Kate walks at an average speed of (x + 2) km/h for (x-3) hours and cycles at an average speed of (3x + 5) km/h for x hours. She covers a total of 74 km. Find the time taken for her entire journey​

law of contraposition = if p, then q. if not q, then not p.

example: if it's snowing, then there's no school. if there is school, then it's not snowing.

the probability of getting red on at least one spin is 1 - 9/16 = 7/16 or 0.4375 in decimal form.

hope that helps!

After answering the provided question, we can conclude that Therefore, derivatives the function f(x, y) = ycos(x) has no local minimum or maximum points, only two saddle points at (π/2, 0) and (3π/2, 0).

In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.

∂f/∂x = -ysin(x)

∂f/∂y = cos(x)

-ysin(x) = 0 (Equation 1)

cos(x) = 0 (Equation 2)

Therefore, the critical points are:

(π/2, 0) (saddle point)

(3π/2, 0) (saddle point)

∂²f/∂x² = -ycos(x)

∂²f/∂y² = 0

∂²f/∂x∂y = cos(x)

At the point (π/2, 0), ∂²f/∂x² = 0 and ∂²f/∂x∂y = 1, so it is a saddle point.

At the point (3π/2, 0), ∂²f/∂x² = 0 and ∂²f/∂x∂y = -1, so it is also a saddle point.

Therefore, the function f(x, y) = ycos(x) has no local minimum or maximum points, only two saddle points at (π/2, 0) and (3π/2, 0).

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Answer:

18

Step-by-step explanation:

6 divided by 5 is 1.2. 1.2 times 15 is 18. Via your answer.

a. The relation is an equivalence relation, and its corresponding partition has blocks {1, 4}, {2}, and {3}.

b. The relation is not specified.

c. The relation is not an equivalence relation because it is not transitive.

d. The relation is not an equivalence relation because it is not reflexive.

a. The relation is an equivalence relation because it is reflexive, symmetric, and transitive. The blocks of its corresponding partition are {1, 4} and {2} and {3}.

b. The relation is not specified, so it is impossible to determine whether it is an equivalence relation or not.

c. The relation is not an equivalence relation because it is not transitive. Specifically, (3, 1) and (1, 3) are in the relation, but (3, 3) is not.

d. The relation is not an equivalence relation because it is not reflexive (i.e., 1 and 4 are not related to themselves).

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Answer:

 [tex]2\sqrt{21}[/tex]

Step-by-step explanation:

I'm not sure if you know how to simplify radicals or not, but the [tex]\sqrt{84}[/tex] can be further simplified to [tex]2\sqrt{21}[/tex]

To simplify a radical, you just need to divide by squares you already know

In this case, divide 84 by 4 (which is the square of 2)

This will give you 21. Leave that inside the radical. Outside the root, leave the 2 as multiplier to [tex]\sqrt{21}[/tex].

The rates and the car value are 86.3% and 7679.66 respecyivelt

A) The annual rate

The function is represented as

y = ab^x

Where

a = 45000 i.e. value in 1991

So, we have

y = 45000b^x

In 2000, we have

45000b^9 = 12000

This gives

b^9 = 0.266

Solving for b, we have

9ln(b) = ln(0.266)

So, we have

ln(b) = ln(0.266)/9

This gives

b = e^(ln(0.266)/9)

Evaluate

b = 0.863

B) To convert the rate to a percentage, we multiply by 100 and add the percent symbol:

b = 0.863

So, we have

b = 86.3%

C) If the car value continues to drop by the same percentage, we can use the formula:

Value = 45000* (0.863)^12

Evaluate

Value = 7679.66

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Answer: J=39 H=9

Step-by-step explanation:

J+H=48

J-3=6(H-3)

Use the substitution method and isolate one variable to do so.

J-3=6h-18

J=6h-15

plug J into first equation

6h+h-15=48

7h-15=48

7h=63

h=9

J+H=48

J+9=48

48-9=39

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = final amount

P = principal (initial amount)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time (in years)

In this case:

P = $11,000

r = 2.5% = 0.025 (since it's compounded monthly, we need to divide by 12 to get the monthly rate)

n = 12 (compounded monthly)

t = 21 years

Plugging in these values, we get:

A = 11000(1 + 0.025/12)^(12*21)

A ≈ $16,180.64

Therefore, the value of the account at the child's twenty-first birthday will be approximately $16,181.

The inverse transform method can be used to produce a random variate for a random variable X with p.d.f[tex]f(x) = e^{2x}[/tex].

The cumulative distribution function (CDF) of X is given by [tex]F(x) = 1 - e[/tex], and we must first determine its inverse (-2x). When x is solved for, the answer is x = -(1/2)ln(1 - u), where u is an evenly spaced random number between 0 and 1.

As a result, we can take the following actions to create a random variate for X:

Create an even, random number between 0 and 1, u.

Determine[tex]x = -(1/2)ln (1 - u)[/tex].

A random variate for X is the produced value of x.

The generated values will adhere to the specified probability distribution thanks to this procedure.

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Correct question is:

Develop a random variate generator for a random variable X with the probability density function: [tex]f(x) = e^2x x < 0 e^ -2x x > 0[/tex] Use the generator to generate two random variates using the following uniform random numbers: U1= 0.95 and U2= 0.35.

The sum of the given fractions is equal to -3/22.

Here we have the sum of 3 fractions:

-2/3 + 1/33 + 2/4

To solve this we needto find common denominators, we can write:

3*44 = 132

33*4 = 132

4*33 = 132

Then we can rewrite each of the fractions as:

-2/3 = -88/132

1/33 = 4/132

2/4 = 66/132

Then the sum becomes:

-88/132 +  4/132 + 66/132  = -18/132 = -9/66 = -3/22

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The width οf the field is 80 yards.

Pythagοras Theοrem is the way in which yοu can find the missing length οf a right angled triangle.

Assuming the field is rectangular, we can use the Pythagοrean theοrem tο sοlve fοr the width:

Let the width οf the field be x. Then, we have a right triangle with legs x/2 and 80/2 = 40 and hypοtenuse 100:

[tex](x/2)^2 + 40^2 = 100^2[/tex]

[tex]x^2/4 + 1600 = 10000[/tex]

[tex]x^2 = 6400[/tex]

[tex]x = 80[/tex]

Hence, the width οf the field is 80 yards.

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The expected value of the raffle if you buy 1 ticket is -$0.56, which means, you can expect to lose $0.56 for each ticket you buy.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To calculate the expected value of the raffle if you buy 1 ticket, we need to find the expected monetary value of the prizes you could win, and then subtract the cost of the ticket, which is $1.

The probability of winning each prize can be calculated as follows:

1 prize of $500: 1/7000 chance of winning

3 prizes of $100: 3/7000 chance of winning each prize

5 prizes of $20: 5/7000 chance of winning each prize

19 prizes of $5: 19/7000 chance of winning each prize

To calculate the expected value of each prize, we multiply the probability of winning by the amount of the prize:

$500 prize: (1/7000) x $500 = $0.07

$100 prize: (3/7000) x $100 = $0.04

$20 prize: (5/7000) x $20 = $0.01

$5 prize: (19/7000) x $5 = $0.01

To find the expected value of the raffle if you buy 1 ticket, we add up the expected values of all the possible prizes:

$0.07 + ($0.04 x 3) + ($0.01 x 5) + ($0.01 x 19) = $0.44

Therefore, the expected value of the raffle if you buy 1 ticket is $0.44 - $1 = -$0.56, which means that on average, you can expect to lose $0.56 for each ticket you buy.

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After answering the provided question, we can conclude that As a result, the scatter plot  correct answer is A. quadratic model, 0.840.

"Scatter plots are graphs that depict the relationship between two is that variables in a data set. Data points are represented using a two-dimensional plane or a Cartesian system. The independent variable or characteristic is represented by the X-axis, while the dependent variable is represented by the Y-axis. These plots are often known as scatter graphs or scatter diagrams."

To find the best-fit model, we must examine the pattern of the data points. To visualise the trend, we can make a scatter plot of the data.

Using a regression tool, we obtain the quadratic model shown below:

[tex]y = -0.027x^2 + 0.33x + 2.19[/tex]

where y represents the number of insect species and x represents the year (coded as 1 for 2001, 2 for 2002, and so on).

