When 6 is substituted for the value of n, which expression has a value of 44?

Based on the hypothesis test, we fail to reject the null hypothesis that the standard deviation of hole diameter is less than or equal to 0.02 mm. Therefore, there is not enough evidence to indicate that the standard deviation of hole diameter exceeds 0.02 mm.

To test whether there is strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 mm, we can use a hypothesis test.

Let's assume that the hole diameter measurements follow a normal distribution. Then, the null hypothesis is that the standard deviation of the hole diameter, σ, is less than or equal to 0.02 mm

H0: σ ≤ 0.02

The alternative hypothesis is that the standard deviation of the hole diameter is greater than 0.02 mm

Ha: σ > 0.02

We can use a chi-square distribution with n-1 degrees of freedom to test this hypothesis. The test statistic is calculated as

χ2 = (n-1) × s^2 / σ^2

where s is the sample standard deviation, σ is the hypothesized population standard deviation (0.02 mm), and n is the sample size (15).

Plugging in the numbers, we get:

χ2 = (15-1) × 0.016^2 / 0.02^2 ≈ 4.08

The corresponding p-value for this test statistic can be found using a chi-square distribution with 14 degrees of freedom. Using a calculator or statistical software, we find that the p-value is approximately 0.931.

Since the p-value is much greater than the significance level (α = 0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the standard deviation of hole diameter exceeds 0.02 mm.

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Answer:

5301

Step-by-step explanation:

There are 9 companies that needed to print 589 coupons each. Multiply the two numbers:

9 * 589 = 5301

Answer:

Always true

Step-by-step explanation:

Three Planes Intersecting in a Line, Three Parallel Planes.

========================================================

Explanation:

We'll need the slope first

m = slope

m = (y2-y1)/(x2-x1)

m = (0-(-4))/(-3-(-5))

m = (0+4)/(-3+5)

m = 4/2

m = 2

The slope is 2.

Next, pick either of the two given points to play the role of \((x_1,y_1)\)

Let's say we picked on (-5,-4). The order doesn't matter so you could easily pick the other point as well.

We'll plug these items into the point slope equation below to solve for y.

\(y - y_1 = m(x - x_1)\\\\y - (-4) = 2(x - (-5))\\\\y + 4 = 2(x +5)\\\\y + 4 = 2x +10\\\\y = 2x +10-4\\\\y = 2x +6\\\\\)

Or we could have picked on (-3,0). The m value stays the same (at m = 2)

\(y - y_1 = m(x - x_1)\\\\y - 0 = 2(x - (-3))\\\\y = 2(x +3)\\\\y = 2x+6\\\\\)

This one takes a few less steps. Either way, we get to the same answer.

You only need to pick one of the points, but doing both of them helps show that the two points are on the same line. It helps confirm the answer.

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

Another way to check the answer is to plug the (x,y) coordinates into y = 2x+6 for each point.

So let's say we check (x,y) = (-5,-4)

y = 2x+6

-4 = 2(-5)+6 ... replace x with -5, replace y with -4

-4 = -10+6

-4 = -4

This confirms the first point. I'll let you check the second point.

Answer:

y = 2x+6

Step-by-step explanation:

Attached below is my graph

I graphed the two points, and formed a line

From the point (0,0), i counted the units till the first point the line touches on the y axis (6)

This is the y intercept

The slope-intercept form is written as y = mx+b

m = slope

b = y intercept

So so far we have y = mx + 6

The slope is the rise to the next point the line touches, over the run

You can see that as it rises 2, it runs 1

Rise / Run = 2/1 = 2

Slope = 2

Equation: y = 2x + 6

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

To construct a 98% confidence interval,  the critical value is 2.624.

We have,

98% Confidence Interval

Sample size, n= 15

At 98%,

Degree = n-1

             = 15-1= 14

So, For a 98% confidence level with 14 degrees of freedom, the critical value is 2.624.

Therefore, to construct a 98% confidence interval, the critical value is 2.624.

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The Maclaurin series expansion of f(x) is: f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

To find the coefficients of the series, we need to evaluate the derivatives of f(x) at x = 0. Let's find the first few derivatives:

f(x) = (9x)arctan(5x^2)

f'(x) = 9arctan(5x^2) + 18x^2/(1 + 25x^4)

f''(x) = 90x/(1 + 25x^4) - 90x^3(1 - 5x^4)/(1 + 25x^4)^2

f'''(x) = 90(1 - 25x^4)/(1 + 25x^4)^2 - 270x^2(1 - 5x^4)/(1 + 25x^4)^2 - 270x^4(1 - 5x^4)/(1 + 25x^4)^2 + 360x^6(1 - 5x^4)/(1 + 25x^4)^3

By evaluating these derivatives at x = 0, we can find the coefficients of the Maclaurin series expansion of f(x).

However, calculating the derivatives and evaluating them at x = 0 can be quite involved and require significant algebraic manipulation. Therefore, it is best to use computational software or tools to calculate the coefficients of the Maclaurin series expansion accurately.

Once we have the coefficients, we can express the Maclaurin series of f(x) by substituting the coefficients into the general formula.

The Maclaurin series expansion allows us to approximate the function f(x) for values of x close to 0, providing a polynomial representation of the function.

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Answer:

A

Step-by-step explanation:

Perpendicular lines always have the negative (opposite) reciprocal slope. Therefore, the slope of the line would be -2 because the reciprocal is just switching the numerator and denominator around (1/2 changes to 2/1 which is 2) and the negative means the opposite sign of which was originally given... i.e, since the 1/2 was positive, now it would be negative. That is why the slope is -2.

The equation of a line is y=mx+b with m representing the slope and b representing the y-intercept. Now to find the y-intercept, plug in the given components of the point (4,0) for the equation and solve for b (the y-intercept). Use 4 for x and 0 for y.

0=-2(4)+b

0=-8+b

8=b

Answer:

3.6 3/6 3.6 percent 3:6

Step-by-step explanation:

10:9

15:14

20:19

Answer:

7.  3:6, 3/9 (or 6/9), .33..... (or .66......), 33.3......% (or 66.6.....7)

8. 10 roses, 8 daisies, 10:8 ratio

15 roses, 13 daisies, 15:13 ratio

20 roses, 16 daisies, 20:16 ratio

( the 15 roses part was hard so if its wrong im sorry)

The modulus is 1, argument is π/4 and the principal value is π/4 mod 2π

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

\(z = \sqrt{ \frac{1 + i}{1 - i}\)

Rationalize the expression

So, we have

\(z = \sqrt{ \frac{1 + i}{1 - i} = \frac{(1 + i)(1 + i)}{(1 - i)(1 + i)} = \frac{1 + 2i + i^2}{1 - i^2} = \frac{1 + 2i - 1}{1 + 1} = \frac{2i}{2} = i\)

This means that

z = √i

The modulus of a complex number is calculated as

|z| = √(a^2 + b^2)

where z = a + bi. In this case, a = 0 and b = 1

So, we have

|z| = √(0^2 + 1^2)

|z| = 1

The argument of a complex number is calculated as

\(\arg(z) = \tan^{-1} \left( \frac{b}{a} \right)\)

So, we have

\(\arg(z) = \tan^{-1} \left( \frac{1}{0} \right)\)

This gives

arg(z) = π/4

The principal value of the argument of z is

arg(z) mod 2π

So, we have

π/4 mod 2π

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The proportional relationship between the price and quantity of ears of corn can be represented using a table or a graph, showing how the price and quantity vary in a consistent manner.

One way to represent the proportional relationship between the price and quantity of ears of corn is by using a table:

Price (in dollars) Quantity (in ears of corn)

             2             5

             4             10

This table shows the corresponding values of the price and quantity.

As we can observe, when the price is $2, the quantity is 5 ears of corn, and when the price is $4, the quantity is 10 ears of corn.

The relationship is proportional because as the price doubles, the quantity also doubles.

Another representation of this proportional relationship is through a graph.

We can plot the points (2, 5) and (4, 10) on a coordinate plane, where the x-axis represents the price and the y-axis represents the quantity.

By connecting these two points with a straight line, we can visualize the proportional relationship.

The line will pass through the origin (0, 0) since zero price corresponds to zero quantity.

The slope of the line will indicate the rate of change between price and quantity.

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Answer:

Juan has lost 61 points, or has gained negative 61 points.

Step-by-step explanation:

0 - 28 = -28

-28 + 22 = -6

-6 + -20 = -26

-26 + -35 = -61

Answer:

48 minutes long

Step-by-step explanation:

For a total amount of minutes the lessons are, take 4x60. 4 for the total time in the lessons and 60 for 60 minutes in an hour. 4x60= 240 minutes.

Take 240/5. 240 is the total number of minutes and with the five lessons being the same amount of time, you divide the total number of minutes by the number of lessons. 240/5= 48 minutes

The following data shows the daily production of cell phones. 7, 10, 12, 15, 18, 19, 20. Mean The formula for finding the mean is: mean = (sum of observations) / (number of observations).

Therefore, the mean for the daily production of cell phones is: Mean = (7+10+12+15+18+19+20) / 7

= 101 / 7

Mean = 14.43

Variance The formula for finding the variance is: Variance = (sum of the squares of the deviations) / (number of observations - 1) Where the deviation of each observation from the mean is: deviation = observation - mean First, calculate the deviation for each observation:7 - 14.43

= -7.4310 - 14.43

= -4.4312 - 14.43

= -2.4315 - 14.43

= 0.5718 - 14.43

= 3.5719 - 14.43

= 4.5720 - 14.43

= 5.57

Now, square each of these deviations: 56.25, 19.62, 5.91, 0.33, 12.75, 20.9, 30.96 The sum of these squares of deviations is: 56.25 + 19.62 + 5.91 + 0.33 + 12.75 + 20.9 + 30.96

= 147.72

Therefore, the variance for the daily production of cell phones is: Variance = 147.72 / (7-1) = 24.62 Standard deviation ) Mean = 14.43b) Variance per Day = 24.62c) Standard Deviation = 4.96

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The answers to all parts shown below.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

1. 3x² + 4x² = 35

7x² = 35

x² = 5

x = ±√5

2. 3x² - 28= 2x² + 33

x² = 61

x = ±√61

3. x²-25= 25

x² = 50

x = ±5√2

4. 2x² - 30 = 70

2x² = 100

x² = 50

x= 5√2

5. 8x² - 6x² = 54

2x² = 54

x² = 27

x= 3√3

6. 3x² - 6 = 34 - 2x²

5x² = 40

x² = 8

x = 2√2

7. x²+49 = 196

x²= 174

x= 7√3

8. 5x² – 40 = 100

5x² = 140

x² = 28

x= 2√7

9. 9x² = 4x² + 10

5x² = 10

x= √2

10. x²-4=80

x² = 84

x= 2√21

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Answer:

m > 30

Step-by-step explanation:

Is that what you were looking for? :)

Answer:

-6/5

Step-by-step explanation:

Answer: x=0 or 6/5

Step-by-step explanation:

Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

The two numbers that have a difference of 152 and whose product is a minimum are 120 and -32.  To find these numbers, we can set up an equation. Let's call the larger number x and the smaller number y. Since we want the numbers to have a difference of 152, we can write the equation as x - y = 152.

To find the product, we can multiply the two numbers together. So the equation for the product is xy.

To find the minimum product, we can use the concept of quadratic equations. The product xy can be expressed as x(x - 152) or -y(y - 152). We can then find the minimum value by finding the vertex of the parabola formed by these quadratic equations.

Using calculus, we can find that the vertex occurs at x = 76 and y = -76. Therefore, the two numbers are 76 and -76, which have a difference of 152.

However, these numbers don't meet the condition of having a minimum product. To find the numbers with the minimum product, we need to consider the constraint that the numbers must be positive. The closest positive numbers to 76 and -76 are 120 and -32, respectively. These numbers have a difference of 152 and their product, 120 x -32, is equal to -3840.

Therefore, the two numbers whose difference is 152 and whose product is a minimum are 120 and -32.

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Answer:

Step-by-step explanation:

16 ae =x

The values of x

and y  that would prove that the quadrilateral is a parallelogram are 4 and 6 respectively.

Find the diagram attached. In order to prove that the quadrilateral is a parallelogram, we need to find the values of x and y that make the diagram a parallelogram.

From the parallelogram;

Given the following parameters

EC=4,

BD=12,

Since AE = EC, hence the measure of AE is 4.

Similarly, BD = BE + ED

BD = BE + BE

BD = 2BE

12 = 2BE

BE = 6 = y

Hence the values of x

and y  that would prove that the quadrilateral is a parallelogram are 4 and 6 respectively.

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Answer:

D = 36

Step-by-step explanation:

x = Number of DVDs in Maria's collection

So, number of DVDs Emma has is 3x

Given,

x+3x=144

4x=144

x=144/4 = 36

The given principle is called the multiplication principle of counting.

This is called the multiplication principle of counting. It states that if there are m ways in which one event can occur and for each of these ways the second event can occur in n ways, then the total number of ways in which the two events can occur together is the product of m and n, which is mn.

