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2 years ago

10

Rayhana has a coupon for 15% off a single item at a store. If the item has a regular price of p dollars, then the sale price can

be represented by p – 0.15p. Which expression is equivalent? A. 0.85p

2 answers:

klemol [59]2 years ago

4 0

Answer:

the expression 0.85p is equivalent expression to our given expression.

Step-by-step explanation:

We have been given an expression p - 0.15p,

This represents the price of an item p after a 15% off,

Now, the equivalent expression is.

We can find 85% of p (100%-15%)

85% of p

$\frac{85}{100}p\\\\=0.85p$

Thus, the expression 0.85p is equivalent expression to our given expression.

Klio2033 [76]2 years ago

3 0

Answer:

0.85p is equivalent

Step-by-step explanation:

In this question, we are asked to find which expression is equivalent to p -0.15p, representing 15% discount off an item purchase.

We need to understand that if she is buying at 15% discount, this automatically means she is paying 85% of the price. As the price paid plus the discount would be equal to 100%.

Now let’s cost what she paid.

Mathematically, the amount paid would be 85/100 * p = 0.85p

Hence the expression 0.85p is equivalent to p - 0.15p

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The infield of a baseball field is a square

AnnZ [28]

Answer:

106.1 ft/s

Step-by-step explanation:

You know the diagonal of a square is √2 times the length of one side, so the distance from 3rd to 1st is 90√2 feet ≈ 127.2792 ft.

The speed is the ratio of distance to time:

speed = distance/time = 127.2972 ft/(1.2 s) ≈ 106.1 ft/s.

_____

In case you have never figured or seen the computation of the diagonal of a square (the hypotenuse of an isosceles right triangle), consider the square with side lengths 1. The diagonal will cut the square into halves that are isosceles right triangles with leg lengths 1. Then the Pythagorean theorem can be used to find the diagonal length d:

d² = 1² + 1²

d² = 2

d = √2

Since this is the diagonal for a side length of 1, any other side length will serve as a scale factor for this value. A square with a side length of 90 ft will have a diagonal measuring 90√2 ft.

7 0

2 years ago

Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled

Pavel [41]

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They finish when their covered distance is equal to 5 kilometers. For Alice:

t/4 = 5

t = 5*4 = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 5²

2t = 25 + 1

t = 26/2

t = 13 minutes

c. They are side by side when they have covered the same distance, that is:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16*(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using quadratic formula:

$t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)}$

$t = \frac{32 \pm 30.98}{2}$

$t_1 = \frac{32 + 30.98}{2}$

$t_1 = 31.49$

$t_2 = \frac{32 - 30.98}{2}$

$t_2 = 0.51$

Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.

4 0

2 years ago

Read 2 more answers

Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours. At this rate of growth, how many bacteria will

Alik [6]

The number of bacteria grown in 32 hours is 15771

<u>Step-by-step explanation:</u>

It is given that,

Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours.

Therefore, the bacteria has grown from 100 to 7000 in 14 hours.

<u> To calculate number of bacteria grown in 14 hours :</u>

⇒ 7000 - 100 = 6900

6900 bacteria grows in 14 hours. We need to find out the growth of bacteria in 1 hour in order to calculate its growth in 32 hours.

<u>To calculate number of bacteria grown in 1 hour :</u>

⇒ Total bacteria growth in 14 hours / 14

⇒ 6900 / 14

⇒ 492.85

<u>To calculate number of bacteria grown in 32 hours :</u>

⇒ 492.85 × 32

⇒ 15771.2

⇒ 15771 (rounded to nearest whole number)

∴ The number of bacteria grown in 32 hours is 15771

6 0

2 years ago

Read 2 more answers

A 12 pack of cola costs $5.46. How much does one can of cola cost? In other words, find the unit rate of one can of cola.

Travka [436]

Answer:

.45

Step-by-step explanation:

5.46 is a 12 pack

5.46/12 = .455

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2 years ago

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World wind energy generating1 capacity, W , was 371 gigawatts by the end of 2014 and has been increasing at a continuous rate of

Sunny_sXe [5.5K]

Answer:

a) $W(t) = 371(1.168)^{t}$

b) Wind capacity will pass 600 gigawatts during the year 2018

Step-by-step explanation:

The world wind energy generating capacity can be modeled by the following function

$W(t) = W(0)(1+r)^{t}$

In which W(t) is the wind energy generating capacity in t years after 2014, W(0) is the capacity in 2014 and r is the growth rate, as a decimal.

371 gigawatts by the end of 2014 and has been increasing at a continuous rate of approximately 16.8%.

This means that

$W(0) = 371, r = 0.168$

(a) Give a formula for W , in gigawatts, as a function of time, t , in years since the end of 2014 . W= gigawatts

$W(t) = W(0)(1+r)^{t}$

$W(t) = 371(1+0.168)^{t}$

$W(t) = 371(1.168)^{t}$

(b) When is wind capacity predicted to pass 600 gigawatts? Wind capacity will pass 600 gigawatts during the year?

This is t years after the end of 2014, in which t found when W(t) = 600. So

$W(t) = 371(1.168)^{t}$

$600 = 371(1.168)^{t}$

$(1.168)^{t} = \frac{600}{371}$

$(1.168)^{t} = 1.61725$

We have that:

$\log{a^{t}} = t\log{a}$

So we apply log to both sides of the equality

$\log{(1.168)^{t}} = \log{1.61725}$

$t\log{1.168} = 0.2088$

$0.0674t = 0.2088$

$t = \frac{0.2088}{0.0674}$

$t = 3.1$

It will happen 3.1 years after the end of 2014, so during the year of 2018.

7 0

2 years ago