multiple polynomials to find area

The probability of selecting a person who wears a watch given that they wear a ring is 2/5 or 0.4.

From the Venn diagram, we can see that there are 10 people who wear rings, 2 of whom also wear watches. This means that the probability of randomly selecting a person who wears a ring is 10 out of the total number of people in the class. That is:

P(Ring) = 10 / (10+2) = 10/12

Similarly, we can find the probability of selecting a person who wears both a watch and a ring. From the diagram, we can see that there are 4 such people. Thus,

P(Watch and Ring) = 4 / (10+2) = 4/12

Using the formula for conditional probability, we get:

P(Watch|Ring) = P(Watch and Ring) / P(Ring)

Substituting the values we obtained earlier, we get:

P(Watch|Ring) = (4/12) / (10/12) = 4/10 = 2/5 or 0.4

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Answer:

The surface area of the square pyramid is approximately 28.2 square units.

Explanation:

The base area and the areas of each triangle face must be determined to calculate the surface area of a square pyramid.

Since the base is a square with four units for each edge, its area is:

The base area equals 42 to 16 square units.

We must determine the length of the slant height, which is the height of each triangular face, to get the area of each triangle.

The Pythagorean theorem may be used to get the slant height: a2 + h2 = s2,

where an equals half the base's length (2 units), h is similar to the pyramid's size (3 units), and s is the slant height.

Inputting the values, we obtain:

2^2 + 3^2 = s^2

4 + 9 = s^2

13 = s^2 s = √13

Using the following formula, we can now get the area of each triangle face:

The area of the triangular face equals 0.5 base height, where the base is the slant height (13 units), and the size is the square base's edge length (4 units).

The triangular face area equals 0.5 x 4 x 13 = 213 square units.

Given that there are four triangular faces, their combined area is:

Units of area: 4 x 2 x 13 = 8 x 13

The total surface area is then calculated by summing the base and triangle face areas:

Base area plus triangle face area equals total surface area.

Surface area total = 16 + 8 x 13

28.2 square units total surface area (rounded to the nearest decimal point)

Therefore, the square pyramid's surface area is around 28.2 square units.

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Answer: 288

Step-by-step explanation:

2 × 6 × 2 × 4 × 3=288

Lakeside Olds should expect to have approximately 3 automobiles lined up at opening time on a typical day based on the probability distribution provided.

To find the expected number of automobiles lined up at the Lakeside Olds dealer at opening time, we use the concept of expected value. The expected value is the average value we would expect to see if we repeated the experiment many times. In this case, the experiment is the number of automobiles lined up at the dealer at opening time.

We are given the probability distribution for the number of automobiles, which tells us the probability of each possible outcome. We use these probabilities to calculate the expected value as the weighted average of all possible outcomes.

Expected number of automobiles = (1 x 0.05) + (2 x 0.30) + (3 x 0.40) + (4 x 0.25)

= 0.05 + 0.60 + 1.20 + 1.00

= 2.8

≈ 3

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The given question is incomplete, the complete question is:

The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.) for service is:

how many automobiles should Lakeside Olds expect to be lined up at opening time?

Neither student's work properly verifies the identity and  csc x = 1/sin x,  sin² x + cos² x = 1 are the  two identities that were used in Student A's verification.

Part A:

Both Student A and Student B did not verify the identity properly. Student A started with the correct expression, but then manipulated it incorrectly.

In Step 1, multiplying cosine x over sine x times cosine x does not equal cosecant x minus sine x.

In Step 2, dividing cosine squared x by sine x also does not equal cosecant x minus sine x. Student B also started with the correct expression, but made a mistake in Step 2.

Subtracting sine squared x over sine x from 1 does not equal 1 over sine x minus sine squared x over sine x.

Therefore, neither student's work properly verifies the identity.

Part B:

Identity 1: csc x = 1/sin x

Student A uses this identity in Step 4 when they rewrite 1/sin x as csc x.

Identity 2: sin² x + cos² x = 1

Student A uses this identity in Step 3 when they rewrite cos² x as 1 - sin²x.

Hence, neither student's work properly verifies the identity and  csc x = 1/sin x,  sin² x + cos² x = 1 are the  two identities that were used in Student A's verification.

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The piecewise function in the graph is:

f(x) = 3   if -8 < x < - 2

f(x) = -0.5x + 5 for -2 < x - 6

First we can see a constant segment at y = 3 that starts at x = -8 and ends at x = -2

So we have:

f(x) = 3   if -8 < x < - 2

Then we have a line that starts at x = -2, and ends at x = 6

We can see that the y-intercept is 5, then we can write:

y = ax + 5

It also passes through (4, 3), replacing that:

3 = a*4 + 5

3 - 5 = a*4

-2 = a*4

-2/4 = a

-0.5 = a

Then the second part is:

f(x) = -0.5x + 5 for -2 < x - 6

The piecewise function is:

f(x) = 3   if -8 < x < - 2

f(x) = -0.5x + 5 for -2 < x - 6

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Answer:

Step-by-step explanation:

The percent of students in grade 8 those who like to join dance club is equal to 25%.

Total number of students in grade 8 = 20

Total number of students of grade 8  join in dance club = 5

Percent of students of grade 8 prefer to join dance club

= ( total number of students prefer dance club ) / ( Total number of students in grade 8 ) × 100

Substitute the value in the formula we get,

⇒ Percent of students of grade 8 prefer to join dance club

= ( 5 ) / ( 20 ) × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 0.25 × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 25%

Therefore, percent of grade 8 students who preferred to join dance club is equal to 25%.  

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The above question is incomplete, the complete question is:

What percent of students in grade 8 prefer to join a dance club?

                      Dance club      Hiking club     Total

Grade 7               15                       15                 30

Grade 8               5                        15                  20

Total                    20                     30                    50

Answer:

This can be figured out from the equation:

2n = 11

If he walks 2 miles/hour, then you can just say "2n" to say the miles in the unknown variable for hours.  Set it to equal 11, the number of miles he will walk in n hours.

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Answer:

6 cm

Step-by-step explanation:

let, missing side be x cm

then, x+x+3 = 15

=> 2x = 12

=> x = 6 cm

Thus, missing side is 6 cm long

Step-by-step explanation:

6 blocks ÷ 14 sudents =    6/14 =   3/7  of a block each

The value of x that would make triangle ABC a right triangle is x= 2. The justification is that the product of the slopes of two perpendicular lines is -1/2, and when the points are plugged into the distance formula, the sides satisfy the Pythagorean theorem.

To determine a value of x that would make triangle ABC a right triangle, we need to check if the square of the length of any two sides equals the square of the length of the third side.

We can use the distance formula to find the lengths of the sides of the triangle

AB = √((x + 3)² + 4²)

BC = √(2² + 3²)

CA = √((x + 1)² + 1²)

To make triangle ABC a right triangle, we need to find a value of x that satisfies the Pythagorean theorem

AB² + BC² = CA²

[(x + 3)² + 4²] + [2² + 3²] = [(x + 1)² + 1²]

Simplifying this equation yields

x² + 2x - 8 = 0

Solving for x, we get

x = 2 or x = -4

So, if x = 2 or x = -4, then triangle ABC is a right triangle.

To justify this, we can find the slopes of the line segments connecting the vertices of the triangle

mAB = (3 - (-1)) / (x - (-3)) = 4 / (x + 3)

mBC = (-4 - (-1)) / (-1 - (-3)) = -3/2

mCA = (3 - (-4)) / (x + 1 - (-1)) = 7 / (x + 2)

When x = 2, we get

mAB = 4/5

mBC = -3/2

mCA = 7/3

mAB * mBC = -2/5

mBC * mCA = -7/6

mCA * mAB = 14/15

when x = 2, triangle ABC is right triangle.

When x = -4, we get

mAB = 4/(-1) = -4

mBC = -3/2

mCA = 7/(-3) = -7/3

mAB * mBC = 6

mBC * mCA = 14/3

mCA * mAB = 7/2

when x = -4, triangle ABC is not a right triangle.

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Answer:

yes

Step-by-step explanation:

If the graph of a relationship is a line or a ray through the origin, then it is proportional. If it is a line or ray that does not pass through the origin, then it is not proportional. Also, if it is not linear, then it is not proportional.

Answer:

25ft

Step-by-step explanation:

The total number of boxes purchased using $11.40 and the remaining expected changed money received is 28 boxes and $0.20 respectively.

Total amount of money to buy drink boxes = $11.40

Cost of each drink box = $0.40

Number of drink boxes bought

= $11.40 ÷ $0.40/drink box

= 28.5 drink boxes

Since you cannot buy a fractional part of a drink box.

Round down to the nearest whole number.

Here,  28 drink boxes can be bought with the available money.

To determine expect change,

Subtract the total cost of the drink boxes from the amount of money available.

$11.40 − ($0.40/drink box × 28 drink boxes)

= $11.40 − $11.20

= $0.20

The amount of change is $0.20.

Therefore,  the number of boxes bought with given amount is 28 boxes and the remaining expected amount of money received is $0.20 .

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The function that is shown in the graph is y = √(2x - 6) + 1

From the question, we have the following parameters that can be used in our computation:

The graph

The parent function of the graph is

y = √2x

The graph is shifted right by 6 units

So, we have

y = √(2x - 6)

The graph is shifted up by 1 unit

So, we have

y = √(2x - 6) + 1

hence, the function is y = √(2x - 6) + 1

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Equations in the system are accurate and coincident.

Solve the system using any approach, such as elimination or substitution, and then categorize the equations as consistent independent, inconsistent, or coincident.

Using the substitution technique:

x - 2y = -4 => x = 2y - 4

Substituting x = 2y - 4 into the first equation:

3x - 6y = -12

3(2y - 4) - 6y = -12

6y - 12 - 6y = -12

-12 = -12

Identity -12 = -12 is a constant. Since the two equations represent the same line and have an infinite number of solutions, the system of equations is consistent and coincident.

Any value of y can be chosen, and x = 2y - 4 can be used to calculate the equivalent value of x.

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The linear function f with the values f(10) = 5 and f(2) = -3 is f(x) = x - 5.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

hence, to write a linear function f with the values f(10) = 5 and f(2) = -3, we need to find the slope and y-intercept of the function.

The slope of a linear function can be found by using the formula:

Slope m = (y2 - y1) / (x2 - x1)

Using the values of f(10) = 5 and f(2) = -3,

we can find the slope:

Slope m = (5 - (-3)) / (10 - 2)

= 8 / 8

= 1

Now that we have the slope, we can use the point-slope form to find the equation of a line:

y - y1 = m(x - x1)

Where m is the slope and (x1, y1) is one of the points on the line.

Using the point (10, 5) and slope m = 1, we have:

y - y1 = m(x - x1)

y - 5 = 1(x - 10)

Simplifying, we get:

y - 5 = x - 10

y = x - 5

f(x) = x - 5

Therefore, the linear function is f(x) = x - 5.

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Answer:

-3+0i

Step-by-step explanation:

have a good day :)

Answer:

The answer to your problem is, A. Larger

Step-by-step explanation:

First in order to know to the answer lets learn about different types of fractions:

For example, 1/4, 3/4, 3/8, are all proper fractions.

4/3, 5/2, are all improper fractions.

When we have to multiply a whole number with fractions less than 1, then the resulting number will be less the number originally

Example; 3 x [tex]\frac{3}{4}[/tex]

If we then multiplying numerators together and the denominators together.

3 x [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{1}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{4}[/tex] = 2[tex]\frac{1}{4}[/tex] < 3

Example /\

Thus the answer to your problem is, A. Larger OR Multiply.

To compute the distance dd from yy to the line through uu and the origin, we can use the formula for finding the distance between a point and a line. The line through uu and the origin can be represented by the equation

y = (u2/u1)x, where u1 and u2 are the x and y coordinates of uu, respectively.
To find the distance dd, we first need to find the coordinates of the point where the line through uu and the origin intersects with the line perpendicular to it that passes through yy. Let (a,b) be the coordinates of this point. Then we have:
b = (u2/u1)a  (since (a,b) lies on the line through uu and the origin)
u1a + u2b = 0  (since (a,b) lies on the line perpendicular to it that passes through yy)
Solving these equations simultaneously, we get:
a = -u1u2/(u1^2 + u2^2)
b = u1^2/(u1^2 + u2^2) * y
Now we can use the distance formula to find dd:
dd = sqrt((x - a)^2 + (y - b)^2)
where x and y are the coordinates of yy.

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To find the limit of ln(5x)/√5x as x approaches infinity, we can use l'Hospital's Rule since it is an indeterminate form of ∞/∞.

Taking the derivative of the numerator and denominator separately, we get: lim [(1/5x) / (1/2√5x)] x→[infinity]

Simplifying this expression, we get: lim 2/5√5x x→[infinity]

Since the denominator approaches infinity as x approaches infinity, the limit is equal to 0.

Therefore: lim ln(5x)/√5x = 0 x→[infinity]

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Answer:

The cost is $115.20

Step-by-step explanation:

The locker is 8ft by 12ft by 9ft.

The volume is:

V = 8 × 12 × 9

V = 864 cubic feet

But the price is given by cubic yards so we need to find that first. (we have cubic feet)

A cubic yard is

1yd × 1yd × 1yd

And a yard is 3 feet, so that is the same as:

3ft × 3ft × 3ft

= 27cubic feet

Divide:

864/27

= 32

The locker is 32 cubic yards.

The price is $3.60 per cubic yard. Multiply.

32 × 3.60

= 115.2

The cost of the locker will be $115.20.

Katy traveled more distance than Roger by 84.9 miles.

Subtraction is a basic arithmetic operation that involves finding the difference between two numbers, by taking away one number from another. It is denoted by the minus (-) sign and is the inverse operation of addition

To find out who traveled more distance, we need to calculate the difference between the distance traveled by Roger and Katy.

So, Katy traveled 205.65 miles and Roger traveled 120.75 miles.

To find out who traveled more, we subtract the distance traveled by Roger from the distance traveled by Katy

= 205.65 miles - 120.75 miles

Subtract the numbers

= 84.9 miles

Therefore, Katy traveled 84.9 miles more than Roger.

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The first four terms of the geometric sequence are -1, 11, -121, and -1210.

We have,

To find the first four terms of the geometric sequence, we need to determine the common ratio, r, and then use it to calculate the other terms.

We can start by using the formula for the nth term of a geometric sequence:

an = a1 x r^(n - 1)

where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.

Since we are given a2 and a3, we can use them to form two equations:

a2 = a1 x r

a3 = a1 x r²

We can then solve for a1 and r:

a1 = a2 / r = 11 / r

r = a3 / a2 = -121 / 11

Substituting these values into the formula for the nth term, we get:

an = (11 / r) x (-121 / 11)^(n - 2)

Simplifying this expression, we get:

an = -11 x 11^(n - 2)

Now we can calculate the first four terms:

a1 = 11 / r = 11 / (-121 / 11) = -1

a2 = 11

a3 = -121

a4 = -11 x 11^(4 - 2) = -1210

Therefore,

The first four terms of the geometric sequence are:

-1, 11, -121, -1210

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The change in the allocation of congressional seats based on changes in the population is called redistricting.

The process of altering the borders of electoral districts or constituencies in response to population changes is known as redistricting. The census is taking a note of the population in an interval of ten years to check the population of the united states nationally and also in each and every state.

Further on the data from the census will be helping to calculate the number of the states in the house of representative from the states. This is done to make sure the one person one vote agenda. Redistricting has the potential to significantly affect political power and representation.

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Answer:

[tex]x = \sqrt{ {28.46}^{2} - {27}^{2} } = \sqrt{80.9716} = 9.00[/tex]

Using unit conversions, the height of  the International Space Station in kilometers is 400 kilometers.

Unit conversion enables the conversion of one unit to another.

Division and multiplication operations are heavily deployed in unit conversions.

These two basic mathematical operations help create the conversion factors for unit conversions.

The orbiting height of the International Space Station = 250 miles

5 miles = 8 kilometers

250 miles = 250 x 8/5 kilometers

= 400 kilometers

Thus, a height of 250 miles is the same as a height of 400 kilometers.

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Answer:

The original recipe calls for 1 1/4 cups of dip and 1/2 cup of veggies, so you + both together which is a total of 1 3/4 cups of ingredients.

If Austin wants to use 1 cup of veggies instead of 1/2 cup, he needs to double the recipe. To keep the same ratio of dip to veggies, he will also need to double the amount of dip.

1 3/4 cups (original recipe) x 2 = 3 1/2 cups

Therefore, Austin will need 3 1/2 cups of dip to make the recipe using 1 cup of veggies.