Aliyah and Diego started to run in a 5 kilometer-long race at exactly the same time. By 3:00 P. M. , Aliyah had completed half of the race. For the rest of the race, Aliyah ran at a constant rate of 0. 25 kilometer per minute. Diego did not run the race at a constant speed.

A linear function can be used to model the total distance d(t)d(t) , in kilometers, that Aliyah runs from the beginning of the race in t minutes, where t=0t=0 represents 3:00 P. M. Write an equation that defines the linear function d. Explain how you determined the equation for the function

Answer:

sin23=x/12

sin23(12)=x

0.391(12)=x

x=4.7 or 5

The probability that Rob completes the race successfully is:

1 - 0.1 - 0.09 + 0.02 = 0.83

The probability of getting an odd number or a number divisible by 4 can be found by adding the probabilities of getting an odd number and a number divisible by 4, and subtracting the probability of getting a number that is both odd and divisible by 4 (which is 4). The probabilities of getting an odd number, a number divisible by 4, and a number that is both odd and divisible by 4 are:

Odd number: There are 6 odd numbers out of 12 total numbers, so the probability of getting an odd number is 6/12 = 1/2.

Number divisible by 4: There are 3 numbers divisible by 4 (4, 8, 12), so the probability of getting a number divisible by 4 is 3/12 = 1/4.

Number that is both odd and divisible by 4: The only number that is both odd and divisible by 4 is 4, so the probability of getting this number is 1/12.

Therefore, the probability of getting an odd number or a number divisible by 4 is:

1/2 + 1/4 - 1/12 = 5/12

The probability of getting a red face or a white face can be found by adding the probabilities of getting a red face and a white face. The probability of getting a red face is 2/6 = 1/3, and the probability of getting a white face is also 1/3. Therefore, the probability of getting a red face or a white face is:

1/3 + 1/3 = 2/3

To find the probability that Rob completes the race successfully, we need to subtract the probability of getting a flat tire, the probability of the chain breaking, and the probability of both occurring from 1 (the probability of completing the race successfully). The probability of getting a flat tire is 0.1, the probability of the chain breaking is 0.09, and the probability of both occurring is 0.02. Therefore, the probability that Rob completes the race successfully is:

1 - 0.1 - 0.09 + 0.02 = 0.83

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Answer:

The following model(shown ---) is a example to how the Pythagorean theorem works. The 6 and 8 squares , if you replace them the 10 square is going to be the same as the on created by replacing the 6 and 8 squares.

hope this helps

Answer:

the pythagorean theorem is a squared + b squared = c squared

Step-by-step explanation:

Using the equations x + y = 17 and 6x + 3y = 75 the number of batches of fudge brownies and peanut butter brownies is obtained as 8 and 9 respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's use variables to represent the unknown quantities we're trying to find. Let -

x be the number of batches of fudge brownies that Sandra made

y be the number of batches of peanut butter brownies that Sandra made

From the problem, we know that -

Each batch of fudge brownies makes 6 pans, so the total number of pans of fudge brownies is 6x.

Each batch of peanut butter brownies makes 3 pans, so the total number of pans of peanut butter brownies is 3y.

Sandra made 17 batches in total, so x + y = 17.

Sandra ended up with 75 pans of brownies in total, so 6x + 3y = 75.

We can now use these equations to solve for x and y.

First, let's use the equation x + y = 17 to solve for x in terms of y -

x + y = 17

x = 17 - y

Substituting this into the second equation, we get -

6x + 3y = 75

6(17 - y) + 3y = 75

102 - 3y = 75

-3y = -27

y = 9

So Sandra made 9 batches of peanut butter brownies.

To find the number of batches of fudge brownies, we can use the expression x + y = 17 -

x + y = 17

x + 9 = 17

x = 8

Therefore, Sandra made 8 batches of fudge brownies and 9 batches of peanut butter brownies.

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Slope in the x-direction is 20.

Slope in the y-direction is 20.

To find the slopes of the surface z = 5xy at the point (4, 4, 20/4), we need to take the partial derivatives of the function with respect to x and y, evaluated at that point.

Taking the partial derivative with respect to x, we get:
∂z/∂x = 5y

Evaluating at (4, 4, 20/4), we have:
∂z/∂x = 5(4) = 20

This is the slope in the x-direction.

Taking the partial derivative with respect to y, we get:
∂z/∂y = 5x

Evaluating at (4, 4, 20/4), we have:
∂z/∂y = 5(4) = 20

This is the slope in the y-direction.

Therefore, the slope in the x-direction is 20 and the slope in the y-direction is also 20.

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Answer:

Yes

Step-by-step explanation:

Answer:

yes it is a rational number

Answer:

10x-20

Step-by-step explanation:

x times 10 is 10x

10x - 20 = 10x - 20

in conclusion you cannot subtract a number from a variable

20 subtracted from the product of x and 10?

answer : 10x-20

Answer:

The slope would be -1/4. The line is going 1 unit down and 4 units to the right.

Approximately 79433 times stronger the wave amplitude a of the earthquake was than a₀

Two or more expressions with an Equal sign is called as Equation.

Given that,

An earthquake in California measured 4.9 on the Richter scale.

We have to use formula R=log(a/a₀)

The Richter scale is a logarithmic scale (log base 10),

which means

log(a/a₀) = R = 4.9

log10(a/a₀) = 4.9

\(10^{log10(\frac{a}{a_{0} }) } =10^{4.9}\)

a/a₀ =\(10^{4.9}\)

a/a₀= 79432.8

a/a₀ =79433

a = 79433×a₀.

Hence approximately 79433 times stronger the wave amplitude a of the earthquake was than a₀

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Answer:

120/25 = 4.8

Step-by-step explanation:

To set up the equation you would do this-

\(\frac{4.8}{1} =\frac{x}{25} \\\)

Then cross multiply (multiply 4.8 by 25 and x by 1)

\(4.8(25) = x(1)\\120 = x\)

Answer:

Mean = 125.136

Median = 110

Mode = 180

Step-by-step explanation:

Given the data:

75 95 180 136 89 75 110 180 100 136 180 95 180 136 75 100 110 180 180 136 75 90

Frequency distribution:

Value(X) ___freq (F) ____cumm frequency

85 _________ 4 _______ 4

89 _________ 1 _______5

90 __________1 _______6

95 __________2 ______ 8

100 _________ 2 ______10

110 __________2______ 12

136 __________4 _____ 16

180 __________6______22

2) Using the frequency distribution :

Mean = Σfx / Σf

[(85*4) + (89*1) + (90*1) + (95*2) + (100*2) + (110*2) + (136*4) + (180*6)]/ 10

= 2753 / 22

= $125.136

Median of grouped data :

Frequency + 1 / 2 = 23/2 = 11.5 th term

The median value = $110

Mode of the data:

Most frequently occurring = 180 (frequency of 6)

The mean of the frequency distribution is $125.136, the median of the frequency distribution is $110, and the mode of the frequency distribution is $180.

Given :

a) The frequency distribution is given below:

Prices              Frequency       Cumulative Frequency

85                           4                                 4

89                            1                                 5

90                            1                                  6

95                            2                                  8

100                           2                                 10

110                            2                                  12

136                            4                                 16

180                            6                                 22

b) The mean is calculated as:

\(\rm Mean = \dfrac{85\times4 + 89\times1 +90\times1 +95\times 2+100\times2 +110\times2 +136\times4 +180\times6 }{10}\)

Simplify the above expression.

Mean = $125.136

c) The median of the frequency distribution is calculated as:

\(\rm Term= Frequency + \dfrac{1}{2}=11.5\)

So, the median is $110.

The mode of the frequency distribution is $180.

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Answer:

To plan a route for the city road race that meets the given rules, we can use the following steps:

Determine a starting and ending point that is not on Central Avenue. For example, we can choose the intersection of Maple Street and Oak Street.

Choose a path that is more than 3 miles but less than 5 miles in length. One possible path is to go east on Oak Street for 0.5 miles, then turn right (south) on Pine Street for 1 mile, then turn right (west) on Elm Street for 1 mile, then turn left (south) on Cedar Street for 0.5 miles, then turn left (east) on Maple Street for 1 mile, and finally turn right (south) on Oak Street for 0.5 miles to return to the starting point.

Verify that no part of the race runs through Central Avenue. This is satisfied by the chosen path.

Draw the race route on a coordinate grid, labeling the vertices with coordinate pairs.

The race route can be represented by the following polygon:

(5,0) (6,0)

+-----+

| |

| |

| |

| |

| |

+-----+

(6,-2) (5,-2)

Here is a description of the race route using directional words and street names:

Start at the intersection of Maple Street and Oak Street. Go east on Oak Street for 0.5 miles, then turn right (south) on Pine Street for 1 mile, then turn right (west) on Elm Street for 1 mile, then turn left (south) on Cedar Street for 0.5 miles, then turn left (east) on Maple Street for 1 mile, and finally turn right (south) on Oak Street for 0.5 miles to return to the starting point at the intersection of Maple Street and Oak Street.

Answer:

The point that lies in the solution set to the following system of inequalities is (1,10).

To check, substitute the values of x and y into each inequality:

ys > x-5

y < x+4

For the point (1,10):

10 > 1-5 is true (10 > -4)

10 < 1+4 is true (10 < 5)

Therefore, (1,10) satisfies both inequalities and lies in the solution set. The other three points do not satisfy at least one of the inequalities, and thus do not lie in the solution set.

Step-by-step explanation:

Step-by-step explanation:

a = 71/36

Alternate form

a = 1 35/36, a = 1.972

the answer is b, 7/25

The area under the curve between z = −2.0 and z = −1.0 is 0.1359.

We can use tables to find the area under the normal curve between two values of z.

However, tables give areas from z = 0 to z = 3.9 (beyond which there is literally no change). But as the normal curve is symmetric at z = 0, we can use it to find between any two given z values.

For example, for the area under the curve between z = −2.0 and z = −1.0, we can take values for z = 2.0 and z = 1.0; their difference will give the area between z = −2.0 and z = −1.0.

From tables for z = 1.0, we have 0.8413 and for z = 2.0, we have 0.9772 and

Hence, the Area under the curve between z = −2.0 and z = −1.0 is 0.9772−0.8413 = 0.1359.

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The possible numbers of hours Yolanda could rent the boat is 6 hours.

The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().

Here the given boat cost per hour = $7.

Offer he gets = $3.

Now writing a inequality then, t represent number of hours,

=> 7t-3\(\le\)39

Now solving this inequality for t then,

=> 7t\(\le\)39+3

=> 7t\(\le\)42

=> t\(\le\)42/7

=>t\(\le\)6

Hence the possible numbers of hours Yolanda could rent the boat is 6 hours.

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3120 different types of colorings are possible . Thus, Option C is the correct option. There are 3 cases involved

6! = 720 cases

No rotation is necessary because all permutation are already accounted for.

6 × 5 × 4 × 3 = 360

There are 5 different locations where the pair can be present.

360 × 5 = 1800 one pairs is possible

6 × 5 × 4 = 120

There are 5 rotations in the pentagon so the total number of possibilities is  

120 × 5 = 600 two pairs are possible

now, we add the 3 cases to find the total number of possibilities

720 + 1800 + 600 =  3120

3120 different types of colorings are possible. Thus, Option C is the correct option.

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Answer:

See explanation

Step-by-step explanation:

\(tan \: A = \frac{2 \sqrt{a} }{a - 1} ...(given) \\ \because \: {sec}^{2} \: A = 1 + {tan}^{2}\: A \\ \therefore\: {sec}^{2} \: A = 1 + \bigg(\frac{2 \sqrt{a} }{a - 1} \bigg)^{2} \\\\ \hspace{38 pt} = 1 + \frac{4a}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{(a - 1)^{2} + 4a}{ {(a - 1)}^{2} } \\ \\\hspace{38 pt} = \frac{a^{2} - 2a + 1+ 4a}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{a^{2} + 2a+ 1}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{(a + 1)^{2}}{ {(a - 1)}^{2} } \\ \\ \therefore {sec}^{2} \: A = \bigg(\frac{a + 1}{ {a - 1}} \bigg) ^{2} \\ \\ \therefore \: {sec} \: A = \pm \bigg(\frac{a + 1}{ {a - 1}} \bigg)\\ \\ \)

In the question It is not mentioned that in which quadrant does angle A lie, so we will assume it to be in first quadrant.

\( \therefore \: {sec} \: A = \bigg(\frac{a + 1}{ {a - 1}} \bigg)\\ \\

\red{ \boxed{ \bold{\therefore \: {cos} \: A = \bigg(\frac{a - 1}{ {a + 1}} \bigg)}}} \\ \\ {sin} \: A ={cos} \: A \times {tan} \: A \\ \\ \hspace{25 pt}=\bigg(\frac{a - 1}{ {a + 1}} \bigg) \times \frac{2 \sqrt{a} }{a - 1} \\ \\ \purple {\boxed { \bold{{sin} \: A = \frac{2 \sqrt{a} }{a + 1}}}}\)

Answer:

negative slope.............

Answer:

c

Step-by-step explanation:

when the area of the square is 16 cm², the area is increasing at a rate of 48 cm²/s.

When the area of the square is 16 cm², the length of each side is 4 cm. Using the formula for the area of a square, A = s², we can see that the area is increasing at a rate of:
dA/dt = 2s(ds/dt)
Plugging in the values we know, we get:
dA/dt = 2(4 cm)(6 cm/s)
dA/dt = 48 cm²/s
Therefore, when the area of the square is 16 cm², the area is increasing at a rate of 48 cm²/s.
let's first find the side length of the square when its area is 16 cm². Since the area of a square is calculated as side², we can take the square root of the area to get the side length: √16 = 4 cm. Now, we know that each side of the square is increasing at a rate of 6 cm/s. To find the rate at which the area is increasing, we'll use the formula for the derivative of area with respect to time: dA/dt = 2 * side * d(side)/dt. Plug in the values we have: dA/dt = 2 * 4 cm * 6 cm/s = 48 cm²/s. So, the area of the square is increasing at a rate of 48 cm²/s when the area is 16 cm².

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Answer:

The answer to this is 1,256

The correct factor of both terms of the expression 2d - 10 is,

⇒ 2

Since, A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

We have to given that;

An expression is,

⇒ 2d - 10

Since, There are two terms in expression which are 2d and - 10.

And,

2d = 2 × d

- 10 = - 2 × 5

Therefore, The correct factor of both terms of the expression 2d - 10 is,

⇒ 2

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The median price from the given data is 648,303.

To find the median price from the given data, we need to arrange the prices in ascending order and then locate the middle value. If there is an odd number of data points, the median will be the middle value. If there is an even number of data points, the median will be the average of the two middle values.

Let's arrange the data in ascending order:

181,386,243,922,355,008,406,791,542,820,648,303,782,200,845,053,924,494,1,089,774,1,175,704,1,274,928,1,308,954

There are a total of 13 data points, which is an odd number. So, the median price is the middle value.

The middle value is the 7th value:

Median Price = 648,303

Therefore, the median price from the given data is 648,303.

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The linear regression model for the weekly cost data is given by C(z) = ma + k, where z is the independent variable representing the weekly demand.



The values of m and k are determined through the regression analysis. Using this model, we can estimate the total weekly cost for a given weekly demand and calculate the per unit variable cost and weekly fixed cost.To find the linear regression model, we need to perform a regression analysis on the given weekly cost data. This analysis will determine the values of m and k in the equation C(z) = ma + k, where C(z) represents the weekly cost and z represents the weekly demand.

Once the values of m and k are obtained, we can use the model to estimate the total weekly cost when the weekly demand is 210. By plugging in z = 210 into the equation C(z) = ma + k, we can calculate the total weekly cost rounded to the nearest dollar.The per unit variable cost can be determined by the value of m in the model. It represents the change in cost per unit change in demand. By rounding m to one decimal place, we can obtain the per unit variable cost rounded to one decimal place.

The weekly fixed cost can be determined by the value of k in the model. It represents the cost that does not depend on the weekly demand. By rounding k to the nearest integer, we can obtain the weekly fixed cost rounded to the nearest dollar.Overall, by applying the linear regression model to the given data, we can estimate the total weekly cost, calculate the per unit variable cost, and determine the weekly fixed cost of producing sleeping bags.

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Answer:

480 tiles

Step-by-step explanation:

First we will find the area of Nico's backyard

Formula for area of a rectangle is length * width

24ft * 20ft = 480ft²

This means Nico will need 480 1ft² tiles

That is your answer

- Kan Academy Advance

Answer:

ngee hirap Naman niyan sayang

Given equation is: (x + 1)²y" + 5(x + 1)y + 4y = 0

To solve the given equation, we have to determine the following: (a) Find all ordinary points and singular points of this equation. For singular points, are they regular or irregular? Explain your reason.(b) Find the general solution of the equation.

(a) Here, the coefficient of y" is (x + 1)².

The singular point(s) of the given equation occurs where (x + 1)² = 0.

Since (x + 1)² ≥ 0 for all x, then it follows that (x + 1)² = 0 if and only if

x = -1.∴ x = -1 is the singular point of the given equation.

Since the coefficient of y" in the given equation is zero at x = -1, then it follows that the singular point x = -1 is an irregular singular point of the given equation.

(b) To find the general solution of the given equation, let us try to write the given equation in the form of a hypergeometric equation.

Let y = (x + 1)α. Then

y' = α(x + 1)α - 1 y, and

y" = α(α - 1)(x + 1)α - 2.

Substituting these derivatives of y into the given equation, we have

(α² - α) (x + 1)α + 5α(x + 1)α + 4(x + 1)α = 0

Canceling (x + 1)α from the above equation, we have

=(α² + 4α + 4) - α - 4α

= (α + 2)² - 5α

= 0Or (α + 2)²

= 5α Or α² - α + 4

= 0

Therefore, \(a= \frac{1 \pm \sqrt{1 - 16}}{2}\) or \(a = -2 \pm \frac{3i}{2}\)

There are three cases to consider when finding the general solution of the given equation.

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Answer:

Step-by-step explanation:

lm.ao I don't know 3,4,5,7,8 I'm sincerely apologise for this!!

#keep learning!!

Answer:

Here is your Answer : )

Step-by-step explanation:

1. experiment

2. survey

3.  Interview

4. observation

5. questionnaire

6. Data collection

7. Schedule

8. Manager

9. primary data

10. Primary data

Plz mark as brainiest this took long time

Hope U like it : )