NUMBER SENSE Events A and B are independent. Suppose P(B)=0.4 and P(A and B)=0.13 . Find P(A) .

Answer:

See Below.

Step-by-step explanation:

1) Given:

\(\angle PRS\text{ and } \angle SRT \text{ are a linear pair.}\)

2) Definition of Linear Pair:

\(m\angle PRS+m\angle SRT=180\)

3) Given:

\(m\angle PRS=2x+12\)

4) Given:

\(\displaystyle m\angle SRT=6x+8\)

5) Substitution Property:

\((2x+12)+(6x+8)=180\)

6) Combine Like Terms:

\(8x+20=180\)

7) Subtraction Property of Equality (subtract 20 from both sides):

\(8x=160\)

8) Division Properety of Equality (divide both sides by 8):

\(x=20\)

9) Given (this step is optional. You don’t have to include this):

\(m\angle PRS=2x+12\)

10) Substitution:

\(\displaystyle m\angle PRS=2(20)+12\)

11) Multiplication:

\(m\angle PRS=40+12\)

12) Addition:

\(m\angle PRS=52\)

Answer:

sorry i dont realy understand that

Step-by-step explanation:

Answer:

\( = 2 \times 4 = 8 \\ = 5 \times 5 = 25 \ \\ \frac{1}{2} \times 5 \times 3 = 7.5 \\ 7.5 + 8 + 2.5 = 18\)

Answer:

A. 491.67

Step-by-step explanation:

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From the  X coordinate is -0.45 centimeter and Y coordinate is -2.0 cm of the center of mass for the uniform plate.

According to the Question:

Since the plate is uniform, we can divide it into three rectangles, each with a mass proportional to its area and with its barycenter at its geometric center. We will refer to the large piece of 35cm x 10cm; it occupies 63.6% of the total surface and its barycenter is at

(x₁, y₁) = (−5.0cm,−2.5cm).

Now,

The top 20cm× 5cm piece has 18.2 % of the total area; its center of mass is at (x₂, y₂) = (10cm,12.5cm).  

Now,

The bottom 10cm× 10cm piece (section 3) also has 18.2 % of the total area; its center of mass is at (x₃, y₃)​ = (5cm,−15cm).

(a) The x coordinate of the center of mass for the plate is

   \(X_{com} = (0.636)X_1 + (0.182)X_2 + (0.182)X_3\)

            = -0.45 cm

(b) The y coordinate of the center of mass for the plate is

    \(Y_{com} = (0.636)Y_1 + (0.182)Y_2 + (0.182)Y_3\)

             = -2.0 cm.

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The linear equation of the line through A and D is given by:

y = 3.33x + 43.33.

A linear function is modeled by:

y = mx + b

In which:

Point A is the (-10,10) because f(-10) = 10, as follows:

y = -0.5 x -10 + 5 = 5 + 5 = 10.

The line through A and D goes through points (-13,0) and (-10,10), hence the slope, which is change in y divided by change in x, is given by:

m = (10 - 0)/(-10 - (-13)) = 10/3 = 3.33.

Then:

y = 3.33x + b.

When x = -13, y = 0, hence we use it to find b.

0 = 3.3333333(-13) + b

b = 43.33.

The equation is:

y = 3.33x + 43.33.

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The organizers buys candy at $4.59 per pound and nuts at $3.25 per pound.

Equation is an expression which is used to show the relationship between two or more variables and numbers.

Let e be the price per pound for the candy and let n be the price per pound for the nuts.

They mix 3 pounds of candy with 5 pounds of nuts and the total price of the mix is $30.02.. Hence:

They decide to add an additional 2 pounds of candy and 1 pound of nuts, which adds $12.43 to the total price. Hence:

Solving equations 1 and 2 simultaneously gives:

e = 4.59, n = 3.25

The organizers buys candy at $4.59 per pound and nuts at $3.25 per pound.

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The heights (in inches) of 25 individuals were recorded and the following statistics were calculated mean = 70 range = 20 mode = 73 variance = 784 median = 74 The coefficient of variation equals  to the answer is C. 40%.

The coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean, expressed as a percentage.

To calculate the CV, we first need to find the standard deviation. The variance is given as 784, so the standard deviation is the square root of the variance:

standard deviation = sqrt(variance) = sqrt(784) = 28

Now we can calculate the CV:

CV = (standard deviation / mean) x 100%

= (28 / 70) x 100%

= 40%

Therefore, the answer is C. 40%.

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Answer:

B.  The mass is conserved

Step-by-step explanation:

A.  The identity of the substance does not change.          [FALSE]

B.  The mass is conserved.                                                  [TRUE]

C. The substance always changes from solid to liquid.     [FALSE]

D. The particles are not rearranged.                                   [FALSE]

The newer machine works at a unit rate of

(5400 cans) / (180 min) = 30 cans/min

while the older machine operates at

(5400 cans) / (217 min) ≈ 24.88 cans/min

So working together, the two machines work at a rate of about 54.88 cans/min. Producing 5400 cans would then take about

(5400 cans) / (54.88 cans/min) ≈ 98.39 min

Answer:

Step-by-step explanation:

Step one:

given

Price

\(P= -20x^2+1800x\)

where P is the maximum profit

           x is the price of one shirt

Step two:

To rewrite the expression let us first divide through by 20

\(P= \frac{-20x^2}{20} +\frac{1800x }{20}\\\\P=-x^2+90x\)

Factoring x out we have

\(P=-x^2+90x\\\\P=x(-x+90)\)

Hence the rewritten expression equation for the price is

P=x(-x+90)

The sales tax rate for a specific type of wood-frame door priced at $1480 is 25%, or $370.

Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 questions correctly out of 100 on a test (75/100), you would have received a 75%. A percentage is a relative value that represents one hundredth of a quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given quantity. A percentage is a fraction of a whole expressed as a number between 0 and 100.

Here,

Sale tax=$370

Price of door=$1480

Sales tax percent=370/1480*100

=25%

The rate of sales tax for a particular type of wood-frame door is priced at $1480 is 25% that is $370.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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Answer:

The area of the circle is 314 inches

Step-by-step explanation:

Area if a circle = πr²

r = radius

r= d/2

r=20 /2

r=10 inches

Area =3.14×10²

= 3.14×100

=314 inches

Answer:

314 in. cubed

Step-by-step explanation:

The formula to find the area of a circle is:

A= πr²

Pi is 3.14 so substitute that in

A= 3.14(r)²

The radius is 10 because the radius is half of the diameter.  Half of 20 is 10.  So substitute that in the radius symbol.

A= 3.14(10)²

Square 10, which is 10 times 10.  10 times 10 equals 100.

A= 3.14(100)

100 times 3.14 is 314 because 100 has two zeroes which means you move the decimal point in 3.14 two places to the right.  It gets you 314.0 which is just 314.

A= 314

Answer:

379-68=p

Step-by-step explanation:

379 is the total number of tissues. If you take away the single pack tissues then you will have the amount of three pack tissues

The correct equation that shows the number of tissue three-packs, p, Johnson's sold in January is, p = 379 - 68.

Use the concept of subtraction defined as:

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that,

At Johnson's Pharmacy, tissue boxes can be purchased as single boxes or in packs of three boxes.

Here, During January, Johnson's sells a total of 379 boxes of tissues, 68 as single boxes, and the rest in three-packs.

Let us assume that, the number of tissue three-packs = p

Hence we get;

p = 379 - 68

p = 311

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Answer:gamble that,on average,will leave a person with the same amount of money.

Step-by-step explanation:

The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

300 gallons

Step-by-step explanation:

A saline solution is a solution of salt in water.

The percent is the percent of salt in the total amount of solution.

A 40% saline solution has 40% of salt out of the total volume.

Let the amount of pure water needed = x.

The amount of existing 40% solution is 500 gal.

Let the total amount of 25% saline solution made = y.

Equation of volumes of solutions:

500 + x = y

y = x + 500          Eq. 1

Equation of volume of salt:

500 gal of 40% saline solution has 0.4 × 500 gal = 200 gal of salt

Pure water has 0% salt.

The final product is a solution that is 25% saline. Its volume is y.

The volume of salt in the y gallons of 25% saline solution is 25% of y = 0.25y

The equation of salt content is:

200 + 0 = 0.25y

y = 800       Eq. 2

Eq. 1 and Eq. 2 form a system of equations.

y = x + 500

y = 800

Substitute 800 for y in Eq. 1.

y = x + 500

800 = x + 500

x = 300

Answer: 300 gallons of pure water

Answer:

32

Step-by-step explanation:

3 x 8 = 24, 24 + 8 = 32

Based on the information, it can be inferred that this salesperson must make sales equivalent to $28,000 to obtain an equal profit with both options.

To find the amount of money that we must sell to have the same profit with both options we must carry out the following mathematical procedure.

1. We must calculate how much you would earn with option A in a week.

$28 * 40 = $1,120

2. We must make a rule of three to find a value of which 4% is equal to 1,120

Based on the above, the salesperson must sell $28,000 to make the same profit on both options in one week.

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First, we have to acknowledge that the spinner's outcome is independent from the disc pulled from the bag.

For the spinner, there are 7 outcomes (7 spots we could land upon) and only 1 of which is pink.  We have a 1/7 chance of landing on pink.

For the bag of discs, there are 12 possible outcomes (12 discs we could pick) and 4 are red.  We have a 4/12 chance of pulling a red disc.  4/12 = 1/3

For the overall probability, since the two events are independent, we multiply the individual probabilities to find the overall probability:

    1/7 · 1/3 = 1/21

We have a 1/21 (about 4.762%) chance of having the spinner land on pink and then pulling a red disc from the bag.

Answer:

1.06bar is not equal to zero

Answer:

commutative property

Step-by-step explanation:

happy to help ya :)

Answer:

X=15

Step-by-step explanation:

By observing the graph, we can see that the amplitude of the function is 9 because the function oscillates between +9 and -9. The period of the function is 360 degrees, which means that the function completes one cycle in 360 degrees.

The given graph can be described by the sine function. The standard form of the sine function is given as f(x) = a sin(bx + c) + d, where:

a: amplitude, b: period, c: phase shifted: vertical shift

By observing the graph, we can see that the amplitude of the function is 9 because the function oscillates between +9 and -9. The period of the function is 360 degrees, which means that the function completes one cycle in 360 degrees. The sine function starts at 0, which means there is no phase shift, and the vertical shift of the function is 0 because the middle line of the graph is the x-axis. Therefore, the equation of the sine function that describes the given graph is f(x) = 9 sin(x) or f(x) = -9 sin(x), where x is in degrees. Graphing sine and cosine functions: When graphing sine and cosine functions, we use the unit circle to determine the points on the graph. The unit circle is a circle with a radius of 1 unit, centered at the origin.

We start at the point (1,0) and rotate counter-clockwise around the circle, measuring angles in degrees or radians, to find the coordinates of other points on the circle. The x-coordinate of each point on the circle is the cosine of the angle, and the y-coordinate is the sine of the angle.The sine function is an oscillating function that repeats itself every 360 degrees (or 2π radians). The sine function has a maximum value of 1 and a minimum value of -1. The cosine function is also an oscillating function that repeats itself every 360 degrees (or 2π radians). The cosine function has a maximum value of 1 and a minimum value of -1. The cosine function is a shifted version of the sine function. The sine and cosine functions are used to model many real-world phenomena, such as sound waves and electromagnetic waves.

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Fatma's account needs to earn a rate of return of approximately 0.2957% per month to stretch her money out for 17 years.

To determine the required rate of return for Fatma's account, we can use the future value formula:

FV = PV * (1 + r)^n

Where:

FV = Future value (amount needed for 17 years of expenses)

PV = Present value (initial amount Fatma has)

r = Rate of return

n = Number of compounding periods (monthly withdrawals over 17 years)

Given:

PV = $182,000.00

Monthly expenses = $1,350.00

Number of years = 17

Number of compounding periods = 17 years * 12 months = 204 months

We can rearrange the formula to solve for the required rate of return (r):

r = (FV / PV)^(1/n) - 1

Substituting the given values:

FV = $1,350.00 * 204 = $275,400.00

r = ($275,400.00 / $182,000.00)^(1/204) - 1

Calculating this expression:

r ≈ 0.002957 (approximately 0.2957%)

Therefore, Fatma's account needs to earn a rate of return of approximately 0.2957% per month to stretch her money out for 17 years.

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