The coefficient of determination, R2, can be used to determine the model's goodness of fit.

The quadratic model has an R value of 0.840, which is relatively high and indicates a decent match.

As a result, the correct answer is A. quadratic model, 0.840.

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Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

Given that the current fridge

electricity charges= $60 monthly,

maintenance costs=$ 170

let the number of months be = x

and the total cost is y

the expression for the cost of the old fridge is

y=170+60x       ...say (1)

new fridge

electricity charges=$5

costs= $1140

let the number of months be x,

and the total cost be y'

the expression for the cost of the new fridge is

y'=1140+5x,       ... say(2)

For 10 year , there are 12*10=120 months

put x=120 in both equations,

y=170+60x  

y=170+60*120

y=170+7200

y=$7370

y'=1140+5*120

y'=1140+600

y'=$1740

Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

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Using probability, the percentage of people who test positive for the virus who actually have the virus is approximately 99.85%.

What is probability?

Probability is a measure of the likelihood or chance that an event will occur. It is a numerical value between 0 and 1, where 0 represents an impossible event (i.e., an event that will never occur) and 1 represents a certain event (i.e., an event that will always occur).

Now,

To determine the percentage of people who test positive for the virus who actually have the virus, we can use Bayes' theorem.

Let A be the event that an individual has the virus, and B be the event that an individual tests positive for the virus. Then, we want to calculate the conditional probability of A given B, denoted as P(A|B), which is the probability that an individual has the virus given that they test positive.

Using Bayes' theorem, we can write:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that an individual has the virus, P(A) is the overall probability of having the virus, and P(B) is the overall probability of testing positive.

We are given that the test returns a positive result for 99.5% of individuals who have the virus, so P(B|A) = 0.995. We are also given that the test returns a positive result for 0.5% of those who do not have the virus, so the probability of testing positive given that an individual does not have the virus is 1 - 0.005 = 0.995.

We are given that overall, 1% of people tested positive, so:

P(B) = 0.01

We can calculate the overall probability of having the virus as:

P(A) = (number of people with the virus) / (total number of people tested)

We do not have enough information to calculate these values directly, but we can use the fact that the test returns a positive result for 99.5% of individuals who have the virus to estimate the number of true positives.

Let n be the total number of people tested. Then, we can estimate the number of true positives as:

(number of true positives) = 0.995 * (number of people with the virus)

We know that overall, 1% of people tested positive, so:

(number of true positives) / n = 0.01

Substituting the estimate for the number of true positives, we get:

0.995 * (number of people with the virus) / n = 0.01

Solving for the number of people with the virus, we get:

(number of people with the virus) = 0.01 * n / 0.995

Substituting this into the expression for P(A), we get:

P(A) = (0.01 * n / 0.995) / n = 0.01005

So the overall probability of having the virus is approximately 0.01005.

Finally, substituting all the values into the expression for P(A|B), we get:

P(A|B) = 0.995 * 0.01005 / 0.01 ≈ 0.9985

Therefore, the percentage of people who test positive for the virus who actually have the virus is approximately 99.85%.

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The equation of the line is 2y+3x=-38

To find the equation of a line perpendicular to 3x= -20-2y that passes through the point (-6,-8), we can use the point-slope form of a line. The point-slope form of a line is[tex]y - y_1 = m(x - x_1)[/tex], where m is the slope of the line and [tex](x_1,y_1)[/tex] is an arbitrary point on the line. Since the given line has a slope of -2/3, the perpendicular line has a slope of 3/2. Therefore, the equation of the line can be written as y - (-8) = (3/2)(x - (-6)). Solving for y, we get 2y + 3x = -38. Therefore, the equation of the line is 2y + 3x = -38.

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Answer:

3

Step-by-step explanation:

unit rate means slope

y2-y1/x2-x1

12-9/4-3

3/1

3

Answer:

Step-by-step explanation:

1/2 x 1/8 : 1/24 =

1/16 x 24 =

24/18 =

3/2

It can be  estimated that 60 deliveries will be to the Forest Park neighborhood if the driver makes 200 deliveries.

We can deduct that  from  the sample of 80 deliveries, the Forest Park neighborhood received 24 deliveries.

