If the destination is within the caller's own local exchange, then no trunks will be used. Assume that the number of trunks used, X, is a modified geometric ...

The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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Answer:

500 grams

Step-by-step explanation:

The total mass of the two containers:

  ⇒ mass of both containers added to each other

      Total Mass = Mass of First Container + Mass of Second Container

                          250 grams + 250 grams = 500 grams

Thus the total mass is 500 grams

Answer: 500 grams

Hope that helps!

For Snowman A:

The initial height of Snowman A is 28 inches, and it decreases by 4 inches per hour. So, the equation for the height of Snowman A in terms of t hours after sunrise is:

A = 28 - 4t

For Snowman B:

The initial height of Snowman B is 46 inches, and it decreases by 7 inches per hour. So, the equation for the height of Snowman B in terms of t hours after sunrise is:

B = 46 - 7t

To find when both snowmen have an equal height, we need to set A and B equal to each other and solve for t:

28 - 4t = 46 - 7t

3t = 18

t = 6

Therefore, both snowmen will have an equal height of 16 inches after 6 hours.

The four-sided geometric object known as a tetrahedron (WXYZ) has four triangle faces that are joined to one another at their edges. Its vertices are all linked, and its faces are all equilateral triangles.

The three-dimensional geometric structure known as a tetrahedron (WXYZ) has four triangle-shaped faces. The edges of each of the tetrahedron's faces are joined to one another. All of the faces are triangular shapes with equal sides, or equilateral triangles. The tetrahedron is a solid shape because all of its vertices are joined together. The tetrahedron's four vertices are joined to one another, forming a pyramid-like shape. The tetrahedron's four vertices are the only points that do not form the triangle faces. The tetrahedron's four faces come together to produce a point in the middle of the shape. The apex of the tetrahedron is where this point is located. The faces of the tetrahedron are all congruent, or identical, as they are a regular polyhedron.

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Answer:

6.828125

Step-by-step explanation:

However, if the points deviate from a straight line, it means that the residuals aren't normally distributed.

Therefore, it is important to check normality and other assumptions of the regression model.

The error term in the regression models is assumed to be normally distributed. This assumption is known as the normality assumption, and it is critical in several regression models. The model assumes that the residuals of the model are uncorrelated and normally distributed. If this assumption is not met, the model's estimates may be incorrect, which might affect the hypothesis testing and predictions.The normality assumption implies that the residuals should have a mean of zero and a constant variance.

Therefore, it's necessary to evaluate the normality assumption of the residuals by examining the residual plot and conducting normality tests. A residual plot is a graph of the residuals against the predicted values. It should be random and not show any clear patterns such as arcs or curves.

Normally, a normal probability plot is used to determine if the residuals are normally distributed. A normal probability plot graphs the residuals against a normal distribution's quantiles. If the points on the plot fall along a straight line, the residuals are distributed normally.

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Answer:

Step-by-step explanation:

\mathrm{Multiply\:the\:numerator\:and\:denominator\:by:}\:100

\mathrm{Multiply\:the\:quotient\:digit}\:\left(0\right)\:\mathrm{by\:the\:divisor}\:505

\mathrm{Subtract}\:0\:\mathrm{from}\:23

Answer:

3x+9

Step-by-step explanation:

Answer:

67.5

Step-by-step explanation:

The perimeter of the resulting rectangle is 67.5 ft

What is the perimeter of the resulting rectangle?

Given that

Perimeter = 45 ft

Scale factor = 1.5

So, we have

Resulting perimeter = 45 * 1.5

Evaluate

Resulting perimeter = 67.5

What is the area of this figure?

The area is the sum of the individual areas

The figure can be divided into two trapezoids

Using the above and the area formulas as a guide, we have the following:

Area = 1/2 * (3 + 5) * 2 + 1/2 * (3 + 7) * 4

Evaluate

Area = 28

Hence, the area is 28 sq units

Answer:

Negative 80 x + 28 y minus 56

4 (negative 20 x + 7 y minus 14)

Given:

A new type of pump can drain a certain pool in 9 hours.

An older pump can drain the pool in 11 hours.

To find:

The required time when both pumps work together to drain the pool.

Explanation:

One hour's work of the new pipe is,

One hour's work of the old pipe is,

So, one hour's work of both the pipe together is,

Therefore, the time taken to drain the pool for both the pipes together is,

Final answer:

The required time to drain the pool for both the pipes together is 4 hours 57 minutes.

300m of the fruit farm land will produce 300 kilograms of oranges. Given that 1 acre of land produces 2 tons of oranges, we can calculate the equivalent amount of oranges produced on 300m of land.

We know that 1 acre of land produces 2 tons of oranges. To find the equivalent amount of oranges produced on 300m of land, we need to convert the units of measurement.

First, we convert 1 acre to square meters. 1 acre is equal to 4046.86 square meters.

Next, we need to determine the proportion of land used. We have 300m of land, which is equivalent to 300 square meters.

Now we can calculate the amount of oranges produced on 300m of land. Since 1 acre produces 2 tons of oranges, we can set up a proportion:

1 acre / 2 tons = 300 square meters / x kilograms

Cross-multiplying the proportion, we get:

1 acre * x kilograms = 2 tons * 300 square meters

Simplifying the equation, we find:

x = (2 tons * 300 square meters) / 1 acre

x = (2 * 300) kilograms

x = 600 kilograms

Therefore, 300m of the fruit farm land will produce 600 kilograms of oranges.

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Answer:

D = 0; one real root

Step-by-step explanation:

Discriminant Formula:

\( \displaystyle \large{D = {b}^{2} - 4ac}\)

First, arrange the expression or equation in ax^2+bx+c = 0.

\( \displaystyle \large{ {x}^{2} + 6x = - 9}\)

Add both sides by 9.

\( \displaystyle \large{ {x}^{2} + 6x + 9 = - 9 + 9} \\ \displaystyle \large{ {x}^{2} + 6x + 9 = 0}\)

Compare the coefficients so we can substitute in the formula.

\( \displaystyle \large{a {x}^{2} + bx + c = {x}^{2} + 6x + 9 }\)

Substitute a = 1, b = 6 and c = 9 in the formula.

\( \displaystyle \large{D = {6}^{2} - 4(1)(9)} \\ \displaystyle \large{D = 36 - 36} \\ \displaystyle \large{D = 0}\)

Since D = 0, the type of solution is one real root.

The total number of boats that are in this marina would be 48 boats

To solve this problem, you can set up an equation using the information given in the problem. Let x be the total number of boats in the marina.

According to the problem, two-thirds of the boats in the marina are white, so:

x * 2/3 = number of white boats

The remaining boats are split between blue and red, so:

(x * 2/3) = number of white boats

x - (x * 2/3) = number of remaining boats

Five-eighths of the remaining boats are blue, so:

(x - (x * 2/3)) * 5/8 = number of blue boats

The rest of the remaining boats are red, so:

(x - (x * 2/3)) - (x - (x * 2/3)) * 5/8 = number of red boats

And we know that there are 6 red boats, so we can substitute that into the equation:

6 = (x - (x * 2/3)) - (x - (x * 2/3)) * 5/8

Solving for x, we can get the number of boats in the marina.

x = 48.

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The amount of minute to reach a distance of 9 inches from the rock is 3 minutes

The complete question is added at the end of this solution

From the question, we have the equation to be

d = 3t

A distance of 9 inches from the rock means that

d = 9

So, we have

3t = 9

Divide both sides by 3

t = 3

Hence, the amount of time is 3 minutes

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Complete question

The equation d=3t represents the relationship between the distance (d) in inches that a snail is from a certain rock and the time (t) in minutes.

How many minutes does it take for the snail to reach a distance of 9 inches from the rock?

Answer:

3.7 degrees

Step-by-step explanation:

98.8-32 = 66.8

66.8/18 = 3.7 degrees

Answer:

23

Step-by-step explanation:

Follow the PEMDAS rule

Parenthesis, exponents , Multiplication, Division, Addition, Subtraction

9 + 8 x 3 - (5x2)

9 + 8 x 3 - 10

9 + 24 - 10

9 + 14

23

Answer:

23

Step-by-step explanation:

The solution is on the link

PLS MARK ME BRAINLIEST I NEED IT

The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

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

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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The mean, standard deviation, of the average number of moths in 30 traps is approximately 0.5 ± 0.018 and is approximately 0.5 respectively. The probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

The mean of the average number of moths in 30 traps can be calculated as the mean of a sample of 30 trap counts, where the mean of each sample follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30) (using the standard error of the mean formula). Therefore, the mean of the average number of moths in 30 traps is:

mean = 0.5 ± 0.1/sqrt(30) = 0.5 ± 0.018

So the mean of the average number of moths in 30 traps is approximately 0.5 ± 0.018.

The standard deviation of the average number of moths in 30 traps can also be calculated using the standard error of the mean formula:

standard deviation = standard error of the mean * sqrt(sample size)

standard deviation = 0.5/sqrt(30) * sqrt(30) = 0.5

So the standard deviation of the average number of moths in 30 traps is approximately 0.5.

Using the central limit theorem, we can assume that the sample mean of the 30 traps follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30). We want to find the probability that the average number of moths in 30 traps is greater than 0.4.

To do this, we can standardize the sample mean using the formula:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

z = (0.4 - 0.5) / (0.5/sqrt(30)) = -1.8257

Using a standard normal distribution table or calculator, we can find the probability that Z is greater than -1.8257, which is approximately 0.965. Therefore, the probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

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Answer:

It is answer A) 5x^8y^8z^3 (sq rt 2y)

Step-by-step explanation:

1. Factor out the perfect square

(sqr rt) 5^2 × 2x^16 × y^16 xyz^6

2. Split each factor to their own square root

3. Simplify these roots

Answer:

A

Step-by-step explanation:

First let's factor 50. This will look like this: 2*5*5. Since there are two 5s, together they form a perfect square so we can bring it out of the square root. This is what we have so far now: \(5\sqrt{2x^{16} y^{17} z^{6} }\). Now we should move on to \(x^{16}\), since 16 is an even number, we can just divide it in half and put x to the power of 16/2 outside the square root. This is what we have so far: \(5x^{8} \sqrt{2y^{17}z^{6} }\). Now let's work on \(y^{17}\). Since 17 is an odd number, we will separate it like this: 16 + 1. Now we can divide 16 by 2 and put y to the power of 16 divided by 2 outside of the square root, but the last \(y^{1}\) will need to continue inside. So this is what we have so far: \(5x^{8}y^{8} \sqrt{2y z^{6}}\). Now all we have to do is take care of the \(z^{6}\). Since 6 is even we can just divide it by 2 and put the z to the power of 6 divided by 2 outside of the square root. This is what we have: \(5x^{8}y^{8} z^{3} \sqrt{2y}\).

We are done!

I hope this made sense. Please give Brainliest!

A. SAS Inequality Theorem , theorem can be used to prove triangle congruence, as congruent sides and angles can be used to determine the length of the third side, thereby proving congruence.

The SAS Inequality Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the third side of the triangle must be greater in the triangle with the larger included angle.

The SAS Inequality Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the third side of the triangle must be greater in the triangle with the larger included angle. This theorem is important to remember when comparing similar triangles, as it can help determine which triangle has the greater side length. This theorem can also be used to determine if a triangle is acute or obtuse, as the greater included angle will lead to the longer side being on the opposite side of the triangle. Additionally, this theorem can be used to prove triangle congruence, as congruent sides and angles can be used to determine the length of the third side, thereby proving congruence.

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Answer:

12

Step-by-step explanation:

First, you will have to use trigonometry. Since the side of the triangleis the opposite of the angle 53 and the hypotenuse, you will use sin.

Sin 53 degrees = opposite side / hypotenuse side.

The opposite side is x and the hypotenuse side equals 15.

sin53= x/15

15 ( sin 53 ) =x

x= 11.97953

Round

x=12

Answer:

48 years.

Step-by-step explanation:

Consider the complete question is "The ratio of ages of kissi and esinam is 3:5 and that of esinam and lariba is 3:5. The sum of ages of all 3 is 147 years. whats the age difference between oldest and youngest ?"

It is given that

Kissi : Esinam = 3:5 = 9:15

Esinam : Lariba = 3:5 = 15:25

So, the combined ratio is Kissi : Esinam : Lariba = 9:15:25

Let ages of Kissi, Esinam, Lariba are 9x, 15x and 25x.

Sum of ages of all 3 is 147 years.

\(9x+15x+25x=147\)

\(49x=147\)

\(x=3\)

The value of x is 3. So, the age of all three are

\(Kissi=9x=9(3)=27\)

\(Esinam=15x=15(3)=45\)

\(Lariba=25x=25(3)=75\)

Since Lariba is oldest and Kissi is youngest, therefore, the difference between their ages is

\(75-27=48\)

Hence, difference between oldest and youngest is 48 years.

Answer:

No

Step-by-step explanation:

Hope this helps :)

Answer:

38/35

Step-by-step explanation:

slope = (y2 - y1)/(x2 - x1) = (56 - (- 20))/(81 - 11) = 76/70 = 38/35

Answer:

\( = \frac{38}{35} \)

Step-by-step explanation:

\((81 \: \: \: , \: \: \: 56) = > (x1 \: \: \: ,\: \: \: y1) \\ (11 \: \:, \: - 20) = > (x2 \: \: \: ,\: \: y2)\)

\(slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{56 - ( - 20)}{81 - 11} \\ = \frac{56 + 20}{70} \\ = \frac{76}{70} \\ = \frac{38}{35} \)

hope this helps

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Therefore, the only claim that the interval would tend to refute is option E: The population mean is less than 125.

Based on the 90% confidence interval of 135 to 160, we can conclude that the population mean is likely to be within this interval with a 90% degree of confidence.

A. The claim that the population mean is more than 110 is not refuted by the confidence interval since the lower limit of the interval is above 110.

B. The claim that the population mean is less than 150 is not refuted by the confidence interval since the upper limit of the interval is above 150.

C. The claim that the population mean is between 140 and 150 is not refuted by the confidence interval since both values are within the interval.

D. The claim that the population mean is more than 140 is not refuted by the confidence interval since the lower limit of the interval is above 140.

E. The claim that the population mean is less than 125 is refuted by the confidence interval since the lower limit of the interval is above 125.

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Answer:

3 bags per weekday

Step-by-step explanation:

Total bags of leaves at the end of the week = 26 bags

Bags of leaves she fills over the weekend = 11 bags

Bags of leaves she fills during weekdays = x bags

Total bags of leaves at the end of the week = Bags of leaves she fills over the weekend + Bags of leaves she fills during weekdays

26 = 11 + x

Subtract 11 from both sides

26 - 11 = 11 - 11 + x

15 = x

x = 15 bags

If she fills the same number of bags with leaves on each of the 5 weekdays.

how many bags she filled each weekday.

Bags she filled each weekday = Total Bags of leaves she fills during weekdays / 5 weekdays

= 15 bags / 5 weekdays

= 3 bags per weekday

Answer:

3

Step-by-step explanation:

1. Bags filled on weekdays + bags filled on weekends = total bags filled

2. 5b + 11 = 26

3. Isolate variable (subtract 11 from both sides) = 5b=15

4. Divide both sides by 5 = 15/5 = 3

5. How many bags does Grace fill each weekday? = 3

Answer:

f(x)=2x-1

(the first option)

Step-by-step explanation:

Linear functions always take the form f(x)=mx+c, where m is the slope and c is the y-intercept.

The y-intercept is the value of y when x is 0, and we can see from the table that when x=0, y=-1. So our value for c is -1.

The slope can be found using the formula \(\frac{y2-y1}{x2-x1}\), where (x1,y1) and (x2,y2) represent two points that satisy the funciton. Let's talk the first two sets of values for the table to use in this formula -  (-5,-11) for (x1,y1) and (0,-1) for (x2,y2) :

m=  \(\frac{y2-y1}{x2-x1}\) = \(\frac{-1-(-11)}{0-(-5)}\)=\(\frac{-1+11}{0+5}\)=\(\frac{10}{5}\)=2

So now we know m=2 and c=-1. Subbing this into f(x)=mx+c and we get:

f(x)=2x-1

Answer:

f(x)=2x-1

Step-by-step explanation:

for each inout of x, if you multiply it by 2 and subtract 1, you get y. :)