The numbers 6+5i and 6-5i, which differ only in the sign of their imaginary parts are?

-If the null hypothesis is: Mu = 350, the corresponding alternative hypothesis for a two-sided test is: Mu ≠ 350.
-To calculate the t-statistic, use the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt (sample size)).

In this case: t = (342 - 350) / (16 / sqrt(24))
t = -8 / (16 / 4.898)
t = -8 / 3.265
t ≈ -2.45
3.) To calculate the critical value for a two-sided test with an alpha level of 0.05, you need to find the t-value corresponding to 0.025 in each tail (since 0.05/2 = 0.025) and degrees of freedom (df) = sample size - 1 = 24 - 1 = 23. Using a t-table or calculator, the critical value is approximately ±2.069.
4.) The conclusion of our test is based on comparing the calculated t-statistic (-2.45) with the critical value (±2.069). Since -2.45 is less than -2.069, we reject the null hypothesis. This indicates that there is a significant difference between the average weight of the sampled green sea turtles and the known average weight of 350 pounds.

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Answer:

n≥-5

Step-by-step explanation:

-3n+2≥-4n-3

add 4n on both sides

n+2≥-3

subtract 2 on both sides

n≥-5

Answer:

-7n-1 isthe answer :)  = too ....

Step-by-step explanation:

Answer:

x = 1 8/9 or 17/9

Step-by-step explanation:

Step 1: Add 7 to both sides.

Step 2: Divide both sides by 9.

#10

The vertical angles are formed when two lines intersected at a point

The vertical angles are equal in measures

Let us draw a sketch for them

Lines AB and CD intersected at point M

, then

m

To draw an accurate drawing do these steps

1. Draw the line AB

2. Put point M in any place on it

3. Put the vertex of the protractor at the point M, then read the degrees from the right to left till 55, then put a point label it C

4. Draw a line passes through points M and C

5. Label the endpoint of this line D

6. Label the measures of the angles by 55 degrees

Now, you can draw the vertical angles with a measure of 55 degrees

Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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Answer:

there are a total of 20 boys and 30 girls in the choir of 50 students

Step-by-step explanation:

Scale the ratio 2:3. so that the numbers on either side sum to 50 . 2+3=5 , and 50÷5=10 , so we scale our ratio by a factor of 10 . So there are a total of 20 boys and 30 girls in the choir of 50 students

Answer:

63

Step-by-step explanation:

k=y/x

y/x=k

y=k×x

y=7×9

y=63

Answer:40

Step-by-step explanation:

100+10+10=3x

3x=120

Divide both sides by 3

X=40

Answer:

40

Step-by-step explanation:

add 100+10+10 and divide it by 3

(a) The system described by the equation y(t) = 133x(t) + 2.05 - 2 is linear and time-invariant but not causal.

To determine linearity, we check if the system satisfies the superposition property. Given inputs x1(t) and x2(t) with corresponding outputs y1(t) and y2(t), let's denote the system as H. We have:

H[x1(t) + x2(t)] = 133[x1(t) + x2(t)] + 2.05 - 2 = 133x1(t) + 133x2(t) + 2.05 - 2

On the other hand, H[x1(t)] + H[x2(t)] = (133x1(t) + 2.05 - 2) + (133x2(t) + 2.05 - 2) = 133x1(t) + 133x2(t) + 2.05 - 2

Since H[x1(t) + x2(t)] = H[x1(t)] + H[x2(t)], the system satisfies the superposition property and is linear.

To determine time-invariance, we check if a time shift in the input results in an equivalent time shift in the output. Let's consider a time shift δ:

H[x(t - δ)] = 133x(t - δ) + 2.05 - 2

If we compare this to the original equation y(t) = 133x(t) + 2.05 - 2, we can see that the shift δ is applied in both cases. Therefore, the system is time-invariant.

To determine causality, we need to check if the output y(t) depends only on the past and present values of the input x(t). In this case, we see that the output y(t) depends on the future value x(t + 1) due to the term 2. Therefore, the system is not causal.

The system described by y(t) = 133x(t) + 2.05 - 2 is linear, time-invariant, but not causal.

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Answer:

m = 36

Step-by-step explanation:

.................

Answer:

yes it has a right angle

Step-by-step explanation:

Answer:

198 in²

Step-by-step explanation:

triangle (A=1/2)bh [A=1/2(22×8)] b=22 H=8

rectangle (A=bh) [A= 22×5] B=22 H=5

triangle = 88

rectangle = 110

So, 88+110 = 198

On average, students using method 1 score between 6.46 and 11.94 points higher than students using method 2.

To find the critical value for constructing the 95% confidence interval, we need to use a t-distribution since the sample sizes are relatively small and the population standard deviations are not known.

The degrees of freedom for the t-distribution can be calculated using the following formula:

df = [(s1^2/n1 + s2^2/n2)^2] / [((s1^2/n1)^2)/(n1-1) + ((s2^2/n2)^2)/(n2-1)]

where s1 and s2 are the standard deviations for method 1 and method 2, n1 and n2 are the sample sizes for method 1 and method 2, and df represents the degrees of freedom.

Substituting the given values, we get:

df = [(5.87^2/169 + 17.66^2/128)^2] / [((5.87^2/169)^2)/(169-1) + ((17.66^2/128)^2)/(128-1)]

= 249.00

Using a t-table with 249 degrees of freedom and a 95% confidence level, we find the critical value to be 1.971.

Therefore, to construct the 95% confidence interval for the true difference between testing averages for students using method 1 and students using method 2, we can use the following formula:

CI = (x1 - x2) ± t*(sqrt(s1^2/n1 + s2^2/n2))

where x1 and x2 are the sample means for method 1 and method 2, s1 and s2 are the standard deviations for method 1 and method 2, n1 and n2 are the sample sizes for method 1 and method 2, and t is the critical value we just calculated.

Substituting the given values, we get:

CI = (81.7 - 72.5) ± 1.971*(sqrt(5.87^2/169 + 17.66^2/128))

= 9.2 ± 2.74

= (6.46, 11.94)

Therefore, we can be 95% confident that the true difference between the mean testing scores for method 1 and method 2 lies between 6.46 and 11.94.

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Answer:

x = 12

Step-by-step explanation:

x² = 24 x 6 = 144

x = 12

These cycles are known as the eccentricity cycles, and they are one of the factors that contribute to the long-term climate variations on Earth

The aspect of Earth's orbital relationship to the Sun that varies with a periodicity of both 400 Ka and 100 Ka is the eccentricity of Earth's orbit. The eccentricity refers to the shape of Earth's orbit around the Sun, which is not a perfect circle, but an ellipse. The eccentricity of Earth's orbit changes over time due to gravitational interactions with other planets, particularly Jupiter and Saturn. When Earth's orbit is more elliptical, its distance from the Sun varies more throughout the year, leading to variations in climate and the amount of solar radiation received on Earth's surface. The periodicity of 400 Ka corresponds to a cycle of variations in Earth's eccentricity that affects the amount of solar radiation received at different latitudes and the distribution of ice ages. The periodicity of 100 Ka corresponds to a cycle of variations in Earth's eccentricity that affects the intensity of the seasons and the distribution of glacial periods. These cycles are known as the eccentricity cycles, and they are one of the factors that contribute to the long-term climate variations on Earth.

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Answer:

15 packs of crayons and 20 packs of pens

Step-by-step explanation:

you have to the multiply the amount that comes in each pack together

Answer:

3^16

Step-by-step explanation:

The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%

The proportion of customers that buy a magazine = 8.4%

If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%

Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;

probability = 8.4% × 27.27%

probability = (8.4/100) × (27.27/100)

probability = 0.084 × 0.2727

probability = 0.0223

Converting it into percentage as follows;

probability = 0.0223 × 100

probability = 2.23%

Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.

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To determine the 95% energy bandwidth (B) of the signal g(t) = [0.5sinc²(0.5 t) cos(2 t)], we can apply Parseval's Theorem. Parseval's Theorem states that the total energy of a signal in the time domain is equal to the total energy of the signal in the frequency domain. Mathematically, it can be expressed as:

∫ |g(t)|² dt = ∫ |G(f)|² df

In this case, we want to find the frequency range within which 95% of the energy of the signal is concentrated. So we can rewrite the equation as: 0.95 * ∫ |g(t)|² dt = ∫ |G(f)|² df

Now, we need to evaluate the integral on both sides of the equation. Since the given signal is in the form of a product of two functions, we can separate the terms and evaluate them individually. By applying the Fourier transform properties and integrating, we can find the value of B.

For part (b), when we consider g(2t), the time domain signal is compressed by a factor of 2. This compression results in a corresponding expansion in the frequency domain. Therefore, the 95% energy bandwidth of g(2t) will be twice the value of B determined in part (a). This can be justified by considering the relationship between time and frequency domains in Fourier analysis, where time compression corresponds to frequency expansion and vice versa.

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The constant of proportionality in the equation:

P = 0.45*n

Is k = 0.45, so we can conclude that Julie is correct.

A proportional relationship between two variables x and y is written as:

y = k*x

Where k is the constant of proportionality.

In this case, we have the variables P and n, and the proportional relationship is:

P = 0.45*n

So we can see that the value of the constant of proportionality is k = 0.45, so yes, Julie is correct.

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The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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If you work for the company for 5 years, you will earn approximately $44,925.

To calculate the total earnings after working for the company for 5 years with a 3% raise each year, we need to determine the salary for each year and then sum them up.

In the first year, you will earn $38,900. For subsequent years, you will receive a 3% raise on the previous year's salary. This means that each year's salary will be the previous year's salary multiplied by 1.03.

Year 1: $38,900

Year 2: $38,900 × 1.03 = $40,067

Year 3: $40,067 × 1.03 = $41,270.01 (rounded to the nearest dollar: $41,270)

Year 4: $41,270 × 1.03 = $42,504.10 (rounded to the nearest dollar: $42,504)

Year 5: $42,504 × 1.03 = $43,771.12 (rounded to the nearest dollar: $43,771)

To calculate the total earnings, we add up the salaries for each year:

Total earnings = Year 1 salary + Year 2 salary + Year 3 salary + Year 4 salary + Year 5 salary

Total earnings = $38,900 + $40,067 + $41,270 + $42,504 + $43,771

Total earnings ≈ $206,512

Therefore, if you work for the company for 5 years, you will earn approximately $206,512. Rounded to the nearest dollar, this is approximately $44,925.

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Answer:

2.05 cm

Step-by-step explanation:

3.14× (n+3)²×10 = 800

31.4(n+3)²=800

(n+3)²= 800/31.4

(n+3)²= 25.48

n+3 =√25.48

n+3= 5.05

n = 5.05 -3 = 2.05

so, the radius should be increased :

2.05 cm

The balance sheet that correctly represents the engineer's income, expenses and balance is illustrated below.

We should know that a balance sheet is a summary of assets and liabilities and income and expenses of a  legal person. We are told that the balance sheet shows a bi-weekly net pay.

This implies that a month has two bi-weeks, therefore every income and expense is multiplied by 2 to get the following figures.

Income                                             Amount

Bi-weekly income                          $2,175.25

Total Monthly Income                   $4,350.50

Expenses                 Percent                              Amount

Housing                        35%                                $1,522.68

Food/Household          10%                               $435.05

Savings                         10%                                $435.05

Transportation              15%                                $652.58

Debt                              5%                                   $217.53

Entertainment               6%                                   $261.03

Medical/Personal Care 5%                                  $217.53

Giving                             5%                                 $217.53

Clothing                         4%                                  $174.02

Miscellaneous               5%                                 $217.53

                                                                          $4,350.50

Balance

Income $4,350.50

Expenses $4,350.50

Balance $0

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The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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Answer:

Step-by-step explanation: