Solve the following....
\(5x+3y=7\\3x-5y=-23\)

The Brewster's angle for an air-glass (n=1.58) surface is approximately 56.309 degrees.

Brewster's angle is the angle of incidence at which light with a specific polarization, known as p-polarization, is perfectly transmitted through a transparent dielectric surface, with no reflection.

The formula for Brewster's angle is:

θB = arctan(n)

Where θB is Brewster's angle and n is the refractive index of the second medium (in this case, glass).

Substituting n=1.58, we get:

θB = arctan(1.58)

Using a calculator, we find:

θB ≈ 56.309°

Therefore, the Brewster's angle for an air-glass (n=1.58) surface is approximately 56.309 degrees.

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a. The sampling method that I would use for the given scenario is stratified random sampling.

b. The sampling method that I would use for the given scenario is systematic sampling.

Stratified random sampling is the most effective way to get accurate results in this situation. The university wants to conduct a mail survey of its alumni to collect information about their current employment status to justify charging a higher tuition rate than other universities. Stratified random sampling divides the population into strata based on certain characteristics.

In this case, strata would be the alumni that have different degrees from the university. The information collected through this method will be more representative of the population than simple random sampling. It ensures that each stratum is represented accurately in the sample. It also minimizes the variability within each stratum. It is an effective way of ensuring that each stratum is properly represented.  

Systematic sampling involves selecting every kth element from a list of the population. In this situation, the Environmental Protection Agency (EPA) wants to inspect a sample of 1000 containers from the 40,000 containers known to be in landfills to determine if leakage from the containers has occurred. As the exact location of the containers is no longer known, systematic sampling can be used.

EPA can select every 40th container from the list of the population, as 40,000/1000 = 40. In this way, they will have a random sample of 1000 containers from the 40,000 containers. This sampling method is less time-consuming and more cost-effective than other sampling methods. It also ensures the sample is representative of the entire population.

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Answer:

I think personification

Step-by-step explanation:

The transformation of the graph f(x) = x² to the graph g(x) = -3(x+5)² + 12 involves a horizontal shift, a vertical stretch, and a vertical translation.

The graphs of f(x) = x² and g(x) = -3(x+5)² + 12 are the parabola.

The transformation of the graph is following as:

Firstly, the parabola has been shifted horizontally by 5 units to the left, which is reflected in the expression (x+5)².

Secondly, the parabola has been stretched vertically by a factor of -3, which is reflected in the coefficient in front of (x+5)².

Finally, the parabola has been raised up to 12 units. This means that the vertex of the parabola has been shifted upwards from the origin to the point (−5,12).

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Answer:

First, we have to determine the slope as we're provided with two points. If there are two points, you can determine the slope of the line using: \(\frac{y_2-y_1}{x_2-x_1}\)

It looks like the coordinates provided are (1,1) and (3,-2)

So now, we have to plug these values into the equation provided, which should look like: \(\frac{-2-1}{3-1} = -\frac{3}{2}\)

Our slope is equal to -3/2.

Answer:

2.25 miles

Step-by-step explanation:

If she can walk 3/4 of a mile in 20 minutes you need to multiply 3/4 by 3 because 20 times 3 is 60 and there is 60 minutes in a hour

Answer

1953125

Step-by-step explanation:

Answer:

9765625

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Trust me, this is the answer, PLEASE GIVE ME BRAINLIEST

Answer:

a,0

Step-by-step explanation:

Look at point (a,b). Point (a,b) has the same x-coordinate as P. And then the y coordinate is 0 because it just sits on the x axis and doesn't go up any. Therefore the answer is P: (a,0).

Answer:

(might have to round) 1.168224299 euros (I guess round to 1.17)

Step-by-step explanation:

Basically what I did was I made both of the quantities equal to one dollar so £0.8 is a dollar and 100/107 euros is a dollar.

They were both on the same basis so i multiplied by 1.25 to get £1 = 1.168224299 euros

A) The total commission she earned is $475

B) Total sales for commission of $1375 is $20000

A) Total Commission = Commission 1+ Commission 2

Where:

Commission 1 = 5% of first $5000

Commission 2 = 7.5% of the amount left after $5000 is subtracted

thus

Commission 1 = $5000 * 0.05 = $250

Commission 2= $3000 * 0.075 = $225

Commission total = $250 + $225 = $475

The total commission she earned is $475

B) Total sales = Sales with 5% commission + Sales with 7.5% commission

Sales with 5% commission = $5000

Commission At 7.5% = Total commission -Commission with 5% =    $1375 - $250

Sales * 0.075 =  $1125

Sales with 7.5% commission = $15000

Total sales = $5000+$15000

Total sales = $20000

Total sales for commission of $1375 is $20000

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Complete question is:

A salesperson earns commission on the sales that she makes each month. The salesperson earns a 5% commission on the first $5,000 she has in sales.

The salesperson earns a 7.5% commission on the amount on her sales that are greater than $5,000.

Part A:

This month the salesperson had $8,000 in sales. What amount of commission, in dollars, did she earn?

Part B:

The salesperson earned $1,375 in commission, last month. How much money, in dollars, did she have in sales last month?

Answer: y > 4/5x + 2

Step-by-step explanation: The slop is 4/5x, and the y-intercept is 2. The line is dotted and the shaded area is above the line. Therefore the inequality is >.

The first ten terms of the arithmetic progression (A.P.) are: 6, 9, 12, 15, 18, 21, 24, 27, 30, 33.

Let's assume that the first term of the A.P. is 'a' and the common difference is 'd'.

We are given that the 21st term of the A.P. is 37, so we can write the 21st term as:

a + (21 - 1)d = 37

Simplifying the equation, we get:

a + 20d = 37   ---(1)

We are also given that the sum of the first twenty terms is 320. The sum of an A.P. can be calculated using the formula:

Sum = (n/2) * [2a + (n - 1)d]

Substituting the given values, we have:

320 = (20/2) * [2a + (20 - 1)d]

320 = 10 * [2a + 19d]

32 = 2a + 19d   ---(2)

We now have a system of equations (1) and (2). Solving these equations simultaneously will give us the values of 'a' and 'd'.

Multiplying equation (1) by 2 and subtracting equation (2) from it, we get:

2(a + 20d) - (2a + 19d) = 2 * 37 - 32

40d - 19d = 42 - 32

21d = 10

d = 10/21

Substituting the value of 'd' back into equation (1), we can solve for 'a':

a + 20 * (10/21) = 37

a + 200/21 = 37

a = 37 - 200/21

a = (777 - 200)/21

a = 577/21

Now that we have the values of 'a' and 'd', we can find the first ten terms of the A.P. by substituting the values of 'a' and 'd' into the A.P. formula.

The first ten terms of the A.P. are 6, 9, 12, 15, 18, 21, 24, 27, 30, and 33, with a common difference of 10/21. The calculations were done by solving the system of equations formed using the given information about the 21st term and the sum of the first twenty terms.

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Answer:

8.97 x \(10^{6}\)

Step-by-step explanation:

To add in scientific notation, the exponents need to be the same for the bases of 10.  You can either make them both to the exponent of 6 or 5.  It does not matter.  I made them both to the power of 5

(8.6 x \(10^{6}\)) + (3.7 x \(10^{5}\))

(86 x \(10^{5}\)) + (3.7x\(10^{5}\))  

(86 x 3.7) x \(10^{5}\)

89.7 x\(10^{5}\)  Rewrite in scientific notation

8.97 x \(10^{6}\)

Answer:

4π

Step-by-step explanation:

Area = πr^2 or πd

in this case, d = 4, so its 4π

x ≤ 3

Step-by-step explanation:

4x ≤ 12

divide each side by 4

x ≤ 3

The probability that the coin lands head at least 10 times in 12 coin flips is 0.005554028.

We are given a fair coin that is tossed 12 times and we need to find the probability that the coin lands head at least 10 times.

Let’s solve this problem step by step.

The probability of getting a head or tail when flipping a fair coin is 1/2 or 0.5.

To find the probability of getting 10 heads in 12 coin flips, we will use the Binomial Probability Formula.

P(X = k) = (n C k) * (p)^k * (1-p)^(n-k)

Where, n = 12,

k = 10,

p = probability of getting head

= 0.5,

(n C k) is the number of ways of choosing k successes in n trials.

P(X = 10) = (12 C 10) * (0.5)^10 * (0.5)^(12-10)

P(X = 10) = 66 * 0.0009765625 * 0.0009765625

P(X = 10) = 0.000064793

We can see that the probability of getting 10 heads in 12 coin flips is 0.000064793.

To find the probability of getting 11 heads in 12 coin flips, we will use the same Binomial Probability Formula.

P(X = k) = (n C k) * (p)^k * (1-p)^(n-k)

Where, n = 12,

k = 11,

p is probability of getting head = 0.5,

(n C k) is the number of ways of choosing k successes in n trials.

P(X = 11) = (12 C 11) * (0.5)^11 * (0.5)^(12-11)

P(X = 11) = 12 * 0.0009765625 * 0.5

P(X = 11) = 0.005246094

We can see that the probability of getting 11 heads in 12 coin flips is 0.005246094.

To find the probability of getting 12 heads in 12 coin flips, we will use the same Binomial Probability Formula.

P(X = k) = (n C k) * (p)^k * (1-p)^(n-k)

Where, n = 12, k = 12, p = probability of getting head = 0.5, (n C k) is the number of ways of choosing k successes in n trials.

P(X = 12) = (12 C 12) * (0.5)^12 * (0.5)^(12-12)

P(X = 12) = 0.000244141

We can see that the probability of getting 12 heads in 12 coin flips is 0.000244141.

Now, we need to find the probability that the coin lands head at least 10 times.

For this, we can add the probabilities of getting 10, 11 and 12 heads.

P(X ≥ 10) = P(X = 10) + P(X = 11) + P(X = 12)

P(X ≥ 10) = 0.000064793 + 0.005246094 + 0.000244141

P(X ≥ 10) = 0.005554028

We can see that the probability that the coin lands head at least 10 times in 12 coin flips is 0.005554028.

Answer: 0.005554028

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Answer:

attached is the graph and other data

Step-by-step explanation:

Answer:

26.6°

Step-by-step explanation:

The measure of the angle the ramp makes with the ground is approximately 30 degrees.

We have,

To find the measure of the angle the ramp makes with the ground, use trigonometry.

In this case, a right triangle is formed by the ramp, the ground, and the vertical height of 1 meter.

Denote the angle the ramp makes with the ground as θ (theta).

Using the trigonometric function "sine" (sin), we can set up the following equation:

sin(θ) = opposite/hypotenuse

The opposite side is the height of the ramp, which is 1 meter, and the hypotenuse is the length of the ramp, which is 2 meters.

So,

sin(θ) = 1/2

θ = arcsin(1/2)

Using a calculator or a trigonometric table.

θ = arcsin(1/2) = 30 degrees.

Therefore,

The measure of the angle the ramp makes with the ground is approximately 30 degrees.

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The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application",

The equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .

It is given to us that -

The vertex of the parabola = (-8,5)

The directrix of the parabola is y = -3

We have to find the equation of the parabola with the given vertex and directrix.

We know that any point on a given parabola represented as () is equidistant from the directrix and the focus.

So, the equation for the point can be represented as

\([y-(-3)]=\sqrt{([x-(-8} ]^{2} +(y-5)^{2}\)

\((y+3)^2} =(x+8)^{2} +(y-5)^{2} \\=y^{2}+9+2*y*3=(x+8)^{2} +y^{2}+25-2*y*(-5)=6y-10y=(x+8)^{2} +16=-4y=(xx+8)^{2} +16=y=\frac{-1}{4} (x+8)^{2}+4\)

Thus, the equation of the parabola with vertex (-8,5) and directrix y= -3 is given by .\(=y=\frac{-1}{4} (x+8)^{2} +4\)

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Answer:

Second number line represents the [X-5]=1.

Step-by-step explanation:

Given : [X-5]=1 .

To find : Which number line represents the solutions to [X-5]=1.

Solution : We have given that [X-5]=1.

We can se the value x-5 is inside the modulus it may be positive or negative.

So, we will do it by both cases.

1) (x - 5) = 1

On adding by 5 both sides.

x = 1+5 = 6

x = 6.

2) if -(x-5) = 1

remove parenthesis

-x +5 = 1

On subtracting by 5 both side

-x = -4

On dividing by -1 both side

x = 4.

So , x = 4, 6.

Therefore , the second number line represents the [X-5]=1.

Given, Cost to produce designer dog leashes C(x) = 7x + 5 Revenue function R(x) = 3x² + 103x To find, Profit function P(x)Number of leashes that result in the maximum profit (in whole number)

To find the profit function, we need to subtract the cost function C(x) from the revenue function

R(x)P(x) = R(x) - C(x)P(x)

= (3x² + 103x) - (7x + 5)P(x)

= 3x² + 96x - 5

Therefore, the  function is P(x) = 3x² + 96x - 5 To find the number of leashes that result in the maximum profit, we need to find the vertex of the quadratic function P(x) = 3x² + 96x - 5. The vertex of the quadratic function is given by the formula x = -b/2a

Where a = 3 and b = 96

Plugging in the values of a and b, x = -96/(2×3) = -16 The value of x for which the profit is maximum is -16. However, the number of leashes cannot be negative. Hence, we take the next whole number, which is 17.Therefore, the number of leashes that result in the maximum profit is 17.

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Answer: 163 students

Step-by-step explanation:

First find the percentage of students who were in favor of having school  start one hour later based on the sample of 20 students.

= 13/20 * 100%

= 65%

The apply this percentage to the total number of students in school to find your answer:

= 65% * 250 students

= 162.5

= 163 students

The number of students in the school who are in favor of having school start one hour later is; C: 163 students

We are told that 13 out of the 20 surveyed students were in favour of having school start one hour later. Thus;

Probability = 13/20 * 100% = 65%

Now, the school has 250 students and as such, the number of students in the school who are in favor of having school start one hour later is;

65% * 250 students = 162.5 ≈ 163 students

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

The equation of the line is:

y

=

5

6

x

−

15

6

Explanation:

The equation of the line will be in the form:

y

=

m

x

+

c

where  

m

is the slope (gradient) and  

c

is the y-intercept.

To find the slope, we use:

m

=

y

2

−

y

1

x

2

−

x

1

It doesn't matter which point we decide is  

(

x

1

,

y

1

)

and which we choose as  

(

x

2

,

y

2

, since the formula will work either way.

m

=

0

−

(

−

5

)

3

−

(

−

3

)

=

5

6

Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:

y

=

m

x

+

c

0

=

5

6

(

3

)

+

c

=

15

6

+

c

Rearranging:

c

=

0

−

15

6

=

−

15

6

Over all, then, the equation of the line is:

y

=

5

6

x

−

15

6

The equation of the line is:

y

=

5

6

x

−

15

6

Explanation:

The equation of the line will be in the form:

y

=

m

x

+

c

where  

m

is the slope (gradient) and  

c

is the y-intercept.

To find the slope, we use:

m

=

y

2

−

y

1

x

2

−

x

1

It doesn't matter which point we decide is  

(

x

1

,

y

1

)

and which we choose as  

(

x

2

,

y

2

, since the formula will work either way.

m

=

0

−

(

−

5

)

3

−

(

−

3

)

=

5

6

Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:

y

=

m

x

+

c

0

=

5

6

(

3

)

+

c

=

15

6

+

c

Rearranging:

c

=

0

−

15

6

=

−

15

6

Over all, then, the equation of the line is:

y

=

5

6

x

−

15

6

Step-by-step explanation:

We want to find the equation of the line that passes through the points (0, 3) and (5, -3). The linear equation is y = (-6/5)*x + 3

A general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be written as:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

In this case, we know that the line passes through (0, 3) and (5, -3) then the slope is:

\(a = \frac{-3 - 3}{5 - 0} = \frac{-6}{5}\)

Then the line is:

y = (-6/5)*x + b

To get the value of b, we use the fact that the line passes through (0, 3), so we have:

3 = (-6/5)*0 + b

3 = b

Then the linear equation is just:

y = (-6/5)*x + 3

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We can say that the circumference of the cake is (A) 37.68 inches.

The circumference of a circle or ellipse in geometry is its perimeter.

That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The curve length around any closed figure is more often referred to as the perimeter.

So, the circumference of the cake will be:

We know that the way across the cake is 12 inches.

Which means the diameter of the cake is 12 inches.

Then, the radius will be:

Diameter/2 ⇒ 12/2 ⇒ 6 inches

Circumference formula: 2πr

Now, calculate the circumference as follows:

2πr

2(3.14)r

6.28r

(6.28)6

37.68 inches

Therefore, we can say that the circumference of the cake is (A) 37.68 inches.

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Complete question:
A cookie cake has a layer of frosting around the outside of the cake forming the circumference. the distance all the way across the cake is 12 inches. find the circumference of the cookie cake.

(A) 37.68 in

(B) 18.84 in

(C) 113.04 in

(D) 12 in

Answer:

10 i believe

Step-by-step explanation:

Answer:

C = 5pi inches or approximately 15.7 inches

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

The diameter is given by d=5

C = pi *5

If we use pi is approximated by 3.14

C = 3.14 *5 =15.7

C = 5pi inches or approximately 15.7 inches

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:

Step-by-step explanation:

im not sure

Answer:

times 3 cookies per pouch

Step-by-step explanation:

3 times 3 is 9

8 times 3 is 24

etc