find a cubic polynomial in standard form with real coefficients with degree 3 whose zeros are 2, and 1 i

As, we get the same results when we double a number and multiply the number by 2.

So, Yes doubling the number is same as multiplying by 2.

Given, the statement

Doubling is same as multiplying by 2.

we have to answer that, is doubling the same as multiplying by 2.

Let a number be, a

now to double the number, we have to add it to itself or to add it twice

= a + a

= 2a

So, on doubling a number we got 2a

Now, on multiplying a number by 2, we get

= a×2

= 2a

As, we can see that we got the same results when we double a number and multiply the number by 2.

So, Yes doubling the number is same as multiplying by 2.

Hence, Yes doubling the number is same as multiplying by 2.

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By using the concept of stratified sampling, it can be concluded that

In this situation, stratified sampling is used.

What is stratified Sampling?

Suppose, there is a population. If it is required to partition the given population into subpopulation, the sampling technique used in this case is called stratified sampling.

A tv station wishes to obtain information on the tv viewing habits in its market area. The market area contains one city of population 170,000 another city of 70,000, and four towns of about 5,000 residents each.

Here,  it is said that the station suspects that the viewing habits may be different in larger and smaller cities and in the rural areas.

So it is advantageous to partition the given population into subpopulation.

So stratified sampling must be used here.

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The account is compounded 4 times and the rate of interest is 5% per annum.

a) The given equation is : 314,961.92=280,000(1.04)^{t}

The coefficient of t is 1 so the account is compounded 1 times.

here rate = 0.04 , rate percent = 0.04 × 100 = 4%

b) The given equation is :  4,050=1,800(1.0125)^{4 r}

The coefficient of t is 4 so the account is compounded 4 times.

here rate = 0.0125 , rate percent = 0.0125 × 4 × 100= 5%

c) The given equation is :  2,142=350(1.006)^{2 t}

The coefficient of t is 2 so the account is compounded 2 times.

here rate = 0.006 , rate percent = 0.006 × 4 × 100= 2.4%

d)  The given equation is : 10,008=1,200(1.0036)^{12 r}

The coefficient of r is 12 so the account is compounded 12 times.

here rate = 0.006 , rate percent = 0.0036 × 12 × 100 = 4.32%

We know that for compound interest compounded multiple times within a year we take the formula of compound interest to find the amount accumulated in the account.

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Step-by-step explanation:

for that we best use the intercept form of a parabola equation :

y = a(x - p)(x - q)

p and q are the zeroes (x-intercepts) of the parabola.

a is the stretching factor (how wide or how narrow is the curve, and a positive "a" says it is opening upwards, a negative "a" says it is opening downwards).

so, our equation looks like

y = a(x - -2)(x - 5) = a(x + 2)(x - 5)

to get a we use the coordinates of the given point :

-40 = a(3 + 2)(3 - 5) = a×5×-2 = -10a

a = -40/-10 = 4

the equation is then

y = 4(x + 2)(x - 5) = 4(x² -5x + 2x - 10) =

= 4(x² - 3x - 10) = 4x² -12x - 40

The roots of the equation , 2[tex]m^{2}[/tex]+3=m, are non real roots.

The quadratic formula's discriminant is represented by the square root symbol [tex]b^{2}[/tex]-4ac. If there are two solutions, one solution, or none at all, the discriminant informs us.

As of now, 2m²+3=m we need to find the kind of roots they have.

2m²+3=m

2m²-m+3=0

Here, we can derive the following values from the equation:

a = 2, b = -1, c = 3

An equation's discriminant is stated as:

D = b²-4ac

D = (-1)(-1) - 4(2)(3)

D = 1 - 24

D = -23

Discriminant can determine the kind of roots that the equation contains.

In this instance, the discriminant is below 0.

The equation's roots are complex conjugates when D < 0.

Hence the roots for the equation are non real roots.

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The roots of the equation are non real roots.

Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation a[tex]x^{2}[/tex] + bx + c = 0, the discriminant is b2 − 4ac; and it tells what kind of roots it is real, non real.

As of now, 2m²+3=m we need to find the kind of roots they have.

2m²+3=m

2m²-m+3=0

Here, we can derive the following values from the equation:

a= 2, b = -1, c = 3

An equation's discriminant is stated as:

D= b²-4ac

D = (-1)(-1) - 4(2)(3)

D = 1 - 24

D = -23

Discriminant determine the kind of roots that the equation contains.

In this instance, the discriminant is below 0.

The equation's roots are complex conjugates when D < 0.

Hence the roots for the equation are non real roots.

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Answer: i got  

719/12

in decimal form  it is 59.916667

Step-by-step explanation:

Answer:

x=5

y=6

Step-by-step explanation:

3x-2y=3

-3x+3y=3

There are 40 pupil in a class and 30 of them are girl then  the ratio of girl to pupil is 3:4

If there are 40 pupil in total in the class, and 30 of them are girls, that means there are 10 boys in the class

so the ratio of  girls to pupil is 30: 40

to get simplest form, divide by the greatest common factor. which in this case, is 10

3:4

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Since it is observed that I z I = 3.464 > 1.96 it is concluded that the null hypothesis is rejected.

Therefore we reject John's claim.

Here:

we can use 1 sample proportion test to check the claim of John

H₀ : p₀ = 0.4

H₁ : p₀ ≠ 0.4

Test statistic is

z = p - p₀/√p₀(1-p₀)n

Let X be the random variable denoting the number of heads.

Now p = X/n

= 8/50

= 0.16

p₀ = 0.4

1-p₀ = 1-0.4

= 0.6

z = -3.464

since it is observed that I z I = 3.464 > 1.96 it is concluded that the null hypothesis is rejected.

Therefore we reject John's claim.

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if a given  table of values consists of a constant rate of change   it is said to be a linear function.

A linear function could be a function that represents a straight line on the coordinate plane, A straight work is of the shape f(x) = mx + b, where 'm' and 'b' are real numbers, where m is the slope, b is the y-intercept, x is the independent function and ys is the dependent variable. If the given table is showing  a constant rate change, the value of y changes in a constant  value with the value of  x, we consider it to be a linear  

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The expression x³ - 23x² + 142x + 20 cannot be factorized

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

x3 - 23x2 + 142x + 20

Solving further, we need to rewrite the polynomial properly

So, we have the following representation

x³ - 23x² + 142x + 20

Express the polynomial as a function

So, we have the following representation

y = x³ - 23x² + 142x + 20

Next, we represent the above expression on a graph

From the attached graph, we can see that the polynomial expression only cross the x-axis at x = -0.138

This implies that the expression cannot be factored

So, we cannot further rewrite the given expression

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The number of workers in the company are 5000

information from the problem

In a​ company, ​95% of the workers are

If 250 people work for the company who​ aren't

how many workers are there in​ all = ?

The question is a percentage problem, percentage deals with a fraction hundred

95% of the workers are, the remaining percentage are not

the remaining percentage are 100 - 95 = 5%

5% of certain number say x aren't

5% of x = 250

5x/100 = 250

x = 250 * 100 / 5

x = 5000

The number of workers are 5000

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The computed value of t= -0.21 does not fall inside the crucial zone, t= 2.120. As a result, we accept our null hypothesis, which states that, at the 0.05 level of significance, there is no difference in the strength (psi) of liner specimens when a certain fusion approach was applied compared to when it was not.

As per given data

No Fusion :: 2748 2700 2655 2822 2511 3149 3257 3213 3220 2753

above data will be denoted as x1

Yes Fusion :: 3027 3356 3359 3297 3125 2910 2889 2902

above data will be denoted as x2

Using the formula of mean = [tex]\frac{sum of terms}{number of terms}[/tex]

x1 = 2902.8

x2 = 3108.125

Standard deviations for each expression respectively are:

s1 = 277.265

s2 = 205.87

By using Student's t-test we can form null and alternate hypothesis as

H0 : u1-u2=0 in opposition of Ha: u1-u2≠0

Alpha's significance level has been chosen as ∝=0.05

critical region t  ≥ t (0.025, 16) = ± 2.120

Degrees of freedom is df = υ= n1+n2- 2= 10+8-2= 16

Now, the difference between the sample means

=2902.8-3108.125

= -205.325

calculating, pooled estimate for the common variance σ²

Sp² = (n1-1) s1² + (n2-1) s2²/ n1+n2-2

=  9( 277.265)² + 7(3108.125)²/ 16

Sp² = 691,882.922+67,623,087.109/16

Sp= 2066.321

Finding, the test statistic

t = (x`1- x` ) /. Sp √1/n1 + 1/n2

t= -205.325/ 2066.321 √1/10+ 1/8

t= -205.325/980.142

t= -0.2095= -0.21

Note that the full question is:

The deterioration of many municipal pipeline networks across the country is a growing concern. One technology proposed for pipeline rehabilitation uses a flexible liner threaded through existing pipe.

The article "Effect of Welding on a High-Density Polyethylene Liner" (J. of Materials in Civil Engr., 1996: 94-100) reported the following data on tensile strength (psi) of liner specimens when a certain fusion process was used and when this process was not used.

No Fusion :: 2748 2700 2655 2822 2511 3149 3257 3213 3220 2753

Yes Fusion :: 3027 3356 3359 3297 3125 2910 2889 2902

Compare the mean tensile strengths at the 95% confidence level ...

Perform a COMPLETE APPROPRIATE analysis.

Answer the question of interest, check assumptions, etc.

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The probability of Jack taking 2 red candies is 3/28.

What do you mean by a union in probability?
The letter "U" (union) stands for "or." Specifically, P(AB) represents the probability of that event A or event B occurring. The sample points that are present in both event A and event B must be counted in order to determine P(AUB).

The new probability set made up of all the elements from both sets is created when two sets are joined. When two sets intersect, a new set is created that includes every element from both sets.

Solution Explained:

Given in the question,

A bag contains 3 red and 5 green candies.

Total possibilities is 3 + 5 = 8  

Jack takes a candy at random and eats it  

A/Q there are 3 red candies out of 8, the probability is given by,

P(R) = 3/8

Now there are 2 red candies out of 7, so the probability is given by,

P(R') = 2/7

The probability of both events is given by,

P(2R) = P(R) × P (R') = 3/8 × 2/7 = 3/28

Therefore, the probability of Tim taking 2 red candies is P(2R) = 3/28

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3:1 phenotype ratio means that three offspring will have a dominant phonotype. Then there is one offspring that will have a recessive genotype, and thus the recessive phenotype.

A 3:1 ratio is the relative fraction of phenotypes among progeny (offspring) results following mating between two heterozygotes, where each parent possesses one dominant allele and one recessive allele at the genetic locus in question.

A phenotypic ratio is a quantitative relation between phenotypes showing the number of times the frequency of one phenotype correlates with another.

A monohybrid cross results in a phenotypic ratio of 3:1.

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The statements that are true to determine whether x=10 is unusually high number of defective items on the next run of 100 products are given by the following option:

I and III.

Unusual values in the normal distribution are found using the range rule of thumb, which states that if a value is more than two standard deviations from the mean, the measure is unusual.

The measures for the binomial distribution are given as follows:

The parameters for this problem are given as follows:

n = 100, p = 0.04.

Then the mean and the standard deviation are given as follows:

Thus the upper bound for usual values is of:

4 + 2 x 1.96 = 7.92.

Which is less than 10, hence 10 is an unusual measure and statement I is correct.

Statement III is also correct, as:

P(X >= 10) < 0.05.

While statement II is false, as we do not look at the exact measure, but an interval of measures.

The problem is given by the image shown at the end of the answer.

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Ben's expected utility of playing the lottery is 120

Ben bought a lottery ticket that could allow him to win $90,000.00 with probability 0.40

ben values money according to the utility function v(m) = m

Ben's utility = m

We need to find Ben's expected utility

expected utility = 0.4 x √m + 0.6 x 0

= 0.4 x √90000 + 0

= 0.4 x 300

= 120

Therefore, if Ben bought a lottery ticket that could allow him to win $90,000.00 with probability 0.40 (and nothing otherwise). ben values money according to the utility function v(m) = m. Ben's expected utility of playing the lottery is $120

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300,000 is the maximum number of bacteria the petri dish can hold

Given,

In a laboratory, the number of bacteria in a petri dish after t days is modeled by the function b (t) = Start fraction 300,000 over 1 999 e superscript negative 0.5 t baseline End fraction.

Which is equal to B (t) = 300,000/1+999e^-0.5t

We have to find that what does 300,000 represent;

Here,

B = Bacteria

t = Number of days

300,000 = Maximum number of bacteria the petri dish can hold

That is,

300,000 is the maximum number of bacteria the petri dish can hold

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Answer:

D

Step-by-step explanation:

Just took test

4.4306 is the critical point using a 0.01 level of significance, that one would compare to the f statistic in order to make a conclusion.

What is the ANOVA?

This is the term that is used to refer to the short form of the term that says analysis of variance.

The ANOVA is used to show the variation that would be in existence of a group of observations.

The F test is known to be positively skewed at all times. So we would have it that the P value would have to be to the right and not to the left in the ANOVA hypothesis.

Using F Statistics table , we can calculate Critical point using a 0.01 level of significance.

Hence,4.4306 is the critical point using a 0.01 level of significance, that one would compare to the f statistic in order to make a conclusion.

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The area of that rectangle is 150 square inches. The result is obtained by using the formula of the perimeter dan area of pictures.

A rectangle is a two dimensional shape consisting of four joints. It has also four angle points.

The perimeter and area of a rectangle can be expressed as follows.

P = 2 (w + l)

A = w × l

Where

The perimeter of a rectangle is 800 inches. The width of the rectangle is 60% of its length.

From that information, we have:

P = 2(w + l)

800 = 2(0.6l + l)

400 = 1.6l

l = 400/1.6

l = 250 inches

The area of the rectangle is

A = w × l

A = 0.6 l × l

A = 0.6 l²

A = 0.6 × 250

A = 150 square inches

Hence, the area of that rectangle is 150 square inches.

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Answer:

y = 2x + 1

tada

You need to assume that the slope between the dependent Varian and the numerical independent variable is zero.

In regression analysis, to find the effect of one independent variable on the dependent variable, there has to be no interference from the other independent variables whether they be categorical (dummy) or numerical independent variables.

A dummy variable is one which takes on the value of 0 or 1, to represent the absence or presence (respectively) of a given category which is expected to influence the dependent variable.

When a dummy independent variable is included in a regression model, to know the effect of that dummy or category (e.g. day =1, night =0) on the dependent variable, the influence of the numerical independent variable has to be removed temporarily.

In a regression equation,

Y=a+bX+cK

Y is the dependent variable

a is the intercept on the vertical axis on the graph

b is the slope between the dependent variable Y and the independent numerical variable X

c is the slope between the dependent variable Y and the dummy variable K

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Proved that f is pose a continuous function on R. If each of the functions fn is bounded, is  necessarily true that f is bounded.

Given:

Let {fn} be a sequence of continuous functions defined on R, and that fn + f uniformly on every finite interval [a, b]. Prove that f is pose a continuous function on R.

Denote by fn(x) any continuous function such that fn(x)=f(x) if x∈[−n,n], and fn(x)=0 if x∈(−∞,−n−1)∪(n+1,+∞). It is easy to see that such a function exists, and is bounded.

Now, using the fact that every interval [a,b] is contained in a interval [−N,N], you can check easily that (fn) converges to f uniformly on every [a,b] (actually, fn|[a,b] is constant equal to f|[a,b] for n sufficiently large).

No, because this would not give a continuous function. Define fn equal to f on [−n,n], and equal to zero on (−∞,−n−1)∪(n+1,+∞), and complete it as you want and the intervals [−n−1,n) and (n,n+1] to get a continuous function.

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The required values of k for which given matrix is diagonalizable is 0.

A matrix is symmetric if and provided that it is equivalent to its translate. All sections over the primary inclining of a symmetric grid are reflected into equivalent passages beneath the slanting. ■ A lattice is slant symmetric if and provided that it is something contrary to its render.

We have,

A = [tex]\left[\begin{array}{cc}4&k&0&4\\\end{array}\right][/tex]

Keep in mind, each symmetric matrix with genuine coefficients is diagonalizable. Note that the coefficients of An are reals. In this way, on the off chance that we take with the end goal that An is symmetric.

For A is symmetric matrix,

k = [tex]a_{12}=a_{21}[/tex] = 0

Thus, required value of k for given matrix is 0.

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The expected value E(total) = $122,500 and standard deviation for the total discounts is SD(total) = $4,066

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The 90% confidence interval for the mean electricity bill of all UCF students is discovered using the t-distribution to be (117.06, 106.94).

The standard deviation for the sample has been provided to us, so the t-distribution is employed to address this issue.

The information given is:

Sample mean of : x = 112

Sample standard deviation : s =  19

Sample size of : n = 40

The confidence interval is: [tex]\bar{x}\pm t\cdot\frac{S}{\sqrt{n} }[/tex]

Using a t-distribution calculator, the critical value is t = 1.6854 for a two-tailed 95% confidence interval with 40 - 1 = 39 df.

Hence:

Upper bound = 112 + 1.6854 × 19 / √40 = 117.06

Lower bound = 112 -  1.6854 × 19 / √40 = 106.94

A confidence interval is a range of estimates for an unknown parameter (CI). The most common confidence level is 95%, but when calculating confidence intervals, other levels, such 90% or 99%, are also occasionally employed.

The 90% confidence interval for the mean electricity bill of all UCF students is discovered using the t-distribution to be (117.06, 106.94).

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The appropriate sample size for a study by knowing the population standard deviation is:

1/6 of the population range.

A pilot study's sample standard deviation.

The sample standard deviation is the root-mean square of the discrepancies between observations and the sample mean: A large divergence is defined as two or more standard deviations from the mean.

The sample standard deviation (s) is the square root of the sample variance and serves as a measure of the deviation from expected values. In its most basic form, it is the average distance between the observed data and the expected values.

The population standard deviation always depends upon the population range and sample standard deviation.

Therefore, By knowing the population standard deviation it allows us to choose the appropriate sample size for a study that is:

1/6 of the population range.

A pilot study's sample standard deviation.

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The number of can of soups purchased is 10 and the number of frozen dinner purchased is 10.

What are the linear equations in two variables?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.

Let 'x' number of cans of soup purchased and 'y' number of frozen dinners purchased.

By the given condition, we can prepare the equations,

              x + y = 15 --------(I)

       200x + 500y = 4500 -----(II)

now from (I), y = 15 - x

Substitute the value of 'y' in the equation (II), we get

              200x + 500(15 - x) = 4500

              200x + 7500 - 500x = 4500

               300x = 3000

                    x = 3000/300

                    x = 10

Put x = 10 in equation (I), we get

                  y = 5

Hence, the number of can of soups purchased is 10 and the number of frozen dinner purchased is 10.

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Answer:

y = 2/3x - 4/3

Step-by-step explanation:

m = y2 - y1/x2 - x1

m = 2 - (-2)/5 - (-1)

m = 4/6 = 2/3

y - y1 = m(x - x1)

y - (-2) = 2/3(x - (-1))

y = 2/3x - 4/3