Each of the interior angles of a regular polygon is 140 degrees. How many have it

The possible distances from the Earth to Venus at the time of an elongation of 39.4 degrees are 0.709 AU and 1.333 AU.

The elongation of a planet is the angle formed when the planet, Earth, and Sun are in a straight line. At a certain time, the elongation of Venus was found to be 39.4 degrees. To find the possible distances from the earth to Venus at that time in Astronomical Units (AU), the Law of Cosines can be used.

The Law of Cosines states that for a triangle with sides a, b, and c and angles A, B, and C, c2 = a2 + b2 - 2abcosC.

In this case, a is the distance from the sun to Venus (0.723 AU), b is the distance from the Earth to Venus, and C is the elongation (39.4 degrees).

Therefore, b2 = 0.7232 + b2 - 2(0.723)(b)cos39.4.

Solving for b, we get b = 0.709 AU and b = 1.333 AU, so the possible distances from the Earth to Venus are 0.709 AU and 1.333 AU.

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Given:-

To find:-

Solution:-

Here the sum of the two unknown angles will be 90° as they are the angles which make up 90° . So that;

[tex]\implies x^o + 42^o + 3x^o = 90^o \\[/tex]

[tex]\implies 4x^o = 90^o - 42^o \\[/tex]

[tex]\implies 4x^o = 48^o \\[/tex]

[tex]\implies x =\dfrac{48}{4} \\[/tex]

[tex]\implies \boxed{ x = 12} \\[/tex]

Hence the value of x is 12 .

and we are done!

Answer:

x = 15

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 10 to both sides of the equation:

[tex]4x - 10 = 50\\4x - 10 (+10) = 50 (+10)\\4x = 50 + 10\\4x = 60[/tex]

Next, divide 4 from both sides of the equation:

[tex]4x = 60\\\frac{4x}{4} = \frac{60}{4} \\x = \frac{60}{4} = 15\\x = 15[/tex]

~

x = 15 is your answer.

~

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Answer:

Step-by-step explanation:

[tex]\tt 4x -10 = 50[/tex]

Add 10 to both sides:-

Divide both sides by 4:-

___________________

Hope this helps!

Answer:

Let x be the price of one adult ticket, and y be the price of one student ticket.

From the information given in the problem, we can set up the following system of equations:

15x + 5y = 265 (equation 1)

15x + 16y = 419 (equation 2)

We can solve for x by subtracting equation 1 from equation 2:

15x + 16y - (15x + 5y) = 419 - 265

11y = 154

y = 14

Now we can substitute y = 14 into either equation 1 or equation 2 to solve for x. Let's use equation 1:

15x + 5(14) = 265

15x + 70 = 265

15x = 195

x = 13

Therefore, one adult ticket costs $13, and one student ticket costs $14.

The table below shows the number of hybrid vehicles and the total number of vehicles in the parking lot for each day of the weekend:

Day Hybrids Total

Fri x y

Sat x y

Sun x y

Since the ratios for the three days were equivalent, this means that the fraction of hybrid vehicles to total vehicles was the same for each day. In other words:

x/y = x/y = x/y

Therefore, the values of x and y must be the same for each day. This means that the number of hybrid vehicles and the total number of vehicles in the parking lot were the same for each day of the weekend.

In conclusion, the table should be completed with the same values of x and y for each day, as shown below:

Day Hybrids Total

Fri x y

Sat x y

Sun x y

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Option C requires the examination of the data on bowling scores to find out what Molly's mean score is, and this constitutes a statistical inquiry that can be resolved with the information that has been gathered.

The statistical question that can be answered from the data is: C) What was Molly's average bowling score?

Option A is not a statistical question because it only concerns Molly's personal feeling towards one of her bowling scores.

Option B is a factual question that does not require statistical analysis.

Option D is also a factual question that does not require statistical analysis.

However, option C involves analyzing the bowling scores data to determine Molly's average score. This is a statistical question that can be answered using the collected data.

