You have 17 coins in pennies, nickels, and dimes in your pocket. The value of the coins is $0.47. There are four times the number of pennies as nickels. How many of each type of coin do you have? Set up the system and solve.

Answers

Answer 1
12 pennies, 3 nickles, and 2 dimes

p = number of pennies
n = number of nickles
d = number of dimes
p(1) + n(5) + d(10) = 47
that is, the number of pennies x 1 cent + number nickles x 5 cents
+ number of dimes x ten cents equals 47 cents
p = 4n
p + n + d = 17 
Substituting 4n for p in the above
4n + n + d = 17
5n + d = 17
Subtract 5n from each side
d = 17 - 5n
We will now substitute 4n for p and ( 17-5n ) for d in
the equation
p(1) + n(5) + d(10) = 47 
4n(1) +n(5) + (17-5n)(10) = 47

9n + 170 - 50n = 47
-41n + 170 = 47
Subtract 170 from each side
-41n = 47 - 170
-41n = -123
Divide each side by -41
n = 3
Since p = 4n
p = 4(3)
p = 12
Since p + n + d = 17
12 + 3 + d = 17
15 + d = 17
d = 2
So we have 12 pennies, 3 nickles and 2 dimes
12 + 3(5) + 2(10) ?= 47
12 + 15 + 20 ?= 47
Answer 2

Final answer:

By setting up a system of equations and using the elimination method, we concluded that there are 12 pennies, 3 nickels, and 2 dimes to make up the 17 coins totaling $0.47.

Explanation:

The question asks us to determine how many pennies, nickels, and dimes we have, given that there are a total of 17 coins worth $0.47, with four times as many pennies as nickels. To solve this problem, we can set up a system of equations based on the information given.

Let p be the number of pennies, n be the number of nickels, and d be the number of dimes. Therefore, we have three equations:

p + n + d = 17 (total number of coins)

1p + 5n + 10d = 47 (total value of coins in cents)

p = 4n (four times as many pennies as nickels)

Substituting the third equation into the first and second equations, we get:

4n + n + d = 17

4n + 5n + 10d = 47

Simplify the equations:

5n + d = 17

9n + 10d = 47

Now, we solve this system of equations using substitution or elimination. Let's use the elimination method:

Multiply the first equation by 10 so that when subtracted from the second equation, the d variable will be eliminated: 50n + 10d = 170

Now subtract this from the second equation: (9n + 10d) - (50n + 10d) = 47 - 170

This results in -41n = -123, and after dividing both sides by -41, we get n = 3

Substitute n = 3 into the first simplified equation: 5(3) + d = 17, resulting in d = 17 - 15, so d = 2

Substitute n = 3 into the original third equation to find the number of pennies: p = 4(3), so p = 12

Therefore, we have 12 pennies, 3 nickels, and 2 dimes.


Related Questions

Clark Kent walks 3 miles west and then 4 miles north. How far is it for Superman to fly in a straight line back to his starting point? (It makes a right triangle.)

Question 16 options:

3 miles


5 miles


7 miles


9 miles

Answers

It would be 5 miles if the triangle was a right angle
You can use the pythagorean theorem a² + b² = c², where a and b are perpendicular sides of a triangle and c is the hypotenuse.

For this problem, a = 3, b = 4
c = √(3² + 4²) = √5² = 5

What decimal is represented by this expanded form? 5 x 10,000 3 x 1,000 2 x 10 8 x 1 6 1/1,000 4 x 1/,000?

Answers

53028.0064 ...I believe this is ur number...if thats 6 x 1/1000 , 4 x 1/10,000

In how many ways can the letters in the word spoon be arranged?

Answers

60 i believe is the correct answer
Since there are 5 letters in spoon and the 'o' repeats (there are 2 o's) you would do 5!/2!
This equals 60

Which of the following is the equation of a line parallel to the line y = 4x + 1, passing through the point (5,1)?

A. 4x + y = 19
B. 4x - y = 19
C. 4x + y = -19
D. -4x - y = 19
...?

Answers

the solution is B. 4x - y = 19 , because 4(5) -1 = 19, this line passes on (5,1)

4x-y=19 is the correct answer for this problem

A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate?

Answers

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
To answer the above question, if the store donates 24 soccer balls the number of basketballs does the store donate is 28 basketballs

Answer:

Step-by-step explanation:

First you have to know that you if you divide 24 by 6 you would have to take 7 multiplied by 4 to get 28

Let f(x)=x^3-7x^2+25x-39 and let g be the inverse function of f. What is the value of g'(0)? ...?

