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Dmitry [639]
3 years ago
7

5% of the toddlers in a preschool class drink water with their lunch. How many toddlers are in the class if 3 drink water with t

heir lunch? can you plz explain how you got the answer
Mathematics
1 answer:
OLga [1]3 years ago
6 0

Answer:

<u>There are 60 toddlers in the preschool class</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Percentage of the toddlers in a preschool class drink water with their lunch = 5

Number of the toddlers in a preschool class drink water with their lunch = 3

2.  How many toddlers are in the class?

We'll solve the question, using the Direct Rule of Three, this way:

Percentage      Toddlers

      5                       3

    100                     x

*******************************

5x = 3 *100

5x = 300

x = 300/5

x = 60

<u>There are 60 toddlers in the preschool class</u>

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Choose the ratio that is equivalent to this one: 9/10<br><br> A) 30/27<br> B) 27/30<br> C) 27/29
Licemer1 [7]

Answer: B

Step-by-step explanation: if you divide 27/30 by 3 you get 9/10

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Carl is going to make a frame for a picture. The dimensions of the frame need to be 2 feet by 18 inches. How long must the board
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The perimeter of an object is found by adding all of the sides.  The sides of his frame would be 2 ft, 2 ft, 1.5 ft (18 inches / 12 inches per foot = 1.5 feet), 1.5 feet.  Adding these together we get a total length of 7 feet.  However, he may want to use a slightly longer board to account for any errors!
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8 0
3 years ago
1. The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base? Enter
Elodia [21]
Answers:
1. 8 m 
2. 17 m
3. 7 cm
4. 2 s

Explanations:

1. Let x = length of the base
          x + 6 = height of the base

    Then, the area of the triangle is given by

    (Area) = (1/2)(base)(height)
       56 = (1/2)(x)(x + 6)
       56 = (1/2)(x²  + 6x) 
     
    Using the symmetric property of equations, we can interchange both sides      of equations so that 

    (1/2)(x²  + 6x) = 56
    
    Multiplying both sides by 2, we have
   
    x² + 6x = 112
    
    The right side should be 0. So, by subtracting both sides by 112, we have 

    x² + 6x - 112 = 112 - 112
    x² + 6x - 112 = 0

    By factoring, x² + 6x - 112 = (x - 8)(x + 14). So, the previous equation           becomes

    (x - 8)(x +14) = 0

   So, either 

    x - 8 = 0 or x + 14 = 0

   Thus, x = 8 or x = -14. However, since x represents the length of the base and the length is always positive, it cannot be negative. Hence, x = 8. Therefore, the length of the base is 8 cm.

2. Let x = length of increase in both length and width of the rectangular garden

Then,

14 + x = length of the new rectangular garden
12 + x = width of the new rectangular garden

So, 

(Area of the new garden) = (length of the new garden)(width of the new garden) 

255 = (14 + x)(12 + x) (1)

Note that 

(14 + x)(12 + x) = (x + 14)(x + 12)
                          = x(x + 14) + 12(x + 14)
                          = x² + 14x + 12x + 168 
                          = x² + 26x + 168

So, the equation (1) becomes

255 = x² + 26x + 168

By symmetric property of equations, we can interchange the side of the previous equation so that 

x² + 26x + 168 = 255

To make the right side becomes 0, we subtract both sides by 255:

x² + 26x + 168 - 255 = 255 - 255
x² + 26x - 87 = 0 

To solve the preceding equation, we use the quadratic formula.

First, we let

a = numerical coefficient of x² = 1

Note: if the numerical coefficient is hidden, it is automatically = 1.

b = numerical coefficient of x = 26
c = constant term = - 87

Then, using the quadratic formula 

x =  \frac{-b \pm  \sqrt{b^2 - 4ac} }{2a} =  \frac{-26 \pm  \sqrt{26^2 - 4(1)(-87)} }{2(1)}  &#10;\newline x =  \frac{-26 \pm  \sqrt{1,024} }{2}&#10;\newline&#10;\newline x =  \frac{-26 \pm  32 }{2}

So, 

x = \frac{-26 + 32 }{2} \text{  or } x = \frac{-26 - 32 }{2}&#10;\newline x = \frac{6 }{2} \text{  or } x = \frac{-58 }{2}&#10;\newline \boxed{ x = 3 \text{  or } x = -29}

Since x represents the amount of increase, x should be positive.

Hence x = 3.

Therefore, the length of the new garden is given by 

14 + x = 14 + 3 = 17 m.

3. The area of the shaded region is given by

(Area of shaded region) = π(outer radius)² - π(inner radius)²
                                       = π(2x)² - π6²
                                       = π(4x² - 36)

Since the area of the shaded region is 160π square centimeters,

π(4x² - 36) = 160π

Dividing both sides by π, we have 

4x² - 36 = 160

Note that this equation involves only x² and constants. In these types of equation we get rid of the constant term so that one side of the equation involves only x² so that we can solve the equation by getting the square root of both sides of the equation.

Adding both sides of the equation by 36, we have

4x² - 36 + 36 = 160 + 36
4x² = 196 

Then, we divide both sides by 4 so that

x² = 49

Taking the square root of both sides, we have

x = \pm 7

Note: If we take the square root of both sides, we need to add the plus minus sign (\pm) because equations involving x² always have 2 solutions.

So, x = 7 or x = -7.

But, x cannot be -7 because 2x represents the length of the outer radius and so x should be positive.

Hence x = 7 cm

4. At time t, h(t) represents the height of the object when it hits the ground. When the object hits the ground, its height is 0. So,
 
h(t) = 0   (1)

Moreover, since v_0 = 27 and h_0 = 10, 

h(t) = -16t² + 27t + 10   (2)

Since the right side of the equations (1) and (2) are both equal to h(t), we can have

-16t² + 27t + 10 = 0

To solve this equation, we'll use the quadratic formula.

Note: If the right side of a quadratic equation is hard to factor into binomials, it is practical to solve the equation by quadratic formula. 

First, we let

a = numerical coefficient of t² = -16 
b = numerical coefficient of t = 27
c = constant term = 10

Then, using the quadratic formula 

t = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{-27 \pm \sqrt{27^2 - 4(-16)(10)} }{2(-16)} \newline t = \frac{-27 \pm \sqrt{1,369} }{-32} \newline \newline t = \frac{-27 \pm 37 }{32}

So, 

t = \frac{-27 + 37 }{-32} \text{ or } t = \frac{-27 - 37 }{-32} \newline t = \frac{-10}{32}  \text{ or } t = \frac{-64 }{-32}   \newline \boxed{ t = -0.3125 \text{ or } t = 2}

Since t represents the amount of time, t should be positive. 

Hence t = 2. Therefore, it takes 2 seconds for the object to hit the ground.


 




 





3 0
3 years ago
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Angela shared a cab with her friends. When they arrived at their destination, they evenly divided the
FrozenT [24]

Answer:

\frac{48+5j}{j}

Step-by-step explanation:

<u>Complete Question:</u>

Angela shared a cab with her friends . When they arrived at their destination, they evenly divided the $48 fare among "j" of them . Angela gave the cab $5 tip. How much did Angela pay in total?

<u>Solution:</u>

The fare was $48 and including Angela, there were j people, so each paid:

48/j

Also, Angela paid $5 additionally.

So, Angela paid:

48/j  ---  when dividing evenly

5  ---   as a tip

Total Angela Paid:  =\frac{48}{j}+5\\=\frac{48+5j}{j}

Total Payment:  \frac{48+5j}{j}

8 0
3 years ago
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