A synthetic fiber used in manufacturing carpet has tensile that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. (a) Find the probability that a random sample of n = 6 fiber specimens will have a sample mean tensile strength that exceeds 75.75 psi. 75.75 - р X- р M P[X > 75.75] = P o In o Tn 75.75 – 75.5 P[X > 75.75] = P2> 3.5 va = P[Z > 0.175] = 1-0(0.175) = 0.4325 BC (b) How is the standard deviation of the sample mean changed when the sample size is increased from n = 6 to n = 49?

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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Answer:

12 m

Step-by-step explanation:

1200 mm = 1.2 m

Step-by-step explanation:

no

10 times smaller

1,200 mm = 1.2 m

a) The rate at which the top of the ladder is sliding down the wall when the bottom of the ladder is 5 m from the wall is -0.1 m/s.

b) The rate of change of the angle between the ground and the ladder when the bottom of the ladder is 5 m from the wall is -25/676 rad/s.

c) The rate of change of the area of the triangle bounded by the ladder, the building, and the ground, when the bottom of the ladder is 5 m from the wall is 3.5 m^2/s.

a) To find the rate at which the top of the ladder is sliding down the wall, we start by expressing the length of the ladder, z, in terms of the distances x and y using the equation z^2 = x^2 + y^2.

By differentiating this equation with respect to time, we obtain 2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt), where dz/dt represents the rate of change of z, dx/dt is the rate at which x is changing, and dy/dt is the rate at which y is changing.

Given that dx/dt = 0.6 m/s, x = 5 m, and z = 13 m, we can substitute these values into the equation and simplify to find 13(dz/dt) = 3 + y(dy/dt).

To isolate dy/dt, we differentiate equation (1) with respect to t, resulting in dy/dt = [2z(dz/dt) - 2x(dx/dt)] / (2y).

Substituting the given values and dz/dt = 0.6, we find dy/dt = (13/12)(dz/dt) - (1/2). Plugging in dz/dt = 0.6, we obtain dy/dt = (13/12) * 0.6 - 0.5 = -0.1 m/s. The negative sign indicates that the top of the ladder is sliding down the wall.

b)

This can be determined by differentiating the equation involving the tangent of the angle and applying the chain rule.

To find the rate of change of the angle, θ, between the ground and the ladder, we start with the equation tan θ = y/x. By differentiating both sides with respect to t,

we get sec^2θ(dθ/dt) = (1/x)dy/dt,

where dθ/dt represents the rate of change of θ.

Substituting x = 5, y = 12, and dy/dt = -0.1, we find sec^2θ = 25/169.

Taking the square root of both sides, we get secθ = 13/5.

To find dθ/dt, we have (dθ/dt) = [(1/x)dy/dt] / sec^2θ = (5/169)(-0.1) / (169/25) = -25/676 rad/s.

c)

This can be determined by differentiating the equation for the area of the triangle.

The area of the triangle, A, can be expressed as A = (1/2)xy. By differentiating with respect to t, we find dA/dt = (1/2)[x(dy/dt) + y(dx/dt)], where dA/dt represents the rate of change of the area.

Substituting the given values and calculating, we find

dA/dt = (1/2)[5*(-0.1) + 12*0.6] = 3.5 m^2/s.

Thus, the rate of change of the triangle's area is 3.5 m^2/s.

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The exact value of tan(105°) is -2 - √3.

Tangent function of an angle in a right angled triangle is defined as the ratio of the opposite side to the adjacent side.

Given that, we have to find the exact value of tan(105°).

We know that,

105° = 60° + 45°

tan(105°) = tan (60° + 45°)

We know,

tan (A + B) = (tan A + tan B) / (1 - tan A tan B)

So,

tan (60° + 45°) = (tan 60 + tan 45) / (1 - tan (60) tan (45))

tan 60 = √3 and tan 45 = 1

tan (60° + 45°) = (√3 + 1) / (1 - √3)

Multiplying both numerator and denominator by (1 - √3),

                        = (√3 + 1)² / (1 - 3)

                        = -(3 + 2√3 + 1) / 2

                        = -(4 + 2√3) / 2

                        = -(2 + √3)

                        = -2 - √3

Hence the value of tan(105°) is -2 - √3.

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Answer:

4(7 + 6)

Step-by-step explanation:

Step 1:  Find the greatest common factor (GCF) of 28 and 24.

The greatest common factor (or the highest that evenly divides into) 28 and 24 is 4.

Step 2:  Divide 28 and 24 by GCF and place the result in parentheses.

28 / 4 = 7 and 24 / 4 = 6.

Thus, the final answer is 4(7 + 6).

Optional Step 3:  Check validity of answer:

We can check that our answer is correct by seeing if we get the same result for 28 + 24 and 4(7 + 6)

28 + 24 = 4(7 + 6)

52 = 4(13)

52 = 52

Thus, our answer is correct.

1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD

1b) The additional information required using ASA Congruency postulate  is BC ≅ QR

2a) The symbolic form of the congruent triangles is written as;

ΔABC ≅ ΔADC

2b) The congruence Postulate that is used is SAS Congruency postulate.

1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate denotes Side - Angle - Side. That is 2 congruent sides and the included angle. This means we have our additional information as;

∠AOB ≅ ∠BOD

1b) We want to prove that the given triangle ABC is congruent to the other triangle PQR by the ASA Congruency. ASA Congruency means 2 congruent angles and the included side. We are given;

∠Q = ∠B

∠R = ∠C.

Therefore, the additional information is BC ≅ QR

2a) The symbolic form of the given congruent triangles is expressed as;

ΔABC ≅ ΔADC

2b) The congruence postulate that was used here is SAS Congruency postulate.

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Answer:

\(270 \:m^2\)

Step-by-step explanation:

The area of the triangle.

\(bh\frac{1}{2}\)

\(b \times h \times \frac{1}{2}\)

\(20 \times 27 \times \frac{1}{2}\)

\(540 \times 1/2\)

\(=270\)

The area of triangle would be;

⇒ Area of triangle = 270 m²

Since, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Here, Given that;

Base of triangle = 20 m

Height of triangle = 27 m

Now, We know that;

Area of triangle = 1/2 × Base × Height

Substitute all the values, we get;

⇒ Area of triangle = 1/2 × Base × Height

⇒ Area of triangle = 1/2 × 20 × 27

⇒ Area of triangle = 270 m²

Thus, The area of triangle would be;

⇒ Area of triangle = 270 m²

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The area enclosed by the curves y=x³-8x² 18x-5 and y=x + 5 is 71/6 or 11.83 square units.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have two curves:

y=x³-8x² 18x-5 and

y=x + 5

The intersection point will be:

(1, 6), (2, 7), and (5, 10)

From the graph, we can integrate to evaluate the area enclosed by the curves:

\(=\rm \int\limits^2_1 {[(x^3-8x^2+18x- 5)-(x+5)]} \, dx + \int\limits^5_2 {[(x+5)-(x^3-8x^2+18x- 5)]} \, dx\)

After calculating, we get:

Area = 142/12 = 71/6 or 11.83 square units

Thus, the area enclosed by the curves y=x³-8x² 18x-5 and y=x + 5 is 71/6 or 11.83 square units.

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The coefficient of the third term in the given expression is -4

From the question, we are to determine the coefficient of the third term in the given expression.

A coefficient is the numerical value that is written along with a variable or it is multiplied by the variable.

The given expression is

5 – 2t3 – 4t3u3 + 8v

This can be properly written as

5 - 2t³ - 4t³u³ + 8v

The third term in this expression is - 4t³u³

In this term, the numerical value that is written along with the variable is -4

Hence, the coefficient is -4

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Answer:

\(1. \: \: \: a = \frac{5}{7} \\ 2. \: \: \: 4 \\ 3. \: \: \: 15 {x}^{2} + 60x + 135 \\ 4. \: \: \: m = {75}^{o} \\ \)

Step-by-step explanation:

\(1. \: \: 7a - 8 = 13 \\ 7a - 8 + 8 = 13 + 8 \\ 7a = 5 \\ \frac{7a}{7} = \frac{5}{7} \\ a = \frac{5}{7} \\ \)

\(2. \: \: \: 4 = 2 \times 2 \\ 8 = 2 \times 2 \times 2 \\ 4 \\ \)

\(3. \: \: \: 15 {(x + 3)}^{2} \\ 15(x + 3)(x + 3) \\15 (x + 3)(x + 3) \\ 15 |x(x + 3) + 3(x + 3)| \\ 15 ({x}^{2} + 3x + 3x + 9 )\\ 15( {x}^{2} + 6x + 9) \\ {15x}^{2} + 60x + 135 \\ \)

\(4. \: \: \: m = {75}^{o} (opposite \: angles)\)

Answer:

a=-2

Step-by-step explanation:

-29=6a-17

add 17 on both sides

-12=6a

divide by 6 on both sides

-2=a

a=-2

The property described by that mathematical statement is:

The associativity of addition.

The operations on the left side of the equals sign are done in the order they appear, from left to right.

The operations on the right side are done using the associative property, first doing the operations inside the parentheses, then adding the remaining terms.

And the statement shows that for addition, the order of operations does not matter as long as you associate in the proper way using parentheses.

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

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Answer:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y

.

x-intercept(s): None

y-intercept(s): (0,5)

Step-by-step explanation:

False, the population mean will always not be the same as the mean of all possible that can be computed from samples of size 15.

The mean of all possible samples of size 15 (also known as the sampling distribution mean) will be centered around the population mean, but it may not necessarily be exactly the same as the population mean. The sampling distribution mean can be thought of as an estimate of the population mean, and its accuracy will depend on factors such as the sample size and the variability of the population. However, as the sample size increases, the sampling distribution mean will become a better and more accurate estimate of the population mean.

In statistics, a sample is a subset of a population that is used to estimate or infer information about the population. The mean of a sample is the average of the observations in the sample, and the population mean is the average of all the observations in the entire population.

The mean of all possible samples of a fixed size, taken from a population, is called the sampling distribution mean. The sampling distribution mean is a theoretical concept and is not based on any specific sample. It is the distribution of all possible sample means that could be obtained from the population.

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Answer:

solid A

Step-by-step explanation:

I'm sorry for late

Answer:

Step-by-step explanation:

Happy Ramadan!

Hope this help :)

Answer:

yes but no a statistical question is determined by requiring multiple data

Step-by-step explanation:

Answer:

well A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question.

Step-by-step explanation:

mark braniliest pls

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

1,176 | 588

Step-by-step explanation:

118 + 168 + 151 + 151 = 588

588 x 2 = 1,176

Answer:

B

Step-by-step explanation:

You can see it would come out to be one with 44/4 so if you made it m/7 it would have to come out with a one so it would be 77.

The proportion 44/4=m/7 can be used to determine the value of m.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The  ratio of miles biked to hours biked is constant.

The given table is

Miles biked    11        44     m        132    165

Hours biked    1         4       7         12      h

We have to find the value of m.

m is the number of miles biked in 7 hr.

By using the proportion we can find m.

44/4=m/7

11=m/7

Apply cross multiplication

m=77

Hence, the proportion 44/4=m/7 can be used to determine the value of m.

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Answer:

Yes, lines M and N intersect because their slopes are different.

Step-by-step explanation:

First, we can start out by finding the slope of Line M and Line N. The slope formula is (y_2 - y_1)/(x_ 2- x_1)

Slope of Line M:

(3--11) / (3--4)

(3+11) / (3+4)

14/7

2

Now we know that the slope of Line M is 2.

Slope of Line N:

(9--2) / (-6-5)

11/-11

The slope of Line N is -1!

Since the slopes of Line N and M are different, they intersect. The answer is Yes, lines M and N intersect because their slopes are different.

If the slopes were the same, Line N and M would NEVER intersect because they are parallel.

Hope this helps

Answer: 55% of the seats in the theater were filled by the 6th graders on the trip.

Step-by-step explanation:

Given: Total seats = 3100

Seats vacant=  1395

Seats occupied by 6th graders = 3100-1395 = 1705

The percentage of the seats in the theater were filled by the 6th graders on the trip = \(\dfrac{\text{Seats occupied by 6th graders}}{\text{Total seats}}\times100\)

\(=\dfrac{1705}{3100}\times100\\\\= 55\%\)

Hence, 55% of the seats in the theater were filled by the 6th graders on the trip.

Answer:

Let be "x" the cost in dollars of a hamburger and "y" the cost in dollars of a soft drink.

The cost of 4 hamburguers can be represented with this expression:

4x4x

And the cost of 6 soft drinks  can be represented with this expression:

6y6y

Since the total cost for 4 hamburgers and 6 soft drinks is $34, you can write the following equation:

4x+6y=344x+6y=34   [Equation 1]

 The following expression represents the the cost of 3 soft drinks:

3y3y

According to the information given in the exercise, the total cost for 4 hamburgers and 3 soft drinks is $25. Then, the equation that represents this is:

4x+3y=254x+3y=25 [Equation 2]

Therefore, the Equation 1 and the Equation 2 can be used to determine the price of a hamburger and the price of a soft drink

Answer:

3x + 6y = 27

3x + 3y = 18

x = $3, y = $3

Step-by-step explanation:

I will solve by using the elimination method.

3x + 6y = 27

3x + 3y = 18

Subtract top equation by bottom.

3x + 6y = 27

- (3x + 3y = 18)

_____________

  0 +  3y  =  9

3y = 9

y = 3

Plug y in for three

3x + 6*3 = 27

3x + 18 = 27

3x = 9

x = 3

So, your solution is x = $3, y = $3

Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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The four second-order fractional subsidiaries are ∂²f/∂x², ∂²f/∂y, ∂²f/∂x∂y, ∂²f/∂y∂x.

To calculate all four second-order fractional subsidiaries of a work, we ought to separate the work twice with regard to each variable. Let's indicate the work as f(x, y).

The four second-order fractional subsidiaries are:

∂²f/∂x²: This speaks to the rate of change of the work with regard to x, twice. We are able calculate it by separating ∂f/∂x with regard to x.

∂²f/∂y²: This speaks to the rate of alter of the work with regard to y, twice. Ready to calculate it by differentiating ∂f/∂y with regard to y.

∂²f/∂x∂y: This speaks to the rate of alter of the work with regard to x and after that y. We are able calculate it by separating ∂f/∂x with regard to y.

∂²f/∂y∂x: This speaks to the rate of alter of the work with regard to y and after that x. Ready to calculate it by separating ∂f/∂y with regard to x.

It's vital to note that the arrange of separation with regard to diverse factors can surrender diverse comes about in common. In any case, in the event that the blended halfway subordinates (∂²f/∂x∂y and ∂²f/∂y∂x) are rise to, at that point the work shows symmetry within the factors x and y.

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Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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well if that's in a math problem then its division. Because you are sharing equally.

Answer:

tanθ = \(\frac{15}{8}\)

Step-by-step explanation:

let the unknown side be x , then

Using Pythagoras' identity in the right triangle

x² + 5² = 17²

x² + 25 = 289 ( subtract 25 from both sides )

x² = 225 ( take the square root of both sides )

x = \(\sqrt{225}\) = 15

Then

tanθ = \(\frac{opposite}{adjacent}\) = \(\frac{15}{8}\)

The interval where the derivative function f'(x) has a relative maximum is -2.478 and 1.732 (B) only.

To find the relative maximum of a function, we need to find the critical points of the derivative function. Critical points are where the derivative function is equal to zero or undefined. In this case, the derivative function is f'(x) = sin(x^2 − 3).

To find the critical points, we need to set the derivative function equal to zero and solve for x:
sin(x² − 3) = 0

x² − 3 = nπ, where n is an integer

x² = nπ + 3

x = ±√(nπ + 3)

We need to find the values of x that are in the interval −3 < x < 3. By plugging in different values of n, we can find the critical points in this interval:

n = 0: x = ±√3 ≈ ±1.732

n = 1: x = ±√(π + 3) ≈ ±2.478

n = 2: x = ±√(2π + 3) ≈ ±2.915 (not in the interval)

So the critical points in the interval are -2.478, -1.732, 1.732, and 2.478.

To determine which of these are relative maximums, we need to look at the sign of the derivative function on either side of the critical points. If the derivative function changes from positive to negative at a critical point, then that point is a relative maximum.

At x = -2.478, the derivative function changes from positive to negative, so this is a relative maximum.

At x = -1.732, the derivative function changes from negative to positive, so this is not a relative maximum.

At x = 1.732, the derivative function changes from positive to negative, so this is a relative maximum.

At x = 2.478, the derivative function changes from negative to positive, so this is not a relative maximum.

Therefore, the values of x in the interval −3 < x < 3 where f has a relative maximum are -2.478 and 1.732.

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Answer: 1182

Step-by-step explanation: