a survey of athletes at a high school is conducted, and the following facts are discovered: 43% of the athletes are football players, 56% are basketball players, and 4% of the athletes play both football and basketball. an athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player? enter your answer as a percentage.

Answer:

y=55x+160

Step-by-step explanation:

i might be wrong, but i think it would be y=55x+160

Answer:

y=55x+160

Step-by-step explanation:

she starts at 160 mi which is like your y-intercept so the "b" in y=mx+b. the slope or "m" would be 55 because thats how much she's travelling per 1 x or 1 hour

A dot plot that corresponds to the values in the table include the following: dot plot B.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the values contained in the table, the high school students' essays score on a scale of 0 to 10 should be plotted on a dot plot as follows:

An essay score of 3 would have 1 dot.

An essay score of 4 would have 1 dot.

An essay score of 5 would have 2 dots.

An essay score of 6 would have 5 dots.

An essay score of 7 would have 4 dots.

An essay score of 8 would have 7 dots.

An essay score of 9 would have 3 dots.

An essay score of 10 would have 2 dots.

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9514 1404 393

Answer:

  3

Step-by-step explanation:

Vertical angles share a vertex point, and have opposite rays for sides. In short, they are across the point of intersection from each other. Vertical angles do not have a common side (they are not adjacent).

The first part of the problem is to identify angle NCA. That is shown in red in the attachment. The vertical angle is across the point of intersection. It is angle 3.

The appropriate Function and their behavior are

1. f(x) = x² - 6x + 11; Option B

2. f(x) = -4x⁶ -3x² + 6; Option D

3. f(x) = 2x⁵ + 4x² + 1; Option C

4. f(x) = x⁷ - 6x -15; Option C

Lets analyze their behavior using the quadratic function form f(x) = ax² + bx + c,

1. Looking at the equation  x² - 6x + 11 we notion at a coefficient is positive and the x term (polynomial function) is a positive. this then determines the  "opening" of the parabola.

It means that as x approaches positive or negative infinity (± ∞), f(x) approaches positive infinity (+ ∞)

2. For f(x) = -4x⁶ -3x² + 6 It is a polynomial function of degree 6; an even number. The leading coefficient is -4, which is negative. It means that the End behavior will be that as x approaches both positive or negative infinity (±∞), f(x) approaches negative infinity (- ∞) because it has a negative leading coefficient.

3. For the function f(x) = 2x⁵ + 4x² + 1, it is a polynomial function of degree 5, which is odd. The leading coefficient is 2, which is positive. Therefore, the end product will be as x approaches negative infinity (-∞), f(x) approaches negative infinity (-∞). As x approaches positive infinity (+∞), f(x) approaches positive infinity(+∞).

4. For the f(x) = x⁷ - 6x -15, it has an odd degree. The leading coefficient is 1, which is positive. This means that the End behavior will be that as x approaches negative infinity (-∞), f(x) approaches negative infinity(-∞). As x approaches positive infinity (+∞), f(x) approaches negative infinity (+∞).

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Answer:

Fraction it's 21/25      Decimal it's 0.84        Percent is 84%

Step-by-step explanation:

Answer:

Slope: 0

Slope: Undefined

Step-by-step explanation:

\((-3,3) (8, 3)\)

\(\frac{y_2-y_1}{x_2-x_1}\)

\(\frac{3-3}{8-(-3)}\)

\(\frac{0}{11}\)

\(0\)

\((-8,6)(-8,-3)\)

\(\frac{y_2-y_1}{x_2-x_1}\)

\(\frac{-3-6}{-8-(-8)}\)

\(\frac{-9}{0}\)

Undefined

Hello !

Answer:

Step-by-step explanation:

Considering two points \(\sf A(x_A, y_A)\) and \(\sf B(x_B, y_B)\), the slope of the line that passes through A and B is given by \(\sf m=\frac{y_B-y_A}{x_B-x_A}\).

Given :

Now we can calculate the slope with the previous formula :

\(\sf m=\frac{3-3}{8-(-3)}\)

\(\sf m=\frac{0}{11}\)

\(\boxed{\sf m=0}\)

The slope of the line is 0.

Given :

The only line that passes through these two points is a vertical line with equation x=8.

The slope of a vertical line is undefined (because we can't divide by 0)

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Given P(-4,17), Q (1,-3), R(-9,3), S(-5,4), slope of line PQ m(PQ) = -4 and slope of line RS m(RS) = 1/4 and Both lines are perpendicular.

If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular. Horizontal and vertical lines are perpendicular to each other i.e. the axes of the coordinate plane.

To calculate the slope of the two lines;

Mathematically;

Slope = y2-y1/x2-x1

For PQ; slope will be;

Slope of line PQ m(PQ) = (-3-17)/(1-(-4)

Slope of line PQ m(PQ) = -20/5

Slope of line PQ m(PQ) = -4

For RS; slope will be;

Slope of line RS m(RS) = (4-3)/(-5-(-9))

Slope of line RS m(RS) = 1/4

We want to determine the relationship between the two lines.

The product of both is 1/4 * -4 = -1

When two lines are perpendicular, the product of their slopes is -1

We can conclude that both lines are perpendicular to one another.

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Answer:

x-2y=7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

  -1/2

Step-by-step explanation:

Zeros of a polynomial function are its x-intercepts, the values of x that make the polynomial zero. Each zero x=p corresponds to a linear factor (x-p) of the polynomial.

A monic polynomial is one that has a leading coefficient of 1. For a monic polynomial of degree n, the coefficient of the term of degree n-1 is the opposite of the sum of all of the zeros. The constant term of any odd-degree monic polynomial is the opposite of the product of the zeros.

The given polynomial can be made monic by dividing by its leading coefficient:

  (2x^3 -x^2 -5x -2)/2 = x^3 -(1/2)x^2 -(5/2)x -1

The given polynomial has degree 3, so we're interested in the coefficient of the x^2 term. That coefficient is -1/2, so the sum of zeros will be ...

  sum of zeros = -(-1/2) = 1/2

If z represents the third zero, then we have the sum ...

  1/2 = -1 +2 +z

  z = -1/2 . . . . . . subtract 1 from both sides

The third zero is -1/2.

The given polynomial is of odd degree, so the product of the zeros is the opposite of the constant.

  (-1)(2)(z) = -(-1)

  z = 1/(-2) = -1/2 . . . . . divide by the coefficient of z

The third zero is -1/2.

Of course, a graph will show all of the (real) zeros. The attached graph from a graphing calculator shows the third zero is -1/2.

The solution of the system of equations f(x) = 2^x + 1 and g(x) = 3^x is x = 1

From the question, we have the following parameters that can be used in our computation:

f(x) = 2^x + 1

g(x) = 3^x

The above expression is a system of exponential equations

We are required to solve by graph

That implies that we graph the equations in the system on the same plane and write out ordered pairs from the point of intersection of the equations in the system

Next, we plot the graph

See attachment for the graph of the equations

The ordered pairs of the intersection point is (1, 3)

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Answer:

X = 10

Step-by-step explanation:

if we say 1/2 base = a

a² = 13² - 12²

a² = 25

a = √25

a = 5

if 1/2 base = 5 then x = a × 2

hence X = 5 × 2 = 10

The cost of the Crayons will be $4 and the cost of the Pen will be $2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Krishnan had $10. He had to purchase a box of pastels and a pen. A case of pastels costs two times as much as a pen. He got a $4 change.

Let c be the cost of crayons and p be the cost of a pen. Then the equations are given as,

c = 2p                       ...1

c + p = 10 - 4            ...2

From equations 1 and 2, then we have

2p + p = 10 - 4

3p = 6

p = 2

Then the cost of the crayons will be given as,

c = 2 x 2

c = 4

The cost of the Crayons will be $4 and the cost of the Pen will be $2.

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The average number of rounds fired each day is 140.

The average number of rounds fired by each gun during the eight days is 1122.

A mean simply means the average of the set of numbers. It is calculated by adding the numbers and then dividing.

In this situation, the British bombarded the German trenches for eight days and some 1,537 British guns fired 1,723,873 rounds without letting up. The average will be:

= 1,723,873 / 1,537

= 1122 rounds .

The average per day will be

= Average / Number of days

= 1122 / 8

= 140 per day.

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Answer:

24/25

Step-by-step explanation:

sin 2 θ = 3÷25/8 =24/25

from web2calc

Answer:

24/25

Step-by-step explanation:

P(u, v) = (3, 4) describes a triangle:  One vertex is at the origin (0, 0) and the other at (3, 4).  According to the Pythagorean Theorem, 3^2 + 4^2 = 5^2, so we know the hypotenuse length is 5 units.

