Solve each equation by completing the square:
0.1²-0.6x+0.9=0
2x²-12x+18=0

The values of m and n required to form perfect square trinomials are given as follows:

a) m = -10, n = 25.

b) m = 6, n = 9.

c) m = 12, n = 180.

d) m = -7/2, n = 49/16.

Perfect square trinomials are expressions that have either of these two formats:

The term that multiplies x is always the multiplication of 2 by both of the two terms that are added.

Hence in item 1, the expression is completed as follows:

x² - 10x = (x - 5)² - 25 = x² - 10x + 25 - 25

Meaning that m = -10, n = 25.

In item 2, the expression is completed as follows:

x² + 6x = (x + 3)² - 9 = x² + 6x + 9 - 9.

Hence m = 6, n = 9.

In item 3, the expression is completed as follows:

5x² + 60x = 5(x² + 12x) = 5(x + 6)² - 180 = 5(x² + 12x + 36) - 180 = 5(x² + 12x + 180 - 180).

Hence m = 12, n = 180.

In item 4, the expression is completed as follows:

2x² - 7x = 2(x² - 7/2x) = 2(x² - 7/4x)² - 49/32 = (2x² - 7/2x + 49/16 - 49/16).

Hence m = -7/2, n = 49/16.

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Treatment remains the same. Do not Reject.

Test Statistics:

[tex]f = \frac{\text{treatment}}{\text{error}} = 5.37[/tex]

Reject Null Hypothesis if [tex]f > f(a, a-1, N-a)[/tex]

Critical Value [tex]f(0.01, 3, 15) = 5.42 \text{ (From F Table)}[/tex]

[tex]\because 5.37 < 5.417[/tex]

We fail to Reject [tex]H0[/tex]

[tex]\therefore[/tex] Do not Reject.

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The given integral is:

∫ ∫ ( x) ×(8 × (√ x)) dx dy

By changing the order in which we integrate with respect to the variables x and y, we can rewrite this integral as an iterative integral of the other five orders. The other five commands are:

a. ∫ ∫ (√ x) ×(8 × (√t x)) dy dx

b. ∫ ∫ (8 × (√ x)) × (√ x) dx dy

c. ∫ ∫ (8 × (√ x)) × (√ x) dy dx

d. ∫ ∫ (√ x) × (√x) dx (8 × y)

e. ∫ ∫ (√ x) × (√ x) (8 * y) dx

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The number of students and adult ticket sold are 988 and 758 respectively .

Students pay $2 per ticket and adults pay $5 per ticket. The stadium is filled to its capacity of 2000 but 254 of those seats are given free of charge to band members, pep squad members, and faculty members.

The total income from the sale of tickets for the current game is $5766.

The number of student and adult tickets that were sold can be calculated as follows:

let

x = number of student ticket sold

y = number of adult ticket sold

Hence, using equation,

Students pay $2 per ticket and adults pay $5 per ticket and the total total sale is 5766.

2x + 5y = 5766

The stadium is filled to its capacity of 2000 but 254 of those seats are given free. This means the actual number of people that paid for the seats is 2000 - 254 = 1746.

x + y = 2000 - 254

x + y = 1746

Combine the equation

2x + 5y = 5766

x + y = 1746

multiply equation(ii) by 2

2x + 5y = 5766

2x + 2y = 3492

subtract equation(ii) from equation(i)

3y = 2274

y = 2274 / 3

y = 758

x = 1746 - 758

x = 988

Therefore,

number of student tickets = 988

number of adult tickets = 758

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If a<0, then there is no x-null lines, the system has no equilibrium points.

If a=0, it has only one equilibrium points.

If a>0, the system has two equilibrium points.

Points are (-√a,0) and (√a,0)

The system changes from no fixed points to two fixed points when it increases through a=0.

a is a bifurcation point.

The Jawbian matrix,

                        J = [tex]\left[\begin{array}{ccc}2x&0\\-2xy&x^{2}-1\\\end{array}\right][/tex]

Now,

      J[0,0] = [tex]\left[\begin{array}{ccc}0&0\\0&-1\\\end{array}\right][/tex] =0

      J[-√a,0] = [tex]\left[\begin{array}{ccc}-2\sqrt{a} &0\\0&-a-1\\\end{array}\right][/tex] = 2a√a + 2√a

If a=0, then it will be a live equilibrium, one of the values are 0, For a>0, the point (-√a,0) is sink and (√a,0) is a saddle points.

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Yes, it is significant evidence of a difference between the age distribution of jurors and the countrywide age distribution.

No, there is no age bias in the selection of jurors.

P             Oi       Ei        ( Oi-Ei) ^2/Ei

0.421     399     421     1.149643705

0.229     231     229     0.017467249

0.157     158     157     0.006369427

0.193     193     193     1.870466321

  1         1000  1000    3.043946702

The above can be represented in graphs.

Now,

Ei = n × pi

TS = 3.04394672

From TS < value

Value (7.81472)

We fail to reject the null hypothesis at 5% value of significance

No, there is no age bias in the selection of jurors.

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Answer:

x = 5

Step-by-step explanation:

assuming you mean the slope of the line id undefined and passes through (5, 0 )

A line with an undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (5, 0 ) with x- coordinate 5 , then

x = 5 ← equation of line

All polynomials of the form p(t) = a + bt2, where a and b are in sets is a subspace of Pn for an appropriate

Consider the following subsets of Pn given by

The 0 vector of V is in W.

- Given v,w in W then v+w is in W.

- Given v in W and a a real number, then av is in W.

So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.

First property:

Hence the first criteria is not met. Then, W2 is not a subspace of Pn.

For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.

W1 and W3 are subspaces of Pn for n= 2

and W2 is not a subspace of Pn.  

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Answer:

x = 15

y = 4

Step-by-step explanation:

18/6 = x/5

3/1 = x/5

x = 15

12/y = 3/1

3y = 12

y = 4

Therefore , the answer to this problem is that planned delivery time is the amount of time required to get material.

Time scheduling is a group of methods for creating and presenting schedules that indicate when work will be done. All of these methods' outcomes are typically displayed as activities or bars on a timeline known as a Gantt chart.

Here,

Obtaining the substance requires the following scheduling if it is externally manufactured.

So ,

When a material is purchased outside, the planned delivery time is the amount of time required to get the material.

Therefore , the answer to this problem is that planned delivery time is the amount of time required to get material.

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The complete question is "which of the following scheduling times is needed to obtain the material if it is externally produced or not ?

a.In-house production time.

b.Goods issue processing time.

c.  Planned delivery time.

d. Goods receipt processing time."

4) Lower bound = 24.06

Use Dergy Willing

upper bound = 28.55

5)Lower bound = 18.12

upper bound = 34.4

Healthy body=A healthy body is maintained by good nutrition, regular exercise, avoiding harmful habits, making informed and responsible decisions about health, and seeking medical assistance when necessary. Health is a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity .A  state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity'.

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The size of the sample after two hours with an initial population of 1000 and a growth rate of 11% is found to be 1246.

A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth. The formula of continuous exponential growth is  P=P₀e^{rt} where P is the population after time t, P₀ is the initial population, and r is the growth rate.

Given P₀ is 1000 bacteria, r is 11% = 0.11, and t is 2 hours. Then, the size of the sample after two hours is,

[tex]\begin{aligned}P&=P_0e^{rt}\\&=1000e^{0.11\times2}\\&=1000e^{0.22}\\&=1000\times1.246\\&=1246\end{aligned}[/tex]

The answer is 1246.

The complete question is -

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 11% per hour. Suppose also that a sample culture of 1000 bacteria is obtained from this population. Find the size of the sample after two hours. Round your answer to the nearest integer.

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when model building using the build-down method, you want to start with the complete 2nd-order model and build down to the most data model.

when working on a workbook which requires a team of people to work with you on the workbook, it is important you create transparency and also ensure you complete the workbook on time.

one very important way to complete the task on time is to share the workbook with your team so that they can input their own contributions towards the task, this practice ensures speedy completion of the task. and reduces the level of errors which might have occurred if you where working on it alone.

granting access to the workbook is a very good way to create trust and transparency.

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Answer:

1/9

Step-by-step explanation:

f(-1)=1/3(3)^-1

f(-1)=1/3(1/3)

f(-1)=1/9

The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....

Given that,

We have to get the first four nonzero terms of the series for f(x), centering at the specified value of a, use the definition of a Taylor series. (Separate your responses into a list using commas.)

f(x)=5/1+x and a=2

We know that,

Take

f(x)=5/1+x and a=2

f(2)=5/1+2=5/3

f'(x)=-5/(1+x)²         f'(2)=-5/(1+2)²=-5/9                  (differentiating)

f''(x)=10/(1+x)³        f''(2)=10/(1+2)³=10/27

f'''(x)=-30/(1+x)⁴     f'''(2)=-30/(1+2)⁴=-30/81=-10/27

Using the taylor series

F(x)=f(a)-(x-a)f'(a)+(x-a)²/2!f''(a)-(x-a)³/3!f'''(a)+....

F(x)=f(2)-(x-2)f'(2)+(x-2)²/2f''(2)-(x-2)³/3!f'''(2)+....

F(x)=5/3-(x-2)(5/9)+(x-2)²/2(10/27)-(x-2)³/6(-10/27)+....

F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....

Therefore, The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....

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The Total Probability of getting exactly two 3s in two throws is 1/36

What is Probability?

A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Solution:

Probability of Obtaining 3 in the first throw = 1/6

Since, the number of possible outcome is 11 and total outcomes are 6

Similarly the probability of getting 3 in the second throw is 1/6

Therefore, total probability = 1/6 * 1/6 = 1/36

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As per the concept of hypothesis, the value of p is 0.47 the value of the static hypothesis is 4.3893 and the statistical division when the alpha = 0.05 is 0.1085.

What is meant by hypotheses?

in math, hypotheses refers a an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

Here we have given that, a movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a 2nd time. The target is to have 40 million viewers and they want more than 40% of the viewers to return to see the movie again.

And they show the movie to a test audience of 140 people.

Of the test audience, 66 people said they would see it again.

And we have to determine, the p-value is, the p-value for the test statistic.

And the statistical division when the alpha = 0.05 and explain the managerial conclusion for this situation.

Based on the question, the null hypothesis is,

H0: P = 3

H1: P > 0.03

Here we know that they show the movie to a test audience of 140 people.

So, n = 140

Here the test audience, 66 people said they would see it again.

So, x = 66

Therefore, the value of p is,

=> 66/140 = 0.47

Then the test hypothesis is,

=> Z = (0.47 - 0.3) / √[(0.3(1 - 0.3))/140]

When we simplify this one, then we get,

=> Z = 4.3893

Therefore, value of the static hypothesis is 4.3893.

Then the p-value = 0.1085 at 5% level of significance.

Here, 0.1085 <  4.3893,

Therefore, the null hypothesis is not rejected.

Therefore, p-value  = 0.1085, and we will not reject the null hypothesis.

So, the value of the static hypothesis is greater than the null hypothesis and the value of p so the value of not rejects the null hypothesis.

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The percentage increase in her jump length would be 8.77%.

What is a percentage increase?

The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in percentage.

The initial jump was 5.7m and the second jump is 6.2m

By using the percentage increase formula, we can write

         Percentage increase = (final value - initial value)/|Final value| * 100

                                             = ((6.2 - 5.7)/6.2)*100

                                             = 8.77%

Hence, the percentage increase in her jump length would be 8.77%.

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The exponential equation that represents the population of wolves over time is -

y = 12(1.12)ˣ

        [tex]y = log_{e}x[/tex]

Given is a table as shown in the question.

Assume the exponential equation to be -

y = A(B)ˣ

At [x] = 0, [y] = 12 -

12 = A(B)⁰

A = 12

and

At [x] = 2, [y] = 15 -

15 = A(B)²

(B)² = 15/12

(B)² = 1.25

(B) = √(1.25)

(B) = 1.118

(B) = 1.12

The equation will be -

y = 12(1.12)ˣ

Therefore, the exponential equation that represents the model is -

y = 12(1.12)ˣ

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Answer:

It's answer B

Step-by-step explanation:

The integral for the work required to pump the water out of a spout that rises 2 m above the tank is

w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

Integral

An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).

Given that:

r = 2m

l = 5m

sinθ = [tex]\frac{x}{r}[/tex]

dv = 2l  [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

Let p be the density of water and g be the acceleration due to gravity.

dm = p dv

dw = dmg (h + r - x)

dw = pg (h + r - x) dx

dw = 2l pg  (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

w = ∫dw

w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

Therefore, the integral for the work required to pump the water out of a spout that rises 2 m above the tank is

w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

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Answer:

All natural numbers

Step-by-step explanation:

I'm assuming that you mean 36-(n^2/n^2)

A natural number is a positive integer

n^2/n^2 is always 1 for natural numbers.

so 36-1=35 which is a natural number

The test statistic is 1.507 and the corresponding p value is 0.175539

Fail to reject H₀ because the p value is greater than the significance level  0.05.

There is enough evidence to warrant rejection of the claim  that the mean difference between their jumping and relaxed times would be zero.

To find the mean and standard deviation for the paired differences, prepare the table:

Calculate the value of d bar:

d bar = ∑d/n

= 5+7+...+(-3)/8

= 14/8

= 1.75

Calculate the standard deviation of the (d)

Sd = √(d₁-dbar)²/n-1

= √(5-1.75)²+(7.1-75)²+..+(-3-1.75)²/8-1

= √10.785714

= 3.284

The mean and standard deviation of the eight girls were timed to see how long they could be zero.

Null hypothesis H₀: meand = 0

Alternative hypothesis H₁ : mean d ≠ 0

Level of significance α = 0.05

Decision rule : Reject H₀ when p value < 0.05 level of significance.

The null hypothesis is the 8 girls mean difference between their jumping and relaxed time is equal to the zero and alternative hypothesis is the 8 girls mean difference between their jumping and relaxed time is not equal to the zero.

from the available info, d bar = 1.75 Sd = 3.284

Calculate the  test statistic value.

t = 1.75 - 0/3.284/√8

= 1.507

calculate the degree of freedom.

df = n-1

= 8-1

= 7

Calculate the p value of the test

P value = (=TDIST(1.507,7,2)) (use MS Excel function)

= 0.175539

Hence the test statistic is 1.507 and the corresponding p value is 0.175539

Fail to reject H₀ because the p value is greater than the significance level  0.05.

There is enough evidence to warrant rejection of the claim  that the mean difference between their jumping and relaxed times would be zero.

There is no evidence to warrant rejection of the claim that the mean difference between their  jumping and relaxed times would be zero.

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Answer: This comes out to be 0.1031.

Step-by-step explanation:

in this case, we are given that the rate of power cuts in the city is 3/day, so the rate parameter for our Poisson distribution is $\lambda=3$. We want to find the probability that there are at least 7 cuts but at most 4 cuts in a given day. This means we need to find the probability that $k=7$, $k=8$, $k=9$, ..., $k=4$. We can use the formula for the probability mass function to find the probability for each of these values of $k$ and add them together to get the total probability.

Answer:

The area of the wall is:

11520 inches²

Step-by-step explanation:

Area of a rectangle = high * long

Then:

Area = 96 inches * 120 inches

Area = 11520 inches²

Answer: Option B: 14%

Step-by-step explanation: The only option that seems suitable is option B. You can't have celiac disease and test negative.

Answer:

I think it is 51% or 22%

I am not sure which one, but I think it should be 51% or 22%.

The multiplication that will give a value of 12✓6 from the numbers will be:

3✓2 × 4✓3

3 × 4✓6

It should be noted that addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, it should be noted that:

3✓2 × 4✓3 = 12✓6

3 × 4✓6 = 12✓6

It should be noted both scenarios highlight the given value of 12✓6.

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The value of ∠q is 72 degree. So the option B is correct.

In the given question we have to find the value of q.

The given options are:

A 25 degree

B 72 degree

C 108 degree

D 180 degree

As we know that the angle of straight line is 180 degree.

From the given diagram we can see that the two angel of one line that is cut by another line, is given.

So the third angle of one line that is cut by another line is

25 + 83 + x = 180

x + 108 = 180

Subtract 108 on both side, we get;

x = 72

Using the corresponding angle theorem

∠q = 72 degree

Hence, the value of ∠q is 72 degree. So the option B is correct.

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The probability that the largest of the three random variables is greater than the sum of the other two is:P(x1 > x2 + x3) = 1/4

The probability of an event occurring is equal to the number of favorable outcomes divided by the total number of outcomes. In this case, the total number of outcomes is 8, since each of the three random variables can take on any value between 0 and 1 independently. The favorable outcomes are those in which x1 is greater than the sum of the other two variables, which is 1/4 of the total number of outcomes. Therefore, the probability that the largest of the three random variables is greater than the sum of the other two is 1/4.

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Answer:

20.0°C

Step-by-step explanation:

To find the final temperature of the water after it has transferred thermal energy to the ice cube, we need to use the equation:

Q = cmΔT

where Q is the amount of thermal energy transferred, c is the specific heat capacity of the substance, m is the mass of the substance, and ΔT is the change in temperature.

In this case, we are given that Q = 4,200 J and m = 200 g. The specific heat capacity of water is 4.184 J/g°C.

Substituting these values into the equation gives us:

4,200 J = (4.184 J/g°C)(200 g)(ΔT)

Solving for ΔT gives us:

ΔT = 4,200 J / [(4.184 J/g°C)(200 g)] = 10°C

Since the initial temperature of the water was 10.0°C, the final temperature of the water is 10.0°C + 10°C = 20.0°C.

Therefore, the temperature of the water in the glass is 20.0°C after it has transferred 4,200 J of thermal energy to the ice cube.