + 10

The ratio of red counters to blue counters then became 6:5. Therefore, we can write:

(4x + 10) : y = 6 : 5

We can simplify this equation by cross-multiplying:

5(4x + 10) = 6y

20x + 50 = 6y

Dividing both sides by 6, we get:

y = (20x + 50)/6

Simplifying, we get:

y = (10x + 25)/3

Since y has to be a whole number, 10x + 25 has to be divisible by 3. The only value of x that satisfies this condition is x = 2.

Therefore, the initial number of red counters was 4x = 8, and the initial number of blue counters was 5x = 10.

After adding 10 more red counters, the new number of red counters was 18, and the new ratio of red counters to blue counters was 6:5.

To find the new number of blue counters, we can use the equation we derived earlier:

y = (10x + 25)/3

Substituting x = 2, we get:

y = (10(2) + 25)/3 = 15

Therefore, there are 15 blue counters in the bag.

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Answer:

oni chan chu papi

Step-by-step explanation:

Answer:

$42,840

Step-by-step explanation:

yw yw guysss

Step-by-step explanation:

A student divided the given number by 100 that resulted to 28.003 in his chart. So what we are looking for in the given situation is that the value of the number before it was divided by 100.

To get the desired value, we can simply multiply the obtained result by 100

=> 28.003 x 100

=> 2800.3

So, by dividing 100 to the given number, we simply move the value to the right in a value of hundreds.

Answer:

59

Step-by-step explanation:

i hope this halp

Answer:

Step-by-step explanation:

-0.5