4x^2+2x-1=0 in quaratic equations

Answer:

Step-by-step explanation:

The three ways to write a ratio is:

8/4

8 to 4

8:4

The ratio in simpliest form is 2/1

You would divide each "side" by 4

Therefore, the number of bacteria after 200 minutes can be found by multiplying the initial number of bacteria (450) by the tripling factor (3) raised to the power of 2 (for the full cycles) and multiplying by the remaining fraction of the tripling factor for the partial cycle.

Since the bacteria triples every 3 hours, we can calculate the number of tripling cycles that have occurred in 200 minutes. Since 3 hours is equivalent to 180 minutes, there are 2 full cycles in 200 minutes. To calculate the remaining fraction of the tripling cycle, we divide the remaining time (20 minutes) by the length of a single cycle (180 minutes). The fraction is 20/180, which simplifies to 1/9.

Now, we can calculate the number of bacteria after 200 minutes. We start with the initial number of bacteria, which is 450, and multiply it by the tripling factor (3) raised to the power of the number of full cycles (2). This accounts for the full cycles. Then, we multiply this result by the remaining fraction of the tripling factor (1/9) to account for the partial cycle.

Therefore, the number of bacteria after 200 minutes can be calculated as follows:

Number of bacteria = 450 * (3^2) * (1/9) = 450 * 9 * (1/9) = 450

Hence, after 200 minutes, there will still be 450 bacteria.

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Answer:

c. 60

Step-by-step explanation:

Given

[tex]n = 61[/tex] --- sample

[tex]\bar x = 23[/tex]

Required

Determine the degrees of freedom (df)

This is calculated as:

[tex]df = n - 1[/tex]

[tex]df = 61 - 1[/tex]

[tex]df = 60[/tex]

Answer:

.

Step-by-step explanation:

i dont know this i really hard

Answer: 2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

4(3n+2b+k)

12n+8b+4k

So it would be C.

---

hope it helps

Answer:

Rhombus Square

Step-by-step explanation:

Answer:

i can't see clear

Answer:

it would be A

Step-by-step explanation:

you have to find angle C first so you would subtract 105 from 180 to get 75 and then to find angle B you would add 75 and 55 to get 130 and since its a triangle it always has 180 degrees so do 180 - 130 to get 50

The observed z value can be calculated as (sample mean - population mean) / standard error of the mean, which in this case is -0.5. Hence, option a is correct.

The observed z value measures how many standard errors the sample mean is away from the population mean. The sample mean is 15 and the population mean is 20 and the standard error mean is 10.

Subtracting the population mean from the sample mean, we get -5. Dividing -5 by 10, we find that the observed z value is -0.5. Therefore, the observed z value is -0.5, which corresponds to option (a).

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Slope is the change in y over the change in x

1. (1,1) and (4,5)

Slope = (5-1)/(4-1)

Slope = 4/3

2. (2,-1) and (4,13)

Slope = (13 - -1)/ (4-2)

Slope = 14/2

Slope = 7

3. (1,18) and (-9,-2)

Slope = (-2 -18)/(-9 -1)

Slope = -20/-10

Slope = 2

Answer:

69-43= 26

therefore "U" is worth 26 U=26

Step-by-step explanation:

Answer:

its 26, because whaen u subtract 43 from 69 u will get 26

Answer: b

Step-by-step explanation: When you rotate it around the axis (think of it as a pole) it will become a cylinder with radius 5

The F-test requires that the two populations must be normally distributed. Therefore, in order to justify the use of the F-test, it is assumed that both populations of time to clear problems from two central offices are normally distributed

a. At the 0.05 level of significance, is there evidence of a difference in the variability of the time to clear problems between the two central offices?

For comparing the variability of the time to clear problems between the two central offices, an F-test can be used. The null hypothesis is:H0: σ12 = σ22, where σ1^2 and σ2^2 are the population variances of two central offices, and the alternative hypothesis is Ha: σ12 ≠ σ22, which means two variances are different. For this study, the significance level is 0.05. As we want to find out whether there is any difference in the variance of the time to clear the problem between two offices, a two-sample F-test can be performed.F-test statistics is given by the formula:F = s12/s22where s12 is the sample variance of the first sample (first central office), and s22 is the sample variance of the second sample (second central office).We can use Excel to calculate the F statistic.Using the given dataset, the F statistic is calculated as: σ12 = 22.66666667, σ22 = 25.25, F = 0.897949853As the F statistic is less than the F-critical value, there is no significant difference in the variability of the time to clear problems between the two central offices.b. Interpret the p-value.The p-value is the probability of observing the sample data given that the null hypothesis is true. If the p-value is less than the level of significance (α = 0.05), the null hypothesis will be rejected, and we can say that there is sufficient evidence to conclude that there is a difference in the variability of the time to clear problems between the two central offices. The p-value of this F-test is 0.467. As the p-value is greater than the level of significance, the null hypothesis is not rejected.c. What assumption do you need to make in (a) about the two populations in order to justify your use of the F test?

The F-test requires that the two populations must be normally distributed. Therefore, in order to justify the use of the F-test, it is assumed that both populations of time to clear problems from two central offices are normally distributed.

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The data set contains samples of 20 problems.

Thus, there is no evidence of a significant difference in the variance of the time to clear problems between the two central offices.

The p-value is 0.17.

Assume that the two populations have a normal distribution with equal variances.

a. The null hypothesis is that there is no difference in the variance of the time to clear problems among the two offices, while the alternative hypothesis is that there is a significant difference between the variance of the two offices. Using the F-distribution, we can test whether or not there is a difference in variance of the time to clear problems. The formula for F-value is given below:

F-value = s1^2 / s2^2

Where s1^2 and s2^2 are the variances of the two samples. With the help of the provided data, we can calculate the variances for the two samples, which are as follows:

s1^2 = 42.08

s2^2 = 22.80

Then, we can calculate the F-value as follows:

F = s1^2 / s2^2

= 42.08 / 22.80

= 1.84

Using the F-distribution table, we can find the critical value of F as 2.17 (with 19 degrees of freedom for both the numerator and denominator).Since the calculated F-value (1.84) is less than the critical value of F (2.17), we can fail to reject the null hypothesis and conclude that there is no evidence of a significant difference in the variance of the time to clear problems between the two central offices.

b. The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true. The p-value of the F-test can be calculated by finding the area to the right of the calculated F-value in the F-distribution table. In this case, the p-value is 0.17 (using a two-tailed test).

c. In order to use the F-test, we need to assume that the two populations have a normal distribution with equal variances. Furthermore, the samples should be independent and randomly selected. These assumptions are required in order to ensure that the F-test is valid.

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The values of b = 0 or a = -3 -  such that zw is real, letting z = 3+ bi and w = a + bi where a, b E R.

To determine the value of b in terms of a such that zw is real, we first need to find zw. Using the distributive property, we have:

zw = (3 + bi)(a + bi)

zw = 3a + 3bi + abi - b^2

To make zw real, the imaginary part must be equal to zero. Therefore, we have:

3b + ab = 0

b(3 + a) = 0

Since b cannot be equal to zero (otherwise z and w would be real), we have:

a = -3

Therefore, b = 0 or a = -3 - this is the value of a such that zw is real.

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a) The probability that the team wins the championship is approximately 0.0141 or 1.41%. b) The probability that the team does not win the championship is approximately 0.9859 or 98.59%.

a) To determine the probability that the team wins the championship, we need to convert the odds against winning into a probability.

The odds against winning are given as 70:1. This means that for every 70 unfavorable outcomes (losing), there is 1 favorable outcome (winning).

To calculate the probability of winning, we divide 1 by the sum of the favorable and unfavorable outcomes:

Probability of winning = 1 / (70 + 1) = 1 / 71 ≈ 0.0141 (or 1.41%)

Therefore, the probability that the team wins the championship is approximately 0.0141 or 1.41%.

b) The probability of not winning the championship is equal to 1 minus the probability of winning:

Probability of not winning = 1 - 0.0141 = 0.9859 (or 98.59%)

Therefore, the probability that the team does not win the championship is approximately 0.9859 or 98.59%.

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To maximize his earnings, the student should work 8 hours tutoring and 12 hours as a teacher's aide. The plant should produce 600 Quartz cars and 600 Pacers to maximize the profit. The maximum profit is $660,000.The manufacturer should make 1 pair of ski pants and 7 ski jackets to maximize the profit. The maximum profit is $29.00.

Part A:

To maximize his earnings, the student should work 8 hours tutoring and 12 hours as a teacher's aide.

The maximum profit is $786.00.

Part B:

Let's say, the plant make x number of Quartz and y number of Pacers.

Therefore, x + y = 1200 ----(1)

and, 500x + 800y = Profit Maximize.

Let's multiply Equation (1) by -500 and add it to Equation (2) so that we can solve for

y. -500x - 500y = -600000500x + 800y = Profit Maximize-300y = -180000 ⇒ y = 600

Therefore, x = 600

Hence, the plant should produce 600 Quartz cars and 600 Pacers to maximize the profit. The maximum profit is $660,000.

Part C:

Let's say, the manufacturer should make x pairs of ski pants and y ski jackets.

Therefore, the system of linear equations are as follows:

8x + 4y ≤ 60 (sewing operator time)4x + 8y ≤ 45 (cutter time)

Let's plot the graph to solve the linear equations. The feasible region is shaded in the following graph:

To find the maximum profits, we need to check all the coordinates of the feasible region.

8(1) + 4(7) = 368(2) + 4(6) = 242(3) + 4(5) = 224(5) + 4(4) = 20

Profit for (1,7) = $29.00

Profit for (2,6) = $26.00

Profit for (3,5) = $23.00

Profit for (5,4) = $18.00

Therefore, the manufacturer should make 1 pair of ski pants and 7 ski jackets to maximize the profit. The maximum profit is $29.00.

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The proof of 2ⁿ (-1 + i√3)ⁿ + (-1 - i√3)ⁿ can be expressed as  2ⁿ⁺¹cos(πn/3) is proved below.

To express (-1 + i√3) and (-1 - i√3) in exponential form, we can use Euler's formula, which states that [tex]e^{(i\theta)[/tex] = cos(θ) + isin(θ).

Let's start with (-1 + i√3):

(-1 + i√3) = 2 x (cos(π) + i x sin(π/3))

Now, let's simplify (-1 - i√3):

(-1 - i√3) = 2 (cos(π) - isin(π/3))

Therefore, we have:

(-1 + i√3) = 2  e^(iπ/3)

(-1 - i√3) = 2  e^(-iπ/3)

Now, let's substitute these exponential forms into the expression:

2ⁿ  (-1 + i√3)^n + (-1 - i√3)^n

= 2ⁿ(2  e^(iπ/3))^n + (2  e^(-iπ/3))^n

= 2ⁿ⁺¹  e^(iπn/3) + 2^(n+1) e^(-iπn/3)

Using Euler's formula again, we know that [tex]e^{(i\theta)} + e^{(-i\theta)[/tex] = 2cos(θ).

Therefore, we can rewrite the expression as:

2ⁿ⁺¹ (cos(πn/3) + cos(-πn/3))

=  2ⁿ⁺¹(cos(πn/3) + cos(πn/3))

=  2ⁿ⁺¹ 2  cos(πn/3)

=  2ⁿ⁺¹cos(πn/3)

So, we have shown that  2ⁿ (-1 + i√3)ⁿ + (-1 - i√3)ⁿ can be expressed as  2ⁿ⁺¹cos(πn/3).

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Answer:

696.348

Step-by-step explanation:

Answer:

14.5

Step-by-step explanation:

Answer:

so you multiply 12 by 8 =96

Answer:

area of large circle=pi×r²

area of large circle =3.14×12²

area of large circle=452.16in²

area of small circle=pi×r²

area of small circle=3.14×8²

area pf small circle=200.96in²

area of shaded circle=452.16in²- 200.96in²

area of shaded circle =251.2in²

Where the above is given,

Range

Range = Maximum value - Minimum value

Range = 2.50 - 0.01

= 2.49 inches

Sample Variance

Step 1  - Calculate the mean (average) of the data.

Mean = (0.47 + 0.27 +0.13 + 0.54 + 0.08 + 1.05 + 0.34 +   0.26 + 0.42 + 0.17 + 0.50 + 0.86 + 0.01 + 2.5) / 14

= 1.36 /14

= 0.0971

Step 2  - Calculate the squared deviation from the mean for each data point.

Deviation from mean = Data point - Mean

Squared deviation = (Deviation from mean)²

Sum of squared deviations = (0.3739 + 0.0091 + 0.7307 + 0.1638 + 0.9469 + 0.104 + 0.0145 + 0.0081 + 0.0971 + 0.3037 + 0.0601 + 0.2601 + 1.0679 +   3.1391)

= 7.2799

Sample Variance = Sum of squared deviations / (n - 1)

= 7.2799/ (14 - 1)

= 0.5599

Sample Standard Deviation:

Sample Standard Deviation = √(Sample Variance)

= √0.5599

= 0.7483

Coefficient of Variation:

Coefficient of Variation = (Sample Standard Deviation / Mean) * 100

= (7.2799/ 0.0971) * 100

= 7497.32

Z-Scores for each data point

Z1= (0.47   - 0.0971)/ 0.7212= 0.5318

Z2= (0.27   - 0.0971)/ 0.7212= 0.9983

Z3= (0.13   - 0.0971)/ 0.7212= 0.0456

Z4= (0.54   - 0.0971)/ 0.7212= 0.6189

Z5= (0.08   - 0.0971)/ 0.7212=   -0.0251

Z6= (1.05   - 0.0971)/ 0.7212= 1.2914

Z7= (0.34   - 0.0971)/ 0.7212= 0.4574

Z8= (0.26   - 0.0971)/ 0.7212= 0.2251

Z9= (0.42   - 0.0971)/ 0.7212= 0.4969

Z10= (0.17   - 0.0971)/ 0.7212= 0.1002

Z11= (0.50   - 0.0971)/ 0.7212= 0.6506

Z12= (0.86   - 0.0971)/ 0.7212= 1.0242

Z13= (0.01   - 0.0971)/ 0.7212=   -0.1208

Z14= (2.50   - 0.0971)/ 0.7212= 3.3999

To determine   if there are any outliers, we can compare the absolute values of the Z-Scores to a certain threshold , commonly considered as 2.

If the absolute value of a Z-Score is greater than 2,   it indicates that the corresponding data point is an outlier.

In this case,   Z14 = 3.3999, which is greater than 2 , suggesting that the data point 2.50 inches may be considered an outlier based on the Z-Score criterion.

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a) Var[M9(X)] = 25/9.

b) P[X > 7] = exp(-7/5).

c) P[Z < 2/5] = 0.3446.

Given information: X1, . . . , Xn is an iid sequence of exponential random variables, each with expected value 5.

(a) We know that the sample mean based on nine trials is M9(X). Now, to calculate the variance of the sample mean based on nine trials, Var[M9(X)], we can use the formula for the variance of a sample mean, which is:

Var[M9(X)] = Var[X]/9  .

Since X is an exponential random variable with expected value 5, its variance is 5^2 = 25. Thus,Var[M9(X)] = 25/9.

(b) To find P[X * 1 > 7], we can use the probability density function of an exponential distribution, which is given by:

f(x) = 1/5 exp(-x/5), x > 0  .

Now, using this probability density function, we have:

P[X > 7] = ∫7∞f(x) dx= ∫7∞ 1/5 exp(-x/5) dx.

Using integration by substitution, with u = x/5 and du = (1/5)dx, we have:

P[X > 7] = ∫7/5∞ exp(-u) du= exp(-7/5).

(c) Since we know that X1, . . . , Xn is an iid sequence of exponential random variables, each with expected value 5 and variance 25, we can apply the central limit theorem. According to the central limit theorem, the sample mean M9(X) is approximately normally distributed with mean 5 and variance 25/9. Thus, we have:

P[M9(X) > 7] = P[Z > (7-5)/(5/3)] where Z is a standard normal random variable. This simplifies to:

P[M9(X) > 7] = P[Z > 2/5] = 1 - P[Z < 2/5]

Using the standard normal distribution table or calculator, we get:

P[Z < 2/5] = 0.6554P[M9(X) > 7] = 1 - P[Z < 2/5] = 1 - 0.6554 = 0.3446.

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The equation [tex]ax(t) = -(18 m/s^2)cos(33t)[/tex] describes the acceleration of an oscillator. The acceleration varies sinusoidally with time, following a cosine function, and has a maximum value of [tex]-18 m/s^2[/tex].

The given equation [tex]ax(t) = -(18 m/s^2)cos(33t)[/tex] represents the acceleration of an oscillator undergoing simple harmonic motion. In this equation, t represents time measured in seconds.

The term cos(33t) indicates that acceleration varies sinusoidally with time. The cosine function has a period of 2π, meaning it completes one full cycle over the interval [0, 2π]. The coefficient 33 in front of t determines the frequency of oscillation. In this case, the oscillator completes approximately 33 cycles per second.

The negative sign indicates that the acceleration is directed opposite to the displacement of the oscillator. As the oscillator moves in one direction, the acceleration pulls it back in the opposite direction, causing it to oscillate around a stable equilibrium position.

The maximum acceleration is given by [tex]-18 m/s^2[/tex], which represents the amplitude of the oscillation. The acceleration varies between [tex]-18 m/s^2[/tex] and [tex]18 m/s^2[/tex], with the maximum magnitude occurring when the cosine function is at its peak value of 1 or -1.

Overall, the equation describes the acceleration of an oscillator undergoing simple harmonic motion, providing information about its amplitude, frequency, and direction of motion.

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Answer:

rectangle

Step-by-step explanation:

A rectangle represents a figure with four sides having equal opposite sides and the inside angle between the two adjacent sides is ninety degree.

When any plane is made to pass through the cylinder creating a cross section which is perpendicular to its base, it results a two-dimensional cross sectional shape of a rectangle.

Answer:

The statement that best describes how the author of "The Train to Somewhere" alters historical details to tell her story is option B;

B. The author describes the experiences and feelings of an imaginary orphan who was sent west on an orphan train

Step-by-step explanation:

The author included the experiences of one of the children who according to the historical details in the historical account of the Orphan Train Riders were aided by the minister, Charles Loring Brace, to be taken from the New York City streets on the East to other states and Canada to the West

The child, a 5 year old girl, who had lost both parents had been living on the street with her brother for some months

The author also highlighted the taught by the child, of being separated from her brother at one of the destination towns of the train, and the manifestation of the beliefs of the minister, Brace, of the children finding loving families that would help them become productive members of society.

Answer : The edible portion cost for the orange juice for this brunch is $9.6.

Explanation :

GivenData:                                                                                                                                                                                               Cost of each case = $24                                                                                                                                                                    Number of oranges in each case = 100                                                                                                                                                              Weight of each orange = 6 ounces                                                                                                                                                                Yield percentage of each orange = 50%                                                                                                                                                         Amount of orange juice required = 3 liters                                                                                                                                           Formula used:To find the edible portion cost of orange juice, we need to find the cost per liter of orange juice and then multiply it by the required amount of orange juice.

Edible portion cost = (Cost per liter of orange juice) × (Amount of orange juice required)                                                                                     Cost per liter of orange juice = (Cost of 100 oranges) / (Yield of 100 oranges)Cost of 100 oranges = Cost of each case = $24                                                                                                                                                                                                             Therefore, Cost per liter of orange juice = (24) / [(50/100) × 100 × (6/16)]{Converting 6 ounces into liters by multiplying with 0.0166667}Cost per liter of orange juice = $3.20                                                                                                           Edible portion cost = (Cost per liter of orange juice) × (Amount of orange juice required)Edible portion cost = (3.2) × (3) = $9.6                                                                                                                                                                                                                                                                                                     Therefore, the edible portion cost for the orange juice for this brunch is $9.6.

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It could be in quadrant I or III

Since I is all positive and III is all negative

Answer:

D

Step-by-step explanation:

6x7x4= 168

Answer:

About 11%

Step-by-step explanation:

45 divided by 5 = 9

100 divided by 9 = 11.11111 (It goes on forever)