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Select the correct answer. A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed shee

svetlana [45]

Okay, let's represent the price of a bed sheet with 'b' and a towel with 't':

54b + 50t = 923

38b + 61t = 791.50

Now, if we subtract both sides by 54b (on the first equation), we get this:

50t = 923 - 54b

Divide both sides by 50:

t = 18.46 - 1.08b

Now that we know this, we can move on to the 2nd equation:

38b + 61t = 791.50

Input the variable 't':

38b + 61(18.46 - 1.08b) = 791.5

38b + 1126.06 - 65.88b = 791.5

38b - 65.88b = 791.5 - 1126.06

Simplify:

-27.88b = -334.56

Because both sides are negative, we can turn it into a positive:

27.88b = 334.56

b = 334.56/27.88

b = 12

Now that we know that b = 12, we can easily input it into any equation:

648 + 50t = 923

50t = 275

t = 5.5

One bed sheet costs $12 and one towel costs $5.50

Option C is the answer.

6 0

3 years ago

A car company has found that there is a linear relationship between the amount of money it spends on advertising and the number

svetoff [14.1K]

Answer:

a) It is expected to sell 560 cars.

b) The total amount invested is $145,000.

c) $y=0.004x+200$

m is the slope of the linear function, and represents <em>the additional amount of cars it will sell due to an additional dollar invested in advertising</em>. Its units of m is [cars/dollar].

b is the y-intercept and represent t<em>he amount of cars the company would sell if there is 0 dollars invested in advertising</em>. It may or not be a representative point in the real world (it depends on how accurate is the linear function and the range where it is valid). The unit of b is [cars].

Step-by-step explanation:

a) If the company invest $90,000, that is 3 times $10,000 plus the originals $60,000. Then, it is expected to sell 560 cars.

$440+3*40=440+120=560$

b) If the company sold 800 cars, we have 440 cars that corresponds to the original $60,000 and (800-440)=360 cars that correspond to the additional invest.

If an additional 40 cars are sold by an additional $10,000 invest, 340 cars are sold by 340*10,000/40= $85,000.

Then the total amount invested is 60,000+85,000=$145,000.

c) We can estimate the parameters m and b of the equation taking into account one known point ($60,000 corresponds to 440 sold cars) and the known variation (40 sold cars for every $10,000 invested).

$m=\frac {\Delta y} {\Delta x }=\frac{40}{10,000}=0.004 \, \frac{cars}{dollar}$

Then we can use the known point to estimate b:

$b=y-mx=440-(0.004)*60000=440-240=200 \, cars$

The equation is then

$y=0.004x+200$

m is the slope of the linear function, and represents <em>the additional amount of cars it will sell due to an additional dollar invested in advertising</em>. Its units of m is [cars/dollar].

b is the y-intercept and represent t<em>he amount of cars the company would sell if there is 0 dollars invested in advertising</em>. It may or not be a representative point in the real world (it depends on how accurate is the linear function and the range where it is valid). The unit of b is [cars].

5 0

4 years ago

how high up a vertical wall will a 26-foot-long extension ladder reach if its base is placed 10 feet away from the wall

allsm [11]

Answer:

24ft high

Step-by-step explanation:

Assuming the wall is perpendicular to the ground (so that it forms a right angle, and that when the ladder is placed on the ground and leaned up against the wall that it forms a right triangle), we can use the Pythagorean Theorem to describe the situation mathematically.

<h3><u>The Pythagorean Theorem</u></h3>

For any right triangle (a triangle that has a right angle) the Pythagorean Theorem applies. The Pythagorean Theorem describes the relationship between side lengths as $a^2+b^2=c^2$ , where "c" is the length of the "hypotenuse" (the side across from the right angle), and "a" and "b" are the lengths of the "legs" (the other two sides that are touching the right angle). Since addition is commutative, it doesn't matter which leg you pick for side "a" or side "b", it only matters that the hypotenuse must be "c".

Given that the ladder is across from the right angle (the angle formed by the wall and the ground... the two "legs"), the ladder represents the hypotenuse in this situation.

<h3><u>Substituting known values, and solving the equation</u></h3><h3> $a^2+b^2=c^2$ </h3>

Substitute known values, and simplify...

$a^2+(10)^2=(26)^2$

$a^2+100=676$

Subtract 100 from both sides...

$(a^2+100)-100=(676)-100$

$a^2=576$

Apply the square root property...

$\sqrt{a^2}=\pm \sqrt{576}$

$a=\pm 24$

$a=24$ or $a=- 24$

Since the distance height the ladder will reach is not a negative number, we reject the negative solution. Hence, the ladder will reach 24ft high, if placed 10ft from the base of the wall.

8 0

2 years ago

Centimeter, millimeter, decameter, meter, kilometer.

Nataly [62]

Millimeter, Centimeter,Meter, Decameter,Kilometer

8 0

4 years ago

In the same year, the average finishing time for u.s. women was four hours and 41 minutes. What was their average speed in miles

AleksAgata [21]

Answer:

They never asked the question properly. They never said how many miles equals four hours and 41 minutes.

Step-by-step explanation:

3 0

3 years ago