You and your classmates create 18 watercolor paintings to sell at the PTA auction to raise money for your school. In order to pay for the materials you bought to make the watercolor paintings, you need to sell each of the watercolor paintings for $2.25. When transporting the watercolor paintings to the auction, one of your parents accidentally drops four of the watercolor paintings in the street and they are run over by a garbage truck. What is the new minimum price you need to set for the remaining watercolor paintings in order to pay for the materials?

Answer:

  {-3, 3, 4, 5, 6}

Step-by-step explanation:

The complement of a set is the set of all elements in the universe that are not in the given set.

The set U is defined as ...

  U = { x | x ∈ and -3 ≤ x ≤ 6 }

In roster form, this is ...

  U = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

The given set is defined as ...

  S = { x | x ∈ and -2 ≤ x < 3 }

In roster form, this set is ...

  S = {-2, -1, 0, 1, 2} . . . . . note that 3 is not in set S

If we remove the elements of set S from set U, we have ...

  S' = {-3, 3, 4, 5, 6}

The price of a painting in the year 2022 will be $ 568,000.

A rise in the amount of a certain product or service is known as inflation.

Given data;

Cost of painting in the year 2021, P₁ = $560,000

Cost of painting in the year 2022, P₂ =?

The amount increases every year,x = $8,000

The cost of painting in the year 2022 is found as;

P₂ = P₁ + x

P₂= $560,000 + $8,000

P₂ = $ 568,000

Hence the price of a painting in the year 2022 will be $ 568,000.

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Using proportions, it is found that the number of hours for which she practiced her role on Tuesday is:

[tex]\frac{5}{9}[/tex]

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

On Wednesday, she practiced 5/6 of an hour, and on Tuesday she practiced 2/3 of Wednesday's amount, hence the number of hours she practiced on Tuesday was of:

[tex]n = \frac{5}{6} \times \frac{2}{3} = \frac{10}{18} = \frac{5}{9}[/tex].

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Your question is incomplete. Please find the missing content below

You go to the shops on Monday and buy 1 apple, 1 banana, and 1 carrot; the whole transaction totals €15. On Tuesday you buy 3 apples, 2 bananas, 1 carrot, all for €28. Then on Wednesday 2 apples, 1 banana, 2 carrots, for €23.

Construct a matrix and vector for this linear algebra system.

Matrix is A = [ [ A₁₁ , A₁₂ , A₁₃]

                      [ A₂₁ , A₂₂ , A₂₃]

                      [ A₃₁ , A₃₂ , A₃₃] ]

Vector S = [sMon , sTue , sWed]

(i) consider A as fruits

A₁₁ = 1

A₁₂ = 1

A₁₃ = 1

A₂₁ = 3

A₂₂ = 2

A₂₃ = 1

A₃₁ = 2

A₃₂ = 1

A₃₃ = 2

(ii) Consider s as days

sMon = 15

sTue  = 28

sWed = 23

Hence the matrix and vector is:  A = [ [ A₁₁ , A₁₂ , A₁₃]

                                                           [ A₂₁ , A₂₂ , A₂₃]

                                                           [ A₃₁ , A₃₂ , A₃₃] ]

Vector S = [sMon , sTue , sWed]

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Answer:

  (x, y) = (16/3, -1/9)

Step-by-step explanation:

A system of two linear equations can be solved a number of ways. One of the easiest is by graphing. Algebraic methods usually work better when the equations are in standard or general form.

A graphing calculator can work with the given equations. The solution it shows in the first attachment is ...

  (x, y) = (16/3, -1/9)

An algebraic method of solving a pair of linear equations can start with them in general form. We can obtain that form by subtracting one side of the equation from both sides. Here, we choose to do that so the coefficient of x is positive.

First equation

  5(x -3y) -6 -(4x +1) = 0 . . . . . . . subtract (4x+1) from both sides

  5x -15y -6 -4x -1 = 0 . . . . . . eliminate parentheses

  x -15y -7 = 0 . . . . . . . . . . collect terms

Second equation

  3(x +6y) +4 -(9y +19) = 0 . . . . . . subtract (9y+19) from both sides

  3x +18y +4 -9y -19 = 0 . . . . . . eliminate parentheses

  3x +9y -15 = 0 . . . . . . . . . . . collect terms

  x +3y -5 = 0 . . . . . . . . . . . remove common factor of 3

We notice the coefficients of x and y are related by convenient factors, so we can use the "elimination method" to solve these equations. Subtracting the first from the second, we get ...

  (x +3y -5) -(x -15y -7) = 0 -0

  18y +2 = 0 . . . . . . collect terms

  y +1/9 = 0 . . . . . . . divide by 18, reduce the fraction

  y = -1/9

Using this in the second equation, we have ...

  x +3(-1/9) -5 = 0

  x = 5 1/3

The solution to the system of equations is (x, y) = (5 1/3, -1/9).

The computation shows that the distance from the base of the wall that the cannonball land will be 132.2m

The peak height equation will be illustrated as:

v²sinx = 2h

(47.4)²x = 2(9.81)(10.5)

Divide to get the value of x

x = 17.63°

Therefore, the distance will be:

d ° (47.4)² × 2(17.63) / 9.81

= 132.2m

Therefore the distance is 132.2m.

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Answer:

its 69.8

Step-by-step explanation:

The approximate value of cos theta in the quadrant indicated is 0.4232

Given the expression below;

sin theta = -0.906

Determine the value of theta

sin theta = -0.906

theta = arcsin(-0.906)
theta = -64.95 degrees

In the 4th quadrant;

theta = 360 - 64.95

theta = 295.04 degrees

Determine the value of cosine theta

Cos theta = cos 295.04
cos theta = 0.4232

Hence the approximate value of cos theta in the quadrant indicated is 0.4232

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Using a system of equations, the meaning of point R is given as follows:

A number of books and their cost where both subscriptions cost the same.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable. In a graph, the solution to the system is the intersection point of the two equations.

In this problem, the point R is the point in which:

3y = 96.

That is, the point in which the prices are equal, hence:

A number of books and their cost where both subscriptions cost the same.

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Hello,

2,75 % = 2,75/100 = (2,75 × 100)/(100 × 100) = 275/10000 = 11/400

The expression 1.54x10^28 not in scientific notation form is 15400000000000000000000000000

The expression is given as:

1.54x10^28

Evaluate the product

1.54x10^28 = 15400000000000000000000000000

Hence, the expression 1.54x10^28 not in scientific notation form is 15400000000000000000000000000

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Using the combination formula, it is found that 525 combinations can be created.

The order in which the employees are chosen is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

Then the number of combinations is given by:

[tex]n = C_{7,3}C_{6,2} = \frac{7!}{3!4!} \times \frac{6!}{2!4!} = 525[/tex]

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Answer:

E.  5

Step-by-step explanation:

Define the variables:

Given information:

Use the given information and the defined variables to create two equations:

[tex]\implies \sf 6b = 13f[/tex]

[tex]\implies \sf 2f = 5g[/tex]

Rewrite the second equation to isolate f:

[tex]\implies \sf \dfrac{2f}{2}=\dfrac{5g}{2}[/tex]

[tex]\implies \sf f = 2.5g[/tex]

Substitute this into the first equation to get an expression with just bleeps and geebles:

[tex]\implies \sf 6b = 13(2.5g)[/tex]

[tex]\implies \sf 6b = 32.5g[/tex]

Finally, divide both sides by 6 to isolate b:

[tex]\implies \sf \dfrac{6b}{6}=\dfrac{32.5g}{6}[/tex]

[tex]\implies \sf b=5.42g\;(2\:d.p.)[/tex]

Round 5.42 to the nearest integer  →  5

Therefore, N = 5

Step-by-step explanation:

Solve from the least onwards

Then

So

5 is correct most

Option E

Answer:

vhggghkhy

Step-by-step explanation:

ggggggggghgghggggggggggggggggggggggggggggggggggg jjhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

The heights of the gondola are the same at 8.019 seconds and 26.446 seconds

Ferris wheel 1

The given parameters are:

The above means that:

The sine function is represented as:

y = Asin(2π/T)t + c

Where

c = Amplitude - Minimum

c = 7 - 1.5

c = 5.5

So, we have:

y = 7sin(2πt/16) + 5.5

y = 7sin(πt/8) + 5.5

Shift to the left by π/2

y = 7sin(πt/8 - π/2) + 5.5

Ferris wheel 2

The given parameters are:

The above means that:

The sine function is represented as:

y = Asin(2π/T)t + c

Where

c = Amplitude - Minimum

c = 8 - 2

c = 6

So, we have:

y = 8sin(2πt/20) + 6

y = 8sin(πt/10) + 6

Shift to the left by π/2

y = 8sin(πt/10 - π/2) + 6

Hence, the equations of the wheels are y = 7sin(πt/8 - π/2) + 5 and y = 8sin(πt/10 - π/2) + 6

See attachment for their graphs

From the attached graph, we have:

f(x) = g(x) = 12.5 at x = 8.019

f(x) = g(x) = 9.511 at x = 26.446

Hence, the heights of the gondola are the same at 8.019 seconds and 26.446 seconds

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Step-by-step explanation:

charging the phone for 1 minute ,it has 2%

i.e,1----->2

After 2 minutes from that time ,i.e total 3 minutes

it has 6% charge

i.e,3--------->6

from the both the above cases ,1 minute provide 2%=6/3

=2

Hence,

for getting 50%charge=50/2

=25 min

and,for 90 %charge=90\2

=45 min

Answer:

The third option. he didnt make a mistake

Step-by-step explanation:

Answer:

Gabi did not make a mistake.

Step-by-step explanation:

To find j, Gabi needs to multiply both sides of the equation by 10. 80*10 = 800, so therefore j = 800. Both steps are correct.

Answer: [tex]35^{\circ}[/tex]

Step-by-step explanation:

The labeled angle is [tex]100^{\circ}[/tex] by the alternate interior angles theorem.

Thus, as angles in a triangle add to [tex]180^{\circ}[/tex], [tex]x=35^{\circ}[/tex]

Answer:

Step-by-step explanation:

Parameterize each line segment from [tex](x_0,y_0,z_0)[/tex] to [tex](x_1,y_1,z_1)[/tex] by

[tex]\vec r(t) = (1-t) (x_0\,\vec\imath + y_0\,\vec\jmath + z_0\,\vec k) + t (x_1\,\vec\imath + y_1\,\vec\jmath + z_1\,\vec k[/tex]

with [tex]0\le t\le1[/tex]. The work done by [tex]\vec F[/tex] on the particle along each segment is given the line integral of [tex]\vec F[/tex] with respect to that segment,

[tex]\displaystyle \int_{C_i} \vec F \cdot d\vec r = \int_0^1 \vec F(\vec r_i(t)) \cdot \dfrac{d\vec r_i(t)}{dt} \, dt[/tex]

• (3, 0, 0) to (3, 5, 1)

[tex]\vec r_1(t) = 3\,\vec\imath + 5t\,\vec\jmath + t\,\vec k[/tex]

[tex]W_1 = \displaystyle \int_0^1 \left(t^2\,\vec\imath + 75t\,\vec\jmath + 50t^2\,\vec k\right) \cdot \left(5\,\vec\jmath + \vec k\right) \, dt \\\\ ~~~~~~~~ = \int_0^1 (375t + 50t^2) \, dt = \frac{1225}6[/tex]

• (3, 5, 1) to (0, 5, 1)

[tex]\vec r_2(t) = 3(1-t)\,\vec\imath + 5(1-t)\,\vec\jmath + \vec k[/tex]

[tex]W_2 = \displaystyle \int_0^1 \left(\vec\imath + 75(1-t)\,\vec\jmath + 50 \,\vec k\right) \cdot \left(-3\,\vec\imath - 5\,\vec\jmath\right) \, dt \\\\ ~~~~~~~~ = -3 \int_0^1 \,dt = -3[/tex]

• (0, 5, 1) to (0, 0, 0)

[tex]\vec r_3(t) = 5(1-t)\,\vec\jmath + (1-t)\,\vec k[/tex]

[tex]W_3 = \displaystyle \int_0^1 \left((1-t)^2\,\vec\imath + 50(1-t)^2\,\vec k\right) \cdot \left(-5\,\vec\jmath - \vec k\right) \, dt \\\\ ~~~~~~~~ = \int_0^1 (-50 + 100t - 50t^2) \, dt = -\frac{50}3[/tex]

Then the total work done by [tex]\vec F[/tex] on the particle is

[tex]W = W_1 + W_2 + W_3 = \boxed{\dfrac{369}2}[/tex]

There is one solution in the system of equation

The system of equations is given as:

8x=12y-9 and 27y+18x=21

Divide 8x=12y-9 by 8

x = 1/8(12y-9)

Substitute x=1/8(12y-9) in 27y+18x=21

27y + 18 * 1/8(12y-9) =21

Expand

27y + 27y - 20.25 =21

Evaluate the like terms

54y = 41.25

Divide by 54

y = 0.7639

Hence, there is one solution in the system of equation

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For a solution to be the solution to a system, it must satisfy all the equations of that system. There exists no solution for the system of equations.

For a solution to be the solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at a single point(as we need a common point, which is going to be the intersection of course)(this can be one or many, or sometimes none)

For the three equations,

2x−2y+6z=16

3x+3y−4z=−5

x−y+3z=9

Solve the first equation for x,

2x−2y+6z=16

x = 8 + y - 3z

Now substitute the value of x in both the equations, if the two equations are satisfied, then the equation will have a solution, if it's not then no solution exists.

[tex]3\left(8+y-3z\right)+3y-4z=-5\\6y-13z+24=-5\\\\\\ 8+y-3z-y+3z=9\\ 8=9[/tex]

Hence, There exists no solution for the system of equations.

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The initial start-up fee for signing up with Rita's lawn mowing service is $20, using simultaneous equations.

Simultaneous equations are two or more algebraic equations that share variables like x and y and can be solved at the same time.

Let y = fixed cost (initial start-up cost)

Let x = variable cost per lawn mowing

Equation 1: Customer A = y + 10x = $370

Equation 2: Customer B = y + 7x = $265

Subtract equation 2 from equation 1 to get:

3x = $105

x = $35

Substitute x in any of the two equations to find the value of y, thus:

Customer A:

y + 10($35) = $370

y + #350 = $370

y = $20 ($370 - $350)

Thus, the initial start-up fee for signing up with Rita's lawn mowing service is $20, using simultaneous equations.

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The option that is better is that compounded twice annually with 61.5 interest than the simple interest for 60.

Simple interest is the amount obtained from a money invested or loaned over a specific period of time with a specific interest rate.

Analysis.

Let the principal to be used be 600

Compound interest compounded annually twice, which means the tenor of interest is two years.

first year interest

I = PRT/100

P= 600, R = 5%, T = 1

I = 600 x 5 x 1/ 100 = 30

Principal for second year = principal first year + interest

                                          = 600 + 30 = 630

interest for second year = 630 x 5 x 1/ 100 = 31.5

Compound interest  = 30+31.5 = 61.5

For simple interest, duration is 2 years,

I = PRT/100

I = 600 x 5 x 2/100 = 60

In conclusion, The account that earns 5% compounded twice annually is the better one since it accrues more interest.

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Answer:

A.  butterscotch

Step-by-step explanation:

The flavor of candy that is most likely to be picked is the flavor with the highest probability.

To find the highest probability, order the decimals from smallest to largest.  When ordering decimal numbers, always compare the digits immediately after the decimal point first, i.e. the 'tenth place'.

Therefore, from inspection of the table, the probabilities in order of smallest to largest are:  0.095 < 0.125 < 0.21 < 0.57

So the flavor with the highest probability of 0.57, and therefore the flavor that is most likely to be picked, is butterscotch.

Here

As butterscotch has highest probability it is most likely to be randomly picked

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation

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Using proportions, it is found that the same job will take Mrs. Squirrel 6 hours.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The times are given as follows:

The ratios are as follows:

Turtle/Squirrel = Squirrel/Pigeon.

Hence:

[tex]\frac{3}{x} = \frac{x}{\frac{1}{48}}[/tex]

[tex]x^2 = \frac{3}{48}[/tex]

[tex]x^2 = \frac{1}{16}[/tex]

[tex]x = \sqrt{\frac{1}{16}}[/tex]

x = 1/4.

It takes 1/4 of a day for Mrs. Squirrel to do the job, hence 1/4 x 24 hours = 6 hours.

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Answer:

240

Step-by-step explanation:

h+c=320

c=3h ( since 3 times the cheeseburger)

Now plug in 3h for C

h+3h=320 =  4h=320

Now divide 320 by 4 to get "h" alone

h=80

now plug 80 back t the eqation of c=3h

so now it is...

c=3 x 80

which is 240

so ur andswer is 240

Answer:

the scale factor is either 4 or 1/4 depending if you are going from the model to the actual or the actual to the model.

Step-by-step explanation:

s= scale factor

2s = 8  Divide both sides by 2

x = 4

If I do the other way:

8s = 2 Divide both sides by 8

s = 1/4

The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)

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The values of the expressions are -17/3, -29/3 and 13/3

The equation is given as:

z-​4/​4+​8= z + 9

Rewrite properly as

[tex]\frac{z-4}{4}+8= z + 9[/tex]

Subtract 8 from both sides

[tex]\frac{z-4}{4}= z + 1[/tex]

Multiply through by 4

z - 4 = 4z + 4

Evaluate the like terms

3z = -8

Divide by 3

z = -8/3

Substitute z = -8/3 in z - 3, z - 7 and z + 7

z - 3 = -8/3 - 3 = -17/3

z - 7 =  -8/3 - 7 = -29/3

z + 7 =  -8/3 + 7 = 13/3

Hence, the values of the expressions are -17/3, -29/3 and 13/3

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