From 2008 to 2010, the cost of houses rose by 60%. if the cost of houses rose by 40% from 2008 to 2009, to the nearest percent, how much did the cost rise from 2009 to 2010?

Using composite functions, we have that:

a) f(x) = x² + 3.

b) [tex]g(x) = \sqrt{x}[/tex]

c) f(g(x)) = x + 3.

d) [tex](g \circ f)(6) = \sqrt{39}[/tex]

The composite function of f(x) and g(x) is given by:

(f ∘ g)(x) = f(g(x)).

For item a, we want a non-linear function, which has a highest exponent different of 1, that does not go through the origin, hence the function can be:

f(x) = x² + 3.

For item b, we also want a non-linear function with a radical, hence the function can be:

[tex]g(x) = \sqrt{x}[/tex].

For item c, the composite function is:

[tex]f(g(x)) = f(\sqrt{x}) = (\sqrt{x})^2 + 3 = x + 3[/tex]

For item d, the composite function is:

[tex]g(f(x)) = g(x^2 + 3) = \sqrt{x^2 + 3}[/tex]

At x = 6, we have that:

[tex](g \circ f)(6) = \sqrt{6^2 + 3} = \sqrt{39}[/tex]

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The average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given,

The function f(x)=80(1.5)x

where x is the time in hours

Then,

f(4)=80(1.5)4=480

f(8)=80(1.5)8=960

f(0)=80(1.5)0=0

Then the average rate of change between 4 and 8 hours =[tex]\frac{960-480}{4}[/tex]

=120 units per hour

The average rate of change between 0 and 4 hours=[tex]\frac{480-0}{4}[/tex]

=120 units per hour

Hence, the average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

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Step-by-step explanation:

24-(14)

10

use bidmas...

Answer:

you have it right.

Domain is 3[tex]\leq[/tex]x[tex]\leq[/tex]positive infinity

Range is 5[tex]\leq[/tex]y[tex]\leq[/tex]positive infinity

Step-by-step explanation:

To decide the power of 10 multiplies an equation with repeating digits; Round the equation to the required significant numbers.

when the numerator of an equation is divided by the denominator and the result is not a whole number ( i.e. number with some decimals)and sometimes the decimal places are unending. to present the result properly we have to round off the number to the nearest significant number, then you can multiply the equation with the power of 10, in relation to the number of significant places you rounded off.

Example :

5/200 = 0.025

To express this answer with the power of 10

0.025 = 2.5 * 10 ^-2

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It is not possible that the intersection case is P(A B)=0.5 .

The set of all objects that are members of both sets A and B is represented by the intersection of the two sets A and B, abbreviated as A∩B.

If there is any element x that is an element of both A and B, then we can also say that A intersects (meets) B at x. If A∩B is an inhabited set, which means that there must be some x such that x∈A∩B exists, then A intersects B equivalently.

If A does not intersect B, then A and B are said to be disjoint. They share no elements, to put it simply. If the intersection of A and B contains nothing—A∩B=Ф—then A and B are disjoint.

Explanation:

The likelihood of occurring of an event is called probability.

Consider two events A and B are occurred with probabilities P(A) and P(B)  respectively.

The probability that both the events occurs is,

P(A and B)=P(A∩B)

When both the events are independent,

P(A and B)=P(AB) = P(A)x P(B)

The probability that either A or B occurs is,

P(A or B)= P(AUB) = P(A)+P(B)-P(A∩B)

When both the events are mutually exclusive the probability that either A or B occurs is,

P(A or B)=P(AUB) = P(A)+P(B)

The compliment of the probability is,

P(A)=1-P(A)

The conditional probability of occurring of an event A when it is given that B had already occurred is,

P(A|B)=P(A∩B)/P(B)

Let A represent the situation where the chosen person has a Visa credit card and B represent the situation where they have a Master card. The probability of occurring event A is 0.6 and the probability of occurring event B is 0.4 that is, P(A)=0.6, P(B)=0.4 .

It is known that P(A B)∠P(A) and P(A B)∠P(B) . So, it is not possible that the intersection case, P(A B)=0.5 .

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The frequency tells us how many times the integer appears in the set of numbers.

The integer tells us the numbers that appear in the set of numbers.

To find the mean, we add up all the numbers in the set and divide the sum by the number of integers.

Let's write the information on the graph as a list of numbers:

0, 1, 2, 3, 3, 3, 4, 4, 6, 7, 8, 10

Find the sum:

51

Divide the sum by the number of integers (which is 12):

51/12

= 4.25

The mean is 4.25.

The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Triangle law of vectors states that for a ΔABC

The sum of vectors of two sides is equal to the third side vector.

Two vectors are said to be Parallel if one vector is scalar multiple of other.

In the given figure

In ΔABC , D is mid point of AB and E is the mid point of AC .

By using triangle law of vectors for ΔADE

AE+AD=ED......(1)

Now using triangle law of vectors addition for ΔABC

CA+AB=CB    ....(2)

(as given that E is the mid point of CA , we can write [tex]AE=\frac{1}{2} CA[/tex]

CA=2AE.....(3)

and D is mid point of AB , we can write [tex]AD=\frac{1}{2} AB[/tex]

AB=2AD......(4)

Substituting (3) & (4) in (2) we get

2AE+2AD=CB

2(AE+AD)=CB

SUBSTIUTTING VALUES OF (AE+AD) from (1) we get

2ED=CB

[tex]ED=\frac{1}{2} CB[/tex]

Hence , the line joining the midpoints of two sides of a triangle is  half of third side.

Since ED is (1/2) of CB i.e. ED is scalar multiple of CB.

Hence they are parallel.

Therefore , The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

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The coordinates of its center will be (2,10)

(x - h)²+ (y - k)² = r² is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius.

A circle with a radius of r and a center is represented as

(x - a)² + (y - b)² = r² where (a, b) is the center of the circle.

Circle passes points (-4, 2) and (2, 0):

Both (-4 - a)² + (2 - b)² and (2 - a)² + (-b)² are equal to r²

Currently, the center's x coordinate (a) is 2 due to the tangent at (2, 0)

The equations then read:

6² + (2 - b)² = r²

b² = r²

⇒ 36 + (2 -b)² -b² = 0

⇒ 36 + 4 + b² - 4b - b² = 0

⇒ 4b = 40

⇒ b = 10.

So, the center is (2,10)

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The sample standard deviation is 0.89

In the given statement is:

A sample n = 5 scores which means that there are 5 sample having m = 20 which is the arithmetic mean (A.M.)of these samples, and [tex]s^{2}[/tex] = 4 is the variance of these samples.

Let us know the :

What is meant by Sample Standard deviation?

The sample standard deviation (s) is the square root of the sample variance and is also measure of the spread from the expected values.

Standard deviation is the square root of the variance.

Therefore, [tex]s^{2}[/tex] =4 => s = 2

(Where, s denotes sample standard deviation ,σ)

Also, Standard error of the sample S(E) = Sample standard variance / [tex]\sqrt{number of samples}[/tex]

= σ /[tex]\sqrt{n}[/tex] = 2/[tex]\sqrt{5}[/tex]

and, root 5 = 2.24

put the value of root 5

=2 / 2.24

= 0.89

Hence, The sample standard deviation is 0.89

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Answer:

[tex]\textsf{(a)} \quad -4 < x\leq 1[/tex]

[tex]\textsf{(b)} \quad [3, 19)[/tex]

Step-by-step explanation:

Given compound inequality:

[tex]\dfrac{9+x}{5} < 5+x\leq 6[/tex]

[tex]\textsf{If\: $a < u\leq b$ \:then\: $a < u$ \:and\: $u\leq b$}.[/tex]

[tex]\textsf{Therefore \:$\dfrac{9+x}{5} < 5+x$ \:and\: $5+x\leq 6$}[/tex]

Solve the inequalities separately:

Inequality 1

[tex]\begin{aligned}\dfrac{9+x}{5} & < 5+x\\9+x & < 5(5+x)\\9+x & < 25+5x\\9+x -5x& < 25+5x-5x\\9-4x & < 25\\ 9-4x-9 & < 25-9\\-4x & < 16\\-x & < 4\\x & > -4\\ \end{aligned}[/tex]

Inequality 2

[tex]\begin{aligned} 5+x & \leq 6\\ 5+x-5 & \leq 6-5\\x & \leq 1 \end{aligned}[/tex]

Combine the intervals:

[tex]-4 < x\leq 1[/tex]

Given equation:

[tex]y=x^2+3[/tex]

As the domain is restricted to  -4 < x ≤ 1, the range is also restricted.

