1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rosijanka [135]
3 years ago
9

Kevin and Randy Muise have a jar containing 82 ​coins, all of which are either quarters or nickels. The total value of the coins

in the jar is ​$12.10. How many of each type of coin do they​ have? The jar contains nothing quarters.
Mathematics
1 answer:
mezya [45]3 years ago
7 0

Answer: The jar contains 40 quarters and 42 nickels.

Step-by-step explanation:

The worth of a quarter is 25 cents. Converting to dollars, it becomes

25/100 = $0.25

The worth of a nickel is 5 cents. Converting to dollars, it becomes

5/100 = $0.05

Let x represent the number of quarters that they have in the jar.

Let y represent the number of nickels that they have in the jar.

Kevin and Randy Muise have a jar containing 82 ​coins, all of which are either quarters or nickels. This means that

x + y = 82

The total value of the coins in the jar is ​$12.10. This means that

0.25x + 0.05y = 12.1 - - - - - - - - - - - 1

Substituting x = 82 - y into equation 1, it becomes

0.25(82 - y) + 0.05y = 12.1

20.5 - 0.25y + 0.05y = 12.1

- 0.25y + 0.05y = 12.1 - 20.5

- 0.2y = - 8.4

y = - 8.4/ - 0.2

y = 42

x = 82 - y = 82 - 42

x = 40

You might be interested in
Jada volunteers at the animal shelter. She divided 5 cups of cat food equally to feed 20 cats. Each cat received x cups of food.
zmey [24]
It would be option 3
5x=20
7 0
3 years ago
Read 2 more answers
What is 1.1 in scientific notation?
kondaur [170]
1,100,000,000 is the answer
4 0
3 years ago
The daily average temperature in Santiago, Chile, varies over time in a periodic way that can be modeled approximately by a trig
natali 33 [55]

Answer:

a) the trigonometric function is;

y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5

b) y = 28.36^0 \ C    ( to two decimal places)

Step-by-step explanation:

This data can be represented by the sinusoidal function of the form :

\mathbf{y = A sin (Bt -C)+D}

where A = amplitude and which can be determined via the formula:

A = \dfrac{largest \ temperature -  lowest \ temperature}{2}

A = \dfrac{29-14}{2}

A = \dfrac{15}{2}

A = 7.5° C

where B = the frequency;

Since the data covers a period of 3 days ; then \dfrac{2 \pi}{B } =365

B = \dfrac{2 \pi}{365}   ( where 365 is the time period )

The vertical shift is found by the equation D;

D =  \frac{largest \ temperature + lowest \ temperature}{2}

D = \frac{29+14}{2}

D = 21.5

Replacing the values of A ; B and D into the above sinusoidal function; we have :

y = 7.5 sin (\frac{2 \pi}{365}t -C) + 21.5

From the question; when it is 7th of the year ( i.e January 7);

t =  7 and the temperature (y) = 29° C

replacing that too into the above equation; we have:

29= 7.5 sin (\frac{2 \pi}{365}*7 -C) + 21.5

29= 7.5 sin (\frac{14 \pi}{365} -C) + 21.5

\frac{29-21.5}{7.5}=  sin (\frac{14 \pi}{365} -C)

1=  sin (\frac{14 \pi}{365} -C)

sin^{-1}(1)=   (\frac{14 \pi}{365} -C)

\frac{\pi}{2}=   (\frac{14 \pi}{365} -C)

C=   (\frac{14 \pi}{365} -\frac{\pi}{2})

C=   (\frac{28 \pi- 365 \pi}{730} )

C=  \frac{-337 \pi}{730}

Thus; the trigonometric function is;

y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5

Similarly; to determine the temperature o Jan 31; i.e when t= 31 ; we have :

y = 7.5 sin ( \frac{2 \pi}{365}*31+ \frac{337 \pi}{730})+ 21.5

y = 7.5 sin ( \frac{62 \pi}{365}+ \frac{337 \pi}{730})+ 21.5

y = 7.5 sin ( \frac{124 \pi+ 337 \pi }{730})+ 21.5

y = 7.5 sin ( \frac{461 \pi }{730})+ 21.5

y = 7.5 *( 0.915)+ 21.5

y = 6.8689+ 21.5

y = 28.36^0 \ C    ( to two decimal places)

7 0
3 years ago
Read 2 more answers
Lisa has 6 hours of studying to do. If she divides her study time into 1/2-hour sessions, how many study sessions will she need?
-Dominant- [34]

Answer:

12 i think?

Step-by-step explanation:

5 0
3 years ago
(Hypothetical.) Suppose a certain person's reaction time, in seconds, for pressing a button on a visual cue has the following cu
Sonbull [250]

Answer:

the probability the person's reaction time will be between 0.9 and 1.1 seconds is 0.0378

Step-by-step explanation:

Given the data in the question;

the cumulative distribution function F(x) = 1 - \frac{1}{(x + 1)^3} ; x > \theta

probability the person's reaction time will be between 0.9 and 1.1 seconds

P( 0.9 < x < 1.1 ) = P( x ≤ 1.1 ) - P( x ≤ 0.9 )

P( 0.9 < x < 1.1 ) = F(1.1) - F(0.9)

= [ 1 - \frac{1}{(x + 1)^3}  ] - [1 - \frac{1}{(x + 1)^3} ]

we substitute

= [ 1 - \frac{1}{(1.1 + 1)^3}  ] - [1 - \frac{1}{(0.9 + 1)^3} ]

= [ 1 - \frac{1}{(2.1)^3}  ] - [1 - \frac{1}{(1.9)^3} ]

= [ 1 - \frac{1}{(9.261)}  ] - [1 - \frac{1}{(6.859)} ]

= [ 1 - 0.1079796998 ] - [ 1 - 0.1457938 ]

= 0.8920203 - 0.8542062

= 0.0378

Therefore, the probability the person's reaction time will be between 0.9 and 1.1 seconds is 0.0378

5 0
3 years ago
Other questions:
  • Free Response - calculator may be used. Please help 50 points and brainliest
    13·2 answers
  • Y = 3x - 1 has a gradient of 3 write the equation of a line parallel to it
    6·1 answer
  • WHAT IS THE EQUATION OF LINE A
    8·2 answers
  • Solve for V in V=s 3square if S=4
    12·1 answer
  • 7 times the quantity y divided by 4
    12·1 answer
  • Kenya is solving the equation 5 3/4 - 1/6x = 4 1/2. She gets to 1 1/4 = 1/6x. Is this a valid way to solve the equation? answer
    6·1 answer
  • Pls help I really need a good grade on this
    5·1 answer
  • John makes $63.70 cutting grass for 5 Hours. How much does he make per hour
    11·2 answers
  • Martin wants to build an additional closet in a corner of his bedroom. Because the closet will be in a corner, only two new wall
    8·1 answer
  • What is the area of a parallelogram with the base of 4.5 mm and a height of 6.7 mm
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!