Recall that the sine function is defined as opp/hyp, which here is 4/5, and that the cosine function as adj/hyp, which here is 3/5.  

Finally, we'll apply the double angle formula sin 2x = 2 sinx cos x.

Substituting the values found above,              sin 2x = 2(4/5)(3/5) = 24/25.

The sine of 2x (where x is the smaller acute angle whose vertex is (0, 0) ) is 24/25.

Answer:

B. 63°

Step-by-step explanation:

The distance around a circle is 360°

This means that 297° + n = 360°

Equation:

297 + n = 360

We can find the value of n by subtracting:

297 + n = 360

-297        -297

n = 63

Therefore, the value of n is 63 degrees.

Answer:56.548

Step-by-step explanation:

The formula for this is A=2πrh+2πr2

so A = 2π0.75(10) + 2π0.75(2)

So our surface area is 56.548

Answer:

lays

Step-by-step explanation:

To find the value of s3 in the given sigma summation series and calculate the truncation error, let's first analyze the series and determine its pattern.

The series can be written as:

s = (0.2 * 1) / 0.8 + (0.2 * 2) / 0.8 + (0.2 * 3) / 0.8 + ...

We notice that each term in the series has the form (0.2 * n) / 0.8. We can simplify this expression by dividing both the numerator and denominator by 0.2:

s = n / 4

Now, let's calculate s3 by substituting n = 3:

s3 = 3 / 4

s3 = 0.75

So, the value of s3 in the series is 0.75.

Now, let's calculate the truncation error. The truncation error is the difference between the actual sum of the series and the sum obtained by truncating or stopping at a certain term.

Given that the series sum is 0.3125 and we have s3 = 0.75, we can calculate the truncation error:

Truncation error = |Actual sum - Sum truncated at s3|

Truncation error = |0.3125 - 0.75|

Truncation error = |-0.4375|

Truncation error = 0.4375

The truncation error in this case is 0.4375.

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The number of ants after 1 year=464 and the table will follow no-linear function as the equation will be a exponential equation for the growth of ants.

What is a exponential equation?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 6^2y - 7 = 121 etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.

Now,

The exponential equation that will be followed by given ant's growth will be

y=29(2)^t/3

where 29=initial population

t=Number of months

and It will represent a non-linear function as a exponential function is a no-linear function.

Population after 1 year

                                   y=29(2)^12/3

                                     =29*16

                                      =464

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Answer:

The polynomial is positive.

Answer:

60.03

Step-by-step explanation:

Use the Pythogaras therom

now, we're assuming the deposits of $5000 are made at the beginning of the year.

\(~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)\)

\(\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 5000\\ r=rate\to 3.2\%\to \frac{3.2}{100}\dotfill &0.032\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &25 \end{cases}\)

\(A=5000\left[ \cfrac{\left( 1+\frac{0.032}{1} \right)^{1 \cdot 25}-1}{\frac{0.032}{1}} \right]\left(1+\frac{0.032}{1}\right) \\\\\\ A=5000\left[ \cfrac{\left( 1.032 \right)^{ 25}-1}{0.032} \right]\left(1.032\right) \implies A \approx 193148.73\)

The speaking turn, the adjacency pair, and the sequential implicativeness are the three fundamental components of conversation that conversation analysts identify.

The three essential elements of conversation that conversation analysts identify are the speaking turn, the adjacency pair, and the sequential implicativeness.

Mary: Hello! Mary is my name.

Andrew: Hey Mary I'm Andrew, and how are you? Nice to meet you.

Mary: Thank you; I just arrived from Memphis; I'm OK. , From where do you hail?

Andrew: You are a Memphis native? I'm a Cleveland native; is this also your first day of classes?

Mary: Indeed! I recently met someone from Cleveland at the front desk, and I'm a freshman.

Andrew: Really...? I don't know many Clevelanders who come here.

Clarissa is there, Mary, there she is! Let me introduce you to my pal, please come over!

Clarissa was undoubtedly a student of mine in high school, Andrew

Oh, Clarissa Hello Andrew Hey Mary Are you prepared for the semester to begin?

Mary: Obviously!

Andrew: I can't even find my dorm room, so not really.

The complete question is:

Write a conversation between two students who are meeting for the first time. Have them greet each other, ask each other how they are doing, ask each other where they are from, introduce a third person and say goodbye.

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