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3 years ago

7

Jack left a tip of $5.75 for his waiter. If this represents 20% of his meal, what was the cost, in dollars, of Jack’s meal witho

ut the tip?

1 answer:

Readme [11.4K]3 years ago

7 0

Answer:

Step-by-step explanation:

This is a commission problem. Here is the formula:

P x R

= 5.75 x 0.20

= $1.15

<em>Jack's tip was $1.15. :D</em>

Key: P = Original Price R = Commission Rate

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10 of the students in Miss Ransom‘s class play an instrument. These 10 students make up 40% of the class how ,many students are

Mashutka [201]

Answer:

250 students

Step-by-step explanation:

Given data

Let the total number of students be x

Number of students that plays instrument = 10

Hence

40% of x = 10

40/100*x= 100

0.4x=100

x=100/0.4

x= 250

Hence there are 250 students in total

3 0

3 years ago

it costs $3.45 to buy 3/4 lb of chopped walnuts. how much would it cost to purchase 7.5 lbs of walnuts?

Vesna [10]

Answer:

$6.75 I THINK

Step-by-step explanation:

I struggled to figure this out and I'm pretty sure its $6.75 but im not sure :(

4 0

3 years ago

Read 2 more answers

slega [8]

Idk, why does the world need problems like this, not like everyone is going to grow up to be a math teacher.

8 0

3 years ago

Bill wants to rent a car.Rental Company A charges $35 per day plus $0.10 per mile driven.Rental Company B charges $25 per day pl

zlopas [31]

Answer:

m = 200 miles

Step-by-step explanation:

Rental Co. A: A(m) = $35 + ($0.10/mile)(m), where m is the number of miles driven

Rental Co. B: B(m) = $25 + ($0.15/mile)(m)

Set these two dollar amounts equal to each other and solve for m:

$25 + ($0.15/mile)m = $35 + ($0.10/mile)(m). Combine like terms, obtaining:

($0.05/mile)m = $10; then m = ($10) / ($0.05/mile), or 200 miles.

The price charged by the two companies would be the same when the car has been driven 200 miles.

7 0

3 years ago

The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

3 years ago