A rectangle has a length of 6 inches, and a width
of 4 inches. What is the area of this rectangle

To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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The area of the canvas which was covered by the painted red rose is given by the equation A = 429 inches²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular canvas be R

Let the area of the painted rose be A

Now , the painted rose covers 50 % of the canvas

And , the length of the canvas L = 33 inches

The width of the canvas = 26 inches

So , the area of the rectangular canvas = 33 x 26

The area of the rectangular canvas = 858 inches²

Now , the area of the painted rose = ( 1/2 ) x area of the rectangular canvas

So , the area of the painted rose A = ( 1/2 ) x 858

The area of the painted rose A = 429 inches²

Hence , the area of the painted rose is 429 inches²

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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Andualem needs to sell approximately 113 furniture pieces in order to break even.

To break even, Andualem needs to sell enough furniture to cover the total investment cost and the cost per item. By dividing the total investment cost by the profit per item, we can determine the volume of furniture Andualem needs to sell in order to break even.

To calculate the volume of furniture necessary for Andualem to break even, we need to consider the total investment cost and the cost per item.

The total investment cost includes the cost of plant and equipment, which is estimated to be $225,000. The cost per item includes labor, materials, packaging, and shipping, which amounts to $1,000 per item.

To break even, Andualem needs to cover both the total investment cost and the cost per item through the sale of furniture. The profit per item can be calculated as the selling price minus the cost per item, which is $3,000 - $1,000 = $2,000.

Now, to determine the volume of furniture necessary for Andualem to break even, we divide the total investment cost by the profit per item.

Volume = Total investment cost / Profit per item

Volume = $225,000 / $2,000

Volume = 112.5

Therefore, Andualem needs to sell approximately 113 furniture pieces in order to break even. It is important to note that the volume calculated is rounded up to the nearest whole number, as selling fractional furniture pieces is not feasible.

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Answer:

the first step is to change the mixed fraction into an improper fraction so 4 and 1/5 will be 21/5 so then you question will be three times 21/5 and the answer is 12 and 3/5

Answer:

Third Option: It is not a good fit for the data. Most of the data points are above the line.

Step-by-step explanation:

First of all, if we graph the line y = 100x, we get the following data points:

0, 0

1, 100

2, 200

3, 300

4, 400

5, 500

6, 600

7, 700

8, 800

9, 900

10, 1000

11, 1100

12, 1200

Once we graph the following data points and draw a line connecting them in the scatter plot, we can check if the line is the best fit.

Then we get the answer.

No, the line y = 100x is not the line of best fit for the given scatter plot. The line of best fit is a straight line that is the best approximation of the given set of data. It is used to study the nature of the relation between two variables. A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible).

Look at the picture I attached.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.

There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.

To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.

As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.

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The time it takes for the wave to travel from point A to point B is 0.0086 seconds.

Assuming the question is referring to a sinusoidal wave with a frequency of 50 Hz, we can use the wave speed formula to calculate the time it takes for the wave to travel from point A to point B.

Wave speed (v) = frequency (f) x wavelength (λ)

Since the frequency is given as 50 Hz, we need to determine the wavelength to find the wave speed.

To calculate the wavelength, we can use the distance between two consecutive points on the wave that is in phase, such as points A and D or B and C. From the given information, we know that the distance between A and D or B and C is one wavelength. Therefore, we can calculate the wavelength as follows:

wavelength (λ) = distance between A and D or B and C = 10 m - 3 m = 7 m

Using the wave speed formula and the calculated wavelength, we can find the wave speed:

v = f x λ = 50 Hz x 7 m = 350 m/s

Now we can use the wave speed formula to find the time it takes for the wave to travel from point A to point B:

v = d / t

where d is the distance between A and B (which is 3 m) and t is the time it takes for the wave to travel that distance.

Rearranging the formula, we get:

t = d / v = 3 m / 350 m/s = 0.0086 s

Therefore, the time it takes for the wave to travel from point A to point B is 0.0086 seconds.

To find the amplitude of the wave, we would need additional information, as the amplitude is the maximum displacement of the wave from its equilibrium position.

As for whether points A and B are in phase, we need to compare the phase difference between the two points to the wave period. The period of a wave is the time it takes for one complete oscillation, and it is given by:

period (T) = 1 / frequency (f) = 1 / 50 Hz = 0.02 s

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The price of the watch before the discount is calculated to be £24.44.

As the total price of the watch and a pair of trainers is £53. 55 and the price of the trainer before the discount was £38, we first calculate the price of the trainers after the discount as follows;

discount on a pair of trainers = 15/100 × 38 =  £5.7

cost of trainers after discount =  £38 - 5.7 =  £32.3

Now the price of the watch after the discount can be calculated by subtraction as follows;

price of watch after discount = total price - price of trainers after discount

price of watch after discount =  £53. 55 - £32.3

price of watch after discount = £21.25

Now the price of the watch before the discount can be calculated as follows;

price of watch before discount = £21.25 × 15/100

price of watch before discount = £21.25 + £3.1875

price of watch before discount = £24.44

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The height of the cone in discuss as required to be determined is; 16.38 cm.

Since the height of the cone is three times the length of the diameter of its base;

h = 3d;

d = h/3

Therefore, radius,

r = d/2

r = h/3 ÷ 2

multiply by the reciprocal of 2

r = h/3 × 1/2

r = h / 6.

Volume of a cone, V = (1/3) πr²h

128 = (1/3) × (22/7) × (h³/36)

h³ = 4398.55

h = 16.38 cm.

Ultimately, the height of the cone is; 16.38 cm.

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Answer:

the perimeter is 960

Step-by-step explanation:

The computation of the perimeter is shown below;

If we assume

= (24 × 2) + (6 × 2)

= 48 + 12

= 60

And, the area is 16 times to that of original So

= 60 × 16

Hence, the perimeter is 960

Answer:

x-intercept= (5,0)

y-intercept= (0,-2)

Slope= 2/5

Step-by-step explanation:

Answer:

|x - 2| = 15 ; |x + 2| = 15

Step-by-step explanation:

Given that:

Wait time = 15 minutes

Variation in wait time depending on level of hotness = 2 minutes

X ± 2 = 15

x + 2 = 15 or x - 2 = 15

x = 15 - 2 = 13 or x = 15 + 2 = 17

Hence, to express the above as an absolute value equation :

|x - variation| = mean time

|x - 2| = 15 ; |x + 2| = 15

Answer:

c = 202 children use the pool, and 284 - 202, or 82 adults.

Step-by-step explanation:

Represent the number of children by c and the number of adults by a.

There are a total of 284 people using the pool, so c + a = 284.

Admission fees are $1.50/child and $2.00/adult.  $1.50c is the amount taken in through ticket sales for c children;  $2.00a for adults.

Then total ticket sales are ($1.50/child)c + ($2.00/adult)a = $467.

Going back to c + a = 284, a = 284 - c, and so the above equation becomes

($1.50/child)c + ($2.00/adult)(284 - c) = $467

After simplifying this equation in c, we get:

1.50c + 568 - 2c = 467, or

101 = 0.5c.  Thus, c = 202 children use the pool, and 284 - 202, or 82 adults.

Answer:

-7

Step-by-step explanation: kahn

Answer:

(0,-7)

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 3x-7

The slope is 3 and the y intercept is -7

(0,-7)

Answer:

41.4

Step-by-step explanation:

92 x .45 =41.4

6

6/3

isthe simplestform pls markme as brainlist

The sum of expression \(1.723 \times 10^{2}\) and \(7.38 \times 10^{3}\) is \(7.5523 \times 10^{3}\). The numbers in scientific notation are added by summing the coefficients while keeping the exponent unchanged.

In scientific notation, numbers are expressed as a coefficient multiplied by a power of 10. To add numbers in scientific notation, we need to ensure that the powers of 10 are the same.

In this case, both numbers are already in scientific notation with powers of 10. We can directly add the coefficients while keeping the exponent the same.

Adding \(1.723 \times 10^2\) and \(7.38 \times 10^3\) gives us a sum of \(7.5523 \times 10^3\). The coefficient represents the numerical value, and the power of 10 indicates the magnitude.

Thus, the expression \(1.723 \times 10^2 + 7.38 \times 10^3\) evaluates to \(7.5523 \times 10^3\), indicating a significant increase in magnitude compared to the individual numbers.

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Answer:

(3,6)

(4,7)

(5,8)

(6,9)

Step-by-step explanation:

Basically, you plug in the x value into the equation to get your y value.

Answer:

(3,6)(4,7)(5,8)(6,9)

Step-by-step explanation:

Use the numbers in the x column by inserting them into the equation to get y.

y=x+3

3+3=6

4+3=7

5+3=8

6+3=9

(hope this helps :P)

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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The probability that a child chosen at random from the class has both a cat and a dog is 1/10.

Suppose b is the total number of kids that have both:

• children having a cat Only must be 14 - b

• children having a dog Only must be 19 - b

We also get:

We also know there are 30 kids, therefore

⇒ (14 - b) + b + (19 - b) = 30

⇒ 33 - b = 30

⇒ b = 3

Consequently, we now understand:

3/30 = 1/10

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The odds that a woman will get divorced from her first marriage by the time she is 40 depend on various factors such as location, cultural norms, socioeconomic status, and individual circumstances.

Therefore, a specific value cannot be provided without more information about the population being studied.

However, according to statistics from the United States Census Bureau, the estimated probability of a first marriage ending in divorce by the 20th wedding anniversary is about 52%. This suggests that the odds of a woman getting divorced from her first marriage before age 40 are relatively high.

It's worth noting that divorce rates and probabilities can vary widely based on factors such as age, education level, income, and race/ethnicity. Additionally, divorce is a complex and often emotionally charged issue that is influenced by a wide range of individual and societal factors.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

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The detail from “The Gold Coin” that best supports the inference that Juan is beginning to enjoy reconnecting with people is when he helps the old woman carry her basket of fruit.

Juan is a thief, and he has been for many years. He has no friends, and he doesn't care about anyone but himself. But when he sees the old woman struggling with her groceries, he stops and helps her.

This act of kindness shows that Juan is beginning to change. He is starting to care about other people, and he is starting to understand that there is more to life than just stealing. This is a significant development in Juan's character, and it suggests that he is on the road to redemption.

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The sample mean is X[bar]=$1500

The sample standard deviation is S=$100

The sample size is n=70

The data set has a bell shaped distribution

The empirical rule states that

The values $1400 and $1600 are within one standard deviation away from the mean:

X[bar]+S=$1500+$100=$1600

X[bar]-S=$1500-$100=$1400

Following the rule you can expect 68% of the sample to be between them.

Whats left to do is to calculate the 68% of the sample

Around 47.6 of the farms have values per acre are between $1400 and $1600

it do be 1/4 tho not gonna lie

The average age of the two classes is 12.73 yrs.

Total age of 25 students =25×10=250years.

Total age of 30  students =30×15=450years

∴ Total age of 55 students =250+450=700years

∴ Required For 55 students   =  700/55 = 12.73 yerars

∴ The average age of the two classes is 12.73 yrs.

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Answer:

5*10^-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Midpoint  =  (x₁+ x₂)/2 , (y₁ +y₂)/2

 =   [(-1)+(-3))/2] , (-2 + 9)/2

 =   (-4/2) , (-7/2)

 =   (-2 , -3.5)

(1)  The samples being compared should be independent of each other.

(2) The populations from which the samples are drawn should follow a normal distribution.

(3) The two samples being compared should have equal variances.

To use a two-sample f-test, three conditions must be met.

Firstly, the samples being compared should be independent of each other. Independence means that the observations in one sample do not influence or depend on the observations in the other sample. This condition is important to ensure that the variability between the samples is not confounded or biased by any relationship or dependence between the observations.

Secondly, the populations from which the samples are drawn should follow a normal distribution. The assumption of normality is required for the f-test to accurately assess the differences in means between the two groups. If the data deviates significantly from a normal distribution, alternative non-parametric tests may be more appropriate.

Finally, the two samples being compared should have equal variances. This assumption, known as the assumption of equal variances or homogeneity of variances, implies that the variability within each group is similar. Violation of this assumption can affect the accuracy of the f-test results. In cases where the variances are unequal, modified versions of the f-test, such as the Welch's t-test, can be used.

In summary, the three conditions for using a two-sample f-test are independence between samples, normality of the populations, and equality of variances. These conditions ensure that the f-test accurately evaluates the differences in means between the two groups being compared.

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