By definition of conditional probability you know that

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]Now, replace the values that you have and solve for P(A and B)

[tex]\begin{gathered} P(B|A)=\frac{P(A\cap B)}{P(A)} \\ 0.37=\frac{P(A\cap B)}{0.28} \\ \text{ Multiply by 0.28 on both sides of the equation} \\ 0.37\cdot0.28=\frac{P(A\cap B)}{0.28}\cdot0.28 \\ \text{ Therefore,} \\ 0.1036=P(A\cap B) \end{gathered}[/tex]Find the distance between the two points in simplest radical form.

(-6, 5) and (-3, 7)

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

**Step-by-step explanation:**

Using the distance formula,

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

What can I do to decrease my bill by $25.00 per month?"

Employee: "Your bill is currently __________ per month, so we'll make a change to a less expensive option that will result in a 30% decrease in your monthly payment."

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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The table shows information recorded about the location and speed of an airplane during an overseas flight.

a) Determine the altitude in miles.

b) Determine the ground speed in miles per hour.

c) Determine the headwind in miles per hour.

d) Determine the temperature in degrees Fahrenheit using the formula

F=9/5 C+32

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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Please help me on my assignment The ? Options are x and y

x, x

1.7

[tex]\lbrack1,7\rbrack[/tex]**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

[tex]f(x)>0[/tex]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

[tex]\begin{gathered} x=1\text{ and x=7} \\ so \\ Input\text{ in the blank} \\ 1,7 \end{gathered}[/tex]Finally, check the interval where the graph is above the x-axis, it is from a to 7, in interval notation

[tex]\lbrack1,7\rbrack[/tex]

I hope this helps you

What is the sign of 37+(-37)? Choose 1 answer: Positive Negative Neither positive nor negative the sum is zero

the sing is (673618 -37)

Discuss the relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses. Explain the positioning of the roots of the polynomial on its graph with respect to the discriminant and the sign of the discriminant.

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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F(x) = 3 + 5x to the second power - x + 5, 2f(3-) - f(4) =

the given equation is

[tex]f(x)=3x^2-x+5[/tex]calculate f(-3) by putting x = -3

[tex]\begin{gathered} f(-3)=3(-3)^2-(-3)+5 \\ f(-3)=27+3+5=35 \\ \end{gathered}[/tex]now, f(4)

[tex]\begin{gathered} f(4)=3(4)^2-4+5 \\ f(4)=48+1=49 \end{gathered}[/tex]now the final calculation

[tex]\begin{gathered} 2f(-3)-f(4) \\ 2\times35-49 \\ 70-49 \end{gathered}[/tex]that is 70 -49 = 21

**so the correct answer is 21**

**2f(-3) - f(4) = 21 .**

For the following, find f(2.1) and f(4).

**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.

for f(2.1), you want to use the definition for the domain 2 < x < 4for f(4), you want to use the definition for the domain 4 ≤ x < 8Function evaluationOnce you have identified the function you are evaluating, substitute the argument for the variable and carry out the arithmetic in the usual way.

f(2.1) = 1/2(2.1)² = 1/2(4.41) = 2.205f(4) = log₂(4) = log₂(2²) = 2**The desired function values are f(2.1) = 2.205 and f(4) = 2**.

> Question 1

In 2 to the 4th power = 16 number 2 is called what?

and number 4 is called what?

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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You are 37 years old have accumulated 150000 in your savings account. You intend to add a fixed amount each month for twenty years. For first 5 years you add 100 at the end of each month.

What is the question?

Veronika has 3 daughters. Today the eldest is 7 years older the the second who is 2 years older than the youngest. The sum of their ages 12 years from now will be 56. How old are they today?

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:

[tex]\begin{gathered} x=7+y, \\ y=2+z, \\ x+y+z=44. \end{gathered}[/tex]**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:

[tex]\begin{gathered} x=9+11=20, \\ y=2+11=13. \end{gathered}[/tex]**Answer**

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

I just need to quickly know if my answers are correct thank you!

[tex]D,D,E,D[/tex]

**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)**

The recommended dosage of a drug for pediatric patients is 200 mg per kilogram of a patient's weight. If Janine weighs 102 lb, how much of the drug should she receive? Use the fact that 1 lb = 0.45 kg

Janine should receive about ____ milligrams of the drug.

(Round to the nearest milligram as needed.)

**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

What values complete each statement?Enter your answers in the boxes.(16−−√)2 = in simplest form.By the Power of Power rule, (16 1/2)2=16 2/2. So, 16 1/2 must equal in radical form.

Box 1 )

[tex](\sqrt[]{16})^2=16[/tex]Box 2 )

[tex]16^{\frac{1}{2}}=\sqrt[]{16}[/tex]Ubicar las siguientes fracciones en la recta numérica: 3/9

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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Rewrite the following percents as decimals. i. 4% ii. 76% ii. 120% iv. 100% V. 32.5%

**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 mode of data 33, 22, 10, 0, 33, 40, 33 is _____

The given data is :

33,23,10,0,33,40,33

Mode of the data is 33

•The most repeated observation is known as Mode , here 33 is repeated 3 times while rest occur only once ! Hence the mode of the given data is 33.

Other info:-

•Mean = Sum of all observation/No.of Observations

33,23,10,0,33,40,33

Mode of the data is 33

•The most repeated observation is known as Mode , here 33 is repeated 3 times while rest occur only once ! Hence the mode of the given data is 33.

Other info:-

•Mean = Sum of all observation/No.of Observations

3 9/13 to a improper fraction

**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 mean of 40,50 and 90 is P. If the mean of 40,50,90 and P is Q. What is the value of Q

**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,

[tex]\frac{40+50+90}{3}=\frac{180}{3}=60[/tex]So the value of **p **is **60.**

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

[tex]\frac{40+50+90+60}{4}=\frac{240}{4}=60[/tex]So the value of **q **is **60.**

In one classroom homework is worth 25% of the final grade, each of the three projects is worth 10%, and the final exam is worth 45%. If student has an 87 on a homework average and a 94 on the first project, what is the students grade at this point if that same student from part a gets a 71 on the second project and a 78 on the third project what is the lowest grade the student can get on the final exam to get an 80 over on the course

**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:

[tex]TG=86(0.25)+94(0.10)[/tex]Simplifying:

[tex]TG=21.5+9.4[/tex][tex]TG=30.9[/tex]• b)

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

[tex]TG=FE+30.9+71\cdot(0.1)+78\cdot(0.1)[/tex][tex]TG=FE+30.9+7.1+7.8[/tex][tex]TG=FE+45.8[/tex]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:

[tex]80=x\cdot0.45+45.8[/tex]where x is the grade of the exam.

Solving for x:

[tex]x=\frac{80-45.8}{0.45}[/tex][tex]x=76[/tex]Pls help (give right answer)!!

seems hard very xd oihfoidhfoidshfodjsklfdsfdsfsdfdsf

The answer:

9ab^2*(6a^5+1)

9ab^2*(6a^5+1)

Mr. Anderson grows fruit which hesells at a farmers' market.- His truck has a total payloadcapacity (total weight ofpassengers and cargo) of1,200 pounds.- Mr. Anderson weighs 190 pounds.- The table he sells his fruit onweighs 10 pounds.- He transports his fruit in crates.Each crate weighs 3 pounds.- A crate can hold up to 22 poundsof fruit.Write and solve an equation to findC, the greatest number of fullcrates of fruit that Mr. Anderson cancarry in his truck along with himself and the table

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

[tex]1200>(3+22)C+190\Rightarrow1200>25C+190[/tex][tex]\Rightarrow1010>25C\Rightarrow C<40.4[/tex]So, **at most he will be able to carry 40 crates with him**.

Some researchers developing a new Intelligence test are trying to decide how much time to allow to complete the test. The researchers have recorded the times(in minutes) for completion of 26 people who took the test for practice. The frequency distribution below summarizes the completion times recorded by theresearchers.Time for completion(in minutes)Frequency9 to 1112 to 14715 to 1785318 to 2021 to 233Based on the frequency distribution, using the midpoint of each data class, estimate the mean completion time of the people who took the test. For yourintermediate computations, use four or more decimal places, and round your answer to one decimal place.

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

[tex]Mean\text{ of a gruop data =}\frac{Sum\text{ of (}Interval\text{ midpoint }\cdot\text{ frecuen}c\text{y)}}{sum\text{ of frecuency}}[/tex]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 =

[tex]Mean\text{ of a gruop data =}\frac{Sum\text{ of (}Interval\text{ midpoint }\cdot\text{ frecuen}c\text{y)}}{sum\text{ of frecuency}}[/tex][tex]Mean\text{ of a gruop data =}\frac{374}{26}=14.38461[/tex]The mean is given using five decimals.

Which value of X Satisfy 2(x +5.3) =4.2

**SOLUTION **

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

[tex]2\mleft(x+5.3\mright)=4.2[/tex]First we expand by using 2 to multiply the items in the bracket, we have

[tex]\begin{gathered} 2\times x+2\times5.3=4.2 \\ 2x+10.6=4.2 \\ 2x=4.2-10.6 \\ 2x=-6.4 \\ \text{dividing both sides by 2, we have } \\ \frac{2x}{2}=\frac{-6.4}{2} \\ x=-3.2 \end{gathered}[/tex]**Hence the answer is -3.2**

Simplify the expression. Write your answer as a power.(-8.3)8 (-8.3)4(-8.3)? (-8.3)3The simplified expression is

[tex]\frac{(-8.3)^8}{(-8.3)^7}\cdot\frac{(-8.3)^4}{(-8.3)^3}[/tex]

This will be simplified with this law of indices

[tex]\frac{a^e}{a^y}=a^{e-y}[/tex][tex]\begin{gathered} \text{Therefore the initial question becomes:} \\ ((-8.3)^{8-7})\text{ }\cdot\text{ (}(-8.3)^{4-3}) \end{gathered}[/tex][tex]\begin{gathered} (-8.3)^1\cdot(-8.3)^1 \\ (-8.3)^{1+1} \\ (-8.3)^2 \\ \end{gathered}[/tex]Going further, we can simplify to:

[tex]\begin{gathered} (-8.3)\times(-8.3) \\ =68.89 \end{gathered}[/tex]Mathematics. Sets Question. Answer Fast

**Answer:**

B

**Step-by-step explanation:**

the full domain is

(-∞,-7[ ∪ ]-7,+∞)

True or false?

In centrally planned economies, the distribution of goods costs nothing to administer

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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True or false? In deductive thinking, you start with a given set of rules and cinditions and determine what must be true as a consequence

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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In January 1, Juan weighed 247 pounds and decided to diet and exercise. Kn June 30, Juan weighed 221 pounds. Determine the percent decrease in Juans weight from January 1 to June 30.

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

[tex]P=\frac{w_1-w_2}{w_1}\times100\%[/tex]The initial value is 247 and the final one is 221, so:

[tex]\begin{gathered} P=\frac{247-221}{247}\times100\% \\ P=\frac{26}{247}\times100\% \\ P=0.10526\ldots\times100\% \\ P\approx10.53\% \end{gathered}[/tex]So, the percent decrease is **approximately 10.53%**.

At a computer manufacturing company, the actual size of a computer chip 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. What is the standard error for the sample mean?

0.029

0.050

0.120

0.091

The **standard error** for the **sample mean** exists

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

How to find the standard error for the sample mean?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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25 Which wavefront is travelling at a speed closest to that of a sound wave through a solid? A one that moves 10m in 0.01 s B one that moves 50m in 0.5s C one that moves 1000 m in 100 s D one that moves 2000 m in 2000 s
Come up with a Research Question about First-Generation College Students.
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