The amount of money raised at a fundraiser is directly proportional to the number of attendees. The amount of money raised for 12 attendees is $300. How much money is raised for 75 attendees? $300 $1,875 $900 $2,775

Answer: D. 18 + 7

Step-by-step explanation:

If we get 18$ and want to find the TOTAL cost it would be the last one

.

The linear function that represents the relationship is:

\(c = 18n + 7\)

A linear function is modeled by:

\(y(n) = an + b\)

In which:

In this problem:

Thus, the relationship is modeled by:

\(c = 18n + 7\)

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Answer:

No, but you can graph them by converting to mx+b form

Step-by-step explanation:

The procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.[4]

Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.

The first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.[5]

In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb.

Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in {\displaystyle \mathbb {C} }\mathbb {C}  have a difference w – z, and the line segments {\displaystyle {\overline {wz}}}{\displaystyle {\overline {wz}}} and {\displaystyle {\overline {0(w-z)}}}{\displaystyle {\overline {0(w-z)}}} are of the same length and direction. The segments are equipollent. The four-dimensional system {\displaystyle \mathbb {H} }\mathbb {H}  of quaternions was started in 1843. The term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q also produces a segment equipollent to {\displaystyle {\overline {pq}}.}{\displaystyle {\overline {pq}}.} Other hypercomplex number systems also used the idea of a linear space with a basis.

Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".[5]

Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later.[6]

The telegraph required an explanatory system, and the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.

The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.[5]

Vector spaces

Main article: Vector space

Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.

A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.)[7]

Answer:

The unit of measure appropriate is cubic metre or cubic meter (m³)

Step-by-step Explanation:

we know that

The volume of a cube is equal to

V = b^3

where b is the length side of the cube

In this problem we have

b = 2m

substitute in the formula of volume

V = 2^3

V = 8 m^3

therefore

The unit of measure appropriate is cubic metre (m³)

Answer:

exponent

Step-by-step explanation:

A summary description of a given variable in a survey sample is called a statistic.

What is statistic?

Any quantity calculated from sample values and taken into consideration for statistical purposes is known as a statistic (singular) or sample statistic. A population parameter estimate, a sample description, or a hypothesis evaluation are examples of statistical aims. A statistic is the average (or mean) of sample values. Both the function and the result of the function on a particular sample are referred to as statistics. A statistic may be referred to by a term that indicates its purpose when it is being utilized for that reason only.

Therefore, Option a is correct answer, a summary description of a given variable in a survey sample is called a statistic.

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Answer:

y\(\sqrt{5}\)

Step-by-step explanation:

Like radicals are radicals that have the same radical (the number into the square root) and the same radicand (the number above the root)

Here, only the last expression \(\sqrt{5}\) can be chosen.

Answer:

All are functions

Step-by-step explanation:

A.  y = x + 9  A graph of a line. There are no x-values that are the same on the graph. The graph passes the vertical line test.

B.    x + y = 9

       y = -x + 9   A graph of a line.  There are no x values that are the same number on the graph.  The graph passes the vertical line test

C.  x + 3 = y²

   \(\sqrt{x + 3} = y\)  The graph passes the vertical line test. On the graph, there are no x-values that are the same number.

D.   y = x² - 3   The graph is a parabola. The graph passes the vertical line test (there are no x- values are the same number on the graph).

The probability that a randomly selected athlete uses a stair climber for,

(a) P(X < 18) = 0.2514

(b) P(22 < X < 31) = 0.4332

(c) P(X > 30) = 0.0918

Let X be the amount of time an athlete uses a stair climber. Then, X ~ N(22, 6^2) represents a normal distribution with mean 22 and standard deviation 6.

(a) To find the probability that a randomly selected athlete uses a stair climber for less than 18 minutes, we need to calculate P(X < 18).

Z-score for 18 minutes = (18 - 22) / 6 = -0.67

Using a standard normal table or calculator, we find that P(Z < -0.67) = 0.2514.

Therefore, P(X < 18) = P(Z < -0.67) = 0.2514.

(b) To find the probability that a randomly selected athlete uses a stair climber for between 22 and 31 minutes, we need to calculate P(22 < X < 31).

Z-score for 22 minutes = (22 - 22) / 6 = 0

Z-score for 31 minutes = (31 - 22) / 6 = 1.5

Using a standard normal table or calculator, we find that P(0 < Z < 1.5) = 0.4332.

Therefore, P(22 < X < 31) = P(0 < Z < 1.5) = 0.4332.

(c) To find the probability that a randomly selected athlete uses a stair climber for more than 30 minutes, we need to calculate P(X > 30).

Z-score for 30 minutes = (30 - 22) / 6 = 1.33

Using a standard normal table or calculator, we find that P(Z > 1.33) = 0.0918.

Therefore, P(X > 30) = P(Z > 1.33) = 0.0918.

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Given:

Amount Marty spent per day = $3

Number of days = 14

Remaining amount = $68

Since the amount left depends on the number

To determine the intervals where f is concave up/down and find the inflection point(s), we need to follow these steps:

1. Find the second derivative of f(x).

2. Solve for the critical points by setting the second derivative equal to 0.

3. Analyze the concavity of the function using the critical points.

Let's apply these steps to each function:

(a) f(x) = x^2 - 2x - 8

1. First derivative: f'(x) = 2x - 2

  Second derivative: f''(x) = 2

Since the second derivative is a constant (2) and is positive, the function is concave up for all values of x. There is no inflection point.

(b) f(x) = -x + 6x^2 - 5

1. First derivative: f'(x) = -1 + 12x

  Second derivative: f''(x) = 12

Similarly to the first function, the second derivative is a constant (12) and is positive, so the function is concave up for all values of x. There is no inflection point.

(c) f(x) = x(x - 4)^3

1. First derivative: f'(x) = (x - 4)^3 + 3x(x - 4)^2

  Second derivative: f''(x) = 6(x - 4)(x - 2)

2. Set f''(x) = 0 to find critical points: 6(x - 4)(x - 2) = 0 => x = 2, 4

3. Analyze concavity:

  - For x < 2, f''(x) > 0, so f is concave up.

  - For 2 < x < 4, f''(x) < 0, so f is concave down.

  - For x > 4, f''(x) > 0, so f is concave up.

Inflection points: x = 2, 4

In summary:

(a) f(x) is concave up for all x, with no inflection points.

(b) f(x) is concave up for all x, with no inflection points.

(c) f(x) is concave up for x < 2 and x > 4, and concave down for 2 < x < 4, with inflection points at x = 2 and x = 4.

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The limit of (2 - f(x))/(x + g(x)) as x approaches 2 is 7/4. To find the limit of (2 - f(x))/(x + g(x)) as x approaches 2, we substitute the given limit values into the expression and evaluate it.

lim(x→2) f(x) = -5

lim(x→2) g(x) = 2

We substitute these values into the expression:

lim(x→2) (2 - f(x))/(x + g(x))

Plugging in the limit values:

= (2 - (-5))/(2 + 2)

= (2 + 5)/(4)

= 7/4

Therefore, the limit of (2 - f(x))/(x + g(x)) as x approaches 2 is 7/4.

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The 95% confidence interval for the mean is (1.6048, 1.6352).Hence, option (d) is the correct answer.

As given, a machine that is programmed to package 1.60 pounds of cereal is being tested for its accuracy in a sample of 40 cereal boxes, the sample mean filling weight is calculated as 1.62 pounds. The population standard deviation is known to be 0.06 pounds. We are required to find the 95% confidence interval for the mean. Here are the steps to solve this problem:

The formula to find the confidence interval is as follows;

Lower limit = x - zα/2 (σ/√n)

Upper limit = x + zα/2 (σ/√n)

Where,

x= sample mean

zα/2 = z-value of the level of significance

σ = population standard deviation

n = sample size

We are given;

x = 1.62 pounds

σ = 0.06 pounds

n = 40

We need to find the z-value of the level of significance, which can be found using the z-table or by using the calculator.Using the z-table, we get the z-value at 95% confidence interval as zα/2 = 1.96

Substituting the values, we get

Lower limit = 1.62 - 1.96(0.06/√40)

Upper limit = 1.62 + 1.96(0.06/√40)

Lower limit = 1.6048, Upper limit = 1.6352

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The function f has a vertical asymptote at x = 5 and is continuous on its domain of (-∞, 5) ∪ (5, ∞). It has a point of inflection at x = 3 and is increasing on (-∞, 2) and (5, ∞), while decreasing on (2, 5).

The given information provides us with various characteristics of the function f. We start by observing that the function is not defined at x = 5, as it has a vertical asymptote there. The limits of f as x approaches -∞ and ∞ indicate that the function decreases to -∞ as x approaches -∞ and approaches 0 as x approaches ∞.

The first derivative of f provides information about the function's increasing and decreasing behavior. We know that f′(x) > 0 on (-∞, 2) and (5, ∞), which means that f is increasing on these intervals. On the interval (2, 5), f′(x) < 0, which implies that f is decreasing on this interval.

The second derivative of f tells us about the concavity of the graph. We know that f′′(x) < 0 on (-∞, 3) and (5, ∞), which means that the graph is concave down on these intervals. On the interval (3, 5), f′′(x) > 0, which implies that the graph is concave up on this interval. Therefore, we can conclude that f has a point of inflection at x = 3.

Using the given information, we can sketch a rough graph of the function f. We start by drawing a vertical asymptote at x = 5 and marking the point (2, 4) and (-6, -3) on the graph. We can then draw the function increasing on (-∞, 2) and (5, ∞), and decreasing on (2, 5). The point of inflection at x = 3 can be marked on the graph. Finally, we can draw the graph concave down on (-∞, 3) and (5, ∞), and concave up on (3, 5).

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Answer:

5x²+7x-4

Step-by-step explanation:

Given: (7x²+2x-1)-(2x²-5x+3)

Distribute: 7x²+2x-1-2x²+5x-3

Rearrange: 7x²-2x²+5x+2x-3-1

Combine like terms: 5x²+7x-4

Your final answer is thus 5x²+7x-4

Answer:

It's 70, big man

Step-by-step explanation:

It's a forth of 280

Answer:

3(8-x) I think

Step-by-step explanation:

Answer:

3(8-x)

Step-by-step explanation:

Answer:

sorry i coldent find the anser

Step-by-step explanation:

ello

+v+

Answer:

The slope indicates that the soup kitchen uses 63 cans per day. The y-intercept shows that there were initially 825 cans at the soup kitchen.

Step-by-step explanation:

There are 12 ways to pick a sequence of two different letters of the alphabet that appear in the word CRAB? In STATISTICS?

and There are 6 ways to pick first a vowel and then a consonant from CRAB? From STATISTICS?

A) There are 12 ways to pick a sequence of two different letters of the alphabet that appear in the word CRAB, and 20 ways to pick a sequence of two different letters of the alphabet that appear in the word STATISTICS.

B) There are 6 ways to pick first a vowel and then a consonant from CRAB, and 10 ways to pick first a vowel and then a consonant from STATISTICS.

Sequence and series are the basic topics in Arithmetic. An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas a series is the sum of all elements

The fundamentals could be better understood by solving problems based on the formulas. They are very similar to sets but the primary difference is that in a sequence, individual terms can occur repeatedly in various positions.

The length of a sequence is equal to the number of terms and it can be either finite or infinite.

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1. When the population mean shifts to 7.8, the probability of detecting the change is approximately 0.0495 (or 4.95%).

2.  The probability of detecting the change is 0.0495 or 4.95%.

To solve this problem, we'll use the concept of control limits and the sampling distribution of the sample means.

When the population mean shifts to 7.8: First, let's calculate the standard deviation of the sampling distribution, also known as the standard error (SE). The formula for SE is given by SE = σ / sqrt(n), where σ is the standard deviation of the population (1.0 ounce) and n is the sample size (47).

SE = 1.0 / sqrt(47) ≈ 0.145

Next, we need to determine the z-score corresponding to the lower and upper tails of the sampling distribution that capture 5% each. Since the total probability in both tails is 10%, each tail will have a probability of 5%. We can find the z-scores using a standard normal distribution table or calculator.

The z-score corresponding to the lower tail of 5% is approximately -1.645.

The z-score corresponding to the upper tail of 5% is approximately 1.645.

Now, let's calculate the lower and upper control limits:

Lower Control Limit (LCL) = Population Mean - (z * SE)

Upper Control Limit (UCL) = Population Mean + (z * SE)

LCL = 7.8 - (-1.645 * 0.145) ≈ 8.026

UCL = 7.8 + (1.645 * 0.145) ≈ 9.574

To find the probability of detecting the change, we need to calculate the area under the sampling distribution curve that falls beyond the control limits. In this case, we're interested in the area above the upper control limit.

Since the distribution is assumed to be normal, we can use the standard normal distribution's cumulative distribution function (CDF) to calculate this probability.

Probability of detecting the change = 1 - CDF(z-score for UCL)

Using the z-score for the upper control limit (UCL), we can calculate the probability.

Probability of detecting the change ≈ 1 - CDF(1.645) ≈ 0.0495

Therefore, when the population mean shifts to 7.8, the probability of detecting the change is approximately 0.0495 (or 4.95%).

When the population mean shifts to 8.6: We'll follow the same steps as before.

SE = 1.0 / sqrt(47) ≈ 0.145

The z-score corresponding to the lower tail of 5% is still approximately -1.645.

The z-score corresponding to the upper tail of 5% is still approximately 1.645.

LCL = 8.6 - (-1.645 * 0.145) ≈ 8.926

UCL = 8.6 + (1.645 * 0.145) ≈ 10.274

Probability of detecting the change = 1 - CDF(z-score for UCL)

Probability of detecting the change ≈ 1 - CDF(1.645) ≈ 0.0495

Therefore, when the population mean shifts to 8.6, the probability of detecting the change is also approximately 0.0495 (or 4.95%).

In both cases, the probability of detecting the change is 0.0495 or 4.95%.

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Answer: To find the percentage of people with an IQ score less than 117, we need to calculate the z-score first. The z-score measures how many standard deviations an individual score is from the mean in a normal distribution.

The z-score formula is given by:

z = (x - μ) / σ

Where:

Let's calculate the z-score:

Now, we need to find the percentage of people with a z-score less than 1.1333. We can look up this value in the standard normal distribution table (also known as the Z-table) or use statistical software/tools.

Using the Z-table, we find that the percentage of people with a z-score less than 1.1333 is approximately 0.8708, or 87.08% (rounded to the nearest hundredth).

Therefore, approximately 87.1% of people have an IQ score less than 117.

Answer:

B

Step-by-step explanation:

On a graph you go rise over run (or Y divided by X) which in this equation is 1 divided by 2 which equals 1/2. You also need to look at what number is being crossed on the y axis, which in this case is 1. Slope intercept form is y=mx+b with m being the slope (1/2) and b being the y intercept (1)

Answer:

B. y = 1/2x + 1

Step-by-step explanation:

I went ahead and graphed each of the answer options for you and when I graphed for B it gave me:

To calculate the wavelength of a radio wave, we can use the formula: wavelength = speed of light / frequency  the wavelength of the radio wave used by this radio station is approximately 3.41 meters.

The speed of light is a constant value, approximately 3.00 × 10^8 meters per second.

Given that the frequency of the radio station is 8.81 × 10^7 Hz, we can substitute these values into the formula:

wavelength = (3.00 × 10^8 m/s) / (8.81 × 10^7 Hz)

Performing the calculation, the wavelength of the radio wave used by this radio station is approximately 3.41 meters.Therefore, the wavelength of the wave used by this radio station for its broadcast is approximately 3.41 meters, with three significant figures.

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Answer:

trinomial..............

Answer:

The answer is 225

Step-by-step explanation:

Because you first need to subtract 350-125 and you get 225

Answer:

Mean= the average of the number set= 18+18+63+63+84=246/5=49.2

Median- the number in the middle of the set= 63

Mode- the number(s) that repeat=1 8, 63

Range- the amount between the highest and lowest numbers= 84-18=66

Step-by-step explanation:

The mode, mean, and median of the data will be 18 or 63, 49.2, and 63, respectively.

Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.

The data set is given below.

18, 18, 63, 63, 84

The mode of the data is given as,

Mode = Frequency of the repeated number

Mode = 18 and 63

The mean of the data is given as,

Mean = (Sum of observations) / (Number of observations)

Mean = (18 + 18 + 63 + 63 + 84) / 5

Mean = 246 / 5

Mean = 49.2

The median of the data is given as,

Median = (n + 1)th / 2

Median = (5 + 1)th / 2

Median = 6th / 2

Median = 3th

Median = 63

The mode, mean, and median of the data will be 18 or 63, 49.2, and 63, respectively.

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Answer:

it is a horizontal line resting at 15 on the y axis

Step-by-step explanation:

because there is no x on the left side of the equation, it must be flat. it is 15, so that is where it lies

The graph of the function y=15 is the horizontal line resting at 15 on the y-axis

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the function y=15 is the horizontal line resting at 15 on the y-axis because there is no x on the left side of the equation, it must be flat. it is 15, so that is where it lies.

Therefore the graph of the function y=15 is the horizontal line resting at 15 on the y-axis. The graph is attached with the answer below.

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Answer:

13

Step-by-step explanation:

Answer:

true, theres nothing inside the parenthesis meaning that you remove it as a first step

Step-by-step explanation:

The person who mows the lawn in less time is given as follows:

Daniel.

To obtain who mows the lawn in less time, we calculate the hourly rates for each person, applying the proportion, which is the division of the amount of area mowed by the time needed.

Daniel can mow 15,000 ft³ in 3/4 = 0.75 hours, hence his hourly rate is calculated as follows:

Daniel hourly rate = 15000/0.75 = 15000 x 4/3 = 20,000 ft² per hour.

Bronwyn can mow 12,000 ft² in hour, hence her rate is of:

12,000 ft² per hour.

20,000 > 12,000, hence Daniel can mow the law in less time, as he has a higher rate.

The missing sentence is of:

"Bronwyn can mow 12,000 ft² in hour".

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