for events A and B, P(A)= 3/14 and P(B)= 1/5. Also, P(A and B)= 3/65. Are A and B independent events?

Answer:

11%

Step-by-step explanation:

To fine the percentage decrease, we use the formula change/original x 100. In this case, the change is $11000-$9799=$1201 while the original is $11000. So 1201/11000 x 100 = 10.9% ≈ 11%

Answer:

The number of each coin she have are 17 dimes and 14 nickels.

Step-by-step explanation:

Given:

A coin collector has 31 dimes and nickels with a total face value of $2.40.

Now, to find each does she have.

Let the number of dimes be [tex]x[/tex].

Let the number of nickels be [tex]y[/tex].

So, total number of coins are:

[tex]x+y=31[/tex]

[tex]x=31-y.............(1)[/tex]

Value of a dime = 10 cents

Value of a nickel = 5 cents

Total face value = 240 cents

(1$ = 100 cents.  $2.40×100 =240 cents)

Now, total value of coins:

[tex]10x+5y=240[/tex]

Putting the equation (1) in the place of [tex]x[/tex]:

[tex]10(31-y)+5y=240[/tex]

[tex]310-10y+5y=240[/tex]

[tex]310-5y=240[/tex]

Moving variables on one side and the numbers on other:

[tex]310-240=5y[/tex]

[tex]70=5y[/tex]

Dividing both sides by 5 we get:

[tex]14=y[/tex]

The number of nickels = 14.

Now, putting the value of [tex]y[/tex] in equation (1) we get:

[tex]x+y=31[/tex]

[tex]x+14=31[/tex]

Subtracting both sides by 14 we get:

[tex]x=17.[/tex]

The number of dimes = 17.

Therefore, the number of each coin she have are 17 dimes and 14 nickels.

Answer: 12 small candles and 16 large candles.

Step-by-step explanation:

Notice that an small candle costs $4 and a large candle costs $6.

Let be "s" the number of small candles you sold and "l" the number of large candles you sold.

Set up a System of equations:

[tex]\left \{ {{4s+6l=144} \atop {s+l=28}} \right.[/tex]

Use the Elimination Method to solve it:

- Multiply the second equation by -4.

- Add the equations.

- Solve for "l".

Then:

[tex]\left \{ {{4s+6l=144} \atop {-4s-4l=-112}} \right.\\.......................\\2l=32\\\\l=16[/tex]

- Substitute the value of "l" into the second equation and solve for "s":

[tex]s+16=28\\\\s=12[/tex]

Answer:

b

Step-by-step explanation:

The student is probably asking about the cube root function multiplied by 3, which is an increasing function and is defined for all real numbers, including negative values.

The phrase 'f(x)=3 square root x' seems to be a typo. Assuming this refers to the cube root function, such as 'f(x) = 3 √x,' then this function represents the cube root of 'x' multiplied by 3. To graph this function, start by plotting points, taking the cube root of various values of 'x' and scaling these by 3.

The graph will pass through the origin and rise less steeply than a linear function; it will be an increasing function for all 'x' as the cube root of a real number is always real. This also means that the function will be defined for all real numbers, including negatives, as cubing can produce both positive and negative results.

Option B

The choice has a value that is closest to the value of the following expression 17/12 - 49/40 is [tex]\frac{1}{5}[/tex]

Solution:

Given that we have to find the value that is closest to the value of following expression

[tex]\frac{17}{12} - \frac{49}{40}[/tex]

Let us take L.C.M of denominators and solve the sum

L.C.M of 12 and 40

List all prime factors for each number

prime factorization of 12 = 2 x 2 x 3

prime factorization of 40 = 2 x 2 x 2 x 5

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 2, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 3 x 5 = 120

Thus the given expression becomes:

[tex]\rightarrow \frac{17 \times 10}{12 \times 10} - \frac{49 \times 3}{40 \times 3}\\\\\rightarrow \frac{170}{120} - \frac{147}{120}\\\\\rightarrow \frac{170-147}{120}\\\\\rightarrow \frac{23}{120} = 0.1916 \approx 0.2[/tex]

[tex]0.2 = \frac{1}{5}[/tex]

Thus correct answer is option B

Answer:

B

Step-by-step explanation:

Answer: 700 adults and 1500 children

Step-by-step explanation:

Let the number of adults be x and the number of children be y , then

x + y = 2200 ........................... equation 1

4x + 1.5y = 5050 ............................ equation 2

solving the system of linear equation by substitution method , from equation 1 make x the subject of the formula , that is

x = 2200 - y ....................... equation 3

substitute x = 2200 - y into equation 2 , that is

4 ( 2200 - y ) + 1.5y = 5050

8800 - 4y + 1.5y = 5050

8800 - 2.5y = 5050

2.5y = 8800 - 5050

2.5y = 3750

y = 3750/2.5

y = 1500

substitute y = 1500 into equation 3 , we have

x = 2200 - y

x = 2200 - 1500

x = 700

Therefore , 700 adults and 1500 children entered

The solution for y in 2x − 5y ≤ 15  is [tex]y \geq \frac{2x}{5} - 3[/tex]

Solution:

Given that we have to find solution for given inequality for y

2x − 5y ≤ 15

Let us solve above equation for "y"

[tex]2x - 5y \leq 15[/tex]

Add -2x on both sides

[tex]-2x + 2x - 5y\leq 15 - 2x\\\\-5y \leq 15 - 2x[/tex]

Divide by -5 on both sides

Remember that You can perform on operations on both sides of inequality, and have its truth value unchanged

But if we multiply or divide by a negative number, we must flip the sign

[tex]\frac{-5y}{-5} \geq \frac{15}{-5} - \frac{2x}{-5}\\\\y \geq -3 + \frac{2x}{5}\\\\y \geq \frac{2x}{5} - 3[/tex]

Thus solution for "y" is found

Answe 72

Step-by-step explanation:

360 divided by 5 is 72

A circle is a curve sketched out by a point moving in a plane. The measure of the angle is 72°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Let the angle that turns through 1/5 of the circle be x.

We know that the measure of the centre of a circle is 360°, while it is given that the angle turns through 1/5 of the circle. Therefore, the angle will turn 1/5 of 360°.

[tex]x = \dfrac15 \times 360^o = 72^o[/tex]

Thus, the measure of the angle is 72°.

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Answer:

y-5=4(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-5=4(x-(-3))

y-5=4(x+3)

Answer:

y=1/2x-5/4

Step-by-step explanation:

y=2x+5/2

x=2y+5/2

2y=x-5/2

y=1/2x-(5/2)/2

y=1/2x-(5/2)(1/2)

y=1/2x-5/4

Answer:

Adverage of 20 mph

30 1/5 = 30.2

2/3 = .6667

30.2 x .6667 = 20.13

Answer:

45.3 miles/hour

Step-by-step explanation:

the information we have is:

distance:

[tex]d=30\frac{1}{5}miles=30.2miles[/tex]

time:

[tex]t=\frac{2}{3} hour[/tex]

the formula for the average speed is:

[tex]v=\frac{distance}{time} =\frac{d}{t}[/tex]

substituting all the known values we get:

[tex]v=\frac{30.2miles}{2/3hour} =\frac{3(30.2miles)}{2hour}= 45.3miles/hour[/tex]

the average speed in miles per hour is: 45.3

Answer:

x-intercept - x = 1/2y - 3.15

y-intercept - y = 2x + 6.3

Step-by-step explanation:

For x,

-6x + 3y = 18.9

-6x = -3y + 18.9

x = -3y/-6 + 18.9/-6

x = 1/2y - 3.15

For y,

-6x + 3y = 18.9

3y = 6x + 18.9

y = 6x/3 + 18.9/3

y = 2x + 6.3

Answer:

6 1/2

Step-by-step explanation:

So basically 8 2/3 is equally to 26/3 so 45 minutes is 45/60.

45/60=3/4

26/3*3/4=6 1/2

Jordan, with a speed of 8 2/3 miles per hour, will cover a distance of 6.5 miles in a 45 minute bike ride.

First, we need to understand that Jordan is biking at a speed of 8 2/3 miles per hour. This means in 1 hour, or 60 minutes, he covers that distance. If we want to know how much he covers in a different timeframe - 45 minutes in this case - we have to adjust proportionally.

As a step-by-step calculation, first change 8 2/3 to a decimal, which equal to 8.67.

To find out how far Jordan bikes in 45 minutes, you need to multiply his speed (8.67 mph) by the time in hours. Since 45 minutes is 0.75 of an hour (45/60), the mathematical calculation will be:

Distance = Speed x Time = 8.67 miles/hour x 0.75 hour = 6.5 miles

Therefore, Jordan will bike 6.5 miles in 45 minutes.

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The bug's speed is approximately 5.33 meters per minute, which is closest to option (2).

To find the bug's speed in meters per minute, we need to convert its speed from inches per second to meters per minute.

First, let's convert the bug's speed from inches per second to inches per minute:

[tex]\[3.5 \text{ inches per second} \times 60 \text{ seconds per minute} = 210 \text{ inches per minute}\][/tex]

Now, let's convert inches to meters:

[tex]\[210 \text{ inches} \times \frac{2.54 \text{ centimeters}}{1 \text{ inch}} \times \frac{1 \text{ meter}}{100 \text{ centimeters}} = 5.33 \text{ meters per minute}\][/tex]

So, the bug's speed is closest to option (2) 5.33.

Complete Question:

There are 2.54 centimeters in every inch. If a bug moves at a rate of 3.5 inches per second, then which of the following is closest to its speed in meters per minute?

(1) 3.86

(3) 6.25

(2) 5.33

(4) 7.19

Answer:

The net pay of her will be $4702.21

Step-by-step explanation:

The State Tax plus Social Security Taxes plus Medicare takes (3 + 6.2 + 1.45) = 10.65% from Jessica's monthly gross pay.

If the gross pay is $5660 then the after the above deduction the remaining pay will be [tex]5660(1 - \frac{10.65}{100}) = 5057.21[/tex] dollars.

Now, again there is a deduction of $355 from her payment each month.

Therefore, the net pay of her will be = $(5057.21 - 355) = $4702.21 (Answer)

Answer:

4/15 cocoa would be left if we made cookies

Step-by-step explanation:

4/6- 2/5

= 4(5)- 2(6)/30

= 20-12/30

=8/30

=4/15

After making the cookies using 2/5 cup of cocoa from the initial 4/6 cup, you would subtract 12/30 cup from 20/30 cup to find that you would have 4/15 cup of cocoa left.

To determine how much cocoa you would have left after making the cookies using 4/6 cup of cocoa and using 2/5 cup for the recipe, you would need to subtract the amount used from the initial amount. To perform the subtraction, you first need to have the quantities expressed with a common denominator. The least common denominator for 6 and 5 is 30.

Convert 4/6 cup to an equivalent fraction with a denominator of 30: (4 × 5) / (6 × 5) = 20/30 cup.

Convert 2/5 cup to an equivalent fraction with a denominator of 30: (2 × 6) / (5 × 6) = 12/30 cup.

Now you can subtract the amount of cocoa used for the cookies from the total amount you have:

Remaining cocoa = Initial amount - Amount used = 20/30 cup - 12/30 cup.

Remaining cocoa = (20 - 12) / 30 = 8/30 cup of cocoa.

To simplify this, divide both the numerator and denominator by their greatest common divisor, which is 2:

Remaining cocoa = 4/15 cup. So you would have 4/15 cup of cocoa left after making the cookies.

Answer:

It's B.

Step-by-step explanation:

Have a good day.

Answer:

  (x, y) = (6, 1) is the solution

Step-by-step explanation:

Each of the equations is written in "slope-intercept" form:

  y = mx + b . . . . . . . . where m is the slope and b is the y-intercept

First equation

  The y-intercept is +7 and the slope is -1. That means the line goes down 1 unit for each unit it goes to the right. It will go through the points (0, 7) and (7, 0).

Second equation

  The y-intercept is -2 and the slope is 1/2. That means the line goes up 1 unit for each 2 units it goes to the right. It will go through the points (0, -2) and (4, 0).

The lines will intersect at the point (6, 1), which is the solution found by graphing.

Answer:

[tex]105.84\ cm^2[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=21.2/2=10.6\ cm[/tex] ----> the radius is half the diameter

substitute

[tex]A=\pi (10.6)^{2}[/tex]

[tex]A=112.36\pi\ cm^2[/tex]

step 2

Find the area of a sector

Remember that

The area of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector with a central angle of 108 degrees

[tex]\frac{112.36\pi}{360^o}=\frac{x}{108^o}\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]33.708(3.14)=105.84\ cm^2[/tex]

Answer:

32 cars

Step-by-step explanation:

we know that he can paint 12 cars in 3 weeks.

that means that he can paint 4 cars per week.

4cars x 8weeks = 32 cars in 8 weeks

Answer:

Step-by-step explanation:

12 cars in 3weeks

Then in 1week he will paint= 12/3 car

= 4 cars

so in 8weeks = 4 × 8 cars

= 32cars

The equation which is equivalent to [tex]\log _{x} 36=2[/tex] is [tex]x^{2}=36[/tex] or x = 6 ([tex]\log _{6} 36=2[/tex]).

Step-by-step explanation:

Given Equation:

           [tex]\log _{x} 36=2[/tex]

As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:

           [tex]b^{y}=a[/tex]

Then, the base b logarithm of x is equal to y

           [tex]\log _{b}(x)=y[/tex]

Now, use the logarithmic rule for the given equation by comparing with above equation. We get b = x, y = 2, and x = 36. Apply this in equation,

            [tex]b^{y}=a[/tex]

            [tex]x^{2}=36[/tex]

When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as [tex]\log _{6} 36=2[/tex]

Answer:D

Step-by-step explanation:

i got it right

Answer:

The food at the fast food restaurant of chicken nuggets is  having higher unit price.

Step-by-step explanation:

Given:

A fast food restaurant had 5 boxes of chicken nuggets for $33.95.

A competing restaurant had 4 boxes of chicken fingers for $26.96.

Now, to get the food which has a higher unit price.

So, to get the unit price we use unitary method:

In, a fast food restaurant:

5 boxes of chicken nuggets cost for = $33.95.

Thus, 1 box of chicken nuggets cost for = [tex]\$33.95\div 5 = \$6.79.[/tex]

In a competing restaurant:

4 boxes of chicken fingers cost for = $26.96.

Thus, 1 box of chicken fingers cost for = [tex]\$26.96 \div 4 = \$6.74.[/tex]

Now, as comparing the prices of both restaurant the price of chicken nugget in fast food restaurant is $6.79 per box which is higher than the price of chicken fingers cost of $6.74 per box in competition restaurant.

Therefore, the food at the fast food restaurant of chicken nuggets is  having higher unit price.

Answer:

The coordinates of point D are (7,11)

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

In this problem we have

[tex]M=(3,5)\\C(x1,y1)=(-1,-1)\\D(x2,y2)=?[/tex]

substitute the given values

[tex](3,5)=(\frac{-1+x2}{2},\frac{-1+y2}{2})[/tex]

Solve for x2

[tex]\frac{-1+x2}{2}=3[/tex] ---> [tex]-1+x2=6[/tex] --->[tex]x2=6+1=7[/tex]

Solve for y2

[tex]\frac{-1+y2}{2}=5[/tex] ---> [tex]-1+y2=10[/tex] ---> [tex]y2=10+1=11[/tex]

therefore

The coordinates of point D are (7,11)

Answer:

75%

Step-by-step explanation:

2 x 1.75 = 3.5

The required percentage increase in the distance she can run is 75%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Shelby could run 2 miles.
she can run 3.5 miles.
percentage increase = 3.5 - 2 / 2 × 100%
percentage increase = 75%

Thus, the required percentage increase in the distance she can run is 75%.

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Answer:

Step-by-step explanation:

1) 1/5 + 1/7 = 1*7/5*7 + 1*5/7*5

=7/35 + 5/35 = 7+5/35 = 12/35

2) Let the number be x

x +6*1/x = -5

x + 6/x = -5

(x² + 6 ) / x = -5

x² + 6 = -5x

x² +5x + 6 = 0

x² + 3x +2x + 2*3 = 0

x(x+3) + 2(x+3)= 0

(x+3)(x+2) = 0

x + 3 = 0  or x +2 = 0

x = -3    or x = -2

the number is (-3)   or (-2)

Answer:

405.224

Step-by-step explanation:

From 2 hours to 4 hours she traveled 7 miles.

7 miles  / 2 hours = 3.5 miles per hour.

The slope is 3.5 , which is 3.5 miles per hour, which is how fast she is walking.

Ashley sold 98 small cups and 57 large cups of lemonade.

Step-by-step explanation:

Given,

Price of small cup of lemonade = $1.25

Price of large cup of lemonade = $2.50

Total cups sold = 155

Total worth of cups = $265

Let,

x represent the number of small cups sold

y represent the number of large cups sold

According to given statement;

x+y=155    Eqn 1

1.25x+2.50y=265    Eqn 2

Multiplying Eqn 1 by 1.25

[tex]1.25(x+y=155)\\1.25x+1.25y=193.75\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](1.25x+2.50y)-(1.25x+1.25y)=265-193.75\\1.25x+2.50y-1.25x-1.25y=71.25\\1.25y=71.25[/tex]

Dividing both sides by 1.25

[tex]\frac{1.25y}{1.25}=\frac{71.25}{1.25}\\y=57[/tex]

Putting y=57 in Eqn 1

[tex]x+57=155\\x=155-57\\x=98[/tex]

Ashley sold 98 small cups and 57 large cups of lemonade.

Keywords: linear equation, elimination method

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