# Two Mechanics Worked On A Car. The First Mechanic Worked For 5 Hours, And The Second Mechanic Worked (2023)

Mathematics High School

The first mechanic = a
the second mechanic = b

the first mechanic works for 4 hours = 4 * a
the second mechanic works for 15 hours = 15 * b
total charged = t

t = 4a + 15b

sum of their rates:
a + b = 160
b = 160 - a

t = 4a + 15b
1450 = 4a + 15 * (160 - a)
1450 = 4a + 2400 - 15a

now let's make the formula easier.

15a - 4a = 2400 - 1450
11a = 950

a = 86.36
b = 160 - 86.36 = 73.64

## Related Questions

A principal of \$2600 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 8 years?

To add 7.5% to a number you simply multiply the number by 1.075. To compound that amount year after year, you raise 1.075 to an exponent that corresponds to the number of years.2600*(1.075^8)=4637.04234646

If s is a sequence of consecutive multiples of 3, how many multiples of 9 are there in s? (1) there are 15 terms in s. (2) the greatest term of s is 126.

Now, we have the sequence :

It implies 5 multiples of 9

At a glance : {90, 99, 108, 117, 126}

You need to have a password with 55 letters followed by 33 odd digits between 00 and 99, inclusive. if the characters and digits cannot be used more than once, how many choices do you have for your password?

Mahtematical and statistical reasoning makes it evident that there is a mistake in the writing of the question and the digits were duplicated. So the right question is:

"You need to have a password with 5 letters followed by 3 odd digits between 0 and 9, inclusive. If the characters and digits cannot be used more than once, how many choices do you have for your passwor?"

The solution is:

5 letters from 26 with no repetition => 26*25*24*23*22 different choices.

odd digits are 1, 3, 5, 7 and 9 => 5 different digits to choose

3 digits from 5 with no repetition => 5*4*3 = 60

Then, the total number of choices is: 26*25*24*23*22*60 = 473,616,000

Two hikers on opposite sides of a canyon each stand precisely 525 meters above the canyon floor. they each sight a landmark on the canyon floor on a line directly between them. the angles of depression from each hiker to the landmark meter are 37° and 21°. how far apart are the hikers? round your answer to the nearest whole meter.

The hikers are 2064 m apart

The situation forms two right angle triangle.

Right angle triangle:

A right angle triangle has one of its sides as 90 degree.

Therefore,

First hiker distance

tan 37 = opposite / adjacent

tan 37° = 525 / x

x = 525 / tan 37

x = 696.711059326

x = 696. 711 m

Second Hiker distance:

tan 21 = 525 / y

y = 525 / tan 21

y = 1367.68613557

y = 1367.686 m

Distance apart = 696.711 + 1367.686 = 2064.39713557 = 2064 m

For the hiker whose angle of depression is 37°, you can write:

tan (37°) = 525m / x , where x is the horizontal distance from the hiker to the landmark

=> x = 525 / tan(37) = 696.7m

For the hiker whose angle of depression is 22°, you can write

tan (22°) = 525m / y, where y is the horizontal distance from the hiker to the landmark

=> y = 525m / tan(22) = 1,299.4 m

The distance that separate both hikers is x + y = 696.7 + 1,299.4 = 1,996.1m ≈ 1,996m (rounded to the nearest whole meter)

Find the critical value zα/2 that corresponds to a 98% confidence level.

Acritical valueis the point on the scale of the test statistic (z test in this case) outside which we reject the null hypothesis, and is taken from the level of significance of the test. The critical values can be obtained from the standard distribution tables for z and for this case, it is equivalent to:

critical value zα/2 at 98% confidence level = 2.326

2.33

Step-by-step explanation:

The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.

X + y = 61
y - 3x = 5...y = 3x + 5

x + (3x + 5) = 61
4x + 5 = 61
4x = 61 - 5
4x = 56
x = 56/4
x = 14

y - 3x = 5
y - 3(14) = 5
y - 42 = 5
y = 42 + 5
y = 47

ur 2 numbers are 14 and 47

True or False.
A binomial is also a polynomial.

True. A binomial is a polynomial that is the sum of two terms.

Laura is now trying to come up with a number where three less than 8 times the number is equal to half of 16 times the umber after it was increased by 1

8n-3=1/2(16n+1)
is the equation i come up with which would have no solutions.

A store sells two sizes of fresh wreaths. an? 18-inch wreath costs ?\$1515?, and a? 22-inch wreath costs ?\$3535. in one? day, the number of? 22-inch wreaths sold was fourfour more than twicetwice the number of? 18-inch wreaths, for a total of ?\$820820. how many of each were? sold

The number of 18 inches of wreaths sold was 9 while 22 inches were 51.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say a number of 18 inches of wreaths is x while 12 inches is y.

Given that,

In one day, the number of 22-inch wreaths sold was six more than five times the number of 18-inch wreaths.

So,

y = 5x + 6

And

Total amount

15x + 35y = 1920

⇒ 3x + 7y = 384

By substitution,

3x + 7(5x + 6) = 384

38x = 342

x = 9

So y = 5(9) + 6 = 51

Hence "The number of 18 inches of wreaths sold was 9 while 22 inches were 51".

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The given question is incorrect, the correct question is ;

A store sells two sizes of fresh wreaths. An 18-inch wreath costs \$15, and a 22-inch wreath costs \$35. In one day, the number of 22-inch wreaths sold was six more than five times the number of 18-inch wreaths, for a total of \$1920. How many of each were sold? .... The number of 18-inch wreaths sold was and the number of 22-inch wreaths sold was

X = 18 inch wreath, y = 22 inch wreath

15x + 35y = 820
y = 2x + 4

15x + 35(2x + 4) = 820
15x + 70x + 140 = 820
15x + 70x = 820 - 140
85x = 680
x = 680/85
x = 8

Find all solutions in the interval [0, 2pi): sin5x+sinx=sin3x

This is the concept of trigonometry, to solve for the value of x we proceed as follows;
sin5x+sinx=sin3x
this can be written as:
(sinx)^5+sinx=(sinx)^3
dividing through by sin x we get:
(sinx)^4+1=(sinx)^2
let y=(sinx)^2
thus our expression will be given by:
y^2+1=y
y^2-y+1=0
solving the quadratic equation above we get:
y=(-1)^(1/3) or -(-1)^(2/3)
the above is a complex equation, therefore our expression has no defined answer

The distance between points (3, 7) and (x1, y1) is the square root of (x1 - 3)2 + (y1 - 7)2. True or false?

True

Step-by-step explanation:

By the distance formula,

The distance between two points and is,

Here, , , and

Thus, the distance would be,

= the square root of

The answer is True because the distance formula is √(x2-x1)²+(y2-y1)²

TRUE

Lana Powell has cumulative earnings of \$110,000 at the end of September. In the first week in October she earns \$2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on \$110,100 and Medicare of 1.45%):

Lana Powell has cumulative earnings of \$110,000 at the end of September. In the first week in October she earns \$2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on \$110,100 and Medicare of 1.45%):

Step-by-step explanation:

In the first week of October on the \$ 2,000, we must deduct the two expenses, that of 6.2% and 1.45%, and then add them between them and subtract them from the \$ 2000.

It would be the following: 2000 x 6.2% = \$ 124; 2000 x 1.45% = 29; 124 + 29 = \$ 153 is the amount to be deducted from the \$ 2,000; \$ 2000 - \$ 153 = \$ 1847.

Which of the following is the best approximation for the product of 42.081 x 99.91?

The one with two decimals! But show them?

A local university accepted 2300 students out of 4500 applicants for admission. What was the acceptance rate expressed as a percent

(2300 / 4500) * 100 = 51.1%

Hope this helps! :)

Find s10 for a geometric series with first term 10 and a common ratio 4

The sum of a geometric sequence where the first term is a1 and the common ratio is r and n is which term is

so
given first term of 10 and common ratio 4 and n=10

Evaluate the expression and enter your answer in the box below. 8 + |10|

Well the absolute value of 10 is 10 and 8+10 would be 18

Hope this helped :)

8 + |10| =
8 + 10 =
18

Is it possible for one ray of an angle to be longer than the other ray?

No, because all rays are infinite, and if they are infinite, they never end, so rays are always the same length because they are never ending
hope this helps!

Please Help! Math Question! Variable g is 8 more than variable w. Variable g is also 4 less than w. Which pair of equations best models the relationship between g and w?

A) g = w − 8
g = w + 4

B) w = 8g
w = g − 4

C) g = w + 8
g = w − 4

D) w = 8g
w = g + 4

"g is 8 more than w" means
g = 8 more than w
g = 8+w
g = w+8

"g is also 4 less than w" means
g = 4 less than w
g = w-4

The two equations are therefore:
g = w+8
g = w-4

which means the answer is choice C

g = w + 8

g = w − 4

Hope This Helps!

A quadratic equation is shown below: 4x^2 − 12x + 10 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 2x^2 − 13x + 21 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

A.
if it is in form ax²+bx+c

when it is
greater than 0, then 2 real roots
equal to 0, then 1 real root
less than 0, then no real roots

so
a=4
b=-12
c=10

b²-4ac=(-12)²-4(4)(10)=144-160

A projectile is thrown upward so that it's distance above the ground after t seconds is h=-16t^2 +672t. After how many seconds does it reach its maximum height?

Step-by-step explanation:

We know that a parabola with equation attains its maximum height at :-

The given function:

It will attain its maximum height at :

Hence , after 21 seconds the projectile will reach its maximum height .

It will reach its maximum height at the vertex of the parabola. Which is always:

(-b/(2a), (4ac-b^2)/(4a))

So the time when this occurs is the x coordinate, or t in this case.

-b/(2a), and b=672 and a=-16 so

t=-672/-32

t=21 seconds

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