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Complete question:

Molly joined an after-school bowling club. The club members go bowling once a week throughout the school year. The bowling scores are recorded for each game so that they can be analyzed at the end of each week. Which of these is a statistical question that can be answered from the data?

A) Which bowling score made Molly the proudest?

B) How many times did the bowling club meet?

C) What was Molly's average bowling score?

D) On what day did the bowling club begin?

Answer:

dghcŕhĝt5dfg9yd6grdy6cjbjbknygug4ximpohyvug5h7h6g6

1. 6:15 has a ratio of 2:5

2. 10:40 has a ratio of 1:4

3. 6:28 has a ratio of 3:14 but it would be 12:56 based on the answer choices

4. 15:25 has a ratio of 3:5 but it would be 15:25 based on the answer choices

The exponential function between (-1, 2/5) and (3, 250) is as follows:

[tex]f(x) = 2 * 5^x[/tex]

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

[tex]f(x) = 2 * 5^x[/tex]

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

This is the shape of the exponential function:

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

where a represents the starting point and b represents the exponential function's base.

We must solve the system of equations to determine the values of a and b that meet the requirements:

a * [tex]b^(-1)[/tex] = 2/5 (equation 1) 

a *[tex]b^3[/tex]= 250 (equation 2) 

We can solve for an in equation 1 by multiplying both sides by b:

a = (2/5) * b

Substituting this expression into equation 2, we get:

(2/5) * b *[tex]b^3[/tex] = 250

Simplifying, we get:

[tex]b^4 = 3125[/tex]

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

[tex]f(x) = 2 * 5^x[/tex]

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Answer:

5/2

Step-by-step explanation:

substitute the values into the cosine rule:

(2[tex]\sqrt{7}[/tex])² = ((2x - 1)² + (2x + 1)²) - 2(2x - 1)(2x + 1)cos(60))

work out each part separately:

(2[tex]\sqrt{7}[/tex])² = 28

(2x - 1)² = 4x² - 4x + 1

(2x + 1)² = 4x² + 4x + 1

(2x - 1)² + (2x + 1)² = (4x² - 4x + 1) + (4x² + 4x + 1) = 8x² + 2

2((2x - 1)(2x + 1)cos(60)):

(2x - 1)(2x + 1) = 4x² - 1

cos(60) = √1/2 = 1/2

2(4x² - 1)(1/2) = 4x² - 1

substitute back in:

28 = (8x² + 2) - (4x² - 1)

28 = 4x² + 3

25 = 4x²

25/4 = x²

x = √(25/4)

x = 5/2

The container holds 99.223 grams of tablets.

One-sixteenth of a pound is represented by the weight measurement called an ounce (oz). A slice of bread and a pencil are two items that weigh about one ounce. One fluid ounce is the same as one-eighth of a cup in terms of volume. A medication cup has a volume of roughly one liquid ounce.

To convert ounces to grams, we can use the conversion factor 1 oz = 28.3495 g.

So, the container holds:

[tex]$3.5\ \text{oz} \times 28.3495\ \frac{\text{g}}{\text{oz}} = 99.223\ \text{g}$[/tex]

Therefore, the container holds 99.223 grams of tablets.

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Answer:

9) 15

10)22

11)25

Step-by-step explanation:

9)

[tex]area=\frac{bh}{2} \\30=\frac{(2x+1)4}{2} \\\\30=4x+2\\\\28=4x\\x=7\\[/tex]

substitute:

=2x+7

=2(7)+1

=15

10)

[tex]area=\frac{bh}{2} \\114=\frac{12(3x-2)}{2} \\114=18x-12\\126=18x\\7=x[/tex]

substitute:

=3x-2

=3(7)+1

=22

11)

[tex]area=h\frac{b1+b2}{2} \\\\69=\frac{4x-2}{2} \\\\69=\frac{24x-12}{2} \\\\69=12x-6\\75=12x\\x=6.25\\\\=4x\\=4(6.25)\\=25[/tex]

The value of q is 6

The constant is k

The first step the to calculate the value of the constant which is k

k= qr

Write out the parameters given in the question

The value of q is 2.8

The value of r is 11.25

k= 2.8 × 11.25

= 31.5

The value of q can be calculated by the value of k which is 31.5 and r which is 5.25

k= qr

31.5= q × 5.25

31.5= 5.25q

q= 31.5/5.25

q= 6

Hence the value q is 6

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As a result, when x = -5a /, the subject of the formula a/b = 2x/(x + 5) is x. (a - 2b).

For instance, C is the subject of the formula C = 2r, which calculates the circumference of a circle. To modify the subject of a formula is to rewrite it such that the quantities are still related in the right way. M/2 equals D if M = 2D.

In order to eliminate the fraction and make x the subject of the formula a/b = 2x/(x + 5), we can cross-multiply:

a(x + 5) = 2bx

Next, we can distribute the a:

ax + 5a = 2bx

We can now separate the x terms from the constant terms on each side:

ax - 2bx = -5a

x(a - 2b) = -5a

Finally, we can solve for x by dividing both sides by (a - 2b):

x = -5a / (a - 2b).

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Answer:

True

Step-by-step explanation:

A factorial means a number multiplied by all of the positive integers before it. That means both n+3! and n! have a common factor of n!. When you take out this factor of N, the fraction (n+3)!/n! ‘s denominator would be one, and the numerator would have all of the positive integers before n+3 and also being greater than n. Thus, (n+1)(n+2)(n+3)

a) The system of inequalities that can be used to represent the situation is x + y ≤ 15 and 4x + 8y ≥ 80

b) One combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours is 10 hours babysitting and 5 hours as a library assistant.

To start, we know that Edith can work no more than 15 hours per week. Therefore, we can write the following inequality:

x + y ≤ 15

Next, we know that Edith earns $4 per hour babysitting and $8 per hour as a library assistant. We want her to earn at least $80 per week, so we can write the following inequality:

4x + 8y ≥ 80

This inequality states that the total amount Edith earns from both jobs (4x + 8y) must be greater than or equal to $80.

Now that we have two inequalities, we have a system of inequalities that can be used to represent the situation:

x + y ≤ 15

4x + 8y ≥ 80

To determine one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours, we can solve this system of inequalities.

Let's solve the first inequality for y:

y ≤ 15 - x

Now we can substitute this expression for y into the second inequality:

4x + 8(15 - x) ≥ 80

Simplifying and solving for x, we get:

-4x + 120 ≥ 80

-4x ≥ -40

x ≤ 10

To find the number of hours she should work as a library assistant, we can substitute x = 10 into our expression for y:

y ≤ 15 - x

y ≤ 15 - 10

y ≤ 5

So Edith should work no more than 5 hours as a library assistant per week.

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Check the picture below.

Answer: 0.72 pts.

Step-by-step explanation:

The number of balls, given the ratio of white balls to yellow balls that could not be in the bag is C. 42 balls.

The number of balls that could not be in the bag, given the ratio of white balls to yellow balls, is the number that would not give a whole number when multiplied by the ratio of white balls to yellow balls.

26 balls :

= 3 / ( 10 + 3 white balls ) x 26

= 3 / 13 x 26

= 6 balls

39 balls :

= 3 / 13 x 39

= 9 balls

42 balls :

= 3 / 13 x 42

= 9.69 balls

There therefore cannot be 42 balls.

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Options for this question include:

Step-by-step explanation:

Your debt ratio is the ratio of the credit limit you have spent.

Your debt ratio is the amount you have spent on the credit card/ the limit

You have spent $9000- $3200 = $5800

Debt ratio = 5800/9000

=58/90 = 29/45

2. Acceptable ratio is less than 43%

Is 29 out of 45 less than 43%

Convert 29/45 to percentage

29/45 /100/1 = 64.44%

You have exceeded acceptable ratio at 64.4%

Answer:

Your debt ratio is the percentage of your credit limit that you have spent.

spent $9000- $3200 = $5800

Debt to income ratio = 5800/9000 = 58/90 = 29/45

2. A satisfactory ratio is less than 43%.

Is 29 percent of 45 less than 43%?

29/45 converted to a percentage 29/45 /100/1 = 64.44%

Step-by-step explanation:

Brainliest pls

lim_{x\to{\frac{\pi}{2}}^-} \tan x is 0.

The given function can be rewritten as;$$\frac{\sin x}{\cos x}$$Let us calculate the left hand limit$$\lim_{x\to{\frac{\pi}{2}}^-} \frac{\sin x}{\cos x}=\lim_{x\to{\frac{\pi}{2}}^-} \frac{1}{\cos x}= \frac{1}{\cos \frac{\pi}{2}}=0$$Thus, the evaluation of  $$\lim_{x\to{\frac{\pi}{2}}^-} \tan x$$ is 0.

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Answer:I could possibly be wrong but I say no. From what I remember, with these things you can put the points wherever as long as it follows the rules you were given for each triangle.

Step-by-step explanation:

I actually drew it out, and to me it appears as it’s not, yet I could be wrong and I’m sorry if I am! Angles aren’t my best, but I’m really good at math! If you have other problems I can go over them

The intersection of A and B' is an empty set because there are no elements that are in both A and B'. The correct answer is (option E) the empty set.

What is a set ?

A set is a collection of distinct objects, called elements or members, that are well-defined and unordered.

We can start by finding the complement of set B, which consists of all the elements in U that are not in B:

B' = {r, t, v, x, z}

Then, A ∩ B' consists of all the elements that are in A and also in B':

A ∩ B' = {u, w, y} ∩ {r, t, v, x, z} = { }

Therefore, The intersection of A and B' is an empty set because there are no elements that are in both A and B', the correct answer is (option E) the empty set.

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The probability that the next patient arrives during the following 20 minutes is approximately 0.776.

(a) The probability that exactly 7 patients will arrive during a 90-minute period can be found by using the Poisson distribution formula.Poisson distribution formula:P(X = x) = (e-λ * λx) / x!Where: λ is the average number of events per unit of time or space, x is the number of occurrences, e is the exponential constant equal to 2.71828.x! means x factorial that is x(x − 1)(x − 2)⋯(2)(1).Here, λ = 9/60 = 0.15 (since there are 9 arrivals in one hour, there would be 9/60 arrivals in 1 minute)We are to find the probability of exactly 7 patients arriving in 90 minutes.The time period is 90/60 = 1.5 hours. Hence, λ = 0.15 × 1.5 = 0.225P(X = 7) = (e-λ * λ7) / 7! = (e-0.225 * 0.2257) / 7! = 0.085 ≈ 0.09Therefore, the probability that exactly 7 patients will arrive during a 90 minutes period is approximately 0.09(b) We can calculate the probability of at least 30 minutes passing until the next patient arrives by using the cumulative distribution function (CDF) of the exponential distribution.Exponential distribution formula:f(x) = λe-λxwhere λ is the rate parameter, x is the time period, and e is the exponential constant equal to 2.71828.The mean waiting time between two successive arrivals is 60/9 = 6.67 minutes.Hence, λ = 1/6.67 = 0.15The probability of at least 30 minutes passing until the next patient arrives can be calculated as follows:P(X > 0.5) = 1 - P(X ≤ 0.5) = 1 - (1 - e-λx) = e-λx = e-0.15×0.5 ≈ 0.776Therefore, the probability that at least 30 minutes will pass until the next patient arrives is approximately 0.776.(c) The probability that the next patient arrives during the following 20 minutes can be calculated as follows:P(X > 1) = 1 - P(X ≤ 1) = 1 - (1 - e-λx) = e-λx = e-0.15×1/3 ≈ 0.776Therefore, the probability that the next patient arrives during the following 20 minutes is approximately 0.776.

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Answer:

Step-by-step explanation:

To solve this system of equations, we can use either substitution or elimination method.

Let's use the elimination method to eliminate y.

Multiplying the first equation by 2 and the second equation by 5, we get:

14x - 10y = 76

10x + 50y = -60

Now, we can add the two equations to eliminate y:

(14x - 10y) + (10x + 50y) = 76 - 60

Simplifying the left side and right side, we get:

24x = 16

Dividing both sides by 24, we get:

x = 2/3

Now that we have the value of x, we can substitute it back into either of the original equations to find y.

Let's substitute it into the first equation:

7x - 5y = 38

7(2/3) - 5y = 38

Simplifying and solving for y, we get:

-5y = 38 - 14/3

-5y = 100/3

y = -20/3

Therefore, the solution to the system of equations is (x, y) = (2/3, -20/3).

The inverse of the function is t = (r - 1.13) / 0.83.

What is function ?

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output. A function can be thought of as a rule or a machine that takes an input value and produces a corresponding output value.

The given equation is: r = 0.83t + 1.13

To find the inverse of the function, we need to solve the equation for t.

r = 0.83t + 1.13

Subtract 1.13 from both sides:

r - 1.13 = 0.83t

Divide both sides by 0.83:

(r - 1.13)/0.83 = t

So the inverse function is:

t = (r - 1.13)/0.83

Or we can write it as:

[tex]f^{(-1)(r)} = (r - 1.13)/0.83[/tex], where [tex]f^{(-1)}[/tex]  represents the inverse function.

Therefore, the inverse of the function is t = (r - 1.13) / 0.83.

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b.  [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex] is an equivalent expression of y√x.

d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex] is an equivalent expression of y√x.

Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value(s) fοr the variable(s).

Given expression y√x

a. Is not equivalent as power is rational and exponent are non equal,

b. [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex]

=  [tex]\dfrac{\sqrt{x} }{\frac{1}{y}}[/tex]

= y√x

Thus, b.  [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex] is an equivalent expression of y√x.

c. Is not a n equivalent expression at has a different variable.

d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex]

[tex]\rm\sqrt{ (xy^2)} }[/tex]

[tex]\rm y \sqrt{ (x)} }[/tex]

Thus,  d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex] is an equivalent expression of y√x.

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The correlation coefficient for the SAT math score and the GPA of the students is given as follows:

r=0.94668.

A correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is represented by the symbol "r" and ranges from -1 to 1.

The value of the correlation coefficient indicates the strength of the linear relationship between the variables. The closer the value of "r" is to -1 or +1, the stronger the linear relationship between the variables. A value of 0 indicates that there is no linear relationship between the variables.

The correlation coefficient is calculated inserting the points of the data-set into a correlation coefficient calculator.

The points from the graph are given as follows:

(595, 3.4), (520, 3.2), (715, 3.9), (405, 2.3), (680, 3.9), (490, 2.5), (565, 3.5).

Inserting these points into a calculator, the coefficient is given as follows:

r = 0.94668.

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The expected value of X is given byE(X) = 1/p= 1/(1/4) = 4

To obtain either h, h, h or t, t, t, let's consider the sequence h, h, h, t, t, t. The probability of obtaining h, h, h or t, t, t is (1/2)^3 + (1/2)^3 = 1/4. Also, the probability of the first head or tail occurring on the nth flip is (1/2)^n-1. If X denotes the number of flips of a coin required to get h, h, h or t, t, t, then X has a geometric distribution with parameter p = 1/4. Hence, the expected value of X is given byE(X) = 1/p= 1/(1/4) = 4The expected number of flips of a coin, which comes up heads with probability 0.5, that are necessary to obtain either h, h, h or t, t, t is 4.

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