What is the mean and median of 38,22,23,41

The terminal point P(x, y) on the unit circle determined by the given value of t = 9π/2 is (0, -1).

A terminal point is a point at which a line or curve ends. An example of a terminal point is the point where the line x=5 ends. This point is 5 on the x-axis and has no y-value because the line does not extend beyond that point.

Another example of a terminal point is the point where the circle x2 + y2 = 25 ends. This point is (5,0), where x=5 and y=0. This means that the circle has a radius of 5 and the point (5,0) is the end of the circle.

The unit circle is centered at the origin (0, 0) and has a radius of 1. To find the terminal point with an angle of 9π/2, use the trigonometric functions sine (sin) and cosine (cos).

By calculating the x-coordinate of the point. This can be done using cosine:

x = cos(9π/2)

Since cosine of an angle of 9π/2 is equal to 0, the x-coordinate of the point is 0.

Calculate the y-coordinate of the point. This can be done using sine:

y = sin(9π/2)

Since sine of an angle of 9π/2 is equal to -1, the y-coordinate of the point is -1.

Therefore, the terminal point P(x, y) on the unit circle determined by the given value of t = 9π/2 is (0, -1).

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Answer:

x = 11

Step-by-step explanation:

divide both sides by 7

x = 11

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

He is on the 5th floor

Step-by-step explanation:

9 - 2 = 7

7 + 4 = 11

11 - 6 = 5

Answer:

he goes 1 +9=10

10-2=8

8+4=12

12-6=6

so he is ont the sixth floor

Answer:

-4

Step-by-step explanation:

Find the gradient of the line segment between the points (0,2) and (-2,10).​

Given data

x1= 0

x2= -2

y1= 2

y2=10

The expression for the gradient is given as

M= y2-y1/x2-x1

substitute

M= 10-2/-2-0

M= 8/-2

m= -4

Hence the gradient is -4

In water, a strong acid will dissociate completely into its component ions, while a weak base will undergo partial dissociation.

When a strong acid is dissolved in water, it will dissociate completely into its component ions. For example, if we consider hydrochloric acid (HCl), it will dissociate into hydrogen ions (H+) and chloride ions (Cl-) in water:

HCl → H+ + Cl-

In contrast, a weak base will undergo partial dissociation in water. It will only release a fraction of its component ions. For example, if we consider ammonia (NH3) as a weak base, it will partially dissociate into ammonium ions (NH4+) and hydroxide ions (OH-) in water:

NH3 + H2O ⇌ NH4+ + OH-

The equilibrium arrow (⇌) indicates that the reaction can occur in both directions, with the weak base partially dissociating and reforming in water.

The difference between strong acids and weak bases lies in their ability to dissociate in water. Strong acids have strong bonds that easily break in water, leading to complete dissociation. On the other hand, weak bases have weaker bonds, resulting in partial dissociation.

It's important to note that the degree of dissociation for weak bases can vary depending on factors such as concentration and temperature. However, in general, weak bases do not completely break down into their component parts like strong acids do in water.

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it will take approximately 13.4 years for the combine harvester to lose half of its value.

What are exponential decay function?

These are exponential functions that reduce in value as the input value increases.

We can use the formula for exponential decay to determine the value of the combine harvester after t years:

\(V = V_{0} (1 - r)^t\)

\(V = V_{0} (1 - r)^t = V_{0}/2\)

Dividing both sides by V₀ and taking the natural logarithm of both sides, we get:

\(ln(1 - r)^t = ln(1/2)\\\\t\ ln(1 - r) = ln(1/2)\\\\t = ln(1/2) / ln(1 - r)\)

Substituting V₀ = $500,000 and r = 0.052, we get:

t = ln(1/2) / ln(1 - 0.052) ≈ 13.4

Therefore, it will take approximately 13.4 years for the combine harvester to lose half of its value.

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Answer:

y intercept when x is 0, so the answer is 3

Jane has 6 - 14 - 12 = -20 boxes of beads left.

Jane initially had 6 boxes of beads.

She used 14 of those boxes to make face mask holders and gave 12 boxes to her sister.

To find out how many boxes of beads she has left, we need to subtract the boxes used and given away from the initial number.

First, let's calculate the total number of boxes used and given away:

Total boxes used and given away = Boxes used for face mask holders + Boxes given to sister

Total boxes used and given away = 14 + 12

Total boxes used and given away = 26

Next, we can subtract the total boxes used and given away from the initial number of boxes Jane had:

Boxes left = Initial number of boxes - Total boxes used and given away

Boxes left = 6 - 26

Boxes left = -20

The result is -20, which implies that Jane has a deficit of 20 boxes of beads.

This means she doesn't have any boxes of beads left; she has a shortage of 20 boxes based on the activities she performed.

It's important to note that having a negative value indicates that Jane doesn't have enough boxes to fulfill her activities.

If the result were positive, it would represent the number of boxes remaining.

However, in this case, Jane has used and given away more boxes than she initially had, resulting in a negative value.

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Answer:

x=6

Step-by-step explanation:

4x-15=2x-3

+15 +15

4x=2x=12

/2 /2 +12

2x=12

/2 /2

x=6

Answer:

#1:

\(4x - 15 + 2x + 3 = 48\\\\2x + 18 = 48\\\\2x = 30\\\\x = 15\)

#2:

Part 1: Solve for x

\(6x - 7 = 5x + 1\\\\x - 7 = 1\\\\x = 8\)

Part 2: Plug in x for PQ

\(6(8) - 7\\\\48 - 7\\\\41\)

The length of segment PQ is 41.

Part 3: Plug in x for QR

\(5(8) + 1\\\\40 + 1\\\\41\)

The length of segment QR is 41.

Part 4: Length of PQ + length of QR = length of PR

PQ + QR = PR

41 + 41 = PR

82 = PR

The length of segment PR is 82.

The ratio 8:73 represents B: The ratio 8:73 represents the ratio of 6th grade football players to total athletes.

It should be noted that ratio demonstrates how many times one number can fit into another number as they contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point to another data point.

In this case, the football players for 6rh grade is 8 and the total number of athletes is 73.

Therefore, the ratio that illustrates this is 8:73.

In conclusion, the correct option is B.

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Answer:

b

Step-by-step explanation:

i took the test and its right :)

The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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Answer:

    \(\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1\)

Step-by-step explanation:

Slope intercept form of a line equation is

y = mx + b

where

m = slope

b = y-intercept

A perpendicular line to y = mx + b will have a slope of -1/m

Let's first find the equation for line z in slope-intercept form
Slope m for a line  = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line

Slope of line z is
\(m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}\)

So line z will have an equation of the form
\(y = -\dfrac{3}{5}x + b\)

We know that a line perpendicular to this line will have a slope of
\(- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}\)

So the equation of the perpendicular line is
\(y = \dfrac{5}{3}x + b\)

Only one of the 4 choices, name choice A has this slope of 5/3

Therefore the correct answer choice is A

There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:

The perpendicular line passes through (3, 6). This means when x = 3, y =6

Substitute these values of x, y into the equation for the perpendicular line and solve for b

\(y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1\)

This corresponds to Choice A

Let us have a sketch of the rectangle

Since we have obtained the sketch, the perimeter can be obtained as follow.

The perimeter of any shape is simply the sum of all its sides

So we will have the perimeter to be

The perimeter is 22 inches

Step-by-step explanation:

The total amount of money collected from the ticket sales is:

$5/ticket x 3000 tickets = $15,000

The expected value for a person that buys a ticket can be calculated by adding up the probabilities of winning each prize multiplied by the amount of money for each prize:

E(X) = (1/3000) x $500 + (1/3000) x $250 + (1/3000) x $125 + (1/3000) x $50 - (2996/3000) x $5

Simplifying this expression:

E(X) = $0.1666667 + $0.0833333 + $0.0416667 + $0.0166667 - $4.9833333

E(X) = -$4.65

Therefore, the expected value for a person that buys a ticket is -$4.65, which means that on average, a person can expect to lose $4.65 for every ticket they buy.

Answer: $0.31

Step-by-step explanation:

1/3000 tickets will be worth $500.

1/3000 tickets will be worth $250.

1/3000 tickets will be worth $125.

1/3000 tickets will be worth $50.

The remaining 2996/3000 tickets will be worth $0. (Nobody else wins.)

So (1/3000)x500 + (1/3000)x250 + (1/3000)x125 + (1/3000)x50 + (2996/3000)x0 = $0.31.

Please note: This question asks for expected value. Expected value is a measure of what you should expect to get per game. The payoff of a game is the expected value of the game minus the cost.

Answer:

Find the Least Common Multiple of the denominators (which is called the Least Common Denominator).

Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator.

Then add (or subtract) the fractions

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The line of best fit for the set of data in this problem is given as follows:

y = 0.613x + 4.142.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.

The points for this problem are given as follows:

(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 0.613x + 4.142.

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Answer: 5 is the smaller number and 21 is the larger number

Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.

Answer:

A sample drawn and recorded by a method which is free from bias. This implies not only freedom from bias in the method of selection, e.g. random sampling, but freedom from any bias of procedure, e.g. wrong definition, non-response, design of questions, interviewer bias, etc.

Answer:

Sampling Criteria is one must remember that two costs are involved in a sampling analysis viz., the cost of collecting the data and the cost of an incorrect inference resulting from the data. Researcher must keep in view the two causes of incorrect inferences viz., systematic bias and sampling error.

Answer:

L = 18,4 ft

Step-by-step explanation:

The building, the ground, and the ladder make up a right triangle, with legs:

The distance (a) between the bottom of the ladder and the building 12 ft

The distance (b) between the gound and the window 14 ft up

The hypothenuse is the length of the ladder (L)

According to Pythagoras theorem

L²  = a²  + b²

L  = √  (12)²  +  (14)²

L = √ 144 + 196

L = √ 340

L = 18,4 ft

Answer:

rate goes up every 50 dollars for eatch number of deposits

well, the profit is clearly just 490 - 350 = 140.

Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)

Answer:

The general solution to this differential equation is \(P(t) = \frac{Ke^{kt} + h}{k}\)

Step-by-step explanation:

We are given the following differential equation:

\(\frac{dP}{dt} = kP - h\)

Solving by separation of variables:

\(\frac{dP}{kP-h} = dt\)

Integrating both sides:

\(\int \frac{dP}{kP-h} = \int dt\)

On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then

\(\frac{1}{k} \ln{kP-h} = t + K\)

In which K is the constant of integration.

\(\ln{kP-h} = kt + K\)

\(e^{\ln{kP-h}} = e^{kt + K}\)

\(kP - h = Ke^{kt}\)

\(kP = Ke^{kt} + h\)

\(P(t) = \frac{Ke^{kt} + h}{k}\)

The general solution to this differential equation is \(P(t) = \frac{Ke^{kt} + h}{k}\)

Step-by-step explanation:

16 - 10 × 1/5 + 13

16 - 5 + 13

11 + 13

24

Step-by-step explanation:

10/5=2

16-2+13=27.

d. 27

Answer:

\(g_n = 49+ 2n\)

Step-by-step explanation:

Given

\(g_1=51\)

\(g_n=g_{n-1}+2\)

Required

Determine the explicit formula (missing from the question)

First, calculate g2

\(g_n=g_{n-1}+2\)

\(g_2 = g_{2-1} +2\)

\(g_2 = g_1 +2\)

\(g_2 = 51 +2\)

\(g_2 = 53\)

So, we have:

\(g_1=51\)

\(g_2 = 53\)

Calculate the common difference:

\(d = g_2 - g_1\)

\(d = 53 - 51\)

\(d = 2\)

The explicit formula is calculated using:

\(g_n = g_1 + (n-1)d\)

This gives:

\(g_n = 51 + (n-1)*2\)

\(g_n = 51 + 2n-2\)

Collect Like Terms

\(g_n = 51 -2+ 2n\)

\(g_n = 49+ 2n\)