Pls help due today!!!!! -

The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

\(((\bar p_{1} -\bar p_{2})\)±\(Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })\)

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±\(1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })\)

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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The upper and lower limits for the sample mean control chart are:

UCL = 6.66

LCL = 3.36

To calculate the upper and lower limits for the sample mean control chart, we need to use the given data and formulas.

Sample size (n) = 15

Sample mean values: 13.30, 3.16, 3.21, 3.30, 3.27, 3.20

Range values: 0.49, 1.41, 2, 3, 0.47, 14, 5, 6, 0.49, 0.46, 0.54

First, we calculate the average range (R-bar) using the range values:

R-bar = (Sum of ranges) / (Number of samples)

R-bar = (0.49 + 1.41 + 2 + 3 + 0.47 + 14 + 5 + 6 + 0.49 + 0.46 + 0.54) / 11

R-bar ≈ 2.86 (rounded to 2 decimal places)

Next, we use the average range (R-bar) to calculate the control limits for the sample mean chart:

Upper Control Limit (UCL) = X-double bar + A2 * R-bar

Lower Control Limit (LCL) = X-double bar - A2 * R-bar

Where X-double bar is the average of sample means and A2 is a constant based on the sample size (n). For n = 15, A2 is 0.577.

Calculating the average of sample means (X-double bar):

X-double bar = (Sum of sample means) / (Number of samples)

X-double bar = (13.30 + 3.16 + 3.21 + 3.30 + 3.27 + 3.20) / 6

X-double bar ≈ 5.01 (rounded to 2 decimal places)

Calculating the control limits:

UCL = 5.01 + 0.577 * 2.86 ≈ 5.01 + 1.65 ≈ 6.66 (rounded to 2 decimal places)

LCL = 5.01 - 0.577 * 2.86 ≈ 5.01 - 1.65 ≈ 3.36 (rounded to 2 decimal places)

Therefore, the upper and lower limits for the sample mean control chart are:

UCL = 6.66

LCL = 3.36

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The equation has no real solutions, the graph of (x^2 + 9)/x does not cross the x-axis. Hence, the area bounded by the given equations is 0.

To find the area of the region bounded by the graphs of the equations y = (x^2 + 9)/x, x = 1, x = 4, and y = 0, we can set up an integral and evaluate it. However, there seems to be a mistake in your calculation as the area cannot be negative.

Let's proceed with finding the correct area using integration:

We need to find the definite integral of the function y = (x^2 + 9)/x between the limits x = 1 and x = 4. Since the graph is below the x-axis for certain values of x, we'll split the integral into two parts to ensure we only consider the positive area.

First, let's find the area below the x-axis:

∫[1 to a] [(x^2 + 9)/x] dx

And the area above the x-axis:

∫[a to 4] [(x^2 + 9)/x] dx

We need to find the value of a where the function (x^2 + 9)/x crosses the x-axis. To find this, we set the numerator equal to zero:

x^2 + 9 = 0

x^2 = -9 (which has no real solutions)

Since the equation has no real solutions, the graph of (x^2 + 9)/x does not cross the x-axis. Hence, the area bounded by the given equations is 0.

Using a graphing utility to verify this result would also confirm that the region bounded by the given equations does not have any positive area.

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The area of the region bounded by the graphs of the equations is 14.793, calculated using calculus and definite integrals.

The area of the region is found by computing the definite integral of the function y = (x^2 + 9)/x from x = 1 to x = 4.

This is a calculation involving calculus and definite integrals.

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351,520,000   different license plates could there be in south carolina.

Choose the 3 positions where you put the letters:

C(6,3) = 6!/(3!3!) = 720/36 = 20

Then choose any letter for each of those positions:

263 = 17,576

Then choose any digit for each of the other positions:

103 = 1,000

Total number of license plates:

20 × 17,576 × 1,000 = 351,520,000

A digit is a part of a set that, when taken as a whole, makes up a numeration system. A digit is a number in that particular circumstance. The elements of the set 0 through 9 make up the digits in the decimal (base-10) Arabic numbering system.

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Answer:

14999.62

Step-by-step explanation:

Answer:

570

Step-by-step explanation:

I used the answer given to the problem and it was wrong my math teacher told me the answer was 570.

Answer:

40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The required equation of the directrix is y = 11.

For a parabola in standard form, y = a(x - h)^2 + k, the focus is located at the point (h, k + 1/(4a)) and the directrix is given by the equation y = k - 1/(4a).

Comparing the given equation, y = -1/20 (x - 3)^2 + 6, to the standard form, we have h = 3, k = 6, and a = -1/20.

So, the focus is located at the point (3, 6 + 1/(4*(-1/20))) = (3, 1).

To find the equation of the directrix, we can use the formula y = k - 1/(4a) with the values we have:

y = 6 - 1/(4*(-1/20)) = 6 + 5 = 11

Therefore, the equation of the directrix is y = 11.

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The inverse of 2 modulo 17 is 9.

To find an inverse of 2 modulo 17 by inspection, we have to try the values one by one like in hit and trial.

