Francis heard that a car stereo system was on sale for 30% off. If the sale price was 57.75, what was the original price of the stereo?

Final answer:

The conditional probability formula for event B given event A is represented as P(B|A), which is calculated using P(A and B) / P(A). Using dice as an example, the events are described and demonstrated to be neither mutually exclusive nor independent due to overlapping outcomes and interdependence.

Explanation:

The conditional probability of event B given that event A has occurred is represented as P(B|A). To fill in the blanks in the provided formula, it would be P(B | A) = P(B ∩ A) / P(A). Using the provided scenarios, we need to calculate P(A), which is the probability that the sum of numbers on both cubes is less than 10, P(B), which is the probability that the sum of numbers on both cubes is a multiple of 3, and P(A and B), which is the probability that both events occur simultaneously. Finally, we use the formula P(A|B) = P(A and B) / P(B) to calculate the conditional probability.

For example, event A could be rolling a 3 or 4 first, followed by any even number, and event B could be rolling a sum at most 7 on two dice. These events are not mutually exclusive since they can both occur simultaneously, nor are they independent since the occurrence of one affects the likelihood of the other happening.

The completed conditional-probability formula is: P(B|A) = P(A ∩ B) / P(A)

To complete the conditional-probability formula for event B given that event A occurs first, we need to fill in the blanks with the appropriate terms:

P(B|A) = P(A ∩ B) / P(A)

Let's break down each term:

a0: Event A occurs

a1: Event B occurs

a2: Event A and B occur simultaneously (intersection of A and B)

a3: Event A occurs

a4: Event B occurs

Therefore, the completed conditional-probability formula is:

P(B|A) = P(A ∩ B) / P(A)

Answer:

it is 1905.88%

Step-by-step explanation:

We have,85%x X=1620

Or 85/100*x=1620

multiplying both sides by 100 and dividing both sides by 85

we have x = 1620 * 100/85

x=1905.88

if you are using a calculator ,simply enter 1620x100÷85,which will give you the answer

85 dinner rolls represent approximately 5.25% of 1620 dinner rolls. The calculation is done by dividing 85 by 1620 and then multiplying by 100.

To find what percent of 1620 dinner rolls is 85 dinner rolls, we use the basic formula of (part/whole) x 100. In this case, the 'part' is the 85 rolls, and the 'whole' is the 1620 rolls. So we calculate the percentage as follows:

(85 / 1620) x 100 = (0.05247) x 100 [10pt] [10pt]= 5.247%

Thus, 85 dinner rolls are approximately 5.25% of 1620 dinner rolls.

each vertical line is 1 unit.

Place dots on the 3rd, 9th and 16th line to the right of the line at 0

Count from 0 to the right 3 units then plot the point 3

From 3 count to the rights 6  more and plot the point 9

From 9, continue to count to the right 9 more and plot the last point 18

It will take 16 tiles to cover 1 square yard.

To find out how many tiles it will take to cover 1 square yard, we need to calculate the area of one tile.

The tiles are 1/4 by 1/4 yard, so the area of one tile is (1/4) * (1/4) = 1/16 square yard.

To cover 1 square yard, we need to divide the total area by the area of one tile:

1 square yard / (1/16 square yard) = 1 * (16/1) = 16 tiles.

The answer would be 1/8.

Answer:

5.6%

Step-by-step explanation:

The value of m is -2 for 9 = -7m + 1 - 6.

Given Equation;

9 = -7m + 1 - 6

Add 6 on both side,

9 + 6 = -7m + 1 - 6 +6

15 = -7m + 1

Subtract 1 on both side,

15 -1 = -7m + 1 -1

14 = -7m

m = - 2

Therefore, the value of m is -2.

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m=3/2 is the answer for the equation

[tex]\frac{g}{20}[/tex]≤5

Multiplying by 20 in all sides gives:

g≤(20×5)

Answer: g≤100

Hello Belleoberry2005, I am here to answer your question.

Here we do a simple rule of 3, like this: 14*100/56, and that gives us 25.

So the answer is: 25%

Hope this helped answer your question.

To calculate the percentage of cars that received oil changes at an auto repair shop, divide the number of cars with oil changes (14) by the total number of cars (56) and multiply by 100 to get 25%.

The student asks how to calculate the percentage of cars that received oil changes at an auto repair shop. To find the percentage, divide the number of cars that received an oil change by the total number of cars and then multiply by 100. There were 14 out of 56 cars that received oil changes.

Here is the step-by-step calculation:

So, 25% of the cars received oil changes.

divide the two numbers.

50/10 = 5

there are 5 campers per counselor, or

5/1 (camper/counselor)

hope this helps

50/10 or a simplified version 5/1 !! This Means For every 5 studens their are 1 counselor for them!

The width of the city is 104/5

Length of city is 5/2 times of width i.e. 5/2 × 104/5 = 520/10 = 52 metres

The 3 outside angles of a triangle need to equal 360.

n = 360 - 133 - 142 = 85

The answer is D.

In 2009, there were 3 million more flex fuel vehicles than in 2004.

There is asked how many more flex fuel vehicles were available in 2009 compared to 2004. A flex fuel vehicle is one that can run on more than one type of fuel, usually gasoline combined with either ethanol or methanol fuel.

In 2004, there were approximately 5 million flex fuel vehicles. By 2009, this number rose to about 8 million. To find the increase, we subtract the initial number from the final number:

Number of flex fuel vehicles in 2009 - Number of flex fuel vehicles in 2004 = Increase in flex fuel vehicles

8 million - 5 million = 3 million

Answer:

Please find the attachment.

Step-by-step explanation:

We are asked to graph the equation [tex]y-5=-\frac{2}{3}(x+9)[/tex].

We know that point-slope form of an equation is in form [tex]y-y_1=m(x-x_1)[/tex], where, m represents slope of line and [tex](x_1,y_1)[/tex] is a point on the line.

We can see that slope of the line is [tex]-\frac{2}{3}[/tex], so line will be a decreasing line.

We can represent the given equation as [tex]y-5=-\frac{2}{3}(x-(-9))[/tex].

The line will pass through the point [tex](-9,5)[/tex].  

The graph of the linear equation can be seen in the image at the end.

To graph any line, we just need to identify two points in the line, and then we can connect them with a line.

Here the equation is:

y - 5 = (-2/3)*(x + 9)

We can see that this equation contains the point (-9, 5) (both sides of the equation become zero in that point)

5 - 5 = (-2/3)*(-9 + 9)

0 = 0

And evaluating in x = 0 we get:

y - 5 = (-2/3)*(0 + 9)

y = 5 + (-2/3)*9

y = 5 - 6

y = -1

So we have the point (0, -1)

Just graphing these two points and conecting them with a line we will get the following graph:

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there are 12 square numbers between 1,000 and 2,000.

starts off at 32 bc 32^2=1024

ends at 44 bc 44^2=1936

A square number is the product of an integer multiplied by itself. There are 13 square numbers between 1,000 and 2,000, which are found by squaring all whole numbers from 32 to 44.

To determine how many square numbers are between 1,000 and 2,000, we must first understand what a square number is. A square number, sometimes called a perfect square, is an integer that is the square of an integer. In other words, it's the product of an integer multiplied by itself. For example, 10² is a square number because it equals 100, which is 10 times 10.

To find the square numbers in the given range, we need to find the square roots of 1,000 and 2,000 and then count the whole numbers between them. The square root of 1,000 is approximately 31.62, and the square root of 2,000 is approximately 44.72. Since we are looking for whole numbers, the first possible square number would be 32² and the last one would be 44². By squaring all the whole numbers from 32 to 44, we can list the square numbers within the range.

Next, we list the squares of these numbers:

By counting all the squares from 32² to 44², we find that there are 13 square numbers between 1,000 and 2,000.

12. the square route of 36 is 6 and 6 times 2 is 12.

Twice the square root of 36 is equal to 12.

Here, we have,

given that,

what is twice the square root of 36

now, we have,

Twice the square root of 36 can be calculated as follows:

Twice the square root of 36 = 2 * √36

Since the square root of 36 is 6:

Twice the square root of 36 = 2 * 6 = 12

Therefore, twice the square root of 36 is equal to 12.

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Integer generally means number.

if s = seconds then

2s = 18

solve for s,

18/2 = 7

s = 7 seconds

Answer:

ball took 9 seconds to reach at the end o the ramp.

Step-by-step explanation:

Whitney rolls a ball down a ramp.

Length of the ramp = 18 feet

Speed by which the ball rolls down = 2 feet per second

Let the ball takes T seconds to reach the end of the ramp.

By the formula,

Time taken = [tex]\frac{\text{Distance rolled}}{\text{Speed}}[/tex]

                   = [tex]\frac{18}{2}[/tex]

                   = 9 seconds

Therefore, ball took 9 seconds to reach at the end o the ramp.

Answer:

The value of the (RIC) will increase from 4 to 5.75, that is, 44%

Step-by-step explanation:

To answer this question you have to know the definition of Rank well.

The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin

The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.

Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%

Answer:

Hence the interquartile range increased by 3(7-4) when we included the eight weight.

Step-by-step explanation:

The weight of the seven rocks is given as:

11     13     14     6     10     9      10

on arranging the data in the ascending order we get the observation as:

6     9    10    10    11     13    14

we divide our data into 3 sets:

the median of data([tex]Q_2[/tex]) is: 10 (as it is the middle value among the data)

The lower set of data is:

6    9    10

[tex]Q_1=9[/tex] ( as it is the middle value)

The upper set of data is:

11     13     14

[tex]Q_3=13[/tex]  ( as it is the middle value in the upper set of data)

Hence, the interquartile range is: [tex]Q_3-Q_1=13-9=4[/tex]

The weight of eight rocks is given as:

11      13     14      6      10     9    10     5

On arranging the data in ascending order we get:

5       6        9     10     10    11      13     14

The median of the data is denoted by [tex]Q_2[/tex] which is the middle value of the given data.

Hence the median here is between 10, 10.

so, the median is given by:

[tex]\dfrac{10+10}{2}=10[/tex]

thus [tex]Q_2=10[/tex]

also the lower set of data is:

5    6    9

Thus [tex]Q_1=6[/tex] (as it is the middle value in the lower set of data)

the upper set of data is:

11   13   14

Thus [tex]Q_3=13[/tex]

Hence, the interquartile range is:

[tex]Q_3-Q_1=13-6=7[/tex]

So when we were having seven weights the interquartile range was: 4

and when we included the eight weight the interquartile range becomes: 7

Hence the interquartile range increased by 3(7-4) when we included the eight weight.

Seeing as there are 5280 feet in each mile. They are 160ft apart.

5280/33 is 160

Your answer is 160 ft apart because if you turn 1 mile into feet it would be 5280 feet, then divide by 33 posts and you would get an even answer of 160 feet apart.

4 2 inch cubes are needed to fill the cubic box

The volume of the larger cube is 64 cubic inches and the volume of the smaller cube is 8 cubic inches. By dividing the larger volume by the smaller, we find that 8 two-inch cubes can fit in a four-inch cube.

The question is asking how many 2 inch cubes can fit into a bigger cube that has 4 inch edges. Firstly, we need to calculate the volume of the bigger cube by using the formula for volume of a cube which is the edge length cubed. So, 4 inches x 4 inches x 4 inches gives us a total of 64 cubic inches.

To find out how many 2 inch cubes can fit into the 64 cubic inch box, we would divide the volume of the bigger box by the volume of the smaller cube. The volume of the 2 inch cube is 2 inches x 2 inches x 2 inches which equals 8 cubic inches.

