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Naily [24]
3 years ago
10

Elsa got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store

. The price of the ribbon was 7 cents per yard. If after that purchase there was $12.83 left on the card, how many yards of ribbon did Elsa buy?
Mathematics
1 answer:
Alex3 years ago
4 0

Answer:

31 yards

Step-by-step explanation:

If she has $12.83 left, that means she spent $2.17 out of the $15

15 - 12.83 = 2.17

One cent is .01 of a dollar

So that would be $0.07 per yard

To find the number of yards, we need to divide the total amount she spent by the price per yard.

2.17 ÷ 0.07 = 31

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Triangle ABC has vertices A(–2, –3), B(–5, –3), and C(–4, –2). The triangle is rotated 90° counterclockwise around the origin.
Ulleksa [173]
The rule for this rotation is (x, y) converted into (-y, x). So, to find the answer you would make the y negative and switch the values in the ordered pair. A would be (3, -2), B would be (3, -5), and C would be (2, -4). So, your answer would be B. Hope this helps!
4 0
3 years ago
Read 2 more answers
Each of a group of 20 intermediate tennis players is given two rackets, one having nylon strings and the other synthetic gut str
sergeinik [125]

Answer:

Find answers below

Step-by-step explanation:

H0: P <= 0.5

Ha: P > 0.5

, the number who prefer gut strings is <= a number or the test tends towards the  left-tailed.

{0,1,2,3,4,5} ;  

{15,16,17,18,19,20} is a right-tailed test and not appropriate for H0:

{ 0,1,2,3,17,18,19,20} is two-tailed and not appropriate for H0:

b)

Does the region specify a level .05 test? No

 

P = proportion who prefer gut strings to nylon

P = X /20

Assume alpha = 0.05

z(alpha) = -1.645

Reject if (x/20 - 0.5) / sqrt[ (0.5)(0.5)/20 ] < -1.645

Reject if (x/20 - 0.5) <  < (-1.645) sqrt ( (0.5)(0.5)/20 )

Reject if x/20   < (-1.645) sqrt ( (0.5)(0.5)/20 ) + 0.5

Reject if x/20   < 0.316

Reject if x   < (0.316)(20) = 6.32

{0,1,2,3,4,5,6} is the region for the best level 0.05 test

c)

According to (a),  reject H0 if x <= 5

P( Type II error) = P( do not reject H0/ when Ha is true)

P( Type II error) = P( x > 5/ P=0.6)

x ---p(x)

6  0.004854  0.998388  

7  0.014563    

8  0.035497  

9  0.070995  

10  0.117142  

11  0.159738  

12  0.179706  

13  0.165882  

14  0.124412  

15  0.074647  

16  0.034991  

17  0.012350  

18  0.003087  

19  0.000487  

20  0.000037  

add: 0.9984 --  proba bility of a type II error

Assuming P=0.8

P( Type II error) = P( x > 5/ P=0.8)

6  0.000002  1.000000  

7  0.000013  

8  0.000087  

9  0.000462  

10  0.002031  

11  0.007387  

12  0.022161  

13  0.054550  

14  0.109100  

15  0.174560  

16  0.218199  

17  0.205364  

18  0.136909  

19  0.057646  

20  0.011529  

add: 1.0000  probability of a type II error

d)

P( x <= 13) =  

0  0.000001  

1  0.000019  

2  0.000181  

3  0.001087  

4  0.004621  

5  0.014786  

6  0.036964  

7  0.073929  

8  0.120134  

9  0.160179  

10  0.176197  

11  0.160179  

12  0.120134  

13  0.073929  

add: 0.9423 < 0.10 ,  H0 cannot be rejected

5 0
3 years ago
The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars
stellarik [79]

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

      = 253x-2x^2

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

                      = 3*x

                      = 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= 253x-2x^2 - (3x + 6972)

= 253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

-2x^2+250x-6972=0\\

now we have to solve the above equation for x

Dividing both sides by -2 we get

x^2-125x+3486=0

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

5 0
3 years ago
If x = 7, find the value of<br> a) x2<br> b) (x + 3)*2
Fynjy0 [20]

Answer:

a) 49

b) 100 (I'm assuming that the 2 was supposed to be a square)

Step-by-step explanation:

Substitute the value in for x (the value being 7):

7² = 49

(7 + 3)² = (10)² = 100

3 0
3 years ago
The school you want to go to has an acceptance rate of 15%. That means that 15% of the students who apply to the school get in.
timama [110]

15/100 = 1800/x

15x=180,000

The answer is 12,000.

7 0
3 years ago
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