in the picture .............................................................................................................................................

The sum of the first 50 terms is 3775. Let a be the first term and d be the common difference of the arithmetic sequence.

Then, the tenth term is a + 9d = 28, and the sum of the fifth and seventh terms is 2a + 12d = 32.

Solving these equations simultaneously, we get a = 2 and d = 3.

To find the sum of the first 50 terms, we use the formula for the sum of an arithmetic sequence:

S50 = (50/2)(2a + (50-1)d) = 25(2 + 49(3)) = 3775.

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The equation that represents the situation is (4 + x) / (10 + 25 + x) = 0.25

Let's start by finding the amount of medicine in the original mixture before adding any pure medicine.

The amount of medicine in the 10 grams of 15% solution is

0.15 × 10 = 1.5 grams

The amount of medicine in the 25 grams of 10% solution is

0.10 × 25 = 2.5 grams

So the total amount of medicine in the original mixture is,

1.5 + 2.5 = 4 grams

Now let x be the amount of pure medicine added.

The total amount of medicine in the final mixture is,

4 + x

The total amount of solution in the final mixture is,

10 + 25 + x

So the concentration of the final mixture is,

(4 + x) / (10 + 25 + x)

We know that this concentration is 25%, so we can write:

(4 + x) / (10 + 25 + x) = 0.25

This is the equation that represents the situation.

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The given question is incomplete, the complete question is:

A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation that represents the situation

The bottom of the ladder is moving at a rate of 4/3 ft per second.

To solve the problem, we can use the Pythagorean Theorem:[tex]$x^2 + y^2 = 64$[/tex], where x is the distance from the wall to the bottom of the ladder and y is the length of the ladder. We differentiate this equation with respect to time t and use the chain rule to get [tex]$\frac{d}{dt} (x^2 + y^2) = \frac{d}{dt} 64$[/tex]

Simplifying, we get

[tex]$2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0$[/tex]

When the bottom of the ladder is 4 feet from the wall, we have x = 4 and y = 8, so we can substitute these values into our equation and solve for [tex]$\frac{dx}{dt}$[/tex]:

[tex]$2(4)\frac{dx}{dt} + 2(8)(-2) = 0$[/tex]

[tex]$\frac{dx}{dt} = \frac{16}{8} = \frac{4}{3}$[/tex]

Therefore, the bottom of the ladder is moving at a rate of [tex]$\frac{4}{3}$[/tex] ft/s.

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An exponential model for the worth of the savings account is [tex]W = 1250(1.045)^t[/tex]

The worth predicted by the exponential model is greater than predicted by the linear model at the end of 2020 by $131.2.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided about the savings account, we would determine the growth rate as follows;

[tex]W = P_{0}e^{rt}[/tex]

Growth rate, r = 1/(1 - 0)ln(1250/1306)

Growth rate, r = ln(1250/1306)

Growth rate, r = 0.0438

In the form [tex]W = a(b)^t[/tex], the required exponential function is given by;[tex]W = 1250(1.045)^t[/tex]

Years = 2020 -2010 = 10 years.

From the linear function, we have:

W = 56t + 1250

W = 56(10) + 1250

W = $1,810.

From the exponential function, we have:

[tex]W = 1250(1.045)^t\\\\W = 1250(1.045)^{10}[/tex]

W = $1,941.2

Difference = $1,941.2 - $1,810

Difference = $131.2.

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The perimeter of the updated blueprint will be 24 times the sum of the original length and width.

If Ezra wants to multiply the dimensions of the stage by a certain percentage to make the image 12 times larger than the original, he needs to find out what percentage that is.

To do this, he can divide the desired size of the new stage by the original size of the stage, and then multiply by 100 to get the percentage increase. So, if the original blueprint dimensions are x by y, and he wants to make the image 12 times larger, the new dimensions will be 12x by 12y.

To find the percentage increase, he can use the following formula:

Percentage increase = [(new size - original size) / original size] x 100

In this case, the new size is 12 times the original size, so the formula becomes:

Percentage increase = [(12x * 12y - x * y) / (x * y)] x 100

Simplifying this expression gives:

Percentage increase = [(144xy - x * y) / (x * y)] x 100 = 14300%

Therefore, Ezra needs to multiply the dimensions of the stage by 14300% to make the image 12 times larger than the original blueprint.

To find the perimeter of the updated blueprint, he can use the formula for the perimeter of a rectangle, which is: Perimeter = 2(length + width)

In this case, the length and width have been multiplied by 12, so the new perimeter becomes:

Perimeter = 2(12x + 12y) = 24(x + y)

Therefore, the perimeter of the updated blueprint will be 24 times the sum of the original length and width.

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a. The probability that all four units are good is 0.2067 (approx),

b. The probability that exactly two units are good is 0.0226 (approx).

Given a shipment of 13 microwave ovens contains four defective units and a vending company purchases four units at random, we need to calculate the probability of the following events:

(a) all four units are good.

(b) exactly two units are good.

(a) What is the probability that all four units are good?

To solve this, we need to use the formula for the probability of an intersection of independent events.

Since the probability of getting a good unit is 9/13, then the probability of getting 4 good units in a row is calculated as follows:

P(All 4 units are good) = P(Good unit) × P(Good unit) × P(Good unit) × P(Good unit) = 9/13 × 9/13 × 9/13 × 9/13 = 47829609/232044048 = 0.2067 (approx)

(b) What is the probability that exactly two units are good?

Here, we need to use the binomial probability formula since the number of good units follows a binomial distribution. We need to find the probability of getting exactly 2 good units, given that we are purchasing 4 units.

P(exactly 2 units are good) = C(4,2) × P(Good unit)² × P(Defective unit)²

= 6 × (9/13)² × (4/13)²

= 52488/2320440

= 0.0226 (approx)

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The probability of selecting two non-defective DVD players from a group of six is 2/5. This is based on the assumption that the selection is done without replacement.

We can use the formula for calculating probabilities of combinations:

P(not defective) = number of ways to choose 2 non-defective DVD players / total number of ways to choose 2 DVD players

Total number of ways to choose 2 DVD players out of 6 is:

C(6,2) = 6! / ([2!] [4!]) = 15

Number of ways to choose 2 non-defective DVD players out of 4 is:

C(4,2) = 4! / ([2!] [2!]) = 6

Therefore, the probability that Cecil chooses 2 non-defective DVD players is:

P(not defective) = 6/15 = 2/5

So the value of P(not defective) is 2/5.

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To represent the value of the bond after x years, we can use the function:f(x) = 100 * (1 + 0.04)^xwhere x is the number of years the bond has been held.The expression (1 + 0.04) represents the growth factor of the bond per year, since the bond grows in value by 4 percent each year. By raising this factor to the power of x, we obtain the cumulative growth of the bond over x years.Multiplying the initial value of the bond, 100$, by the growth factor raised to the power of x, gives us the value of the bond after x years. This is the purpose of the function f(x).

A causal study is a study that seeks to determine whether one variable causes another variable.

The independent variable is the variable that is believed to cause the change in the dependent variable, while the dependent variable is the variable that is believed to be influenced by the independent variable.

In a causal study of the effect of shelf placement on sales of a brand of cereal, the independent variable is where the cereal was placed on the shelf. The dependent variable is sales of the cereal.

This is because the sales of the cereal are influenced by where it is placed on the shelf.The answer to the question is sales of the cereal.

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The best type of inspection to use depends on the nature of the purchase. Each type of inspection has its own advantages and disadvantages, and should be chosen based on the requirements of the product and the level of risk associated with the inspection.

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2= 2

4=10

i cant see 6 or 8

So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75. As a result, the answer is y = 31/4.

An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.

the system of equations,

[tex]y = 1 - 2x\\2x - 3(1 - 2x) = -30\\2x - 3 + 6x = -30\\8x = -27\\x = -27/8\\2(-27/8) + y = 1\\-27/4 + y = 1\\y = 1 + 27/4\\y = 31/4[/tex]

So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75.

As a result, the answer is y = 31/4.

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Answer: No

Step-by-step explanation:

Because the length of the box is shorter than the length of the club

20in<26in

The width of the box is also shorter than the width of the club

13in<16in

The height of the box is also shorter than the height of the club

11in<16in

But what about putting it at an angle?

So we know  [tex]a^{2} +b^{2} =c^{2}[/tex]

so let's try [tex]20^{2} +13^{2} =x^{2}[/tex]

                               [tex]x^{2}[/tex]=569

                               [tex]x=\sqrt{159}[/tex]

x is near 23.85 in, but 23.85<26. So no.

Answer:

The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.

Given the diameter of both the cylinder and the cone is 8 inches, the radius is 8/2 = 4 inches.

The volume of the cylinder is Vcyl = π(4)²(3) = 48π cubic inches.

The formula for the volume of a cone is V = (1/3)πr²h.

The volume of the cone is Vcone = (1/3)π(4)²(18) = 96π/3 = 32π cubic inches.

Therefore, the relationship between the volume of the cylinder and the cone is that the volume of the cone is exactly two-thirds of the volume of the cylinder.

We can see this by dividing the volume of the cylinder by the volume of the cone:

Vcyl/Vcone = (48π) / (32π) = 3/2

So, the volume of the cylinder is 1.5 times greater than the volume of the cone.

The probability that a randomly selected adult weighs between 120 and 165 lbs is approximately 0.8186.

Since the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs, we can use the standard normal distribution to calculate the probability.

We first need to standardize the values using the formula: z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation.

For x = 120 lbs, z = (120 - 140) / 25 = -0.8, and for x = 165 lbs, z = (165 - 140) / 25 = 1.0. We can then use a calculator to find the probability between -0.8 and 1.0, which is approximately 0.8186.

Thus, the chance of picking an adult at random who weighs between 120 and 165 lbs is roughly 0.8186.

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Step-by-step explanation:

2x + 2y  = 28   <=====given

x * y = 40     <===given .....  re-arrange to :

           y = 40 / x    <===substitute this 'y'  into the first equation

2x + 2 ( 40/x) = 28   <=====solve for x

2x^2 -28x + 80 = 0

x^2 -14x +40 = 0

(x -10)(x-4) = 0                        shows x = 10 or 4    then y = 4 or 10

dimensions    10    and 4   inches

Answer:

4 or 10 inches

Step-by-step explanation:

I added a photo of my solution

The measure of the larger acute angle of the triangle can be calculated using trigonometric ratios or by subtracting the measure of the smaller acute angle from 90 degrees. Without further information or given measurements, it is not possible to determine the exact measure of the angle.

Let's consider the general formula for a right triangle where A, B, and C are the angles and a, b, and c are the corresponding sides opposite to each angle:

sin A = a/c, sin B = b/c, and sin C = a/b.

For an acute triangle, we know that the sum of all the angles is equal to 180 degrees, so A + B + C = 180. If the triangle is a right triangle, then one of the angles, say C, is equal to 90 degrees, and A + B = 90 degrees.

In this case, we are only given that the angles of the triangle are acute. Therefore, we can use the formula sin A = a/c, sin B = b/c and sin C = a/b to solve for the angles or use the fact that A + B + C = 180 degrees and A + B = 90 degrees to find the measure of the larger acute angle by subtracting the measure of the smaller acute angle from 90 degrees. However, without specific measurements or additional information, we cannot determine the exact measure of the angle.

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Answer: It should be -1,7

Step-by-step explanation: x=1-2=-1

y=8-1=7

Answer:

(-1, 7)

Step-by-step explanation:

A left translation is a negative number affecting the x-coordinate.

1 - 2 = -1

A down translation is a negative number affecting the y-coordinate.

8 - 1 = 7

(1, 8) --------> (-1, 7)

Using the identity sin² 0 + cos² 0 = 1, the value of cos 0 is 0.951 (to the nearest hundredth)

Using the identity sin² 0 + cos² 0 = 1, we can solve for cos 0:

cos² 0 = 1 - sin² 0

cos² 0 = 1 - (-0.31)²

cos² 0 = 1 - 0.0961

cos² 0 = 0.9039

Taking the square root of both sides, we get:

cos 0 ≈ ±0.951

Since 0 is in the interval ³ < 0 < 2π, we know that cos 0 must be positive. Therefore, to the nearest hundredth, cos 0 ≈ 0.95.

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Answer: 6

Step-by-step explanation:

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

The factors of 78 are: 1, 2, 3, 6, 13, 26, 39, 78

Then the greatest common factor is 6.

Heres something you need to learn about the greatest common factor (gcf)

What is the Greatest Common Factor?

The largest number, which is the factor of two or more numbers is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors that are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

Let us consider the example given below:

Greatest Common Factor (GCF)

For example – The GCF of 18, 21 is 3. Because the factors of the number 18 and 21 are:

Factors of 18 = 2×9 =2×3×3

Factors of 21 = 3×7

Here, the number 3 is common in both the factors of numbers. Hence, the greatest common factor of 18 and 21 is 3.

Similarly, the GCF of 10, 15 and 25 is 5.

How to Find the Greatest Common Factor?

If we have to find out the GCF of two numbers, we will first list the prime factors of each number. The multiple of common factors of both the numbers results in GCF. If there are no common prime factors, the greatest common factor is 1.

Finding the GCF of a given number set can be easy. However, there are several steps need to be followed to get the correct GCF. In order to find the greatest common factor of two given numbers, you need to find all the factors of both the numbers and then identify the common factors.

Find out the GCF of 18 and 24

Prime factors of 18 – 2×3×3

Prime factors of 24 –2×2×2×3

They have factors 2 and 3 in common so, thus G.C.F of 18 and 24 is 2×3 = 6

Also, try: GCF calculator

GCF and LCM

Greatest Common Factor of two or more numbers is defined as the largest number that is a factor of all the numbers.

Least Common Multiple of two or more numbers is the smallest number (non-zero) that is a multiple of all the numbers.

Factoring Greatest Common Factor

Factor method is used to list out all the prime factors, and you can easily find out the LCM and GCF. Factors are usually the numbers that we multiply together to get another number.

Example- Factors of 12 are 1,2,3,4,6 and 12 because 2×6 =12, 4×3 = 12 or 1×12 = 12. After finding out the factors of two numbers, we need to circle all the numbers that appear in both the list.

Greatest Common Factor Examples

Example 1:

Find the greatest common factor of 18 and 24.

Solution:

First list all the factors of the given numbers.

Factors of 18 = 1, 2, 3, 6, 9 and 18

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24

The largest common factor of 18 and 24 is 6.

Thus G.C.F. is 6.

Example 2:

Find the GCF of 8, 18, 28 and 48.

Solution:

Factors are as follows-

Factors of 8 = 1, 2, 4, 8

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 28 = 1, 2, 4, 7, 14, 28

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest common factor of 8, 18, 28, 48 is 2. Because the factors 1 and 2 are found all the factors of numbers. Among these two numbers, the number 2 is the largest numbers. Hence, the GCF of these numbers is 2.

If you know it, dont read it

There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.

We are given the boundary-value problem:

y" + 16y = 0, y(0) = 1, y(L) = 1

The characteristic equation is r^2 + 16 = 0, which has roots r = ±4i.

The general solution to the differential equation is then y(x) = c1cos(4x) + c2sin(4x).

Using the boundary conditions, we get:

y(0) = c1 = 1

y(L) = c1cos(4L) + c2sin(4L) = 1

Substituting c1 = 1 into the second equation, we get:

cos(4L) + c2*sin(4L) = 1

Solving for c2, we get:

c2 = (1 - cos(4L))/sin(4L)

Thus, the general solution to the differential equation that satisfies the given boundary conditions is:

y(x) = cos(4x) + (1 - cos(4L))/sin(4L)*sin(4x)

Now, we can answer the questions:

(a) To have precisely one nontrivial solution, we need the coefficients c1 and c2 to be uniquely determined. From the above expression for c2, we see that this is only possible if sin(4L) is nonzero. Thus, if sin(4L) ≠ 0, there exists precisely one nontrivial solution.

(b) If sin(4L) = 0, then c2 is undefined and we have a family of solutions that differ by a constant multiple of sin(4x). Hence, there are infinitely many solutions.

(c) There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.

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The 4 in the hundredths place has a smaller value than the 4 in the tens place.

In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.

In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.

Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.


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Answer:

Step-by-step explanation:

a. 100 divided by 75 = 1.3333333333333333333333333333333

1.3333333333333333333333333333333 times 43 = 57.333333333333333333333333333332

round it to the nearest whole number: ≅ 57%

Answer:

Step-by-step explanation:

The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

We are given that V = 1607 and r = 4. We can plug these values into the formula and solve for h:

1607 = π(4^2)h

1607 = 16πh

h = 1607/(16π)

h ≈ 25.5

Therefore, the height of the cylinder is approximately 25.5 units. Note that we rounded the answer to one decimal place since the radius was given to one decimal place.

BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Triangle congruence: Two triangles are said to be congruent if their three corresponding sides and their three corresponding angles are of identical size.

You can move, flip, twist, and turn these triangles to produce the same effect. When relocated, they are parallel to one another.

Two triangles are congruent if they satisfy all five conditions for congruence.

They include the right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and angle-side-angle (SSS) (RHS).

So, in the given △DAB and △DCB:

AC = AC = Common

∠DAC = ∠BAC = AC is the angle bisector

∠DCA = ∠BCA = AC is the angle bisector

Then, △DAB ≅ △DCB under the ASA congruency rule,

Then, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Therefore, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

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The data should come from a binomial distribution. There should be no non-response or other forms of bias. The sample size should not be more than 10% of the population size, and the sample should be independent of one another.

When making inferences about one population proportion, the following assumptions need to be made:

Option 1: The sample is a simple random sample from the population.

Option 2: The sample size should be large enough so that both np ≥ 10 and n(1 − p) ≥ 10.

Option 3: The data comes from a binomial distribution.

Option 4: There is no non-response or other forms of bias.

Option 5: The sample size is no more than 10% of the population size.

Option 6: The sample is independent of one another.In order to make inferences about one population proportion, the assumptions mentioned above need to be made. It is vital to make sure that the sample is a simple random sample from the population, and that the sample size is large enough so that both np ≥ 10 and n(1 − p) ≥ 10.

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The probability of getting all tails when flipping a coin three times can be calculated using the multiplication rule of probability. For each flip of the coin, there are two possible outcomes: heads or tails.

Assuming the coin is fair, both outcomes are equally likely, so the probability of getting tails on any one flip is 1/2.

P(all tails) = P(tails on first flip) x P(tails on second flip) x P(tails on third flip)

= (1/2) x (1/2) x (1/2)

= 1/8

Therefore, the probability of getting all tails when flipping a coin three times is 1/8 or 0.125 when expressed as a decimal rounded to four decimal places.

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The measure of angle R in ΔSRT which is drawn inside the circle is 77.5°.

Circle is a two-dimensional shape that is defined as the set of all points that are equidistant from a central point. It is often represented as a round shape with a curved boundary.

Since SR is a diameter of the circle, it follows that angle STR is a right angle (90°). Therefore, we can find the measure of angle SRT using the following equation:

∠SRT + ∠STR = 180°

(2x-23°) + 90° = 180°

2x + 67° = 180°

2x = 180° - 67°

2x = 113°

x = 56.5°

∠TRS = 5x-97°

∠TRS = 5(56.5°)-97°

∠TRS = 192.5°

Finally, we can find the measure of angle SRT:

∠SRT = 180° - ∠STR - ∠TRS

∠SRT = 180° - 90° - 192.5°

∠SRT = -102.5°

Therefore, to find the measure of angle R, we need to add 180° to angle SRT:

∠R = ∠SRT + 180°

∠R = -102.5° + 180°

∠R = 77.5°

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The longest side of a triangle with angles of 50°, 60°, and 70° and a length of 9 furlongs on the shortest side is approximately 12.2 furlongs.

             The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle are known (SAS) or the lengths of the three sides (SSS) are known.

         To calculate this, using the Law of Cosines formula,

  which is:

                [tex]c^2 = a^2 + b^2 - 2abcosC[/tex]

where c is the longest side, a is the shortest side, b is the other side of the triangle, and C is the angle

between a and b.

In this case, c = 12.2 furlongs,

                    a = 9 furlongs,

                    b is the side opposite the angle 70°, and C = 70°.

So the formula becomes:

        [tex]c^2 = 92 + b^2 - 2(9)(b)cos70^{o}[/tex]

Solving for b gives us b = 12.2 furlongs, which is the length of the longest side.

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If a sample of 50 items are chosen at random.  the probability that the sample mean length is greater than 9.1 inches is 0.0571, or 5.71%.

The sample mean of the 50 items follows a normal distribution with mean equal to the population mean (μ), and standard deviation  equal to σ/√n, where n is the sample size.

Substituting the given values, we have:

= μ = 9 inches

= σ/√n = 1/√50 inches

Now, we need to standardize the sample mean distribution to find the corresponding z-score using the formula:

z = (X- μX) / σX

Substituting the given values, we have:

z = (9.1 - 9) / (1/√50) = 1.58

The probability of getting a z-score of 1.58 or less is 0.9429. Therefore, the probability of getting a z-score of 1.58 or greater is:

P(z > 1.58) = 1 - P(z ≤ 1.58) = 1 - 0.9429 = 0.051

Therefore the probability that the sample mean length is greater than 9.1 inches is 0.0571.

Learn more about probability here:https://brainly.com/question/24756209

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