2 = 2(m − 8) − 2
m =

The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

A numerical expression is characterized as the assortment of numbers factors and works by utilizing operations like expansion, deduction, multiplication, and division.

Considering that;

The expression is,

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

Presently, We can place x and y in the above expression as;

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

⇒ [- 5/(- 2 - 1) ] (- 4) - [-5×-2 + (- 3)]/(- 1)

⇒ [ - 5/ - 3 ] (- 4) - [10 - 3]/(- 1)

⇒ - 20/3 + 7

⇒ 1/3

In this way, The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

to know more about multiplication click here:

https://brainly.com/question/1135170

#SPJ4

The boat travels at  18 miles per hour.

What is speed?

Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed.

The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.

Given:  A boat travels 30 miles up the river in the same amount of time it takes to travel 42 miles down the same river. The current is 3 miles per hour.

From the above information we can write,

Let, u is the boat speed in still water, then

\(\frac{30}{u-3} = \frac{42}{u+3}\)

Taking cross multiplication,

30(u + 3) = 42(u - 3)

Solving,

30u + 90 = 42u - 126

42u - 30u -126 -90 = 0

12u = 216

u = 18

Therefore, the speed of boat in still water is, 18 miles per hour.

To know more about the speed, click on the link

https://brainly.com/question/13943409

#SPJ4

The calculated test statistic lies in the rejection region. So, we reject the null hypothesis and conclude that the chicks differ from 1:1. The rejection region lies between  zα/2 = 1.96 for α = 0.05So, 2.5 > 1.96.

1. To test the claim that a coin is biased, it is tossed 12 times. It comes down heads three times. Test at the 10% significance level whether this claim is justified.

Given, Total number of tosses, n = 12

Number of heads, X = 3

Hence, number of tails, (n-X) = (12-3)

                                               = 9

Now, Null hypothesis H0: Coin is unbiased or p=1/2

Alternative hypothesis Ha: Coin is biased or p ≠1/2(where p is probability of getting a head in a single toss)

Significance level, α = 0.10

Now, the test is conducted using normal distribution as np(1−p) ≥ 10. and nq(1−q) ≥ 10

Here, np = 12 × 1/2

               = 6 and

nq = 12 × 1/2

    = 6

Both are greater than or equal to 10.

So, we use normal approximation. Hence, the test statistic is given by

z = (X - μ) / (σ / √n),where μ = np

                                              = 12 × 1/2

                                              = 6,

σ = √npq

   = √(12 × 1/2 × 1/2)

   = 1.73.

Now, the test statistic is

z = (3 - 6) / (1.73 / √12)

  = -1.73 × √12 / 1.73

  = -4.71 [using calculator]

Now, for two-tailed test, the rejection regions are given by

z > zα/2 or z < -zα/2 or |-z| > zα/2

where, zα/2 = 1.645 for α = 0.10

So, |-4.71| > 1.645 or -4.71 < -1.645

Hence, the calculated test statistic lies in the rejection region.

So, we reject the null hypothesis and conclude that the coin is biased.

2. A biologist discovers a color out the 16 chicks that hatch during his period of incsting in a cavestigation, 13 are female. Test at the 5% significance level whether the chicks differs from 1:1.

Total number of chicks, n = 16

Number of female chicks, X = 13

Hence, number of male chicks, (n-X) = (16-13)

                                                             = 3

Now, Null hypothesis H0: Sex ratio is 1:1

Alternative hypothesis Ha: Sex ratio differs from 1:1

Significance level, α = 0.05

Now, the test is conducted using binomial distribution

Here, the test statistic is given by

z = (X - μ) / (σ), where μ = np

                                       = 16 × 1/2

                                       = 8,

σ = √npq

  = √(16 × 1/2 × 1/2)

  = 2.

Now, the test statistic is

z = (13 - 8) / 2

 = 2.5 [using calculator]

Now, for two-tailed test, the rejection regions are given by

z > zα/2 or z < -zα/2

where, zα/2 = 1.96 for α = 0.05So, 2.5 > 1.96

To learn  more on  probability :

https://brainly.com/question/23417919

#SPJ11

Answer:

It depends on the numbers

Step-by-step explanation:

Give some examples

Answer:

Shredder A shreds about 3.67 pounds of paper per minute.

Step-by-step explanation:

1100 pounds/(5 * 60 minutes)

1100 pounds/300 minutes

3.6666...7 pounds/minute

3.67 lb/min

Answer:

B. (2x + 10)(2x + 9)

Step-by-step explanation:

Length (L) of the garden and walkway = x + 10 + x = (2x + 10) ft

Width (W) of the garden and walkway = x + 9 + x = (2x + 9)

Area of the garden and walkway = area of rectangle = L*W

= (2x + 10)(2x + 9)

The polynomial representing the total area of the garden and walkway = (2x + 10)(2x + 9)

The probability that fewer than 4 are independent = 0.971

Let X be a random variable representing the number of independent people out of 12 people.

Then X follows binomial distribution.

A binomial distribution considers two possibilities in 'n' trials -  success or  failure. Here the case of success is being independent and the case of failure is being either republican or democrat.

The probability distribution function of a binomial distribution is,

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

Where n is the number of trials, p - the probability of success

Here, n = 12

Since 6% of voters are independent, probability of being an independent = 6/100 = 0.06

Probability that fewer than 4 are independent = P( X = 0 or 1 or 2 or 3)

                                                                             = P( X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Now, P(X=0) = ¹²C₀ (0.06)⁰ (1-0.06)¹²⁻⁰

                      = 1 x 1 x 0.4759

                      = 0.4759

P(X = 1) = ¹²C₁ (0.06)¹ (1-0.06)¹²⁻¹

           = 12 x 0.06 x 0.94¹¹

           = 0.3645

P(X = 2) = ¹²C₂ (0.06)² (1-0.06)¹²⁻²

             = 66 x (0. 06)² x 0.94¹⁰

            = 0.128

P(X = 3) =  ¹²C₃ (0.06)³ (1-0.06)¹²⁻³

             = 22 x 0.000216 x 0.94⁹

             = 0.00272

Therefore, Probability that fewer than 4 are independent = P( X = 0) + P(X = 1) + P(X = 2) + P(X = 3) =  0.4759 + 0.3645 +  0.128 + 0.00272 = 0.971

Learn more about probability distributions at https://brainly.com/question/23286309

#SPJ4

After your grandmother makes a $5,000 deposit on your 18th birthday, the amount in the savings account can be calculated using compound interest. Assuming the account pays an interest rate of 7%, the amount in the account immediately after the deposit can be determined by applying the compound interest formula.

To calculate the amount in the savings account after the deposit on your 18th birthday, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A represents the final amount, P is the principal (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the initial deposit is $5,000, the interest rate is 7% (or 0.07 as a decimal), and the deposit is made on your 18th birthday, which means the time is 17 years. Since no information is given about the compounding frequency, let's assume it is compounded annually (n = 1).

Plugging in the values into the compound interest formula, we have A = 5000(1 + 0.07/1)^(1*17) = 5000(1.07)^17 ≈ $15,128.

Therefore, the amount in the savings account immediately after your grandmother makes the deposit on your 18th birthday is approximately $15,128, rounded to the nearest dollar.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ11

Answer:

4. Corresponding angles

5. alternative interior angles

6. Same-side interior angles

7. Supplementry

Step-by-step explanation:

I can't see the numbers so I can't solve for x. Sorry.

Probability Distributions for Discrete Random Variables are

a. P(X = 3) = 0.2

b. P(X < 3) = 0.3

c. P(2 < X < 5) = 0.5

To solve the given problems, we need to determine the missing probability value for X = 3. Let's calculate it and then proceed with the rest of the questions.

Given:

X 1 2 3 4 5

P(x) 0.1 0.2 ? 0.3 0.2

To find the missing probability value:

0.1 + 0.2 + P(X = 3) + 0.3 + 0.2 = 1

0.8 + P(X = 3) = 1

P(X = 3) = 1 - 0.8

P(X = 3) = 0.2

Now, we can answer the questions:

a. P(X = 3) = 0.2

b. P(X < 3) = P(X = 1) + P(X = 2)

= 0.1 + 0.2

= 0.3

c. P(2 < X < 5) = P(X = 3) + P(X = 4)

= 0.2 + 0.3

= 0.5

Therefore,  Probability Distributions for Discrete Random Variables are

a. P(X = 3) = 0.2

b. P(X < 3) = 0.3

c. P(2 < X < 5) = 0.5

For such more questions on Probability Distributions

https://brainly.com/question/30390163

#SPJ11

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

Learn more about direction from

https://brainly.com/question/29248951

#SPJ11

The method-of-moments estimator for θ is θ = (2 * Y_bar) / 3.

To derive the method-of-moments estimator for θ using the given interval and variables, follow these steps:

1. Given that y1, y2,..., yn are independent and identically distributed uniform random variables on the interval (0, 3θ), their probability density function (pdf) can be expressed as f(y) = 1/(3θ) for 0 < y < 3θ.

2. Calculate the expected value (mean) of the uniform distribution. The expected value E(Y) for a uniform distribution on the interval (0, 3θ) is (3θ - 0) / 2 = 3θ / 2.

3. The method-of-moments estimator involves matching the sample moments with the population moments. In this case, we match the sample mean with the population mean. Let Y_bar be the sample mean, which can be calculated as Y_bar = (y1 + y2 + ... + yn) / n.

4. Now, equate the sample mean Y_bar with the population mean E(Y) to get the method-of-moments estimator for θ:

Y_bar = 3θ / 2

5. Solve for θ:

θ = (2 * Y_bar) / 3

So, the method-of-moments estimator for θ is θ = (2 * Y_bar) / 3, where Y_bar is the sample mean of the independent and identically distributed uniform random variables on the interval (0, 3θ).

Learn more about method-of-moments estimator

brainly.com/question/30526036

#SPJ11

Therefore, the indicated z-score is 2.45.

To find the indicated z-score, we need to use a standard normal distribution table. From the graph, we can see that the area to the right of the z-score is 0.9850.
Looking at the standard normal distribution table, we find the closest value to 0.9850 in the body of the table is 2.45. This means that the z-score that corresponds to an area of 0.9850 is 2.45.
It's important to note that the standard deviation of the standard normal distribution is always 1. This is because the standard normal distribution is a normalized version of any normal distribution, where we divide the difference between the observed value and the mean by the standard deviation.

To know more about standard deviation visit:

https://brainly.com/question/31516010

#SPJ11

hhhahahshhehrhhehrhrhrhrh

The expression \((3xy^{-3})^{-2}\) without negative exponents is  \(\frac{y^6}{9x^2}\).

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An expression in exponents \((3xy^{-3})^{-2}\).

Now, Changing the place of exponents from the numerator to the denominator or vice versa changes its sign.

Therefore, \((3xy^{-3})^{-2} = 3^{-2}x^{-2}y^{6}\).

\(3^{-2}x^{-2}y^{6} = \frac{y^6}{3^2x^2}\).

\(\frac{y^6}{3^2x^2} = \frac{y^6}{9x^2}\).

learn more about exponents here :

https://brainly.com/question/5497425

#SPJ1

Answer:

3 days.

Step-by-step explanation:

Simple ratio:

8/2=12/x

4/1=12/x

4x=12

x=3

Hope this helps!

The total distance traveled over the interval 0 < t < 8 is: 32/3 + 16/3 + 176/3 = 224/3.

To find the displacement over the given interval, we need to integrate the velocity function:

∫v(t)dt = ∫(t^3 - 10t^2 + 24t)dt = (1/4)t^4 - (10/3)t^3 + 12t^2

Now we can evaluate the displacement over the different intervals:

0 < t < 4:

(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2 = 32/3

4 < t < 6:

(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2 - [(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2]

= -16/3

6 < t < 8:

(1/4)(8)^4 - (10/3)(8)^3 + 12(8)^2 - [(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2]

= 176/3

Therefore, the displacement over the entire interval 0 < t < 8 is:

32/3 - 16/3 + 176/3 = 64/3

To find the distance traveled over the given interval, we need to break down the motion into the different intervals of direction:

0 < t < 4: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 32/3.

4 < t < 6: The particle is moving in the negative direction, so the distance traveled is the absolute value of the displacement, which is 16/3.

6 < t < 8: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 176/3.

Learn more about displacement here:

https://brainly.com/question/29769926

#SPJ11

The total distance traveled over the interval 0 < t < 8 is: 32/3 + 16/3 + 176/3 = 224/3.

To find the displacement over the given interval, we need to integrate the velocity function:

∫v(t)dt = ∫(t^3 - 10t^2 + 24t)dt = (1/4)t^4 - (10/3)t^3 + 12t^2

Now we can evaluate the displacement over the different intervals:

0 < t < 4:

(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2 = 32/3

4 < t < 6:

(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2 - [(1/4)(4)^4 - (10/3)(4)^3 + 12(4)^2]

= -16/3

6 < t < 8:

(1/4)(8)^4 - (10/3)(8)^3 + 12(8)^2 - [(1/4)(6)^4 - (10/3)(6)^3 + 12(6)^2]

= 176/3

Therefore, the displacement over the entire interval 0 < t < 8 is:

32/3 - 16/3 + 176/3 = 64/3

To find the distance traveled over the given interval, we need to break down the motion into the different intervals of direction:

0 < t < 4: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 32/3.

4 < t < 6: The particle is moving in the negative direction, so the distance traveled is the absolute value of the displacement, which is 16/3.

6 < t < 8: The particle is moving in the positive direction, so the distance traveled is the same as the displacement, which is 176/3.

Learn more about displacement here:

https://brainly.com/question/29769926

#SPJ11

The correct answer for the given expression is 99.22.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

The expression will be solved as:-

E = \(({5 -\dfrac{10}{27}})^3\)

E = \((\dfrac{135-10}{27})^3\)

E =\(\dfrac{125}{27}^3\)

E = 99.22

Therefore the correct answer for the given expression is 99.22.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ1

Answer:

-3

Step-by-step explanation:

The Binomial Theorem (a+b)2 (a+b)(a+b) a2 +2ab + b2

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

The inverse of (- 2 . 3 ) is (1 / - 2.3 ).

In mathematics, the inverse of a number refers to the concept of taking its reciprocal; for instance (2 . w ) results in its reciprocal as ( 1/ 2. w ). When a number is multiplied by its inverse the result yields 1, meaning that the product of the number and its inverse, i.e. reciprocal always equals 1.

As per the given number which is (-2.3) and its inverse is ( 1 / -2.3 ), when these two numbers are multiplied together they result in 1. Such as:

(-2.3) x ( 1 / -2.3 ) = 1

You can learn more about inverse at

https://brainly.com/question/27839002

#SPJ4

Answer:

108

Step-by-step explanation:

You divide by 6 each time

Answer:

2/3

Hope that helps!

Answer:

x > 9

Step-by-step explanation:

x - 6 > 3

all you have to do is solve for x so

add 6 to both sides to make x alone

x > 9

I hope it helps you ❤️❤️❤️

Answer:

61.504

Step-by-step explanation:

Answer:

There are £61.50 in 992

Step-by-step explanation:

Here, we shall be doing some currency conversions.Now, £31 = 500 rublesThen;£x = 992 rubles To get c, what we do is simply cross multiply £x * 500 rubles = £31 * 992 rubles £x = (£31 * 992 rubles)/500 rubles £x = £61.504which is £61.50 to two decimal places

hope this helps!!

Answer: hi beautiful here ya go the answers and also merry christmas Have a lovely day

Step-by-step explanation:

here's your solution

=> cost of 10 apple = $ 8.95

=> cost of 1 apple = $8.95/10 = $ 0.895

=> cost of 4 apple = $ 0.895*4

=> cost = $3.580

hope it helps