There are 40 girls and 32 boys who want to participate in the relay race. If each team must have the same number of girls and boys, A) what is the greatest number of teams that can race? B) How many boys and girls will be on each team?

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).

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

:)

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.

Find out more about "Ratio" here: https://brainly.com/question/2328454

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Answer:

Store D has the best deal

Step-by-step explanation:

We will divide cost per minutes

Store A: $25 for a 45 minute lesson

$25/45 minutes

$.5555555  per minute

Store B: $30 for a 1 hour lesson

1 hour = 60 minutes

$30/60  

$.5 per minute

Store C: $45 for a 1.5 hour lesson

1.5 hours* 60 minutes/ hour = 90 minutes

$45/ 90

$.5 per minute  

Store D: $80 for three 1 hour lessons

3 * 1 hour = 3 hours

3 hours * 60 minutes/ 1 hour = 180 minutes

$80/ 180 =

$.4444 per minute

After calculating the cost per minute for swim lessons at each store, Store D is revealed to have the best deal at approximately $0.44 per minute.

We need to calculate the cost per minute for each option Julie has. Here's the breakdown:

Store A: $25 for a 45-minute lesson = $25 / 45 minutes = approximately $0.56 per minute

Store B: $30 for a 1-hour lesson = $30 / 60 minutes = $0.50 per minute

Store C: $45 for a 1.5-hour lesson = $45 / 90 minutes = $0.50 per minute

Store D: $80 for three 1-hour lessons = $80 / 180 minutes = approximately $0.44 per minute

Comparing these rates, we see that Store D offers the lowest cost per minute for swim lessons. Therefore, the best deal would be with Store D.

Answer:

27 units^3

Step-by-step explanation:

A cube's volume is denoted

[tex]x^{3}[/tex]

where x is a side. 3 is the side so it is

[tex]3^{3}[/tex]

which is 27.

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]

Answer:

n= 40

Step-by-step explanation:

(60-5)divided by 1 3/8 =n

Answer:

Number of albums in the crate are 40.

Step-by-step explanation:

Lets start the sum to form the equation as per language given.

As given number of albums = n

Therefore n albums will weigh = n×( 11/8) Pounds

Weight of the crate given = 5 pounds

So total weight of the crate including albums = weight of the     crate + weight of albums.

                  So the equation will be           60 = 5 + n×11/8

                                                                 8×60 = 8×(5+11n/8)

                                                                   480 = 40 + 11n

                                                                 11n = 480 - 40

                                                                 11n = 440

                                                                  n = 440÷11

                                                                  n = 40

so number of albums in the crate will be 40.

3. ΔPQR ≅ ΔSRT

3. ASA  (Angle - Side - Angle) - we have two triangles where we know two angles and the included side are equal

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

4. PR ≅ SR

4. ΔPQR ≅ ΔSRT - the corresponding sides are congruent.

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

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

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 height of the new rectangle is 7.5cm

We shall use the proportion of the lengths of the original and enlarged rectangles to find the height of the new rectangle

Let the height of the new rectangle = h.

The proportion of the lengths of the original and enlarged rectangles = original length / enlarged length = original height / enlarged height

Plugging in the values, we have:

12/18 = 5/h

12 * h  = 18 * 5

We solve for h:

12h = 90

h = 90/12

h = 7.5cm

Thus, the new rectangle's height is 7.5cm.

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

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 = 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:

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

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[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]

[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.

https://brainly.com/question/545403

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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:

$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.

Answer:The measure of the flour is greater than the measure of the sugar

Step-by-step explanation:

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.

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:

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