2,759 divided by 89?

Answer:

Makayla can type 25 words per minute. At this rate, how long will it take her to type a

Answer:

40 minutes

Step-by-step explanation:

1000÷ 25 = 40

this makes it 40 minutes

The soccer team can have 1,716 different starting lineups. The number of ways to choose 1 player out of 13 for the goalkeeper position is given by the combination formula: C(13, 1) = 13.

To calculate the number of different starting lineups, we need to determine the combinations of players that can be chosen for the starting lineup. Since there are 13 players on the team and 11 positions in the starting lineup, we need to choose 1 player for the goalkeeper position and 10 players for the regular positions. Similarly, the number of ways to choose 10 players out of the remaining 12 players for the regular positions is given by the combination formula:

C(12, 10) = 66.

To find the total number of different starting lineups, we multiply the number of choices for the goalkeeper position by the number of choices for the regular positions: 13 * 66 = 858.

However, the order of the players in the lineup doesn't matter, so we need to divide the result by the number of permutations of the 10 regular players: 858 / 10! = 1716. The soccer team can have 1,716 different starting lineups.

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The system of equations has infinite solutions.

Given:

y = -6x +2

-12x - 2y= -4

To solve for Equation 2,

The value of y is already given in equation 1,

Thus,

substituting the value of y in equation 2,

-12x -2(-6x +2) = -4

-12x - 12x = -4 +4

0=0

The solution of the two equations is 0. Also, we can see that both equations are in ratio.

Further, the image also shows that the line of the two equations are coinciding.

Hence, the system of equations has infinite solutions.

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How many solutions does this linear system have?

y = -6x +2

-12x - 2y= -4

one solution: (0, 0) one solution: (1, –4) no solution infinite number of solutions.

Answer:

a)  Approximately 95% of healthy women in this group have blood platelet counts between 109.1 and 381.9 (1000 cells/μL).

b)  Approximately 99.7% of healthy women in this group have blood platelet counts between 40.9 and 450.1 (1000 cells/μL).

Step-by-step explanation:

The Empirical Rule (also known is the "68-95-99.7" rule) states that nearly all of the data within a normal distribution will fall within three standard deviations of the mean.

Given the blood platelet count of a group of women has a bell-shaped distribution with:

To determine the lower and upper bounds for blood platelet counts for 95% of the women, subtract and add two standard deviations to the mean:

\(\begin{aligned}\text{Lower bound}&= \mu - 2\sigma \\&= 245.5 - 2(68.2)\\&=245.5-136.4\\&=109.1\end{aligned} \qquad \begin{aligned}\text{Upper bound}&= \mu + 2\sigma \\&= 245.5 + 2(68.2)\\&=245.5+136.4\\&=381.9\end{aligned}\)

Therefore, approximately 95% of healthy women in this group have blood platelet counts between 109.1 and 381.9 (1000 cells/μL).

To determine the lower and upper bounds for blood platelet counts for 99.7% of the women, subtract and add three standard deviations to the mean:

\(\begin{aligned}\text{Lower bound}&= \mu - 3\sigma \\&= 245.5 - 3(68.2)\\&=245.5-204.6\\&=40.9\end{aligned} \qquad \begin{aligned}\text{Upper bound}&= \mu + 3\sigma \\&= 245.5 + 3(68.2)\\&=245.5+204.6\\&=450.1\end{aligned}\)

Therefore, approximately 99.7% of healthy women in this group have blood platelet counts between 40.9 and 450.1 (1000 cells/μL).

Answer:

Student ticket: $12, Adult ticket: $14

Equations: 260=10x+10y, 94=2x+5y

Step-by-step explanation:

Set adult tickets as y

Set student tickets as x

First day: Total made is 260 so set that equal to 10x + 10y

--> 260=10x+10y

Second day: Total made is 94 so set that equal to 2x + 5y

--> 94=2x+5y

I find it easier to have simplified terms so simplify (divide by 2) the first equation to get: 130=5x+5y

All you have to do now is solve for the two variables.

94=2x+5y - (130=5x+5y) --> x=12, y=14

Answer:

First find slope. m = (y2 - y1)/(x2 - x1) = (6 -1)/(-6 --3) = 5/-3. then. use. y - y1 =. m (x - x1). which gives. y - 1 = -5/3(x - 3)

Step-by-step explanation:

Answer:

x=17

Step-by-step explanation:

First, Isolate the variable x by transposing it.

24-3x=-27

-3x=-27-24

Add the equation.

-3x=-51

Simplify x by multiplying both sides by 1/-3.

-3x/-3= -51/3

x=17

Answer:

X =17

Step-by-step explanation:

24-3x = -27

collect like terms

-3x = -27 -24( crossing the = sign turns 24 negative)

-3x = -51

divide both sides by the coefficient of x

-3x/-3 = -51/-3( negative signs cancels each other out)

x = 17

Answer:

3x√5 + 6√10x + 5√3x + 10√6

Step-by-step explanation:

(√3x + √5)(√15x + 2√30)

The above expression can be evaluated as follow:

(√3x + √5)(√15x + 2√30)

Expand

√3x (√15x + 2√30) + √5(√15x + 2√30)

x√45 + 2√90x + √75x + 2√150

Express in the best possible surd form.

x•3√5 + 2•3√10x + 5√3x + 2•5√6

3x√5 + 6√10x + 5√3x + 10√6

We can not simplify further.

Therefore,

(√3x + √5)(√15x + 2√30) =

3x√5 + 6√10x + 5√3x + 10√6

Answer:

No Mode

Step-by-step explanation:

The mode is the answer that occurs most in a set of numbers, but there are no repetitive numbers in your set, so the answer is no mode.

Answer:

2nd choice: constructing a line perpendicular to a given line

Step-by-step explanation:

a. Place your compass on the given point (point P)

b. From each arc on the line, draw another arc on the opposite side of the line

   from the given point (P)  

c. Use your ruler to join the given point (P) to the point where the arcs

   intersect (Q)

Answer:

\(\leq\)

Step-by-step explanation:

No more than 13 people

Check the picture below.

Answer:

12, -6

Step-by-step explanation:

,

Energy consumption is the amount of power used over time, measured in watt-hours (Wh) or kilowatt-hours (kWh). It is calculated by multiplying the power (measured in watts) by the time for which it is used.

To calculate energy consumption, you will need to know the amount of power being used and the time over which it is being used. Power is typically measured in watts (W), and energy is the product of power and time, so energy consumption is the number of watts used multiplied by the number of hours for which they are used.

For example, let's say you want to calculate the energy consumption of a light bulb that uses 60 W of power and is left on for 4 hours. The energy consumption would be:

Energy consumption = 60 W * 4 hours = 240 Wh (watt-hours)

This is the amount of energy that the light bulb used over the 4-hour period.

You can also convert watt-hours to other units of energy, such as kilowatt-hours (kWh). To do this, you would divide the watt-hours by 1,000. In the example above, the energy consumption would be 0.240 kWh.

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Answer:

The answer is 9².

Step-by-step explanation:

9⁵ = 59049

9³ = 125

59049 ÷ 125 (9⁵ ÷ 9³) = 81

9² (9 × 9) = 81

The following cases are described:

Algebraically speaking, rational functions are expressions of the form f(x) = p(x) / q(x), such that q(x) ≠ 0, where p(x) is the numerator and q(x) is the denominator. Rational functions can be found by using the defintion of division between two functions:

(f / g) (x) = f(x) / g(x)

And the domain of (f / g) (x) is every value of x such that g(x) ≠ 0. Now we proceed to find all the required information for each case:

Case 1 - f(x) = x² - 3 · x - 18, g(x) = x + 3

Rule: (f / g) (x) = (x² - 3 · x - 18) / (x + 3)

         (f / g) (x) = [(x - 6) · (x + 3)] / (x + 3)

         (f / g) (x) = x - 6

Domain: Since the resulting expression is a linear function, then the domain of (f / g) (x) is all the real numbers.

Case 2 - f(x) = x - 3, g(x) = x² - x - 6

Rule: (f / g) (x) = (x - 3) / (x² - x - 6)

         (f / g) (x) = (x - 3) / [(x - 3) · (x + 2)]

         (f / g) (x) = 1 / (x + 2)

Domain: The domain of the rational function is any real number except x = - 2.

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The width of a confidence interval except increased sample size.

What is the Confidence Interval?

An area surrounding a measurement that indicates how accurate it is is called a confidence interval.

The following points clear the answer of given question:

Hence, The width of a confidence interval except increased sample size.

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Answer:

P = 16w - 4

Step-by-step explanation:

P = (5w-2 + 3w)2

P = (8w-2)2

P = 16w - 4

Answer:

180°

Step-by-step explanation:

The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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Answer:

irrational

Step-by-step explanation:

Answer:

it's irrational because it can't be a fraction and it keeps repeating

Answer:

please first answer my question

Based on the below analysis, the relation R is reflexive, symmetric, and transitive. Therefore, it is an equivalence relation.

To examine the relation R1 = {(1,1),(1,2),(2,1),(4,3),(2,2),(3,3),(4,4),(3,4)} on the set {1,2,3,4}, we need to check if it is reflexive, symmetric, and transitive.

Reflexivity: For the relation R1 to be reflexive, every element in the set {1,2,3,4} must be related to itself. In this case, we have (1,1), (2,2), (3,3), and (4,4), which satisfies reflexivity.

Symmetry: To check symmetry, we need to verify if for every pair (a,b) in R1, the pair (b,a) is also in R1. In this case, we have (1,2) in R1, but (2,1) is also present, satisfying symmetry. Similarly, we have (3,4) in R1, and (4,3) is also present, satisfying symmetry.

Transitivity: To examine transitivity, we need to ensure that if (a,b) and (b,c) are in R1, then (a,c) must also be in R1. In this case, we have (1,2) and (2,1) in R1, but (1,1) is not present. Hence, transitivity is not satisfied.

Based on the above analysis, the relation R1 is reflexive and symmetric, but it is not transitive. Therefore, it is not an equivalence relation.

For part b, we will examine the relation R on the set A = {1,2,3,5,6} defined as (a,b) ∈ R if a.b is a square of an integer number.

Reflexivity: For the relation R to be reflexive, every element in the set A must be related to itself. In this case, every number multiplied by itself is a square of an integer, satisfying reflexivity.

Symmetry: To check symmetry, we need to verify if for every pair (a,b) in R, the pair (b,a) is also in R. Since multiplication is commutative, if a.b is a square, then b.a is also a square. Hence, symmetry is satisfied.

Transitivity: To examine transitivity, we need to ensure that if (a,b) and (b,c) are in R, then (a,c) must also be in R. In this case, if a.b and b.c are squares, then a.c is also a square since multiplication of two squares gives another square. Hence, transitivity is satisfied.

Based on the above analysis, the relation R is reflexive, symmetric, and transitive. Therefore, it is an equivalence relation.

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To find the expected value of a continuous random variable X with a given probability density function (pdf), we integrate X multiplied by the pdf over its entire range. In this case, the pdf of X is f(x) = 4x^3, where x ranges from 0 to 1.

To calculate E(X), we integrate x*f(x) from 0 to 1. Substituting the given pdf, we have:

E(X) = ∫(x * 4x^3) dx

= 4∫(x^4) dx

Integrating this expression, we get:

E(X) = 4 * (x^5/5) evaluated from 0 to 1

= 4 * (1^5/5) - 4 * (0^5/5)

= 4/5

Therefore, the expected value of X is 0.8.

In summary, the expected value (E(X)) of the continuous random variable X, with a probability density function f(x) = 4x^3, is 0.8.

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The standard deviation is the best measurement of spread for games and movies.

To determine the spread of data, various measures can be used. These measures are referred to as measures of spread, dispersion, or variability.

The two most widely used measures of spread are the interquartile range (IQR) and standard deviation (SD).The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

That is, IQR = Q3 - Q1. The IQR gives the range of the middle 50% of data points.

The main advantage of using IQR is that it is not affected by outliers. Outliers are extreme values that lie far away from the bulk of the data points. IQR is more robust than SD when it comes to outliers.

However, IQR ignores the values in the top and bottom 25% of data, which may not give a complete picture of the spread of the data.SD is calculated by first finding the mean of the data and then finding the deviation of each data point from the mean.

The deviations are then squared, summed, and divided by the total number of data points minus one.

The square root of this value gives the SD. SD measures the average ditance of data points from the mean. Unlike IQR, SD takes into account all the data points.

The advantage of using SD is that it gives a complete picture of the spread of the data. SD is also more sensitive to small changes in data than IQR.

Based on the above explanations, it is clear that the standard deviation is the best measurement of spread for games and movies.

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3.31 it will take her to complete the triathlon.

To find this, we can apply the equation distance = rate x time.

We are aware of the length and pace of each triathlon leg. Let's name them, respectively, d and r. We must locate the time, which we shall designate as t.

d = r x t    or

t = d/r

The distance is 0.93, or 93/100, and the rate is 1.2, or 12/10 when swimming. As a result of our formula, we have:

12/10 divided by 93/100 yields the same result as

93/100 * 10/12

time to swim = 93/120 = 31/40

We have a distance of 24.8 miles, or 248/10, and a speed of 18.8 miles, or 188/10, for biking. Using the same formula, we obtain:

248/10 divided by 188/10 or

248/10 * 10/188 = 248/188 = 62/47 = time to bike

Finally, for the run, the distance is 6.2 = 62/10 and the rate is 5.1 or 51/10. Plugging this into the formula gives:

62/10 divided by 51/10 or

62/10 * 10/51 = 62/51 = time to run

= 31/40 + 62/47 + 62/51

=3.31

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Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To convert degrees to radians, we can use the following formula:

Then, for 35 degrees: