Create one word problem for each for the followings; polynomial function , Rational function, log and expo, trigonometric function and provide it and the solution. It should not be copied from the text or from online.

Therefore, the fair price of one raffle ticket is $2.60, which is slightly less than the amount Raul paid ($3).

a) The fair price of one raffle ticket is $3. This is because 500 tickets were sold at this price and one prize of $200 is to be awarded. Therefore, the 500 tickets collected add up to $1,500, while the prize to be awarded is $200. The net amount to be divided among all the ticket holders is $1,300.

b) The fair price of one raffle ticket is $2.60. This is calculated by dividing the total prize money of $200 by the total number of tickets sold (500). Therefore, 500 tickets multiplied by $2.60 gives a total prize money of $1,300 which is equal to the total ticket sales of $1,500 less the prize money of $200.

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Answer:

y=4

Step-by-step explanation:

Since you know that x=1 , you can substitute 1 into the equation wherever there is an x . y=5x−1.

Answer:

yes

Step-by-step explanation:

plug the values in -2>-6(1)-3 which equals -2>-9 which is a true statement. Brainliest please!!

Answer: 0.4

Step-by-step explanation:

Answer:

It looks like 35 miles per hour

Step-by-step explanation:

if you look at the vertical line between 0 and 2 (which is the one hour mark) on the horizontal axis of the graph you can see the line of the graph crossed under the 40 mi. Therefore the train traveled about 35 miles in one hour (or 35 mph) because there are no other answers under 40.

9514 1404 393

Answer:

  4.17 hours

Step-by-step explanation:

The speed of light is about 670,616,629.4 miles per hour, so the travel time to Neptune is ...

  (2,798,842,000 mi)/(670,616,629.4 mi/h) ≈ 4.17 h

It takes about 4.17 hours for light to travel from the sun to Neptune.

the tangent line of the curve x = 6t2 + 8, y = t3 − 4 has a slope of 1/2 at the point (2, -2).

we can use the formula for finding the slope of a tangent line to a curve at a given point, which is dy/dx. To find the value of t at which the tangent line has a slope of 1/2, we need to set dy/dx equal to 1/2 and solve for t.

Taking the derivatives of x = 6t2 + 8 and y = t3 − 4, we get dx/dt = 12t and dy/dt = 3t2. Then, using the formula for dy/dx, we have:

dy/dx = (dy/dt) / (dx/dt)
dy/dx = (3t2) / (12t)
dy/dx = 1/4 * t

Setting this equal to 1/2, we have:

1/4 * t = 1/2
t = 2

Therefore, the tangent line has a slope of 1/2 at the point (2, -2) on the curve.

we can find the point on a curve where the tangent line has a given slope by setting the derivative of y with respect to x equal to that slope, solving for t, and then plugging that value of t back into the equations for x and y to find the corresponding point on the curve.

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Step-by-step explanation:

(x₁, y₁) = (-3, -4) and (x₂, y₂) = (0, 4)

\(m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ 4 - ( - 4)}{0 - ( - 3)} \\ m = \frac{4 + 4}{3} \\ m = \frac{8}{3} \)

Answer:

a₂₇ = -81

Step-by-step explanation:

Given that,

The first term of an AP is, a₁ = 49

8th term of the AP, a₈ = 14

nth term of an AP is given by :

\(a_n=a_1+(n-1)d\\\\a_8=49+7d\\\\14=49+7d\\\\7d=-35\\\\d=-5\)

27th term of the AP is given by :

\(a_{27}=a_1+26d\\\\=49+26(-5)\\\\=-81\)

So, 27th term of the AP is -81.

ANSWER:

STEP-BY-STEP EXPLANATION:

We have to rule for reflection about the line y = x is:

Therefore:

Answer:

lets say they are a,b,c,d

a*b*c*d=67184

a<10

a=d-30

also bear in mind that b and c are in between

the rest is just trial and error as long as you satisfy all those equations above

Step-by-step explanation:

Total number of articles = 60

CP of each article = Rs. 150

Price at which he sell the remaining so as to to gain 10% on the whole deal.​

CP of 60 articles = 150 * 60 = Rs. 9000

1/3 of the articles are sold at Loss of 6%.

1/3 of articles = 1/3 * 60 = 20

⟹ CP of 20 articles = 20 * 150 = Rs. 3000

We know that,

SP = (100 - loss%)/100 * CP

⟹ SP of 20 articles = (100 - 6)/100 * 3000

⟹ SP of 20 articles = 94 * 30

⟹ SP of 20 articles = Rs. 2820

Also given that,

Total gain% = 10%

Gain% = Gain/CP * 100

⟹ 10 = Gain/9000 * 100

⟹ 10 * 9000 * 1/100 = Gain

⟹ Rs. 900 = Gain

We know,

Gain = Total SP - Total CP.

We have:

Total SP = SP of 20 articles + SP of 40 articles.

Total CP = CP of 60 articles = 9000.

So,

⟹ 900 = 2820 + SP of 40 articles - 9000

⟹ 900 - 2820 + 9000 = SP of 40 articles

⟹ Rs. 7080 = SP of 40 articles

∴ The remaining articles should be sold for Rs. 7080 to gain 10% on the whole transaction.

I hope it will help you.

Regards.

Answer:

→ 11(2 + y) + 11y

→ 22 + 11y + 11y = 154

→ 22y + 22 = 154

→ 22y = 154 - 22

→ 22y = 132

→ y = 132/22

→ y = 6

Step-by-step explanation:

The number of people in the survey is 25, s = 2 and mean = 33, the margin of error is given as 0.5532

Given,

In the question:

25 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $33 and standard deviation of $2.

To find the margin of error at a 80% confidence level.

Now, According to the question;

How to solve for the margin of error?

The margin of error can be used to provide the data that has to do with the amount of sampling error that would be in a given data statistic.

We would have to calculate the amount of error using the data that we have below.

We have the following values

number n = 25

mean u = 33

standard deviation (sd) = 2

The level of confidence c i = 80% = 0.80

we have to find the critical value

degree of freedom = 1 - 0.80

= 0.20

zα/2

= 0.20 / 2 = 0.10

= 1.383

The margin of error

= zα / 2 x s / √n

= 1.383 x 2/√25

= 1.383 x 2/5

= 0.5532

Hence,  the number of people in the survey is 25, s = 2 and mean = 33, the margin of error is given as 0.5532

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Using 3 different methods, we can find that YZ = 25m

Method 1:

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations -

sin(θ) = (opposite side)/Hypotenuse

cos(θ) = (adjacent side)/Hypotenuse

tan(θ) = (opposite side)/(adjacent side)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent side

YZ = opposite side.

We want to find YZ, so with the known things, we can use the first relation:

sin(30°) = YZ/50m

YZ = sin(30°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 2:

We know that the sum of the measure of all the internal angles of a triangle is always equal to 180°.

In a right-angled triangle, we have an angle equal to 90°.

Then we can write -

Z + 90° + 30° = 180°

Z = 180° - 90° - 30°

Z = 60°

From this angle, the side YZ is the adjacent side, then we can use the second trigonometric relation:

cos (60°) = YZ/50m

YZ = cos(60°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 3:

With the same angle of 60° we could find side XY, the opposite side as follows:

sin(60°) = XY/50m

XY = sin(60°) * 50m

XY = √3/2 *50m

XY = 25m

Now that we know one of the sides, we can use the last trigonometric relation-

tan(60°) = XY/YZ

tan(60°) = 43.3m/YZ

YZ =  43.3m/tan(60°)

YZ = 25m

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The complete question is -

Describe three ways to determine the measure of segment YZ.

Triangle XYZ is shown. Angle XYZ is a right angle and angle ZXY is 30 degrees. The length of hypotenuse XZ is 50 meters.

Answer:

$7

Step-by-step explanation:

If 6 people-$42.40

then 1 person-?

then cross multiply

$42.40*1=6?

divide both sides by 6

$42.40/6=?

=$7.066~$7(to nearest hundred)

Answer:

function:

graph and table A and B

not function:

mapping A and B

Based on the given figure; the below is the answer

Shape 10:

Acute angle: None

Right angle: 4

Obtuse angle: None

Perpendicular line: No

Parallel lines: Yes

Shape 11:

Acute angle: 2

Right angle: None

Obtuse angle: 1

Perpendicular line: Yes

Parallel lines: No

An acute angle refers to an angle that has a degree measure that is below 90 degrees, in order words, it is smaller than a right angle.

Shape 10:

Acute angle: None

Right angle: 4

Obtuse angle: None

Perpendicular line: No

Parallel lines: Yes

Shape 11:

Acute angle: 2

Right angle: None

Obtuse angle: 1

Perpendicular line: Yes

Parallel lines: No

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Step-by-step explanation:

Let $x be the normal price and $y be the sale price.

y = x-0.75 ---(1)

7y = 2.80 ---(2)

(1)x7 : 7y = 7(x-0.75) ---(3)

(2) - (3) : 2.80 - 7(x-0.75) = 0

2.80 = 7(x-0.75)

x-0.75 = 0.40 ---(4)

x = 1.15

Sub (4) into (1)

y = 0.40.

Therefore the normal price is $1.15 and the sale price is $0.40.

Answer:

z = 81/10 = 8.100

Step-by-step explanation:

It is difficult to determine which sample will be the most representative without more information.

There are a few factors to consider when evaluating the representativeness of a sample:

Sample size: Larger sample sizes are generally more representative because they include more individuals, which makes it less likely that the results will be biased.

Sampling method: Random sampling methods, such as Ruth's method of calling randomly selected registered voters, are generally more representative than other methods because they aim to include a representative sample of the population.

Population: The population being surveyed will also impact the representativeness of the sample. For example, if Levonia's friends are not representative of the general population, her sample may not be representative.

Overall, it is important to consider all of these factors when evaluating the representativeness of a sample.

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Answer:

Please explain it in English

No, the determinant of a matrix can only be calculated for square matrices. A square matrix has an equal number of rows and columns, while a non-square matrix has a different number of rows and columns.

The determinant is a mathematical property that is defined for square matrices only. It is a scalar value that represents certain characteristics of the matrix. To calculate the determinant of a square matrix, you can use various methods such as expansion by minors, cofactor expansion, or using the properties of determinants.

For example, let's consider a 3x2 non-square matrix:

```

A = [[1, 2],

    [3, 4],

    [5, 6]]

```

Since A is a non-square matrix, we cannot calculate its determinant.

the determinant is a concept applicable only to square matrices. Non-square matrices do not have a determinant.

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Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

Answer:

= 24.

Step-by-step explanation:

-(-5+(-8))-(-9-2)

= -(-5-8)-(-9-2)

= 5 + 8 + 9 + 2

= 13 + 11

= 24

Answer:

Step-by-step explanation:

3 ft

4yd  x 3 ft = 12 ft

3 ft/12ft = 1/4 ft

The triangle is the essential geometric form in the construction and support of a geodesic dome.

        A geodesic dome is a spherical structure like a round tent that is formed by the simultaneous placements of triangular structures one along the other. The triangles are placed in such a way it seems that rhombuses are placed one after the other.

         They are lightweight, and a layer of canvas or transparent material is placed over the structure to make it water-proof.

          It was first created by the American designer Richard Buckminster Fuller in the 20th century.

          Although these homes save energy and give a perfect place to live in nature, they can also pose some issues like the placement of the chimney, creating rooms within the dome, leakage in the roof, and so on.

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The minimum sample size required for the estimate (to the next integer) is given as 404.

Note that a sample size is the number of observations or individuals in a sample selected from a population.

The formula for Sample Size (n) is given as:

Sample size = n = [(Z\(_{\alpha/2 }\) * σ ) / E]²

Where:

α = 1-90%

Margin of Error (E) = 0.18

Standard Deviation = σ = 2.2

At 90% confidence level the z is,

α = 1 - 90% = 1 - 0.90 = 0.10

α /2 = 0.10/2 = 0.05

Z\(_{\alpha/2 }\) = Z₀.₀₅ = 1.645

Thus, Samples Size =
= [(1.645 * 2.2) /0.18]²

= (3.619/0.18)₂

= (20.1055555556)²

= 404.2333641993; thus

n \(\approx\) 404

Therefore, the minimum sample size required for the estimate to the next integer is 404.

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Answer:

\((x - y) \times (x + y)( {x }^{2} + {y}^{2} )\)

Step-by-step explanation:

\((x ^{2} - y ^{2} ) \times (x ^{2} + y ^{2} )\)

\( ({x} - y) \times (x + y) \times {x }^{2} + y ^{2} )\)

Answer:

6 markers

Step-by-step explanation:

1) Find the number of red markers

Firstly, we know that Ms. Peters has a total of 36 markers. There are 3 colours within these 36 markers. Because she has an equal number of each colour, divide 36 by 3 to find the number of red markers.

36÷3=12

Therefore, Ms. Peters has 12 red markers.

2) Find the number of red markers in each group

Ms. Peters then divides the red markers into 2 equal groups. Because we now know that there are 12 red markers, divide 12 by 2 to find this number.

12÷2=6

Therefore, there are 6 red markers in each group.

I hope this helps!

Answer: C is correct answer

Step-by-step explanation: