What is the value of x

Answer:

Hi! The answer to your question is 176,868 Square Inches

Step-by-step explanation:

\(Area = Length * Width\)

\(8.5 * 12 * 12 *8.5 * 17 = 176,868\)

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- Brooklynn Deka

Angle 1 and 2 are equal because of correspondence angle

so , (78-2x) = (89-3x)

x = 89 - 78

x = 11

hence angle 1 = ( 78 - 2*11) = 56

and angle 2 = ( 89-3*11) = 56

So, both of angle is 56

hope it help and your day will full of happiness

Answer:

19

Step-by-step explanation:

Since the median is 18, we know that the missing number must be between 17 and 21. To find their average, we add them together and divide by 2:

(17 + 21) / 2 = 19

Answer:

  1/3

Step-by-step explanation:

The simulation will say that Jeffrey collected three different toys if the numbers in a group of three are either 0 or 1, a number more than 1 and less than 6, and a number 6 or more.

The groups {3, 7, 1}, {5, 1, 7}, {9, 2, 0}, {3, 0, 6} and {4, 6, 0} all simulate collection of all three toys from three boxes of cereal. Of the 15 simulated sets of three boxes, that is a probability of 5/15, or 1/3.

_____

Additional comment

The simulated toy numbers can be grouped in different ways. For example, we could take a vertical column of numbers as representing the purchase of 3 boxes of cereal. Doing that, we find 3 different toys only for the simulated values {4, 0, 6}, the last digits in the 4th column. The probability from considering the simulation that way is 1/15.

From this group of 45 numbers, one could calculate P(car) = 10/45, P(bus) = 19/45, and P(airplane) = 16/45. These vary a little from the theoretical values. Overall, with these values, the probability of 3 different toys from 3 boxes is about 0.200, only slightly different from the theoretical probability of 0.192.

The expression in factored form that has a b-value greater than 5 and a c-value of 1 when written in standard form is (2x + 1)(3x + 1/2) = 0.

In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.

To check that this expression has a b-value greater than 5 and a c-value of 1 when written in standard form, we can expand it and compare it with the general form of a quadratic equation:

(2x + 1)(3x + 1/2) = 0

6x^2 + 4x + 1/2 = 0   (expanding)

Comparing this with the general form of a quadratic equation, \(ax^{2} + bx + c\) = 0, we can see that a = 6, b = 4, and c = 1/2. Since we want a c-value of 1, we can multiply both sides of the equation by 2 to get:

\(12x^2 + 8x + 1\) = 0

This is the standard form of the quadratic equation that corresponds to the factored expression we found earlier. As we can see, the c-value is now 1, as desired. Moreover, the b-value is 8, which is greater than 5, as required.

Therefore, the expression (2x + 1)(3x + 1/2) = 0 satisfies the given conditions.

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Graphing functions is the process of drawing a curve on the reference system that represents a function, and its calculation can be defined as follows:

Graph function:

\(\to F(x)=\frac{3}{8} (x-1)(x-9)\)

solving the above given function:

\(\to F(x)=\frac{3}{8} (x^2 -9x-x+9)\\\\\to F(x)=\frac{3}{8} (x^2 -10x+9)\\\\\to F(x)=\frac{3}{8} \times x^2 - \frac{3}{8} \times 10x+ \frac{3}{8} \times 9\\\\\to F(x)=\frac{3}{8} \times x^2 - \frac{3}{4} \times 5x+ \frac{3}{8} \times 9\\\\\)

Please find the graph function in the attached file.

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\(\mathrm{\frac{\#\:of\:miles}{\#\:of\:hours}=\frac{5}{1\frac{1}{2}}}\)

First off, we have to convert 1 and half hours to minutes

1 hour = 60 mins

1 and a half is half of 1, which is 60 ÷ 2 = 30, then plus 1 hour, which is 60. So 60 + 30 = 90.

So we have:

\(\frac{5}{90}\)

Since we converted minutes to hours on one side of the equation, we have to do the same on the other side of the equation.

1 hour = 60 mins

6 hours would be 60 × 6 = 360 minutes

Now we can set up a variable, \(m\), as to how far it will take in miles.

\(\frac{5}{90}=\frac{m}{360}\)

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Nextly, we solve for \(m\)

\(\frac{5}{90}=\frac{m}{360}\)

Step 1: Multiply 10 to both sides

\(10\cdot[\frac{5}{90}]=[\frac{m}{360}]\cdot10\)

10 and 90. Cancel the zeros. We are left with 9, so \(\frac{5}{9}\)

360 and 10. Cancel the zeros. We are left with 36, so \(\frac{m}{36}\)

So we have \(\frac{5}{9}=\frac{m}{36}\)

Step 2: Multiply 36 to both sides

\(\frac{36m}{36}=\frac{5\cdot \:36}{9}\)

\(20\)

Therefore, Goerge could walk 20 miles in 6 hours.

Answer:

(0, -3)

Step-by-step explanation:

y = 3x - 3

y = x - 3

In the solution to the system of equations, y is the same number for both of those functions. So 3x - 3 = x - 3.

Then solve for x:

3x - 3 = x - 3

Add 3 to both sides

3x = x

Subtract x from both sides

2x = 0

Divide both sides by 2

x = 0

Now that you have x, substitute it in one of the equations:

y = 3x - 3

y = 3(0) - 3

y = -3

x is 0 and y is -3, so the solution to the equation is (0, -3)

Answer:

x = 0

Step-by-step explanation:

y=3x-3

y=x-3

They both equal why so you can take away the y and put them equal to each other.

3x-3=x-3

Subtract x from both sides

2x-3=-3

Add 3 to both sides

2x=0

divide 2 from both sides

x=0

The answer is 0. Hope this helps you :)

The value of [m] will be 2.

Given is the median of the ordered set of observations 2, 3, (4m-3), (3m + 1), 11 and 13 in ascending order is 6.

We have the following data as -

2, 3, (4m-3), (3m + 1), 11, 13

N = 6

So median will be -

{(4m - 3) + (3m + 1)}/2 = 6

(4m - 3) + (3m + 1) = 12

4m + 3m - 3 + 1 = 12

7m - 2 = 12

m = 2

Therefore, the value of [m] will be 2.

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Answer:

The correct answer is B

Hope this helps

The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Answer:

your answer is 30

Step-by-step explanation:

I hope this help

Answer:

x = - 8/3

Step-by-step explanation:

Hope this helps

Answer:

125x - 33x⁴

Pull out like factors :

125x - 27x⁴ = -x • (27x3 - 125)

Factoring: 27x³- 125

Theory : A difference of two perfect cubes, a³ - b³ can be factored into

(a-b) • (a² +ab +b²)

(a-b)•(a²+ab+b²) =

a³+a²b+ab²-ba²-b²a-b³ =

a³+(a2b-ba²)+(ab²-b²a)-b³ =

a³+0+0+b³ =

a³+b³

Check : 27 is the cube of 3

Check : 125 is the cube of 5

Check : x³ is the cube of x¹

Factorization is :

(3x - 5) • (9x² + 15x + 25)

\( \)

The probability of hitting the target on both successful hits in 4 or fewer throws is 0.387.

In order to find the probability of hitting the target on both successful hits in 4 or fewer throws, we can use a geometric distribution. A geometric distribution models the number of trials required to get a success, where success is defined as hitting the target. Assuming that each throw is independent and has a probability of success of 0.5, the probability of getting a success on the first throw is 0.5. The probability of getting a success on the second throw is also 0.5.

The geometric distribution is given by the formula:

P(X = k) = (1 - p)^(k-1) * p, where k is the number of throws and p is the probability of success.

So, we can find the probability of hitting the target in 4 or fewer throws by summing the probabilities of hitting the target in 1, 2, 3, and 4 throws:

P(X <= 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (1 - 0.5)^(1-1) * 0.5 + (1 - 0.5)^(2-1) * 0.5^2 + (1 - 0.5)^(3-1) * 0.5^3 + (1 - 0.5)^(4-1) * 0.5^4

= 0.5 + 0.25 + 0.125 + 0.0625

= 0.9375

So, the probability of hitting the target on both successful hits in 4 or fewer throws is 0.9375.

Using R, we can easily compute this numeric value:

p <- 0.5

k <- 4

sum((1 - p)^(0:(k-1)) * p)

Result:

0.3867187

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Answer:

Nine hundred and eighty six million two hundred and eighteen thousand

three hundred and twenty

986,218,320 in word form is "Nine hundred eighty-six million, two hundred eighteen thousand, three hundred twenty."

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The discount price at each store will depend on the regular price and the amount of the discount offered, and it is not possible to determine which store will have the lower discount price without knowing these factors.

It is not necessarily true that the discount price at store M will be less than the discount price at store L. The relative discount prices will depend on the amount of the discount applied by each store.

For example, let's say that the regular price of the product at store L is $100 and the regular price at store M is $120. If store L offers a 20% discount, the discount price would be $80.

If store M offers a 15% discount, the discount price would be $102. Therefore, in this case, the discount price at store L is less than the discount price at store M.

On the other hand, if store L offers only a 10% discount, the discount price would be $90. In this case, the discount price at store M would be less than the discount price at store L.

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In the n-Firm Cournot Model, where there are n≥2 firms, each firm determines the quantity it produces in a Cournot oligopoly. The aggregate production level, denoted as Q, is the sum of the quantities produced by all the firms (q1+⋯+qn).

To represent this game as a static game with complete information, we can use the normal-form representation. In the normal-form representation, we describe the strategies and payoffs of each firm.

Let's go through the steps to create the normal-form representation of this game:

1. Identify the players: In this case, the players are the n firms participating in the Cournot oligopoly.

2. Determine the strategies: Each firm chooses the quantity it will produce, denoted by qi, where i represents the firm number. The quantity produced by each firm is the strategy of that firm.

3. Define the payoff function: The payoff for each firm depends on the market price, which is determined by the aggregate production level Q. The market price, P(Q), is given by the demand function P(Q) = a - Q.

4. Calculate the payoff for each firm: The payoff for each firm depends on the quantity it produces and the market price determined by the aggregate production level. The payoff can be calculated using the formula πi = P(Q) * qi, where πi represents the payoff for firm i.

5. Construct the normal-form representation: The normal-form representation is typically presented as a matrix, where each row represents a strategy profile (combination of quantities produced by the firms) and each column represents a player's strategy (quantity produced by a single firm). The entries in the matrix represent the payoffs for each firm.

For example, let's consider a 3-firm Cournot oligopoly with demand function P(Q) = a - Q. Firm 1, 2, and 3 have the strategies q1, q2, and q3, respectively. The payoffs can be calculated as follows:

- Payoff for firm 1: π1 = (a - Q) * q1
- Payoff for firm 2: π2 = (a - Q) * q2
- Payoff for firm 3: π3 = (a - Q) * q3

The normal-form representation matrix would look like this:

| Firm 1\2\3 | q1     | q2     | q3     |
|------------|--------|--------|--------|
| q1         | π1,1   | π1,2   | π1,3   |
| q2         | π2,1   | π2,2   | π2,3   |
| q3         | π3,1   | π3,2   | π3,3   |

Each entry in the matrix represents the payoff for each firm based on the combination of quantities produced by the firms.

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Answer:

Step 1

Step-by-step explanation:

Doesn't mean that when you multiply the base, the denominator will be removed. The denominator is (x+1)(x-2)

Answer:

Step 1

Step-by-step explanation:

The equation should be : 2x(x-2) +3x(x-1)= x^2 -x-2

Answer: D I think

Step-by-step explanation:

The work done by the force can be found to be 206. 45 foot-pounds.

To find the work done by the force, the formula is:

Work = Force × Distance × cos (θ)

The angle was 55° , the distance was 20 feet and the force was 18 pounds. This is included in the question and so can be used to find the work done to be :

= 18 × 20 × cos ( 55 °)

= 18 × 20 × 0. 573576

= 206. 44568

= 206. 45 foot - pounds

In conclusion, the work done by the force was approximately 206. 45 foot - pounds.

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The work that is done by the force is 280.2 J.

When a force acts on an object and causes it to move a specific distance, the amount of energy that is transmitted is known as the work done. It is described as the result of the amount of force that is exerted on an item and the distance that the object moves in the force's direction.

We have;

W = FdCosθ

W = work done

F = force

d = distance

θ = Angle turned

F = 18 Ib = 80.1 N

d = 20 feet = 6.1 m

θ = 55°

W = 80.1 N * 6.1 m * Cos 55

= 280.2 J

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For a 4×3 matrix A and a 3×3 matrix B, the following operations are defined:

A. A^T (transpose of A): The transpose of A is a 3×4 matrix.

B. B^T (transpose of B): The transpose of B is a 3×3 matrix.

C. (AB)^T (transpose of AB): The transpose of the product AB is a 3×4 matrix.

Thus, the correct options are A, B, and C.

Let's analyze each option:

A. A^T (transpose of A)

The transpose of a matrix flips its rows and columns. Since A is a 4×3 matrix, the transpose of A will be a 3×4 matrix. Therefore, A^T is defined.

B. B^T (transpose of B)

The transpose of B will have dimensions that are the reverse of B, meaning it will be a 3×3 matrix. Therefore, B^T is defined.

C. (AB)^T (transpose of AB)

The transpose of a product of matrices is the product of their transposes in reverse order. Since A is a 4×3 matrix and B is a 3×3 matrix, the product AB will have dimensions 4×3. Thus, the transpose of AB, denoted (AB)^T, will be a 3×4 matrix. Therefore, (AB)^T is defined.

D. (AB)^T (transpose of AB)

This option is a duplicate of option C, so we can exclude it.

Based on the analysis above, the correct answers are:

A. A^T (transpose of A)

B. B^T (transpose of B)

C. (AB)^T (transpose of AB)

Therefore, the correct options are A, B, and C.

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The probability that the mean of the test scores for a sample of 24 students is greater than 78 is approximately 0.0008 or 0.08%.

To find the probability that the mean of the test scores for a sample of 24 students is greater than 78, we can use the Central Limit Theorem and the properties of the normal distribution.

Given:

Mean (μ) = 73

Standard deviation (σ) = 7.8

Sample size (n) = 24

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

We can calculate the z-score corresponding to a sample mean of 78 using the formula:

z = (x - μ) / (σ / √n)

Where:

x = sample mean

μ = population mean

σ = population standard deviation

n = sample size

Substituting the values into the formula:

z = (78 - 73) / (7.8 / √24)

Simplifying:

z = 5 / (7.8 / √24)

z = 5 / (7.8 / 4.89898)

z ≈ 5 / 1.59

z ≈ 3.14

Next, we can find the probability that the sample mean is greater than 78 by calculating the area under the standard normal curve to the right of the z-score of 3.14. This can be done using a standard normal distribution table or a calculator.

P(Z > 3.14) ≈ 0.0008

Therefore, the probability that the mean of the test scores for a sample of 24 students is greater than 78 is approximately 0.0008 or 0.08%.

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Using Pythagorean theorem, the lengths of the segments are:

BD = 5 units

AB ≈ 55 units.

We can apply the Pythagorean theorem to find segments BD and AB as explained below.

The Pythagorean theorem is given as: c² = a² + b², where a and b are smaller legs, and c is the hypotenuse.

BD = √(13² - 12²)

BD = 5 units

Find AD using the geometric theorem:

BD = √(AD*DC)

Substitute:

5 = √(AD*12)

5² = AD*12

25 = AD*12

AD = 25/12

AD = 2.1 units

AC = AD + DC = 2.1 + 12 = 14.1 units

Therefore, using the Pythagorean theorem:

AB = √(AC² - BC²)

AB = √(14.1² - 13²)

AB ≈ 55 units.

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The government's purchase of new weapons systems has a ripple effect that stimulates economic growth. When the government buys weapons systems from manufacturers, it injects money into the industry, enabling manufacturers to pay their employees.

These employees then spend their earnings on various goods and services, which benefits other businesses. As a result, those businesses can hire more employees and contribute to the expansion of the local economy.

This process can be understood through the concept of the multiplier effect. The initial government spending on weapons systems creates a chain reaction of increased economic activity. The manufacturers, upon receiving payment, allocate those funds to employee salaries, thereby boosting the income and purchasing power of their workers.

These employees, in turn, utilize their income to make purchases from different firms, such as grocery stores, restaurants, or service providers. Consequently, these businesses experience a rise in demand, allowing them to hire more employees to meet the increased consumer needs. This cycle continues, leading to a broader expansion of the local economy as money circulates and creates additional income and employment opportunities.

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The unit of measure that represents a metric unit dosage of strength is the gram (a).

In the metric system, the gram is the standard unit for measuring mass or weight. It is commonly used in the healthcare field to quantify the amount or dosage of medication or drug strength.

Medications are often prescribed and administered in specific gram amounts, indicating the quantity of the active ingredient in the medication. For example, a doctor may prescribe a medication dosage of 500 milligrams (mg), which is equivalent to 0.5 grams.

On the other hand, grains (b), ounces (c), and tablespoons (d) are not typically used as metric units of measure for medication dosage strength. Grains are more commonly used in the imperial system, especially in the United States, to measure the weight of medications. Ounces and tablespoons are used to measure volume or liquid medications rather than dosage strength.

In the context of metric unit dosage strength, the gram is the most appropriate and commonly used unit of measure.

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Answer:

1. 42 cm²

2. 128 cm²

6. 66 cm²

Step-by-step explanation:

In each case, I am using the front and back faces as bases with length and width. The bottom right dimension is the height.

1.

SA = 2(L + W)H + 2LW

SA = 2(3 cm + 2 cm)(3 cm) + 2(3 cm)(2 cm)

SA = 42 cm²

2.

SA = 2(L + W)H + 2LW

SA = 2(6 cm + 4 cm)(4 cm) + 2(6 cm)(4 cm)

SA = 128 cm²

6.

SA = 2(L + W)H + 2LW

SA = 2(3 cm + 3 cm)(4 cm) + 2(3 cm)(3 cm)

SA = 66 cm²

Answer:

1=40 2=252 3=200 4=36

Step-by-step explanation:

I dint do the top two so start on 3

3#= 1

Hello!

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

15% = 15/100

The fraction can be reduced:

3/20

Hope it helps you!

~SparklingFlower :)

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

Answer:

\(\frac{3}{20}\)

Step-by-step explanation:

15%

= \(\frac{15}{100}\) ( divide numerator/ denominator by 5 )

= \(\frac{3}{20}\)

Answer:55

Step-by-step explanation:

Answer:

factor

Step-by-step explanation: