In a production line of a pharmaceutical company, 10g pills are made, one of
plant managers (head 1) state that the mean weight of the pills is 10g with a deviation
of 0.3g. On a visit to the plant, one of the company's managers selects 1 pill at random.
and weighs it, giving as a measurement 9.25g, the manager informs of this novelty since he believes that there is
a serious problem with the weight of the pills because values​​below 9.25g and above
of 10.75g are very rare.
a) With this information, what is the probability that the plant manager's statement (head 1)
be rejected when this is true?
b) Another of the plant managers (head 2) assures that due to adjustments in the production line the
average pill weight has decreased. The following hypothesis test is performed:
0: = . 1: < 10
And the following set is defined as its critical region:
= {(1 2…n) n|(1+2+⋯+n) / < }
Agreement has been reached that the test has a significance level of 0.05 and that the Power
of the Test is 95% when the true mean is 9.75g. Find the values​​of and that
satisfy these conditions.

The major axis for the ellipse, x² + 16y² - 96y + 128 = 0 is the x-axis

To answer the question, we need to write it in the standard form of the equation of an ellipse

The equation of an ellipse centered at  (h,k) is

(x - h)²/a² + (y - k)²/b² (1) where a > b and the major axis is parallel to the x axis

Given x² + 16y² - 96y + 128 = 0, we convert it into the standard equation of an ellipse.

So, x² + 16y² - 96y + 128 = 0

Dividing through by 16, we have

x²/16 + 16y²/16  - 96y/16 + 128/16 = 0/16

x²/16 + y² - 6y + 8 = 0

Completing the square in y by adding and subtracting (-6/2)² = (-3)²

x²/16 + y² - 6y + (-3)² - (-3)² + 8 = 0

x²/16 + (y - 3)² - 9 + 8 = 0

x²/16 + (y - 3)² - 1 = 0

x²/16 + (y - 3)² = 1

x²/4² + (y - 3)²/1² = 1  (2)

Comparing equations (1) and (2), we have that a = 4 and b = 1.

Since a = 4 > b = 1, the major axis for the ellipse is the x-axis

So, the major axis for the ellipse, x² + 16y² - 96y + 128 = 0 is the x-axis

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First, let's calculate the monthly interest rate (i), which is the APR divided by 12 months:

i = APR / 12 months

i = 5.3% / 12

i = 0.00442 or 0.442%

Next, let's calculate the number of months (n) for the mortgage, which is 15 years multiplied by 12 months:

n = 15 years x 12 months/year

n = 180 months

Now, let's calculate the monthly payment (PMT) using the following formula:

PMT = P * i / \((1 - (1 + i)^(-n)\))

where P is the principal amount, i is the monthly interest rate, and n is the number of months.

PMT = $325,000 * 0.00442 / (1 - \((1 + 0.00442)^(-180)\)

PMT = $2,613.67 (rounded to the nearest cent)

Now, let's create the amortization table for the first two months:

Month | Payment | Interest | Principal | Remaining Balance

1 | $2,613.67 | $1,431.25 | $1,182.42 | $323,817.58

2 | $2,613.67 | $1,428.60 | $1,185.07 | $322,632.51

For each month, the Payment column shows the fixed monthly payment, the Interest column shows the calculated interest based on the remaining balance multiplied by the monthly interest rate, the Principal column shows the portion of the payment that goes towards reducing the principal, and the Remaining Balance column shows the remaining balance after subtracting the principal payment from the previous remaining balance.

The amortization table will continue in this manner for the remaining months until the mortgage is paid off.

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The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

To complete the two-month amortization table, we need to calculate the monthly payment, as well as the principal and interest amounts for each payment.

The formula for calculating a fixed-rate mortgage payment is:

\(Payment = P * r * (1 + r)^n / [(1 + r)^n - 1]\)

Where:

P = Principal amount borrowed

r = Monthly interest rate

n = Total number of payments

First, let's calculate the monthly interest rate.

Since the APR is an annual rate, we need to divide it by 12 to get the monthly rate:

Monthly interest rate = 5.3% / 12 = 0.0044167

Next, we need to calculate the total number of payments.

Since this is a 15-year mortgage, and we're completing a two-month amortization table, the total number of payments is:

Total number of payments = 15 years * 12 months per year = 180

Number of payments for two months = 2

Now we can plug these values into the formula to calculate the monthly payment:

Payment = \($325,000 * 0.0044167 * (1 + 0.0044167)^180 / [(1 + 0.0044167)^180 - 1]\)

= $2,549.67

So the monthly payment is $2,549.67

Now we can use this value to complete the two-month amortization table:

Payment Interest Principal Balance

Month 1 $1,426.25 $1,123.42 $323,876.58

Month 2 $1,420.47 $1,129.20 $322,747.38

To calculate the interest and principal amounts for each payment, we use the following formulas:

Interest = Balance * Monthly interest rate

Principal = Payment - Interest

Balance = Balance - Principal

We start with the initial balance of $325,000 and apply the formulas for each payment.

The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

And so on, for each subsequent payment.

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Answer:

5

Step-by-step explanation:

By the Pythagorean Theorem:

\( {x}^{2} + {10}^{2} = {(5 \sqrt{5} )}^{2} \)

\( {x}^{2} + 100 = 125\)

\( {x}^{2} = 25\)

\(x = 5\)

options B, D, and E are correct. Option A is incorrect because it uses the wrong length measurement.

what is a rectangle?

A rectangle is a four-sided flat shape with straight sides, where opposite sides are parallel and equal in length. It has four right angles (90-degree angles) at each corner. The length and width of a rectangle are its two main dimensions, and the area of a rectangle is calculated by multiplying its length by its width.

Based on the picture, we can see that the glass has a rectangular shape with dimensions of 4 feet and 5 2/12 feet. Therefore, the equations that can be used to find the area, in square feet, of the piece of glass are:

B. A = 5 2/12 + 4 = 9 2/12 = 7/3 square feet

D. A = 5 2/12 × 4 = 20 1/3 square feet

E. A = (2 × 2 1/2) + (2 × 4) = 9 square feet

Therefore, options B, D, and E are correct. Option A is incorrect because it uses the wrong length measurement. Option C is incorrect because it adds the dimensions instead of multiplying them. Option F is also incorrect because it adds the dimensions instead of multiplying.

Options B, D, and E correctly calculate the area of the glass by multiplying the length by the width. Option B adds the length and width before multiplying them, while option D multiplies the length and width directly.

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Answer:

2 solutions:

(-2.899, 0.899) and (6.899, -8.899)

Step-by-step explanation:

x+y=2

y=-x+2

y=1/4x²+3

Graph both equations into graphing calculator

Graph in attachment shows solutions

The cost of each shirt Bobby and Davonte bought if they both spent $145.20 on 11 shirts is $13.2

Total number of shirts bobby and Davonte bought = 11

Amount Bobby spent on shirts= $92.40

Amount Davonte spent on shirts= $52.80

Total amount both spent= $92.40 + $52.80

= $145.20

Cost of each shirt= Total amount both spent / Total number of shirts bobby and Davonte bought

= $145.20 / 11

= $13.2

Therefore, each shirt Bobby and Davonte bought cost $13.2

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The solution to the systems of equations graphically is (2, 4)

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

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

4

Step-by-step explanation:

The simplified expression √32 * 0.72 is equal to 2.88.

Here, we have,

To simplify the expression √32 * 0.72, we can first simplify the square root of 32.

√32

= √(16 * 2)

= √16 * √2

= 4√2

Now we can substitute this value back into the expression:

√32 * 0.72 = 4√2 * 0.72

To multiply these values, we can simplify further:

4 * 0.72 = 2.88

Therefore, the simplified expression √32 * 0.72 is equal to 2.88.

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Answer:

s = 3

Step-by-step explanation:

First compute the cost of the three apps:

21-12=9

The cost of the three apps is $9 then.

Since s is the price of the apps, we deduce the equation:

3s=9

/3

s = 3

Answer: B is the answer

Step-by-step explanation: I took the quiz on edgunity

Distance = 13 units

Point A: (8, -7)

Point B: (-4, -2)

\(\sqrt{(8 + 4)^{2} + (-7 + 2)^{2} }\)

\(\sqrt{(12)^{2} + (-5)^{2} }\)

\(\sqrt{144 + 25 }\)

\(\sqrt{169}\)

\(13\)

Answer:

\(\boxed {d = 13}\)

Step-by-step explanation:

Use the Distance Formula to help you find the distance between the two following points:

\(d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\)

(where \((x_{1}, y_{1})\) represents the first point and \((x_{2}, y_{2})\) represents the second point)

-Apply the two following onto the formula:

\((x_{1}, y_{1}) = (8, -7)\)

\((x_{2}, y_{2}) = (-4, -2)\)

\(d = \sqrt{(-4 - 8)^{2} + (-2 + 7)^{2}}\)

-Solve for the distance:

\(d = \sqrt{(-4 - 8)^{2} + (-2 + 7)^{2}}\)

\(d = \sqrt{(-12)^{2} + 5^{2}}\)

\(d = \sqrt{144 + 25}\)

\(d = \sqrt{169}\)

\(\boxed {d = 13}\)

Therefore, the distance is \(13\).

Answer:

Hey there!

4t(5t)=20t^2

4t(-4)=-16t

5(5t)=20t

5(-4)=-20

Hope this helps  :)

Step-by-step explanation:

This is just a matter of multiplication. 4t x 5t = \(20t^{2}\), so that will be in your first box. 4t x -4 = -16t, so that'll be in your second box. 5 x 5t = 25t, so that will be in your bottom-first box, and 5 x -4 = -20, so that will be in your last one.

For any m x n matrix A, AAT and ATA are symmetric matrices as  (AAT)^T = AAT and (ATA)^T = ATA.

To prove or disprove that for any m x n matrix A, AAT and ATA are symmetric, we can use the definition of a symmetric matrix and the properties of matrix transposes.
A matrix B is symmetric if B = B^T, where B^T is the transpose of B. So, we need to show that (AAT)^T = AAT and (ATA)^T = ATA.
Step 1: Find the transpose of AAT:
(AAT)^T = (AT)^T * A^T (by the reverse order property of transposes)
(AAT)^T = A * A^T (since (A^T)^T = A)
(AAT)^T = AAT
Step 2: Find the transpose of ATA:
(ATA)^T = A^T * (AT)^T (by the reverse order property of transposes)
(ATA)^T = A^T * A (since (A^T)^T = A)
(ATA)^T = ATA

Since (AAT)^T = AAT and (ATA)^T = ATA, we have proved that for any m x n matrix A, AAT and ATA are symmetric matrices.

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When constructing a frequency distribution for quantitative data, it is important to remember that classes are mutually exclusive, classes are collectively exhaustive, the total number of classes usually ranges from 5 to 20. The correct answer is D: All of above.

(A) Classes are mutually exclusive means that each data point should fit into only one class, with no overlap between classes. For example, if the classes are defined as intervals of height, then a person who is 5'10" should be placed in only one class, such as "5'10" to 6'0"."

(B) Classes are collectively exhaustive means that every data point should be included in a class. This means that there should be no gaps or omissions between classes. For example, if the classes are defined as intervals of weight, then every person's weight should fit into one of the defined weight classes.

(C) The total number of classes usually ranges from 5 to 20 depends on the nature of the data and the purpose of the frequency distribution. Too few classes may result in a loss of information, while too many classes may make it difficult to see patterns or trends in the data. In general, it is recommended to have enough classes to show the shape of the distribution, but not so many that the data becomes difficult to interpret.

Therefore, it is important to keep in mind all three of these factors when constructing a frequency distribution for quantitative data.

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Step-by-step explanation:

let the larger number=n

then the smaller number=½n

We conclude from the question that

n+½n=75

3/2n=75

3n=150

n=150/3=50

Therefore the larger number=50 and the smaller number=½×50=25

To simplify a radical expression, you can use a few different techniques. One common technique is to factor the expression under the radical sign (the radicand) as much as possible.

Another technique you can use is to use the properties of radicals. For example, you can use the product property of radicals to combine like terms under the radical sign

You can also use the quotient property of radicals to divide out a factor under the radical sign. Finally, some radicals are unsimplifiable by these methods. You can approximate a value of radical or try to get it in a form of fraction with radical.

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Answer:

3x + 2(4x − 6) = 8x + 1

3x + (8x-12)=8x+1

-12=19x+1

-11=19x

-11/19     (Im pretty sure i did this right but at the same time im not, im sorry if i got this wrong)

Answer:

=13/3

Step-by-step explanation:

1. Distribute

3+2(4−6)=8+1

3+8−12=8+1

2. Combine like terms

3+8−12=8+1

11−12=8+1

3. Add 12 to both sides of the equation

11−12=8+1

11−12+12=8+1+12

4. Simplify

11=8+13

5. Subtract 8x from both sides of the equation

11=8+13

11−8=8+13−8

6. Simplify

3=13

7. Divide both sides of the equation by the same term

3=13

3x÷3=13÷3

8. Simplify

If you cancel terms that are in both the numerator and denominator you will get:

=13/3

I hope this helps

It is given that PG grading requirement is met if the values of S(t) are between -3.2 and +3.2. As all the calculated values of S(t) lie within this range, the asphalt meets PG grading requirement.

Given data: Bending rheometer: 0.4mm, 0.5mm, 0.65mm, 0.82mm, 0.98mm, and 1.3mm for t = 15s, 30s, 45s, 60s, 75s, and 90s.

We are supposed to calculate the values of S(t) and m to check if the asphalt meets PG grading requirement.

Calculation of m:

Mean wheel track rut depth = (0.4+0.5+0.65+0.82+0.98+1.3)/6

= 0.7933mm

Calculation of S(t)

S(t) = (x - m)/0.3

Where, x = 0.4mm, 0.5mm, 0.65mm, 0.82mm, 0.98mm, and 1.3mm

Given, m = 0.7933mm

Substituting these values into the formula above:

S(15s) = (0.4 - 0.7933)/0.3

= -1.311S(30s)

= (0.5 - 0.7933)/0.3

= -0.9777S(45s)

= (0.65 - 0.7933)/0.3

= -0.4777S(60s)

= (0.82 - 0.7933)/0.3

= 0.128S(75s)

= (0.98 - 0.7933)/0.3

= 0.62S(90s)

= (1.3 - 0.7933)/0.3

= 1.521

It is given that PG grading requirement is met if the values of S(t) are between -3.2 and +3.2. As all the calculated values of S(t) lie within this range, the asphalt meets PG grading requirement.

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Given the lengths of the two sides and the angle between them, only one triangle can be created under the given circumstances.

1. Given that angle B is 32.5°, side AB is 37 cm, side AC is 26 cm, etc.

2. Calculate side BC using the Law of Cosines:

BC = (2(AB)(AC)cosB) + (AB)(AC)2

3. Input the values that are known: BC = (37 2 + 26 2 - 2(37)(26)cos32.5°)

4. Condense: BC = (1369 plus 676 minus 1848 cos 32.5 °)

5. Determine BC =. (2095 - 1539.07)

6. Condense: BC = 556.93

7. Determine BC as 23.701 cm.

8. Since the lengths of the two sides and the angle between them are specified, only one triangle can be formed under the current circumstances.

By applying the Law of Cosines, we can determine the length of the third side, BC, given that side AB is 37 cm, side AC is 26 cm, and angle B is 32.5°. In order to perform this, we must first determine the cosine of angle B, which comes out to be 32.5°. Then, we enter this value, together with the lengths of AB and AC, into the Law of Cosines equation to obtain BC.BC = (AB2 + AC2 - 2(AB)(AC)cosB) is the equation. BC is then calculated by plugging in the known variables to obtain (37 + 26 - 2(37)(26)cos32.5°). By condensing this formula, we arrive at BC = (1369 + 676 - 1848cos32.5°). Then, we calculate BC as BC = (2095 - 1539.07), and finally, we simplify to obtain BC = 556.93. Finally, we determine that BC is 23.701 cm. Given the lengths of the two sides and the angle between them.

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the largest perimeter possible for a rectangle with positive whole-number dimensions and an area of 120 square centimeters is 242 cm.

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.

here, given that,

a rectangle with positive whole-number dimensions and an area of 120 square centimeters.

now, we get,

You could have the width as 1 and the length as 120 making the area 120cm^2 but the perimeter 242.

Hence, the largest perimeter possible for a rectangle with positive whole-number dimensions and an area of 120 square centimeters is 242 cm.

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Exponents represent how many times a number is multiplied by itself. In this case, we have a negative exponent of -1/15625. To simplify this, we can rewrite it as 1 over the base number raised to the positive exponent 1/15625.

So, if the base number is x, then the expression can be written as:
x^(-1/15625) = 1/x^(1/15625)
This means that we take the reciprocal of the base number and raise it to the positive exponent 1/15625. Note that since the exponent is very small, the value of x^(1/15625) will be very close to 1. Therefore, the reciprocal will also be very close to 1, but slightly smaller.
The given value is -1/15625. To express this as an exponent with a base, you can rewrite it as a fraction with a negative exponent:
-1/15625 = (-1)(1/15625)
Now, let's find the exponent for the denominator. Since 15625 is equal to 5^6, we can rewrite the fraction as:
(-1)(1/5^6)
Finally, express the fraction as a single exponent:
(-1)(5^-6)
So, -1/15625 can be written as (-1)(5^-6) in terms of exponents.

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Answer:

You need to find out how much games he had and divide by nine.

Answer:

x ≈ 7.9 ft

Step-by-step explanation:

cos∅ = adjacent over hypotenuse

Since we are dealing with a right triangle, we can use trigonometry to help us solve for missing values:

cos44° = x/11

11cos44° = x

x = 7.91274

x ≈ 7.9 ft

The expected payback for betting $6 on red in this roulette game is approximately -$0.32. This means, on average, you can expect to lose about $0.32 per $6 wagered.

To calculate the expected payback for the game, we need to consider the probabilities and payouts associated with the bet on red.

In a standard roulette wheel, there are 18 red compartments, 18 black compartments, and two green compartments (neither black nor red) representing the 0 and 00. This means there are 38 equally likely outcomes.

If you bet $6 on red, there are 18 favorable outcomes (the red compartments) and 20 unfavorable outcomes (the black and green compartments). Therefore, the probability of winning is 18/38, and the probability of losing is 20/38.

If the color red occurs, you get to keep your bet of $6 and win an additional $6.

To calculate the expected payback, we multiply the probability of winning by the payout for winning and subtract the probability of losing multiplied by the amount wagered:

Expected Payback = (Probability of Winning * Payout for Winning) - (Probability of Losing * Amount Wagered)

Expected Payback = ((18/38) * $6) - ((20/38) * $6)

Expected Payback = ($108/38) - ($120/38)

Expected Payback = -$12/38

The expected payback for betting $6 on red in this roulette game is approximately -$0.32. This means, on average, you can expect to lose about $0.32 per $6 wagered.

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The equation of the line with a slope of -8 and a y-intercept of -7 is y = -8x - 7.

In the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the given values for m and b.

Thus, the equation becomes y = -8x - 7. The negative slope of -8 indicates that the line will have a downward slope, meaning that as x increases, y will decrease at a rate of 8 units. The y-intercept of -7 indicates that the line intersects the y-axis at the point (0, -7). This means that when x is 0, y is -7.

By plugging in different values of x into the equation, we can find the corresponding y-values and plot the points on a graph to visualize the line. This line will have a steep slope and will pass through the point (0, -7).

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Step-by-step explanation:

Given that it has a sunroof = 12 + 20 + 0 + 18 = 50

  with 4 doors = 20

20/50 = 2/5 = .4