the table below shows the number of years of experience that 8 employees at a supermarket have and their hourly wages

On October 24, 218 days after March 20, there will be 10 hours of sunlight.

The number of daily sunlight hours of a particular location is modelled by the trigonometric equation,

l(t) = 12 + 3.5sin (2[tex]\pi[/tex]/365t)

Here , L(t)= Number of sunlight hours in a day.

           t = Number of days after 20th March .

Now we are required to determime the day  during first 365 on which there are 10 sunlight hours ,that is, we need the value of "t" for which L(t) =10 hours. So in the given equation by putting L(t)= 10 and solving for t , follows as,

l(t) = 12 + 3.5sin (2[tex]\pi[/tex]/365t)

10 = 12 + 3.5sin (2[tex]\pi[/tex]/365t)

10-12 = 3.5sin (2[tex]\pi[/tex]/365t)

-2 =  3.5sin (2[tex]\pi[/tex]/365t)

-2/3.5 = sin (2[tex]\pi[/tex]/365t)

-0.574 = sin (2[tex]\pi[/tex]/365t)

For the inverse function of y = sin x

sin ⁻¹(y) =x + 2n[tex]\pi[/tex]

Now as we are required to calculate the day having 10 sunlight hours in first 365 days so putting n=0 we get,

t = -35.3521 or t =217.9422

Now t can not be negative as we want to find the day after march 20 having 10 sunlight hours. So neglecting t=-35.3521 . Now we get t=217.9422 .

Rounding off we get ,t=218 which is the required answer.

Hence, 218 days after march 20 i.e on October 24 it will have 10 sunlights.

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(a) she land to minimize the total travel time is 2.4min

(b) the minimum speed at which she must row so that the quickest way to the restaurant is to row directly is 6

(a)

T(x) = time rowing + time walking

     = [tex]\frac{\sqrt{x^{2} +16} }{2}[/tex] +[tex]\frac{6 - x}{3}[/tex]

T(x) = 1/2[tex]\sqrt{(x^{2} + 16)}[/tex]  + 2 - [tex]\frac{x}{3}[/tex]

  first derivation

T'(x) = 1/4[tex]\sqrt[-1/2]{(x^{2} + 16)}[/tex] .2x - 1/3

       = [tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex] - 1/3

T'(x) = 3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] / 6[tex]\sqrt{(x^{2} + 16)}[/tex]

T'(x) = 0

3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] / 6[tex]\sqrt{(x^{2} + 16)}[/tex]  = 0

3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] =0

3x/2 = [tex]\sqrt{(x^{2} + 16)}[/tex]

9[tex]x^{2}[/tex]/4 = [tex]x^{2}[/tex] + 16

9[tex]x^{2}[/tex] = 4 [tex]x^{2}[/tex] + 64

5 [tex]x^{2}[/tex] = 64

[tex]x^{2}[/tex] =64/5

x = [tex]\sqrt{64/5}[/tex]

x = 8/[tex]\sqrt{5}[/tex]

x = 8[tex]\sqrt{5}[/tex]/5

total travel time = 6 - 8[tex]\sqrt{5}[/tex]/5 = 2.4 min

she land to minimize the total travel time is 2.4min

(b) T(x) = time rowing

           = [tex]\frac{\sqrt{x^{2} +16} }{2}[/tex]

first derivation

T'(x) = 1/4[tex]\sqrt[-1/2]{(x^{2} + 16)}[/tex] .2x

      = [tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex]

T'(x) = 0

[tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex] =0

x = 0

minimum speed = 6-x = 6-0=6

the minimum speed at which she must row so that the quickest way to the restaurant is to row directly is 6

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From the given data

a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks

b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km

In the graph,

The x axis represents the Time since start in minutes and the y axis represents the distance from the start in kilometers.

In x axis each block represents 5 minutes

The maximum value of time taken in table = 35 minutes

Then the number of squares wide does the grid need to be so that the data fits on the graph = 35 / 5

= 7 blocks

Part b

If the grid is 20 squares tall

The maximum value of distance = 1.8 km

Then the value of A will be

1.8 / 20 = 0.09 km

Hence, from the given data

a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks

b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km

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The value of x is -8.

1).

N(-6,-8), O(5, 3), P(0, 9), and Q(x, 1).

slope between NO = y2 - y1 / x2 - x1

= 3 - (-8) / 5 - (-6)

= 3+8 / 5+6

= 11/11

= 1

slope between PQ = 1-9 / x-0

= -8/x.

Given lines are parallel so there slopes are equal

1 = -8/x

x = -8.

Therefore the value of x is -8.

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Answer:

105

Step-by-step explanation:

1. x = mushroom he gather

2. he dry 2/5 from he gather, 2/5 from x

3. he pickled 5/9 of remaining mushroom

find the remaining mushroom value first, x-2/5x = 3/5x

then multiply with 5/9, 5/9(3/5x) = 15/45x

4. total mushroom - dry - pickled, he still have 28 to fry

5. write the equation like this

x - 2/5x - 15/45x = 28

45/45x - 18/45x -15/45x = 28

12/45x = 28

x = 28(45) / 12

x = 105

The money that the group will be able to donate with the savings from all 20 youth is $1400.

Let the daily pay plan for each youth = y.

Daily pay plan for 20 youths = 20y

Weekly pay plan = 7 × 20y = 140y

Assuming each youth saves $10 daily

Daily savings for 20 youth:

= 20 × $10

= $200

Weekly savings for 20 youth:

= 7 × $200

= $1400

If they used the early pay plan 140y to go swimming, they saved $1400 which they donated to the church.

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The function that includes all the ordered pairs in the given table is y = -x - 4

First choose two points

First point = (0, -4)

Second point = (2, -6)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (-6 - (-4) / (2 - 0)

= -6 + 4 / 2

= -2 / 2

= -1

Here at X = 0, the value of Y = -4

Therefore the y intercept of the line = -4

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Substitute the values in the slope intercept form

y = -1x - 4

y = -x - 4

Hence, The function that includes all the ordered pairs in the given table is y = -x - 4

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The equation for the line of best fit for a woman's height, y, based on her shoe size, x is y = 1.36x + 55.6.

From the given table:

To find the equation we need to insert the points (x,y) in calculator.

Points are:

Sum of X = 91

Sum of Y = 624.5

Mean X = 10.1111

Mean Y = 69.3889

Sum of squares (SSX) = 42.8889

Sum of products (SP) = 57.6111

Regression Equation = ŷ = bX + a

b = SP/SSX = 57.61/42.89 = 1.34326

a = MY - bMX = 69.39 - (1.34*10.11) = 55.80699

y = 1.34326X + 55.80699

aproximate:

y = 1.36 + 55.6.

Therefore The equation for the line of best fit for a woman's height, y, based on her shoe size, x is y = 1.36x + 55.6.

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Answer:

[tex]-12x+6[/tex]

Step-by-step explanation:

Take a look at the attachment,,,

Hope this helps! :)

Answer:

[tex]6 + 12x[/tex]

Step-by-step explanation:

The distributive property states that A(B + C) = AB + AC.

Therefore,

[tex]4 \left( \dfrac{3}{2} - 3x \right) = 4 \left( \dfrac{3}{2} \right) + 4(3x)[/tex]

Now we can simplify each term:

[tex]4 \left( \dfrac{3}{2} \right) + 4(3x)[/tex]

[tex]= \dfrac{12}{2} + 12x[/tex]

[tex]= 6 + 12x[/tex]

The values of x and y which are the missing terms of the given triangle have their values as; x = ⁵/₂ and y = ⁹/₄

From the given triangle, we can see that the transverse line intersects both side lengths at their midpoints. Thus, we can say that;

3x - 4 = x + 1   ------(1)

⁴/₃y + 2 = 4y - 4   ------(2)

Let us solve equation 1 by rearranging to get;

3x - x = 1 + 4

2x = 5

x = ⁵/₂

Similarly, we can say that for equation 2;

4y - ⁴/₃y =  2 + 4

4y - ⁴/₃y = 6

Multiply through by 3 to get;

12y - 4y = 18

8y = 18

y = 18/8

y = ⁹/₄

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The fraction left for Mark to read is 17/20.

From the information illustrated, he wants to complete of the 160 pages book by the end of the week and Mark has read 24 pages so far.

The number of pages left will be:

= 160 - 24

= 136 pages

Therefore, the fraction of pages left will be:

= Number of pages left / Total pages

= 136 / 160

= 17/20

The fraction is 17/20.

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The distance between (7,-2) and (-2,3) is 11.2 units using the distance formula.

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. a measurement of the distance between two points along a line or line segment. It's formula is "distance formula=√(x2-x1)²+(y2-y1)²".

Here,

distance formula=√(x2-x1)²+(y2-y1)²

=√(-2-7)²+(3--2)²

=√(-9)²+5²

=√81+45

=√126

=11.225 units

rounding to nearest tenth,

=11.2 units

Using the distance formula, the distance between (7,-2) and (-2,3) is 11.2 units.

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The median for a particular set is one less than the mean.

Given;

List of order for goals scored by a soccer team in 9 matches

= 0, 0, 1, 1, 1, 3, 3, 4, 5

To find the relation between mean and median;

The obtained mean = Sum of observations/number of observations

                                 = 0 + 0 + 1 + 1 + 1 + 3 + 3 + 4 + 5

                                 = 18/9

                                 = 2

Mean = 2

For median;

let us write the given observations in ascending order;

⇒  0, 0, 1, 1, 1, 3, 3, 4, 5

Here no. of observations is r = 9 which is an odd number.

Therefore observation at 5th is a middle position which has 1 as a value.

Median = 1

Therefore, the median is less than the mean by 1.

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Answer:

yes

Step-by-step explanation:

every x value has at least one y value

Answer:

y= [tex]\frac{5}{2}[/tex]X +5

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

(a) The expression of nth term of arithmetic sequence is [tex]a_n=1+(n-1)6[/tex] and (b) 4th term of the series  [tex]a_n=5n^2\\[/tex] is 80.

What is arithmetic sequence?

It is a sequence of numbers which have same difference between two consecutive numbers. The common difference can be any positive number or negative number or even it can be 0.

The six terms of the arithmetic sequence are as follows:

1,7,13,19,25,31

Calculate the common difference as follows:

7-1=6

13-7=6

19-13=6

Since it is an arithmetic sequence hence common difference is 6.

Hence, [tex]d=6[/tex].

Now, substitute value of the first term and the common difference in the following expression of the nth term.

[tex]a_n=a+(n-1)d\\a_n=1+(n-1)6[/tex]

Now, the nth term of another sequence is as follows:

[tex]a_n=5n^2\\[/tex]

Substitute n=4 in the above equation.

[tex]a_4=5(4)^2\\=80[/tex]

Hence, (a) the expression of nth term is [tex]a_n=1+(n-1)6[/tex] and 4th term of the series  [tex]a_n=5n^2\\[/tex] is 80.

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Answer:9072

Step-by-step explanation:

453.6 x 20 = 9072

The difference of the polynomials [tex]2x^2[/tex] - 9x + 8 and [tex]6x^2[/tex] - 5x - 12 is -[tex]4x^2[/tex] - 4x 20

The first polynomial is given that

[tex]2x^2[/tex] - 9x + 8

The second polynomial is

[tex]6x^2[/tex] - 5x - 12

Here we have to find the difference, to find that we need to subtract the second polynomial from the second polynomial

Then,
[tex]2x^2[/tex] - 9x + 8 - ( [tex]6x^2[/tex] - 5x - 12 )

Open the bracket using the distributive property

[tex]2x^2[/tex] - 9x + 8 - [tex]6x^2[/tex] + 5x +12

Combine the like terms

[tex]2x^2[/tex] -  [tex]6x^2[/tex]  -9x +5x + 8 +12

Apply the arithmetic operations on like terms

-[tex]4x^2[/tex] - 4x 20

Hence, the difference of the polynomials [tex]2x^2[/tex] - 9x + 8 and [tex]6x^2[/tex] - 5x - 12  is   -[tex]4x^2[/tex] - 4x 20

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The object moves at a speed of 25.352 m/s

The subject of a formula is the variable that is being worked out. It can be recognized as the letter on its own on one side of the equals sign. It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

In the question given, we have an equation;

s = d/t

d = 180m, t = 7.1s

s = 180 / 7.1

s = 25.352 m/s

The speed (s) of the object is 25.352 m/s

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Answer:

(3x+10)(x+1)

Step-by-step explanation:

This is the answer for 3x^2+13x+10.

I think you made an error while typing.

Hope this helps!

Answer:

[tex] \sf \: 2x + 2[/tex]

Step-by-step explanation:

Given expression,

→ (3x + 4) - (x + 2)

Let's simplify the expression,

→ (3x + 4) - (x + 2)

→ 3x + 4 - x - 2

→ (3x - x) + (4 - 2)

→ (2x) + (2)

→ 2x + 2

Hence, the answer is 2x + 2.

Answer:

8 hours and 35 minutes. (8:35)

Step-by-step explanation:

8 hours and 35 minutes.

515 minutes.

The value of y in the  expression is y= - (x + 4) or,  y= (x -4)

Algebraic expression in mathematics is a phrase that include coefficients, unknown variables  operations, and constants

To solve for y in the equation 10x+5y=5x+20 we apply algebraic rule;

Step 1: Collect the like terms by moving the unknown 'ý' to the left side of the equation

5y =5x -10x+20

Step 2: Evaluate the the expression 5y =5x -10x+20

5y = -5x + 20

Step 3: Divide both sides by 5

[tex]\frac{5y }{5}[/tex] = [tex]\frac{-5x +20}{5}[/tex]  

y = -5x/5  + 20/5

y = - (x + 4) or,  y= (x -4)

Therefore, the value of y in the expression is y= - (x + 4) or,  y= (x -4)

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the answer for your question above is (-1,-1) or you could say option no.3

Answer:

7.07

Step-by-step explanation:

Draw a horizonal line and a vertical line to creat a right triangle.  The horizontal measurement would be 5 and so would the horizontal measurement.

Use the Pythagorean theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]  The c side is the length that you are looking for

[tex]5^{2}[/tex] + [tex]5^{2}[/tex] = [tex]c^{2}[/tex]

25 + 25 = [tex]c^{2}[/tex]

50 = [tex]c^{2}[/tex]

[tex]\sqrt{50}[/tex] = [tex]\sqrt{c^{2} }[/tex]

7.07 = c  Rounded to the nearest hundredths

Answer:

The angle is approximately 111.199 degrees.

Step-by-step explanation:

Cosine is adjacent over hypotenuse.

The hypotenuse is the longest side of the triangle.  

In this cos the hypoteneuse is a. However, we can only use cos on right triangles and on the angles that are not 90 degrees. In this case, p would be the 90 degree angle if we could use cosine.

In this case, you need the law of cosines, not cosine. The law of cosine says [tex]c=\sqrt{a^2+b^2-2 a b cosp}[/tex] where c is the side opposite to the angle, a and b are the sides adjacent to the angle, and p is the angle. The law of cosine works for all the triangles.

Plugging in the numbers:

[tex]5.3=\sqrt{3.6^2+2.8^2-2*3.6*2.8* cosp}\\5.3^2=20.8-20.16* cosp}\\7.29=-20.16*cosp\\cos^{-1}\frac{7.29}{ -20.16}=p\\p=111.198929[/tex]

The value of x that makes lines u and v parallel is 6. Option A is correct.

First, let us understand the angles formed by parallel and transversal lines:

The different types of angles are alternate exterior angles, alternate interior angles, corresponding angles, consecutive angles, etc.

From the picture attached,

If the lines u and v are parallel and a third line (transversal) is intersecting these lines at two distinct points,

Both the angles given in the picture will be equal in measure as these angles are alternate exterior angles if u and v are parallel.

20x + 10 = 130 degrees

20x = 130 - 10 degrees

x = 120 / 20 = 6

So, the value of x is 6.

Thus, the value of x that makes lines u and v parallel is 6. Option A is correct.

For question please check the below figure:

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The expansion of the series  ⁴∑ₙ = ₁ 3ⁿ ⁺ ¹ is; 9 + 27 + 81 + 243

We are given the summation formula of the series as;

⁴∑ₙ = ₁ 3ⁿ ⁺ ¹

At n = 1, we will input 1 for n and we have;

3¹ ⁺ ¹ = 3² = 9

At n = 2, we will input 2 for n and we have;

3² ⁺ ¹ = 3³ = 27

At n = 3, we will input 3 for n to get;

3³ ⁺ ¹ = 3⁴ = 81

At n = 4;

3⁴ ⁺ ¹ = 3⁵ = 243

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