3x (2a - b)-y(2a - b) factorise

For a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.

It is given to us that -

There is 95% confidence

The margin of error is 0.04

We have to do the estimation of the population proportion.

We know that in case of unknown population proportion, we can assume that the value of population proportion can be regarded as 0.5.

It is known that the formula of sample size is given by -

[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }[/tex] ----- (1)

where,

n = sample size

Z = critical value of Z-value

p = population proportion

E = margin of error

Also, we know that for a 95% confidence interval, Z = 1.960

From the given information, we have

p = 0.5

and E = 0.04

Substituting the values in equation (1), we have

[tex]n =\frac{Z^{2}*p(1-p) }{E^{2} }\\= > n = \frac{(1.960)^{2}*0.5(1-0.5) }{(0.04)^{2} }\\= > n = \frac{3.8416*0.25}{0.0016}\\ = > n = 600.25[/tex]

Since this is the value of minimum sample size, rounding up, we have the sample size as 601.

Therefore, for a 95% confidence, the sample size should be equal to 601 to obtain a margin of error of 0.04 for the estimation of a population proportion.

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The equivalent resistance of the circuit is d)11.5 ohms. So, correct option is d.

We know very well that net resistance when resistors are connected in parallel and net resistance when resistors are connected in series is different.

So, we can see that three 4.7kΩ are connected in parallel.

So, using formula of net resistance in parallel

=>1/Rₙ=(1/R₁)+(1/R₂)+(1/R₃)

Therefore,1/Rₙ=1/4.7+(1/4.7)+(1/4.7)

=>1/Rₙ=3/4.7kΩ

=>Rₙ=4.7/3kΩ

=>Rₙ=1.5kΩ

Now, we have net resistance of three resistors.

Now, remaining three resistors are now connected in series

So, using formula of net resistance when resistors are connected in series=Rₙ=R₁+R₂+R₃

So, three resistors have resistance 4.7kΩ,1.5kΩ,5.2kΩ respectively

Therefore, Rₙ=4.7+1.5+5.2=11.5kΩ.

Hence, equivalent resistance is d)11.5kΩ.

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(Complete question) is:

Calculate the equivalent resistance in ohms of the following circuit : a)18100kΩ

b)11470kΩ

c)18.1kΩ

d)11.5kΩ

The required confidence interval for the population mean is  (6.296 , 7.104).

A confidence interval for a populace mean gives potential qualities the genuine populace mean will accompany a specific degree of certainty.

Standard deviation(S) = 1.9, Mean(x) = 6.7,  CL = 0.95 , n = 85

Then, α = 0.05

[tex]Z_{\alpha /2}\\[/tex] = [tex]Z_{0.25}[/tex]  = -1.96

Margin of error (E) = [tex]Z_{0.25}\\[/tex] ×S/√85

E = -1.96×1.9/9.21 = 0.404

Then lower level = x-E = 6.7-0.404 = 6.296

Upper level = 6.7+0.404 = 7.104

Thus, required interval is (6.296 , 7.104)

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Answer:

3 tiles

because 1/4+1/4+1/4=3/4

I hope this helps you!

If W(t) denotes the sumo wrestler's weight then the Function's formula will be w(t) = 5.5t + 79.5

Function formula: This relationship is often represented as y = f(x), or "f of x," and y and x are related in such a way that there is a unique value of y for every x; consequently, f(x) cannot have multiple values for the same x.

if we take y = mx + b,

the slope, m = 5.5, we need to find b,

at x = 11 and y = 14

14 = (5.5) (11) + b

b = 79.5

We plug in the qualities for x, y, and m. Then, we rearrange and deduct 60.5 from the two sides.

This makes the equation,

y = 5.5x + 79.5

or we can write as

w(t) = 5.5t + 79.5

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(complete question)

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms.Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).

Write the function's formula.

W(t)=?

In an acute triangle, all the three angles are less than 90°.

How do triangles work?

The definition of an acute triangle?

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The polynomials are in standard form is x2 + 3x + 2, 3t3 + 3t2 + 2t 14

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on. The standard form of polynomial is given by, f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² .....a₁x + a0, where x is the variable and ai are coefficients.

In the given options, when we analyse

x2 + 3x + 2 is given in standard form that is x2 + 3x + 2

15q 12q2 is not present in standard form

3t3 + 3t2 + 2t 14  is given in standard form

Therefore, the polynomials are in standard form is x2 + 3x + 2, 3t3 + 3t2 + 2t 14

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Standard deviation is used to measure the depth of a dataset relative to its mean and is taken by the square root of its variance.

The correct option is c.

The mean of X is 7 and the variance is 35.

                           2                                 12

Let Y be a random variable.

X and Y are binomials.

E(X-Y) = E (X) - E(Y)

Write the formula for the variance of X and Y.

Var(X-Y) = Var (X) - Var (Y)

where x and y are independent covers (x,y) is 0.

now,

Var(X-Y) = 35 + 35

                12    12

Because the standard deviation is the square root of the variance.

S.D = √((35/12) +(35/12))

So the correct option is c.

your question is incomplete but most probably the full question is

Let X be a random variable whose values are the number of dots that appear on the uppermost face when a fair die is rolled. The possible values of X are 1, 2, 3, 4, 5, and 6. The mean of X is 7/2 and the variance of X is 35/12. Let Y be the random variable whose value is the difference (first minus second) between the number of dots that appear on the uppermost face for the first and second rolls of a fair die that is rolled twice. What is the standard deviation of Y

a. √(35/12)

b. √(35/12) + √(35/12)

c. √{(35/12) + (35/12)}

d. √(35/12) - √(35/12)

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By evaluating the exponential equation, we will see that the amount that Erica owes after 6 years is $8551.56

Here we just need to use the exponential equation:

A = P*(1 + r/n)^(n*t)

Where A represents the amount owed t years after, and the other letters represent:

Replacing all that in the given quadratic equation we will get:

A = $5,300*(1 + 0.08/12)^(12*6) = $8551.56

Then the amount that Erica owes is $8551.56

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Total weight the bowl including the water and fih is 9.22 pound

What does math add mean?

To add is to integrate or bring two things together. The ability to add more than two numbers is then taught to students by building on this understanding. The foundational concept for understanding more complex operations like multiplication and division in higher grades is addition.

Given that :

An empty bowl weighted = 3.4 pound

A water that weighted = 5.12 pound

A fih that weighted = 0.7 pound

Total weight = A bowl + water + fih = 3.4 + 5.12 + 0.7 = 9.22 pound

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The vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

Given, an isosceles triangle

and we are asked that is vertex angle congruent to the base angles,

Let suppose ABC is an isosceles triangle with AB = AC

as we know that the angles opposite to the equal sides are also equal.

so, ∠ABC = ∠ACB

now, if ∠ABC = ∠ACB = x

then, on using angle sum property, we get

∠ABC + ∠ACB + ∠BAC = 180°

x + x + ∠BAC = 180°

∠BAC = 180° - 2x

as, x ≠ 180° - 2x

therefore, ∠BAC ≠ ∠ABC

So, the vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

Hence, the vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

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The Average proportional failure of the instructors is 0.10

From the question  we are told that

Sample size 100  

Instructor    Number of Failures  

Prof. A         13

Prof. B         0

Prof. C         11

Prof. D         16

Confidence level= 0.95

From Z table

Z=1.96

Generally proportion for failure is mathematically given as

proportion of failure = number of failure/ sample size

Prof A

Pa = 13/100

Pa = 0.13

Prof B

Pb = 0/100 = 0

Prof c

Pc = 11/100 = 0.11

Prof D

Pd = 16/100 = 0.16

Average proportional failure = (0.13 + 0.16 + 0.11 +0)/4 = 0.10

Therefore the Range is 0.0412 to 0.1588

Given the range 0.0412 to 0.1588 Prof B and Prof D are outside the Range making them the correct options

Therefore, the Average proportional failure of the instructors is 0.10

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The monthly utility bill (i.e. the x-value) that corresponds to a z-score of -0.75 is 64

Z-score gives you an idea of how far from the mean a data point is.

it’s a measure of how many standard deviations below or above the population mean a raw score is. A z-score can be placed on a normal distribution curve. Z-scores range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve).

The basic z score formula for a sample is:

z = (x – μ) / σ

According of the question,

Monthly utility bills in a city follows normal distribution

Mean of the monthly utility bills in a city : μ = $70

A standard deviation of monthly utility bills in a city : σ = $8

Z-score of utility bill = -0.75

z - score = x - μ / σ

=> - 0.75 = x - 70 / 8

=> -6 = x - 70

=> x = 70 - 6

=> x = 64

Hence , the x-value is 64

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When a 100-n box is suspended by a rope from an overhead support and a horizontal force of 58 n is applied to the box, the angle with the vertical is 30.11°.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.

Here,

If the object is held stationary, then all the forces must balance. This is called static equilibrium.

ΣFx=0

Tsinθ−58=0  ——- equation 1

ΣFy=0

Tcosθ−100=0  ——- equation 2

We now have two equation with two unknowns which allows us to solve for the cord tension  T  and the angle  θ .

Using equation 2:

T=100/cosθ

substitute this into equation 1:

(100/cosθ)sinθ=58

or

tanθ=58/100

θ=30.11°

The angle with the vertical is 30.11° as 100-n box is suspended by a rope from an overhead support and if a horizontal force of 58 n is applied to the box.

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Answer: neither

What we know:

Process:

Slope of line 1

Set up equation                                                                    y2-y1/x2-x1

Substitute                                                                              9-(-3)/3-(-1)

Simplify                                                                                  12/4

Solve                                                                                      slope = 3

Slope of line 2

Set up equation                                                                   y2-y1/x2-x1

Substitute                                                                             11-1/5-0

Simplify                                                                                 10/5

Solve                                                                                     slope = 2

Relationship

3 is not equal to 2, so they are not parallel

The opposite reciprocal of 3 is -1/3, which is not equal to 2, so they are not perpendicular

Computing a one-sample t-test is appropriate when d) all of the above

A statistical hypothesis test called the one-sample t-test is used to examine whether an unknown population mean differs from a given value. The test is applicable to continuous data. When doing a t-test, it is typical to make the following assumptions: the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and equality of variance in standard deviation.

When performing a one-sample t-test, the data should be collected at random from a population that is generally healthy. When each participant is put into a single group and is present on time, it is suitable. Additionally, it is suitable when the population variance is unknown.

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Option E is correct. People who are not registered to vote may bias the sample results is not a legitimate concern about the procedure being used.

People who are not registered to vote may bias the sample results is not a legitimate concern about the procedure being used because the polling firm is specifically interested in surveying a representative sample of registered voters in the United States.

The procedure targets registered voters by calling random phone numbers within the United States.

Since the focus is on registered voters, people who are not registered to vote are not part of the target population for this survey.

Therefore, their presence or absence in the sample does not affect the representativeness of the sample for registered voters. Option E is correct.

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Complete question:

A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called. Each time a number is called, the procedure below is followed. - If there is no response or if an answering machine is reached, another number is automatically called. - If a person answers, a survey worker verifies that the person is at least 18 years of age. - If the person is not at least 18 years of age, no response is recorded, and another number is called. - If the person is at least 18 years of age, that person is surveyed. Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used? (A) Registered voters with children under the age of 18 years may be underrepresented in the sample. (B) Registered voters with unlisted telephone numbers may be underrepresented in the sample. (C) Registered voters who have more than one telephone number may be overrepresented in the sample. (D) Registered voters who live in households consisting of more than one voter may be underrepresented. (E) People who are not registered to vote may bias the sample results.

All the Options (1, 2, 3) are correct i.e., A is always similar to A. and  If A is most similar to B, then we can say B is similar to A. and at last If A is most similar to B and B is also similar to C, then A must be similar to C matrix.

Properties of Similar square Matrices : Similar matrices percentage many residences and it's miles those theorems that justify the selection of the word ``similar.'' First we can display that similarity is an equivalence relation. Equivalence members of the family are essential withinside the have a look at of diverse algebras and might continually be seemed as a sort of susceptible model of equality.

Sort of alike, however now no longer pretty equal. The perception of matrices being row-equal is an instance of an equivalence relation we were operating with on account. Row-equal matrices aren't equal, however they may be lots alike. For instance, row-equal matrices have the identical rank. Formally, an equivalence relation calls for 3 situations hold: reflexive, symmetric and transitive. We will illustrate those as we show that similarity is an equivalence relation.

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The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is through multiplicative distributive property

We will calculate the value of x while showing the first step in solving the inequality, to provide better idea on complete solution. The correct first step is by using multiplicative distributive property as shown -

Rewriting the inequality -

–4(3 – 5x)≥ –6x + 9

Multiplying the values in each side of inequality

-12 + 20x ≥ -6x + 9

Rewriting the inequality according to terms

20x + 6x ≥ 9 + 12

Performing addition on each side of the equation

26x ≥ 21

So, x ≥ 21/26

Hence, the correct step is multiplicative distributive property.

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The complete question is -

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

Answer:

D. -1,1, -1/7,1/7

Step-by-step explanation:

Use all the factors of the leading coefficient, 7. And also, all the factors of the constant, 1.

Put the factors of the constant on top (numerator). Put the factors of the leading coefficient on the bottom (denominator).

+- 1/1 and +- 1/7

Simplifying:

-1, 1, -1/7, 1/7

That's it. Just list of possibilities of the rational zeroes.

For the given cost function, the maximum profit is $250.

What is profit maximization?

According to the firm theory, a company is founded with the intention of maximizing profits.

A company must run at the lowest possible cost while maximizing revenues in order to accomplish this.

When marginal costs and marginal revenue are identical, profits are maximized.

1. Determine the profit maximizing output.

For a firm in a competitive market, the marginal revenue is equal to the price (MR = P)

Get the MC by differentiating the total cost with respect to the quantity (Q)

C = 50 + 3Q^2

dC / dQ =6Q

MC = 6Q

Profit will be maximized when: MR = MC

MR = MC

60 = 6Q

Q =10

This is the profit maximizing output.

2. To get the maximum profits substitute this value into the equation:

Profit = Total revenue - Total cost

Profit = (P*Q) - (50 + 3Q^2)

Profit = (60*10) - (50 + 3*10^2)

Profit = 600 - 350

Profit = 250

Hence, for the given cost function, the maximum profit is $250.

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Answer:

y = -5/3x

Step-by-step explanation:

→ Rearrange to get y as the subject

3x + 4 = 5y

→ Divide both sides by 5

[tex]\frac{3x+4}{5} =y[/tex]   ⇔    [tex]y = \frac{3}{5}x +\frac{4}{5}[/tex]

→ Negatively reciprocate gradient

y = -5/3x

The cost of purchase of celery for the soup is $0.37

1 pound = 16 ounce

Each cup of celery weigh 4½ ounce = 9/2 ounce

16 ounce = 1 pound

9/2 ounce = (9/2)1/16 = 0.281

The yield percent for celery is 72%.

72% of x = 0.281

(72/100) x = 0.281

x = 0.281/(72/100)

x = 0.39 pound

each bunch weigh 1. 75 pound

Amount of bunch needed = 0.39/1.75 = 0.22

the celery for the soup cot if you purchae celery for $1. 66 a bunch

The cost of purchase = 0.22 x 1.66 = 0.37

Therefore, the cost of purchase of celery for the soup is $0.37

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Answer Desisonw 2

Step-by-step explanation:

Perpendicular lines (or segments) really structure four right points, regardless of whether only one of the right points is set apart with a case.

Let m and n be lines that converge line a. Let m be perpendicular to a. This implies that every one 4 of the points framed by the convergence of m and an are 90°.

Allow n to be opposite to a. This implies that every one 4 of the points framed by the convergence of n and an are likewise 90°.

Since the points are all consistent, this implies that the equivalent side inside points (between lines m and n) are harmonious. In the event that two same-side inside points are harmonious, the lines are equal. In a direction plane, two particular nonvertical lines are equal if and provided that they have a similar slant. Any two vertical lines are equal.

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The index value for 5 years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, Year 5: 1,414.74 as it starts at 1000 index points.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement. Rather than being stated as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Here,

Market value of the stocks:

Year 1: 2,645 million

Year 2: 2,957 million

Year 3: 3,318 million

Year 4: 3,193 million

Year 5: 3,742 million

Value of Index in 5 years:

Year 1: 1,000

Year 2: 1,117.96

Year 3: 1,254.44

Year 4: 1,207.18

Year 5: 1,414.74

Calculations:

Year 1: 2,645 million / 2,645 million × 1,000 = 1,000.00

Year 2: 2,957 million / 2,645 million × 1,000 = 1,117.96

Year 3: 3,318 million / 2,645 million × 1,000 = 1,254.44

Year 4: 3,193 million / 2,645 million × 1,000 = 1,207.18

Year 2: 3,742 million / 2,645 million × 1,000 = 1,414.74

Since the index starts at 1,000 points, the values for the subsequent years will be Year 1: 1,000, Year 2: 1,117.96, Year 3: 1,254.44, Year 4: 1,207.18, and Year 5: 1,414.74.

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Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L

According to our question-

Qin = 4 000m3/day

Cin = 25mg/L

V = 20 000m3

k = 0.25/day

Find: Count = ?

outStarting from the mass balance equation for steady state 0 = QCin - QCount - kCountV

manipulate the equation to get:

\(Count=Cin(Q/Q+kV)\)  

Then simple plug in your givens:

Count = (25mg/L)((4000m3/day)/(4000m3/day + 0.25/day(20000m3))

Count = 11mg/L

Hence, Waste stabilization pond is used to treat a dilute municipal wastewater before discharge into a river , Count = 11mg/L.

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A rectangle's area of 28cm2 (measured in cm2) is numerically equal to 4 times the rectangle's circumference (measured in cm). The rectangle's length to width ratio is 5:2.

Given,

l/b = 5/2

l = 5b/2

area = 4 times the rectangle's perimeter,

which equals 4*2(l+b)

= 8(l+b)

= 8(5b/2 + b)

= 28b cm2.

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The answer is regression equation.

What is  regression equation?

The regression of y on x is that the algebraic expression of the regression lines. it's accustomed predict the values of the variable quantity from the given values of freelance variables.

Main Body:

When there is a relation between 2 variables , regression equation is used to describe the relation .

Hence regression equation is the result.

The actual question is like:

Given a collection of paired sample​ data, the​ ____________________ y with caret=b0+b1x algebraically describes the relationship between the two​ variables, x and y.

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