A model robot uses the scale 1 inch : 2 feet. If the model robot was 5 inches tall, the real robot would be __ feet tall​

A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

Answer:

False

Step-by-step explanation:

Check if there is a right angle using the Pythagorean Theorem:

7.2^2 + 9.1^2 ≟ 12^2

134.65 ≠ 144,

so since there isn't a right angle, this is not a rectangle.

Answer:

18.525 or 4.275 Profit

Step-by-step explanation:

Multiplying 14.25 by 1.3 for 30% results in 18.25. Profit can be calculated by subtracting the price they sell it for, 18.525 minus the 14.25 to purchase the original book is $4.275 profit.

Answer:

x = 83 degree

Step-by-step explanation:

x + 43 = 126 (sum of two interior opposite angle is equal to the exterior angle formed)

x = 126 - 43

x = 83 degree

Answer:

83 degrees

Step-by-step explanation:

To find this you first find the angle opposite to 126. To do this you subtract 126 from 180 as 180 degrees is a straight line, and we are looking for that missing angle.

This equals 54 degrees.

Now, 54 + 43 equals 97.

Because all interior angles of a triangle always equal 180, you can find that last angle by subtracting 97 from 180. This leaves you with 83 degrees.

Answer:

each game takes up 7.15 gigabytes (assuming each game takes up the same amount of storage.

Step-by-step explanation:

57.2 divided by 8 is 7.15

The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.

To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.

The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.

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Answer:

The given statement is "True"

Step-by-step explanation:

The right angle triangle is shown below:

The tangent value of an angle is given by the expression as shown below:

\(tan\alpha =\frac{a}{b}\)

Answer:

Step-by-step explanation:

Using the compound interest formula \(A = P(1+\frac{r}{n} )^{nt}\)

A = amount compounded (in $)

P = Principal (in $)

r = rate (in %)

t = time it takes to accumulate fund (in years)

n = time of compounding (in years)

Given P = $10,000, r = 4%, t = 3.5 years n = 1/12 years (since it is compounded monthly)

\(A = 10000(1+\frac{0.04}{(1/12)} )^{(3.5)(1/12)}\\A = 10000(1+0.48)^{0.2916}\\A = 10000(1.48)^{0.2916}\\A = 10000*1.12111\\A = 11,211.1\)

Amount he will compound after 3.5years will be $11,211.1.

Amount he should invest daily = Amount compounded/time taken (in days)

Since 3.5years ≈ 1278 days

Amount he should invest daily = $11,211.1/1278

Amount he should invest daily  = $8.77

Answer:

8.66 x 10 4        the 4 is a tiny number

Step-by-step explanation:

The percentage of the trash bins with a capacity of 50 gallons for each amount is as follows:

The percentages can be determined by dividing one value or amount by the total capacity of the trash bin.

Percentages represents portions or relative values of the whole value.

To expression a number in percentage, the quotient of the division operation is multiplied by 100.

The total capacity of a trash bin = 50 gallons

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Answer:

y=-1 x=26 (26,-1)

Step-by-step explanation:

We know that Mr. Garcia drives 26 miles per gallon, this means that the slope will be (26,-1)

Answer:

10 cats

Step-by-step explanation:

dogs:cats = 3:2=15:x

3x=15.2

3x=30

x=10 cats

The percentage of pregnancies last shorter than 38 weeks is (c) 30.85%.

We can use the normal distribution formula to calculate the percentage of pregnancies that last shorter than 38 weeks:

z = (x - μ) / σ

where z is the z-score, x is the value we are interested in (in this case, x = 38), μ is the mean (μ = 39), and σ is the standard deviation (σ = 2).

Substituting the values, we get:

z = (38 - 39) / 2 = -0.5

We can now use a standard normal distribution table or a calculator to find the percentage of values that fall below the z-score of -0.5. The area to the left of -0.5 is approximately 30.85%.

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Therefore, the expression mR > 90°, mS + mT 90°, mR > mT and mR > mS comes out to be true for the solution to the right angle triangle problem.

Triangles are polygons with three sides and three vertices. The triangle's angles are created by joining its three sides from ends to ends at such a single point. Three angles in the triangle combine to form a 180-degree angle.

Here,

An RST is a triangle.

This means that m∠R+m∠S+m∠T = 180° and m∠S+m∠T = 180° - m∠R.

It is given that mvR > m∠S + m∠T.

'- m∠R' '- (m∠S + m∠T)' 

The formula is changed to 180°-(mS + mT) and 180°-(mR + mS) by appending 180 degrees to both sides.

(m∠S + m∠T) - 180 degrees

The angle becomes 180° by multiplying m∠S + m∠T on both sides.

=>2(m∠S+m∠T) < 180°

=> m∠S+m∠T < 90°

M R > 90° because M ∠R + M∠ S + M ∠T = 180°.

Yet again, mvR > m∠S + mT.

=> "m∠R > m∠T," "m∠R > mS," etc.

This means that the first, second, third, and fifth options are correct.

The fact that m∠S = m∠T can only happen when m∠R=90° should be highlighted

This is why m∠S = m∠T is inaccurate.

Furthermore, there is not enough proof to prove that m∠S > m∠T.

Because of this, mS > mT is likewise incorrect.

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The simple interest rate that is equivalent to the discount rate can be determined by multiplying the discount rate by (Time / 365).

i) To determine the maker of the note, we need to identify who issued the promissory note. Unfortunately, the information provided does not specify the name of the maker or issuer of the note. Without additional information, it is not possible to determine the maker of the note. ii) To calculate the face value of the note, we can use the formula for the maturity value of a promissory note: Maturity Value = Face Value + (Face Value * Interest Rate * Time). Given that the maturity value is RM7,266 and the note matured on 11 June 2022 (assuming a 365-day year), and Zafran held the note for 52 days, we can calculate the face value: 7,266 = Face Value + (Face Value * 0.09 * (52/365)). Solving this equation will give us the face value of the note.

iii) The discount date is the date on which the note was discounted at the bank. From the information provided, we know that Zafran discounted the note after holding it for 52 days. Therefore, the discount date would be 52 days after 10 January 2022. iv) The discount rate can be calculated using the formula: Discount Rate = (Maturity Value - Discounted Value) / Maturity Value * (365 / Time). Given that the discounted value is RM7,130.77 and the maturity value is RM7,266, and assuming a 365-day year, we can calculate the discount rate. v) The simple interest rate that is equivalent to the discount rate can be determined by multiplying the discount rate by (Time / 365). This will give us the annualized interest rate that is equivalent to the discount rate.

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Considering that each input is related to only one output, the correct option regarding whether the relation is a function is:

A. yes.

A relation represents a function when each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are no repeated inputs, hence the relation is a function and option A is correct.

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Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer:

32 feet.

Step-by-step explanation:

We can convert 7 yards to feet and add it to 11 feet to get the total distance in feet.

1 yard is equal to 3 feet, so 7 yards is equal to:

7 yards * 3 feet/yard = 21 feet

Adding 11 feet to this, we get:

21 feet + 11 feet = 32 feet

Therefore, 7 yards and 11 feet is equal to 32 feet.

Answer:

There are 32 feet in 7 yards and 11 feet.

Step-by-step explanation:

To find the answer, we need to convert yards to feet and then add them to the given feet. We can use the following conversion factor: 1 yard = 3 feet. Multiplying both sides by 7, we get: 7 yards = 21 feet. Adding 11 feet to both sides, we get: 7 yards + 11 feet = 21 feet + 11 feet. Simplifying, we get: 7 yards + 11 feet = 32 feet.

The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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The superposition is the imposing of one wave on the other and resulting in the change of the amplitude of the final wave.

When two or more waves travel through the same space in superposition, their combined amplitudes equal the amplitudes they would have produced individually. For instance, two waves moving in the same direction will pass through each other without causing any distortion on the other side.

The pattern you see when shining light through two slits, the sounds you hear in acoustically sound rooms and music halls, the interference radios receive when moved close to other electronic devices, and any tone produced by a musical instrument are all examples of the superposition principle in action.

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The probability of choosing an odd prime number from 1 to 20 is 0.35

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The odd prime numbers between 1 and 20 are 3, 5, 7, 11, 13, 17, and 19. There are 7 odd prime numbers in this range.

The total number of possible choices is 20 (since there are 20 numbers in the range 1 to 20).

Therefore, the probability of choosing an odd prime number is:

number of odd prime numbers / total number of possible choices

= 7 / 20

= 0.35

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Given the data on the length of the metacarpal bone (X) and the height (Y) of 22 sets of skeletal remains, we are asked to find the random variables, the equation of the best-fitting line (least squares regression equation), interpret the slope and Y-intercept, predict the height for a given length of metacarpal, and compute the residual for a specific data point (47, 172).

(a) The random variables are X (length of metacarpal) and Y (height).

(c) To find the equation of the best-fitting line, we need to perform linear regression. Using the given data, we calculate the slope (β₁) and the Y-intercept (β₀) of the regression line. The equation will be in the form ^Y = β₀ + β₁X.

(d) The slope (β₁) represents the expected change in Y (height) for every 1-unit increase in X (length of metacarpal). Its interpretation will include the units of Y divided by the units of X.

(e) The Y-intercept (β₀) represents the expected height when X (length of metacarpal) is 0. The interpretation will include the units of Y.

(g) To compute the residual for the ordered pair (47, 172), we substitute X = 47 into the regression equation ^Y = β₀ + β₁X and subtract the actual Y-value (172). The residual is the difference between the predicted and observed Y-values.

To provide specific numerical values for the equations and predictions, the original data and calculations are needed.

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L = 1.3245 is  the legnths of the pen's sides .

What is area and perimeter?

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)

So W = 30 - 2L.

Area = L x W = L (30 - 2L) = 30L - 2L^2.

This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .

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The co-ordinate of the point of trisection of the line joining the (25,10) (-5,-5)​ is (15,5).

Given - Line joining the points (25,10) (-5,-5)​

To find - The co-ordinate of the point of trisection

The points that divide a line segment AB in a ratio of 1:2 or 2:1 are known as points of trisection.

The point that splits a line segment AB in the ratio m:n is determined by the following formula,

\(\frac{mx_{2}+ nx_{1} }{m+ n}\) , \(\frac{my_{2} + ny_{1} }{m + n}\)

Accordingly,

\(\frac{1(-5) + 2(25)}{3}\) , \(\frac{1(-5) + 2(10)}{3}\)

\(\frac{-5 +50}{3}\) , \(\frac{-5 + 20}{3}\)

Solving,

\(\frac{45}{3}\) , \(\frac{15}{3}\)

(15, 5)

The co-ordinate of the point of trisection of the line joining the (25,10) (-5,-5)​ is (15,5).

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Answer:

.4

Step-by-step explanation: have a good day

The limit of the given function as t approaches 4 is 7.

To evaluate the limit, we substitute the value of 4 into the function. By direct substitution, we get (4*2 - 4 - 12) / (4 - 4). Simplifying this expression, we have (16 - 4 - 12) / 0, which equals 0 / 0. This is an indeterminate form, which means we need to apply further algebraic manipulation to determine the limit.

To find the limit, we can factor the numerator as (t - 4)(t + 3). This allows us to cancel out the common factor of (t - 4) in the numerator and denominator. After canceling out (t - 4), the expression becomes (t + 3). Now we can evaluate the limit by substituting the value of t as it approaches 4 into the simplified expression.

Taking the limit as t approaches 4 of (t + 3), we get (4 + 3), which equals 7. Therefore, the limit of the given function as t approaches 4 is 7.

In summary, by factoring the numerator and canceling out the common factor of (t - 4), we simplified the expression to (t + 3). Substituting the value of t as it approaches 4 into the simplified expression gives us the limit of 7.

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The midpoints of the first and last parts are 4/5m units apart

The length of the line segment is given as

Length = m units

From the question, the number of partitions is given as

Partition = 5

So, the length of each partition is

Each partition = Length/Partition

This gives

Each partition = m/5

The midpoint of a partition is

Partition midpoint = m/5 x 1/2

Evaluate

Partition midpoint = m/10

The distance between the midpoints of the first and last segments is then calculated as

Distance = Length - 2 x Partition midpoint

So, we have

Distance = m - 2 x m/10

Evaluate

Distance = m - m/5

This gives

Distance = 4/5m

Hence, the distance is 4/5m units

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Answer:

3360.

Step-by-step explanation:

That would be the number of permutations of 3 from 16.

= 16P3

= 16!/(16-3)!

= 16*15*14

= 3360

Answer:

3 360 permutations

Step-by-step explanation:

the number of permutations :

16P3 = 16 × 15 × 14 = 3 360

Answer:

Molar Mass Molar mass is defined as the mass of one mole of representative particles of a substance. By looking at a periodic table, we can conclude that the molar mass of lithium is 6.94g, the molar mass of zinc is 65.38g, and the molar mass of gold is 196.97g. Each of these quantities contains 6.02 × 1023 atoms of that particular element.

Step-by-step explanation:

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Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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