Suppose a student named Marcus wants to learn about the sleeping habits of students in his class. Marcus wants to collect data from his classmates to learn how many hours of sleep his classmates get. He then wants to process this data with a computer and visualize it in a Histogram. Which of the following would be the best technique for Marcus to collect this data

Answer:

115 points on her third game.

Step-by-step explanation:

To find the answer add the first and second games together.

128 + 105 = 233 ÷ 2 = 116.5 (then divide by two because there is two games).

This is the average of two games. To find the average of THREE games try different numbers to see which number works.

233 + 110 = 343 ÷ 3 = 114.3

(so we have to try a higher number than 110).

233 + 112 = 345 ÷ 3 = 115 on average (still not enough).

233 + 115 = 348 ÷ 3 = 116. (we found the answer!)

233 + 115 = 348 ÷ 3 = 116

The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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Answer:

180°

Step-by-step explanation:

The "dead spot" is 19.04 thousand miles from the center of the earth

To find the "dead spot" where no net gravitational force acts upon the object, we need to find the value of x that makes F equal to 0.

We know that F = −K x2 + 0.012K (239 − x)2

So, we set F equal to 0 and solve for x:

0 = −K x2 + 0.012K (239 − x)2

0 = −K x2 + 0.012K (239 − x)2

K x2 = 0.012K (239 − x)2

x2 = 0.012 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 x2 - 676.8 x + 568.976

x2 - 2.888 x2 = 676.8 x - 568.976

-1.888 x2 = 676.8 x - 568.976

x2 = 361.6 x - 303.504

x = √(361.6 x - 303.504)

x = √(361.6 x - 303.504)

x = 19.04

So the "dead spot" is 19.04 thousand miles from the center of the earth

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Answer:

If there are no restrictions, the domain is all real numbers.

- infinity < x < infinity

Answer:

Step-by-step explanation:

Functions are a correspondence between two sets, called the domain and the range. When defining a function, you usually state what kind of numbers the domain (x) and range (f(x)) values can be. But even if you say they are real numbers, that doesn’t mean that all real numbers can be used for x. It also doesn’t mean that all real numbers can be function values, f(x). There may be restrictions on the domain and range. The restrictions partly depend on the type of function.

In this topic, all functions will be restricted to real number values. That is, only real numbers can be used in the domain, and only real numbers can be in the range.

The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

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Answer:

B, 2I + 3 = 39

Step-by-step explanation:

work backwards first, so 39 minus 3 is 36, divided by two is 13.

Answer:

975 lbs.

Step-by-step explanation:

9 3/4 = 9.75

9.75 × 100 = 975

Answer:

x = 26

Step-by-step explanation:

If Y= x - 12 and Y = 14

Then we input the value of y which gets us the equation of: 14 = x - 12

Now we add 12 on both sides to isolate the variable.

We ADDED 12 because we needed a way to cross out the - 12 on the right side. Now the equation would be 14+12 = x

Easily we can find that 26=x

Answer:

<C = 54 degrees

b = 123.6

a = 72.6

Step-by-step explanation:

<C = 180 - 90 - 36 = 54 degrees

b = 100/sin54 = 123.6

a = sqrt (123.6^2 - 100^2) = 72.6

The expression that is equivalent to 24³ is 2³³, which means 2 multiplied by itself 33 times.

In mathematics, an expression is a combination of symbols and numbers that represents a mathematical quantity or relationship. It can consist of numbers, variables, operators (such as +, -, x, /), parentheses, and other mathematical symbols. Expressions can be used to represent a wide range of mathematical concepts, from simple arithmetic operations to complex equations.

To see why this is the case, we can perform the multiplication:

24³ = 24 x 24 x 24

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2³³.

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The statement , or 2 multiplied by itself 33 times, is identical to the number 24³.

An expression in mathematics is a group of symbols and numbers that denotes a quantity or relationship in mathematics. It can include letters, integers, variables, brackets, operators (like +, -, x, and /), and other mathematical symbols. Expressions can be used to represent a broad variety of mathematical ideas, including everything from straightforward arithmetic to intricate equations.

We can multiply the following numbers to demonstrate why this is the case:

24³ = 24 x 24 x 24

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 2³³

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The complete question is attached below,

At the value of c = 21 (approx) for which the area enclosed by the curves y = c - x^2 and y = x^2 - c is equal to 128.

The curves are  y = c - x^2 and y = x^2 - c

The area enclosed by these curves is 128.

We must determine the x-coordinates of the places of intersection in order to determine the bounds of integration:

c - x^2 = x^2 - c

Subtract c on both side, we get

-x^2 = x^2 - 2c

Subtract x^2 on both side, we get

-2x^2 = -2c

Divide by -2 on both side, we get

x^2 = c

Taking square root on both side, we get

x = ±√c

The between the curve is given by

\(\int\limits^{\sqrt{c}}_{-\sqrt{c}}{[(c-x^2)-(x^2-c)]} \, dx\) = 128

Simplify

\(\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(c-x^2-x^2+c)} \, dx\) = 128

\(\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(2c-2x^2)} \, dx\) = 128

\(2\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(c-x^2)} \, dx\) = 128

Now integrating with respect to x

\(2\left(cx-\frac{x^3}{3}\right)^{\sqrt{c}}_{-\sqrt{c}}\) = 128

\(2\left[\left(c(\sqrt{c})-\frac{(\sqrt{c})^3}{3}\right)-\left(c(-\sqrt{c})-\frac{(-\sqrt{c})^3}{3}\right)\right]\) = 128

\(2\left[\left(c(\sqrt{c})-\frac{(\sqrt{c})^3}{3}\right)-\left(-c\sqrt{c}+\frac{(\sqrt{c})^3}{3}\right)\right]\) = 128

\(2\left[c\sqrt{c}-\frac{(\sqrt{c})^3}{3}-c\sqrt{c}-\frac{(\sqrt{c})^3}{3}\right]\) = 128

\(2\left[-\frac{2(\sqrt{c})^3}{3}\right]\) = 128

\(-\frac{4}{3}(\sqrt{c})^3\) = 128

\(-\frac{4}{3}(c\sqrt{c})\) = 128

Multiply by -3/4 on both side, we get

c(√c) = -96

Square on both side, we get

c^2(c) = 9216

c^3 = 9216

Taking cube root on both side, we get

c = 20.97

c = 21 (approx)

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The complete question is:

Find the value of c for which the area enclosed by the curves y = c - x^2 and y = x^2 - c is equal to 128.

The measure of the angle m∠CBD that forms an adjacent angle is 35 degrees.

Adjacent angles are angles that have common side and vertex.

Therefore, the common vertex is at point B.

m∠CBD = m∠ABD -  m∠ABC

Therefore,

m∠ABD = 75 degrees

m∠ABC = 40 degrees

Hence,

m∠CBD = 75 - 40

m∠CBD = 35 degrees

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Answer:

super man

Step-by-step explanation:

Answer:

the best way to to do this would be to use a protractor, if you don't have one you would have to guess on the 15 degrees, but it would be a very small angle

The probability that he chooses to reroll exactly two of the dice = 7/36

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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We can group the minterms to obtain the minimum sum of products (SOP):

F(A,B,C,D) = A'B' + CD' + ABC + A'B'CD' + ABCD

Expansion of the function f(A,B,C,D):

f(A,B,C,D) = (A+B+D')(A'C)(C+D)

= A'A'C + A'CC' + BA'C + BC + D'A'C + D'CC' + BD'(A'C) + BD'(C+D)

= 0 + 0 + BA'C + BC + 0 + 0 + BD'A'C + BD'C + BD'D

= BA'C + BC + BD'A'C + BD'C + BD'D

Minterms SOP for the function with K-map 5.16:

The truth table for the given function is:

A B C F

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0

1 1 1 1

The K-map for this function is:

BC

A 00 01 11 10

0 |  0  1  0  1

1 |  1  0  0  1

We can group the minterms to obtain the minimum sum of products (SOP):

F(A,B,C) = A'B' + A'C + BC

Karnaugh map and minimum sum of products for the function F(A,B,C,D)=A'B'+CD'+ABC+A'B'CD'+ABCD:

The truth table for the given function is:

A B C D F

0 0 0 0 0

0 0 0 1 1

0 0 1 0 0

0 0 1 1 0

0 1 0 0 1

0 1 0 1 0

0 1 1 0 1

0 1 1 1 1

1 0 0 0 0

1 0 0 1 0

1 0 1 0 0

1 0 1 1 0

1 1 0 0 1

1 1 0 1 1

1 1 1 0 1

1 1 1 1 1

The K-map for this function is:

   CD

AB 00 01 11 10

00 |   0  1  0  0

01 |   1  0  0  1

11 |   1  1  1  1

10 |   0  0  1  0

We can group the minterms to obtain the minimum sum of products (SOP):

F(A,B,C,D) = A'B' + CD' + ABC + A'B'CD' + ABCD

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Answer:

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

let us first start with some basic information ~

A fraction can be represented as \(\frac{x}{y}\\\) where ,

x is the numerator and y is the denominator !

the question asks us to do something that will help us get same denominator for both the terms !

so let's see what we should do in such a case ~

\( \frac{9}{10} \: and \: \frac{7}{8} \\ \\ \\ lets \: make \: the \: denominator \: of \: both \\ the \: terms \: reach \: 80 \: , \\ \\ \bold\orange{ \implies \: \frac{9}{10} \times \frac{8}{8} = }\bold\red{ \frac{72}{80}} \\ \\\bold\orange{ \implies \: \frac{7}{8} \times \frac{10}{10} =}\bold\red{ \frac{70}{80}} \)

and we're done !

let's add some more info to be lil more clear ~

while converting the denominator of both the terms , we must multiply the same number ( this number refers to the one we'll have to multiply to the denominator to obtain the desired result ) with the denominator as well as with the numerator !

hope helpful :D

Answer:

Step-by-step explanation:

you have to multiply first fraction with '8' and second fraction with '10' :

the fractions will become 72/80 and 70/80 then you can compare it

The table layout and relationship structure of a relational database is called its schema.

A schema in a relational database refers to the overall structure and organization of tables, their attributes (columns), and the relationships between them. It defines the blueprint for how the data is organized and stored in the database.

The schema includes information such as the table names, column names, data types, constraints, and the relationships established through keys (such as primary keys and foreign keys). It provides a logical representation of the database structure and helps ensure data integrity and consistency.

The schema serves as a guide for creating, modifying, and querying the database tables. It defines the structure that enforces rules and relationships between tables, facilitating data manipulation and retrieval.

By designing a well-defined schema, database administrators and developers can establish the foundation for efficient data storage, retrieval, and management within a relational database system.

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Step-by-step explanation:

I think...

18×9=9×18

hope it helps

Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

The maximum amount of water that the pool can hold is 1000 cubic feet.

To find the maximum amount of water that the rectangular prism swimming pool can hold, we need to calculate its volume.

The volume of a rectangular prism is given by:

V = l x w x h

where l is the length, w is the width, and h is the height of the prism.

Given the dimensions of the swimming pool, we have:

l = 16 feet

w = 12.5 feet

h = 5 feet

Therefore, the volume of the swimming pool is:

V = l x w x h

V = 16 feet x 12.5 feet x 5 feet

V = 1000 cubic feet

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Answer:

4. 300    5. 7     6.  2

Step-by-step explanation:

In order to solve these problems, we need to plug in x for the missing number. So, we would set it up like this:

\(\frac{60 mi}{1 hr} =\frac{x}{5 hr}\)

We would then cross multiply in order to find the value of x. Like this:

60 × 5 = 300

1 × x = 1x

300 = 1x

300 = x

So now we know that x is 300.

We would do the exact same thing for the next question. Plug in x, then solve by cross multiplying:

\(\frac{8 hr}{2 days} =\frac{28 hr}{x}\)

8 × x = 8x

2 × 28 = 56

8x = 56

÷8    ÷8

x = 7

We now know that x is 7.

Try the last one on your own. Do the exact same thing I did for the first two. I hope you understand a bit better now. Please let me know if you need any more help. Good luck!

Answer:

Y = 60x

Step-by-step explanation:

Find the slope by finding Y2 - Y1/X2 - X1, 1 and 2 being two separate points on the graph. 120-0/2 = 6

Answer:

Square of 18 is 324

Step-by-step explanation:

\(18^2=18*18\\=180+80+64\\=324\)

hope you have understood this...

pls mark my answer as the brainliest

Answer:

y=-4x+1 is the answer to your question.

Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

The terms adjacent, neighboring, contiguous, and juxtaposed all denote being close by. Although adjacent might indicate a touch or not, it is usually assumed that there is nothing of the same sort in between. a home with a garage close by. Adjoining clearly means coming together and touching at a certain location or line.

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to a stop. When adjacent angles have the same vertex and side, they might be a complimentary angle or supplemental angle.

Thus, adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

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