Captain Brewster captured a pack of aliens. The following data points represent the lengths of each of the aliens' big toes (in centimeters). 18, 16, 17, 17, 16, 15, 16. Using this date, create a dot plot where each dot represents a big toe.

Answer:

7

Step-by-step explanation:

(n-2)180=900/180

n-2=5

n=5+2=7

n=7

The actual width and length of the bedroom are respectively; 9 ft and 12 ft

The parameters are given as;

Width of house = 30 feet = 360 inches

Length of house = 45 feet = 540 inches

Scale drawing width of house = 4 inches

Scale drawing length of house = 6 inches

Thus;

Scale factor width = 360/4 = 90

Scale factor length = 540/6 = 90

Scale drawing width of bedroom = 1.2 inches

Scale drawing length of bedroom = 1.6 inches

Thus;

Actual width of bedroom = 1.2 inches * 90 = 108 inches or 9 ft

Actual length of bedroom = 1.6 inches * 90 = 144 inches or  12 ft

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The probability that the salesman sells a deluxe and a standard encyclopedia on his two appointments is 0.126.

To calculate this probability, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

Let S1 be the event that the salesman makes a sale on his first appointment, and S2 be the event that he makes a sale on his second appointment. Let D1 be the event that the sale is for the deluxe model, and S1 be the event that the sale is for the standard model.

Then, the probability of selling a deluxe model on the first appointment is 0.3 * 0.5 = 0.15 (since there is a 50% chance of selling a deluxe model). The probability of selling a standard model on the second appointment is 0.4 * 0.5 = 0.3 (since there is a 50% chance of selling a standard model).

Therefore, the probability of selling a deluxe model on the first appointment and a standard model on the second appointment is 0.15 * 0.3 = 0.045. However, this can also occur in reverse order (i.e., selling a standard model on the first appointment and a deluxe model on the second appointment), so we need to double the probability to get the final answer: 0.045 * 2 = 0.09.

Finally, the probability that both events occur (selling a deluxe and a standard encyclopedia on his two appointments) is 0.09 * 2 = 0.126.

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Answer:

-2xy+6x

Step-by-step explanation:

Answer:

D. All the above are correct

Step-by-step explanation:

An isocost line will be shifted further away from the origin if the total cost increases, if the price of both inputs increases or there is an advance in technology.

An isocost line can be defined as the graphical representation of various combinations of two inputs factors (labor,L and capital, K) which the firm can afford or purchase with a given amount of money.

An isocost line can be expressed mathematically as:

C = w L + r K

Where,

C = cost of production

w = price of labor or wages

L = units of labor

r = price of capital or interest rate

K =units of capital

Isocost is used to determine what combination of factor inputs the firm will choose for production process.

An iso-cost line will be shifted further away from the origin'' All of the above are correct".

An iso-cost line will shift either because of a change in total outlay or a change in factor prices.

A change in total outlay will cause a parallel shift in the iso-cost line, as there will be no change in its slope, factor prices being constant.

An iso-cost line will be shifted further away from the origin if the total cost increases if the price of both inputs increases or there is an advance in technology.

An iso-cost line can be defined as the graphical representation of various combinations of two inputs factors (labor, L and capital, K) which the firm can afford or purchase with a given amount of money.

Each iso-cost curve represents a fixed level of costs and the isoquant represents a fixed level of output.

Therefore, tracing a line through these set of points represents what combination of labor and capital will be used for a fixed level of costs or output.

The points further away from the origin represent higher levels of costs or output. An iso-cost line can be expressed mathematically as:

\(C = w L + r K\)

Where, C = cost of production

w = price of labor or wages

L = units of labor

r = price of capital or interest rate

K =units of capital

Iso-cost is used to determine what combination of factor inputs the firm will choose for the production process.

Hence, An iso-cost line will be shifted further away from the origin'' All of the above are correct".

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If D be a region bounded by a simple closed path C in the xy-plane, then the centroid of the quarter circle is  (4a/3π , 4a/3π)   .

In the question ,

it is given that D is the region bounded by a simple closed path C in the xy-plane .

the radius of the circle is = "a" ,

let the equation of the circle be x² + y² = a² ,

So , the area of the quarter circle is (A)  = (1/4)*πa²

The coordinate of the centroid x will be :

x = \(\frac{1}{2A} \int\limits x^{2} dy\)

x = \(\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -y^{2} } \, dy\)

Simplifying further ,

we get ,

x = 2/πa² [{a²(a) - a³/3} - 0 ]

x = 2/πa² [a³ - a³/3 ]

x = 4a/3π

The coordinate of the centroid y will be :

y = \(\frac{1}{2A} \int\limits y^{2} dx\)

y = \(\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -x^{2} } \, dx\)

Simplifying further ,

we get ,

y = 2/πa² [{a²(a) - a³/3} - 0 ]

y = 2/πa² [a³ - a³/3 ]

y = 4a/3π

Therefore , the coordinates of the centroid is (4a/3π , 4a/3π) .

The given question is incomplete , the complete question is

Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = \(\frac{1}{2A} \int\limits x^{2} dy\)  ,  y = \(\frac{1}{2A} \int\limits y^{2} dx\) ?  

Find the centroid of a quarter-circular region of radius a.

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Answer:

70 sq. in

Step-by-step explanation:

7*10=70

sorry if im wrong

Answer:

  y = x³ -2x² -13x -10

Step-by-step explanation:

You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.

A polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...

  p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)

Expanding this gives ...

  p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10

This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.

The polynomial function is ...

  y = x³ -2x² -13x -10

Answer: c. The plot of the data was linear

Step-by-step explanation:

If a graphical approach is used to analyze a set of raw data group, if the data set is normally distributed it is linear that is it is (attached to each other), we can conclude that the data set is normally distributed because on the plotted graph the information appears linear.

Answer:

Hey there!

2x+3y=18

2(3)+3(4)=18

6+12=18

18=18, so this is a valid ordered pair.

Let me know if this helps :)

Answer:

5m

Step-by-step explanation:

regla de 3:

1m = 3ft

15 pies ÷ 3 = 5m

Answer:

Neither

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

150/5 = 30

30+30+30+30+30 = 150

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The amount it would cost to put a new floor in the closet is $76.00

From the question, we are to calculate how much it would cost to put a new floor in the closet

From the given information,

A closet in the house is 2 yards by 1 yard.

To determine how much it would cost to put a new floor in the closet,

First,

We calculate the area of the closet

Area of the closet = 2 yard × 1 yard

Area of the closet = 2 square yards

Now,

From the given information,

The flooring costs $38.00 per square yard

Thus,

The amount it would cost to put a new floor in the closet is

2 × $38.00

= $76.00

Hence,

The amount it would cost is $76.00

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Answer:

The mode is the value that appears most frequently in a data set

Step-by-step explanation:

so it will be 0 and 5

Answer:

0 and 5

explanation:

Answer:

the answer will be D

Step-by-step explanation:

Answer:

447.23

Step-by-step explanation:

832.48 - 385.25

The answer is \((x+9)+(x-2)\) .

We have given two statements one is " number increased by nine "

Let the number be x .

Mathematically , first statement is represented by

  x + 9

Second statement is " number decreased by two "

Mathematically , second statement is represented by

  x - 2

According to the question

Sum of first and second statement = \((x+9)+(x-2)\)

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The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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We get that the correct option is option (C) for the graph of the function as it is increasing before x = -2 and from x = 0 to x = 2.

We are given a graph of a function.

A graph of a function is a special case of a relation.

In mathematics, the graph of a function f is the set of ordered pairs, where f(x)=y.

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Here, we can see that function increases before x = - 2, then it decreases till x = 0, then it again increases from x = 0 to x = 2 and then it again decreases.

Therefore, we get that the correct option is option (C) for the graph of the function as it is increasing before x = -2 and from x = 0 to x = 2.

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(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

If the sample size was increased, the 95% confidence interval would decrease. A larger sample size would provide more precise and accurate data, resulting in a narrower confidence interval.

A confidence interval is a range of values within which a population parameter is estimated to lie with a certain level of confidence. It is commonly used in statistical inference to estimate the true value of a population parameter based on a sample from that population.

If the sample size was increased, the 95% confidence interval would likely decrease. This is because a larger sample size typically leads to more precise estimates and less variability in the data, resulting in a narrower confidence interval. However, the exact size of the decrease would depend on various factors such as the amount of variability in the data and the level of statistical significance chosen for the study.

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Answer:

I think it is -12

Multiply -0.75 (3 quarters) by 16.

The negative cancels out the positive number.

Since the exponent is not saying multiply the number by itself a number of times, we could make a hypothesis that this is just multiplication.

Normally, this ↑ is not the case, but here, I could make an exception.

I hope this helps you, let me know if you need something else.

Answer:

-4, 1

Step-by-step explanation:

The exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

An exponential function is represented as:

\(y = b^x\)

The base is 3.

So, we have:

\(y = 3^x\)

It is stretched vertically by 2/3.

So, we have:

\(y = \frac23(3)^x\)

When reflected over the y-axis, we have:

\(y = \frac23(3)^{-x}\)

An asymptote of y = 2, makes the function becomes

\(y = \frac23(3)^{-x} + 2\)

Lastly, it passes through the point (0, 3.5).

So, we have:

\(y = \frac23(3)^{-x+h} + 2\)

This gives

\(3.5 = \frac23(3)^{-0+h} + 2\)

\(3.5 = \frac23(3)^{h} + 2\)

Subtract 2 from both sides

\(1.5 = \frac23(3)^{h}\)

Multiply by 3/2

\(2.25 = (3)^{h}\)

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in \(y = \frac23(3)^{-x+h} + 2\)

\(y = \frac23(3)^{-x+0.74} + 2\)

Hence, the exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

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