Simplify the expression. Write the answer using scientific notation.
a) 2.52 × 10–3
b) 2.52 × 10–2
c) 2.52 × 10–1
d) 4.3 × 10–2

Answer:

At a real estate agency, an agent sold a house for $339,000. The commission rate is 6.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?

commission = commission rate x sales

Step-by-step explanation:

your question is worng

Answer:

Your answer is

Agency= 22,035$

Agent= 5,508.75$

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Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

Answer:

When solving a compound inequality, you can express the solution in two different ways: using a union or intersection.

Using a union:

A union represents the solutions that belong to either one inequality or the other, or both. You can express a union using the symbol "or," or by writing the solutions for each inequality separately and combining them using a "union" symbol (∪). For example, if you have the compound inequality "x > 2 or x < -3," you can express the solution as "x ∈ (-3, 2) ∪ (-∞, -3) ∪ (2, ∞)."

Using an intersection:

An intersection represents the solutions that belong to both inequalities. You can express an intersection using the symbol "and," or by writing the solutions for each inequality separately and combining them using an "intersection" symbol (∩). For example, if you have the compound inequality "x > 2 and x < -3," you can express the solution as "x ∈ (-3, 2) ∩ (-∞, -3) ∩ (2, ∞)."

Which method you use to express the solution will depend on the specific inequalities and the type of solutions you are looking for. It is important to carefully consider the inequality symbols (>, <, ≥, ≤) and the use of "and" or "or" in order to determine the correct solution.

When solving a compound inequality, the solution can be expressed in one of two ways: as an interval or as a union of intervals.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

An interval is a set of all real numbers between two given numbers, and is written in the form (a, b) or [a, b], where a and b are real numbers, and a < b. If a and b are included in the interval, then the interval is written as [a, b]; if a and b are not included in the interval, then the interval is written as (a, b).

A union of intervals is a combination of two or more intervals, and is written in the form (a, b) ∪ (c, d) or [a, b] ∪ [c, d], where a, b, c, and d are real numbers, and a < b and c < d.

When solving a compound inequality, it is important to first simplify the inequality by combining like terms, isolating the variable on one side of the inequality, and combining any separate inequalities into a single inequality. Then, the solution can be found by graphing the inequality on a number line, and shading the portion of the number line that represents the solution.

Once the solution is found the solution can be expressed either as an interval or as a union of intervals depending on the inequality. For example, if the inequality is x>1 and x<3, then the solution would be expressed as (1,3) and this is an example of an interval. If it's x>1 and x≥3 then the solution would be expressed as (1,3] U [3,∞) and this is an example of union of intervals.

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The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

4

Step-by-step explanation:

6 - (-10) - (12) = 16 - 12 = 4

Answer:

Its C. When you are getting ratios, we need to convert the units too...

The correct ratio which is equal to the ratio 5cm:5m:0.02km is,

⇒ 1 : 100 : 400

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

We have to given that;

The ratio is,

⇒ 5cm:5m:0.02km

Now, We can simplify the ratio as;

⇒ 5 cm : 5 m : 0.02 km

⇒ 5 cm : 5 x 100 cm : 0.02 x 100000

⇒ 5 cm : 500 cm : 2000 cm

⇒ 1 : 100 : 400

Thus, The correct ratio which is equal to the ratio 5cm:5m:0.02km is,

⇒ 1 : 100 : 400

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-12v+6y+18

you multiply everything by -3, so -3×4v=-12v
-3×(-2y)=6y, since negative × negative=positive
-3×(-6)=18

i hope this helps :)

Answer:

cot (x) ; D

Step-by-step explanation:

Mathematically;

cosec is 1/sin

So if cosec is 14/10 , then sin is 10/14

Sine refers to opposite/hypotenuse

So to get the adjacent, we use the pythagoras theorem.

According to this, the square of the hypotenuse equals the sum of the squares of the opposite and adjacent

Hence to get the value of the adjacent, we have;

14^2 - 10^2 = O^2

O^2 = 196-100

O^2 = 96

O = square root of 96

Now, mathematically, we know that Tan is opposite/ adjacent

So in this case tan = 10/√96

But cot is 1/tan

Thus cot = √96/10

So cot is our answer

Answer:

A. cos(x)

Step-by-step explanation:

Answer:

\(b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}\)

Step-by-step explanation:

Given

\(f(b) = b^2 - 75\)

Required

Determine the roots

To get the root of the function, then f(b) must be 0;

i.e. f(b) = 0

So, the expression becomes

\(0 = b^2 - 75\)

Add 75 to both sides

\(75 + 0 = b^2 - 75 + 75\)

\(75 = b^2\)

Take square roots of both sides

\(\sqrt{75} = \sqrt{b^2}\)

\(\sqrt{75} = b\)

Reorder

\(b = \sqrt{75}\)

Expand 75 as a product of 25 and 3

\(b = \sqrt{25*3}\)

Split the expression

\(b = \sqrt{25} *\sqrt{3}\)

\(b = \±5 *\sqrt{3}\)

\(b = \±5 \sqrt{3}\)

\(b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}\)

The options are not clear enough; however the roots of the equation are \(b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}\)

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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(a) The sum of the interior angles of a regular octagon is 1,080⁰.

(b) The measure of one interior angle is 135⁰.

(c) The sum of the exterior angles of the octagon is 360⁰.

The sum of the interior angles of a regular octagon is calculated as follows;

The formula for sum of interior angles is given as;

sum of interior angles = (n - 2) x 180

where;

The number of sides of a regular octagon = 8

sum of interior angles = (n - 2) x 180

sum of interior angles = (8 - 2) x 180

sum of interior angles = 1,080⁰

The measure of one interior angle = 1,080 / 8 = 135⁰

The sum of exterior angles of a polygon = 360⁰, so the sum of the exterior angles of the octagon is 360⁰.

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Answer:

a

This process follows is a binomial  process

b

This process is not a binomial  process

Step-by-step explanation:

Considering the first statement

One basketball player attempts 10 free throws and the number of successful attempts is totaled.

  This process is a binomial  process because

One basketball player attempts 10 free throws and the number of successful attempts is totaled.

   This process is not  a binomial  process because chance that is the probability of success and failure will remain constant throughout the trial is not equal (what this means is that given the number of player is more than on their probability of success and failure will differ.)

Answer:

Answer 1008

Step-by-step explanation:

Answer:

The final balance is $571.61.

The total compound interest is $121.61.

Step-by-step explanation:

hope this helps!

The calculated equation of the line parallel to y = -x - 5 that passes through (-2, 2) is y = -x.

To find the equation of the line parallel to y = -x - 5 that passes through (-2, 2),

We first note that any line parallel to y = -x - 5 will have the same slope as this line, which is -1

Using the point-slope form of the equation of a line, we can write the equation of the line we're looking for as:

y - y1 = m(x - x1)

where m is the slope (-1 in this case),

So, we have

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

Evaluate

y - 2 = -x - 2

Adding 2 to both sides, we get:

y = -x

Therefore, the equation of the line parallel to y = -x - 5 that passes through (-2, 2) is y = -x.

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The geometric center of the graph under the function is 5/3

The equation of the function is given as:

f(x) = 3 - |x - 2|

The interval is given as:

x ∈ [0, 3]

The geometric center (gc) of the graph under the function is calculated using

gc = ∫x f(x) dx/∫f(x) dx

Substitute the known values in the above equation

gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx

Integrate the numerator and the denominator of the above equation

gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]

Recall that the interval is given as x ∈ [0, 3]

Substitute the interval values in the above equation.

The equation is then simplified using a graphing calculator.

So, we have

gc = (65/6)/(13/2)

Express the quotient expression as a product

gc = (65/6) * (2/13)

Divide 65 by 13

gc = 5/6 * 2

Divide 2 by 6

gc = 5/3

Hence, the geometric center of the graph under the function is 5/3

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Answer: Let "T" denote households with television

"I" denote households with internet

and "N" denote households with neither of these.

Since P(N) = 0.05 then it means P(TuI) = 0.95. We know from set theory that P(TuI) = P(T) + P(I) - P(TnI). Thus,

0.95 = 0.92 + 0.72 - P(TnI) ==> P(TnI) = 0.69. This means P(T/I) = P(T) - P(TnI) = 0.92 - 0.69 = 0.23, and P(I/T) = P(I) - P(TnI) = 0.72 - 0.69 = 0.03. So,

a)

House                 Probability

Nothing                0.05

Only television      0.23

Only internet         0.03

Both                   0.69

b) P(internet but no television) = P(only internet) = 0.03

c) P(internet | there is television) = (By Bayes' Rule) P(TnI) / P(T) = 0.69 / 0.95 = 0.726 (rounded to 3 decimal points)

d) P(internet | there is no television) = (By Bayes' Rule) P(I/T) / P(T') = 0.03 / 0.08 = 0.375

e) From (c) and (d) ==> In Canada, it is (0.726/0.375 ≈ 2 ) twice more likely that if there's television in the household, then there is internet.

Step-by-step explanation:

Answer: 16%

Step-by-step explanation: Because if you look at that denominator then you can see that its 25 so if you multiplied that by 4 then you'll get 100 which is 100% so whatever you do to the denominator you have to do to the numerator so 4x4 is 16 so thats 16% and there you go.

Answer:  D is the answer. trust me.

Step-by-step explanation:

The problem that could be solved using the equation 10x+5=35 is option D: After a $5 discount, an order of 10 items cost $35. How much did each item cost?

To solve this problem, we can use the equation 10x + 5 = 35, where x represents the cost of each item. The $5 discount reduces the total cost of the 10 items by $5, so the total cost of the 10 items before the discount would be 10x. Therefore, we can set up the equation:

10x + 5 = 35

Subtracting 5 from both sides, we get:

10x = 30

Dividing both sides by 10, we get:

x = 3

So, each item cost $3 before the discount.

Answer:

A

Step-by-step explanation:

1. If you rented the jet ski for 9 RTUs, it would cost $90 USD.

2. If we paid $80 USD for the jet ski rental, the rental time would be 8 RTUs.

3. If you rented the jet ski for 2.5 RTUs, it would cost $25 USD.

We are given that 1 unit of 1 = 1 RTU = $10.

Then, 9 RTUs will cost:

= 9 * $10

= $90

To calculate how long was the rental in RTU, you can divide the total cost by the cost of each unit which is:

= $80 / $10

= 8 RTUs

2 units of 1 = 2 RTUs = $20

1 unit of 0.5 = 0.5 RTUs = $5

So, the total cost of jet ski for 2.5 RTU will be:

= $20 + $5

= $25

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Answer:

y = -3x -12

Step-by-step explanation:

Just solve for y, and you should get the equation is slope intercept form

Hopefully this helps- let me know if you have any questions

Answer:

-3. is a slope intercept.

Step-by-step explanation:

-3x - y=12

-3x-12=y

y=-3x-12

comparing above equation with y =mx+c

we get

m=-3

Answer:Quadrant 1

Only in Quadrant 1, the both y and x-axis is positive. So (10, 15) is in quadrant 1.

Answer:

xy^4+2x^3y^2+xy

Step-by-step explanation:

shown above. Hope this helps :]

Answer:

26904

Step-by-step explanation:

Inequalities help us to compare two unequal expressions. The inequality that model this situation is 1c + 2k ≤ 10. The correct option is C.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Let c represents the number of carrots and k represents the number of leeks.

Given that At the store, carrots are marked at $1.00 per pound, and leeks are marked at $2.00 per pound. Therefore, the total cost can be written as,

1c + 2k

Also, it is given that Emily wants to buy carrots and leeks for a stew, but she only has $10.00 with her. Therefore, she must spend $10 or less than that.

Thus, the inequality can be written as,

1c + 2k ≤ 10

The graph of the given inequality can be made as shown below.

Hence, the inequality that model this situation is 1c + 2k ≤ 10.

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Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

The approximate lateral area of the cone is equal to 200.96 cm².

Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:

Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)

Where

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circular base = πr²

16π = πr²

Radius, r = √16

Radius, r = 4 cm.

Substituting the given parameters into the lateral area of a cone formula, we have the following;

Lateral surface area of a cone, LSA = πrl = πr4(r)

Lateral surface area of a cone, LSA = 3.14 × 4 × 16

Lateral surface area of a cone, LSA = 200.96 cm².

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Answer:

201 beause you are rounding to the nearest whole number

Step-by-step explanation:

The value of side EA is,

EA = 16.9

We have to given that;

Circle E with diameter CD and radius EA.

And, AB is tangent to E at A.

Here, AB = 34 and EB = 38

Hence, By using Pythagoras theorem we get;

AB² + AE² = EB²

34² + AE² = 38²

1156 + AE² = 1444

AE² = 1444 - 1156

AE² = 288

AE = √288

AE = 16.9

Thus, The value of side EA is,

EA = 16.9

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Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

Step-by-step explanation:

13 hours

6 + 4 + 3 = 13

correct if wrong