The length of a planet's orbit around a star is approximately 18,950,000 km.
It takes the planet about 940 Earth days to complete a full orbit.
What is the planet's average speed in kmh-1 to 3sf?

Answer:

6.3 ft

Step-by-step explanation:

To find:-

Answer:-

We are here given that 40ft tree casts a shadow of 12foot . We are interested in finding out the height of the shadow casted by a 21ft tree .

Here we can use Unitary Method to find out the height of the shadow as ,

A 40ft tree casts a shadow of 12ft .

A 1ft tree would cast a shadow of 12/40ft .

A 21 ft tree would cast a shadow of 12/40*21 = 6.3 ft

Hence the height of shadow casted by a 21ft tree is 6.3ft .

TRUE. The pressure to increase profitability and improve operational efficiencies is a common driver for organizations to implement new approaches and technology.

The pressure to increase profitability and improve operational efficiencies often drives organizations to implement new approaches and technology. By adopting innovative methods and leveraging technology, companies can streamline processes, reduce costs, and enhance their overall performance, contributing to higher profits and a competitive advantage in the market. The pressure to increase profitability and improve operational efficiencies is a common driver for organizations to implement new approaches and technology. By adopting innovative methods and leveraging technology, companies can streamline processes.

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Answer:

47%

Step-by-step explanation:

% error = ( (theoretical(correct) – experimental(prediction)) / theoretical(correct) ) × 100%.

% error = |17 – 25| / 17 × 100% =

% error = (8 / 17 × 100)%

% error = (800 / 17)%

% error = (47.0588235294..)%

% error ≈ 47%

The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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Answer:

it is c $10.80

The sales tax on clothing that costs $180 is $10.80 with 6% sales tax. The correct answer is option c.

Given that:

The cost of cloth is $180.

Sales tax is 6%.

To calculate the sales tax on clothing that costs $180 at a rate of 6%, follow these steps:

Convert the sales tax rate to a decimal: 6% = 6/100 = 0.06

Sales tax can be calculated by using the formula given below:

Sales tax = Cost of clothing × Tax rate

Multiply the clothing cost by the sales tax rate to find the sales tax amount:

Sales tax = Cost of clothing × Tax rate

Sales tax = $180 × 0.06 = $10.80

Hence, the required value is $10.80. The correct answer is option c.

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Answer:

Answer:

Raff = 38

Suzie = 19

Step-by-step explanation:

Raff gets 2x

Suzie gets x

2x + x = 57 dollars

3x = 57 dollars

x = 19 dollars

2x = 38 dollars

Answer:

b.) 5t+1-4t^2/t^2(t+1)

Step-by-step explanation:

The triangle midsegment is a very important concept in geometry, and the triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side and has a length equal to half of the length of the third side

The triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side of the triangle and has a length that is equal to half of the length of the third side.

In this explanation, we will define the midsegment of a triangle and explain the triangle midsegment theorem in more detail.

To begin, let's consider a triangle ABC with midpoints D and E on sides AB and AC respectively. The segment DE is the midsegment of triangle ABC.

According to the triangle midsegment theorem, the length of DE is equal to half the length of the third side of the triangle, BC. Mathematically, this can be represented as follows:

DE = BC/2

In addition to the length, the midsegment of a triangle is also parallel to the third side. This means that if we extend the midsegment, it will eventually intersect the third side of the triangle.

The triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side and also has the same length as half of the third side.

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Answer:

so what is the question pls brief it up

Answer:

CAN U CUMMM?

Step-by-step explanation:

The length of |PR| as shown in the diagram is 9.3.

Length is the distance between two points.

To calculate the length of PR, we use the formula below

Note:

Formula:

From the question,

Given:

Substitute these values into equation 1 and solve for y

Hence,  |PR|  = 9.3

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The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:

3 boxes I believe

Step-by-step explanation:

6 friends want 5 cookies each

6×5=30

if there are 12 cookies in each box then 2 boxes would be 24 cookies and 3 boxes would be 36 cookies. there would be left over cookies but there would be enough for monas friends

Answer:

We can use a system of equations to solve this problem. Let x be the number of 1-point shots and y be the number of 2-point shots.

The first equation represents the total number of shots taken:

x + y = 55 (1)

The second equation represents the total number of points scored:

x + 2y = 91 (2)

To solve for x and y, we can use the first equation to substitute for one of the variables in the second equation. Using (1) to substitute for x in (2):

y = 55 - x

Then substitute this value of y in equation (1)

x + (55 - x) = 55

Solving for x, we get:

x = 20

So the team made 20 1-point shots and 35 2-point shots.

Answer:

There are:

19 1-point shots

36 2-point shots

Step-by-step explanation:

Solve for the system of equations. The first equation will give you the value based on the total amount of points, while the other equation will be based on the amount of shots in total:

It is given that the team scores 91 points in all, and that they are all 1- and 2- point shots (no 3 pointers). Set the equation. Let x = 1-point shots, and y = 2-point shots:

x + y = 55

1x + 2y = 91

First, isolate the variable, y, in the first equation. Subtract x from both sides of the equation:

y + x = 55

y + x (-x) = 55 (-x)

y = 55 - x

Next, plug in 55 - x for y in the second equation:

x + 2y = 91

x + 2(55 - x) = 91

Then, simplify. First, distribute 2 to all terms within the parenthesis:

2(55 - x)

= (2 * 55) - (2 * x)

= 110 - 2x

x + 110 - 2x = 91

First, combine like terms. Like terms are terms that share the same amount of the same variable:

(x - 2x) + 110 = 91

-x + 110 = 91

Then, isolate the variable, x. First, subtract 110 from both sides of the equation:

-x + 110 (-110) = 91 (-110)

-x = 91 - 110

-x = -19

Isolate the variable, x, completely, by dividing -1 from both sides of the equation:

(-x)/-1 = (-19)/-1

x = -19/(-1)

x = 19

~

Plug in 19 for x in one of the given equations in the system of equations:

x + y = 55

19 + y = 55

Isolate the variable, y, by subtracting 19 from both sides of the equation:

y + 19 = 55

y + 19 (-19) = 55 (-19)

y = 55 - 19

y = 36

~

There are 19 1-point shots & 36 2-point shots

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Answer:

The answer I got was 2. hope that helps.

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

Answer:

I think it's a clockwise rotational symmetry from the centre of the circle.

Answer:

It is a right triangle

Step-by-step explanation:

The growth constant is 0.69 and the population will increase to 12900 after approximately 3.7 years.

We have, Sunset Lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. Assuming logistic growth with a carrying capacity of 25000,

The logistic growth model is given by the equation

dN/dt=rN[(K-N)/K]

where, dN/dt = rate of change of population with respect to time,

N = population size at time t,

r = intrinsic rate of natural increase (growth constant),

K = carrying capacity.

The population size, "N" after 1 year = 7050

The initial population, "N₀" = 2500

The carrying capacity, K = 25000

We can use the following formula to find the value of the growth constant,

r = 2.303/t{ln(N_t/N₀) }........... (1)

Where, t = time taken for the population to increase from N_0 to N_t= 1 year (given)

Substituting the given values in equation (1), we get

r = 2.303/1 ln(7050/2500) ⇒ 0.688 ≈ 0.69

The value of the growth constant is 0.69.

Now, we can use the logistic growth equation to find the time required for the population to reach 12900.

dN/dt=rN[(K-N)/K]

Given, N₀ = 2500 and K = 25000

Differentiating both sides with respect to t,

dN/dt = rN[(K-N)/K] + Ndr/dt

Substituting the values of N, r, and K in the above equation, we get,

dN/dt= 0.69N[(25000-N)/25000] + N{dN/dt}

Let the population N become 12900 at time t = t₁

Therefore, at time t = 0, the population N₀ = 2500

Also, at time t = 1, the population N₁ = 7050

Substituting these values in the above equation, we get,

dN/dt= 0.69N[(25000-N)/25000] + N₁

dN/dt= 0.69(2500)[(25000-2500)/25000] + N₁

Solving for N₁, we get, N₁ = 7825

Substituting N₁ = 7825 in the above equation,

dN/dt= 0.69(7825)[(25000-7825)/25000] + N₁

dN/dt= 3263.25/1.69 ⇒ 1930.4

Now, to find t1, we can use the following formula;

ln[(K-N₁)/(K-N₀)] = rt₁

Substituting the given values, we get,

ln[(25000-12900)/(25000-2500)] = 0.69t₁

On solving for t₁, we get;

t₁ = ln[(1575/22500)]/0.69 ≈ 3.7 years

Hence, the population will increase to 12900 after approximately 3.7 years.

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Answer:

-38

Step-by-step explanation:

4-(3^4-6^2)+2(3)÷2

=>     4 - (81-36) + 2(3) ÷ 2      

=>     4 -  45 + 2(3)÷2

=>     4 -  45 + 6÷2

=>     4 -   45 + 3

=>     -41 + 3

=>     - 38

hope this helps :)

The two operations needed to write the expression are division and subtraction.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

The given expression in words is "five less than the quotient of a number and three".

The expression can be mathematically written as for a given number x is x/3 - 5.

Here a number x is divided by 3 at first.

So the first operation is division.

The quotient of this has been subtracted by 5.

So the next operation is division.

Hence the two operations used here are subtraction and division.

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Answer:

578 cm^2

Step-by-step explanation:

The surface area is given by one circle of radius 4 (the other is missing!), plus a "rectangle" (the lateral surface) of sides 21 and \(2\pi \times 4\) (the length of the circumference at the base). Adding them up we get:\(\pi \times4^2 + 21\times 2\pi\times4 = 184\pi \approx 578 cm^2\)

To estimate the integral √(ln(2)) ln(x) dx within an accuracy of 0.01 using upper and lower sums for a uniform partition of the interval [1, e], we need to divide the interval into at least n subintervals. The answer is obtained by finding the minimum value of n that satisfies the given accuracy condition.

We start by determining the interval [1, e], where e is approximately 2.718. The function ln(x)^2 is increasing, meaning that its values increase as x increases. To estimate the integral, we use upper and lower sums with a uniform partition. In this case, the width of each subinterval is (e - 1)/n, where n is the number of subintervals.

To find the minimum value of n that ensures the accuracy condition S - S < 0.01, we need to evaluate the difference between the upper sum (S) and the lower sum (S) for the given partition. The upper sum is the sum of the maximum values of the function within each subinterval, while the lower sum is the sum of the minimum values.

Since ln(x)^2 is increasing, the maximum value of ln(x)^2 within each subinterval occurs at the right endpoint. Therefore, the upper sum can be calculated as the sum of ln(e)^2, ln(e - (e - 1)/n)^2, ln(e - 2(e - 1)/n)^2, and so on, up to ln(e - (n - 1)(e - 1)/n)^2.

Similarly, the minimum value of ln(x)^2 within each subinterval occurs at the left endpoint. Therefore, the lower sum can be calculated as the sum of ln(1)^2, ln(1 + (e - 1)/n)^2, ln(1 + 2(e - 1)/n)^2, and so on, up to ln(1 + (n - 1)(e - 1)/n)^2.

We need to find the minimum value of n such that the difference between the upper sum and the lower sum is less than 0.01. This can be done by iteratively increasing the value of n until the condition is satisfied. Once the minimum value of n is determined, we have the required number of subintervals for the given accuracy.

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Since this equation must hold for all values of x, we can substitute x = i and x = -i to get two equations: 2A + 3i = -5i=> 2A - 3i = 5i=> A = -3/2Therefore, A is equal to -3/2.

A polynomial is a mathematical statement with coefficients and uncertainty that uses only additions, subtractions, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to an expression in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression having variables and coefficients. Only addition, subtraction, multiplication, and non-negative integer exponents are permitted in expressions. The word for these expressions is polynomials.

To find A, we need to perform polynomial long division of P(x) by \(x^2 + 1\)and get the remainder equal to -5x.

          x

   --------------

\(x^2 + 1 | x^3 + 3x^2 - 2Ax + 3\)

         \(x^3 + 0x^2 + x\)

          --------------

               \(3x^2 - 2Ax\)

           \(3x^2 + 0x - 3i\)

                ------------

                    \(2Ax + 3i\)

                \(2Ax + 0x - 2iA\)

                       -----------

                        \(3i + 2iA\)

The remainder of the division is (2A + 3i) when the divisor is \(x^2 + 1\). We know that this remainder is equal to -5x, so we can set up the equation:

2A + 3i = -5x

Since this equation must hold for all values of x, we can substitute x = i and x = -i to get two equations:

2A + 3i = -5i

2A - 3i = 5i

A = -3/2

Therefore, A is equal to -3/2.

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We have explained the ASA rule of congruency of the triangle

What is an ASA congruency of triangles?

ASA Congruence. Angle-Side-Angle. If two angles in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent.

If a triangle PQR is congruent to a triangle ABC, we write it as ∆ PQR ≅ ∆ ABC.

Note that when ∆ PQR ≅ ∆ ABC, then sides of ∆ PQR fall on corresponding equal sides of ∆ ABC and so is the case for the angles.

This means that PQ covers AB, QR covers BC, and RP covers CA;

∠P, ∠Q, and ∠R cover ∠A, ∠B, and ∠C respectively.

Also, between the vertices, there is an existence of one-one correspondence.

That is, P corresponds to A, Q corresponds to B, R corresponds to C and it is written as

P↔A, Q↔B, R↔C

Under this condition, the correspondence ∆ PQR ≅ ∆ ABC is true but is not correct for the correspondence ∆QRP ≅ ∆ ABC.

Hence, we have explained the ASA rule of congruency of the triangle

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Answer:

9 * pi inches squared

Step-by-step explanation:

The probability that two red balls are chosen from the vase would be = 1/9

Probability is defined as the concept that proves that an event may occur or not.

The number of red balls = 7

The number of black balls = 2

The number of green balls = 9

The total number of balls in the vase = 18

The probability of getting 2 red balls = 2/18 = 1/9

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We know that the value x we are looking for is even, and is greater than 6 and less than 10.

We start with the condition of being even.

Then x can be 2, 4, 6, 8, 10, 12, 14...

If we know that is greater than 6, we can eliminate 2, 4 and 6 from the list.

x can be: 8, 10, 12, 14...

If we know that x is less than 10, we can eliminate 10 and all the values above 10.

Then, x is 8, as it is the only value left in the list of possible values.

Answer: the number is 8.

If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .

In the question ,

it is given that ,

the number of residents in the local apartment complex is = 71

the mean electric bill for the 71 residents = $62 ;

we know that the sample mean is itself called as the best point estimate ;

So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of  local apartment complex which is given as $62 .

Therefore , the best point estimate is $62 .

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The p-value is a statistical term that represents the probability of observing an outcome as extreme as or more extreme than the observed outcome, given that the null hypothesis is true. It is used to determine whether the null hypothesis should be rejected or accepted. If the p-value is less than the level of significance (alpha), the null hypothesis can be rejected, and the alternative hypothesis can be accepted.

Large p-values indicate that there is not enough evidence to reject the null hypothesis. A large p-value implies that the observed result is not significant, and the null hypothesis is supported.

The alpha level is a significance level that is set in advance of conducting a hypothesis test. It determines the level of evidence required to reject the null hypothesis. The alpha level is usually set at 0.05, meaning that the null hypothesis can be rejected if the p-value is less than 0.05.

A result is statistically significant if it is unlikely to have occurred by chance. In other words, if the p-value is less than or equal to the alpha level, the result is considered statistically significant, and the null hypothesis can be rejected.

A 95% confidence interval corresponds to a two-sided hypothesis test at an alpha level of 0.05. This means that the null hypothesis can be rejected if the observed outcome falls outside the confidence interval with a probability of 0.05 or less.

A 90% confidence interval corresponds to a one-sided hypothesis test at an alpha level of 0.1. This means that the null hypothesis can be rejected if the observed outcome falls outside the confidence interval with a probability of 0.1 or less.

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When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?