Sixteen students in a drama club want to attend a play. The ticket price is $35 for each student, and the transportation and meals for everyone will cost$960. To pay for the trip, the students design sweatshirts to sell for profit of $19per sweatshirt. If each student sells the same number of sweatshirts, how many sweatshirts must each student sell so that there will be enough money to pay for the entire cost of the trip?

Answer:

$300  

Step-by-step explanation:

Let D = Dave's savings and S = Sam's savings.

(1)                     D/S = 5/4

(2) (D – 40)/(S-40) = 13/10                  Multiply (1) by 4S

(3)                     4D = 5S                      Multiply (2) by 10(S-40)

            10(D - 40) = 13(S - 40)            Remove parentheses

(4)       10D – 400 = 13S - 520            Solve (3) for S

                         S = (4/5)D                  Substitute into (4)

         10D – 400 = 13(4/5)D - 520     Multiply each side by 5

     50D – 2000 = 52D – 2600         Subtract 50D from each side

               -2000 = 2D – 2600            Add 2600 to each side

                  600 = 2D                          Divide each side by 2

                      D = $300

Dave's savings at first were $300.

Problem 1

One possible answer is y = -x+5

This equation has a slope of -1 as does the first equation y = -x+3. Parallel lines have equal slopes but different y intercepts.

You can change the "+5" to any number you want.

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

Problem 2

One possible answer is y = (3/4)x - 2. Like before, parallel lines have the same slope, just a different y intercept. The "-2" can be any number (negative or positive) you want as long as the slope remains 3/4.

Answer:

Option no C

Step-by-step explanation:

Given:

Price of crackers $ 9 for 3 boxes

Price of Granola Bars $6 for 3 boxes

Total bought $ 20 worth of snacks

To find the equation

Solution:

Price of cracker $ 9 for 3 boxes

price of one box of a cracker = $ 9 / 3

                                                 =$ 3 per box

Price of granola bars $ 6 for 3 boxes

price of one box of a granola bars = $ 6 / 3

                                                         =$ 2 per box

Let total crackers bought are x

price of x crackers will be 3x

Let granola bars bought are y

price of y granola bars will be 2y

as total price is 20

so price of x crackes + y granolas = 20

which will be

3x + 2y = 20

which will be option no C

Answer:

Arrow C

Step-by-step explanation:

As we can see that when we apply at arrow A the force is downward while the force acting by the board is upward which cancels the effect so no work will be done

Now about the Arrow B when we apply a force on it then a force will act and body will move so work will be done

we knot that

Work done = Force . Displacement

Work = Fd cos Ф

Here in B it will not be maximum because there will be an angle acting on it which is greater then 0 so it will not maximum

while in case of arrow C the angle between force and displacement is 0

as cos(0)=1

so work done = Fd which is the maximum value

[tex]3x+4y=2\qquad\text{subtract 3x from both sides}\\\\4y=-3x+2\qquad\text{divide both sides by 4}\\\\y=-\dfrac{3}{4}x+\dfrac{2}{4}\to y=-\dfrac{3}{4}x+\dfrac{1}{2}\\\\for\ x=0\to y=-\dfrac{3}{4}(0)+\dfrac{1}{2}=0+\dfrac{1}{2}=\dfrac{1}{2}\to\left(0,\ \dfrac{1}{2}\right)\\\\for\ x=2\to y=-\dfrac{3}{4}(2)+\dfrac{1}{2}=-\dfrac{3}{2}+\dfrac{1}{2}=-\dfrac{2}{2}=-1\to(2,\ -1)\\--------------------------------\\[/tex]

[tex]4x+y=-4\qquad\text{subtract 4x from both sides}\\\\y=-4x-4\\\\for\ x=0\to y=-4(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=-1\to y=-4(-1)-4=4-4=0\to(-1,\ 0)\\\\Answer:\ \boxed{A.\ (-1.4,\ 1.5)}[/tex]

The approximate solution for the system of equations 3x + 4y = 2 and 4x + y = –4 will be (–1.4, 1.5). Then the correct option is A.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

3x + 4y = 2      …1

4x + y = -4       …2

From equation 2, we have

y = –4 – 4x

Put in equation 1, we have

3x + 4(–4 – 4x) = 2

3x – 16x – 16 = 2

–13x = 18

x = –18/13

x = –1.38

x ≈ –1.4

Then the value of y will be

y = –4 – 4(–1.38)

y = 1.52

y ≈ 1.5

Then the correct option is A.

More about the solution of the equation link is given below.

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Answer:

B. (-3, -6)

Step-by-step explanation:

(1)   6x  - 4y = 6

(2) -6x + 3y = 0      Add (1) and (2)

              -y = 6       Multiply each side by -1

               y = -6      Substitute in (2)

 -6x +3(-6) = 0       Remove parentheses

    -6x – 18 = 0      Add 18 to each side

           -6x = 18      Divide each side by -6

             x = -3

The solution is (-3, -6).

The total amount shared was $2000.00

According to the problem,

We can say that the amount of money is divided in to $2x and $3x

Clearly 3x is larger and will represent $ 1200

∴ 3x = 1200

⇒ x = 400

∴ The other part will be $ 2x = $ 800

∴ Total amount shared was $ (800 + 1200) = $2000.00

So, option C is correct.

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Answer:

D

Step-by-step explanation:

As the angle Known to us is (2y-3)°

Now

∠B = (2y-3)°              (when two parralel lines are cut by another line then angles opposite are equal)

∠D=180-(2y-3)°           (Because angle to the line is same as B and as on one line total angle is 180° one part equals to B so other equals to 180-∠B)

Similarly

∠Q=∠D = 180-(2y-3)°

Because interior angles of a line cutting by a same line will be equal

The distance between the points (2,-3) and (0,8) can be calculated using the distance formula which derives from the Pythagorean theorem. After plugging in the coordinates into the formula, we get the distance approximately equal to 11.2.

To calculate the distance between the points (2,-3) and (0,8), we can make use of the distance formula derived from the Pythagorean theorem. The distance formula is: d = √[(x2-x1)² + (y2-y1)²].

Here, (x1, y1) = (2, -3) and (x2, y2) = (0, 8).

Now, plug the coordinates into the formula:

d = √[(0 - 2)² + (8 - -3)²]

d = √[(-2)² + (11)²]

d = √[4 + 121]

d = √125

So, the distance to the nearest tenth between (2,-3) and (0,8) is approximately 11.2.

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Answer:

x = 54 cookies

Step-by-step explanation:

We can use ratios to solve this problem

1 1/3 cups chocolate chips    3 cups chocolate chips

------------------------------------  = --------------------------------------

24 cookies                                   x cookies

Using cross products

1 1/3 * x = 3 * 24

Let change 1 1/3 to an improper fraction

1 1/3 = (3*1+1)/3 = 4/3

4/3 x = 72

Multiply each side by 3/4 to isolate x

3/4 * 4/3x = 72*3/4

x = 54 cookies

Answer: second one (B) - 2.045, 2.43, 259

Step-by-step explanation: 2.045 is the lowest value due to the 0 in the hundredths place. 2.43 has a lower value than 259, it being a decimal.

Answer:

250 yellow thumbtacks

Step-by-step explanation:

7:10 ratio (17 thumbtacks)

425 / 17 = 25

7 x 25 = 175 green

10 x 25 = 250 yellow

Answer:

Yes

Step-by-step explanation:

Segments AB and CD are parallel and 3 units apart.

Point D is 2 units left of point A, and point C is 2 units right of point B. The trapezoid is symmetrical about the line x = 3.5, so is isosceles.

Answer:

Isosceles trapezoid

Step-by-step explanation:

1)By definition, an isosceles trapezoid has two congruent sides and four vertices. According to the given coordinate points, what we have is an isosceles trapezoid. Graphically, we can say that:

[tex]\overline{AD} \cong \overline BC[/tex]

2) Proving with Analytical Geometry that

[tex]\overline{AD} \cong \overline BC[/tex]

[tex]D_{BC}=\sqrt{(1-4)^{2}+(7-5)^{2}}\Rightarrow D_{BC}=\sqrt{9+4}\Rightarrow D_{BC}=\sqrt{13}\cong3.61\\D_{AD}=\sqrt{(1-4)^{2}+(0-2)^{2}}\Rightarrow D_{AD}=\sqrt{9+4}\Rightarrow D_{AD}=\sqrt{13}\cong3.61[/tex]

Answer:

x = 90

y = 50

Arc LM = 100

Step-by-step explanation:

Arc  MK = 180 degrees

<x = 1/2  Arc MK

<x  = 90 degrees

<x + <y + 40 = 180    all angles in a triangle add to 180

90 + <y + 40 = 180

130 + < y = 180

Subtract 130 from each side

< y = 50

Arc LM

1/2 Arc Lm =  <y

1/2 Arc LM = 50

Multiply by 2

Arc LM = 100

Answer by YourHope:

Hi! :)

x = 90

y = 50

Arc LM = 100

:)

Answer:

[tex] 38^\circ [/tex]

Step-by-step explanation:

We assume that the ground is horizontal and the tower is vertical. The guy wire, the ground, and the tower form a right triangle. The guy wire is the hypotenuse. I'll call the angle formed by the guy wire and the ground angle A. For angle A, the tower is the opposite leg. Since we know the opposite leg and the hypotenuse, we use the sine ratio.

[tex] \sin A = \dfrac{opp}{hyp} [/tex]

[tex] \sin A = \dfrac{13~m}{21~m} [/tex]

To find the measure of angle A, we use the inverse sine function.

[tex] A = \sin^{-1} \dfrac{13}{21} [/tex]

[tex] A = \sin^{-1} 0.6190476 [/tex]

[tex] A = 38^\circ [/tex]

2x = 15 - 3x -- add 3x to both sides

5x = 15 -- divide both sides by 5

x = 3 -- simplest form

For this case, we must find the value of "x" of the following equation:

[tex]2x = 15-3x[/tex]

We add 3x to both sides of the equation:

[tex]2x + 3x = 15-3x + 3x\\5x = 15[/tex]

We divide between 5 on both sides of the equation:

[tex]\frac {5x} {5} = \frac {15} {5}\\x = 3[/tex]

Thus, the value of x is 3.

Answer:

[tex]x = 3[/tex]

Answer:

268

Step-by-step explanation:

64 divide 2 times 8 plus 12

32 times 8 plus 12

32 times 8

256 plus 12

268

Answer:

10 and 4

Step-by-step explanation:

So let's set up equations. So x+y=14. And 6x+8y=92. So 2y=8 or y=4. So x=10.

Final answer:

For two independent events A and B, the conditional probability P(A|B) is equal to the probability of A. Since P(A) is given as 0.40 and the events are independent, P(A|B) is also 0.40.

Explanation:

The question pertains to the concept of conditional probability for independent events in probability theory. When we have two independent events A and B, the conditional probability P(A|B), which is the probability of event A given that event B has occurred, is simply the probability of A, because the occurrence of B does not affect the probability of A when events are independent. This is expressed as P(A|B) = P(A).

Given P(A) = 0.40 and P(B) = 0.20, and knowing that A and B are independent, we can state that:

P(A\B) = P(A)

The probability that event A occurs given that event B has also occurred is 0.40, which is the original probability of A.

The graph of the equation y=4x²-12x+9 has exactly one x-intercept because the discriminant of the quadratic equation is zero, indicating that there is only one real root.

The graph of the equation y=4x²-12x+9 is a parabola. To determine the number of x-intercepts, we look for solutions to the equation obtained by setting y to zero: 0=4x²-12x+9. The x-intercepts are the points where the graph crosses the x-axis, which correspond to the real roots of the equation.

To find the roots, we can apply the quadratic formula, x = (-b \\u00b1 \\sqrt{b² - 4ac})/(2a), where a=4, b=-12, and c=9. In this case, the discriminant (the part under the square root) is b² - 4ac = (-12)² - 4(4)(9) = 144 - 144 = 0.

Since the discriminant is zero, there is exactly one real root, which means the parabola touches the x-axis at exactly one point. Therefore, the graph of y=4x²-12x+9 has one x-intercept.

Answer:

P (not black ) = 5/7

Step-by-step explanation:

We need to know the total number of marbles

2 red + 3 green + 2 black = 7 marbles

P (not black ) = Not black/ total

                      = ((2 red+ 3 green)/ total

                     = 5/7

Answer:

x=6

Step-by-step explanation:

4-2(2x-7)= -6

Distribute the -2

4 -2*2x -2*-7 =-6

4 -4x+14 = -6

Combine like terms

18 -4x = -6

Subtract 18 from each side

18-18 -4x = -6 -18

-4x = -24

Divide each side by -4

-4x/-4 = -24/-4

x =6

Answer:

Sarah spent 45.76

Jack spent 38.16

Jack spent more on tax

Step-by-step explanation:

Sarahs game costs:

tax = 44 *.04 = 1.76

Total cost = game + tax

                  = 44 + 1.76

                  =45.76

Jacks game costs:

tax = 36 *.06 = 2.16

Total cost = game + tax

                  = 36 + 2.16

                  =38.16

Jack spent more on tax

[tex]\text{The scientific notation:}\\\\a\times10^n\\\\1\leq a<10,\ n\in\mathbb{Z}[/tex]

[tex]a.\\(5\times10^3)\times(3.5\times10^{-1})=(5\times3.5)\times(10^3\times10^{-1})\\\\=15.75\times10^{3+(-1)}=15.75\times10^2=1.575\times10\times10^2\\\\=1.575\times10^{1+2}=\boxed{1.575\times10^3}[/tex]

[tex]b.\\(8\times10^2)\div(4\times10^3)=(8\div4)\times(10^2\div10^3)=2\times10^{2-3}\\\\=\boxed{2\times10^{-1}}[/tex]

[tex]c.\\(6\times10^{-3})^2=6^2\times(10^{-3})^2=36\times10^{-3\cdot2}=36\times10^{-6}=3.6\times10\times10^{-6}\\\\=3.6\times10^{1+(-6)}=\boxed{3.6\times10^{-5}}[/tex]

[tex]Used:\\\\a^n\times a^m=a^{n+m}\\\\a^n\div a^m=a^{n-m}\\\\(a^n)^m=a^{n\cdot m}[/tex]

Answer:

So 30:1/2

So you can times both sides by 2

60:1

Now you can multiply 60 by 4 (The total times the time you need)

Your answer is 240

The baker can make 240 gingerbread cookies in 4 hours

Hope that helps feel free to ask more questions

Brainliest??