Factorise (pls show steps)
12y^2 - 20y - 8

The graph below shows the number of blocks away from home Bentley is 21 minutes after he left his house, until he got back home.

The distance-timed graph is the type of graph that is used to represent the relationship that exists between the distance covered by a moving object and the time take to reach its destination.

The distance covered from house to store= 4 blocks

The time used = 2 minutes

The distance covered from store to the bank = 10 blocks

The time used = 7 minutes

The time used to return home from the bank = 12 minutes

Therefore, Bentley is 21 minutes after he left his house, until he got back home. That is 2+7+12 = 21 minutes.

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The power series representation for f(x) = arccot(x) is

      [tex]\pi /2- \lim_{n \to \infty} (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]

The power series ∑aₙxⁿ is an infinite series and looks like a function of x. An easy way to illustrate the idea of a power series representing a function is to use the geometric series as an example.

The power series is a very important kind of infinite series where the terms contain the powers of a variable. A power series is a series of the general form:

∑aₙ(x-x₀)ⁿ=a₀+a₁(x-x₀)+a₂(x-x₀)²+a₃(x-x₀)³+.........

called a power series centered at x₀

where  x is a variable,

x₀ is a real constant, and the

aₙ's are real constants called the coefficients of the series.

The given power series representation is f(x) = arccot(x).

we observe that f '(x)=-1/(1+x²) and find the required series by integrating the power series for -1(1+x²)

arccot(x)=∫-1/(1+x²)dx

⇒∫-(1-x²+x⁴-x⁶+....)dx

⇒C-x+1/3x³-x⁵/5+1/7x⁷-......

To find C we put x=0 and obtain C=arccot(0)=π/2

Therefore,

C=π/2-x+1/3x³-x⁵/5+1/7x⁷-.......

f(x)=π/2- ∑(-1)ⁿₓ x^2n+1/2n+1

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The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.

The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape. By multiplying the lengths of all the sides and edges that surround an object, the perimeter may be calculated. It is measured in measures of length that are linear, such as centimeters, meters, inches, or feet.

The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.

Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.

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Answer: 10y

Step-by-step explanation:

4(y-2)+6y+8

4(y-2)=4y-8

4y-8+6y-8

*8's cancel out*

6y+4y=10y

Based on the image provided, the actual height of the structure would be 1/975.36.

This refers to a picture or model that is made based on the proportion of an original structure. Most models are smaller than their original.

According to the image, 1 centimeter represents 32 feet of the actual structure, which means there is a 1:32 scale factor, let's calculate then the number of centimeters in total to know the height:

1 foot = 30.48 cm

32 feet = x

x= 30.48 x 32/ 1 = 975.36 cm

Based on this the height can be expressed as  1/975.36.

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It will stand for the 15.1, not The 151.

So therefore here you got almost correct the answer,

but you misunderstood about the leaves because the leaves will stand for the decimal.

The 10th means that after the decimal,

So the foundation must be the 15.1.

15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.

A stem and leaf diagram is a way of displaying a collection of numbers. The ‘stem’ consists of the first part of every number, usually the first digit(s) and the ‘leaf’ consists of the latter part of every number, usually the last digit. We need to know how to draw them and how to use them.

Draw a stem-and-leaf diagram to represent Scott’s data.

Step 1: Figure out what our key will be. The stem will be the first two digits, whilst the leaf will be the last digit. Our key is any number that is in the list, represented in terms of a stem and leaf.

Step 2: Use our key to draw our stem part of the diagram, which will have to include: 15,16,17,18,

Step 3: Rewrite the data in numerical order.

151, 154, 154, 157, 165, 166, 178, 183, 186, 186

Step 4: Fill in the ‘leaf’ values (the last digit of every value) alongside the correct ‘stem’ value, to complete the stem and leaf diagram.

14 15 1447 16 56 17 8 18 366

14  

15       1447

16       56

17        8

18       366

151 , 154 , 154 , 157

165 , 166

178

183 , 186 ,186

it will stand for the 15.1, not The 151. So therefore here you got almost correct the answer, but you misunderstood about the leaves because the leaves will stand for the decimal. The 10th means that after the decimal, So the foundation must be the 15.1, 15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.

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The slope of a given line is m=1.5.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The coordinate points of a line are (1, -3) and (3, 0).

Substitute, (x₁, y₁) and (x₂, y₂) in m=(y₂-y₁)/(x₂-x₁), we get

m= (0+3)/(3-1)

= 3/2

= 1.5

Therefore, the slope of a given line is m=1.5.

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Answer:

x=2

Step-by-step explanation:

4x + 2(x - 4) is equivalent to x +2

first, distribute. 4x+2x-8

next, combine like terms. 6x-8

6x-8 = x+2

we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. (6x-8)+(8-x)=(x+2)+(8-x)

get rid of the parenthesis. 6x-8+8-x=x+2+8-x

combine like terms. 6x-x-8+8=x-x+2+8

solve. 5x=10

divide both by 5. 5x/5=10/5

x=2

Answer:

a)not quadratic

b)quadratic

c)quadratic

d)not quadratic

a) x=-3

b) maximum is (-3,4)

c)[tex](-3-\sqrt{2},0)[/tex] and[tex](-3+\sqrt{2},0)[/tex]

d)(0,-14)

e) Domain: (-∞,∞), {xIx∈ℝ}

   Range: (-∞,4), {yIy≤4}

Step-by-step explanation:

Hope this helps!

In this polygon, all angles are right angles. The area of this polygon = 334 ft²

To calculate the area of a regular polygon, just apply the formula below: Half of a perimeter multiplied by apothem equals area. What it means is as follows: The perimeter is the sum of the lengths of all the sides. A segment known as an apothem joins the midpoint of any perpendicular side to the midpoint of a polygon.

The equation for the area of a regular polygon with n sides is [l2n]/[4tan(180/n)]. where n is the number of sides and l is the length of the sides of the polygon.

To calculate the area of a regular polygon, use the formula Area = (number of sides length of one side apothem)/2.

Given data :

Area of polygon

= Area AGEF + Area BCDG

= 21 x 7 + 17 x 11

= 147 + 187 = 334 ft²

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Answer:334 ft

Step-by-step explanation: i did the test

The area of the circle with diameter 6.4 is 32.15 square centimeters.

A circle closed plane geometric shape. In technical terms, a circle is a locus of a point moving around a fixed point at a fixed distance away from the point.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula:

[tex]A = \pi r^2[/tex]

Given that the diameter of the circle is 6.4 centimeters.

The radius of the circle is thus half of the diameter that is 3.2 centimeters.

The area of the circle is given by the formula:

[tex]A = \pi r^2[/tex]

Substitute the value of r = 3.2 in the formula:

[tex]A = (3.14) (3.2)^2\\\\A = 32.15[/tex]

The area of the circle is 32.15 square centimeters.

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The remaining lemonade in the container after Coach Miller pours g gallons for the players is, (5 - g) gallons.

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.

We have to given that;

There are 5 gallons of lemonade in the container.

Now, Initially lemonade available in Container = 5 gallons

Here, Coach Miller pours g gallons for the players.

Hence, Lemonade remaining in Container = (5 - g)  gallons

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When the number of times you roll an odd number increases, the theoretical probability that you roll an even number would decrease.

As the number of times you roll an odd number increases, the theoretical probability that you roll an even number decreases. This is because the probability of rolling an even number is inversely proportional to the number of times you roll an odd number.

If you are rolling a fair die, the probability of rolling an even number is 3/6 or 1/2, and the probability of rolling an odd number is also 3/6 or 1/2.

As the number of times you roll an odd number increases, the number of rolls that are left for an even number decreases, thus the probability of rolling an even number decreases as well.

For example, if you roll the die 10 times and 6 of them are odd numbers, the probability of rolling an even number in the remaining 4 rolls is 4/4 or 1 (100%) because you are guaranteed to roll an even number.

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Answer:

x = 67°

Step-by-step explanation:

When two parallel lines are cut by a transversal, the pair of angles formed on the interior of the parallel lines but on the opposite sides of the transversal are called alternate interior angles and they are congruent.

          x = 67°

Answer:

[tex]\textrm{P(no yellow on two picks )} = \dfrac{16}{121}[/tex]

Step-by-step explanation:

The total number of pens is 1 + 3 + 7 = 11 out of which 7 are yellow.

(We don't really care what color the other pens are since we are interested only in the yellow pens)

[tex]\textrm{P(yellow on first pick )} = \dfrac{\textrm{Number of yellow pens}}{\textrm{Total number of pens}} = \dfrac{7}{11}[/tex]

The probability of not getting a yellow on first pick is the complement of this probability and is 1 less than the probability of picking an yellow

[tex]\textrm{P(not yellow on first pick )} = 1- \dfrac{7}{11} = \dfrac{4}{11}[/tex]

Since we are putting back the pen after the first pick, the total number of pens as well as pens of each color remain the same.

Therefore the probability of not getting a yellow on second pick is the same as the first pick and is [tex]\dfrac{4}{11}[/tex]

The combined probability of not getting an yellow on both picks is the product of these probabilities

[tex]\textrm{P(no yellow on two picks )} = \dfrac{4}{11}\cdot \dfrac{4}{11} = \dfrac{16}{121}[/tex]

Answer:19

Step-by-step explanation:

I think this is right

The correct option is option D) A statistic is a random variable.

We derive the above answer due to the following reason,

Any statistic is a random variable with its own distribution referred to as the sampling distribution as it is a function of sample values and there may be several samples taken from a given population.

The probability distribution of a statistic that is acquired by the continuous sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or the mode of a variable.

There are three standard types of sampling distributions in statistics:

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Answer:

---------------------------------

Given sequence:

This is decreasing sequence since the common difference is negative, d = - 8.

Therefore the first term is the largest one:

Monthly payment for United bank = $1207.70, monthly payment for capitol bank =$1834.62. Total interest from United bank = $75600 and from capitol bank = $135000.

Total interest is determined by the addition of all the interest payments.

United bank offers mortgage at an APR of 4.2%

APR means annual percentage rate.

mortgage is offered for the period of 15 years.

initial principal amount of Marcy = $120000

we need to determine the monthly payment from United bank.

at first, we will determine the rate of interest per month.

monthly interest rate = (4.2) / (100 × 12) = 0.0035

1 year = 12 months

15 years = 15×12 = 180 months

monthly payment is calculated by the formula = [rate + (rate) / {(1+rate)∧month}⁻¹] ×principal

monthly payment = [ 0.0035 + (0.0035) / {(1+0.0035)∧180}⁻¹] ×120000

                          = $1207.70

from united bank monthly payment = $1207.70

Now we calculate the monthly payment from Capitol bank.

APR for capitol bank = 4.5%

number of years for which mortgage is issued = 25 years

number of months = 12×25 = 300.

monthly interest rate = (4.5) / (100×12) = 0.00375

monthly payment for capitol bank = [0.00375 + (0.00375) / {(1+0.00375)∧300}⁻¹] × 120000

                 = 1834.62

monthly payment from Capitol bank = $1834.62

total interest from Capitol bank = principal money × yearly interest rate × time period.

Total interest = 120000 × 4.5/100× 25

                        = $135000 for the Capitol bank

Total interest from United bank = principal amount × yearly interest × time period

            = 120000× 4.2/100 × 15

total interest from united bank   = $75600

United bank has lower total interest.

difference in monthly payment = 1834.62 - 1207.70

                                                   = 626.92 dollars

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The two factors such that their product is the first number and their sum is the second number are 8 and 5.

A factor is defined as the number that divides another number, leaving no remainder.

In other words, if multiplying two numbers gives us a product, then the number we multiply is a factor of the product and divided by the product.

The factors of 40 and 13 such that their product is the first number and their sum is the second number = 8 and 5.

That is, 8×5 = 40

8+5 = 13

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Answer: The first orange is the best deal at $0.8 per orange. The second cand is the best deal at $0.45 per candy.

Step-by-step explanation:

First orange: 5 for $4 equals $4/5 per orange, which equals $0.8 per orange.

Second orange: 10 for $9 roughly equals $1.111 per orange

Third orange: $0.82 each

The first orange is the best deal at $0.8 per orange

First candy: 3 for $1.5 equals $1.5/3 per candy, which equals $0.5 per candy.

Second candy: 4 for $1.8 equals $0.45 per candy

Third candy, 10 for $4.6 equals $0.46 per candy

The y-intercept of line is at (0, -6) and the domain is (-∞, ∞).

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables..

Given,

The mathematical function has an absolute minimum at x = 15.

The average rate of change of the function between x = 20 and x = 25 is 0.

The mathematical function is increasing for all x such that 15 < x < 22.

The line intersects the y-axis at (0, -6). Then the y-intercept of the line is (0, -6).

The domain of the linear function will be a real number.

And the range of the linear function is also real number.

Hence , The y-intercept of line is at (0, -6) and the domain is (-∞, ∞).

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Consequently, the probability of producing precisely one girl or exactly one male 0.25 + 0.25 = 0.5P(x = 1) = 4C1 * 0.5^1 * 0.5^3; 0.9375 ; 0.5

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.

Due to this:

p = 0.5

Modeling the probability of how many females the couple has:

[tex]P(x =x) is equal to nCx * px * (1 - p) (n - x)\\P(x = 0) = 4C0 * 0.5^0 * 0.5^4 = 0.0625\\\=P(x = 1) = 4C1 * 0.5^1 * 0.5^3 = 0.25\\P(x = 2) = 4C2 * 0.5^2 * 0.5^2 = 0.375\\P(x = 3) = 4C3 * 0.5^3 * 0.5^1 = 0.25\\P(x = 4) = 4C4 * 0.5^4 * 0.5^0 = 0.0625[/tex]

likelihood of having at least one female

N = 4 trials in total.

P(x 1) is equal to p(x = 1) plus p(x = 2) plus p(x = 3) plus p(x = 4)

Employing the relation

P(x =x) is equal to nCx * px * (1 - p) (n - x)

use a calculator

P(x ≥ 1) = 0.9375

Chances of getting just one female or exactly one boy

3 females OR 3 boys OR 1 boy

P(x = 1)

P(x =x) is equal to nCx * px * (1 - p) (n - x)

P(x = 1) = 4 * 0.5 * 0.125

P(x = 1) = 0.25

The likelihood of getting one girl and three males or vice versa is 0.25

Consequently, the likelihood of producing precisely one girl or exactly one male

0.25 + 0.25 = 0.5P(x = 1) = 4C1 * 0.5^1 * 0.5^3 is 0.9375 ; 0.5

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Answer:

[tex]16203[/tex] days

Step-by-step explanation:

There are 60 seconds per minute, so 3600 sec/hour, and 86400 seconds per day, so the answer is about [tex]16203[/tex] days.

The indicated measures:

m∠ABC =  138° and m∠BCD = 52°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠DAE = 16° and m∠EDC = 64°.

The diagonals of the kite intersect at 90°.

(1).

In ΔAED,

the sum of all the angles of the triangle is 180°.

m∠DAE + m∠ADE + m∠AED = 180°

m∠ADE = 180 - 90 - 16

m∠ADE = 74°

According to the angle addition postulate,

m∠ADE + m∠EDC = m∠ADE

m∠ADE = (74 + 64)°

m∠ADE = 138°

From the property of kites,

m∠ADE = 138° =  m∠ABC.

(2).  m∠EBC =  m∠EDC,

m∠EBC = 64°

In ΔBCD,

the sum of all the angles of the triangle is 180°.

m∠DBC + m∠BCD + m∠CDB = 180°

m∠BCD = 180 - 64 - 64

m∠BCD = 52°

Therefore,  138° =  m∠ABC and m∠BCD = 52°.

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The range of the function is {0.01, 0.1, 1, 10, 100}. With an increase in the value of the domain, the range of the function is increasing.

What is a function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given function is

f(x) = 10^x.

Given domain is {-2, -1, 0, 1, 2}.

Now putting x = -2, -1, 0, 1, 2 in the function f(x) = 10^x.

When x = -2:

f(-2) = 10^(-2)

f(-2) = 0.01.

When x = -1:

f(-1) = 10^(-1)

f(-1) = 0.1.

When x = 0:

f(0) = 10^(0)

f(0) = 1.

When x = 1:

f(1) = 10^(1)

f(1) = 10

When x = 2:

f(2) = 10^(2)

f(2) = 100

The range of the function is {0.01, 0.1, 10, 100}

The values of the range increase with the increase of domain.

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The solution to the indices is 50.

Index (indices) is the power or exponent which is raised to a number or a variable. The plural of index is indices. Indices contain constants and variables. The constant is a value which cannot be changed and a variable quantity can be assigned any number or its value can be changed.

Indices are a convenient tool in mathematics to correctly denote the process of taking a power or a root of a number. Taking a power is simply a case of repeated multiplication of a number with itself while taking a root is just equivalent to taking a fractional power of that same number.

8^1/3 / 5^-2

Applying the necessary laws of indices;

= 8^1/3 / 5^-2

= ∛8 / (1/5^2)

= 2 / (1/25)

= 2 x (25/1)

= 50

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A journal entry is a format used in accounting to record transactions. The amount we owe someone else that we must get in the future is known as notes receivable.

Notes receivable are claims for which official documents of credit, like promissory notes, are issued as proof of debt. In most cases, the credit instrument has a minimum term of 30 days and imposes an interest payment obligation on the debtor.

Given the following information:

Note receivable $15,000

Rate of interest 9%

Discount rate    12%

Period              2 months

Preparing journal entry to record accrued interest

To prepare the journal entry, we must first calculate the interest. We can compute interest by multiplying the notes receivable, the interest rate, and the period, i.e.

Interest = Notes receivable × Rate of interest × Period

Interest = 15000 × 0.09 × 2/12

Interest = 225

Now we can prepare the journal entry

Date                          Particulars              Debit ($)               Credit($)

February 28, 2016     Interest receivable        250

                                          Interest                                    250

                           To record accrued interest  

Preparing the journal entry to record discounting

To begin preparing the Journal entry, we must first calculate the necessary data.

We can calculate the cash as the difference between Maturity Value and Discount. That is,

Cash = Maturity Value – Discount

The value of Maturity is unknown. We can compute it as the sum of the receivable notes and interest. That is,

Maturity Value = Notes receivable + Interest

Interest =Notes receivable × Rate of interest × Period

= $15,000 × 0.1 × 6/12

= $1,500 × 0.5

= $750

​Maturity Value = Notes receivable + Interest

= $15,000 + $750

=  $15,750

Discount =Maturity Value × Discount rate × Period

= $15,750 × 0.12 ×  4/12

= $1,890 × 0.33

= $630

Finally, we can calculate cash

Cash = Maturity Value – Discount

= $15,750 − $630

= $15,120

Loss on sale = Cash – Notes receivable - Interest

= $15,120 − $15,000 − $250

= $130

Finally, we can prepare our journal entry.

Date                        Particulars                   Debit ($)            Credit($)

February 28,2016     Cash                            15,120

                              Loss on sale                      130

                              Notes receivable                                               15,000

                                  Interest                                                  250

                       (To record discounting)  

Thus, Cash & Loss are debited, & Notes Receivable & Interest are credited.

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The result of running the code is that x will be 20.

Therefore, your software is saying:

Place x at 30. (I'm assuming that you don't care about the case here because you wrote an X in capital letters that don't exist anywhere else;)

Place y at 20.

If y is not equal to x-10, ask. "If yes, put x to the value of x-5; if no, set x to the value of y," is the next step.

Your question receives the response "no," and x is then set to the value of y since the values of x and y you selected to result in y being equal to x-10. The result of running the code is that x will be 20.

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Full question

After execution of the following code, what will be the value of x? X = 30; y = 20; if (y ! = (x - 10)) x = x - 5; else x = y;