Answers

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

Below are the choices that can be found from other sources:

a) -1/25 

b) 1/25 

c) 1/10 

d) 10 

e) 25

f(x) = x^3 - 7x^2 + 25x - 39 
f'(x) = 3x^2 - 14x + 25 

Since g is the inverse function of f 
f(g(x)) = x 

Differentiate both sides of equation 
f'(g(x)) g'(x) = 1 

Now f(3) = 0, so g(0) = 3 

g'(x) = 1 / f'(g(x)) 
g'(0) = 1 / f'(g(0)) 
g'(0) = 1 / f'(3) 
g'(0) = 1 / 10

Use the vertical line test to determine if the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function. Explain your response.

Answers

When you are trying to figure this out put them into a list vertically. Remember, ONE X CAN'T HAVE TO Y's BUT ONE Y CAN HAVE MULTIPLE X's, But dont worry about the y's right now. Lets focus on the x's.

Ask yourself, Are there 2 or more x's that are the same value? 
     Yes) Continue to next step
     No) It's a function :)

If there are 2 or more of the same x value, ask your self now if those x's have different y Values.
     Yes) It is not a function, one x can not have more that 1 y value
     No) Its a function :)

Write the equation in slope-intercept form of the line that has a slope of 6 and contains the point (1, 1). ...?

Answers

[tex]y-y_1=m(x-x_1) \\m=6 \\(1,1) \Rightarrow x_1=1,y_1=1 \\ \\ y-1=6(x-1) \\y-1=6x-6 \\y=6x-6+1 \\y=6x-5[/tex]

24. a) The average height od sunflowers in a field is 64 in. with a standard deviation of 3.5 in. On a piece of paper, draw a normal curve for the distribution, including the values of the horizontal axis at one, two, and three standard deviations from the mean. Describe your drawing in as much detail as possible, and explain how you came up with each of your labels. b) If there are 3,000 plants in the field, approximately how many will be taller than 71 in.? Explain how you got your answer.

Answers

μ = 64 
σ = 3.5 

a) 

μ - 3σ = 53.5 
μ - 2σ = 57.0 
μ - σ = 60.5 
μ = 64.0 
μ + σ = 67.5 
μ + 2σ = 71.0 
μ + 3σ = 74.5 

b) 

(71 - 64)/3.5 = 2.0 
z = 0.9772 
n = 3000*(1 - 0.9772) 
≈ 68
Hope this helps!

The graph is attached and 68 sunflowers will be taller than 71 inches in the field.

Given that:

- Mean (average height) = 64 inches

- Standard deviation = 3.5 inches

Standardizing the height 71 inches using the z-score formula, we have

[tex]\[ z = \frac{{x - \mu}}{{\sigma}} \][/tex]

Substitute the known values into the equation

[tex]\[ z = \frac{{71 - 64}}{{3.5}} \][/tex]

[tex]\[ z = \frac{{7}}{{3.5}} \][/tex]

[tex]\[ z = 2 \][/tex]

Using the standard distribution table, we have

P(z > 2) = 0.02275

To find the number of sunflowers taller than 71 inches:

[tex]\[ 3000 \times 0.02275[/tex]

Evaluate

68

Hence, 68 sunflowers will be taller than 71 inches in the field.

How do I convert 4/5 to a percent

Answers

(4/5) x 100%
= 80%
=0.8

Which ordered pairs are solutions to the inequality y − 4x ≤ −6?

Select each correct answer.

A.(1, 3)

B. (−2, −14)

C. (−1, −9)

D. (3, 5)

E. (0, −5)

Answers

Choice a:
The order pair given is (1, 3)
y-4x = 3-4(1) = -1
-1 is greater than -6
Therefore, this choice is wrong

Choice b:
The order pair given is (-2, -14)
y-4x = -14-4(-2) = -6
-6 is equal -6
Therefore, this choice is correct

Choice c:
The order pair given is (-1, -9)
y-4x = -9-4(-1) = -5
-5 is greater than -6
Therefore, this choice is wrong

Choice d:
The order pair given is (3, 5)
y-4x = 5-4(3) = -7
-7 is less than -6
Therefore, this choice is correct

Choice e:
The order pair given is (0, -5)
y-4x = -5-4(0) = -5
-5 is greater than -6
Therefore, this choice is wrong

Answer

b and d

Step-by-step explanation:

the form of a linear equation that shows the slope and one point is the...? ...?

Answers

The form of a linear equation that shows the slope and one point is the POINT-SLOPE FORM.

Equations in point-slope form look like this: y - k = m(x - h) where m is the slope of the line and (h, k) is a point on the line (any point works). To write an equation in point-slope form, given a graph of that equation, first determine the slopeby picking two points.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

The form of a linear equation that shows the slope and one point is known as the point-slope form, which is written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

The form of a linear equation that shows the slope and one point is known as the point-slope form. Unlike the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept, the point-slope form is typically written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

For example, if you are given a slope of 3 and a point (2, 5), the equation of the line in point-slope form would be y - 5 = 3(x - 2). To visualize this, consider a line graph with the x-axis as the horizontal axis and the y-axis as the vertical axis.

If this was plotted, the line would rise 3 units on the vertical axis for every 1 unit it rises on the horizontal axis, illustrating the concept of slope as the rise over run, which is consistent along the entire length of a straight line.

List 12 spherical objects that would be around the home. Please do not list all balls, soccer ball, basket ball, etc.

Answers

Ball, marble, orange, onion, apple, melon, globe, tea-strainer, fish bowl, beads, grapes, lamp shade.

round off 15.8% to the nearest whole percent

Answers

15.8%=16%
8 is greater than 5 so round off 
answer=16%

To round 15.8% to the nearest whole percent, we round up due to the digit after the decimal point is 8, resulting in 16%.

To round off 15.8% to the nearest whole percent, we look at the first digit after the decimal point, which is 8. Since this digit is 5 or greater, we round up. Therefore, 15.8% rounded to the nearest whole percent is 16%. This rounding method ensures accuracy in representing percentages, particularly in contexts like statistical analysis, grading, and financial reporting. By rounding to the nearest whole percent, the value becomes more concise and easier to interpret, aiding in clear communication and decision-making processes where precise percentage values are essential for understanding and comparison.

What's the volume of a cube-shaped box with edges 6 centimeters in length? A. 216 cm³ B. 18 cm³ C. 36 cm³ D. 1,296 cm³

Answers

The answer is 216 cm³.

This is because the volume of a cube is worked out by doing [tex] a^{3} [/tex]. [tex]a[/tex] being the edge. Therefore, you just have to do [tex]6^{3} [/tex] (6 × 6 × 6), which is 216. 

Answer:

A. 216

Step-by-step explanation:

This is because the volume of a cube is worked out by doing .  being the edge. Therefore, you just have to do  (6 × 6 × 6), which is 216.

Help please....



35
14
11

Answers

it is 35 that what i think i hope you make a 100  on your test 

A number t multiplied by -4 is a least -2/5

Answers

Always remember to change the direction of the inequality sign when multiplying or dividing by a negative number.

The inequality -4t ≥ -2/5, where t is the variable in question, simplifies to t ≤ 1/10, indicating that t must be less than or equal to 0.1. Negative time values are a conceptual tool used in physics to discuss intervals before a chosen start time.

The student's question is about solving an inequality involving a variable t and understanding the concept of negative time. The inequality is given as a number t multiplied by -4 is at least -2/5. Mathematically, this can be written as -4t ≥ -2/5. To solve for t, we can divide both sides by -4 (remembering that dividing by a negative switches the inequality sign), so t ≤ 1/10 or t is less than or equal to 0.1. This condition must hold true for any value of t for the statement to be correct.

The concept of negative time is often used in physics to describe events that occurred before a certain reference point in time. The references to negative time values represent periods before some initial event, similar to counting backward. A negative t value does not imply 'backward' time travel in the literal sense, but rather a point in time before the designated start (t = 0).

Please someone can help me with #13, 15 and 16 Thanks.

Answers

what's the question though?

Write five and three eights as an improper fraction and as a mixed number

Answers

5 3/8 (mixed number)
43/8 (improper fraction)
5.375 (decimal)

(Distribute , then simplify the remaining expression. Final answer must be in standard form) Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .

Answers

Problem 22
[tex]4x^2(2x^2+x-5) - x(x^3+5x^2-3) + 17[/tex]
[tex]4x^2(2x^2)+4x^2(x)+4x^2(-5) - x(x^3)-x(5x^2)-x(-3) + 17[/tex]
[tex]8x^4+4x^3-20x^2 - x^4-5x^3+3x + 17[/tex]
[tex]7x^4-x^3-20x^2+3x + 17[/tex]

So the final simplified answer to problem 22 is
[tex]7x^4-x^3-20x^2+3x + 17[/tex]

--------------------------------

Problem 23
[tex]-2x(x^3-6x^2+6)+4x^3-(5x^4+10x)[/tex]
[tex]-2x(x^3)-2x(-6x^2)-2x(6)+4x^3-(5x^4)-(10x)[/tex]
[tex]-2x^4+12x^3-12x+4x^3-5x^4-10x[/tex]
[tex]-7x^4+16x^3-22x[/tex]

So problem 23 simplifies to
[tex]-7x^4+16x^3-22x[/tex]

---------------------------------------------------------

Problem 24
[tex]4b[2a^2-5(3ab-2b^2)]+29ab^2[/tex]
[tex]4b[2a^2-5(3ab)-5(-2b^2)]+29ab^2[/tex]
[tex]4b[2a^2-15ab+10b^2]+29ab^2[/tex]
[tex]4b[2a^2]+4b[-15ab]+4b[10b^2]+29ab^2[/tex]
[tex]8a^2b-60ab^2+40b^3+29ab^2[/tex]
[tex]8a^2b-31ab^2+40b^3[/tex]

So problem 24 simplifies to 
[tex]8a^2b-31ab^2+40b^3[/tex]

-------------------------------------------------

Problem 25
[tex]2y(6x-4x^2y)+13x^2y^2-6[/tex]
[tex]2y(6x)+2y(-4x^2y)+13x^2y^2-6[/tex]
[tex]12xy-8x^2y^2+13x^2y^2-6[/tex]
[tex]12xy+5x^2y^2-6[/tex]

The final answer for problem 25 is
[tex]12xy+5x^2y^2-6[/tex]

If the function has jump discontinuity , infinite discontinuity , continuous , or the function has point discontinuity
X^3 + 7x^2 + 10x / x + 5

Answers

It is continuous because the function can be further simplified thus, cancelling the denominator.

f(x) = x(x+5)(x+2) / (x+5)
f(x) = x(x+2)
The function is continuous everywhere/ in any domain.
Final answer:

The function x^3 + 7x^2 + 10x / (x + 5) is discontinuous at x = -5, where it has a jump discontinuity. The function is otherwise continuous and does not approach infinity, indicating no infinite discontinuity.

Explanation:

The given function is x^3 + 7x^2 + 10x / (x + 5). To determine the continuity of the function, it's crucial to identify any values of x that would make the denominator zero since the function is undefined at these points.

In this case, if x is -5, the denominator will be zero, making the function undefined. Therefore, the function has a point of discontinuity or a jump discontinuity at x = -5.

The function does not have an infinite discontinuity because it never approaches infinity as x approaches any particular value. This function is continuous at every point except for x = -5. Therefore, "the function x^3 + 7x^2 + 10x / (x + 5) has one point of discontinuity at x = -5."

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if x>2, then x^2-a-6 / x^2-4=

Answers

We know that x > 2 ( or : x ≠ +/- 2 )
We have to factorize the numerator and the denominator:
x² - x - 6 = x² - 3 x + 2 x - 6 = x ( x - 3 ) + 2 ( x - 3 ) = ( x - 3 ) ( x + 2 )
x ² - 4 = ( x - 2 ) ( x + 2 )
[tex] \frac{(x-3)(x+2)}{(x-2)(x+2)}= \frac{x-3}{x-2} [/tex]


What is bigger 5/6 or 13/18?

Answers

To compare fractions, you need a common denominator.
6 goes into 18 three times.  If we multiply (5/6) by 3 on top and bottom you get
[tex]\frac{15}{18} [/tex]
Now we can compare numerators, since 15 > 13
[tex]\frac{5}{6} \ \textgreater \ \frac{13}{18}[/tex]

The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.
The paraboloids x^2+y^2+ z=4 and x^2 +3y^2=z

Answers

As the paraboloids is given with the following equation

x^2+y^2+ z=4 and x^2 +3y^2=z

So,
x^2+y^2+ z-4 = x^2 +3y^2 - z 
x^2+y^2+ z-4 - x^2 -3y^2 + z =0

= -2y^2 +2z -4 
which is the projection of C onto the xy-Plane and it will be an eclipse.




Final answer:

The projection of the space curve C, resulting from the intersection of the two given paraboloids, onto the xy-plane is the line y=0.

Explanation:

The surfaces provided are of the paraboloids x^2 + y^2 + z = 4 and x^2 + 3y^2 = z. We can find the space curve, which is the curve of intersection of these two surfaces, by setting the two equations equal to each other. We would get x^2 + y^2 + z = x^2 + 3y^2 which simplifies to 2y^2 - z = 0. The projection of this space curve C onto the xy-plane would just be the shadow this curve casts on the xy-plane. Thus, we eliminate the z variable and the result would be 2y^2 = 0 -> y = 0 , so, the projection of the curve on the xy-plane is y=0.

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Using the given figure, the square ABCD is transformed to a new location.

The transformation shown is


RO,90°
DO,3
T(x, y) → (x + 5, y + 2)

Answers

Answer:

C

Step-by-step explanation:

when 1600 is increased by 20% and the resulting number is decreased by y% . the answer is 1536

Answers

Hi, you want the result only or the way how to calculate?

You have already invested $400 in a stock with an annual return of 11%. How much of an additional $1,200 should be invested at 12% and how much at 6% so that the total return on the entire $1,600 is 9%? (Round each answer to the nearest cent.)

Answers

The annual return on $400 in stock is 0.11*400 = $44

The total return you want is 0.09 * 1600 = $144

Let a be the amount invested at 12% and b be the amount invested at 6% 

0.12a + 0.06b = 144 - 44

12a + 6b = 10000

a + b = 1200

Put those 2 equations together and solve for a and b: 

12a + 6b = 10000 

a + b = 1200

Using elimination, a = $466.67 and b = $733.33

So, out of an additional $1200, invest $466.67 at a rate of 12% and $733.33 at a rate of 6%

Final answer:

To determine how much to invest at 12% and 6% to achieve a total return of 9% on $1,600, set up and solve the equation based on the given information.

Explanation:

To calculate how much of the additional $1,200 should be invested at 12% and how much at 6%:

Let x be the amount invested at 12% and 1200-x be the amount invested at 6%.Set up the equation: 0.12x + 0.06(1200-x) = 0.09(1600-400).Solve the equation to find x, which represents the amount to invest at 12%.

1. Which fractions are equivalent to 25/45. Please give two examples.

2. Which describes independent events?

Spinning two fours on a spinner divided into four numbered sections.

Selecting two kings from a standard deck of cards by choosing a card at random, placing it in your pocket, then choosing the second card.

Selecting two green marbles by choosing one from a bag at random, giving the first to a friend, then choosing another.

Selecting the names of two siblings by choosing slips of paper from a hat at random, pinning the selected slip on a bulletin board, and then selecting another.

Answers

1) fractions equivalent to 25/45

Any fraction obtaining by multiplying both numerator and denominator by the same quantity will result in an equivalent fraction.

Examples:

- divide both numerator and denominator by 5 => 5/9 is equivalent

- multiply both numerator and denominator by 2 => 50 / 90 is equivalent

- multiply both numerator and denominator by 10 => 250 / 450  is equivalent.


2)
Spinning two fours on a spinner divided into four numbered sections: these are independent events, becasue one result does not influence the other.

Selecting two kings from a standard deck of cards by choosing a card at random, placing it in your pocket, then choosing the second card: they are not independent, because if the first card is a king the probability of the second card will be different than if the first card is not a king.

Selecting two green marbles by choosing one from a bag at random, giving the first to a friend, then choosing another: they are not independent because whether the first two marbles are green or not, make the probabilities for the second event different.

Selecting the names of two siblings by choosing slips of paper from a hat at random, pinning the selected slip on a bulletin board, and then selecting another.: they are not independent, by similar reason explainded in the two previos options.

Use the area model to find the product of 28×32

Answers

the answer is 76 I think so

Cody is selling chocolate and white chocolate candy bars for a school fundraiser. 30% of the candy bars sold have been white chocolate. If Cody has sold 24 white chocolate candy bars, how many total candy bars has he sold?

Answers

30% of 24 is 7.2, which can be rounded to 7 white chocolate candy bars.

Answer: The answer is 80

Step-by-step explanation: because first of all divide 24 by 30% which equals 80 and second I took the USATP Test and got it right

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