Given the following: P(A)=0.28, P(B)=0.64, P(B|A)= 0.37, calculate P(A and B)

The relationship between the discriminant of a quadratic polynomial and the number of real roots is that the discriminant let us know the number and type of the solutions.

Basically for a quadratic polynomial ax²+ bx + c = 0,  the  b² - 4ac is the  discriminant.if the discriminant is greater than zero (b²- 4ac > 0), the graph intersects the abscissa twice which means it has two real solutions,  whereas if the discriminant is equal to zero ( b² - 4ac = 0), then the graph intersects once the abscissa which means it has a  single real solution and at last  if less than zero (b² - 4ac < 0), then the graph doesn't at all intersect the abscissa which, it has imaginary solutions.

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The following statement "In centrally planned economies, the distribution of goods costs nothing to administer" is true.

A centrally planned economy, often known as a command economy, is an economic system in which a government agency makes economic choices affecting the production and distribution of products. Centrally planned economies vary from market economies in that these decisions are the outcome of hundreds of choices made by producers and consumers.

State-owned corporations provide goods and services in planned economies, however, independent firms may occasionally be brought into economic planning. Prices, salaries, and production schedules are often set by a centralized bureaucracy.

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In deductive thinking, you start with a given set of rules and conditions and determine what must be true as a consequence - True

In deductive thinking, conclusions are reached based on premises that are typically taken to be true. A conclusion is based on the concordance of several premises typically presumed to be true in this logical procedure. Top-down logic is another name for deductive thinking. It only makes use of data that is believed to be reliable. It excludes sentiments, feelings, and unsupported assumptions because it is challenging to assess the integrity of this data.

Making logical assumptions and basing a conclusion on them are the foundations of deductive thinking. It enables the individual to combine the information from two or more assertions to arrive at a sound conclusion. If something is presumptively true and a different object is connected to the first presumption, then the original truth must also apply to the second. Therefore, In deductive thinking, if you start with a given set of rules and conditions and determine what must be true as a consequence holds true.

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Answer:

A

Step-by-step explanation:

Comment

The tricky part is f(4)

Log part

That is defined by log_2 which means that the base used for the log is 2.

We don't have log_2 on our calculators so you have to create it.

Substitute 4 for x

log_2 (4) = log_10(4)/ log_10 (2)     Which your calculator can handle

log_2 (4) = Log(4)/ log(2) = 2

f(x) = 1/2 x^2

x = 2.1

Only answers a and b are correct, but which one is right? 2.1 is between 2 and 4. So you choose f(x) = 1/2 x^2

1/2 2.1^2 = 1/2 4.41 = 2.205

Answer

A

Answer:

  (a)  f(2.1) = 2.205 and f(4) = 2

Step-by-step explanation:

You want to evaluate a piecewise-defined function to find f(2.1) and f(4).

The first step in evaluating a piecewise defined function is to match the argument value with the appropriate domain.

Once you have identified the function you are evaluating, substitute the argument for the variable and carry out the arithmetic in the usual way.

The desired function values are f(2.1) = 2.205 and f(4) = 2.

This will be simplified with this law of indices

Going further, we can simplify to:

Answer:

B

Step-by-step explanation:

the full domain is

(-∞,-7[ ∪ ]-7,+∞)

x, x

1.7

Explanation

Step 1

we can see in the graph, that :

the solutions of the equation f(x)=0, are the values where y =0 , it is when the line crosses the x-axis, so the solution of the first blank is

x

Step 2

and, the solution of the inequality

is the set of values wich the graph is above the x-axis

Step 3

now, for the next question, let's check the points where the line crosses the x-axis, and the intervals where the lines is above the x-axis

we can see the solution of f(X)=0 are

Finally, check the interval where the graph is above the x-axis, it is from a to 7, in interval notation

I hope this helps you

Answer:

48/13

Step-by-step explanation:

To make this into an improper fraction, convert the integer into a fraction using the denominator of the fraction

3 * 13/13 = 39/13

Then add it to the rest of the fraction

39/13 + 9/13

= 48/13

Answer: 48/13

Step-by-step explanation: first multiply 3 x 13 to get 39. do this because you get the fraction for the whole number, 3. then, add 39 to the numerator (9). you will get 48/13. you do this because you are adding the whole number (3) to the fraction so that way it is an improper fraction.

the given equation is

calculate f(-3) by putting x = -3

now, f(4)

now the final calculation

that is 70 -49 = 21

so the correct answer is 21

2f(-3) - f(4) =​ 21 .

Answer

• a) 30.9

• b) 76

Explanation

Given

• Homework: 25%

• Project: 10% (each)

• Final exam: 45%

A student has:

Part A

• Homework: 86

• First project: 94

Part B

• Second project: 71

• Third project: 78

• Total grade: 80

Procedure

• a)

To know the student's grade at the point where he has an 86 homework average and 94 on the first project. We have to multiply the ponderation of each category times the grade to find the final grade (TG), meaning:

Simplifying:

• b)

Following the same procedure, now we have to multiply the ponderations of the new grades, as follows:

Next, as we are asked to find the calculations of the grade of the exam to get a final grade of 80, we have to consider the latter and the ponderation for the exam:

where x is the grade of the exam.

Solving for x:

To find the mean of grouped data, we need to use the next formula:

First, we need to find the midpoint of each interval:

The midpoint of interval = 1/2 (lower class limit + upper-class limit)

Then:

Time for competition (in minutes) ----- frequency ---- midpoint

9 -11 8 1/2(9+11) = 10

12 -14 7 1/2(12+14) = 13

15-17 5 1/2(15+17)= 16

18 - 20 3 1/2(18+20) = 19

21-23 3 1/2(21+23) = 22

Now, multiply the frequency of each interval by its midpoint:

10 * 8 = 80

13* 7 = 91

16 * 5 = 80

19 * 3 = 57

22 *3 = 66

Summ all the results 80 + 91 +80+57+66= 374

Then, sum all the frecuencys = 8 + 7 +5 +3 +3 = 26

Use the mean formula =

The mean is given using five decimals.

The standard error for the sample mean exists

[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].

Let the value of mean be [tex]$P(\bar{X} < 0.95)$$[/tex]

Normal Distribution, [tex]$\mu=1, \sigma=0.1, n=12$[/tex]

[tex]$P(\bar{X} < 0.95)=$[/tex] Area to the left of 0.95

we convert this to standard normal using

[tex]$z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}$[/tex]

[tex]$z=\frac{0.95-(1)}{0.1 / \sqrt{12}} \approx-1.732051 \approx-1.73$[/tex]

[tex]$P(\bar{X}[/tex] < 0.95) = P(Z < -1.73) = 0.0418 (from z-table)

P(Z < -1.73); in a z-table having area to the left of z, locate -1.7 in the left most column. Move across the row to the right under column 0.03 and get value 0.0418.

[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex]

Therefore, the standard error for the sample mean exists

[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].

The complete question is;

What is the probability that the sample mean will be below 0.95 centimeters?

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken.

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Answer: [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]\sqrt{(-6-(-3))^2 +(5-7)^2}=\sqrt{13}[/tex]

We define the following variables:

• x = age (in years) of the eldest,

• y = age (in years) of the second,

• z = age (in years) of the youngest.

From the statement, we know that:

0. the eldest is 7 years older than the second → , x = 7 + y,,

1. the second is 2 older than the youngest → ,y = 2 + z,,

2. the sum of the ages 12 years from now will be 56 → x + y + z + 12 = 56 → ,x + y + z = 56 - 12 = 44,.

We have the following system of equations:

i) Replacing the second equation in the first one, we have:

ii) Summing the ages of the three daughters, we have:

iii) Equalling the last equation with the third one, we have:

Replacing the value of z in the equation of x and y, we get:

Answer

The ages of the daughters are 20, 13 and 11.

Part a

The altitude in miles = 6.07 miles

Part b

Head wind in miles per hour = 439.30 miles per hour

Part c

The headwind in miles per hour = 114.35 miles per hour

Part d

The temperature in degree Fahrenheit = -41.8 degrees Fahrenheit

Part a

The altitude = 9770 meters

To convert meter to miles, divide the length by 1609

Therefore,

9770 meters = 9770/1609

=6.07 miles

Part b

The ground speed = 707 km/hours

To convert km per hour to miles per hour, divide the speed value by 1.609

707 km/hour = 707/1.609

= 439.30 miles per hour

Part c

The head wind = 184 km/hour

To convert km per hour to miles per hour, divide the speed value by 1.609

184 km/hour = 184/1.609

= 114.35 miles per hour

Part d

The outside air temperature = -41 degree C

F = (9/5)C + 32

= (9/5)×-41+32

= -41.8 degrees Fahrenheit

Hence,

Part a

The altitude in miles = 6.07 miles

Part b

Head wind in miles per hour = 439.30 miles per hour

Part c

The headwind in miles per hour = 114.35 miles per hour

Part d

The temperature in degree Fahrenheit = -41.8 degrees Fahrenheit

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Given the initial value, w1, and the final value, w2, the percent decrease can be calculated as:

The initial value is 247 and the final one is 221, so:

So, the percent decrease is approximately 10.53%.

Answer: 9180 mg

Step-by-step explanation:

First we must convert the patients weight from lb to kg.

102lb x [tex]\frac{0.45kg}{1lb}[/tex] = 102 x 0.45 kg = 45.9 kg

Now to calculate the amount of the drug she should receive.

45.9 kg x [tex]\frac{200mg}{kg}[/tex] = 9180 mg

The most appropriate choice for Number line will be given by -

The number line has been shown in the figure attached.

What is a number line?

A visual representation of the real numbers can be shown on a diagrammatic representation of graduated straight lines. The visual representation of the real numbers is known as the number line. Number line can be used for addition or subtraction of two numbers.

Here,

The number line has been attached

[tex]\frac{3}{9}[/tex] lies between 0 and 1

So the space between 0 and 1 is divided into 9 equal parts as the denominator of the given fraction is 9

Now the third small line is the required value i.e  [tex]\frac{3}{9}[/tex]  as 3 is in the numerator of the given fraction

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Box 1 )

Box 2 )

We will have that the expression that represents the problem is:

So, at most he will be able to carry 40 crates with him.

seems hard very xd oihfoidhfoidshfodjsklfdsfdsfsdfdsf

Given:-

The mean of 40,50 and 90 is P. If the mean of 40,50,90 and P is Q.

To find:-

The value of Q.

So now the mean of 40,50 and 90 is P. so we get,

So the value of p is 60.

Also we have the mean of 40,50,90 and P is Q. so we get,

So the value of q is 60.

1) All of these questions are about evaluating those functions for each input.

9) So, let's check them out evaluating each one.

10)

11)

12)

SOLUTION

This question simply means we should find the value of x,

First we expand by using 2 to multiply the items in the bracket, we have

Hence the answer is -3.2

Answer

i) 4% = 0.04

ii) 76% = 0.76

iii) 120% = 1.20

iv) 100% = 1.00

v) 32.5% = 0.325

Explanation

The key to writing percents as decimals is to divide the percents by 100 to get the decimal equivalent.

i) 4% = (4/100) = 0.04

ii) 76% = (76/100) = 0.76

iii) 120% = (120/100) = 1.20

iv) 100% = (100/100) = 1.00

v) 32.5% = (32.5/100) = 0.325

Hope this Helps!!!

The most appropriate choice for exponents will be given by-

In [tex]2^4 = 16[/tex], 2 is called the base and 4 is called the power or index.

What is exponent?

Exponent of a number is the number of times a number is multiplied by itself.

For example: [tex]3^5 = 3 \times 3 \times 3 \times 3 \times 3[/tex], 3 is multiplied by itself 5 times

If [tex]a^m = a \times a \times a \times a .....[/tex](m times)

a is called the base and m is called the power or index,

Here,

In [tex]2^4 = 16[/tex], 2 is called the base and 4 is called the power or index.

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If he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33

The percentage decrease in the monthly payment = 30%

The amount of decrease in the bill per month = $25

Consider the current bill amount as x

Then the equation will be

x × (30/100) = $25

Solve the equation

0.3x = $25

x = 25/0.3

x = $83.33

Hence, if he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33

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