Is all function are relation True or false?.

The roll with a better value, that is, cheap price is 9 packed toilet roll.

In order to determine the roll with a better value, we will consider the unit price of each roll and make comparison.

Unit price refers to the price of a commodity per each unit.

Unit price = Cost / units

= £2.04 / 4

= £0.51 per unit

Unit price = Cost / units

= £4.68 / 9

= £0.52 per unit

Therefore, it can be concluded that the the roll which has a better value is the 9 packed toilet roll.

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Answer:

y = -3x + 10

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

  m = -3

y = -3x + b

Now (6,-8) is passing through this line. So, substitute the x and y coordinates in the above equation and find the value of 'b'.

      -8 = -3*6 + b

     -8 = -18 + b

-8 +18 = b

   b = 10

Equation of the line:

    y = -3x + 10

Answer:

y=-3x+10

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

b is y intercept

So we fill in what we know to find b

-8=-3(6)+b

-8=-18+b

+18 +18

10=b

Now we can finish our equation

y=-3x+10

Hopes this helps please mark brainliest

The expression which gives a difference of 4 3/12 from the given options is 10 2/3 - 5 1/12 - 1 2/6. option C

The Subtraction of the expressions with different denominators are

The expression with a difference of 4 3/12

Check all that applies:

7 3/4 - 1 2/4 - 2 1/3

= 31/4 - 6/4 - 7/3

= (93-18-28) / 12

= 47/12

= 3 11/12

9 8/12 - 1 3/6 - 4 1/2

= 116/12 - 9/6 - 9/2

= (116-18-54) / 12

= 44/12

= 3 8/12

10 2/3 - 5 1/12 - 1 2/6

= 32/3 - 61/12 - 8/6

= (128-61-16) / 12

= 51/12

= 4 3/12

20 2/12 - 14 1/4 - 2 1/6

= 242/12 - 57/4 - 13/6

= (242-171 - 26) / 12

= 45/12

= 3 9/12

2.

= 23/3 - 19/6 - 20/9

common denominator is 18

= (138 - 57 - 40) / 18

= 41/18

= 2 5/18

= 119/12 - 10/3 - 34/8

common denominator is 24

= (238 - 80 - 102) / 24

= 56/24

= 2 8/24

= 2 1/8

In conclusion, the Subtraction of the mixed number with unlike denominators are:

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This can be done using statistical tests such as the t-test or ANOVA, which can determine if there is a statistically significant difference between men and women.

Analysis of variance, or ANOVA, is the term. A statistical test is used to assess if the means of two or more groups differ significantly from one another. It is a method used to compare the means of several groups to see if they are comparable or whether there is a notable different purchase between them. ANOVA is frequently used to compare the means of several data sets, such as the means of various test scores or the means of various populations. The ANOVA test is a potent instrument that enables researchers to establish whether there is a significant difference between the means of various groups and to pinpoint which groups differ from one another.

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The expression √n^2 can be simplified as n

The square root of a number is that factor of a number which when multiplied by itself gives the original number.

Squares and square roots are special exponents. Consider the number 9. When 3 is multiplied by itself, it gives 9 as the product. This can be written as 3 × 3 or 32. Here, the exponent is 2, and we call it a square. Now when the exponent is 1/2, it refers to the square root of the number. For example, √n = n^½, where n is a positive integer.

Therefore √n^2 = n^½×2= n

the value of √n^2 = 2

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Approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

Given,

In the question:

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn without burning it are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds.

Central Limit Theorem:-

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 140, standard deviation of 20, sample of 4:

By the Central Limit Theorem, the distribution is approximately normal.

Mean is the same, of 140.

n = 4 , σ = 20, thus:

s = σ / [tex]\sqrt{n}[/tex]  = 20/[tex]\sqrt{4}[/tex] = 10

Thus, the correct answer is:

Approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

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Answer:

50

Step-by-step explanation:

b

The value of diameter for the given triangle inscribed in a circle will be 22.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circular objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

As per the given triangle inscribed a circle.

The length x +2 and 2x - 7 will be the radius of the circle and the sides of the triangle will be the tangent of the circle.

x + 2 = 2x - 7

2 = 2x - x - 7

x = 9

Thus, radius = 9 + 2 = 11

Diameter = 11 x 2 = 22 units.

Hence "The value of diameter for the given triangle inscribed in a circle will be 22".

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The number of terms and the degree of the polynomial are 3 and 2 respectively.

The terms of the polynomial = The parts of the polynomial

                                                = -8rt ,- s² ,- 3t

The number of terms of the polynomial  = 3    

The degree of the polynomial =  Highest degree of the polynomial

The highest degree of the polynomial = 2

So, the polynomial degree is 2

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For provide normal distribution such that

x ~ n(15, 3), 68.27% of the data lie between the values of x as x= 12 to x= 18 .The range of x-values is centered around the mean of the distribution (that is, 15).

Normal Probability:

This problem uses the Z-score formula to calculate the range such that 68.27% of the data falls within the range. Z-scores are normal scores, plotted on a normal curve with mean 0 and variance 1. The Excel function NORM.S.INV() is used to get the score value.

We have given that

Mean, μ = 15

Standard deviation, σ = 3

P( a <X<b) = 0.6827

P( (a − μ)/(σ < X − μ )/σ <(b− μ)σ) = 0.6827

P ( a- 15) /3 < Z < (b- 15)/3) = 0.6827

P( Z< (b-15)/3) - P( Z< ( a - 15)/3) = 0.6827

1 - P( Z > (b-15)/3) - P( Z< ( a - 15)/3) = 0.6827

(Symmetrical Property)

We know that,

P( Z> (b-15)/3) = P( Z< ( a - 15)/3) ( symmetric)

2 × P( Z< ( a - 15)/3) = 0.3173

P( Z< ( a - 15)/3) = 0.15865

Now,

Excel function for the value of z score:

=NORM.S.INV(0.15865)

(a − 15)/3 = -1.00

=> a-15 = -3

=> a = 12 and b = 15 + 3 = 18

Hence, the values of x are 12 and 18 where 68.27% data lie.

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The value of x from the given equation is x=(c-b)/2. Therefore, in the given steps, the person has done mistake in step 3.

The given equation is 2x+b=c.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation cab solved as follows

Subtract b from both sides

2x+b-b=c-b

Combine like terms/simplify

2x=c-b

Divide 2 from both sides to get x isolated

x=(c-b)/2

The value of x from the given equation is x=(c-b)/2. Therefore, in the given steps, the person has done mistake in step 3.

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Answer:

c = 5m + 10

Step-by-step explanation:

Each moth 5 dollars is charge and a one time fee of 10

The probability that X is greater than 39, P (X>39) is 0.03.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given,

Mean = 33

Variance = 10

Standard deviation = 3.16

Z score,

= x - mean/standard deviation

= 39 - 33/3.16

= 1.89

P value from Z table,

P( x< 39) = 0.9712

P( x > 39) = 1 - P(x <39)

P( x > 39) = 1 - 0.9712

P(x > 39) = 0.0288

The probability that X is greater than 39, P (X>39) is 0.03.

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Answer:

Below

Step-by-step explanation:

Move it to the other side of the fraction ( make it an inverse to change it to a + exponent)

Examples     5^-2 =   1/ ( 5^2)

      1 / (x^-23)   = x ^23

     x^2 y^-3  = x^2 / y^3           etc

Answer:

The radius is 7.

Step-by-step explanation:

To find the radius of this circle, we would have to find the diameter first. This can be found by looking at both the directions of the origin (left and right) and counting how many spots it goes until the circle ends.

On the left, there is 6 spots. On the right, there is 8. So we would add to find the full way around or the diameter (6 + 8) and we get 14.

Now, since radius is halfway around or is half of the diameter, we simply divide 14 by 2 which is 7.

Therefore, the answer is 7.

Answer:

13.  7.5 square units

14.  24.5 square units

Step-by-step explanation:

Given vertices:

As points E and F share the same x-value and points F and G share the same y-value, the polygon is a right triangle with base GF and height FE.

As points F and G share the same y-value, the length of line segment GF is the difference between the x-values:

[tex]\begin{aligned} \implies \overline{GF}&=x_F-x_G\\&=3-(-2)\\&=3+2\\&=5\end{aligned}[/tex]

As points E and F share the same x-value, the length of line segment FE is the difference between the y-values:

[tex]\begin{aligned} \implies \overline{FE}&=y_E-x_F\\&=1-(-2)\\&=1+2\\&=3\end{aligned}[/tex]

Therefore, the area of polygon EFG is:

[tex]\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of polygon $EFG$}&=\dfrac{1}{2} \times \overline{GF} \times \overline{FE}\\\\&=\dfrac{1}{2} \times 5 \times 3\\\\&=\dfrac{15}{2}\\\\&=7.5\;\; \sf units^2\end{aligned}[/tex]

Given vertices:

As points J and K share the same y-value the polygon is a triangle with base JK and height of the difference in y-values of points K and L.

As points J and K share the same y-value, the length of line segment JK is the difference between the x-values:

[tex]\begin{aligned} \implies \overline{JK}&=x_K-x_J\\&=4-(-3)\\&=4+3\\&=7\end{aligned}[/tex]

The height of the triangle is the difference between the y-values of points K and L:

[tex]\begin{aligned} \implies\sf Height&=y_K-y_L\\&=4-(-3)\\&=4+3\\&=7\end{aligned}[/tex]

Therefore, the area of polygon JKL is:

[tex]\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of polygon $JKL$}&=\dfrac{1}{2} \times \overline{JK} \times \sf height \\\\&=\dfrac{1}{2} \times 7 \times7\\\\&=\dfrac{49}{2}\\\\&=24.5\;\; \sf units^2\end{aligned}[/tex]

The correct option are; b. Perpendicular and d. Transversal; are the lines that intersects and are coplaner lines.

Perpendicular lines:

Transversal:

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The point estimator is 0.0129, the 95% CI on variance ([tex]\sigma^2[/tex]) is (0.0082, 0.0233), the 95% CI on standard deviation (σ) is (0.0905, 0.1527), and it is surprised to hear the director that the standard deviation is more than 0.2 seconds.

n = total data = 30

[tex]\bar x[/tex] = mean or average

[tex]\sigma^2[/tex] = variance

σ = standard deviation

α = significance level = 1 - 95% = 0.05

A) First, calculate unbiased point estimator with this formula

[tex]\sigma^2[/tex] = [tex]\frac{1}{n-1}\times \sum(x_i-\bar x)^2[/tex]

[tex]\sigma^2[/tex] = 0.0129 (detail calculation in excel)

Before we calculate confidence interval, we first find out some of the values needed from the chi-square table.

Lower limit = [tex]X^2_{\alpha /2,n-1}[/tex] = [tex]X^2_{0.025,29}[/tex] = 45.722

Upper limit = [tex]X^2_{1-\alpha /2,n-1}[/tex] = [tex]X^2_{0.975,29}[/tex] = 16.047

B) Next, we calculate confidence interval on variance,

CI on [tex]\sigma^2[/tex] = ( [tex]\frac{(n-1)\times \sigma^2}{X^2_{\alpha /2,n-1}}[/tex], [tex]\frac{(n-1)\times \sigma^2}{X^2_{1-\alpha /2,n-1}}[/tex] )

= ( [tex]\frac{(30-1)\times 0.0129}{45.722}[/tex], [tex]\frac{(30-1)\times 0.0129}{16.047}[/tex] )

= (0.0082, 0.0233)

C) Then, for confidence interval on standard deviation,

CI on σ = [tex]\sqrt{\text{CI on }\sigma^2}[/tex] = ( [tex]\sqrt{\frac{(n-1)\times \sigma^2}{X^2_{\alpha /2,n-1}}}[/tex], [tex]\sqrt{\frac{(n-1)\times \sigma^2}{X^2_{1-\alpha /2,n-1}}}[/tex] )

= ([tex]\sqrt{0.0082}[/tex], [tex]\sqrt{0.0233}[/tex])

= (0.0905, 0.1527)

D) Confidence interval on standard deviation guarantee 95% that standard deviation in response time is between 0.0905 and 0.1527. So, it will be surprised if director claim that the standard deviation in response time is more than 0.2 seconds.

Thus, The point estimator of response time data is 0.0129, and the 95% confidence interval on variance is (0.0082, 0.0233), and the 95% confidence interval on standard deviation is (0.0905, 0.1527), and it's surprised if director said standard deviation is more than 0.2 seconds.

