a teacher gets a bag of lollipops for her class. She buys a large bag of 84 lollipop. If she wants each child to have 3 lollipops how many students must be in her class?

Answer: x = 40

Step-by-step explanation:

these two angles are vertical angles, they will equal each other

therefore, move numbers and variables to the opposite sides of the = sign to isolate the X

3x-10 = 2x + 30

   +10        +10           move the -10 by doing opposite

_____________

3x = 2x + 40

-2x   -2x                    move -2x by doing opposite

____________

x = 40

you can check your work by substituting 40 in place of x

3(40) - 10 = 2(40) +30

120-10 = 80 + 30

110 = 110

answer is correct

Answer:

x = 40

Step-by-step explanation:

The given angles are vertical angles, hence they are equal.

=============================================================

Solving for x :

⇒ 3x - 10 = 2x + 30

⇒ 3x - 2x = 30 + 10

⇒ x = 40

The coordinates of the image of triangle are transformation are X = (1,3), Y = (5,-3) and Z = (-1, -7)

From the figure, the coordinates of the triangle are:

A = (-1, -1)

B = (1, 2)

C = (-2,4)

The transformation rule is given as:

[tex]\triangle XYZ = T_{ < 3,1 > }(R_{x-axis}(D_2(\triangle ABC)))[/tex]

This means that, we start by dilating the triangle by a scale factor of 2.

So, we have:

A' = (-2, -2)

B' = (2, 4)

C' = (-4,8)

Next, we rotate the triangle across the x-axis

So, we have:

A'' = (-2, 2)

B'' = (2, -4)

C'' = (-4,-8)

Lastly, we translate the triangle by (x + 3,y + 1) to get the triangle XYZ

So, we have:

X = (1,3)

Y = (5,-3)

Z = (-1, -7)

See attachment for the image of the transformation

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Answer:

5/24

Step-by-step explanation:

Probability of selecting a pen :

⇒ Number of pens / Total items in Box 1

⇒ 5 / 7 + 5

⇒ 5/12

=============================================================

Probability of selecting a crayon :

⇒ Number of crayons / Number of items in box 2

⇒ 4 / 4 + 4

⇒ 4/8

⇒ 1/2

===========================================================

Probability (of both events) :

⇒ 5/12 × 1/2

⇒ 5/24

Answer:

4 days

Step-by-step explanation:

first convert 1/4 to eighths

2/8=1/4

to make 2/8 equal 7/8

you have to multiply by 4 for it to be 8/8

it cant be 7/8 because that would be three and a half days and they only read 1/4 each day

so it would take 4 days to finish

[tex]\\\\\ \textbf{a)}\\\\~~~\displaystyle \int (6x- \sin 3x) ~ dx\\\\=6\displaystyle \int x ~ dx - \displaystyle \int \sin 3x ~ dx\\\\=6 \cdot \dfrac{x^2}2 - \dfrac 13 (- \cos 3x) +C~~~~~~~~~~~;\left[\displaystyle \int x^n~ dx = \dfrac{x^{n+1}}{n+1}+C,~~~n \neq -1\right]\\\\ =3x^2 +\dfrac{\cos 3x}3 +C~~~~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \sin (mx) ~dx = -\dfrac 1m ~ (\cos mx)+C \right]\\[/tex]

[tex]\textbf{b)}\\\\~~~~\displaystyle \int(3e^{-2x} +\cos (0.5 x)) dx\\\\=3\displaystyle \int e^{-2x} ~dx+ \displaystyle \int \cos(0.5 x) ~dx\\\\\\=-\dfrac 32 e^{-2x} + \dfrac 1{0.5} \sin (0.5 x) +C~~~~~~~~~~~~~~;\left[\displaystyle \int e^{mx}~dx = \dfrac 1m e^{mx} +C \right]\\\\\\=-\dfrac 32 e^{-2x} + 2 \sin(0.5 x) +C~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \cos(mx)~ dx = \dfrac 1m \sin(mx) +C\right]\\\\\\=-1.5e^{-2x} +2\sin(0.5x) +C[/tex]

[tex]\textbf{a)}\\\\y = \displaystyle \int \cos(x+5) ~ dx\\\\\text{Let,}\\\\~~~~~~~u = x+5\\\\\implies \dfrac{du}{dx} = 1+0~~~~~~;[\text{Differentiate both sides.}]\\\\\implies \dfrac{du}{dx} = 1\\\\\implies du = dx\\\\\text{Now,}\\\\y= \displaystyle \int \cos u ~ du\\\\~~~= \sin u +C\\\\~~~=\sin(x+5) + C[/tex]

[tex]\textbf{b)}\\\\y = \displaystyle \int 2(5x-3)^4 dx\\\\\text{Let,}\\~~~~~~~~u = 5x-3\\\\\implies \dfrac{du}{dx} = 5~~~~~~~~~~;[\text{Differentiate both sides}]\\\\\implies dx = \dfrac{du}5\\\\\text{Now,}\\\\y = 2\cdot \dfrac 1 5 \displaystyle \int u^4 ~ du\\\\\\~~=\dfrac 25 \cdot \dfrac{u^{4+1}}{4+1} +C\\\\\\~~=\dfrac 25 \cdot \dfrac{u^5}5+C\\\\\\~~=\dfrac{2u^5}{25}+C\\\\\\~~=\dfrac{2(5x-3)^5}{25}+C[/tex]

