Dilate rectangle ABCD by
a scale factor of ½ using E
as the center.

The speed of the current of the river will be 4.47 km per hour.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A riverboat goes at a normal of 14km each hour in still water. the riverboat voyages 110km east up the Ohio waterway and 110km west down a similar stream in a sum of 17.5 hours.

Let 'y' be the speed of the current of the river. Then the equation is given as,

T = T₁ + T₂

17.5 = [110 / (14 + y)] + [110 / (14 - y)]

17.5 / 110 = (14 - y + 14 + y) / (196 - y²)

196 - y² = 176

y² = 20

y = 4.47 km per hour

Then the speed of the current of the river will be 4.47 km per hour.

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The statement if true, for 95% of the samples from the population, the confidence interval we compute will contain the true mean.

In the given question we have to check whether the given statement is TRUE or FALSE.

The given statement is:

For 95% of the samples from the population, the confidence interval we compute will contain the true mean.

Because the underlying approach succeeds on 95% of random samples, we have a 95% confidence that this confidence interval contains the population mean.

Approximately 95% of the estimated intervals will contain the actual value of the population mean if samples are taken frequently and 95% confidence intervals are generated.

So the given statement is true.

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The total change in the stock market from the beginning of the day to the end of the day is 89.75

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

At the beginning of the day, the stock market goes up 30 1/2 points.

At the end of the day, the stock market goes down 120 1/4 points.

The total change in the stock market from the beginning of the day to the end of the day.

= 120(1/4) - 30(1/2)

= 481/4 - 61/2

= 120.25 - 30.5

= 89.75

Thus,

The total change in the stock market from the beginning of the day to the end of the day is 89.75

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Answer:

the remaining mass is 7.3 g

Step-by-step explanation:

a=30g

t=200 years

h=98 years

f(98)=a([tex](\frac{1}{2})^ \frac{t}{h}[/tex]

f(98)=30([tex](\frac{1}{2})^ \frac{200}{98}[/tex]

f(98)=7.3

The area of the triangle as the function of x is [tex]x^2[/tex] / 2x - 4 and the domain of the function is  x∈(2, ∞)

The point on the line = (2, 1)

The give three points are (0, y), (2, 1) and (x, 0)

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

Consider the point (0, y) and (2, 1)

Slope = (1-y) / (2-0)

= (1-y) /2

Consider the point (2, 1) and (x, 0)

Slope = (0-1) / (x-2)

= -1/x-2

Both slopes are equal

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

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

y = 1 + (2/(x-2))

y = x / (x-2)

The area of the triangle = (1/2)bh

Where b is the base

h is the height

The area of the triangle = (1/2) × x × (x / (x-2))

= [tex]x^2[/tex] / 2x - 4

The domain is x∈(2, ∞)

Hence, the area of the triangle is  [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)

The complete question is

A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (2,1). Write the area of the triangle as a function of x, and determine the domain of the function.

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A student can take one of each subject in 40 different ways as calculated using the properties of permutation and combination..

So there are four separate math classes, five different science courses, and two different history courses.

There are now 4 ways to complete a math course.

There are 5 different ways to take science courses.

There are two ways to take a history course.

Total ways are now calculated as the product of the potential ways for each course, which equals 4 × 5 x 2 or 40 ways.

As a result, there are 40 possible combinations for three subjects.

In mathematics, a permutation of a set is, if the set also has an ordered structure, the rearranging of its members into a sequence or linear order. The technique of altering an ordered set's linear order is known as permutation.

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Answer:

Step-by-step explanation:

First of all let's look at the side lengths of both figures.

Let's see how the corresponding sides relate:-

[tex]\sf 6*\cfrac{1}{3} =3[/tex]

[tex]\sf 3*\cfrac{1}{3} =1[/tex]

We can see that all sides scale by the same factor of 1/3.

Therefore, YES A is a scaled copy of Figure B.

______________________

Hope this helps!

Have a great day!

The graph of the line that represents the given equation, 3x - 4y = 8, is shown below

From the question, we are to graph the line that represents the given equation.

The given equation is

3x - 4y = 8

To graph the line, we will determine x-intercept and y intercept of the line.

The x-intercept in the point where y equals zero on the line

and

The y-intercept in the point where x equals zero on the line

Determining the x-intercept

3x - 4y = 8

Set y = 0

3x - 4(0) = 8

3x = 8

x = 8/3

The x-intercept is (8/3, 0)

Determining the y-intercept

3x - 4y = 8

Set x = 0

3(0) - 4y = 8

-4y = 8

y = 8/-4

y = -2

The y-intercept is (0, -2)

Using the x-intercept and y-intercept, the graph of the line is shown below

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Answer:

6115

Explanation:

[tex]70000(1-0.15)^{15} \approx 6115[/tex]

Answer:

12 miles

Step-by-step explanation:

72 x [tex]\frac{10}{60}[/tex] = 12

The length of Rocky Mountain Juniper tree will be 1.269 feet.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches.

Now,

Let the height of Rocky Mountain Juniper tree = x feet

And, A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 81.6 inches.

So, The height of a Rocky Mountain Juniper tree be if at the same time of day it casts a shadow of 20.3 feet will be find as;

⇒ 5.1 / 81.6 = x / 20.3

Solve for x as;

⇒ 5.1 × 20.3 / 81.6 = x

⇒ 103.53 / 81.6 = x

⇒ x = 1.269 feet

Thus, The length of Rocky Mountain Juniper tree will be 1.269 feet.

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Answer: How Weather Exists

Step-by-step explanation:

~I think you mean, how weather exists.

You see, "Weather" exists because of the atmosphere. Evidently, weather  is the movement of the atmospheric gases around the planet that creates weather. Places like the Moon or Mercury do not have weather - only temperature changes.

~Hope this helped :)

The value of x for the given equation is 1.

What is solving an equation?

A General Rule for Equation Solving

Remove parentheses from each side of the equation and combine similar phrases to make it simpler.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

Consider the given expression

0.2(x + 1) + 0.5x = -0.3(x - 4)

Simplifying,

0.2x + 0.2 + 0.5x = -0.3x + 1.2

0.7x + 0.2 = -0.3x + 1.2

Add 0.3x on both sides,

0.7x + 0.2 + 0.3x = -0.3x + 1.2 + 0.3x

x + 0.2 = 1.2

Subtract 0.2 from both sides,

x + 0.2 - 0.2 = 1.2 - 0.2

x = 1

Hence, the value of x for the given expression is, 1.

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If x and y are independent variables such that x has uniform distribution (0,1) and y has exponential distribution means 1 then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3 and E x2 e24 is -1/3

[tex]2^{2}[/tex][tex]e^{ty}[/tex]x ≈ u (0,1) > Independent

y ≈ exp (1) > Independent

E (x) = 0+1/2 = 1/2

v (x) = [tex][1- 0 ] ^{2}[/tex] / 12 = 1/12

E [tex]x^{2}[/tex] = v (x) + [tex][ E x]^{2}[/tex]

       = 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3

E (y) = 1  v(y)=1  E [tex]y^{2}[/tex]= 1+1= 2

E[tex]e^{ty}[/tex] = [tex]\int\limits^_0[/tex][tex]e^{ty}[/tex][tex]e^{-y} dy[/tex]

E[tex]e^{ty}[/tex]  = [tex]\int\limits^_0[/tex][tex]e^{-y} (1-t)[/tex] dy

a : E (x+y) = E (x) + E(y)

       E (x+y) = 1/2+1 = 3/2

b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2

c: E [tex][x-y]^2[/tex] = E ([tex]x^{2}[/tex]-2xy+ [tex]y^{2}[/tex]

   = E [tex]x^{2}[/tex] - 2 Exy + E [tex]y^{2}[/tex]

  =  1/3 - 2 x 1/2 + 2

   = 1/3 + 1 = 4/3

d. E [tex]x^{2}[/tex] [tex]e^{24}[/tex]

   E ([tex]x^{2}[/tex] ) E [tex]e^{24}[/tex] = 1/3 x -1 = - 1/3

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Answer:

[tex]\huge\boxed{\sf 3 \ baskets}[/tex]

Step-by-step explanation:

Let the baskets missed in game 2 be x.

Says that, the shooting of both the games were accurate.

So,

[tex]\displaystyle \frac{Baskets \ made \ in \ game \ 1}{Baskets \ missed \ in \ game \ 1 } =\frac{Baskets \ made \ in \ game \ 2}{Baskets \ missed \ in \ game 2} \\\\\frac{15}{5} =\frac{x}{1} \\\\Cross \ Multiply\\\\15 \times 1 = 5 \times x\\\\15 = 5x\\\\Divide \ 5 \ to \ both \ sides\\\\3 = x\\\\x = 3\\\\\rule[225]{225}{2}[/tex]

The solution is y will increase by 2 units with every unit increase in x1

A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.

X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.

In the above question:-

Interpretation of b1=2

it means that y will increase every 2 units for every unit increase in x1

holding x2 constant.

Hence option B is the correct answer.

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The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.

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

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The function is given below.

f(x) = 28x² - 7

For the zeroes of the function, put f(x) = 0, then we have

f(x) = 0

28x² - 7 = 0

x² = 1/4

x = ± 1/2

The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.

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The 95% confidence interval for the population mean SAT score is given as follows:

(1340, 1460).

The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.

The bounds are obtained according to the equation defined as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

[tex]\overline{x} = 1400, n = 64, s = 240[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.

Then the lower bound of the interval is of:

1400 - 1.998 x 240/sqrt(64) = 1340.

The upper bound of the interval is of:

1400 + 1.998 x 240/sqrt(64) = 1460.

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The balance due on the note at the date of maturity is ​$1010.13.

The offering of a payment by cheque for less than the whole amount sought by the creditor is known as partial payment. It is standard practice to grant debt forgiveness in exchange for the tender of a "payment-in-full" check.

Given permission to apply the US rule

In the United States, a year is deemed to have 360 days for the purposes of calculating interest.

Given that the principal is $ 2000,

Interest rate = 4% = 0.04

The effective date is April 1.

The whole amount is $1,000.

May 1 = partial payment

Duration = 30 days (May 1 - April 1)

Therefore, interest = PTR = 2000 * 0.04 * 30/360 = $6.67

So value = $ 2000 + $6.67 = $6.67

Partial payment received = $1,000

As a result, value = $ 1006.67 = $2006.67 - $ 1000

Time T= 31

Interest = PTR * 31/360 * 0.04 = 3.46

So the total value is $1006.67 + $3.47 = $1010.13.

The note's outstanding balance at maturity is $1010.13.

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The simplification of the expression (3√-5 + 2)(4√-5 -1) gives 5√-5 - 62

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

Given: the expression (3√-5 + 2)(4√-5 -1)

(3√-5 + 2)(4√-5 -1)

Clear the parenthesis:

(3√-5 + 2)(4√-5 -1) = 3√-5(4√-5) + 3√-5 (-1) + 2(4√-5) + 2(-1)

                             = -60 - 3√-5 + 8√-5 -2

                            = 5√-5 - 62

Therefore, the expression (3√-5 + 2)(4√-5 -1) simplifies to 5√-5 - 62

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Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.

Based on the expected value, Rosie's statement is correct.

The expected value, denoted as E(X), represents the average or mean value of a random variable, in this case, the sum of points in a given turn when rolling the five dice.

Tom's statement, "A player will most likely get 17.5 points in any given roll," is not accurate. The expected value of 17.5 points does not necessarily mean that a player is most likely to get exactly 17.5 points in any single roll. Instead, it indicates that over many rolls, the average value of points earned in a turn is 17.5 points.

On the other hand, Rosie's statement, "Over 100 turns, we can expect a total of about 175 points," is correct. Since the expected value is 17.5 points per turn, over 100 turns, we can expect the total sum of points to be approximately 100 turns × 17.5 points/turn = 1750 points.

In summary, the expected value of 17.5 points represents the average outcome over multiple rolls, and based on this value, Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.

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The complete question:

Tom and Rosie are designing a game. In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=5 points, and the highest is 6+6+6+6+6=30 points.

They let X represent the sum in a given turn, and they find the expected value of X is E(X) = 17.5 points.

Tom says, "A player will most likely get 17.5 points in any given roll."

Rosie says, "Over 100 turns, we can expect a total of about 175 points."

Whose statement is correct based on the expected value?

Answer:

[tex]S=\{-2,-3\}[/tex]

Step-by-step explanation:

Required integers are: -2 and -3

Answer:

The three numbers are 3, 7 and 13

Step-by-step explanation:

Considering the 3 numbers: x, y and z

x + z = 16

z=16-x

3x=z-4

3x=16-x-4

4x=12

x=3

3+z=16

z=16-3

z=13

3+13+y=23

y=23-13-3

y=7

Hope this helps :)

1) missing number is 7 (answer #2)

Each circles' numbers add up to 20. (the first one is 1 + 9 + 10, the second is 5 + 4 + 11.)

20 minus 10 minus 3 is 7, so that's the missing number.

2) missing number is 3 (answer #4)

This one's similar to the previous question. Each square's numbers have a sum of 10, this time. (First square is 2 + 7 + 1 + 0, second is 4 + 3 + 1 + 2.)

10 minus 6 minus 1 minus 0 is the same as 10 minus 7. This equals 3- so there's the number that's missing!

Hopefully this helps!

The average rate of change over the interval x = -2 and x = 1 is 4

The equation is given as

f(x) = x² + 5x - 12

The interval is given as:

x = -2 to x = 1

Start by calculating the functions f(-2) and f(1)

So, we have

f(-2) = (-2)² + 5(-2) - 12 = -18

f(1) = (1)² + 5(1) - 12 = -6

So, the average rate over these intervals is calculated as:

Average rate = [f(1) - f(-2)]/[1 - -2]

This gives

Average rate = [-6 - -18]/[1 - -2]

Evaluate

Average rate = 4

Hence, the average rate of change is 4

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The angle ACB would be 80 degrees.

What is tangent to a circle?

The tangent always makes a single-point contact with the circle. It never intersects the circle twice. Tangents from an external point to a circle have the same length.

In the given figure,

angle AOB = 40.

So angle OBA = 40.

Then the angle AOB = 180 - 40 -40

                          AOB = 100.

By the theorem of circles,

          AOB + ACB = 180

          100 + ACB = 180

              ACB = 80.

Hence, the angle ACB would be 80 degrees.

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The had to wait for the second flight for 40 mins.

We know that sometimes when a person is travelling there may be need to have a flight that connects a person from one place to another and at times you would have to wait for a connecting flight and this wait would add to the total time that is required for the journey.

Now we are told in the question that it takes 8 hours and 5 minutes to travel from Hong Kong to Dubai and that they left Dubai at 2250 hrs but landed in Hong King at  1405 hrs. The time in between must be;  2250 hrs - 1405 hrs = 8: 45 hrs thus the time of waiting is 40 minutes.

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Answer:

98.6

Step-by-step explanation:

in photo!!