Solve the following system of equations 7x - 3y = 11

Let 'n' be the number of sides of a regular polygon, in which the measure of 1 interior angle is 11 times the measure of the adjacent exterior angle.

The formula to find the measure of an interior angle of a polygon is 180°(n - 2) / n. The formula to find the measure of an exterior angle of a polygon is 360° / n. We can use these formulas to form an equation that will help us find 'n'.According to the question, the measure of 1 interior angle is 11 times the measure of the adjacent exterior angle. Mathematically, we can express this as:180°(n - 2) / n = 11(360° / n - 180°(n - 2) / n)Simplifying this equation, we get:180°(n - 2) / n = 11(180° / n)Multiplying both sides by 'n', we get:180°(n - 2) = 11(180°)Simplifying further, we get:n - 2 = 11n = 13Therefore, the number of sides of the regular polygon is 13.Answer: 13

Let's denote the measure of the interior angle as x and the measure of the adjacent exterior angle as y. According to the given information, we have the equation:

x = 11y

In a regular polygon, all interior angles are congruent (have the same measure), and all exterior angles are congruent as well. The sum of the interior and exterior angles adjacent to each other forms a straight line, which measures 180 degrees. Therefore, we can write the equation:

x + y = 180

Substituting x = 11y into the equation, we get:

11y + y = 180

Combining like terms:

12y = 180

Dividing both sides by 12:

y = 15

Now, we can substitute this value back into the equation x = 11y:

x = 11 * 15 = 165

So, the measure of each interior angle is 165 degrees, and the measure of each exterior angle is 15 degrees.

In a regular polygon, the sum of the interior angles can be found using the formula:

Sum of interior angles = (n - 2) * 180

where n is the number of sides of the polygon.

Since each interior angle measures 165 degrees, we can set up the equation:

165n = (n - 2) * 180

Expanding the right side:

165n = 180n - 360

Subtracting 180n from both sides:

-15n = -360

Dividing both sides by -15:

n = 2

Therefore, the regular polygon has 24 sides.

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Let the measure of the adjacent exterior angle be x. Then the measure of the interior angle is 11x.

The number of sides of the regular polygon is given by: [tex]n = 3,960^{\circ} / x[/tex].

Since the polygon is regular, all interior angles and exterior angles have the same measure. Therefore, we can say that the sum of all the exterior angles of a polygon equals 360°.

This gives us an equation:

x + 11x + x + 11x + ...

= 360°,

where there are n terms in the sequence (since there are n sides in the polygon).

Simplifying this equation, we get:

[tex]360^{\circ}= nx[/tex]

Therefore, the number of sides of the polygon is:

[tex]n = 360^{\circ} / x[/tex]

Since the polygon is regular, each exterior angle must be congruent to x. Since the sum of all exterior angles in a polygon equals 360°, we can say that the measure of each exterior angle is:

[tex]x = 360^{\circ} / n[/tex]

Therefore, the measure of each interior angle is:

[tex]11x = 11(360^{\circ} / n)[/tex]

[tex]= 3,960^{\circ} / n[/tex]

Therefore, the number of sides of the regular polygon is given by:

[tex]n = 3,960^{\circ} / x[/tex]

Answer: The number of sides of the regular polygon is given by: [tex]n = 3,960^{\circ} / x[/tex].

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To test the claim that the sample is from a population with a standard deviation less than 0.0390 g, and using a 0.05 significance level and a parametric method, certain requirements must be satisfied. The requirements include:

A. Either or both of these conditions are satisfied:

A. the population is normally distributed or the sample size is greater than 30.

C. The sample is a simple random sample.

The normality requirement for a hypothesis test of a claim about a standard deviation differs from the normality requirement for a hypothesis test of a claim about a mean. For a hypothesis test of a claim about a standard deviation, it is not necessary for the population to be normally distributed. Instead, either the population should be normally distributed or the sample size should be sufficiently large (typically greater than 30) for the Central Limit Theorem to apply. In this case, the requirement is satisfied if either the population is normally distributed or the sample size is greater than 30. However, the sample should still be a simple random sample, which ensures that the observations are independent and representative of the population.

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Answer: Y=30x+120

Step-by-step explanation

The x stands for each week, the m stands for the money being added or subtracted. That is why the m and x are being multiplied together in the equation. The b stands for how much the person, Mike, already has. Hope this helps

D) 50%

Explanation: 18 + (18x.50) = 27

Answer:

-3(x-4)

Step-by-step explanation:

to factor, you have to find the gcf of both numbers. the gcf is -3

Answer:

-3 (x-4)

Step-by-step explanation:

Take a negative three out of each part of the problem.

Answer:

29/5

Step-by-step explanation:

Answer:

29/5

Step-by-step explanation:

As an improper fraction, your answer is 29/5.

I'm not sure what it means by writing it as a fraction "greater than 1".

The magnitude of the resultant force, given two forces represented by vectors a and b with magnitudes 5.3 N and 6.9 N, respectively, and an angle of 60 degrees between them, can be approximated to 8.5 N.

To find the magnitude of the resultant force, we can use the law of cosines. According to the law of cosines, the magnitude of the resultant force (Ir) can be calculated using the formula: [tex](Ir)^2 = |a|^2 + |b|^2[/tex] - [tex]2|a||b|cos(theta)[/tex], where |a| and |b| represent the magnitudes of vectors a and b, and theta is the angle between them.

Given that |a| = 5.3 N, |b| = 6.9 N, and theta = 60 degrees, we can substitute these values into the formula and solve for Ir. Plugging in the values, we have [tex]Ir^2 = (5.3)^2 + (6.9)^2[/tex]- 2(5.3)(6.9)cos(60).

Simplifying the equation, we get [tex]Ir^2[/tex] = 28.09 + 47.61 - 36.66. Combining the terms, we have [tex]Ir^2[/tex] = 39.04.

Taking the square root of both sides, we find Ir ≈ √39.04 ≈ 6.2 N. Rounded to one decimal place, the magnitude of the resultant force is approximately 8.5 N.

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The set of integers has the same cardinality as the countably infinite set A. The correct option is b.

A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers (integers starting from 1). This means that we can establish a one-to-one function (bijection) between the countably infinite set A and the set of integers.

Options a, c, and d are not necessarily true.

Option a: There is no guarantee that there is a one-to-one function from the set A to the set of rational numbers. The set of rational numbers, also known as Q, is uncountably infinite, while A is only countably infinite.

Option c: It is possible to have a surjective function (onto) from the set of rational numbers to a countably infinite set. For example, a function that maps every rational number to its numerator can be surjective onto the set of integers.

Option d: The open interval (0, 1) has a higher cardinality (uncountable) than a countably infinite set. The interval (0, 1) contains an uncountably infinite number of real numbers between 0 and 1, whereas A is countably infinite.

The correct option is b.

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Answer:

11+13+16 or 14x15x18

Step-by-step explanation:

HOPE IT HELPS! :)

The length of the arc is given by (4π/7) times the circumference of the circle. Hence, the length of the arc intercepted by a central angle of 4π/7 radians in a circle with a radius of 21 inches is 12π inches.

The circumference of circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is 21 inches. Therefore, the circumference of the circle is C = 2π(21) = 42π inches.

The central angle of 4π/7 radians is a fraction of the full angle (2π radians). The ratio between the central angle and the full angle is (4π/7)/(2π) = 2/7.

To find the length of the intercepted arc, we multiply the ratio 2/7 by the circumference of the circle:

Length of arc = (2/7) * (42π) = 12π inches.

Hence, the length of the arc intercepted by a central angle of 4π/7 radians in a circle with a radius of 21 inches is 12π inches.

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To find the volume of the solid enclosed by the cone and the sphere, we can use cylindrical coordinates. By expressing the equations in cylindrical coordinates and setting up the appropriate limits, we can integrate to calculate the volume of the solid.

In cylindrical coordinates, we have x = r cos θ, y = r sin θ, and z = z.
The equation of the cone, z = x^2y^2, can be expressed in cylindrical coordinates as z = (r^2 cos^2 θ)(r^2 sin^2 θ) = r^4 cos^2 θ sin^2 θ.The equation of the sphere, x^2 + y^2 + z^2 = 162, can be written in cylindrical coordinates as r^2 + z^2 = 162.
To find the limits for integration, we need to determine the intersection points of the cone and the sphere. Setting the equations equal to each other, we have r^4 cos^2 θ sin^2 θ = 162 - r^2.
Simplifying, we get r^4 cos^2 θ sin^2 θ + r^2 - 162 = 0.
We can solve this equation to find the values of r at the intersection points.
Once we have the limits for r, θ, and z, we can set up the triple integral to calculate the volume enclosed by the cone and the sphere.
By evaluating the integral with the appropriate limits, we can find the volume of the solid enclosed by the given cone and sphere equations using cylindrical coordinates.

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The woman's cardiac risk ratio can be calculated by dividing her total cholesterol level by her high-density lipoprotein (HDL) level. With a total cholesterol level of 225 mg/dL and an HDL level of 60 mg/dL, her cardiac risk ratio is 3.8, which falls within the desirable range of 3.0 to 4.5 for women.

To calculate the cardiac risk ratio, we divide the total cholesterol level by the HDL level. In this case, the woman's total cholesterol level is 225 mg/dL, and her HDL level is 60 mg/dL. Thus, her cardiac risk ratio is given by 225 mg/dL / 60 mg/dL = 3.75.

The cardiac risk ratio is typically expressed as a one-place decimal. Rounding the ratio to one decimal place, we get 3.8. Since the desirable range for women's cardiac risk ratio is between 3.0 and 4.5, the woman's ratio of 3.8 falls within this range, indicating a desirable level.

Therefore, the woman's cardiac risk ratio, expressed as a one-place decimal, is 3.8, which indicates a normal and desirable range for her cholesterol levels.

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Hi army! I found the answer!

Answer:

F. An 18-month loan with an annual simple interest rate of 4.75%

Step-by-step explanation:

I just used a credit card payoff calculator to solve this problem. You can use that calculator to solve other problems like this too!

Also, stream BTS Film Out for clear skin and good grades ;)

Have a great day!

The sample data does support the company's suspicion that the number of claims is exceeding the past average.

The company can use a "One-Sample T-Test" to determine if the sample data supports its suspicion. Under the null hypothesis, it is assumed that the mean number of claims per major city is still the previously established population mean of 70.

We can then calculate the test statistic:

T-test statistic = (71.8-70)/(8.9/√100)

= 1.8/0.8931

= 2.02

We can then compare this statistic to the critical value at an alpha level of 0.05. With n=100, and a two-sided test, this value is 1.645.

Because 2.02 > 1.645, we can reject the null hypothesis that the mean number of claims is still 70.

Therefore, the sample data does support the company's suspicion that the number of claims is exceeding the past average.

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The mean of the data set is approximately 1.57 meters. The standard deviation of the data set is approximately 0.0968 meters, indicating the average deviation of data points from the mean.

To compute the mean and standard deviation of the data set, we'll use the following formulas:

Mean (μ) = (sum of all data values) / (total number of data values)

Standard Deviation (σ) = sqrt((sum of squared differences from the mean) / (total number of data values))

Let's calculate the mean and standard deviation for the given data set:

Data set: 1.63, 1.62, 1.61, 1.62, 1.39, 1.55

Mean (μ) = (1.63 + 1.62 + 1.61 + 1.62 + 1.39 + 1.55) / 6 = 9.42 / 6 ≈ 1.57

Next, we calculate the sum of squared differences from the mean:

(1.63 - 1.57)^2 + (1.62 - 1.57)^2 + (1.61 - 1.57)^2 + (1.62 - 1.57)^2 + (1.39 - 1.57)^2 + (1.55 - 1.57)^2 ≈ 0.0666

Finally, we calculate the standard deviation:

Standard Deviation (σ) = sqrt(0.0666 / 6) ≈ 0.0968

Therefore, the mean of the data set is approximately 1.57 meters and the standard deviation is approximately 0.0968 meters.

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Answer:

24

Step-by-step explanation:

[tex]79-7=72[/tex]

[tex]\frac{72}{3} =24[/tex]

Answer:

A is 10 dollar cheaper than B

Step-by-step explanation:

A : 40 dollars plus 45*2=90

90+40= 130 dollars

B:100 dollars 45*1=45

100+45= 145 dollars

Answer:

A is 15$ cheaper than b

Step-by-step explanation:

A= 40+(45*2) = 40+90=130$

b= 100+45 =145$

Answer:

$7.65

Step-by-step explanation:

its the right answer, TRUST ME!!!!

The first 5 terms of the arithmetic sequence are: 5, 9, 13, 17, 21.

Here we have an arithmetic sequence, such that the recursive formula is:

[tex]a_n = a_{n- 1} + 4[/tex]

Such that:

a₁ = 5.

Using that formula we can get the next 4 terms. For the second term we use n = 2, so we get:

[tex]a_2 = a_1 + 4 = 5 + 4 = 9[/tex]

For the third term we have:

[tex]a_3 = a_2 + 4 = 9 + 4 = 13[/tex]

For the fourth term we have:

[tex]a_4 = a_3 + 4 = 13 + 4 = 17[/tex]

For the fifth term we have:

[tex]a_5 = a_4 + 4 = 17 + 4 = 21[/tex]

Then the first 5 terms of the sequence are:

5, 9, 13, 17, 21.

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Step-by-step explanation:

There are 36 possible rolls

to be an odd number product.....both dies must be odd numbers

1st      2nd

1        1  3  5

3        1 3 5

5        1 3                   that is it for less than 20 product

8 rolls that would be less than 20  product

8 out of 36     probability

(i) Express the complex number in the form a+bi:ei (it) bg

The complex number ei(it)bg can be expressed in the form a+bi, where a is the real part and b is the imaginary part of the complex number. In this case, we have:

ei(it)bg = cos(bg) + i sin(bg)

The real part of the complex number is cos(bg) and the imaginary part is sin(bg). Therefore, we can express the complex number as:

ei(it)bg = cos(bg) + i sin(bg)

(ii) Express the complex number in the form a+bi: 1+²

To express the complex number 1+² in the form a+bi, we need to recognize that i² = -1. Therefore, we have:

1+² = 1 - 1 = 0

Since the imaginary part of the complex number is zero, we can express it as:

1+² = 0 + i0

(iii) Express the complex number in the form a+bi: Sen(ci)

To express the complex number Sen(ci) in the form a+bi, we need to use the formula:

Sen(ci) = sin(c) cosh(i) + cos(c) sinh(i)

where sinh(i) = i sin(1) and cosh(i) = cos(1). Therefore, we have:

Sen(ci) = sin(c) cosh(i) + cos(c) sinh(i)
= sin(c) cos(1) + cos(c) i sin(1)

(iv) Express the complex number in the form a+bi: e^zbg(-1)

To express the complex number e^zbg(-1) in the form a+bi, we need to recognize that zbg(-1) is a complex number. Therefore, we have:

e^zbg(-1) = e^(a+bi)
= e^a e^(bi)
= e^a (cos(b) + i sin(b))

where a is the real part of zbg(-1) and b is the imaginary part. Therefore, we can express the complex number as:

e^zbg(-1) = e^a (cos(b) + i sin(b))

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Answer:

20.

Step-by-step explanation:

x^2 = 25^2 - 15^2

x^2 = 400

x = 20

Answer: its 22

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The number of desired outcomes is the total number of blue pens in the bag. There are seven outcomes that can be blue.

Answer:

Step-by-step explanation:

From the given table,

A. The unit rate for each car is,

Car A = [tex]\frac{416}{13}[/tex]

          = 32 miles per gallon

Car B = [tex]\frac{544}{16}[/tex]

          = 34 miles per gallon

Car C = [tex]\frac{665}{19}[/tex]

          = 35 miles per gallon

Car D = [tex]\frac{775}{25}[/tex]

          = 31 miles per gallon

B. From the derived values in A, the car that uses the least amount of gas is Car C.

C. Total distance covered = 496 miles x 4

                                           = 1984 miles

The gallons of gas the Car A would need for the journey can be determined by;

Car A requires 1 gallon for 32 miles

So that for 1984 miles = [tex]\frac{1984}{32}[/tex]

                                    = 62 gallons

Car A would need 62 gallons of gas to make the trip.

D. Amount spent on gas for Car A = $2.12 x 62

                                          = $131.44

E. speed = [tex]\frac{distance}{time}[/tex]

⇒ time = [tex]\frac{distance}{speed}[/tex]

Given the for Car A, speed = 68 miles per hour.

time = [tex]\frac{1984}{68}[/tex]

       = 29.1765

time = 29 hours

It would take approximately 29 hours for Car A to cover the total distance of 1984 miles.

The F-test statistic is approximately 1.455.

To find the F-test statistic to test the claim of equal variances for two populations, you need the standard deviations of both samples. Given that the standard deviation of the first sample is 4.8329 and the standard deviation of the second sample is 5.8304, we can proceed with the calculation.

The F-test statistic is calculated as the ratio of the variances of the two samples. In this case, since we only have the standard deviations, we need to square them to obtain the variances.

First, square the standard deviations:

Variance of the first sample (s1^2) = (4.8329)^2 = 23.3747

Variance of the second sample (s2^2) = (5.8304)^2 = 34.0051

Next, calculate the F-test statistic by dividing the larger variance by the smaller variance:

F-test statistic = (larger variance) / (smaller variance)

F-test statistic = s2^2 / s1^2

F-test statistic = 34.0051 / 23.3747

Using the given values, the F-test statistic is approximately 1.455.

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Answer:

If you look at the bar graphs, histograms, and circle graphs, they all look at one variable at a time and display the number of times or percentage of times an individual point or interval is counted.

Step-by-step explanation:

Answer:

12:6 or $12 for every $6 he saves

Step-by-step explanation:

If he spends $6.00 for every $3.00, he would save $6 if he spends $12. In this case you could multiple or divide 6 by any number, and do the same to 3 to get an equivalent ratio. Ex. Multiple 6 times 2 to get $12 and 3 times 2 to get $6.

Answer:

300

Step-by-step explanation:

Answer: c is the correct opcion

Given data: Outcome 0 1 2 Probability 0.26 0.35 0.39a)

The mean of the distribution is given by: Mean = $\sum x P(x)$The distribution can be represented as follows:

Outcome(x) Probability(P(x)) x P(x) 0 0.26 0 1 0.35 0.35 2 0.39 0.78 $\sum x P(x)=0+0.35+0.78=1.13$

Therefore, Mean = $\frac {\sum xP(x)}{n}=\frac {1.13}{3} =0.3767 ≈ 0.377$ (rounded to three decimal places)

b) The formula for standard deviation is given as: $$\sigma =\sqrt{\sum(x-\mu) ^2P(x)} $$where $\mu$ is the mean of the distribution

Substituting the given values in the above formula, we get:

\begin{align*}\sigma &=\sqrt{\sum(x-\mu) ^2P(x)} \\\sigma &=\sqrt{\sum(x-0.377) ^2P(x)} \end{align*} Outcome(x) Probability(P(x)) $x-μ$ $P(x)(x-μ)^2$ 0 0.26 -0.37746 0.03665 1 0.35 -0.02746 0.00076 2 0.39 1.01254 0.15709 Total 1 0.19450$$\sigma =\sqrt {0.1945}=0.441 ≈ 0.441$$

Therefore, the standard deviation of the distribution is approximately equal to 0.441 (rounded to three decimal places).

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