[tex]\textbf{a)}\\\\y = \displaystyle \int xe^{3x} dx\\\\\text{We know that,}\\\\ \displaystyle \int (uv) ~dx = u \displaystyle \int v ~ dx - \displaystyle \int \left[ \dfrac{du}{dx} \displaystyle \int ~ v ~ dx \right]~ dx\\\\\text{Let}, u =x~ \text{and}~ v=e^{3x} .\\\\y= \displaystyle \int xe^{3x} ~dx\\\\\\~~= x\displaystyle \int e^{3x} ~ dx - \displaystyle \int \left[\dfrac{d}{dx}(x) \displaystyle \int e^{3x}~ dx \right]~ dx\\\\\\[/tex]

  [tex]=x\displaystyle \int e^{3x}~ dx - \displaystyle \dfrac 13 \int \left(e^{3x} \right)~ dx\\\\\\=\dfrac{xe^{3x}}3 - \dfrac 13 \cdot \dfrac{ e^{3x}}3+C\\\\\\= \dfrac{xe^{3x}}{3}- \dfrac{e^{3x}}{9}+C\\\\\\=\dfrac{3xe^{3x}}{9}- \dfrac{e^{3x}}9 + C\\\\\\= \dfrac 19e^{3x}(3x-1)+C[/tex]

The value of the probability P(3≤x<7) is 1

The expression is given as: P(3≤x<7)

This is calculated using:

P(3 ≤ x < 7) = P(3) + P(4) + P(5) + P(6)

Using the figure of the probability density function (see attachment), we have:

P(3 ≤ x < 7) = 0.30 + 0.30 + 0.20 + 0.20

Evaluate

P(3 ≤ x < 7) = 1

Hence, the value of the expression is 1

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Answer:

  Adult market

  Junior market

  Total profit: 13000

  Total consumer surplus: 14600

Step-by-step explanation:

Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.

Each demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).

  R = QP = Q(Pmax -Q)

The profit is the difference between revenue and cost.

  Profit = R - C = Q(Pmax -Q) -20Q

  Profit = Q(Pmax -20 -Q)

Writing the demand equation in terms of P, we find ...

   Q = Pmax -P

Substituting this into the Profit equation gives ...

  Profit = (Pmax -P)(Pmax -20 -(Pmax -P))

  Profit = (Pmax -P)(P -20)

The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:

  Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10

In the adult market, Pmax = 200, so the profit-maximizing ticket price is ...

  Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market

In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...

  Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market

Using the revenue equation, we find the sales in each market to be ...

  Qa = 200 -Pa = 200 -110 = 90

  Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market

  Qj = 160 -Pj = 160 -90 = 70

  Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market

The profit in each market is ...

  Adult market profit = 90(110 -20) = 8100

  Junior market profit = 70(90 -20) = 4900

The overall profit will be the sum of the profits in each market:

  Overall profit = 8100 +4900 = 13000

The consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.

  CSa = (1/2)(200)Qa = 100(90) = 9000

  CSj = (1/2)(160)(Qj) = 80(70) = 5600

The total consumer surplus is ...

  CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus

The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.

The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.

The value of the probability P(multiple of 3) is 0.3333

The spinner that completes the question is added as an attachment

From the attached spinner, we have:

The probability is then calculated as:

P(multiple of 3) = Multiples of 3/Total

This gives

P(multiple of 3) = 4/12

Evaluate

P(multiple of 3) = 0.3333

Hence, the value of the probability is 0.3333

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length = 17 units, breadth = 9 units

Step-by-step explaination:-

Let the length and the breadth of the rectangle be x units and y units respectively.

Then the area of rectangle = xy square units

According to given conditions, we have

(x -5)(y + 3) = xy - 9 and (x + 3)(y + 2) = xy + 67

=> xy + 3x - 5y - 15 = xy - 9

and xy + 2x + 3x + 6 = xy + 67

=> 3x - 5y - 6 = 0......eqn(i)

and 2x + 3y - 61 = 0.....eqn(ii)

Multiplying equation (i) by 2 and equation (ii) by 3, we get...

6x - 10y - 12 = 0....eqn(iii) and,

6x + 9y - 183 = 0....eqn(iv)

Subtracting equation (iii) from equation (iv), we get...

19y - 171 = 0 => y = 9.

Substituting this value of y in equation (ii), we get

2x + 3 × 9 - 61. = 0 => 9x - 34 = 0 => x = 17.

Hence, the length of rectangle = 17 units and

breadth = 9 units.

Answer:

the revenue is 280 by 190

i dont know either your on your own

Step-by-step explanation:

i just dont know

Answer: Point D

Step-by-step explanation:

92 is in between 81 and 100, so [tex]9 < \sqrt{92} < 10[/tex]

The shaded area expressed as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

From the question, we are to express the shaded area as a fraction, a decimal, and a percent of the whole.

