Which set of ordered pairs could represent a function?
o (2, 3), (2, 2), (2, 4), (2, 9), (2,-2)
O (1,5), (2, 6), (1, 6), (4, 5), (1, 4)
O (1, 0), (2, 0), (1, 3), (4,3), (5, 7)
O (5, 1), (7,3), (9,5), (11, 7), (13, 9)

Answer:

48 and 32 6 hours clearing tables and 2 hours tutoring

Step-by-step explanation:

we can rewrite this as a fraction. we will use 1/10s because 80 can be divided by 8 which is in the problem. we then have to find out what two numbers add up to 8 but one is 3 times the other. 6 and 2 fit into this problem so we plug it into the equation and we write it as this 6x+4x=80 where x is 8. we get 48 and 32.

When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.

Answer: If this is algebra your answer will be d= 8/197

Step-by-step explanation: multiply numbers, then divide both sides with same factor, and simplify

The two column proof is written as follows

Statement                                                           Reason

line LQ || Line NP                                   given

< Q is congruent to < N                         Alternate interior angles

< L is congruent to < P                           Alternate interior angles

< LMQ is congruent to < PMN               Vertical angle theorem

Δ LMQ similar Δ PMN                            Definition of similar triangles

Similar triangles are triangles that have the same shape but may differ in size. In other words, they have the same angles but their sides may be of different lengths.

If two triangles are similar, it means that their corresponding angles are equal, and their corresponding sides are in proportion to each other.

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Answer:

The correct answer is B. $13,875.

Step-by-step explanation:

Since X and Y are in partnership with capital contributions of $ 50000 and $ 30000 respectively, and the partnership agreement provides that profits are to be shared in proportion to capital contributions and each partner is entitled to 10% interest on capital, and profit for the year was $ 37000, to determine what was the total amount credited to Y’s current account at the end of the year the following calculation must be performed:

50,000 + 30,000 = 80,000

80,000 = 100

30,000 = X

30,000 x 100 / 80,000 = X

37.5 = X

37,000 x 0.375 = X

13.875 = X

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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the simplified expression is x + 5/6. The given expression is:

1/4x + 1 + 3/4x - 2/3 -1/2

We can simplify this expression by first combining the like terms:

(1/4x + 3/4x) + (1 - 2/3 - 1/2)

= (4/4x) + (6/6 - 4/6 - 3/6)

= (1x) + (5/6)

= x + 5/6

Therefore, the simplified expression is x + 5/6.

To simplify an expression means to write an equivalent expression which contains no similar terms. This means that we will rewrite the expression with the fewest terms possible.

For example, 1/2 (x + 4) can be simplified as x/2 + 2. Let us take one more example to understand it. Example: Simplify the expression: 3/4x + y/2 (4x + 7). By using the distributive property, the given expression can be written as 3/4x + y/2 (4x) + y/2 (7).

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Answer: The cost to make 400 baseball caps is $3,200

Step-by-step explanation:

The answer they gave you is a set of coords, x and y coords to be exact. That means that x value is inputed into the equation and that y value is the asnwer.

You put in 400, you get 3200.

They also gave us that x equals the number of baseball caps. Then y equals the cost of making those baseball caps

Answer:

The cost to produce 400 caps is the same as the income made from selling 400 caps.

The company will break even when it sells 400 caps; it will not make a profit.

Step-by-step explanation:

EDGE 2021

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

On solving the provided question, we can say that - here in this inequality 17\(\leq\)2x - 3\(\leq\)25

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

17\(\leq\)2x - 3\(\leq\)25

\(20\leq 2x\leq 28\\10\leq x\leq 14\)

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Answer:

98 yd²

Step-by-step explanation:

From the diagram attached, The polygon is a square with the distance from the edge of the square to the center of the square = 7 yd.

The distance from the edge of the square to the center of the square is half of the diagonal. Therefore length of the diagonal = (7 yd * 2) = 14 yd

The diagonal and two sides of the triangle form a right angle triangle. Let the side of the triangle be a. Therefore the hypotenuse is the diagonal, using Pythagoras theorem:

a² + a² = 14²

2a² = 196

a² = 98

a = √98 = 7√2

The length of the side of the triangle = a = 7√2 yd

The area of the rectangle = length × length = 7√2 × 7√2  = 98 yd²

To convert Clara's speed from meters per second to kilometers per hour, we need to use the conversion factor:

1 kilometer = 1000 meters

1 hour = 3600 seconds

First, let's convert her speed from meters per second to meters per hour:

Speed in meters per hour = Speed in meters per second * 3600

Speed in meters per hour = 1.5 * 3600

Speed in meters per hour = 5400 meters per hour

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The percentage of patients with type-B blood that are 50 years old or younger is calculated as follows:

P = number of patients with type B blood that are 50 years or younger / number of patients with type B blood x 100%

Two parameters are used to calculate a percentage, as follows:

The proportion is given by the number of desired outcomes divided by the number of total outcomes, while the percentage is the proportion multiplied by 100%.

Hence the rule is given as follows:

P = a/b x 100%.

The problem is incomplete and the table could not be found on the internet, hence the general procedure to obtain the percentage is presented.

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Answer:

-3/7

Step-by-step explanation:

A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

Total amount of book in library are 2500 ,

Out of that 40% are fiction so the number of the non fiction books are 60%

so 60% of 2500 will give us the value of non fiction books,

Number of non fiction = 2500 x 60%

= 2500 x 60/100

= 25 x 60

= 1500

Therefore,  Number of non fiction books are 1500.

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Answer:  y = 2x + 14   x is the number of weeks. 14 (b) was his original performance in miles jogged per week. y is the expected performance.

Sketch attached.

Step-by-step explanation:  Given John's current performance, it is likely that he was able to jog some number of miles per week, the "b" in slope-intercept form.  To calculate:

30 = 2(8) + b

30 = 16 + b

30 - 16 = b

14 = b

Substitute into the slope intercept equation:

y = 2x + b

Answer:

An angle is considered a defined term in geometry because defined terms are terms that have a formal definition and can be defined using other geometrical terms.

Angle: Two rays that share the same endpoint, however, the rays take off in different directions. The area in the middle of the two rays is the angle measure.

The coefficient for the interval -T ≤ x ≤ 0 in the function g(x) is 1. However, the coefficient for the interval 0 ≤ x ≤ 2π depends on the specific form of the function f(x). Without additional information about f(x), we cannot determine its coefficient for that interval.

To solve for the coefficients in the function g(x), we need to consider the conditions given:

g(x) = { 1, -1, -T ≤ x ≤ 0

{ 1, f(x + 2π) = g(x)

We have two pieces to the function g(x), one for the interval -T ≤ x ≤ 0 and another for the interval 0 ≤ x ≤ 2π.

For the interval -T ≤ x ≤ 0, we are given that g(x) = 1, so the coefficient for this interval is 1.

For the interval 0 ≤ x ≤ 2π, we are given that f(x + 2π) = g(x). This means that the function g(x) is equal to the function f(x) shifted by 2π. Since f(x) is not specified, we cannot determine the coefficient for this interval without additional information about f(x).

The coefficient for the interval -T ≤ x ≤ 0 is 1, but the coefficient for the interval 0 ≤ x ≤ 2π depends on the specific form of the function f(x).

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Answer:

100 x 25 x 4 = 10000\(m^{3}\)

Step-by-step explanation:

From the situation described in the problem, we have that:

a) The sinusoidal function that models the depth of the water is given by: D(t) = 2sin(π/6x) + 3.

b) After 4 hours, the depth is of 4.732 meters.

The sine function is defined as follows:

g(x) = a sin(bx+c)+d.

The coefficients are defined as follows:

For this problem, the minimum value is of 1 and the maximum value is of 5, having a difference of 4, hence the amplitude is found as follows:

2a = 4 -> a = 2.

A standard sine function with an amplitude of 2 varies between -2 and 2, while this varies between 1 and 5, meaning that it had a vertical shift up 3 units, and d = 3.

The period is of 12 hours, hence:

2π/B = 12

12B = 2π

B = π/6.

The function has no phase shift, hence c = 0 and the function is given by:

D(t) = 2sin(π/6x) + 3.

From point (4, 4.732) on the graph of the function, after 4 hours, the depth is of 4.732 meters.

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Answer:

The median and mean are two different measures of central tendency that provide different information about a data set. The median is the middle value in a data set, where half of the values are above and half are below. The mean, on the other hand, is the sum of all values divided by the total number of values.

In this case, the median number of reviews is much lower than the mean number of reviews, indicating that there are likely a few very high review counts that are skewing the data towards the higher end. This is because the mean is more affected by extreme values, while the median is not. It is possible that there are a few apps with an extremely large number of reviews, which are driving up the mean.

The mean number of reviews would be significantly higher than the median.

The difference between the median and mean number of reviews can be explained by the fact that some apps have very large numbers of reviews, whereas others have very few. The median is the middle value of the dataset, and does not take into account the outliers, which can have a large effect on the mean. For example, if there is one app with 1 million reviews, the mean number of reviews would be significantly higher than the median.

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Answer:

283

Step-by-step explanation:

15(18) + 12/3 + 9

270 + 4 + 9 = 283

Answer:

283

Step-by-step explanation:

First, we have the equation 15 × 18 + 12/3 + 9.

If we refer to PEMDAS, division comes first, then multiplication, addition, and subtraction.

So, the equation becomes 15 × 18 + 4 + 9.

Now, we can multiply 15 × 18 in the equation.

The equation becomes 270 + 4 + 9.

4 + 9 = 13.

270 + 13 = 283.

There is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

Given that,

Over 62% of a newsletter publisher's subscribers, in their estimation, own a Rolls-Royce. A potential advertiser wants to verify this claim for marketing purposes. The advertiser decides to reject the null hypothesis following a test with a significance threshold of 0.02 after executing the analysis.

We have to find what is the verdict in relation to the publisher's assertion.

We know that,

First we have to write the null hypothesis and alternative hypothesis for the hypothesis test.

H₀:P=0.62

H₁:P>0.62

At 0.02 level of significance, rejecting H₀ then accepting H₁.

That is sufficient evidence that percentage over 62%.

Therefore, there is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

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Answer:

option C. 180 cars

Step-by-step explanation:

24 = 2

x = 15

cross multiply

2x = 24 × 15

2x = 360

x = 360/2

x = 180

Answer:

180

Step-by-step explanation:

It shows that Jade can read 4 pages in 3 minutes, which means she reads approximately 1.33 pages per minute.

A graph is a visual representation of data or mathematical functions. It consists of a set of points, called vertices or nodes, that are connected by lines or curves, called edges or arcs. Graphs are used in a wide range of fields, including mathematics, science, engineering, social sciences, and computer science, to represent and analyze data and relationships between variables. There are several types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and network graphs, each of which is useful for different types of data and analyses.

In the given example, we have a graph that shows the relationship between the number of pages read and the time taken to read those pages. Specifically, it shows that Jade can read 4 pages in 3 minutes, which means she reads approximately 1.33 pages per minute.

If we change the scenario and assume that Jade reads 5 pages every 3 minutes, then the graph would change accordingly. The slope of the line on the graph would change, reflecting the new rate at which Jade is reading. Instead of the slope being approximately 0.44 (which is the slope when reading 4 pages in 3 minutes), the new slope would be approximately 0.56 (which is the slope when reading 5 pages in 3 minutes).

Visually, this means that the line on the graph would become steeper, as Jade is reading more pages per unit of time. The new line would intersect the y-axis at the same point as the previous line (since Jade still starts at page 0), but it would reach higher values on the x-axis in the same amount of time compared to the previous scenario.

Therefore, it shows that Jade can read 4 pages in 3 minutes, which means she reads approximately 1.33 pages per minute.

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The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Assuming that we have two data sets, a and b, with means of 20 and 30, respectively, and the same standard deviation of 5, we can conclude that neither data set is more spread out than the other.

Suppose you have two data sets A and B, with means of 20 and 30, respectively, and the same standard deviation of 5. To determine which data set is more spread out, we need to compare the variance of the two data sets. Since the variance is the square of the standard deviation, we can compare the variances of the two data sets. Using the formula, Var = s², we can calculate the variances of data set A and B.

\(Var(A) = (5)^2 = 25\\Var(B) = (5)^2 = 25\)

Both data sets have the same variance, indicating that they have the same amount of spread, or convergence. Therefore, we can conclude that no data set is more spread out than the other.

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The angle 7π/12 is coterminal with 465.5 degrees.

To find the coterminal angle of 7π/12, we can add or subtract any multiple of 2π until we get an angle between 0 and 2π.

First, we can convert 7π/12 to degrees:

7π/12 = (7/12) * 180 ≈ 105.5 degrees

Next, we can add or subtract 360 degrees to get an angle between 0 and 360 degrees:

105.5 + 360 = 465.5

So the angle 7π/12 is coterminal with 465.5 degrees.

Therefore, the answer is d. 465 degrees.

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