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Alina [70]
3 years ago
15

A sweater is marked down from an original price of $45 to $33.75. By what percent has the original price of the sweater been mar

ked down?
Mathematics
2 answers:
Lera25 [3.4K]3 years ago
8 0
The first step in this problem is to determine the difference between 45 and 33.75. If we subtract, that gives us 11.25.

The second step is to determine what percentage of 45 is 11.25, which can be accomplished two way. The first way is to determine how many times 11.25 goes into 25.

45 divided by 11.25 = 4, so the answer would be 25%.

The other way to do the last step is to divide 11.25 by 45, which gives us .25, and multiply that by 100, which equates to 25%. In either case, the answer is 25%.

Hope this helps!
BlackZzzverrR [31]3 years ago
6 0
<span>33.75/45.00 x 100 = 75%
This means you are paying 75% of the original.

That means that the price has been marked down by 100-75 = 25% because that is how much of the original you are NOT paying.

Therefore, the answer is 25%. </span>
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Blain is two years older than three times Jillians age. Jillian is also 16 years younger than Blain. How old is Blain?
Ipatiy [6.2K]

The age of Blain is 23 years old

<h3><u>Solution:</u></h3>

Let the age of Blain be "a" and age of Jillian be "b"

Given that Blain is two years older than three times Jillians age

So we can frame a equation as:

age of blain = 2 + 3(age of Jillian)

a = 2 + 3b ----- eqn 1

Also given that Jillian is also 16 years younger than Blain

Age of Jillain = Age of Blain - 16

b = a - 16 ---- eqn 2

Substitute eqn 2 in eqn 1

a = 2 + 3(a - 16)

a = 2 + 3a - 48

a - 3a = -46

-2a = -46

a = 23

Thus the age of Blain is 23 years old

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3 years ago
1.6 - 1.3 mathematics
elena-14-01-66 [18.8K]
Answer: 0.3 :) :) :) :)
8 0
3 years ago
Find the sum of the following ap .1) 1/15, 1/12, 1/10,....,to 11 terms​
sertanlavr [38]

Answer:

33/20

Step-by-step explanation:

1/12 - 1/15 = 5/60 - 4/60 = 1/60

d = 1/60

a_n = a_1 + d(n - 1)

a_11 = 1/15 + (1/60)(11 - 1)

a_11 = 1/15 + 1/6

a_11 = 4/60 + 10/60

a_11 = 14/60

a_11 = 7/30

a_12 = 14/60 + 1/60

a_12 = 15/60

a_12 = 1/4

s_n = n(a_1 + a_n)/2

s_11 = 11(1/15 + 7/30)/2

s_11 = 11(2/30 + 7/30)/2

s_11 = 11(9/30)/2

s_11 = 99/60

s_11 = 33/20

8 0
3 years ago
A single die is rolled twice. Find the probability of rolling an
Nady [450]

Answer: 1/6

Step-by-step explanation:

A die has 6 numbers which are 1, 2, 3, 4, 5 and 6.

Odd numbers in a die = 1, 3 and 6

Numbers greater than 4 = 5 and 6

Probability of rolling an odd number = 3/6 = 1/2

Probability of rolling a number greater than 4 = 2/6 = 1/3

We then multiply both values gotten. This will be:

= 1/2 × 1/3

= 1/6

Therefore, the probability of rolling an odd number the first time and a number greater than 4 the second time is 1/6.

6 0
3 years ago
The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form. Fill in the missing step. Given 2x2 − 12x + 1 = 0 Step 1 2(x2
Bezzdna [24]

Answer:

Part 1) 2(x-3)^{2}-17=0  (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

Part 4) x = 3.58, 0.42

Part 5) x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

Part 6) 2(x − 7)2 + 118; x = $7

Part 7) The maximum height of the puck is 4 feet. −(x − 4)^2 + 6

Part 8) (x + 3)^2 − 4

Part 9) 2(x − 1)^2 = 4

Part 10) 8(x − 4)^2 + 592

Step-by-step explanation:

Part 1) we have

2x^{2} -12x+1=0

Convert to vertex form

step 1  

Factor the leading coefficient and complete the square

2(x^{2} -6x)+1=0

2(x^{2} -6x+9)+1-18=0

step 2

2(x^{2} -6x+9)+1-18=0

2(x^{2} -6x+9)-17=0

step 3

Rewrite as perfect squares

2(x-3)^{2}-17=0

Part 3) we have

f(x)=-x^{2}+16x-60

we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

f(x)+60=-x^{2}+16x

Factor the leading coefficient

f(x)+60=-(x^{2}-16x)

Complete the squares

f(x)+60-64=-(x^{2}-16x+64)

f(x)-4=-(x^{2}-16x+64)

Rewrite as perfect squares

f(x)-4=-(x-8)^{2}

f(x)=-(x-8)^{2}+4

The vertex is the point (8,4)

The vertex represent the maximum profit

Part 4) Solve for x

we have

-2(x-2)^{2}+5=0

-2(x-2)^{2}=-5

(x-2)^{2}=2.5

square root both sides

(x-2)=(+/-)1.58

x=2(+/-)1.58

x=2(+)1.58=3.58

x=2(-)1.58=0.42

Part 5) we have

f(x)=-x^{2}+50x-264

we know that

The zeros or x-intercepts are the value of x when the value of the function is equal to zero

so

In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

-x^{2}+50x-264=0

-x^{2}+50x=264

Factor -1 of the leading coefficient

-(x^{2}-50x)=264

Complete the squares

-(x^{2}-50x+625)=264-625

-(x^{2}-50x+625)=-361

(x^{2}-50x+625)=361

Rewrite as perfect squares

(x-25)^{2}=361

square root both sides

(x-25)=(+/-)19

x=25(+/-)19

x=25(+)19=44

x=25(-)19=6

Part 6) we have

-2x^{2}+28x+20

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

Factor the leading coefficient

-2(x^{2}-14x)+20

Complete the square

-2(x^{2}-14x+49)+20+98

-2(x^{2}-14x+49)+118

Rewrite as perfect square

-2(x-7)^{2}+118

The vertex is the point (7,118)

therefore

The video game price that produces the highest weekly profit is x=$7

Part 7) we have

f(x)=-x^{2}+8x-10

Convert to vertex form

f(x)+10=-x^{2}+8x

Factor -1 the leading coefficient

f(x)+10=-(x^{2}-8x)

Complete the square

f(x)+10-16=-(x^{2}-8x+16)

f(x)-6=-(x^{2}-8x+16)

Rewrite as perfect square

f(x)-6=-(x-4)^{2}

f(x)=-(x-4)^{2}+6

The vertex is the point (4,6)

therefore

The maximum height of the puck is 4 feet.

Part 8) we have

x^{2}+6x+5

Convert to vertex form

Group terms

(x^{2}+6x)+5

Complete the square

(x^{2}+6x+9)+5-9

(x^{2}+6x+9)-4

Rewrite as perfect squares

(x+3)^{2}-4

Part 9) we have

2x^{2}-4x-2=0

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 2 the leading coefficient

2(x^{2}-2x)-2=0

Complete the square

2(x^{2}-2x+1)-2-2=0

2(x^{2}-2x+1)-4=0

Rewrite as perfect squares

2(x-1)^{2}-4=0

2(x-1)^{2}=4

The vertex is the point (1,-4)

Part 10) we have

8x^{2}-64x+720

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 8 the leading coefficient

8(x^{2}-8x)+720

Complete the square

8(x^{2}-8x+16)+720-128

8(x^{2}-8x+16)+592    

Rewrite as perfect squares    

8(x-4)^{2}+592

the vertex is the point (4,592)

The population has a minimum at x=4 years ( that is after 4 years since 1998 )

6 0
3 years ago
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