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stellarik [79]
2 years ago
14

In a seventh grade class, 14 out of 30 students are boys. In simplest terms, what is the ratio of the number of boys to the numb

er of girls in this grade?
A. 7:15
B. 15:7
C. 7:8
D. 8:15
Mathematics
1 answer:
Triss [41]2 years ago
8 0

{Hello,\;There!}

They already give you the number of boys {14}, so all you need to do is subtract 30 - 14 which will give you the ratio of girls.

It does this because 14 takes up \frac{14}{30} of the seventh grade class.

\text{30 - 14 = 16}

  So your answer is going to be 14:16 un-simplified.

  However, since they ask you to put it in the simplest terms, we are going to simplify \frac{14}{16}.

  You can do this by dividing both numbers by 2.

=  \frac{14 \div 2}{16 \div 2}=\frac{7}{8}

\bold{So\;your\;answer\;is\;going\;to\;be}

= \frac{7}{8} or \text{7:8}

\rule{300}{1.0}

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Find the slope of the line through P(5.7) and Q(-1,7).​
VARVARA [1.3K]

We can use the points given to solve for the slope.

Slope formula: y2-y1/x2-x1

7-7/-1-5

0/-6

Since the numerator is 0, the slope is 0.

Best of Luck!

8 0
3 years ago
Mary walks 4 miles north and then turns and walks 5 miles west. How far is she from her original starting point?
dusya [7]
Answer:  6.403 miles; or, write as:  6.403 mi.  .
__________________________________________________
Explanation:
_________________________________________________





                                5
--------------------------------------------
`                             right angle   |_ |
   `          (right triangle )                 |
         `                                               |    4 
             `                                           |
                      `    
       "c"                        `                  \        
 (hypotenuse)                          Starting point
                     
__________________________________________________
Since we have a "right triangle, we solve for "c"; using the 
"Pythagorean theorem" ; 
_______________________________________________________
→  a² + b² = c² ; Solve for "c" ; our answer (in "miles"; or, "mi.") ;
__________________________________________________
Given : a = 4; b = 5 ; 
____________________________
Plug these known values into our equation:
________________________________________
 → 4² + 5² = c² ; 
____________________________
 → 16 + 25 = c² ;  ↔  c² = 16 + 25 ;
______________________________
 → c² = 41 ; 
_______________________________
 → Take the positive square root of each side of the equation (since the side of a "triangle" cannot be "negative"; 
__________________________________
 → √(c²) = √(41) ; 
_____________________________
 → c =  √41 ; Use calculator;
________________________________
 → c =  6.40312423743 ; Round to:  

 → c = 6.403 miles; or, 6.403 mi. 
__________________________________________

 

5 0
3 years ago
A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the da
nikklg [1K]

Answer:

x\approx 267\ miles

Step-by-step explanation:

<u>Linear Modeling</u>

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

f(x)=mx+b

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

c = mx+b

We must find the values of m and b with the data provided. Substituting the first point:

79 = 150m+b

Substituting the second point:

63.70 = 65m+b

Both equations form the following system:

\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.

Subtracting both equations:

150m-65m=79-63.70

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

85m=15.3

Solving:

m=15.3/85=0.18

From the first equation

79 = 150m+b

Solving for b:

b=79-150m=79-150(0.18) = 52.

The model for the problem is:

c=0.18x+52

Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100

100=0.18x+52

Solve for x:

0.18x+52=100

0.18x=100-52=48

x=48/0.18=266.67

Rounding to the closest integer:

\boxed{x\approx 267\ miles}

7 0
3 years ago
Given: -2x &lt; 10. Choose the solution set.
nadya68 [22]

Answer:

C

Step-by-step explanation:

given - 2x < 10 ( divide both sides by - 2 )

Remembering that the symbol is reversed when multiplying/ dividing by a negative quantity.

x > - 5 ← note reversal of symbol

solution is {x | x > - 5 } → C


4 0
3 years ago
Prove the following using a direct proof:
hodyreva [135]

Answer:

Step-by-step explanation:

Prove: That the sum of the squares of 4 consecutive integers is an even integer.

An integer is a any directed number that has no decimal part or indivisible fractional part. Examples are: 4, 100, 0, -20,-100 etc.

Selecting 4 consecutive positive integers: 5, 6, 7, 8. Then;

5^{2} = 25

6^{2} = 36

7^{2} = 49

8^{2} = 64

The sum of the squares = 25 + 36 + 49 + 64

                                       = 174

Also,

Selecting 4 consecutive negative integers: -10, -11, -12, -13. Then;

-10^{2} = 100

-11^{2} = 121

-12^{2} = 144

-13^{2} = 169

The sum of the squares = 100 + 121 + 144 + 169

                                     = 534

Therefore, the sum of the squares of 4 consecutive integers is an even integer.

8 0
3 years ago
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