The vertex (minimum point) of  [tex]y = x^2 + 3[/tex]  is when x = 0.

As x = 0 lies within the restricted domain, y = 3 is the lowest value of the range.

[tex]x=-4 \implies y=(-4)^2+3=19[/tex]

Therefore, the range is:

I think using properties can help you mentally find answers to problems because if you know what property you are going to use, then you can know what you are doing, thus it's helping you mentally find answers.

According to the given statement

P(D) 0.7, P(E) = 0.2 and P(D and E) = 0.15.

P(DIE):0.75

The possibility of an event or outcome occurring conditional on the occurrence of a prior event or outcome is known as conditional probability. The conditional probability is calculated by multiplying the probability of the previous event by the present probability of the upcoming, or conditional, occurrence.

Contrast Unconditional probability with conditional probability. The possibility that an event will occur regardless of whether any previous occurrences have occurred or any other circumstances are present is known as Unconditional probability.

According to the given value;

P(DIE): 0.15/0.2

            =0.75.

hence,P(DIE):0.75.

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The quotient of 7/8 divided by 2/5 will be C. 35/16.

The quotient simply means that we have to divide.

Therefore, the quotient of 7/8 divided by 2/5 will be:

= 7/8 ÷ 2/5

= 7/8 × 5/2

= 35/16

In conclusion, the correct option is C

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Answer:

The first one

Step-by-step explanation:

Because the max is 6, the left ones are only right. Also a point is must be negative so it is the top left one.

Solution After Factoring:

[tex]144x^2-144xy+86y^2-25u[/tex]

Hope this helps! If not, comment below and I'll see what else I can do to help. If it does help though, lmk! Thanks and good luck!

Answer:

48º, 96º, 144º and 72º respectively

Step-by-step explanation:

According to the given statement,

366 liters of natural oil is needed to make 671 L synthetic oil.

Essential oils, which are more natural, are slightly different from synthetic oils. An intentionally created chemical component is present in synthetic oils, which are used as lubricants.

Full synthetics and semi-synthetic oils are the two primary types of synthetic oils. Full synthetics originate from crude oil or byproducts in this situation. Conventional oils are produced using chemical procedures rather than distillation. The resulting synthetic oil has a higher molecular make-up and frequently exhibits more consistent characteristics. Synthetic oils are used in many cosmetic and medicinal goods, just like their more natural equivalents.

According to the given values;

The ratio of natural to synthetic oil

= 6:5

If 671 liters have to be made then,

Add 6+5=11

So, 6/11 of 671liters will be = 366 liters of natural oil

and, 5/11 of 671 liters will be = 305 liters of synthetic oil

Hence, 366 liters of natural oil is needed.

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Answer:

Step-by-step explanation:

The Answer is A

The equation for a parallel street that passes through the given point is y = 4x + 12

From the question, we are to determine the equation of the street that is parallel to the first street

NOTE: Two lines are parallel if they have equal slopes.

Thus,

We will determine the slope of the first street.

From the given information,

The street passes through the points (4, 7) and (3, 3)

Using the formula,

Slope = (y₂ - y₁)/(x₂ - x₁)

x₁ = 4

y₁ = 7

x₂ = 3

y₂ = 3

∴ Slope = (3 -7)/(3 -4)

Slope = -4/-1

Slope = 4

Now,

For the equation of the parallel street

The street passes through the point (-2, 4)

Since, the street is parallel to the first street,

Slope = 4

Using the point-slope form

y - y₁ = m(x - x₁)

y - 4 = 4(x - -2)

y - 4 = 4(x + 2)

y - 4 = 4x + 8

y = 4x + 8 + 4

y = 4x + 12

Hence, the equation for a parallel street that passes through the given point is y = 4x + 12

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Answer:

5 x = Solve: 2. 8 x = . x has 2 multiplied to it, so we divide 2 from both sides. 2.

Step-by-step explanation:

According to the question, to investigate through an experiment by telling people to smoke a pack of cigarettes each day by putting their health at risk. This causes serious health issues. And the other half are told not to smoke but might smoke at their own discretion. In the end, it is very difficult to keep track of 50 years of both types of people. That means people who are smoking and others who are not smoking. And, after 50 years, checking their consistency has become extremely difficult, if not impossible. Therefore, this experiment is not possible in both ways, that is, experimental or observational.

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The possible numbers are

( 9 , 9 ,2 ) ;( 9 , 8 , 3 );( 9 , 7 , 4 );( 9 , 6 , 5 )

All 4 combinations have the sum of 20 .

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The electronics retailer is extending a special offer to install the wall mount and television for free. However, Jamie decides to tip the installation specialist 10% of the original purchase price before the discount is applied.  New total be 11x/10.

Let the original purchase price without discount be 'x';

Tip to installation specialist = 10% of original purchase price

 = (10/100) × x

= x/10;

Her new total is x + x/10 = 11x/10;

We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the phrase used to describe a refund or an offer made to clients on the listed price of goods.

Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the refund is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price decrease, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold. Discounts are sometimes referred to as "off" or "reductions." It should be noted that the discount is always determined using the item's marked price (list price).

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Answer : $611.29

Step-by-step explanation:

.10 x 719.99 =71.99

539.30 (from previous answer) +71.99 =611.29

The length of line AB with coordinates A (-5, -2) and B (7, 4) is;  6√5 units

The formula for distance of a line between two coordinates is;

D = √[(x2 - x1)² + (y2 - y1)²]

From the coordinates given as A (-5, -2) and B (7, 4), we can say that;

x1 = -5

x2 = 7

y1 = -2

y2 = 4

Thus;

D = √[(7 - (-5))² + (4 - (-2))²]

D = √(12² + 6²)

D = √180

D = 6√5 units

Thus, we conclude that the length of line AB with coordinates A (-5, -2) and B (7, 4) is;  6√5 units

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Complete question is;

Find the distance of the line AB with coordinates A (-5, -2) and B (7, 4).

Applying exponent properties, it is found that there are 2^9 = 512 bacteria after 120 minutes.

We keep the base and add the exponents.

This is what happens in this problem, when we multiply 2^6 by 2^3, as follows:

[tex]2^6 \times 2^3 = 2^{6 + 3} = 2^9 = 512[/tex]

Hence, there are 512 bacteria after 120 minutes.

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Answer:

Yes, 144>140

Step-by-step explanation:

Since Sinita has 3 boxes of 48 nails, Sinita has a total of 144 nails. (48x3=144)

Sinita needs enough for 35 frames, and each frame uses 4 nails, so she will need a total of 140 nails. (35x4=140)

what Sinita has: 144

what Sinita needs: 140

Sinita has more than what she needs, so yes Sinita has enough nails. (144>140)

Answer:

0.03 is the correct answer

Step-by-step explanation:

0.02866009 = 0.03

If slopes of the given lines are solved and observed, we get the slope of line E is [tex]m_{E}[/tex] = [tex]\frac{-5}{6}[/tex]

As per question statement, the equation for line A is [tex]y = \frac{6x}{5} - 10[/tex] Line A is parallel to line B, which is perpendicular to line C. The line D is perpendicular to line C and perpendicular to line E.

Before solving this question, we need to know about some basic formulas and concepts of equation for a line.

If Lines are parallel, their slopes are equal and if lines are perpendicular, the product of their slopes is -1.

i.e., if [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are slopes of two lines then if,

[tex]m_{1} = m_{2}[/tex] then lines are parallel

Now slope of line A can be found out by formula [tex]y=mx+c[/tex] hence slope of line A   [tex]m_{A}[/tex]= [tex]\frac{6}{5}[/tex]

Line B is parallel to A so, [tex]m_{B}[/tex] = [tex]\frac{6}{5}[/tex]

Line C is perpendicular to B so [tex]m_{C} * m_{B} = -1\\m_{C} = \frac{-5}{6}[/tex]

Line D is perpendicular to C so [tex]m_{D} *m_{C} = -1\\m_{D} = \frac{6}{5}[/tex]

Line E is perpendicular to D hence [tex]m_{E} * m_{D} = -1\\m_{E} = \frac{-5}{6}[/tex]

Therefore the slope of line E is [tex]\frac{-5}{6}[/tex]

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The equation which is equivalent to the given expression 18 − 15 = − 2x/5 + 7x/15 is (-3 = 5x/5).

The basic equation used to demonstrate and overcome for an unknown quantity is a linear equation for one variable.

The given equation is;

18 − 15 = − 2x/5 + 7x/15

Simplifying the constant and variable part.

- 3 = 5x/5

Multiplying both side by 5;

- 15 = x

or, x = -15.

Thus, the required equivalent equation is - 3 = 5x/5 and the value of variable x is -15.

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