If P(A) = 0.7 P(B) = 0.6 and A and B are independent event, find P(A and B)

Answer:

the slope of the line x+y = 6 is -1.

Step-by-step explanation:

slope = - coefficient of x

----------------------

coefficient of y

slope = -1 /1

slope = -1

Answer:

A: -1

Step-by-step explanation:

Respuesta:

175 rad / s²

Explicación paso a paso:

Dado que :

Velocidad angular final = 350 rad / s

Tiempo empleado = 2 segundos

La aceleración angular, a =?

Recordar ; la aceleración angular es igual a la carga en velocidad angular con el tiempo

(velocidad final - Velocidad inicial) / tiempo empleado

Velocidad inicial = 0 rad / s

Aceleración angular = (350 - 0) / 2 = 350/2

= 175 rad / s²

Step-by-step explanation:

To solve the given equations, let's assign variables to each equation and solve them step by step.

Let's assume:

a = x

b = y

c = z

d = w

e = v

From the given equations:

a * b = 1 -> x * y = 1 (Equation 1)

b * c = 4 -> y * z = 4 (Equation 2)

c * d = 9 -> z * w = 9 (Equation 3)

d * e = 16 -> w * v = 16 (Equation 4)

e * a = 25 -> v * x = 25 (Equation 5)

Now, let's solve the equations using substitution:

From Equation 1 (x * y = 1), we can rewrite it as y = 1/x.

Substituting y in Equation 2, we get (1/x) * z = 4, which gives us z = 4x.

Substituting z in Equation 3, we have (4x) * w = 9, which gives us w = 9/(4x).

Substituting w in Equation 4, we get (9/(4x)) * v = 16, which simplifies to v = (16 * 4x)/9.

Finally, substituting v in Equation 5, we have [(16 * 4x)/9] * x = 25.

Simplifying the equation, we get:

(64x^2)/9 = 25.

To solve for x, we can cross multiply and solve the quadratic equation:

64x^2 = 225.

Dividing both sides by 64, we get:

x^2 = 225/64.

Taking the square root of both sides, we have:

x = ±(√(225/64)).

So, x = ±(15/8).

Now, substituting the values of x in the respective equations, we can find the values of y, z, w, and v.

For x = 15/8:

y = 1/(15/8) = 8/15

z = 4 * (15/8) = 30/4 = 15/2

w = 9/(4 * (15/8)) = 9/(30/8) = 9 * (8/30) = 12/5

v = (16 * 4 * (15/8))/9 = (60/2)/9 = 60/18 = 10/3

For x = -15/8:

y = 1/(-15/8) = -8/15

z = 4 * (-15/8) = -30/4 = -15/2

w = 9/(4 * (-15/8)) = 9/(-30/8) = -9 * (8/30) = -12/5

v = (16 * 4 * (-15/8))/9 = (-60/2)/9 = -60/18 = -10/3

Therefore, the possible solutions for the variables are:

x = 15/8, y = 8/15, z = 15/2, w = 12/5, v = 10/3

or

x = -15/8, y = -8/15, z = -15/2, w = -12/5, v = -10/3.

Note: The solution includes both positive and negative values for the variables.

Answer: 9/10

Step-by-step explanation: I know this because 9 times 9 is 81 and 10 times 10 is 100.

The median would be better for describing the income of a typical person in the class because the professor's large salary skews the data to the right while all the students are towards the left and center.

Answer:

25

Step-by-step explanation:

Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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He has mowed the law before he makes a total of Dollar 300, The number of times he has to mow a lawn is 10

Joe mows a lawn, for which he charges = $ 30

Some one-time cleanup work, for which he is paid = $ 60

According to the question:

He has to mow the lawn before he makes a total of Dollar300

Number of times he has to mow a lawn =   300 /  30

The number of times he has to mow a lawn = is 10

He has mowed the law before he makes a total of Dollar 300, 10 times.

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A right triangle has legs, so the rate of change of the area is =  -102.5 \(\frac{inches^{2} }{sec}\).

A right triangle has legs of 15 inches and 20 inches

The short leg is decreasing by 4 in/sec and the long leg is shrinking at 7 in/sec.

Let us assume,

Two legs are a and b

So ,

We can write,

a = 15 - 5t

b = 20 - 7t

The area of a right triangle is the region occupied inside the boundary of the right-angled triangle.

The formula for the area of a right-angle triangle is A = (½)× b× h square units.

If you know the two legs, then use the formula area = a × b / 2, where a, and b are the legs.

The rate of change of the area,

area A = ab /2

A =  \(\frac{(15 - 5t)*(20 - 7t)}{2}\)

We can multiply the coefficients,

A = 300 - 105t - 100t + 35\(t^{2}\) /2

A = 35\(t^{2}\) - 205t +300 / 2

A = 35/2\(t^{2}\) - 205/2t + 300/2

A = 17.5\(t^{2}\) - 102.5t + 150

The rate of change of the area is,

\(\frac{dA}{dt}\) =  d/dt ( 17.5\(t^{2}\) - 102.5t + 150)

\(\frac{dA}{dt}\) = 35t - 102.5

And at t=0,

\(\frac{dA}{dt}\) = 35(0) - 102.5

\(\frac{dA}{dt}\) = -102.5 \(\frac{inches^{2} }{sec}\)

Therefore,

A right triangle has legs, so the rate of change of the area is = -102.5 \(\frac{inches^{2} }{sec}\).

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According to a recent survey, nearly half of the respondents cited better pay as their primary reason for changing jobs.

The survey was conducted on a national level and the results indicate that a majority of people are looking to increase their earnings by switching jobs.

Other reasons are:

In conclusion, the survey clearly showed that the main reason for job changes among respondents was better pay. However, various other factors also play a role in an individual's decision to switch jobs, such as working conditions, career paths, and location.

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The volume if the fish tank purchased by Darren is 17248 in³

Volume is the amount of space occupied by a three dimensional shape or object.

1 feet = 12 inches; hence:

2 ft 4 in = (2 ft * 12 in per ft) + 4 = 28 in

1 ft 10 in = (1 ft * 12 in per ft) + 10 = 22 in

The volume of tank = 28 in * 28 in * 22 in = 17248 in³

The volume if the fish tank purchased by Darren is 17248 in³

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Answer:

Area of a circle = 3.14 X radius X radius

= 3.14 X 4.5 X 4.5 = 63.585 m2

Hope this helps....

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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The probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a population of marks on a biology final test that is normally distributed with a mean of 78 and a standard deviation of 6. We want to know the probability that a class of 50 has an average score that is less than 77.
Using the central limit theorem, we can calculate the standard error of the mean as follows:
standard error of the mean = standard deviation / square root of sample size
standard error of the mean = 6 / √50
standard error of the mean = 0.8485
Next, we need to calculate the z-score for a sample mean of 77:
z-score = (sample mean - population mean) / standard error of the mean
z-score = (77 - 78) / 0.8485
z-score = -1.18
We can use a standard normal distribution table or calculator to find the probability associated with a z-score of -1.18. The probability of a sample mean less than 77 is approximately 0.1190 or 11.90%.
Therefore, the probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

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Answer: 8:1

Step-by-step explanation:

To find the simplest ratio of 4 kg of metal to 500g of plastic, we need to convert both quantities to the same unit of measurement. Let's convert 4 kg to grams:

Now we have 4000 g of metal and 500 g of plastic. To simplify the ratio, we can divide both quantities by their greatest common factor (GCF), which is 500:

Therefore, the simplest ratio of 4 kg of metal to 500g of plastic is 8:1.

________________________________________________________

The total weight of metal and plastic in the ratio 8:1 is indeed 4.5 kg.

The total weight of metal and plastic is:

The simplest ratio of metal to plastic is found by dividing both quantities by their greatest common factor.

The greatest common factor of 4 kg and 0.5 kg is 0.5 kg. Dividing both quantities by 0.5 kg gives:

\(\therefore\) The simplest ratio of metal to plastic is 8:1.

To check, we can verify that:

So the total weight of metal and plastic in the ratio 8:1 is indeed 4.5 kg.

\(\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}\)

Answer:

I Didnt mean to answer sorry i cant help

I dont know

How Go back Srry Again

Answer: Cumulative frequency distribution

Step-by-step explanation: Not entirely sure but I believe you are looking for this definition based on the question. Hope this helps :)

A = $5,800.00

I = A - P = $1,800.00

hey!

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 15%/100 = 0.15 per year.

Solving our equation:

A = 4000(1 + (0.15 × 3)) = 5800

A = $5,800.00

The total amount accrued, principal plus interest, from simple interest on a principal of $4,000.00 at a rate of 15% per year for 3 years is $5,800.00.

---------------------------------------------

hope i helped in some way..have great day!

Answer:

No

Step-by-step explanation:

After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, \(N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}\). Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

\(\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}\)

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

\(\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}\)

The answer is 35 minutes.

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Answer:

y-2=5(x-(-1) ==> y-2 = 5(x+1)

Step-by-step explanation:

The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.

If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050

The population is given to be increasing exponentially, which means it will follow the equation:

\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.

We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:

\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)

Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.

Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:

\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)

where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)

where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)

Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)

To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):

\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.

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3/4 divided by 1/2, when written with common denominators, is equal to 3/2 or 1.5 as a decimal.

In mathematics, common denominators refer to a shared multiple of the denominators of two or more fractions. When fractions have common denominators, their denominators are the same, which makes it easier to add, subtract, or compare them. For example, to add the fractions 1/4 and 3/8, we need to find a common denominator that both 4 and 8 can divide into evenly. One common denominator is 8, so we can rewrite the fractions as:

1/4 = 2/8

3/8 = 3/8.

In the given question,

To divide one fraction by another, we can multiply the first fraction by the reciprocal of the second fraction. Therefore, we can rewrite the expression 3/4 / 1/2 as:

3/4 * 2/1

To simplify this expression, we can multiply the numerators and denominators:

(3 * 2) / (4 * 1) = 6/4

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

6/4 = 3/2

Therefore, 3/4 divided by 1/2, when written with common denominators, is equal to 3/2 or 1.5 as a decimal.

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Answer:

32.82

Step-by-step explanation:

Answer:

32.82 OUNCES

Step-by-step explanation:

It is really easy.

All you have to do is 5.47x6

Answer:

9

Step-by-step explanation:

-5 + (-18) +32

-23 + 32

32 -23

Answer:

All real numbers

All real numbers

Smallest value in the domain of inverse

The complete sentences are shown below:

The domain refers to the set of possible input values. The domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values shown on the y-axis. The easiest method to find the range of function is by graphing it and looking for the y-values covered by the graph. To find the range of a quadratic function, it is sufficient to see if it has a maximum or minimum value. The maximum/minimum value of a quadratic function is the y-coordinate of its vertex. To find the domain of the rational function, set the denominator as 0 and solve for the variable. The domain is denoted by all the values from left to right along the x-axis and the range is given by the span of the graph from the top to the bottom.

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