We then  estimate how many deliveries will be to the Forest Park neighborhood if the driver makes 200 deliveries by applying  proportional reasoning:

In conclusion, the estimate is  that the driver will make 0.3 x 200 = 60 deliveries to the Forest Park neighborhood.

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Answer: To solve the equation 1/x + 1/y = 1/19 for integer solutions, we can use a common method called "diophantine equations" which involves finding solutions to equations with integer variables.

Multiplying both sides by the least common multiple of x, y, and 19, we get:

19y + 19x = xy

Bringing all the terms to one side, we have:

xy - 19x - 19y = 0

Using Simon's Favorite Factoring Trick, we can add 361 to both sides of the equation, which gives:

xy - 19x - 19y + 361 = 361

(x - 19)(y - 19) = 361

Now, we need to find all the pairs of integers (x, y) such that (x - 19)(y - 19) = 361.

The factors of 361 are 1, 19, and 361 itself. So, we can solve the equation by setting x - 19 equal to each factor and finding the corresponding value of y:

x - 19 = 1, y - 19 = 361, then x = 20, y = 380

x - 19 = 19, y - 19 = 19, then x = 38, y = 38

x - 19 = 361, y - 19 = 1, then x = 380, y = 20

Therefore, the integer solutions to the equation 1/x + 1/y = 1/19 are (x, y) = (20, 380), (38, 38), and (380, 20).

Step-by-step explanation:

Answer:

1) 165.7 cm²

2) 736 cm²

3) 155.5 cm²

4) 169 cm²

Step-by-step explanation:

1) To find the area of shaded region, subtract the area of circle from the area of triangle.          

r = 4 cm      

[tex]\boxed{\text{\bf Area of circle = $\pi r^2$}}[/tex]

                          [tex]= 3.14 * 4 * 4 \\\\= 50.27 \ cm^2[/tex]

Triangle :                  

base = b = 18 cm              

height  = h = 24 cm        

[tex]\boxed{\text{\bf Area of triangle = $\dfrac{1}{2}b*h$}}[/tex]

                              [tex]= \dfrac{1}{2}*18*24\\\\= 9 * 24\\\\= 216 \ cm^2[/tex]

Area of shaded part = area of triangle - area of circle                                  

                                  = 216 - 50.27                                  

                                  = 165.73                                    

                                  = 165.7 cm²

3) To find the area of shaded part, subtract the area of semicircle from the area of square.            

side = 16 cm      

[tex]\boxed{\text{\bf Area of square = side * side}}[/tex]

                            [tex]= 16 * 16\\\\= 256 cm^2[/tex]

diameter of semicircle = side of the square

d = 16 cm                                      

r = 16÷ 2                                      

r = 8 cm        

[tex]\boxed{\text{\bf area of semicircle = $\dfrac{1}{2}\pi r^2$}}[/tex]

                                 [tex]= \dfrac{1}{2}*3.14*8*8\\\\= 100.53 \ cm^2[/tex]

Area of shaded part = area of square - area of semicircle

                                 = 256 - 100.53                                  

                                 = 155.47                                  

                                 = 155.5 cm²

2)   To find the area of shaded part, add the area of rectangle I and the area of rectangle II.

Rectangle I:              

l = 32 - 8 = 24 cm              

w = 24 cm

So, it is a square.        

Area of rectangle I = 24 * 24                                        

                               = 576 cm²

Rectangle II:                

l =  8 cm              

w = 24 - 4 = 20 cm

Area of rectangle II = 8 * 20                                

                                = 160 cm²

Area of shaded part =  area of rectangle I + area of rectangle 2

                                 = 576 + 160

                                 = 736 cm²

4)      length =  l = 26 cm  

          width =  w = 13 cm

Rectangle can be divided into two congruent triangles through its diagonal. So, the area of shaded part can be found by dividing the area of rectangle by 2.      

Area of rectangle = l * w                                    

                             = 26 * 13                                    

                             = 338 cm²

Area of shaded part = area of rectangle ÷ 2                                  

                                 = 338 ÷ 2                                  

                                 = 169 cm²

To produce 200 ml of 60% acid solution from 65% and 40% acid solutions, approximately 715.8 ml of the 65% acid solution must be mixed with approximately 484.2 ml of the 40% acid solution.

Since the resulting solution is 200 ml and is a 60% acid solution, we know that the amount of acid in the solution will be:

0.6 * 200 ml = 120 ml

For the quantity 65% acid solution, the amount of acid is 0.65x ml.

For the quantity 40% acid solution, the amount of acid is 0.4y ml.

Since we want to end up with a total of 200 ml of solution, we know that:

x + y = 200

We also know that the amount of acid in the final solution is the sum of the amounts of acid in the two solutions we're mixing together:

0.65x + 0.4y = 120

Solve the second equation for y:

0.4y = 120 - 0.65x

y = (120 - 0.65x) / 0.4

x + (120 - 0.65x) / 0.4 = 200

Solve for x:

1.6x + 120 - 0.65x = 800

0.95x = 680

x = 715.8 ml

So we need to mix approximately 715.8 ml of the 65% acid solution with approximately 484.2 ml of the 40% acid solution to get 200 ml of 60% acid solution.

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The image of the composite figure is composed of 11 smaller cubes

The sum of the composite shape is solved by dividing the shape into two parts and courting using multiplication then adding the two parts

The first part which is the upper part is solved as follows

= length * width

= 2 * 2

= 4

The second part which is the base is solved as follows

= length * width

= 3 * 3

= 9

Sum of the counting

= 9 + 4

= 11

We can say that the composite figure is made up of 11 smaller cubes

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Answer:

Step-by-step explanation:

a. The hypotheses are coded as: H0: μ1 = μ2; Ha: μ1 ≠ μ2; b. The test statistic is: 9.35; c. The p-value is less than 0.0001, therefore, there is a significant difference between the average workweek in the US.

A null hypothesis is a statement that there is no significant difference or relationship between two variables in a population.

a. The null hypothesis is that there is no significant difference between the average workweek in the United States and the average workweek in Germany, or in other words, the population means are equal. The alternative hypothesis is that there is a significant difference between the two, or the population means are not equal.

H0: μ1 = μ2

Ha: μ1 ≠ μ2

Where:

μ1 = population mean of workweek in United States

μ2 = population mean of workweek in Germany

b. To compute the test statistic, we can use the two-sample t-test formula:

t = (x1 - x2) / sqrt((s1²/n1) + (s2²/n2))

Where:

x1 = sample mean of workweek in United States

x2 = sample mean of workweek in Germany

s1 = sample standard deviation of workweek in United States

s2 = sample standard deviation of workweek in Germany

n1 = sample size of United States

n2 = sample size of Germany

Plugging in the values, we get:

t = (42 - 38) / sqrt((5²/600) + (6²/700)) = 9.35

c. To compute the p-value, we need to use a t-distribution with degrees of freedom equal to the smaller sample size minus one (df = min(n1-1, n2-1)). In this case, df = 599. Using a two-tailed test with alpha level of 0.05, the p-value is less than 0.0001.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference between the average workweek in the United States and the average workweek in Germany.

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By answering the presented question, we may conclude that When y is 9 cuboid feet, the volume of the cube is 729 cubic feet.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron with 8 vertices, 12 sides, and 6 rectangular faces. A cuboid is another name for it. A cube is a cuboid because it has six square faces. Objects found in boxes include bricks and books. The following are the primary distinctions between cubic and cubic: In contrast to a cube's rectangular faces, the faces of a cube are square and equal in size. Although the structures of the cube and cuboid are aesthetically similar, they differ significantly in terms of side length, diagonal, and area.

If you want to find the volume of a cube, the formula is:

Volume equals [tex]s^3[/tex]

where s is the length of one cube side.

If y = 9 feet and y indicates the length of one side of the cube, the volume of the cube may be determined as follows:

Volume = [tex]y^3 + 9^3 = 729 cu ft.[/tex]

When y is 9 feet, the volume of the cube is 729 cubic feet.

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Complete question -

Write and expression you can use to find the value of the cube then find the value if y=9 feet

1, D /non linear function table/

2, F /linear function table/

3, C /linear function equation/

4, B /non linear function equation/

5, A /linear function graph/

6, E /non linear function graph/