John is developing a scale model of the solar system for science class where the 1,392,000 km diameter sun is scaled to 1.0 m and given that 1 astronomical unit,

AU, equals 1.5 x 10% km. Determine the scaled distance of Mercury from the sun.

A:28 m

B: 39 m

C: 42 m

D:51 m

The original population is 4,333.33

We have,

After 9 year the population was 183,000.

After 18 year the population was 222,000

So, the rate of change in population

= (222,000 - 183, 000)/ (18-9)

= 39,000/ 9

= 4333.33

So, the original population was 4, 333.33

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Answer:

base=35

Step-by-step explanation:

245/14=17.5

17.5*2=35

(Area of a triangle formula)

Answer:

Base=35 inches

Step-by-step explanation:

245+245=490

490÷14=35

The value of the given integral is\((27/32) \pi.\)

To evaluate the given integral, we need to convert it to polar coordinates.

The region D in the first quadrant bounded by the line y=13, the x-axis, and the circle \(x^2 + y^2 = 3x^2\).

In polar coordinates, the region D is defined by the inequalities:

\(0 \leq r \leq 3cos\theta, 0 \leq \theta \leq \pi/2\)

The integral becomes:

\(\int\int (x^2 + y^2) dA\)

\(= \int\int r^2 r dr d\theta (since x^2 + y^2 = r^2)\)

\(= \int_0^{(\pi/2)} \int_0^{(3cos\theta)} r^3 dr d\theta\)

\(= \int_0^{(\pi/2)}[(1/4r^4)]_0^{(3cos\theta)} d\theta\)

\(= \int_0^{(\pi/2)} (27/4cos^4\theta) d\theta (substituting 3cos\theta for r)\)

\(= (27/4) \int_0^{(\pi/2)} cos^4\theta d\theta\)

To evaluate this integral, we can use the reduction formula for \(cos^n\theta\):

\(\int cos^n\theta d\theta = (1/n) cos^{n-2}\theta sin\theta + [(n-2)/n] \int cos^{n-2}θ d\theta, for n \geq 2\)

Let's apply this formula with n=4:

\(\int cos^4\theta d\theta = (1/4) cos^2\theta sin\theta + (3/4) \int cos^2\theta d\theta\)

\(\int cos^2\theta d\theta = (1/2) (1 + cos2\theta) d\theta\)

\(\int cos^4\theta d\theta = (1/4) cos^2\theta sin\theta + (3/8) (\theta + 1/2sin2\theta) + C\)

Putting everything together:

\(\int\int (x^2 + y^2) dA\)

\(= (27/4) \int_0^{(\pi/2)} cos^4\theta d\theta\)

\(= (27/4) [(1/4) cos^2\theta sin\theta + (3/8) (\theta + 1/2sin2\theta)]_0^{(\pi/2)\)

\(= (27/32) \pi\)

The value of the given integral is\((27/32) \pi.\)

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We must determine the value of y at x = 0.2 in order to numerically solve the equation y = (x + 1) with the initial condition y(0) = 1 and a step size of h = 0.1. The right response is 1.2.

We can utilise the Euler's method or any other numerical integration method to solve the issue numerically. By making small steps of size h and updating the value of y in accordance with the derivative of the function, Euler's approach approximates the value of y at a given x.

We can iteratively proceed as follows, starting with y(0) = 1, as follows:

At x = 0, y = 1.

Y = y(0) + h * f(x(0), y(0)) = 1 + 0.1 * (0 + 1) = 1.1 when x = 0.1.

Y = y(0.1) + h * f(x(0.1), y(0.1)) = 1.1 + 0.1 * (0.1 + 1) = 1.2 for x = 0.2.

So, 1.2 is the right response. This is the approximate value of y at x = 0.2 that was determined by applying a step size of h = 0.1 when solving the given problem numerically.

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Answer:

In a right triangle, as the angle increases, the value of the sine increases.

Step-by-step explanation:

Think of the unit circle, a circle with radius 1 unit centered at the origin which is the point with coordinates (0, 0). Draw a radius of the circle from the center, to point (1, 0) on the positive x-axis. The angle formed by this radius and the positive x-axis is 0 degrees. This is an angle in standard position. The endpoint of the radius on the circle has a y-coordinate. The y-coordinate is the sine of the angle. As you choose points on the circle going up from the positive x-axis, the angle formed by the radius connected to the point on the circle and the positive x-axis increases in measure until it coincides with the positive y-axis, where it has a measure of 90 degrees. The sine of the angle is always the y-coordinate of the point on the circle. As the angle increases from 0 to 90 degrees, the y-coordinate increases from 0 to 1. The acute angles of a right triangle can have measures of only between 0 and 90 degrees.

Answer: In a right triangle, as the angle increases, the value of the sine increases.

9514 1404 393

Answer:

  y -k = m(x -h)

Step-by-step explanation:

To translate a function right by h units, replace x with (x -h).

To translate a function up by k units, replace y with (y -k).

The translated function is ...

  y -k = m(x -h)

_____

Additional comment

You may recognize this as the "point-slope" form of the equation of a line. The "parent function" is the line through the origin with slope m:

  y = mx

The translation above makes it be a line through (h, k) with slope m.

Answer:

Amount earned in 1 hour = $9

In one week Micheal works = 28 hours

So, in one week she gets $9 * 28

=> $252

Hence, she would earn $252 in one week, in Six weeks she will get,

=> $252 * 6 = $1512

If my answer helped, kindly mark me as the brainliest!

Thank You!!

The numbers for 9 faculty members who will be included in the sample are 26, 17, 58, 68, 2, 1, 29, 33, 51

What is a simple random sample?

A subset of a statistical population called a simple random sample is one in which each member has an equal chance of being chosen. A straightforward random sample is intended to offer an unbiased representation of a group.

Given, the President uses technology to produce the following numbers:

26 17 58 68 2 17 1 29 33 51

Now, 9 faculty members will be included in the sample is:

26, 17, 58, 68, 2, 17, 1, 29, 33, 51

In the above data, 17 occurs with repeated frequency then we will make 17 once.

Hence, the required answer is 26, 17, 58, 68, 2, 1, 29, 33, 51

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Answer:

w = 9/2 or 4.5

Step-by-step explanation:

4w + 6 = 6w + (-3)

add 3 to each side,

4w + 9 = 6w

-4w from each side,

9 = 2w

divide each side by 2,

9/2 = w

Step-by-step explanation:

Note: + - 3 = -3, which is why i wrote 6w - 3

4w + 6 = 6w - 3                          CHECK YOUR WORK:

-4w        -4w                         4(4.5) + 6 = 6(4.5) - 3

--------------------------                18 + 6 = 27 - 3

6 = 2w - 3                              24 = 24     when you get answer like 24 = 24,                                              you know your solution for x, in this case 4.5, is correct

+3         +3

-----------------------

9 = 2w

9/2 = 2w/2

4.5 = w

Answer:

Your answer will be y=3x-2

Our form of slope is y=mx+b. B=y intercept...mx=slope y=will usually stay y. The y intercept is at -2 which where the line finally touches that y axis and is why u can see at the end of the equation it says -2. 3 is the slope in the middle because if you start from the y intercept, -2 and go up 3 times and over to the right once you will meet another point. This is called rise over run...the rise is 3 and the run is 1, now we put the rise over run as a fraction, 3/1 which equals 3. Therfore the slope is 3. And if we put those two numbers together you get y=3x-2

The trigonometric ratios of the right triangle can be represented as follows:

tan ∅ =  4 / 5

sec ∅ = √41 / 5

sin ∅ = 4 / √41

A right angle triangle is a triangle that has one of its angles as 90 degrees. The angle of a right angle triangle can be found using trigonometric ratios as follows:

Using trigonometric ratios,

tan ∅ = opposite / adjacent

tan ∅ =  4 / 5

Let's find the hypotenuse side of the right triangle using Pythagoras's theorem.

4²+ 5² = c²

c = √25 + 16

c = √41

Therefore,

sin ∅ = opposite / hypotenuse

sin ∅ = 4 / √41

sec ∅ = 1 / cos ∅ = hypotenuse / adjacent

sec ∅ = √41 / 5

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Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer: Your asnwer is 2.5 lbs Can i have branliest?

Step-by-step explanation:

Answer:

Here is the ans...hope it helps

Answer: 0.045%

Step-by-step explanation:

To solve this problem, we need to use the Central Limit Theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases.

First, we need to find the mean and standard deviation of the sample mean hardness. The mean is simply the population mean, which is given as 50.5. The standard deviation of the sample mean is given by the formula:

standard deviation of sample mean = population standard deviation / sqrt(sample size)

The population standard deviation is given as 0.5, and the sample size is 35, so:

standard deviation of sample mean = 0.5 / sqrt(35) = 0.084

Next, we need to standardize the sample mean hardness using the z-score formula:

z = (sample mean hardness - population mean) / (standard deviation of sample mean)

z = (51 - 50.5) / 0.084 = 5.95

Finally, we need to find the probability that a standard normal distribution is greater than or equal to 5.95. This can be done using a z-table or a calculator. Using a calculator, we get:

P(Z ≥ 5.95) ≈ 0

Therefore, the approximate probability that the sample mean hardness for a random sample of 35 pins is at least 51 is very close to 0.

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The voltage drop across each capacitor in the circuit will be 3 V, 2 V, and 1.5 V, respectively.

It is true that in a series circuit, each capacitor has the same charge, it does not mean that each branch will have the same charge.

In this specific circuit, the charge on the capacitors will be different in each branch, depending on the capacitance of the capacitor and the voltage drop across it.

The total charge on the capacitors in the circuit will be the same.

If we assume that each capacitor has a charge of 6 µC, then the total charge on the three capacitors in the circuit will be:

Q_total = 3 × 6 µC

= 18 µC

The capacitance of each capacitor, we can then calculate the voltage drop across each capacitor using the formula:

Q = CV

Q is the charge on the capacitor, C is its capacitance, and V is the voltage drop across it.

For the capacitor with a capacitance of 2 µF:

V1 = Q/C1

= 6 µC / 2 µF

= 3 V

For the capacitor with a capacitance of 3 µF:

V2 = Q/C2

= 6 µC / 3 µF

= 2 V

For the capacitor with a capacitance of 4 µF:

V3 = Q/C3

= 6 µC / 4 µF

= 1.5 V

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The decimal with the bar is 4.1\(\over6\).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

25/6

= 4.16666666

6 is the repeating number so we put the bar on 6.

= 4.1\(\over6\)

Thus,

The decimal is 4.1\(\over6\).

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Yes, the point (1, -4) is a solution to the given system of equations.

To determine if the point (1, -4) is a solution to the system of equations, we substitute the values of x and y into each equation and check if both equations are satisfied.

Given equations:

y = -4x    ... (1)

y = x - 5  ... (2)

Substituting x = 1 and y = -4 into equation (1):

-4 = -4(1)

-4 = -4

The equation is true when x = 1 and y = -4 in equation (1).

Substituting x = 1 and y = -4 into equation (2):

-4 = 1 - 5

-4 = -4

The equation is also true when x = 1 and y = -4 in equation (2).

Since both equations are satisfied when x = 1 and y = -4, the point (1, -4) is indeed a solution to the given system of equations.

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The probability of obtaining double 6 at least once greater than or equal to 1/2.

Let X be the number of times that double 6 appears when two dice are thrown n times in succession. The probability of obtaining double 6 at least once can be expressed as\(P(X ≥ 1) = 1 - P(X = 0\)).

The probability of not obtaining double 6 at all can be expressed as \(P(X = 0) = (35/36)^n\), since the probability of not getting double 6 in a single trial is 35/36.

Therefore, the probability of obtaining double 6 at least once is \(P(X ≥ 1) = 1 - (35/36)^n\). To make this probability at least 1/2, we need to solve the equation \(1 - (35/36)^n ≥ 1/2\), which yields n ≥ 4.92. Therefore, n must be greater than or equal to 5 to make the probability of obtaining double 6 at least once greater than or equal to 1/2.

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Noel delivered an average of 500 yards of ribbon per day from Tuesday to Monday.

The central value represents the typical or average value of all the numbers in the set.

From Tuesday to Friday, Noel delivered 350 yards of ribbon per day, a total of 4 days. So, the total length of ribbon that he delivered during this period is

=> 4 * 350 = 1400 yards.

From Saturday to Monday, he delivered 700 yards of ribbon per day, a total of 3 days. So, the total length of ribbon that he delivered during this period is

=> 3 * 700 = 2100 yards.

To find the average length of ribbon that Noel delivered per day, we need to find the total length of ribbon he delivered in both periods and divide it by the total number of days.

The total length of ribbon he delivered in both periods is

=> 1400 + 2100 = 3500 yards.

The total number of days is

=> 4 + 3 = 7 days.

So, the average length of ribbon that Noel delivered per day is

=> 3500/7 = 500 yards.

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

After answering the presented question, we can conclude that As a equation result, the $700 suit would sell for $560 during the sale.

An equation is a mathematical statement that validates the equivalent of two expressions linked by the equal symbol '='. For example, 2x - 5 = 13. 2x-5 and 13 are two phrases. The character '=' is used to connect the two expressions. An equation is a mathematical formula that has two algebras on either side of an assignment operator (=). It illustrates the equivalency relationship between the left and middle formulas. In any formula, L.H.S. = R.H.S. (left side = right side).

We can begin by calculating the % price reduction for both the sweater and the jacket:

For the sweater, the percentage decrease is calculated as follows: (original price - reduced price) / original price * 100% = (100 - 80) / 100 * 100% = 20%

For the jacket, the initial price was $300, and the discounted price was $240.

(original price - reduced price) / (original price * 100%) = (300 - 240) / 300 * 100% = 20%

We can use the same percentage reduction to determine the lowered price of the $700 suit:

$700 was the original price.

% reduction = 20% decreased price = original price - % reduction / 100 * original price = $700 - 20 % reduction / 100 * $700 = $560

As a result, the $700 suit would sell for $560 during the sale.

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Answer:

Step-by-step explanation:

Given expressions:

3 of them involves addition, one of them - multiplication

The second expression doesn't belong

Answer:    \(\frac{x^9}{3}\) - \(\frac{7x^4}{5}\) + 9x + C

Step-by-step explanation:

1. Seperate equation

= 3∫x^8dx - 7∫x^4dx + 9∫1dx

2. Solve ∫x^4dx; apply power rule: ∫x^ndx = x^n+1/n+1, where n=8

= x^9/9

3. Solve ∫x^4dx; apply power rule where n=4

= x^5/5

4. Solve ∫1dx; apply constant rule: ∫kf(x)dx = k∫f(x)dx

= x

5. Sub in solved integrals

3∫x^8dx - 7∫x^4dx + 9∫1dx

= \(\frac{x^9}{3}\) - \(\frac{7x^4}{5}\) + 9x

(a) x = -2

Plug in -2 for x in the equation:

2(-2) - 2

Note that when you multiply a negative number and a positive number, the product will be a negative. Also, remember to follow PEMDAS. First, multiply:

2 * -2 = -4

Next, subtract:

-4 - 2 = -6

When x = -2, your answer is -6.

(b) x = 3

Plug in 3 for x in the equation:

2(3) - 2

Remember to follow PEMDAS. First, multiply:

2 * 3 = 6

Next, subtract:

6 - 2 = 4

When x = 3, your answer is 4.

~

Answer:

It is C. r = StartStartRoot (StartRoot 3 EndRoot) squared + (StartRoot 3 EndRoot) squared EndEndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (1) = StartFraction pi Over 4 EndFraction

Step-by-step explanation:

edge2020

The rectangular coordinates (√3,√3) and polar coordinates (√6,\(\frac{\pi}{4}\)) represent the same complex number z=x+iy because,

\(r=\sqrt{(\sqrt3)^2+(\sqrt3)^2}=\sqrt6\) and,

\(\theta=\arctan(\frac{\sqrt3}{\sqrt3})=\arctan(1)=\frac{\pi}{4}\)

The question is not written in an understandable manner look at the question in the below-given image.

In terms of Cartesian coordinates, the polar coordinates r (the radial coordinate) and θ (the angular coordinate, often known as the polar angle),

x = rcosθ

(1)

y = rsinθ, 

(2)

where r is the radial distance from the origin and θ is the counterclockwise angle from the x-axis. In relation to x and y,

\(r=\sqrt{x^2+y^2}\)

(3)

\(\theta=\arctan(\frac{y}{x})\)

Using the above explanation of polar coordinates we have that

\(r=\sqrt{(\sqrt3)^2+(\sqrt3)^2}=\sqrt6\) and

\(\theta=\arctan(\frac{\sqrt3}{\sqrt3})=\arctan(1)=\frac{\pi}{4}\)

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