Draw a unit circle for each of the following then find several positive and negative real
numbers t which determine a point Q with the given coordinates. Then write a formula
for t in terms of 2kπ.
1. ( 0, 1)

From the solution;

x = 62.62°

y = 8.9 cm

The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.

By the use of the sine rule;

a/Sin A = c/Sin C

Sin C = cSin A/a

C = Sin-1(cSin A/a)

C = Sin-1(7.8 * sin 66.4/9.2)

C = 50.98°

B = 180 - (50.98° + 66.4)

B = 62.62°

Then;

a/Sin A = b/Sin B

9.2/Sin66.4 = b/Sin 62.62

b = 9.2 * Sin 62.62/Sin66.4

b = 9.2 * 0.89/0.92

b = 8.9 cm

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If these are your questions:

Dally cola sales in Bholapur 300 ml Shop A 500 ml Shop B Ilitre (a) In which type of packing does the cola sell the most? (b) Which shop sells more cola? (c) What is the total amount of cola sold in Bholapur per day?​

So here are the answers:

In packing 300 ml, it would be sold at a larger volume.

given: there are two shops - shop A, and shop B selling 300 ml and 500 ml bottles.

to find:

(a) In which type of packing does the cola sell the most?

(b) Which shop sells more cola?

(c) What is the total amount of cola sold in Bholapur per day?​

solution: As shop A sells the same product at a low cost because of low quantity, whereas shop B sells the product in 500 ml bottles. So, most chances are people end up buying the cheaper product which is the 300 ml product.

Similar, logic as the number of sales of 300 ml bottles would be much larger than that of 500 ml bottle backing. So, Shop A (300 ml bottle packing) sells more of the goods.

(c ) for option c inappropriate information is there, so can not be calculated. But, according to our findings, Shop A sells more goods.

In packing 300 ml, it would be sold at a larger volume.

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Answer:

The number is 4

Step-by-step explanation:

5x=20

5x/5=20/5

x=4

Step-by-step explanation:

so let the unknown be x

x+5-3=17

x+2=17

so then you carry +2 over to the left hand side which collecting of like terms

so we have

x=17-2

x=15

so therefore the unknown value x is 15

to check

we substitute 15 for x in the equation

let's go

so we have

15+5-3=17

now using this solve it .

I believe u can do it

or I just do it

so we hv the unknown to be x

x*5-3=17

5x-3=17

5x=17+3

5x=20

x=20/5

x=4

Hence, in response to the provided question, we can say that As a result,  equation  A(1,2) and A'(5,12) are not dilations.

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

To evaluate if the points A(1,2) and A'(5,12) reflect a dilation, we must first determine the dilation's scale factor.

Let's use the given points to compute the scale factor:

(length of A' A) / scale factor (length of A)

A's length A [tex]=\ sqrt[(5-1)2 + (12-2)2] = \sqrt[16^2 + 10^2] =\ sqrt(296) (296)[/tex]

A's length is one.

[tex](\sqrt(296)) / 1\\\sqrt(x) = scale factor (296)[/tex]

As a result, the scaling factor is not an integer. That is, the transformation from point A to point A' is not a dilation with a whole number scale factor.

As a result, A(1,2) and A'(5,12) are not dilations.

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The reference angle is given as 45 degrees

the angle is in the 4th quadrant

sin 315 = - sqrt(2) / 2

cos 315 = sqrt(2) / 2

We have θ = 315

θ is seen to lie between 270 degrees and 360 degrees in the 4th quadrant

In the fourth quadrant the reference angle has been solved by:

360 - θ

360 - 315

= 45 degrees

The reference angle is 45 degrees

sin 315 = sin( 360 - 45)

= [tex]-\frac{\sqrt{2} }{2}[/tex]

= - sqrt(2) / 2

cos 315 = cos (360 - 45)

= [tex]\frac{\sqrt{2} }{2}[/tex]

= sqrt(2) / 2

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Answer:

[tex]y = -2(x + 3)^{2} + 3[/tex]

Step-by-step explanation:

The equation for a quadratic graph can be expressed in the Vertex form:

[tex]y = a(x-h)^{2} + k[/tex]

Where:

[tex](h, k)[/tex] = Vertex of the parabola

        = Extreme point of the parabola

Step I:
By reading from the graph:

    [tex](h, k)[/tex]  = [tex](-3, 3)[/tex]

Substitute the values of h and k in the above equation:

[tex]y = a[x- (-3)]^{2} + (3)[/tex]

[tex]y = a(x + 3)^{2} + 3[/tex]

Step II:

Determine a:

Based on the shape of the graph (which is an upside down U), the value of a will be negative:

Count one unit to the right from the vertex and see how far do you go down to touch the graph:

From the graph:

It seems you need to move 2 units down

∴a = [tex]-2[/tex]

Step III:
Substitute this value of a in the above equation:

[tex]y = -2(x + 3)^{2} + 3[/tex]

Answer: B 14.0

Step-by-step explanation:

According to the question the 25 hoodies and 20 performance shirts were ordered.

Performance is the result of an individual or organization's efforts in terms of achieving a desired outcome or goal. It is usually measured in terms of objectives, tasks and outcomes, and is a way of assessing the effectiveness of an individual or organization.

Substitution Method:
Let x = the number of hoodies ordered
Let y = the number of performance shirts ordered
Then, x + y = 45  (The total number of items ordered)
60x + 45y = 2400  (The total cost of the order)
Solve for x by substituting y = 45 - x into the second equation:
60x + 45(45 - x) = 2400
60x + 2025 - 45x = 2400
15x = 375
x = 25 (25 hoodies were ordered)
Substitute x = 25 into the first equation:
25 + y = 45
y = 20 (20 performance shirts were ordered)
Therefore, 25 hoodies and 20 performance shirts were ordered.

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Answer:

Step-by-step explanation:

fork knife

We can be 95% confident that the true population mean difference between the two samples falls within the range of 0.374 to 0.562

To construct a 95% confidence interval for the data, we need to calculate

The formula for the mean difference is:

x₁ - x₂ = 3.4123 - 2.9442 = 0.4681

The formula for the standard deviation of the differences is:

sD = √[(s₁²/n₁) + (s₂²/n₂)]

SD = √[(1.7458²/57) + (2.0382²/57)]

SD = 0.3555

The margin of error is calculated using the following formula:

ME = t * (sD / √(n))

where t is the critical value for a 95% confidence interval with 56 degrees of freedom

So, we have

ME = 2.003 * (0.3555 / √(57))

ME = 0.0943

Finally, we can calculate the upper and lower bounds of the confidence interval:

CI = (x₁ - x₂) ± ME

CI = 0.4681 ± 0.0943

CI = (0.4681 - 0.0943, 0.4681 + 0.0943)

CI = (0.3738, 0.5624)

Approximate

CI = (0.374, 0.562)

Thus, the 95% confidence interval for the mean differences is (0.374, 0.562), rounded to three decimal places.

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Answer:

To divide 3000 rupees between Teena and Beena so that they get 40% and 60% respectively, we need to follow these steps:

Step 1: Find the total percentage that Teena and Beena will receive together:

40% + 60% = 100%

This means that Teena and Beena will receive 100% of the total amount, which is 3000 rupees.

Step 2: Calculate the amount that Beena will receive:

60% of 3000 rupees = 0.6 x 3000 = 1800 rupees

Step 3: Calculate the amount that Teena will receive:

40% of 3000 rupees = 0.4 x 3000 = 1200 rupees

Therefore, Beena will receive 1800 rupees, while Teena will receive 1200 rupees

Answer: Since the spinners have 5 and 6 numbers respectively, the total number of outcomes is 5 x 6 = 30.

If we get the same number as a previous spin, it means that the first spin is irrelevant, and we only care about the second spin. Therefore, the probability of getting the same number as a previous spin is the same as the probability of getting any specific number on the second spin, which is 1 out of 6.

Therefore, the probability of getting the same number as a previous spin is 1/6, or approximately 0.17 to two decimal places.

Step-by-step explanation:

The solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).

A system is an organized set of components that work together to achieve an overall goal. It could be a physical system, such as an automobile, or an abstract system, such as an economic system.

The first step is to isolate one of the variables in one of the equations. To do this, we can multiply both sides of the first equation by -3. This will give us: 6y = 18x + 54.
Next, we need to subtract this equation from the second equation. Doing so gives us: 3x - 6y = -27.
Now we can isolate the variable y. To do this, we can divide both sides of the equation by -6. This will give us: y = -3x - 9.
We have now isolated the variable y in both equations, so we can substitute y = -3x - 9 in the first equation. Doing so gives us: -2(-3x - 9) = -6x - 18.
We can then simplify this equation to get: 6x + 18 = -6x - 18.
Finally, we can solve this equation for x. Doing so gives us x = -3. We can then substitute this value into either equation to find the value of y: y = -3(-3) - 9 = 9.
Therefore, the solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).

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Answer:

The function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]

Step-by-step explanation:

We are given

The costs of a company are represented by the function

[tex]C(x)=3.7x+9,000[/tex]

Its revenues are represented by the function

[tex]R(x) = 4.6x[/tex]

we know that

[tex]\text{Profit = Revenue - Cost}[/tex]

[tex]P(x)=R(x)-C(x)[/tex]

now, we can plug

[tex]P(x)=4.6x-(3.7x+9,000)[/tex]

now, we can simplify it

[tex]P(x)=0.9x-9,000[/tex]

So,

the function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]

The equation used to find the break-even point is 0.9x - 9000.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have,

The costs of a company are represented by the function

C(x) = 3.7x + 9,000

and, revenues function

R(x) = 4.6x

For Break even point

Profit = Revenue - cost

P = 3.7x + 9000 - 4.6x

P = 0.9x - 9000

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Answer:

the sum of a+b+c is 56.

Step-by-step explanation:

If a:b:c = 1:3:4 and c = 28, we can find the values of a and b using the ratios.

Since a:b:c = 1:3:4, we can write:

a = x, b = 3x, c = 4x

where x is some constant of proportionality.

We are given that c = 28, so we can substitute this value to get:

4x = 28

Solving for x, we get:

x = 7

Therefore, a = x = 7 and b = 3x = 21.

The sum of a, b, and c is:

a + b + c = 7 + 21 + 28 = 56

So the sum of a+b+c is 56.

Answer:

The answer is 24 in

Step-by-step explanation:

This solution is for "SIMILAR TRIANGLES";

Let us letter the shape starting from left to right A-B-C-D-E

Angle A is similar to Angle E, so is Angle B similar to Angle D, that is, "Alternate interior angles" while Angle ACB is similar to Angle DCE, that is, "Vertical Angles";

Line AB = 5 in is parallel to line DE = 15 in

So, K = DE / AB = 15 / 5 = 3

Line CD = K * CB = 3 * 8 = 24 in

Answer:

Figure D.

Step-by-step explanation:

The given Figure is a cube , which is a three-dimensional shape that has six square faces, twelve edges, and eight vertices. All of its faces are congruent and perpendicular to each other.

Figure D will turn into Square box when it is folded. Rest all are either Cuboid or Irregular Shaped objects when folded.

The approximate mean of the frequency distribution is of 35.2 miles gallon.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

As we are given a frequency distribution, we take the midpoint of each interval, and thus the sum of the observations is given as follows:

10 x 30 + 12 x 35 + 3 x 40 + 4 x 45 = 1020.

There are 29 observations, hence the mean of these observations is given as follows:

1020/29 = 35.2 miles gallon.

The frequency distribution is given as follows:

28-32 10

33-37 12

38-42 3

43-47 4

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The balance in the account after 4 years is $3,376.50.

The balance in the account after 25 years is $16,050.07.

The tractor will be worth $9,449.11 after 3 years.

All posted credit and debit transactions are included in your account balance. It's the balance in your account before any pending charges are subtracted. The amount that can be used for withdrawals or purchases is your accessible balance.

1. We can use the formula A = P(1 + r/n) to determine the account balance after 4 years with a $3,000 principal receiving 3% compounding annually (nt)

where A represents the balance, P represents the principal, r represents the yearly interest rate, n represents the number of times interest is compounded annually, and t represents the passage of time in years.

By typing in the indicated values, we get:

A = 3000(1 + 0.03/1)^(1*4)

A = 3000(1.03)^4

A = 3000(1.1255)

A = $3,376.50

Thus, $3,376.50 remains in the account after 4 years.

2. We can once more apply the formula: A = P(1 + r/n) to determine the account balance after 25 years with a $2,000 principal, receiving 7% compounding semi-annually (nt)

Then then, it's a case of the same thing happening again.

By typing in the indicated values, we get:

A = 2000(1 + 0.07/2)^(2*25)

A = 2000(1.035)^50

A = $16,050.07

Thus, the account has a balance of $16,050.07 after 25 years.

3. Considering that the tractor loses 15% of its value per year, we can apply the formula A = P(1 - r)t to determine how much it will be worth after three years.

where A represents the final value, P the starting point, r the depreciation rate, and t the passage of time in years.

By typing in the indicated values, we get:

A = 14340(1 - 0.15)^3

A = 14340(0.85)^3

A = $9,449.11

The tractor will therefore be valued $9,449.11 after three years.

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Answer:

It is not a function.

Answer:

105 in

Step-by-step explanation:

4×(8×5) =80

2

5×5=25

25+80=105

Therefore , the solution of the given problem of function comes out to be  y-intercepts of the function will be at y = 1 and y = -1.

Numerous subjects, including mathematics, numbers, and their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between various elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.

Here,

=> 1. Chart for y = tan x

The period of the function, which is, can be found in order to draw y = tan x.

The vertical asymptotes can then be found at x = /2 + n, where n is any number.

At x = n, where n is any positive number, the function will have x-intercepts.

The horizontal asymptotes at y = 1 and y = -1 are also accessible.

=> 2 .Chart for y = csc x

To draw y = csc x, we must first determine the function's period, which is 2.

The vertical asymptotes at x = n, where n is any number, can then be discovered.

The y-intercepts of the function will be at y = 1 and y = -1.

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Answer: Velocity,  v= distance/time

Given: distance=95km & time= 2 hours

Velocity= 95/2 = 47.5km/hour

Step-by-step explanation:

Now, Distance= 165 km and we got velocity= 47.5km/hour

                          = 47.5 =165/time

Time taken =      165/47.5= 3hours and 50 minutes.

Therefore, Time taken to remaining 165 km of her trip is 3hours and 50 minutes.

Answer:

If the ratio of squash to water is 1:2, it means that for every 1 unit of squash, we need 2 units of water.

So, to mix 1 liter of squash, we need 2 liters of water.

Therefore, the number of liters of water needed to mix with 1 liter of squash is 2 liters.

Step-by-step explanation:

Answer:

To find the x and y intercepts, we set x and y to zero respectively:

x-intercept: setting y = 0 gives us 6/(x^2 - 5x - 6) = 0, which has no real solutions.

y-intercept: setting x = 0 gives us s(0) = 6/(-6) = -1.

To find the vertical asymptotes, we set the denominator equal to zero and solve for x:

x^2 - 5x - 6 = 0

(x - 6)(x + 1) = 0

This gives us two vertical asymptotes at x = 6 and x = -1.

To find the horizontal asymptote, we need to look at the behavior of the function as x approaches infinity and negative infinity. As x becomes very large in magnitude, the terms involving x^2 become much larger than the terms involving x or the constant term, and so we can ignore those terms. This gives us:

s(x) ≈ 6/x^2 as x → ±∞

Therefore, the horizontal asymptote is y = 0.

In summary:

x-intercept: none

y-intercept: (0, -1)

vertical asymptotes: x = 6 and x = -1

horizontal asymptote: y = 0

If you have anymore questions, feel free to comment and I will answer them 8-5 I am on.

Step-by-step explanation:

The following is provided: parallelogram ABCD

The following is what we must demonstrate: segments AB, CD, and BC, and segment AD.

According to the definition of a parallelogram, section BC is parallel to segment AD since ABCD is a parallelogram.

The definition of a parallelogram is that segment AB is parallel to segment DC.

Segments BC and AD are transverse to line AC. As illustrated below, this transversal generates the alternate interior angles 1 and 4, which are equivalent.

In the same way, segment AB and segment DC are transversals for line AC. Alternate interior angles 2 and 3 are produced by this transversal, and they are equivalent.

Segment AC is also divided into segments by its reflexive property.

∠1 ≅ ∠ 4

∠2 ≅ ∠ 3

AC segment AC segment

Triangle ABC triangle ADC, by ASA

In light of the fact that similar parts of congruent triangles are also congruent, segment AB segment CD and segment BC AD.

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Therefore , the solution of the given problem of probability comes out to be 0.00439, or about 0.44%.

The main goal of the mathematical field known as model parameters is to determine the probability that a statement is accurate or that a particular event will occur. It is possible to symbolise chance by using any ranging between range 0 and 1, where 1 typically denotes certainty and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

To calculate the likelihood of receiving a hand of five clubs, three cards, and one card from each remaining deck,

Five clubs can be obtained in the following ways:

=> C(13,5) = 1,287

where C(n,r) indicates how many different ways r things were combined from a total of n options.

After selecting the five clubs, we must select three cards, one from each of the remaining three decks.

=> C(13,2) * C(3,2) = 702

As a result, there are three cards from each of the other two decks and five clubs, giving rise to the following combinations:

=> C(13,5) * [C(39,3) - C(13,2) * C(3,2)] = 328,664

Finally, there are C(52,8) = 74,837,381 potential hands with 8 cards.

The likelihood of receiving five clubs and three cards, along with one card from each of the other three decks, is as follows:

=> P = 328,664 / 74,837,381

=> P ≈ 0.00439, or about 0.44%.

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The answer οf the given questiοn based οn the temperature is at the pοint (1, 2, 3) is apprοximately -62.3 °C.

A three-dimensiοnal Gaussian οr nοrmal distributiοn is type οf prοbability distributiοn that describes three-dimensiοnal data set. It is characterized by its mean, which determines center οf  distributiοn, and its standard deviatiοn, which determines spread οr width οf  distributiοn.

The temperature at a pοint:

(x, y, z)

is given by

T(x, y, z)

= 200e − x² − 5y² − 9z²

where T is measured in °C and

x, y, z

in meters.

The expressiοn 200e−x² − 5y² − 9z² represents a three-dimensiοnal Gaussian οr nοrmal distributiοn, with the highest temperature lοcated at the οrigin (0, 0, 0) and the temperature decreasing as we mοve away frοm the οrigin in any directiοn.

Tο find the temperature at a specific pοint (x, y, z), we substitute these values intο the expressiοn T(x, y, z) = 200e−x² − 5y² − 9z² and simplify. Fοr example, the temperature at the pοint (1, 2, 3) is:

T(1, 2, 3) = 200e−12 − 5(2)² − 9(3)²

T(1, 2, 3) = 200e−1 − 20 − 243

T(1, 2, 3) ≈ -62.3 °C

Therefοre, the temperature at the pοint (1, 2, 3) is apprοximately -62.3 °C.

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