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3 years ago

5

What is the total bill for a $54 dinner with a 5% sales tax and a 20% tip? (Total bill is the dinner cost plus the sales tax and

the tip.)

1 answer:

Karo-lina-s [1.5K]3 years ago

4 0

$67.85 is the answer

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Val rented a bicycle while she was on vacation she paid a flat rental fee of $55.00 plus $8.50 each day the total cost was $123

artcher [175]

Answer:

55+8.5x=123

Step-by-step explanation:

The 55 represents the flat fee, the 8.5 represents the daily charge, x represents the number of days she rented it for, and 123 is the total amount

3 0

3 years ago

Read 2 more answers

Farmer bob's square plot ofland is slowly eroding away. Worried about the future of his farm. Farmer Bob measures the rate of er

kow [346]

Answer:

Option A.

Step-by-step explanation:

Area of a square is

$A=x^2$ .... (1)

where, x is side length.

The length of each side of his square plot is decreasing at the constant rate of 2 feet/year.

$\dfrac{dx}{dt}=2$

It is given that bob currently owns 250,000 square feet of land.

Fist find the length of each side.

$A=250000$

$x^2=250000$

Taking square root on both sides.

$x=500$

Differentiate with respect to t.

$\dfrac{dA}{dt}=2x\dfrac{dx}{dt}$

Substitute x=500 and $\frac{dx}{dt}=2$ in the above equation.

$\dfrac{dA}{dt}=2(500)(2)$

$\dfrac{dA}{dt}=2000$

Farmer bob is losing 2,000 square feet of land per year.

Therefore, the correct option is A.

7 0

3 years ago

The differential equation in Example 3 of Section 2.1 is a well-known population model. Suppose the DE is changed to dP dt = P(a

LuckyWell [14K]

Answer:

Decreases

Step-by-step explanation:

We need to determine the integral of the DE;

$dP/dt=P(aP-b)$

$dP=P(aP-b)dt$

$1/(dP^2-bP)dP=dt$

We can solve this by integration by parts on the left side. We expand the fraction 1/P²:

$1/(d-b/P)\cdot{P^2} dP$

let

$u=d-b/P$

$du/dP=b/P^2$

$dP=$ $\int\limits {P^2/b} \, du$

$P=lnu/b$

Substitute u in:

$P=ln(d-b/P)/b$

Therefore the equation is:

$ln(d-b/P)/b=t$

We simplify:

$d-b/P=e^b^t$

$P=b/(d-e^b^t)$

As t increases to infinity P will decrease

6 0

3 years ago

Which of these four sets of side lengths will form a right triangle? Set 1 4 cm, 5 cm, 6 cm Set 2 8 in., 12 in., 20 in. Set 3 10

Alenkasestr [34]

Answer: The correct option is (D) SET 4.

Step-by-step explanation: We are to select the correct set of side lengths that will form a right-angled triangle.

To form a right-angled triangle, we must have the following relation:

<em>Perpendicular² + Base² = Hypotenuse².</em>

<em>Hypotenuse is the length of the largest side; perpendicular and base are the two legs of the triangle.</em>

SET 1 : 14 cm, 5 cm, 6 cm.

We have

$5^2+6^2=25+36=61,\\\\14^2=196.$

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 2 : 8 in., 12 in., 20 in.

We have

$8^2+12^2=64+144=208,\\\\20^2=400.$

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 3 : 10 mm, 20 mm, 30 mm.

We have

$10^2+20^2=100+400=500,\\\\30^2=900.$

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 4 : 12 ft, 16 ft, 20 ft.

We have

$12^2+16^2=144+256=400,\\\\20^2=400.$

Therefore,

<em>Perpendicular² + Base² = Hypotenuse².</em>

So, this set will form a right-angled triangle.

Thus, the SET 4 will form a right-angles triangle.

Option (D) is correct.

5 0

3 years ago

Read 2 more answers

Find the measure of Angle R to the nearest tenth. a. 63.8 degrees b. 67.2 degrees c. 70.9 degrees d. 61.5 degrees

Vikki [24]

The complete question in the attached figure

we know that
tan R°=opposite side angle R/adjacent side angle R
opposite side angle R=72 units
adjacent side angle R=25 units
so
tan R°=72/25
R=arc tan (72/25)---------> R=70.85°-------> R=70.9°

the answer is
R=70.9°

8 0

3 years ago