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(1) $132,000 is the net income

(2) $66,000 total income

Selling price per unit:

= Sales ÷ No. of units

= $456,000 ÷ 5,700

= $80

Variable cost per unit:

= variable cost ÷ No. of units

= $102600 ÷ 5,700

= $18

Alternative 1:

Contribution margin = Sales - variable cost

                                 = (5,700 × $80 × 1.1) - (5,700 × $18)

                                 = $440,000 - $210,000

                                 = $230,000

Net income = Contribution margin - Fixed cost

                  =  $230,000 - $98,000

                  = $132,000

Alternative 2:

Contribution margin:

= sales - variable cost

= $456,000 - ($456,000 × 59%)

= $456,000 - $236,000

= $164,000

Net income = Contribution margin - Fixed cost

                  =  $164,000 - $98,000

                  = $66,000

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After solving the values of x are 0,-2.

Given:

f(x)=2x+1 and g(x)=x^2 and f(g(x))=g(f(x))

f(x^2) = g(2x+1)

2(x^2) + 1 = (2x+1)^2

2x^2 + 1 = (2x)^2 + 1^2 + 2*2x*1

2x^2 + 1 = 4x^2 + 1 + 4x

4x^2 - 2x^2 + 4x = 1-1

2x^2 + 4x = 0

2x(x+2) = 0

2x = 0 and x+2 = 0

x = 0    and x = -2

Therefore After solving the values of x are 0,-2.

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By solving a system of two simultaneous linear equation, it can be calculated that

There are 6 1p coin, 8 2p coin, 5 5p coin and 1 10p coins in the pot

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here a system of two simultaneous linear equation needs to be solved

Let the larger number be x and the smaller number be y

Two times the smaller of two number added with nine time the larger is 215.

9x + 2y = 215 ... (1)

Six time the larger added with seven time the smaller give -89.

6x + 7y = -89

Multiplying (1) by 2

18x + 4y = 430  ..... (3)

Multiplying (2) by 3

18x + 21y = -267 ... (4)

Subtracting (4) from (3)

-17y = 697

y = [tex]-\frac{697}{17}[/tex]

y = -41

Putting the value of y in (1)

9x + 2 [tex]\times[/tex] (-41)  = 215

9x = 215 + 82

9x = 297

x = [tex]\frac{297}{9}[/tex]

x = 33

The two numbers are 33 and -41

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"Reflection and dilation" are the series of transformations that would produce a square that was comparable to the original square but not congruent.

Reflection:

Reflection is a method of transformation which it flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance as from mirror line as its mirrored point.

Dilation:

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The term "Daily Allowance" refers to a sum of money given to an employee for each day he or she is away from the office, covering the employee's regular daily expenses as a result of the absence.

What are daily expenses?

As the name suggests, basic living expenses are those required for daily existence, with the main categories being housing, food, clothing, transportation, healthcare, and pertinent miscellaneous items.

An allowance in the workplace is money given to a worker to cover costs or make up for certain working circumstances. For instance, many employees receive an allowance to cover the cost of entertainment or vacation. In some circumstances, employees may also be required to accept their allowances.

There are three different classifications of allowances: non-taxable, partially taxable, and taxable.

How to Plan Your Allowance Budget;

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Answer:

[tex]\frac{27}{4}[/tex] or [tex]6\frac{3}{4}[/tex]

Step-by-step explanation:

6.75 = [tex]6\frac{3}{4}[/tex] = [tex]\frac{27}{4}[/tex]

Because 0.75 = [tex]\frac{3}{4}[/tex]

I would appreciate it if you mark my answer as brainliest.

Answer:

6 3/4

Step-by-step explanation:

so first 1/4 equals to 0.25

so if 1/4 is 0.25 than 3/4 would be 0.75

6 in this equation represents 24/4

so it would be (24+3)/4

which is 27/4

after simplifying you would get 6 3/4

The number of estimates of expected returns, variances, and covariances are needed to optimize this portfolio is 1,830.

Portfolio

A the definition of portfolio refers the asset allocation refers to an investment strategy whose main goal is to balance the risk and to recompense by allocating the assets portfolio with respective to the individual's objectives, tenure of the investment, and the risk capacity.

Given,

A portfolio management organization analyzes 60 stocks and constructs a mean-variance efficient portfolio using only these 60 securities.

Here we need to find the  estimates of expected returns, variances, and covariances are needed to optimize this portfolio.

As per the Markowitz procedure,

The estimation as follows

Here the Variance as N,

And Co variance will be as follows:

Co variance = (N² -  N) / 2

And the total estimation is calculated as,

=> N +  (N² -  N) / 2

Here, the number of assets is 60

So, the value of N=60

Then the Covariance and estimates will be as follows:

=> 60 +  (60² - 60) / 2

=> 1830.

Therefore, the estimates of expected returns, variances, and covariances are needed to optimize this portfolio is 1830.

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184.04 ft high the tower with a lean of 6 degrees, the degree measure of this lean is 3.6 degrees and most likely because either the 13ft lean has not been measured to the top edge of the tower or the side of the tower isn't straight.

In the given question, the tower was 184.5 feet tall.

(a) If the article states that when work began the tower Leaned 6° or 13 feet, off the perpendicular then we have to draw a sketch and label the two measurements.

According to given statement the sketch is given below:

(b) We have to find how much high is the tower with a lean of 6 degrees.

From the graph using the Pythagorean Theorem:

H^2 = 184.5^2- 13^2

H^2 =34040.25-169

H^2 = 33871.25

Taking square root on both side

H=184.04 ft

(c) The article goes on to say that the tower now leans 16 inches less we have to draw a new sketch that shows this measurement.

The graph is given below:

(d) Now we have to find the degree measure of this lean.

We know that the tower leans 16 in less.

So 16in= 1 1/3ft = 4/3 ft = 1.33 ft

Consequently the lean after the work is: 13ft - 1.33= 11.67 ft

Then we can find the "lean" after the work as:

sin ("lean") =11.67/184.5

sin ("lean")= 0.0633

Angel of ("lean") after work = 3.6degrees.

(e) Now we have to find the height of the tower with this lean.

Height with reduced lean is found by using Pythagorean Theorem again:

H^2 = (184.5)^2 - (11.67)^2

H^2 = 34040.25 - 136.19

H^2 = 33904.06

Taking square root on both side, we get

H = 184.13

(f) Now comment on the fact that sin 4° =13/184.5 = 0.07046 while sin 6° = 0.10453. We have to check can we reconcile this seeming discrepancy.

Most likely because either the 13ft lean has not been measured to the top edge of the tower or the side of the tower isn't straight.

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Answer: Understand the context.

Make a plan.

Identify the “who” and “why”

Weigh the pros and cons.

Get a second opinion.

Limit your choices.

Set deadlines.

Evaluate the outcome.

Step-by-step explanation:

The trigonometric expression (cos²α - cot²α)/(sin²α - tan²α) = cot⁶α

Trigonometric expressions are equations that contain the trigonometric ratios.

Given the trigonometric expression

(cos²α - cot²α)/(sin²α - tan²α)

To simplify the expression, we proceed thus

(cos²α - cot²α)/(sin²α - tan²α) = (cos²α - 1/tan²α)/(sin²α - tan²α)

= (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

=  (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

Factorizing out cos²α and sin²α, we have

=  (cos²α - [cos²α/sin²α])/(sin²α - [sin²α/cos²α])

=  cos²α(1 - 1/sin²α])/(sin²α(1 - 1/cos²α])

= [cos²α(sin²α - 1)/sin²α]/[sin²α(cos²α - 1)/cos²α]

= cos²α(sin²α - 1)/sin²α × cos²α/[sin²α(cos²α - 1)

= cos²α × -(1 - sin²α)/sin²α × cos²α/[sin²α × -(1 - cos²α)

= cos²α(1 - sin²α)/sin²α × cos²α/[sin²α(1 - cos²α)

= cos²α × cos²α/sin²α × cos²α/[sin²α × sin²α] (since cos²α = 1 - sin²α and sin²α = 1 - cos²α)

= cos²α × cos²α × cos²α/[sin²α × sin²α × sin²α]

= cos⁶α/sin⁶α

= (cosα/sinα)⁶

= cot⁶α

So, (cos²α - cot²α)/(sin²α - tan²α) = cot⁶α

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Tyler was gone for 45 minutes

Answer: 45 minutes

Step-by-step explanation: First, do 60-25 to find how much time there is till 3. (60-25=35) Then, add 10 because he came back at 3:10, not 3:00.

hope this helps!

please give brainliest!

Answer:

There’s no restrictions if I’m not mistaken.

Step-by-step explanation:

You’re correct