To do it by inspection, we shall multiply 2 with a number to get an answer 1 modulo 17. This means we have to find a number n such that:

\($n * 2 \equiv 1 \pmod {17}$\)

Let us try to multiply 2 with all the numbers 1 to 16 to find the inverse of 2 modulo 17:

\($2*1 = 2$\)  (mod 17)

\($2*2 = 4$\)  (mod 17)

\($2*3 = 6$\)  (mod 17)

\($2*4 = 8$\) (mod 17)

\($2*5 = 10$\) (mod 17)

\($2*6 = 12$\) (mod 17)

\($2*7 = 14$\) (mod 17)

\($2*8 = 16$\) (mod 17)

\($2*9 = 1$\) (mod 17)

\($2*10 = 3$\) (mod 17)

\($2*11 = 5$\) (mod 17)

\($2*12 = 7$\) (mod 17)

\($2*13 = 9$\) (mod 17)

\($2*14 = 11$\) (mod 17)

\($2*15 = 13$\) (mod 17)

\($2*16 = 15$\) (mod 17)

Since \($2 * 9 ≡ 1 \pmod{17}$\), the inverse of 2 modulo 17 is 9.

Therefore, the inverse of 2 modulo 17 is 9.

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Answer:

1/8 because 1/4 x 1/2 = 1/8

The equation of the parabola is x² - 8x + 16 = 0

To find the equation of the parabola with focus (4, -3) and directrix y = -3, we can use the definition of a parabola.

A parabola is the set of all points that are equidistant to the focus and the directrix.

The distance from a point (x, y) to the directrix y = -3 is simply the vertical distance between the point and the line, which is |y - (-3)| = |y + 3|.

The distance from a point (x, y) to the focus (4, -3) can be found using the distance formula:

d = √[(x - 4)² + (y + 3)²]

Since the point is equidistant to the focus and the directrix, we have:

d = |y + 3|

Squaring both sides, we get:

(x - 4)² + (y + 3)² = (y + 3)²

Simplifying, we get:

(x - 4)² = 0

Thus, the equation of the parabola is simply:

x² - 4x - 4x + 16 = 0

x² - 8x + 16 = 0

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Answer:

6 5/6 miles

Step-by-step explanation:

4 1/2 + 2 1/3

4+2=6

1/2+1/3

3/6+2/6=5/6

6 5/6 miles

Answer:

t = (D/C - 1) (100/r)

Step-by-step explanation:

D = C(1+rt/100)

D/C = 1 + rt/100

D/C - 1 = rt/100

D/C - 1 = t (r/100)

Therfore,

Therefore the last option is correct.

Answer: t = (D/C - 1) / r/100

Step-by-step explanation:

The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

A normal distribution has symmetrically distributed data that is skew-free. As one proceeds away from the center, values tend to decrease and tend to cluster more frequently in that area. The mean, mode, and median of a normal distribution are all equal measures of central tendency.

Given data:

X: height of seaweed.

X~N (μ;σ²)

 μ= 10 cm    

 σ= 2 cm

We will calculate the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

                P(X ≤ x) = 0.30

                P(X ≥ x) = 0.70

Now by using the standard normal distribution,

we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula

                       \(Z = \frac{X-\mu}{\sigma}\)

translates the Z value to the corresponding X value.

                    P(Z ≤ z) = 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

                    z= -0.52

Now you have to clear the value of X:

                  \(Z = \frac{X-\mu}{\sigma}\)

                  X= (Z * σ) + μ

                 X = (-0.52 * 2)

                     = 8.96

hence, the value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

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Answer:

Step-by-step explanation:

e^ lnx  = x

e^ ln5 = 5

e^ ln 3x = 3x

I think you get the idea... e is an inverse operation to ln  :o

Answer:

Simplify.

ln e =

✔ 1

ln e2x =

✔ 2x

ln 1 =

✔ 0

Simplify.

eln x =

✔ x

e ln 5 =

✔ 5

e ln 3x =

✔ 3x

Step-by-step explanation:

A) The formula for standard error is standard deviation / sqrt(n)standard error (to 4 decimals) = 0.0252/ sqrt(340) = 0.0013

B) Probability that the sample proportion will be within ±0.03 of the population proportion is 0.9796

C) Probability that the sample proportion will be within ±0.05 of the population proportion is 1

D) The probabilities in parts (b) and (c) will increase, and the confidence in the results will increase as well.

a) E(P): op = 0.39 and Standard error of the proportion (to 4 decimals) = 0.0252

Given, p = 0.39n = 340

Sample proportion = p = 0.39

The mean of the sampling distribution is equal to the population proportion; hence the mean is p = 0.39.

The standard deviation of the sampling distribution of the proportion is given by the formula sqrt [p (1-p) /n].

standard deviation (to 4 decimals) = sqrt [0.39 x 0.61 / 340] = 0.0252

The formula for standard error is standard deviation / sqrt(n)standard error (to 4 decimals) = 0.0252/ sqrt(340) = 0.0013

b) P(0.36< p < 0.42) = P(z< (0.42-0.39)/0.0013) - P(z< (0.36-0.39)/0.0013) = P(z<2.31) - P(z<-2.31) = 0.9898 - 0.0102 = 0.9796

Probability that the sample proportion will be within ±0.03 of the population proportion is 0.9796

c) P(0.34< p < 0.44) = P(z< (0.44-0.39)/0.0013) - P(z< (0.34-0.39)/0.0013) = P(z<3.85) - P(z<-3.85) = 1 - 0 = 1

Probability that the sample proportion will be within ±0.05 of the population proportion is 1

d) As we take larger sample sizes, the standard error decreases, which means the spread of the sampling distribution decreases. Therefore, the probabilities in parts (b) and (c) will increase, and the confidence in the results will increase as well.

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Answer:

\(m=\frac{-9}{4}\)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (9, 10)

Point (5, 19)

Step 2: Find slope m

The derivative of the function at the given point in the direction of A. f(x,y,z) = 9x - 2y - 4z, 47/7. so the correct option is 3.

Given the function:

f(x,y,z) = 9x-2y-4z, Also,  (4,-9,-6) and A = 3i - 6j - 2k

We need to find the derivative of the function in the direction of A.

Let's solve this problem step by step.

First, we need to find the gradient of the function.

Gradient of the function is defined as the vector consisting of partial derivatives of the function.

The gradient of the function is given by:

∇f(x, y, z) = [∂f/∂x, ∂f/∂y, ∂f/∂z]

∇f(x, y, z) = [9, -2, -4]

Therefore, the gradient of the function is ∇f(x, y, z) = [9, -2, -4]

A=3i-6j-2k.

|A| = √(3² + 6² + 2²) = 7

A becomes (3/7, -6/7, -2/7)

(9x - 2y - 4z) . (3/7, -6/7, -2/7)

(9, -2, -4)(3/7, 6/7, 2/7)

47/7

Therefore, the derivative of the function in the direction of A is 47/7.

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Answer: I think it is C

Step-by-step explanation: 32/4=8 so 1 cm = 8km

Answer:

slope is -2/5

y-intercept is 4

Answer:

See Below

Step-by-step explanation:

Ok, so slope intercept form is:

y = mx +b

Where m = slope and b = your y-intercept

lets line them up

   y = mx + b

y =-2/5 x + 4

Notice that the m and b are lined up each corresponding #.

Therefore,

m = -2/5

B = 4

Slope = -2/5

y - intercept = 4

Answer:

(y-y1)/(x-x1)=(y2-y1)/x2-x1)

(y-20)/(x-10)=(30-20)/(13-10)

......

now you can easily solve it

Two point form

Answer:

first option

Step-by-step explanation:

Using the sine/ cosine ratios in the right triangle and the exact values

sin30° = \(\frac{1}{2}\) , cos30° = \(\frac{\sqrt{3} }{2}\)

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{32}\) = \(\frac{1}{2}\) ( cross- multiply )

2x = 32 ( divide both sides by 2 )

x = 16

----------------------------------------------------------

cos30° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{y}{32}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2y = 32\(\sqrt{3}\) ( divide both sides by 2 )

y = 16\(\sqrt{3}\)

Answer:

45 Tokens

Step-by-step explanation:

3:5:7

Anya = 3

Daniel = 5

Victoria = 7

Daniel + Victoria = 36

5 + 7 = 36

12 = 36

1 = 3

(1 ratio is 3 tokens)

(3 + 5 + 7) × 3 = 45

Using Normal distribution,

Z-test statistic value for given sample is 1.92..

and there is no evidence to support the rejection of the null hypothesis at 1% significance level.

The Z-test is a statistical test performed on approximately normally distributed data..

We have given that

Sample mean (X) = 144

Standard deviations (σ) = 28

Sample size (n) = 80

population mean (μ) = 150

we want to calculate z statistic value for the provided data .

using formula, z = (X- μ)/σ/√n

z = (-150 +144)/28/√80 = 6/28/2√20

= - 1.9166 ~ - 1.92

Now we were asked that it gives us enough evidence to reject the null hypothesis. So we checking to look what the critical value is for rejecting. No hypothesis at alpha equals 0.01, so that would be the value such that the area under the curve right here is 0.01, and if we look up the z table and find out z critical value for alpha = 0.02 is - 2.32.. The negative 1.92 is not passing that threshold, which means that, since it is not less than the significance level z value negative 1.92 is not less than the negative 2.32, which is a significance, level z, value. So, we can't reject the null hypothesis.

Hence, the Z-test statistic value is -1.92 and no evidence to support the rejection of null hypothesis.

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Complete question

Consider the following hypotheses: H0: μ ≥ 150 HA: μ < 150 a sample of 80 observatoins results in a sample mean of 144. the population standard deviation is known to be 28.

calculate the value of the test statistic. does the above sample evidence enable us to reject the null hypothesis at 1% significance level?

Answer:

149

Step-by-step explanation:

JUST TOOK TEST

Answer:

149

Step-by-step explanation:

Answer:

Step-by-step explanation:

Time intervals = 14/7 = 2

Final Amount = 40(1/2)² = 10