2. *
In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern?
a) P=3 n
b) P=n+3
c) P=2 n+1
d) P=3-n
A
B
C
Both A andC

x = number of small boxes

y = number of large boxes

well, we know a total of 20 boxes, large and small were shipped, that means that whatever "x" and "y" may be, we know that x + y = 20.

so the volume of one small box is 8 ft³, so sticking to ft³, we can say that the volume of 1 box is 8(1) ft³, and the volume of 2 boxes will then be 8(2) and three is 8(3) ft³ and the volume of "x" boxes will then just be 8(x) ft³.

now, we can say the same thing about large boxes, volume of 1 is 21(1) ft³, for two is 21(2) ft³, for three 21(3) ft³, and for "y" boxes that'll just be 21(y) ft³.

that said, well hell their volume combined must be 8x + 21y, and we happen to know that's 264 ft³, namely 8x + 21y = 264.

[tex]\begin{cases} x+y=20\\\\ 8x+21y=264 \end{cases}\hspace{5em}\stackrel{\textit{using the 1st equation}}{x+y=20\implies }y=20-x \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{8x+21(\underset{y}{20-x})=264}\implies 8x+420-21x=264 \\\\\\ 8x+420=264+21x\implies 8x+156=21x\implies 156=13x \\\\\\ \cfrac{156}{13}=x\implies \boxed{12=x}\hspace{13em}\stackrel{20~~ - ~~12}{\boxed{y=8}}[/tex]

Answer:

D

Step-by-step explanation:

The equation is like this :

Popcorn + 5(Price of each juice bottle) = total cost

1.59 + 5j = 13.34

Subtract both sides with 1.59

5j = 11.75

A and C are obviously wrong

B is wrong because there is only one of the juice bottle in the diagram

The answer is D

Amount of money needed to carry to the sari sari store is 59.

a) According to question

Amount of eggs to buy = 3

Rate of eggs = 8

Total amount for eggs = 3x8=24

Amount of  hotdogs to buy = 2

Rate of hotdogs = 10

Total amount to pay for hotdogs = 2x10=20

Amount of  bread to buy = 3

Rate of bread = 5

Total amount to pay for bread=3x5=15

So money needed to take to the sari sari store=24+20+15=59

b) Polynomial is 4x²+2x-3

1) x=1

  4(1)²+2(1)-3

  4+2-3

  3

2) x=2

 4(2)²+2(2)-3

 4(4)+4-3

 16+4-3

 17

3) x=3

 4(3)²+2(3)-3

 4(9)+6-3

 36+6-3

 39

4) x=5

 4(5)²+2(5)-3

 4(25)+10-3

 100+10-3

 107

5) x=6

 4(6)²+2(6)-3

 4(36)+12-3

 144+12-3

 153

For further information related polynomials

https://brainly.com/question/4142886

We can prove the formula given in the question as a theorem using the truth table method.

A Truth Table is referred to as a logic table that can be used to perform logic functions with some formulas. The logic functions that can be performed include Boolean algebra.

Let A, B, and C represent propositions. We construct a truth table as follows:

A B C (A → (B − C)) (B → (A → C))

T T T T T

T T F T F

T F T T T

T F F T T

F T T T T

F T F T T

F F T T T

F F F T T

From the truth table, we can see that the formula holds for all possible truth values of A, B, and C. Therefore, the formula is a theorem.

Learn more about Truth Table at:

brainly.com/question/28605215

#SPJ4

a) The distribution of X is a discrete geometric distribution with pmf p(x) = (5/36)(1/6)^(x-1).b) The theoretical mean (mu) of X is 6.c) The theoretical variance of X is 35.d) The expected value of Y is 6 and the variance of Y is 3.875.

The distribution of X is a discrete geometric distribution, which means that the probability of X taking on any particular value is given by the formula p(x) = (5/36)(1/6)^(x-1). The theoretical mean (mu) of X is 6, which means that on average it should take 6 trials to obtain a sum of 7. The theoretical variance of X is 35, which means that there is a considerable amount of variability in the number of trials needed to obtain a sum of 7. If we consider the random variable Y, the average number of trials needed to roll a sum of 7 based on 25 trials, then the expected value of Y is 6 and the variance of Y is 3.875. This indicates that the average number of trials needed to obtain a sum of 7 is 6 and that the variability decreases as more trials are taken.

a) p(x) = (5/36)(1/6)^(x-1)

b) theoretical mean (mu) of X mu = 6

c) Var(X) = (5/36)*∑x=1∞(1/6)^(x-1)^2 - mu^2

       = (5/36)*(1-1/36^2) - 6^2

       = 35

d) The expected value of Y , E(Y) = 6

Var(Y) = Var(X/6)

       = Var(X)/6^2

       = 35/6^2

       = 3.875

Learn more about mean here

https://brainly.com/question/15323584

#SPJ4

CSC 23° can be written as sec 67° in as its cofunction.  

A branch of mathematics called trigonometry in geometry focuses on the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to angles and sides.

The six trigonometric ratios are sin, cos, tan, cot, cosec, and sec.

From Trigonometrical Ratios of (90° - θ)

=> sin (90° - θ) = cos θ

=> cos (90° - θ) = sin θ

=> tan (90° - θ) = cot θ

=> csc (90° - θ) = sec θ

=> sec (90° - θ) = csc θ

=> cot (90° - θ) = tan θ

Here we have CSC 23°

Here we need to write csc 23° into its cofunction

From Trigonometrical Ratios of (90° - θ)

csc (90° - θ) = sec θ

23° can be taken as (90 - 67)°  

=>  csc 23° = csc (90 - 67)° = sec 67°    

Therefore,

CSC 23° can be written as sec 67° in as its cofunction.

Learn more about Trigonometric Ratios at

https://brainly.com/question/1201366

#SPJ1

The Greatest Common Divisor (GCD) of 85 and 51 is 17.

The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Explanation

Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.

Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.

Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.

Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.

The GCD of 85 and 51 is 17.

To know more about GCD visit here:

https://brainly.com/question/5252620

#SPJ4

By using logic gate, it can be concluded-

XOR table is used in this case?

What is logic gate?

Logic gate is a device which is used to build digital circuit.

Logic gate can make passage for a system to pass through when some logical conditions are fulfilled.

Different types of logic gates are-

AND gate, OR gate, NAND gate, XOR gate, NOR gate etc.

Here one switch is in the entrance hallway and other is in the living room.

The lights are on if the switches mismatch.

For this case, XOR table is used

A  B  Result

0  1     1

1   0    1

0  0   0

1   1    0

To learn more about logic gate, refer to the link-

https://brainly.com/question/24708297

#SPJ4

The total monthly rent for these three stores is $8,786.25.

What is total ?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.

The outcome of adding two or more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding two or more numbers together results in a new result or total.

The monthly cost for a square foot of rental space in each city is as follows:

   Place            Monthly Cost for a Square Foot

Los Angeles                      $5.75

San Francisco                    $6.95

   Seattle                           $4.25

It is also provided that the store in Los Angeles will be 580 square feet, the store in San Francisco will be 500 square feet, and the store in Seattle will be 465 square feet.

Compute the total monthly rent for these three stores as follows:

Total Monthly Rent = Monthly Cost for a Square Foot × Area

                 = (5.75 * 580) +(6.95 * 500) +(4.25 * 465)

                 = 3335 + 3475 + 1976.25

                 = 8786.25

Thus, the total monthly rent for these three stores is $8,786.25.

To learn more about total from the given link  

https://brainly.com/question/18798695

#SPJ1

The arithmetic mean of a and b in the expression  1/a + 1/b = 1/c is 2c.

Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Given, An expression of the form 1/a + 1/b = 1/c.

We know average of two numbers is sum of those numbers divided by 2.

So,  {(1/a) + (a/b)}/2 = 1/c.

Now to keep the equality we also have to divide the RHS by 2.

Therefore,   {(1/a) + (a/b)}/2 = (1/c)/2.

{(1/a) + (a/b)}/2 = (1/c)×((1/2).

{(1/a) + (a/b)}/2 = 1/2c.

So, The arithmetic mean of 1/a + 1/b is 1/2c.

Now taking the reciprocal of 1/a and 1/b which is a and b the arithmetic mean is

2c.

learn more about the arithmetic mean here :

https://brainly.com/question/15196910

#SPJ1

The exponential representation is a decreasing function

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

y = 200(0.75)x

Rewrite properly

So, we have the following representation

y = 200(0.75)ˣ

An exponential function is represented as

y = abˣ

Where

b = rate

This means that

b = 0.75

Since b is less than 1, then the function is a decreasing function

Read more about exponential functions at

https://brainly.com/question/11464095

#SPJ1

The construction that the figure represents is perpendicular bisector

A perpendicular bisector is a line that cuts through the intersection of two other line segments at a right angle.

So, a perpendicular bisector always splits a line segment through its middle, as we can see. By definition, the word "bisect" denotes an even or uniform division.

Perpendicular Bisector Properties for AB in the figure

It cuts AB in half, or into two equal halves.

It is perpendicular to AB or at right angles to it.

The distance between each point along the perpendicular bisector from points A and B is equal.

Learn more about perpendicular bisector at:

https://brainly.com/question/11006922

#SPJ1

The region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative

Without calculation we need to state if the each of the integrals below are positive, negative, or zero. let d be the region inside the unit circle centered at the origin

xeˣ is positive for positive , and negative for negative , but the exponential factor makes the positive part dominating, so that the integral over D is positive overall.

The integrals over B and T are identical by symmetry, and both are equal to half the value of the integral over D, so they are both positive as well.

The integral over L is negative because it takes strictly non-positive values of x .

Similarly, the integral over R is positive because it considers non-negative values of x.

Therefore, the region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative

To learn more about integrals refer here

https://brainly.com/question/22008756

#SPJ4

Answer:1/4 (I think)

Answer:

8x + y > 4

y > -8x + 4

f 57 and 63 are the 90% confidence limits for the population mean, then [60, 60] might be the 97% confidence limit.

A population is a discrete collection of things having observable traits, such humans or animals, for the purpose of analysis and data collection. It is made up of a comparable collection of species that live in a specific area and have the ability to interbreed.

The average calculated from the whole population, distribution, or group is known as the population mean. It is calculated by dividing the total number of population variables by the sum of all population variables. The population mean can be found here as. Observations in the population are added together to form X.

To know more about population visit:

https://brainly.com/question/27991860

#SPJ4

Answer:

  A, B, C

Step-by-step explanation:

You want to find the dimensions, perimeter, and area of a foundation such that the length is 6 feet more than twice the width, and the area is 1046 more that the value of the perimeter.

We can let x and y represent the length and width, respectively. Then the given relations translate to the equation ...

  A = LW . . . . . . . area formula

  P = 2(L +W) . . . . perimeter formula

  y = 2x +6 . . . . . relation between dimensions

  xy = 2(x +y) +1046 . . . . . relation between perimeter and area

Using the first equation to substitute for y, we have ...

  x(2x +6) = 2(x +(2x +6)) +1046

  2x² +6x = 6x +1058 . . . . . . . . . . . . eliminate parentheses

  x² = 529 . . . . . . . . . . . . . subtract 6x and divide by 2

  x = √529 = 23 . . . . . . . . . width; matches B

  y = 2(23) +6 = 52 . . . . length

  area = (23)(52) = 1196 . . . area; matches A

  perimeter = 2(23 +52) = 2(75) = 150 . . . . matches C

The area is 1196 square feet. (A)

The width is 23 feet. (B)

The perimeter is 150 feet. (C)

answer: Mean:5

median:4

range: 9

mode: 2

Step-by-step explanation:

Answer:

g = 18(1/3)

Step-by-step explanation:

The sub is made of 18 sections of 1/3, so it is 18(1/3) feet long (or 6ft when simplified)

∠4=∠6 because each pair of alternate interior angles is equal ( The two column proof is attached ).

Every two-column proof has exactly two columns. One column represents our statements or conclusions and the other lists our reasons. In other words, the left-hand side represents our “if-then” statements, and the right-hand side explains why we know what we know.

We can clearly observe here that ∠1=∠5 , ∠2=6, ∠3=∠7, ∠4=∠8 as Corresponding angles are equal.

∠4 + ∠3 = 180°……..(1) PQ is the straight line

∠6 + ∠7 = 180°……..(2) t is the straight line

therefore from the two equations we get

∠4 =∠6

Hence, ∠4  ≅∠6 ( The two column proof is attached )

Learn more about the two column proof here:

https://brainly.com/question/29047207

#SPJ1

Preferred shares = 0.40/25.00 = 1.60%    

Common shares = 0.07/17.50 = 0.40%

What is stock  market?

The phrase "stock market" describes a number of marketplaces where shares of publicly traded firms can be purchased and sold. Such financial transactions take place on official exchanges and in over-the-counter (OTC) markets that adhere to a predetermined set of rules.

Year Total         Preference   Common   Dividend per

             dividend     dividend      dividend    common share

1       80000 80000 0 0.32 0.00

2       90000 90000 0 0.36 0.00

3       150000 130000 20000 0.52 0.04

4       150000 100000 50000 0.40 0.10

5       160000 100000 60000 0.40 0.12

6       180000 100000 80000 0.40 0.16

Note:       2.40 0.42

Preference dividend per year = 250000*$20*2%=  100000  

Preference dividend for the 3rd year includes arrear dividend of $20000 for the 1st year

and $10000 for the second year, in addition to the $100000 dividend of that year.

Average annual dividend per share:      

Preferred shares = 2.40/6 = $0.40      

Common shares = 0.42/6 = $0.07      

Average annual percentage return:      

Preferred shares = 0.40/25.00 = 1.60%    

Common shares = 0.07/17.50 = 0.40%

Learn more about stock market link below

https://brainly.com/question/690070

#SPJ1

the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted

Given that many high school students take either the SAT or the ACT.

However, some students take both.

Data were collected from 60 students who took both college entrance exams.

                          SAT score            ACT score with a  of 180.

Average                    912                      21

standard deviation   180                        5

Correlation between the two variables r = 0.817

WE have for two variables if we have correlation coefficient then the square of correlation coefficient gives the fraction of variation in the values of the SAT scores is accounted for by the linear relationship between the SAT and ACT scores

So we find square of r

i.e. r by the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted

learn more about of coefficient here

https://brainly.com/question/13830532

#SPJ4

Answer:

j

Step-by-step explanation:

Answer:

That looks correct to me!

Answer:

(−3, 2); 2 < y < ∞

Step-by-step explanation:

It's either (−3, 2); 2 < y < ∞ or (−3, 2); −∞ ≤ y < ∞ but I'm pretty sure its (−3, 2); 2 < y < ∞

The expressions for the total costs are 2L + 0.7L  and 2.7L

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

Number of litres = 3

Regular price = L

Discount = 30%

This means that there is a discount on the third item

So, we have the following expression

Total amount = 2 * L + L * (1 - discount)

Substitute the known values in the above equation, so, we have the following representation

Total amount = 2 * L + L * (1 - 30%)

Total amount = 2 * L + L * 0.7

This gives

Total amount = 2L + 0.7L

Evaluate the sum

Total amount = 2.7L

Hence, the expression is 2.7L

Read more about expressions at

https://brainly.com/question/15775046

#SPJ1

The expression for the total cost of 3 liters of shampoo is written as

Let L be the regular price of a liter bottle

The expression is written in decimal and in fraction

For the promotion buy 2 liters get 30% of 3rd liter

30% off = 0.3 off

= (1 - 0.3)

= 0.7

The total cost will be

= 2 * L + 0.7 * L

= 2L + 0.7L

= 2.7 L

The cost of three bottles of shampoo is 2.7L

In another way

= 2L + (1 - 0.3)L

= 2L + 0.7L

using fractions

= 2L + 7L/10

= 27L/10

the other way is writing in fraction

Learn more about fractions:

https://brainly.com/question/29402981

#SPJ1

Answer:

[tex]\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]

Step-by-step explanation:

Given:

[tex]\tan \left(\sin^{-1}\left(\dfrac{x}{2}\right)\right)[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Trigonometric Identity}\\\\$\tan(\arcsin(x))=\dfrac{x}{\sqrt{1-x^2}}$\\ \end{minipage}}[/tex]

Use the tan(arcsin(x)) trigonometric identity and replace x for (x/2):

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\left(\dfrac{x}{2}\right)^2}}[/tex]

Simplify the denominator:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\dfrac{x^2}{4}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{\dfrac{4-x^2}{4}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{\sqrt{4}}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{2}}}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{\frac{a}{c}}{\frac{b}{c}}=\dfrac{a}{b}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}}[/tex]

Multiply the numerator and denominator by the denominator to eliminate the radical from the denominator:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}} \cdot \dfrac{\sqrt{4-x^2}}{\sqrt{4-x^2}}[/tex]

Simplify:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]

The value of the estimated standard error is 1.

The set of d (differneces) scroes: 4, 8, 4 ,4

Consider,

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Mean of the D-score is [tex]$$\begin{aligned}\bar{d} & =\frac{1}{n} \sum d_i \end$[/tex]

[tex]=\frac{1}{4}[/tex](4+8+4+4)

=5

Standard deviation of D-score is given by [tex]$$\begin{aligned}\hat{\sigma} & =\sqrt{\frac{1}{n-1} \sum_{i=1}^n\left(d_i-\bar{d}\right)^2} \\& =\sqrt{\frac{1}{4-1}\left\{(4-5)^2+(8-5)^2+(4-5)^2+(4-5)^2\right\}} \end[/tex]

The value of the estimated standard error for the following set D scores is

[tex]$$\begin{aligned}\widehat{\mathrm{SE}(d)} & =\frac{\hat{\sigma}}{\sqrt{n}} \\& =\frac{2}{\sqrt{4}}\end{aligned}$$[/tex]

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

Therefore, the value of the estimated standard error for the following set of d scroes is 1.

For such more questions about standard error

https://brainly.com/question/13179711

#SPJ4

Answer:

True

Step-by-step explanation: