Word problem involving permutations
There are 3 cyclists in a race. There will be a first-place and a second-place prize awarded. In how many different ways can the 2 prizes be awarded?

Answer:x=2+2√3 OR x=2−2√3

Step-by-step explanation: The answer is too long to write down. For complete step-by-step, go to mathpapa algebra calculator and type in your question. It would be a bit too long and difficult to write down.

Hope this helps

BRAINLIEST please?

Answer: 78

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

Answer: 79%

Step-by-step explanation:

min —> 30 mins because half an hour is 30 mins.

(1 - 0.5)^30 = .214638..

1 - .214638 = .78536

round that to the closest percent equals 79%

The side b is 24 cm, angle A is approximately 16.3 degrees, and angle B is approximately 73.7 degrees using Pythagorean theorem.

Using the Pythagorean theorem, we can solve for b:

\(a^2 + b^2 = c^2 \\7^2 + b^2 = 25^2 \\49 + b^2 = 625 \\b^2 = 576\)
b = 24 cm

Now, to find angle B:

\(sin(B)\) = opposite/hypotenuse = a/c = 7/25
\(B = sin^-1(7/25) = 16.3 degrees\)

To find angle A:

A = 90 degrees - B = 73.7 degrees

Therefore, the angles are:
A ≈ 73.7 degrees
B ≈ 16.3 degrees
C = 90 degrees

To solve the given right triangle with a = 7 cm and c = 25 cm, we will first find the missing side b using the Pythagorean theorem, then find the angles A and B using trigonometric functions.

Step 1: Find side b using the Pythagorean theorem.
In a right triangle, a² + b² = c²
Given, a = 7 cm and c = 25 cm, so:
\(7² + b² = 25²49 + b² = 625\\b² = 625 - 49\\b² = 576\\b = \sqrt{576}\)
b = 24 cm

Step 2: Find angle A using sine or cosine.
Using sine, we have sin(A) = a/c
\(sin(A) = 7/25\\A = arcsin(7/25)\)
A ≈ 16.3 degrees (rounded to the nearest tenth)

Step 3: Find angle B using the fact that the sum of angles in a triangle is 180 degrees.
Since it's a right triangle, angle C is 90 degrees. Thus:
A + B + C = 180 degrees
16.3 + B + 90 = 180
B ≈ 180 - 16.3 - 90
B ≈ 73.7 degrees (rounded to the nearest tenth)

Learn more about Pythagorean theorem here:

https://brainly.com/question/29769496

#SPJ11

Answer:

The first answer is segment bisector

Type 1 survivorship curve: Asian elephants and primate species that have few offspring and high levels of parental care.

Type 2 survivorship curve: a songbird species.

Type 3 survivorship curve: a plant and a frog species that lays massive numbers of eggs.

Survivorship curves classify the pattern of mortality (death rate) within a population over the lifespan of individuals. Type 1 survivorship curves are characterized by high survival rates until late in life, followed by a rapid increase in death rate.

This pattern is observed in long-lived species like Asian elephants and primate species with low reproductive rates and extensive parental care.

Type 2 survivorship curves have a relatively constant death rate throughout the lifespan. This is exemplified by songbird species where the chance of death remains roughly equal across different age groups.

Type 3 survivorship curves indicate high mortality rates early in life and a steep decline in death rate thereafter. This is seen in plants with low seedling survival rates and frog species that lay large numbers of eggs, of which only a few reach sexual maturity.

Learn more about Survivorship curves

brainly.com/question/29437954

#SPJ11

Answer:

Step-by-step explanation:

-2

Apply this particular rule of logs:

log a - log b = log a/b

Therefore, log2 (3) - log2 (12) = log2 (3/12) = log2 (1/4)

This last result simplifies to  log2 1 - log2 4 = 0 - 2 = -2

Answer:

-2

Step-by-step explanation:

\(log_2(3)-log_2(12)\)

~Simplify using log properties

\(log_2(\frac{3}{12})\)

\(log_2(\frac{1}{4})\)

~Apply log rules

\(-log_2(4)\)

~Rewrite

\(-log_2(2^2)\)

~Apply log rules

\(-2log_2(2)\)

~Apply log rules

-2 * 1

~Simplify

-2

Best of Luck!

Answer:

use theorem of Pythagoras

Answer:

they are not ?

Step-by-step explanation:

2/5 is not proportianl to 7/12.

Answer:

y=x+5 or y=1x+5

Step-by-step explanation:

i hope this helps :)

The median is the value in the middle of a data set, meaning that 50% of data points. The y intercept of the median line for the dataset 2 3 4 5 7 8 10 12 is 1.65.

To find the y-intercept of the median-median line for the given dataset, we first need to find the median of the x-values and the median of the y-values.

The median of the x-values can be found by first arranging the dataset in ascending order:

2, 3, 4, 5, 7, 8, 10, 12

The median of this dataset is the middle value, which is 5.

The median of the y-values can be found in a similar way:

2, 3, 4, 5, 7, 8, 10, 12

The median of this dataset is also 5.

Now that we have the medians of the x- and y-values, we can use them to find the slope of the median-median line. The slope is given by:

slope = (median of y-values for points above median of x-values - median of y-values for points below median of x-values) / (median of x-values for points above median of y-values - median of x-values for points below median of y-values)

To apply this formula, we need to split the dataset into two parts: the points above the median of x-values (5) and the points below the median of x-values.

Points above median of x-values:

7, 8, 10, 12

Points below median of x-values:

2, 3, 4, 5

The median of the y-values for the points above the median of x-values is 9, and the median of the y-values for the points below the median of x-values is 3.

Plugging these values into the slope formula, we get:

slope = (9 - 3) / (10 - 2) = 0.67

Now we can use the point-slope form of a line to find the equation of the median-median line:

y - median of y-values = slope × (x - median of x-values)

y - 5 = 0.67 × (x - 5)

Simplifying this equation, we get:

y = 0.67x + 1.65

Therefore, the y-intercept of the median-median line for the given dataset is 1.65.

Learn more about median here:

https://brainly.com/question/1157284

#SPJ11

Answer:

4

Step-by-step explanation:

Let x represent the number. The problem statement tells us ...

10x² = 40x

x = 4 . . . . . . . divide by 10x

the number is 4. Hope that helps love!

Answer:

16

Step-by-step explanation:

Answer:

Ok all u need to know is that radius is half of the diameter ,which mean the diameter is 16 yw:) pls give brainliest id really appreciate it

Step-by-step explanation:

Answer:

9/4

Step-by-step explanation:

y2 - y1 / x2 - x1 = 6 - (-3) / 2 - (-2) = 9/4

Each outcome represents the result of two spins, with the first element indicating the outcome of the first spin and the second element indicating the outcome of the second spin in the sample space.

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is spinning a spinner twice with two equally sized sections labeled "stop" and "go."

The possible outcomes of the first spin are "stop" (s) and "go" (g). Similarly, the possible outcomes of the second spin are also "stop" and "go."

Therefore, the sample space can be represented by all possible combinations of the first and second spin outcomes, which gives us the following four outcomes:

(s,s): the spinner stops on "stop" twice

(s,g): the spinner stops on "stop" on the first spin and on "go" on the second spin

(g,s): the spinner stops on "go" on the first spin and on "stop" on the second spin

(g,g): the spinner stops on "go" twice

Hence, the sample space for spinning a spinner twice with two equally sized sections labeled "stop" and "go" is given by the set: {(s,s), (s,g), (g,s), (g,g)}.

To know more about sample space,

https://brainly.com/question/30206035

#SPJ11

The value of f(-4) when the function is x⁴+3x²-2 is 292.

Given that,

The function as x⁴+3x²-2.

We have to find the value of f(-4)

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f from a set A (the function's domain) to a different set B (the function's co-domain) is referred to as a function.

Take the function

f(-4)=(-4)⁴+3(-4)²-2

f(-4)=256+3(16)-2

f(-4)=246+48-2

f(-4)=294-2

f(-4)=292

Therefore, the value of f(-4) when the function is x⁴+3x²-2 is 292.

To learn more about function visit: https://brainly.com/question/28193995

#SPJ9

The best interpretation of this regression is: As the variable "City" rises by 1 unit, consumption of fast food rises by 1.9 on average.

This interpretation is based on the regression coefficient associated with the variable "City." In this case, the regression coefficient of 1.9 indicates the change in the dependent variable (fast food consumption) associated with a one-unit increase in the independent variable (City).

Therefore, the correct answer is: As City rises by 1 unit, consumption of fast food rises by 1.9 on average.

Learn more about statistics here:

brainly.com/question/29765147

#SPJ11

Given data:

The given equation is y=-2x^2+16.

Subtiute -x for x in the given equation.

y=-2(-x)^2+16

=-2x^2+16

Thus, the y-axis is the axis of symmetry.

Answer:

y=-4

Step-by-step explanation:

The answer is going to be -4 as when y=-16 x=8.

The price that will maximize profit is $ 5.50.

Since an auditorium has seats for 1200 people, and for the past several days, the auditorium has been filled to capacity for each show, and tickets currently cost $ 5.00 and the owner wants to increase the ticket prices, and he estimates that for each $ 0.50 increase in price, 100 fewer people will attend, to determine which is the price that will maximize profit, the following calculation must be made:

Therefore, the price that will maximize profit is $ 5.50.

Learn more in https://brainly.com/question/25313241

The tube of toothpaste will last Alexa 48 days if she uses a pea-sized amount, or about 250 milligrams, of toothpaste twice a day as recommended by her dentist.

Since Alexa is using 250 milligrams of toothpaste twice a day, the total amount of toothpaste she uses per day is:

250 mg/toothbrushing x 2 toothbrushings/day = 500 mg/day

To find out how many days the tube of toothpaste will last, we need to divide the total amount of toothpaste in the tube (24 grams) by the amount of toothpaste Alexa uses per day (500 milligrams). However, we need to make sure the units are the same, so we need to convert 24 grams to milligrams:

24 g = 24,000 mg

Now we can divide 24,000 mg by 500 mg/day:

24,000 mg ÷ 500 mg/day = 48 days

To learn more about toothpaste here:

https://brainly.com/question/9778900

#SPJ1

The equation of the tangent line at the point (4,9) on the graph of the function y = f(x) = 2√x - x + 9 is y = -1/2x + 11.

To find the value of (3v - u) at x = 1, we can substitute the given values of u(1), v(1), u'(1), and v'(1) into the expression (3v - u).

Given:

u(1) = 2

u'(1) = -6

v(1) = 6

v'(1) = -4

Substituting these values, we have:

(3v - u) = 3(6) - 2 = 18 - 2 = 16

Therefore, the value of (3v - u) at x = 1 is 16.

Using logarithmic differentiation, we can find the derivative of y with respect to the independent variable x for the given function y = xln(x).

Taking the natural logarithm of both sides:

ln(y) = ln(xln(x))

Applying the logarithmic differentiation rule, we differentiate both sides with respect to x, using the product and chain rules:

d/dx[ln(y)] = d/dx[ln(xln(x))]

(1/y)(dy/dx) = (1/x)(1 + ln(x)) + (ln(x))(1/x)

Simplifying, we have:

(dy/dx)/y = (1 + ln(x))/x + ln(x)/x

dy/dx = y((1 + ln(x))/x + ln(x)/x)

Substituting y = xln(x) back in, we get:

dy/dx = xln(x)((1 + ln(x))/x + ln(x)/x)

Therefore, the derivative of y with respect to the independent variable x is given by dy/dx = xln(x)((1 + ln(x))/x + ln(x)/x).

For the equation x^3 + y^3 = 9, we are given dx/dt = -3. To find dy/dt when x = 1 and y = 2, we can differentiate both sides of the equation implicitly with respect to t:

3x^2(dx/dt) + 3y^2(dy/dt) = 0

Substituting the given values, we have:

3(1)^2(-3) + 3(2)^2(dy/dt) = 0

-9 + 12(dy/dt) = 0

12(dy/dt) = 9

dy/dt = 9/12

dy/dt = 0.75

Therefore, when x = 1 and y = 2, the value of dy/dt is 0.75.

To find the equation of the tangent line at the point (4,9) on the graph of the function y = f(x) = 2√x - x + 9, we can use the point-slope form of a linear equation.

First, we find the derivative of f(x):

f'(x) = d/dx(2√x - x + 9) = 1/sqrt(x) - 1

Substituting x = 4 into the derivative, we get:

f'(4) = 1/sqrt(4) - 1 = 1/2 - 1 = -1/2

Using the point-slope form (y - y1) = m(x - x1), where (x1, y1) is the given point and m is the slope, we have:

(y - 9) = (-1/2)(x - 4)

Simplifying, we get:

y - 9 = -1/2x + 2

y = -1/2x + 11.

For more such questions on Tangent line:

https://brainly.com/question/4470346

#SPJ8

x=14 in is the smaller part of lumber

55-x=55-14=41 in is the larger  part of lumber

Linear equations are described for strains withinside the coordinate system. If an equation has  homogeneous variables of diploma 1 (that is, best one variable), the equation is stated to be a linear equation in a single variable. A linear equation may have more than one variables. When linear equations have  variables, they may be known as bivariate linear equations.

Examples of linear equations are 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x - y + z = 3. This article gives definitions of linear equations, preferred types of linear equations in a single, , and 3 variables,  and  examples of them with complete explanations.

Let x=the smaller part

Then 55-x=the larger part

Now we are told the following:

2(55-x)=5x+12 simplify

110-2x=5x+12 add 2x to and subtract 12 from each side

110-2x+2x-12=5x+2x+12-12 collect like terms

98=7x

x=14 in--------------------smaller part

55-x=55-14=41 in-----------larger part

CK

2 times larger part=2*41=82 in

5 times smaller part=5*14=70 in

70+12=82

82=82

learn more about linear equation here :

brainly.com/question/11897796

#SPJ4

Answer:

D = 272 ft

Step-by-step explanation:  hope this helps. pls mark me brainliest

Answer:

44,572.42

Step-by-step explanation:

Answer:

Step-by-step explanation:

√324=18

√576=24

√704=26.532....

Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

To know more about profits, visit:

https://brainly.com/question/29987711

#SPJ11