In the diagram, there are 100 total squares and 23 of them are shaded

Expressing the shaded area as a fraction, we get

[tex]\frac{23}{100}[/tex]

Expressing the shaded area as a decimal, we get

[tex]\frac{23}{100}[/tex] = 0.23

Expressing the shaded area as a percent , we get

[tex]\frac{23}{100}\times 100\%[/tex] = 23%

Hence, the shaded area as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

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Answer:

Step-by-step explanation:

hope this helps !

Answer:

Step-by-step explanation:

10+u-17u=14

Starts by combining like terms:

u-17u=14-10

Solve:

-16u=4

u=-16/4

u= -4

Answer:

The graph has been moved 7 units to the left and 8 units down.

Step-by-step explanation:

When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.

When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.

Answer: x = 6

Step-by-step explanation: If you take 88.56 + 5x = 19.76x, an equation, you should first rearrange the variables to the left side of the equation: 5x - 19.76x = -88.56.

Next, you should combine your like terms. So, -14.76 = -88.56.

Then, divide both sides of the equation by the coefficient of variable. So, x = -88.56 / -14.76./

Lastly, calculate. Determine the sign for multiplication or division, so x = 88.56 / 14.76. Multiply both the numerator and denominator with the same integer. So, x = 8856 / 1476. Cross out the common factor, then you get your answer of x = 6

Using the slope concept, considering it's value of 0.3415, it is found that the angle of elevation is of 18.86º.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

Hence, we have that:

[tex]\tan{\alpha} = 0.3415[/tex]

[tex]\alpha = \arctan{0.3415} = 18.86^\circ[/tex]

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The plot of the graph is attached and points have been determined

The two among them are (5,-2) ,(15,4).

What is a  Line Function ?

A line function is what can be written in the form of

y =mx +c

where m is the slope and c is the intercept on y axis.

The equation given here is y = (3/5)x -5

m = 3/5

c = -5

The plot of the graph is attached and points have been determined

The two among them are (5,-2) ,(15,4)

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Answer:

  4 square units

Step-by-step explanation:

The vertices of the figure are on grid points, so it is appropriate to use Pick's theorem to find the area.

__

Pick's theorem tells you the area is ...

  A = i +b/2 -1

where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).

Using the counted values in the formula, we find the area to be ...

  A = 0 +10/2 -1 = 4

The area of the polygon is 4 square units.

_____

Additional comment

There are several other ways to find the area. Here are a couple:

decompose the figure

A horizontal line 1 unit up from the bottom will divide the figure into a trapezoid and a triangle. The trapezoid has bases 4 and 1, and height 1, so its area is ...

  A = 1/2(b1 +b2)h = 1/2(4 +1)(1) = 5/2

The triangle has base 1 and height 3, so its area is ...

  A = 1/2bh = 1/2(1)(3) = 3/2

Then the total area is 5/2 +3/2 = 8/2 = 4 square units.

subtract empty space

The figure occupies a 4×4 square with triangles removed from the left side and the top. Each of those triangles has a base of 4 and a height of 3. The remaining (shaded) area is ...

  A = s² -1/2bh -1/2bh

  A = 4² -1/2(4)(3) -1/2(4)(3) = 16 -12 = 4 square units

Answer: Length of side QR is 16 units.

Step-by-step explanation: Given that dimensions of  PQR

QPR= 90degrees

Answer:

Step-by-step explanation:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

in this case there is a rotation same angles and same sides

your answer is: TRUE

Answer:

Ali is a boy

Step-by-step explanation:

Ali is a good boy

Answer:

x<_-5

Step-by-step explanation:

-4(x+3)<_-2-2x

-4x-12<_-2-2x

-4x+2x<_-2+12

-2x<_+10

divide both side by -2

-2x/2<_10/-2

x<_-5

it is D

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Here's what we need to know ~

Non decimal/Fractional values that starts from 0, and includes only positive integers are known as whole numbers.

Eg. 0, 1, 2, 3.... 45.... 90977..... 62626777, etc

Here we got two decimal values 1.06 and 10.28 that are both greater than 1 and less than the number 2

So, the required numbers are 1 and 2

Answer:

1 and 2

1.06 and 1.28 its greater than 1 but smaller than 2

1 < 1.06 < 1.28 < 2

Answer:

Step-by-step explanation:

Ar of circle

A= 49π

B=100π

C=169π

D=121π

Ar of circle A is less than Ar of circle D

Answer:

9.3*10^11

Step-by-step explanation:

4/3πr^3=9.3*10^11

The solution to the equation below to the nearest fourth of a unit is 0.7142

Equations and expressions

Given the equation as shown below;

2-5x=2x-3

Collect the like terms

-5x - 2x = -3 - 2

-7x = -5

Divide both sides by -7

x = -5/-7

x = 5/7

x= 0.7142

Hence the solution to the equation below to the nearest fourth of a unit is 0.7142

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