Dividing the volume of the bigger cube by the volume of the smaller cube gives us 64 divide by 8 equals 8. So, 8 cubes of 2 inch sides can fit into one cube of 4 inch sides.

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the answer to this question is 21 dollars are left

Answer:

a) circumference of great circle=40212.4km

b) circumference of latutude circle=40212.4cos[tex]\theta[/tex] kilometers

c)The latitude circle is at an angle of 84.9°

d)Circumference of equator=40212.4km

Step-by-step explanation:

Refer to the figure shown below, we are given that earth has been charted with vertical and horizontal line and horizontal lines are called latitude lines.

So every horizontal line corresponds to a circle.

So the great circle will have radius equal to earth radius.

a)we are given with earth radius=6400km.

Hence circumference of a great circle= 2πX6400=40212.4km

b)At a latitude with angle x=[tex]\theta[/tex], the circumference of latitude circle = [tex]40212.4cos\theta[/tex]

c)If a latitude circle has a circumference of about 3593km,

then [tex]40212.4cos\theta=3593[/tex]

        [tex]cos\theta=\frac{3593}{40212.4} =0.0894[/tex]

         [tex]\theta=cos^{-1}(0.0894)[/tex]=84.9°

Hence the latitude circle is at an angle of 84.9°

d) At equator angle is 0.

Hence circumference of equator=40212.4cos(0)=40212.4km

For the small tables, it will be 6X, because since they fit 6 people, you will need to multiply 6 times the amount of tables(which is X), then for the larger table, it will be 10Y, because since they fit 10 people, you will multiply 10 times the amount of tables (which is Y).

This leaves you with 6X+10Y

If they are expecting AT LEAST 150, then the equation needs to be set to greater than or equal to 150, but if they are expecting exactly 150, no more no less, then the equation will be set equal to 150.

Therefore it is either:

A: 6X+10Y>or=150

B:6X+10Y=150

Final answer:

The relationship between the number of small tables (x) and large tables (y) needed to seat 150 people can be described by the equation 6x + 10y = 150, where 6x represents the number of guests at small tables and 10y represents the number of guests at large tables.

Explanation:

The student's question deals with creating an equation to describe the relationship between the number of small tables seating 6 people and the large tables seating 10 people required to accommodate 150 guests at a wedding. To solve this, you can write an equation based on the total seating capacity that needs to be provided by both types of tables.

The total number of people that can be seated at small tables is represented by 6x, and the total number of people that can be seated at large tables is represented by 10y. Since we know that the total number of guests is 150, the relationship between x and y can be represented by the following equation:

6x + 10y = 150

This equation states that the total number of guests (150) is equal to the sum of guests seated at small tables (6x) and the guests seated at large tables (10y).

5/12 - 4/5 = -23/60. You can't simplify -23/60. Hope this is right

To find the fraction of cornbread that Val eats, we multiply the fraction of leftover cornbread by the fraction that Val eats.

To find the fraction of the cornbread that Val eats, we first need to find the fraction of cornbread that is leftover after the picnic. The question tells us that 5/12 of the cornbread is leftover. Next, we need to find the fraction of the leftover cornbread that Val eats. The question states that Val eats 4/5 of the leftover cornbread. To find the final fraction, we multiply the two fractions together: 5/12 * 4/5 = (5 * 4) / (12 * 5) = 20 / 60. This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 20, resulting in 1/3. Therefore, Val eats 1/3 of the cornbread.

The answer is 111 lol

1 multiplied by anything is the given number

so 111 x 1 = 111

D

given the equation of a parabola in standard form : ax² + bx + c = 0 ( a ≠ 0 )

then the x-coordinate of the vertex  = - [tex]\frac{b}{2a}[/tex]

y = - 2x² + 4x + 12 is in standard form

with a = - 2, b= 4 and c = 12

[tex]x_{vertex}[/tex] = - [tex]\frac{4}{-4}[/tex] = 1

substitute x = 1 into the equation for y

y = - 2(1)² + 4(1) + 12 = 14

vertex = (1, 14 )

Answer: the answer is d