The multiplication principle of counting can be extended to more than two events as well. For example, if there are three events and the first event can occur in m ways, the second event can occur in n ways for each of these m ways, and the third event can occur in p ways for each of the mn ways, then the total number of ways in which the three events can occur together is mnp.

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\(\\ \tt\longrightarrow 3=\dfrac{3}{10}=0.3\)

\(\\ \tt\longrightarrow 8=\dfrac{8}{10}=0.8\)

\(\\ \tt\longrightarrow 15=\dfrac{15}{100}=0.15\)

\(\\ \tt\longrightarrow \dfrac{18}{10}=1.8\)

\(\\ \tt\longrightarrow 33=\dfrac{33}{100}=0.33\)

\(\\ \tt\longrightarrow 49=\dfrac{49}{100}=0.49\)

\(\\ \tt\longrightarrow 64=\dfrac{64}{100}=0.64\)

\(\\ \tt\longrightarrow 108=\dfrac{108}{100}=1.08=1.1\)

\(\\ \tt\longrightarrow 251=\dfrac{251}{1000}=0.251\)

The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.

If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:

nPr = n!/{(n - r)!}.

In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.

Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.

Substituting n = 8, and r = 4 in the formula, we get:

8P4 = 8!/{(8 - 4)!}

= 8!/4!

= 5 * 6 * 7 * 8

= 1680.

Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

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Answer

1. 9

1. 13

1. 147

1. 7/3

1. 9

Step-by-step explanation:

Algebraic equations

1. 2x=18

2. x-5=8

3. (x/7)=21

4. 3x+5=12

5. 2x=18

Answer: k = √27-i

Step-by-step explanation:

Answer:

30 cm is the perimeter.

Step-by-step explanation:

To find the perimeter of this figure, add up all the lengths of the sides:

6 cm

4 cm

9.5 cm

4 cm

6.5 cm

-----------

30 cm is the perimeter.

Answer:

The perimeter will be 30 cm

Step-by-step explanation:

The perimeter is the distance around the composite figure.

The perimeter= 9.5+6.5+4+4+6=30 cm

perimeter=30

Given differential equation is y"-9y'+20y=0We can write this equation asy²-9y+20y=0Here, a = 1, b = -9, and c = 20Now, we have to find the roots of this equation.

Now, let us find the value of the discriminant. b²-4ac= (-9)²-4(1)(20)= 81-80= 1Since the value of the discriminant is greater than zero, therefore, we have two real and distinct roots for this equation.Roots are given by the quadratic formula.x= (-b±√(b²-4ac))/2aOn substituting the values of a, b, and c we get,x = (9±√1)/2Now,x1= 5x2= 4/1These roots give two linearly independent solutions as follows: y1=e^5t and y2=e^4tTherefore, the general solution to the differential equation is:y=c1e^5t+c2e^4tWhere c1 and c2 are constants.

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The given differential equation is y"-9y'+20y=0.

Let us use the characteristic equation to solve this differential equation.

The characteristic equation of y"-9y'+20y=0 isr² - 9r + 20 = 0.

Solve for r by factoring the characteristic equation(r - 5)(r - 4) = 0. 

Therefore, r = 5 and r = 4.

Thus, the general solution of the differential equation y"-9y'+20y=0 isy(x) = c₁e⁴x + c₂e⁵x

where c₁, c₂ are constants.

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To determine the convergence or divergence of an alternating series, you can use the Alternating Series Test. This test states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges.

Additionally, if the terms do not approach zero, the series diverges.

To apply the Alternating Series Test, you need to check two conditions:

1. The terms of the series must alternate in sign.

2. The absolute value of the terms must decrease or approach zero.

If both conditions are satisfied, you can conclude that the alternating series converges. However, if either condition fails, the series diverges.

If you want to determine the convergence or divergence more precisely, you can use the Integral Test or the Comparison Test. The Integral Test allows you to compare the convergence or divergence of a series to the convergence or divergence of an improper integral. If the integral converges, the series converges, and if the integral diverges, the series diverges.

The Comparison Test is another method to determine the convergence or divergence of a series. It involves comparing the given series with a known series whose convergence or divergence is already known. If the known series converges and the terms of the given series are less than or equal to the corresponding terms of the known series, then the given series also converges. Conversely, if the known series diverges and the terms of the given series are greater than or equal to the corresponding terms of the known series, then the given series also diverges.

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Answer:

It is the same-side interior angle of B which is the vertical angle of 100 (?)

Step-by-step explanation: