In two or more complete sentences, describe how to find the interval(s) where the function is increasing and how interval notation is used to express the interval(s). In your final answer, include the interval in which the function is increasing

Answer:

( x-7)^2 + ( y+12) ^2 = 81

Step-by-step explanation:

The equation of a circle can be written in the form

( x-h)^2 + ( y-k) ^2 = r^2  where ( h,k) is the center and r is the radius

( x-7)^2 + ( y--12) ^2 = 9^2

( x-7)^2 + ( y+12) ^2 = 81

Answer:

(x - 7)² + (y + 12)² = 81

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

Here (h, k) = (7, - 12) and r = 9, thus

(x - 7)² + (y - (- 12))² = 9², that is

(x - 7)² + (y + 12)²= 81

Answer:

$104

Step-by-step explanation:

If the cost in the store is x we can write:

75%x = 78

0.75x = 78

x = 78 / 0.75 = 104

Answer:

$104 in the store

Step-by-step explanation:

To find the original cost before the discount, you divide the discounted price by the percentage, getting 104.

Answer:

       Age                               Frequency                   Cumulative Frequency

 Less than 30                             27                                       27

 Less than 40                             37                                27 + 37  =  64

 Less than 50                              1 1                                 64 + 11   =  75

 Less than 60                               3                                  75 + 2   =  77

 Less than 70                               5                                   77 + 5   =  82

 Less than 80                               1                                     82 + 1  =  83

 Less than 90                              2                                    83 +2  =  85

Step-by-step explanation:

Given:

The Frequency Distribution table of ages of best actresses when award was won

To find:

Construct the cumulative frequency distribution

Solution:

In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40  is 37 and the previous frequency (less than 30) is 27 so in order to calculate cumulative frequency 27 i.e. previous frequency is added to 37 (frequency of less than 30). The complete table is given above.

Answer: 1 real and 2 complex.

Step-by-step explanation:

A cubic polynomial is written as:

a*x^3 + b*x^2 + c*x + d

And the zeros are such that:

a*x^3 + b*x^2 + c*x + d  = 0

As the degree of the polynomial is 3, then we have 3 solutions (where some of them may be equal)

Now, an easy way to see the real and complex zeros of a polynomial is:

If after a change in curvature, the line touches the x-axis : that is a real zero

if it does not, then there we have a complex zero.

Here we can see two lines that do not touch the x-axis and one line that does touch the x-axis.

Then we have 2 complex zeros and one real zero.

Answer:

Explained below.

Step-by-step explanation:

The z-test statistic is given as follows:

[tex]Z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}[/tex]

Here,

[tex]\bar X=\text{Sample Mean}\\\\\mu=\text{Population Mean}\\\\\sigma=\text{Population standard deviation}\\\\n=\text{Sample size}[/tex]

The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.

(i)

The difference between the sample mean and the original population mean are directly proportional to the z-test statistic.

So, increasing the  difference between [tex]\bar X[/tex] and [tex]\mu[/tex] will lead to an increase in the z-score.

And as the Z-score increases the p-value of the test decreases.

Thus, the complete statement is:

"Increasing the difference between the sample mean and the original population mean will result in an increase in the absolute value of z, and a decrease in the probability of obtaining a sample with that mean."

(ii)

The population standard deviation is inversely proportional to the z-test statistic.

So, increasing the population standard deviation will lead to a decrease in the z-score.

And as the Z-score decreases the p-value of the test increases.

Thus, the complete statement is:

"Increasing the population standard deviation will result in a decrease in the absolute value of z, and an increase in the probability of obtaining a sample with that mean"

(iii)

The number of scores in the sample is directly proportional to the z-test statistic.

So, increasing the number of scores in the sample will lead to an increase in the z-score.

And as the Z-score increases the p-value of the test decreases.

Thus, the complete statement is:

"Increasing the number of scores in the sample will result in an increase in the absolute value of z, and an decrease in the probability of obtaining a sample with that mean."

Answer:

Hey there!

Angle QRS is 70, and since it is located on the circle, we have a useful formula. If 141x-1 is called y, then 70 is half of that.

Thus, we have 141x-1=140

141x=141

x=1

Hope this helps :)

The division of 12e⁵ by 3e³ will be 4e².

In mathematics, the arithmetic operation has four main operators such as addition, subtraction, multiplication, and division.

The symbol of + represents the addition

The symbol of ÷  represents the division

The symbol of - represents subtraction

The symbol of × represents multiplication

Given the division,

12e⁵ by 3e³

⇒ 12e⁵ / 3e³

⇒ 12/3 × e⁵/e³

⇒ 4e²

Hence "The division of 12e⁵ by 3e³ will be 4e²".

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Answer:   simplified algebraic expression  : x

Step-by-step explanation:

The given phrase : 100 % of x

We can write 100 as 1 because 100% means complete or entire part.

Also, replace 'of' by '×' (Multiply sign).

So, the given phrase will become

1 × x   [Algebraic expression]

= x         [Simplified]

hence, the simplified algebraic expression is 'x'.

Answer: [tex]4\sqrt{3}[/tex] .

Step-by-step explanation:

Distance formula : Distance between points (a,b) and (c,d) is given by :-

[tex]D=\sqrt{(d-b)^2+(b-a)^2}[/tex]

Distance between points [tex](-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3})[/tex].

[tex]D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}[/tex]

Hence, the correct option is [tex]4\sqrt{3}[/tex] .

Answer:

A. an = 3(6)^(n-1)

Step-by-step explanation:

1st generation: n = 1:

a1 = 3*6^(1-1) = 3*6^0

= 3

n = 2:

a2 = 3*6^2-1

= 3*6

=18

n = 3

a3 = 3*6^(3-1)

= 3*6^2

= 106.

The solution is Option A.

The geometric progression is given by the equation aₙ = 3 ( 6 )ⁿ⁻¹ , where n is the number of terms

What is Geometric Progression?

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric progression be represented as A

Let the number of terms be represented as n

Now , the first term a₁ = 3 rabbits

The second term a₂ = 3 x 6 = 18 rabbits

The third term a₃ = 18 x 6 = 108 rabbits

So , the common ratio r = second term / first term

Substituting the values in the equation , we get

Common ratio r = 18/6 = 6

Now , the geometric progression A is given by the equation ,

The nth term of a GP is aₙ = arⁿ⁻¹

Substituting the values in the equation , we get

aₙ = 3 ( 6 )ⁿ⁻¹

Therefore , the value of A is aₙ = 3 ( 6 )ⁿ⁻¹

Hence , the equation is aₙ = 3 ( 6 )ⁿ⁻¹

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146

Step-by-step explanation:

Given:

[tex]x - \dfrac{1}{x} = 12[/tex]

To Find:

[tex] \sf \: The \: value \: of \: {x}^{2} + \dfrac{1}{ {x}^{2} } [/tex]

How to find:

Just square both side, Solve as a equation and get the answer. Simple, Isn't it?

Solution:

See in attachment.

Answer:

146

Step-by-step explanation:

The answer of this question id 146 .

you can do this type of numericals by above process.

Answer:

This is my first question but I think it's c

Step-by-step explanation:

25,000-4334=20,666

20,666/2712=7.62 which rounds to 8

Answer:

y = 100

Step-by-step explanation:

x = 25

x+y + 55 = 180 since it is a straight line

25+y+ 55 = 180

Combine like terms

80+y = 180

Subtract 80 from each side

y = 180-80

y = 100

Step-by-step explanation:

this is substitution method

Answer:

2x + y = 21

+

x - y = 6

_________

3x = 27

x = 27 ÷ 3

x= 9

x - y = 6

9 - y = 6

9 - 6 = y

3 = y

Therefore, x= 9 and y = 3

Answer:

A. 141.4 cm

Step-by-step explanation:

The piramide is 141.4cm

Answer:

y = -5x - 1

Step-by-step explanation:

Let the equation of a line parallel to the given line is,

y - y' = m(x - x')

Where m = slope of the line

And line passes through (x', y')

Equation of a line has been given as,

5x + y = 4

y = -5x + 4

Slope of this line = -5

By the property of parallel lines "slope of the parallel lines are same",

m = -5

Parallel line passing through (-1, 4) and slope 'm' = -5 will be,

y - 4 = -5(x + 1)

y - 4 = -5x - 5

y = -5x - 5 + 4

y = -5x - 1

Therefore, equation of the parallel line will be,

y = -5x - 1  

Answer: 9.9

Step-by-step explanation:

SINE RULE:

7/sin(31) = q / sin(47)

Therefore q = 7 / sin(31) * sin(47)

which equals: 9.9 to the nearest tenth.

Answer:

q = 9.9

Step-by-step explanation:

We can use the rule of sines

sin R             sin Q

------------- = ------------

PQ                 PR

sin 31            sin 47

------------- = ------------

 7                q

Using cross products

q sin 31 = 7 sin 47

Divide by sin 31

q = 7 sin 47 / sin 31

q =9.939995043

To the nearest tenth

q = 9.9

Answer:

the first one has one solution because eventually they will cross

Answer: 6

Step-by-step explanation: 1. 5c-c= 4c. The equation would then be 4c+10=34.

2. From there, you subtract 10 from both sides of the equation. By doing this, you have the variable and the nonvariable on separate sides of the equation.

3. After doing that, you should have 4c=24. To get the variable by itself, divide both sides by 4. 4c/4 is c and 24/4 is 6.

The final answer is 6. Hope this helped you:)

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

The Patel, Lopez, and Russo families all had parties recently. There were 152 adults at the Lopez party. The ratio of adults to children at the Russo party was 5 to 4. What was the ratio of adults to children at the Patel party?

(1) The Russo party had 31 more adults than children, and 47 more adults than did the Patel party.

(2) The Patel party had 40 more children, though 4 fewer people in total, than did the Lopez party, where the ratio of adults to children was 8 to 5.

Answer: Let the number of children in Russo party be x, The Russo party had 31 more adults than children, therefore the number of adults at the Russo party = x + 31. The ratio of adults to children at the Russo party was 5 to 4, we can find the number of children using:

[tex]\frac{5}{4}=\frac{x+31}{x}\\ 5x=4x+124\\x=124[/tex]

The number of children at the Russo party is 124 and the number of adult is 155 (124 + 31).

They  are 47 more adults at the Russo party than the Patel party, the number of adult at the Patel party = 155 - 47 = 108

the ratio of adults to children was 8 to 5 at the Lopez party, There were 152 adults at the party. Let x be the number of children at the Lopez party therefore:

[tex]\frac{8}{5}=\frac{152}{x}\\ 8x=760\\x=95[/tex]

The Patel party had 40 more children than the Lopez, the number of children at the Patel party = 135 (95 + 40).

The ratio of adults to children at the Patel party is [tex]\frac{108}{135} =\frac{4}{5}[/tex]

Answer:

Matched pairs design

Step-by-step explanation:

Looking at the options;

-It's not a completely randomized design because a randomized design will assign all individuals to a group which in this case it doesn't.

- It's not a randomized block design because randomized block design will group the subjects in question into 2 or more blocks which have a common characteristic and will then randomly assign subjects in each of the blocks.

-It's a matched pair because every individual/subject undergoes measurements both before and after being treated with the drugs.

Thus, the correct option is matched pairs design.

Answer:

D

Step-by-step explanation:

To be a function each value of x must correspond to only one, unique value of y.

In the given ordered pairs

Each x- value corresponds to exactly one y- value

Answer:

cost to rent each chair=$1.75, cost to rent each tabble=$10.75

Step-by-step explanation:

Hello, I can help you with this

Step 1

Define

cost to rent a chair=x

cost to rent a table=y

9x=total cost for rent 9 chair

7y = total cost for rent 7 tables

a)The total cost to rent 9 chairs and 7 tables is $91.

in mathematical terms it is

9x+7y=91....equation 1

b) The total cost to rent 3 chairs and 5 tables is

3x+5y=59.... equation 2

and you have 2 equation and 2 unknown terms

let's solve this

from equation 1 isolate x

[tex]9x+7y=91\\9x=91-7y\\x=\frac{91-7y}{9}\\ \\[/tex]

from equation 2 isolate x

[tex]3x+5y=59\\3x=59-5y\\x=\frac{59-5y}{3}[/tex]

now, x= x, so

[tex]x=\frac{91-7y}{9}\\\\\\x=\frac{59-5y}{3} \ \\\ \frac{91-7y}{9}=\frac{59-5y}{3}\\ 3(91-7y)=9(59-5y)\\273-21y=531-45y\\273-531=-45y+21y\\-258=-24y\\y=\frac{258}{24}\\ y=10.75\\[/tex]

now, we know y, use it to find x

[tex]x=\frac{59-5y}{3}\\x=\frac{59-5(10.75)}{3}\\x=\frac{59-53.75}{3}\\\\x=\frac{5.25}{3}\\ x= 1.75\\[/tex]

Have a nice day

Answer: D

Step-by-step explanation:

In synthetic division, if the divisor is an expression like x+3, you should always switch it to if x+3 were equal to 0.

[tex]x+3=0\\x=-3[/tex]

So, you should use -3. The only options with -3 are B and D.

The coefficients for the dividend are 7, -2, and 4, so D is the correct answer.

Hope this helps! If you still have questions, please ask.

Answer:

x=8

Step-by-step explanation:

Area is equal to

A = l * w

50 = ( x+2) ( x-3)

FOIL

50 = x^2 -3x+2x -6

Combine like terms

50 = x^2 -x -6

Subtract 50 from each side

0 = x^2 -x -56

Factor

What two numbers multiply to -56 and add to -1

-8*7 = -56

-8+7 = -1

0 = ( x-8) ( x+7)

Using the zero product property

x-8 =0   x+7 =0

x = 8   x=-7

Since the length cannot be negative x cannot be negative

x=8

Answer:

8

Step-by-step explanation:

put the 50 under area and continue with like that

Answer:

r = -0.83

strong negative correlation

r = -0.08

weak negative correlation

r = 0.96

strong positive correlation

r = 0.06

weak positive correlation

Step-by-step explanation:

In this question, what we are expected to do is to match the values of the correlation given with the type of correlation in which the values are.

When we talk of correlation, we are simply referring to the extent of agreement between the values in the data field.

Correlation has a value between -1 and +1, meaning it could be negative or positive.

Values closer to the extremes i.e (-1 or +1) indicates strong correlation while values farther away, i.e closer to zero indicates a weak relationship.

Let’s answer the questions specifically now:

r = -0.83

This is closer to -1 and it indicates a strong negative correlation

r = -0.08

This indicates a weak negative correlation as it is closer to zero and farther away form -1

r = 0.96

This indicates a strong positive correlation

r = 0.06

This indicates a weak positive correlation

Answer:

(3x + 20)° + 70° = 180°

Step-by-step explanation:

Answer:

0.0398 dollars

Step-by-step explanation:

We are told in the question that

An apple picker in China earns an average wage of 45 cents per hour.

Mathematically

1 hour= 45 cents............ Equation 1

An apple picker can harvest about 2.0 bushels of apples each hour.

Mathematically

2.0 bushels = 1 hour ..............Equation 2

We are told that each bushel contains about 126 apples

1 bushel = 126 apples

2 bushels =

126 × 2

= 252 apples

Combining Equation 1 and 2 together,

We can say

An apple picker in 1 hour harvests 2 bushels of apples which is 252 apples and is paid 45 cents

1 hour = 2 bushels of apples

1 hour = 252 apples

1 hour = 45 cents

Hence we can say fro harvesting 252 apples, an apples picker is paid 45 cents

Mathematically,

252 apples = 45 cents

One gallon of apple juice requires 40 apples

We are to calculate the labor cost of one gallon of apple juice in dollars

If : 252 apples = 45 cents

40 apples = X cents

Cross Multiply

40 × 25 = 252 × X

X = (40× 25) ÷ 252

X = 3.984063745 cents

Hence the labor cost of 40 apples = 3.984063745 cents

Approximately = 3.98 cents

Converting 3.98 cents to dollars

100 cents = 1 dollar

3.98 cents =

= 3.98/100

= 0.0398 dollars.

Therefore, the labor cost of one gallon of apple juice in dollars is 0.0398 dollars.

Answer:

[tex]m\angle Z\approx22.0\textdegree[/tex]

Step-by-step explanation:

First, note that we have a right triangle. Second, we need to find angle Z, and we are given the sides opposite to angle Z and the hypotenuse. Therefore, we can use sine.

Recall that:

[tex]\sin(\theta)=opp/hyp[/tex]

The opposite side is 3 while the hypotenuse is 8. Plug in the numbers and simplify. Use a calculator:

[tex]\sin(\angle Z)=3/8\\\angle Z=\arcsin(3/8)\\\angle Z\approx 22.0243\textdegree[/tex]

Answer:

Fred's

Step-by-step explanation:

Igloo 1.75(60) + 75 = 180

Tasty 2(60) + 80 = 200

Fred's 1.25(60) + 90 = 151.25

Answer: fred's

Step-by-step explanation: