Suppose that E and F are two events and that P(E)=.8 and P(F/E)=.6 What is P(E and F)?​

Answer:

3/4 * 6 x 10 = 45/1 = 45

Step-by-step explanation:

Multiple: 3/4 * 6 = 3 · 6/4 · 1 = 18/4 = 9 · 2/2 · 2 = 9/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18, 4) = 2. In the following intermediate step, cancel by a common factor of 2 gives 9/2.

In other words - three quarters multiplied by six is nine halfs.

Multiple: the result of step No. 1 * 10 = 9/2 * 10 = 9 · 10/2 · 1 = 90/2 = 45 · 2/1 · 2 = 45

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(90, 2) = 2. In the following intermediate step, cancel by a common factor of 2 gives 45/1.

In other words - nine halfs multiplied by ten is forty-five.

Answer:

Step-by-step explanation:

[tex]\dfrac{5}{6}<\dfrac{w}{8}\Rightarrow\dfrac{w}{8}>\dfrac{5}{6}\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup\cdot\dfrac{w}{8\!\!\!\!\diagup}>8\!\!\!\!\diagup^4\cdot\dfrac{5}{6\!\!\!\!\diagup_3}\\\\w>\dfrac{20}{3}\\\\w>6\dfrac{2}{3}\\\\7>6\dfrac{2}{3}[/tex]

Answer:   D ) 7

Step-by-step explanation:

7 is greater than 5

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The value of x is 10

Step-by-step explanation:

We know that the sum of internal angles of a quadrilateral is 360 degrees

So,

Given

Angle 1 = A1 = 3x+10

Angle 2 = A2 = 9x+50

Angle 3 = A3 = 4x

Angle 4 = A4 = 13x+10

So,

[tex]A_1+A_2+A_3+A_4 = 360\\(3x+10)+(9x+50)+(4x)+(13x+10) = 360\\3x+10+9x+50+4x+13x+10 = 360\\3x+9x+4x+13x+10+50+10 = 360\\29x+70 = 360[/tex]

Subtracting 70 from both sides

[tex]29x+70-70 = 360-70\\29x = 290[/tex]

Dividing both sides by 29

[tex]\frac{29x}{29} = \frac{290}{29}\\x = 10[/tex]

Hence,

The value of x is 10

Keywords: Angles, Quadrilateral

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Answer:

24 Teaspoons

Explanation:

1 tablespoon is equivalent to 3 teaspoons

8 · 3 = 24

Therefore 24 teaspoons is equivalent to 8 tablespoons.

Answer: f(3)=11.5

Step-by-step explanation:

In order to solve this equation, all you have to substitute the value inside of the parenthesis with the value of x in the equation after the equals sign. SO...

f(3)=3x+2.5

f(3)=3(3)+2.5

f(3)=9+2.5

f(3)=11.5

Hope this helps!

Answer   5

Step-by-step explanation:

Answer:

ℝ

Step-by-step explanation:

[tex]\displaystyle 10 - 2x = [5 - x] - [x - 5][/tex]

All linear functions have a range and domain of all real numbers.

I am joyous to assist you anytime.

Answer:

Graph is below

Step-by-step explanation:

y>3x+10 is represented by the red line, which is dotted because it's values are not included in the solution. Everything above it is shaded red because it is greater than. y<-3/4x-1 is represented by the blue line, which is dotted because it's values are not included in the solution. Everything beneath is shaded blue, because it is less than. The intersection of the two shaded areas is purple. (8,10) is not part of the solution because it does not have an x value beneath -3.

(this was a hard question, but i'm certain that at least the graph is correct.)

Answer:

37i-16

Step-by-step explanation:

(4+7i)(3+4i)

12+21i+16i+28i^2

12+37i+28(-1)

37i+12-28

37i-16

Answer:

Step-by-step explanation:

1. [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex]

2. [tex]y=-5x+30[/tex]

Preliminary Material:

A line that is perpendicular to another has the opposite reciprocal slope of the other line.

A line parallel to another has the same slope.

With this in mind, we can begin to answer this question.

1.

Setup for question 1:

A line perpendicular with [tex]-5x+5[/tex] that goes through the point (7, 5).

Before going over the point this perpendicular line must go through, let's make an equation with the slope of the perpendicular line.

A linear function can be represented with this formula: [tex]y=mx+b[/tex].

We know the slope of this function must be an opposite reciprocal to -5, and using the information I first gave in the beginning of this problem, we can have the slope of the function.

If we take this slope and insert it into the linear equation, we will have the function...

So we now know the slope of this function, but what about the y intercept, [tex]b[/tex]? This is where the point given to us in the beginning of this problem comes into play. If we plug the point (7, -5) into our x and y coordinates in the above equation, we can solve for [tex]b[/tex].

Algebra:

[tex]-5=\frac{1}{5}(7)+b[/tex]

[tex]-5=\frac{7}{5}+b[/tex]

[tex]-\frac{25}{5}=\frac{7}{5}+b[/tex]

[tex]-\frac{32}{5}=b[/tex]

Answer:

Our final answer is: [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex].

2.

There will be no setup for 2. I'll show the algebra without explanation as well. If there's any confusion you can ask me :).

Algebra:

[tex]y=mx+b[/tex]

[tex]y=-5x+b[/tex]

[tex]-5=-5(7)+b[/tex]

[tex]-5=-35+b[/tex]

[tex]b=30[/tex]

Answer:

Answer:

Step-by-step explanation:

[tex]3.6x-12.2=-1.5x+8.2\qquad\text{multiply both sides by 10}\\\\36x-122=-15x+82\qquad\text{add 122 to both sides}\\\\36x-122+122=-15x+82+122\\\\36x=-15x+204\qquad\text{add}\ 15x\ \text{to both sides}\\\\36x+15x=-15x+15x+204\\\\51x=204\qquad\text{divide both sides by 51}\\\\\dfrac{51x}{51}=\dfrac{204}{51}\\\\x=4[/tex]

Mei charges $15 per hour as her regular hourly rate before applying a 40% discount to her next door neighbor, resulting in a discounted rate of $9 per hour.

To calculate the regular hourly rate Mei charges before the 40% discount, we set up an equation where the discounted rate is equal to 60% of the original rate, because 100% - 40% = 60%. Mei charges her neighbor $9 per hour after the discount. Let h represent Mei's regular hourly rate before the discount.

So, the equation would be 0.60h = $9. To find h, we divide both sides of the equation by 0.60:

h = $9 / 0.60

h = $15

Thus, Mei's regular hourly rate before the discount is $15 per hour.

Mei's regular hourly rate before the discount is $15.

To find Mei's regular hourly rate before the discount, let's denote it as h .

Given that Mei offers her neighbor a 40% discount, her neighbor pays only 60% of the regular rate. This can be represented as:

[tex]\[ 0.60h = 9[/tex]

To find ( h ), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.60:

[tex]\[ \frac{0.60h}{0.60} = \frac{9}{0.60} \][/tex]

This simplifies to:

[tex]\[ h = \frac{9}{0.60} \][/tex]

Now, we can calculate:

[tex]\[ h = \frac{9}{0.60} = 15 \][/tex]

So, Mei's regular hourly rate before the discount is $15.

Question:

You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 1/3 of one section of the fence.  What fraction of the fence did you paint?

Answer:

The fraction of the fence painted is [tex]\frac{1}{12}[/tex]

Solution:

Given that:

You have a 32-foot fence around a square garden. There are 4 equal sections

Find the length of each section:

4 sections = 32 foot

[tex]\text{ 1 section } = 32 \div 4 = 8 foot[/tex]

Find the length that is painted:

[tex]\text{ Fence painted }= \frac{1}{3} \text{ of one section }\\\\\text{ Fence painted }= \frac{1}{3} \times 8 = \frac{8}{3} \text{ foot }[/tex]

Therefore [tex]\frac{8}{3}[/tex] foot of fence is painted

Find the fraction that that is painted:

Total length of fence = 32

[tex]\text{ Fraction of the fence painted } = \frac{8}{3} \div 32 = \frac{8}{3} \times \frac{1}{32}\\\\\text{ Fraction of the fence painted } = \frac{1}{12}[/tex]

Therefore [tex]\frac{1}{12}[/tex] fraction of the fence is painted

Answer:

[tex]12x^2+4x[/tex]

Step-by-step explanation:

The area of a square or rectangle can be found by multiplying the width by the height. Since we now both, we can create an expression.

[tex](3x+1)*(4x)[/tex]

Now we can apply the distributive law/property to expand the expression.

[tex]3x(4x)+1(4x)[/tex]

Finally, we can simplify.

[tex]12x^2+4x[/tex]

Answer:

It is important to know that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C)

Step-by-step explanation:

It is important to know that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C).  

Lets take an example, if we have 81°F and want to convert in (°C). So, here is the procedure:

                            C = (5/9) (81 - 32)

                                = (5/9) (49)

                                 = 27.22 °C

So, it is clear that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C).

Keywords: linear equation, converter, C = (5/9)(F-32)

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To promote economic growth, countries would most likely act so that inflation "remains at a low level".

Answer: Option c

Explanation:

The Central Bank and the government basically command Inflation or either of them. The monetary policy is helpful from its changing interest rates parameters . Although there are a different types of tools which can control inflation are as follows

Monetary policy: The demand in the economy is reduced by higher interest rates, and result into lower economic growth with lower inflation.

Commanding supply of money: Monetarists debt huge by setting a close bond between the inflation and money supply.

Supply-side Policies: The scheme to hike the efficiency of the economy and competitiveness by declining pressure on long-term costs.

Fiscal policy: The reduction of spending, demand and inflationary pressures resulted from a higher rate of income tax.

Wage controls: Inflationary pressures can be reduced by controlling wages  , but after 1970 such act is rarely performed.

Answer:

The answer is 74%

Step-by-step explanation:

Method One:

1) Un-reduce the fraction to ger 74/100

2) Your answer is 74%

Method 2:

1) Divide 37 by 50

2) You get .74

3) Your answer is 74%

Answer:-523/52

Step-by-step explanation:

The simplified form of the expression is [tex]\(-3245.2\).[/tex]

To simplify the given expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). The expression given is:

[tex]\[ -3152 - 10(4.32 + 5 = 5) \[/tex]

First, we address the equality within the parentheses. The expression \[tex](4.32 + 5\) equals \(9.32\),[/tex] but the equality [tex]\(4.32 + 5 = 5\)[/tex] is not true. However, in the context of this expression, the equality sign does not affect the numerical computation; it seems to be a typographical error or a misplacement. We will treat the expression within the parentheses as [tex]\(4.32 + 5\)[/tex]and ignore the equality for the calculation.

Now, let's simplify the expression step by step:

1. Calculate the expression inside the parentheses:

[tex]\[ 4.32 + 5 = 9.32 \][/tex]

2. Multiply the result by -10 (note that the multiplication comes before addition/subtraction in the order of operations):

[tex]\[ -10 \times 9.32 = -93.2 \][/tex]

3. Finally, subtract the result from -3152:

[tex]\[ -3152 - 93.2 = -3245.2 \][/tex]

So, the simplified form of the expression is [tex]\(-3245.2\).[/tex]

Answer:

Therefore the required sentence into an equation is

[tex]5+(C\times a)=2[/tex]

Step-by-step explanation:

Given:

5 more than a product of a number and a

equals 2

Use a variable C for the unknown number

To Find:

Translate above sentence into an equation . ?

Solution:

Let ' C ' for the unknown number

and ' a ' for the other number.

Then according to given condition we have

5 more Product of ( C and a ) = 2

Therefore the required sentence into an equation is

[tex]5+(C\times a)=2[/tex]

Answer:

x = 11

Step-by-step explanation:

Vertical angles mean that their values are equivalent, which means that:

5x + 10 = 7x -12

Solve for x

22 = 2x

x = 11

Hope this helps :)

Answer:

TU ⊥ MN and MN ║ PQ

Step-by-step explanation:

TU ⊥ MN

As the angle that is created where TU and MN intersect is a 90° angle, these two lines must be perpendicular to each other.

MN ║ PQ

As both MN and PQ intersect the line TU, we can use this to prove that they are parallel.

Both MN and PQ create a 90° angle where they intersect with TU. This means that MN is ⊥to TU and PQ is ⊥ to TU.

As both MN and PQ are perpendicular to TU, they must be parallel.

The liquid started cooling from 194 degrees. This is calculated by determining the rate of cooling, which is 8 degrees per minute, and extrapolating back to find the initial temperature.

The subject of the question is about determining the initial temperature of cooling liquid. To solve this, we have to first identify the rate at which the temperature is decreasing. Given, after 2 minutes it was 178 degrees and after 5 minutes it was 154 degrees. That's a decrease of 24 degrees over 3 minutes, or 8 degrees per minute.

Since the liquid started cooling 2 minutes before it was first observed at 178 degrees, we can estimate that the liquid would have been 16 degrees hotter at the start of the cooling period. So, it would have started cooling at 178 + 16 = 194 degrees.

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Answer:

800

Step-by-step explanation:

Look at the tens if it's 0-4 keep the number the same if 5-9 go up one number

Answer:

832 --> ???

832 - we must round the underlined digit

832 --> ???

832 --> 800

The rounding rule is:

4 and below, stay down low! [Round down]. 5 and above, soar like a dove! [Round up].

So with that rule, 832 becomes 800.

800 is your answer.

I hope this helps!

Step-by-step explanation:

I don't know if this helps, but none of the above.

first of all, complementary angles mean that the 2 (or more) angles add up to 90 degrees. so, if you were to combine the angles, you'll get an angle that's way larger than 90 degrees. (a and b won't work cause 830 isn't an angle)

P.S. but 83 degrees and 7 degrees would be complementary...

hope you at least know why i say none of the above

Answer:

The relationship between time and distance is Velocity = Distance / Time

Step-by-step explanation:

The height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]

Solution:

Given that shrub in Pam's backyard is about [tex]1\frac{3}{8}[/tex] feet tall

A small tree in her back yard is about 7 times as the shurd

To find: height of tree

From given information,

Height of shrub = [tex]1\frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} \text{ feet}[/tex]

Given that small tree in her back yard is about 7 times as the shurb

So we get,

height of tree = 7 times the height of shrub

[tex]\text{ height of tree } = 7 \times \text{ height of shrub}\\\\\text{ height of tree } = 7 \times \frac{11}{8}[/tex]

Therefore on solving we get,

[tex]\text{ height of tree } = \frac{77}{8} = 9\frac{5}{8} \text{ feet}[/tex]

Thus the height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]

Chris baked 95 cookies.

Step-by-step explanation:

Given,

Cookies baked by Haley = 50

Cookies baked by Chuck = 65

Cookies baked by Dana = 90

Average of them = 75

Let,

Cookies baked by Chris = x

Average = [tex]\frac{Sum\ of\ quantites}{No.\ of\ people}[/tex]

[tex]75=\frac{50+65+90+x}{4}[/tex]

Multiplying both sides by 4

[tex]4*75=\frac{50+65+90+x}{4}*4\\300=205+x\\300-205=x\\95=x\\x=95[/tex]

Chris baked 95 cookies.

Keywords: addition, average

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Answer:

The shipping and handling charge that Bryce paid is $109.65

Step-by-step explanation:

Given as :

The online price of the treadmill = $510

The charge of shipping and handling = 21[tex]\dfrac{1}{2}[/tex] % of online price

Let The shipping and handling charge that Bryce paid = $x

Now, According to question

∵ The charge of shipping and handling = 21[tex]\dfrac{1}{2}[/tex] % of online price

So, x = [tex]\dfrac{43}{2}[/tex] % of $510

Or, x = [tex]\dfrac{43\times 510}{100\times 2}[/tex]

Or, x = $109.65

The shipping and handling charge that Bryce paid = x = $109.65

Hence,The shipping and handling charge that Bryce paid is $109.65 Answer

Answer:

f(x): {y| y > 0 }

g(x): {y| y > 6 }

Step-by-step explanation:

Hope this helps!

Because both of these are exponential functions with positive bases, we conclude that the range for both is:

{y| y > 0}.

Here we have two exponential functions:

f(x) = (4/5)^x

g(x) = (4/5)^(x + 6).

You can see that both of these are exponential functions with positive bases, then neither of these can have negative outcomes, while, as x increases, the outcome will also increase.

Then we can see both functions are exponential growths, so the range for both of these are the set of all real positive values, written in both cases as:

{y| y > 0}

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