A piggy bank contains $2.40 in nickels and dimes. If there are 33 coins in all, how many nickels are there?

Answers

Answer 1

Final answer:

To find the number of nickels in the piggy bank, you can set up a system of equations based on the total number of coins and the total value of all the coins. By solving this system, you can determine the number of nickels.

Explanation:

To find the number of nickels in the piggy bank, we need to set up a system of equations. Let's use n to represent the number of nickels and d to represent the number of dimes.

The total value of the nickels can be calculated by multiplying the number of nickels (n) by the value of each nickel, which is $0.05. So, the value of the nickels is 0.05n.

The total value of the dimes can be calculated by multiplying the number of dimes (d) by the value of each dime, which is $0.10. So, the value of the dimes is 0.10d.

We can set up two equations based on the given information:

Equation 1: n + d = 33 (total number of coins)

Equation 2: 0.05n + 0.10d = 2.40 (total value of all coins)

Now we can solve this system of equations to find the number of nickels (n).

Multiplying Equation 1 by 0.05 gives us: 0.05n + 0.05d = 1.65

Subtracting Equation 2 from this gives us: 0.05d - 0.10d = 1.65 - 2.40

Simplifying, we get: -0.05d = -0.75

Dividing both sides by -0.05, we find: d = 15

Substituting this value back into Equation 1, we get: n + 15 = 33

Subtracting 15 from both sides, we find: n = 18

Therefore, there are 18 nickels in the piggy bank.

Answer 2

Final answer:

To find the number of nickels in the piggy bank, set up a system of equations and solve. There are 18 nickels in the piggy bank.

Explanation:

To find the number of nickels in the piggy bank, you need to set up a system of equations based on the information given. Let's assume that the number of nickels is represented by 'n' and the number of dimes is represented by 'd'. From the problem, we know that there are 33 coins in total, so we can write the equation 'n + d = 33'. We also know that the value of the nickels, in cents, is 5n and the value of the dimes, in cents, is 10d. Since the total value of the coins is $2.40, we can write the equation '5n + 10d = 240'. Now we can solve this system of equations to find the number of nickels.

To solve the system of equations, we can use the substitution method. Rearrange the first equation to get 'n = 33 - d', and substitute this expression for 'n' in the second equation: '5(33 - d) + 10d = 240'. Simplify the equation to get '165 - 5d + 10d = 240'. Combine like terms to get '5d = 75'. Divide both sides by 5 to get 'd = 15'. Substitute this value of 'd' back into the first equation to find 'n': 'n + 15 = 33', 'n = 18'.

Therefore, there are in the piggy bank.

Related Questions

Please help me with this

Answers

for an isosceles right triangle the legs would be 2 times the square root of the hypotenuse

so for this:

the legs would be 2sqrt(10)

Line segment AB is the perpendicular bisector of line segment XZ. Which statement is true? A) XZ = AB B) XB = XZ C) ∠ABZ = ∠ABX D) ∠BAZ = ∠ABX

Answers

A perpendicular bisector is a special type of bisector because it intersects a segment at a 90 degree angle, and it passes through the segments midpoint.

Therefore based from this, we can create two true statements:

XB = BZ

and

∠ABZ = ∠ABX

Therefore the answer is:

Answer:

The answer is C. <ABZ = <BAX hop this hope this help

6 shirts 4 different pairs of pants, how many different combinations could she wear?

Answers

The shirts can be called A, B, C, D, E, F.
the pants can be called 1, 2, 3, 4.
if you combine these together you get
A1, A2, A3, A4, B1, B2, B3, B4, C1, C2, C3, C4, D1, D2, D3, D4, E1, E2, E3, E4, F1, F2, F3, F4 OR 24
You get 24 outfits.

Describe how to graph the solution of y ≤ −x² + 2x.

Answers

that's how you describe the answer of y ≤ −x² + 2x.

Graph the parabola opening down,
with the vertex at (1, 1),factor the quadratic as y < (less than or equal to) –1(x)(x – 2),find the roots of the parabola to be 0 and 2,graph the parabola with a solid boundary line,test a point that is not on the boundary,and shade inside the parabola.

Some of the cds produced by a manufacturer are defective. from the production line, 5 cds are selected and inspected. how many sample points exist in this experiment?

Answers

Final answer:

There are 32 sample points in this experiment.

Explanation:

In this experiment, the manufacturer selects 5 CDs from the production line to inspect. To determine the number of sample points in this experiment, we need to consider the possible outcomes for each CD. For each CD, it can either be defective or non-defective, meaning there are 2 possible outcomes. Since there are 5 CDs being inspected, we multiply the number of outcomes for each CD by itself 5 times to find the total number of sample points. Therefore, there are 32 sample points in this experiment.

Therefore, the total number of sample points in this experiment is 32, calculated by multiplying the number of outcomes for each CD (2) by itself 5 times . This accounts for all possible combinations of defective and non-defective CDs in the sample of 5.

Rita earns $17.00 per hour. If she gets a 6% raise, what will be her new hourly wage?

Answers

multiply 17 by 6%

17 * 0.06 = 1.02 increase

17 +1.02 = 18.02 new hourly wage

Use laws of sine to answer

Answers

By sine rule:
[tex] \frac{18}{ \sin(32) } = \frac{bc}{ \sin(118) } [/tex]
so:
[tex]bc = \frac{18 \times \sin(118) }{ \sin(32) } \\ bc = 29.991... \\ bc = 30.0 \: (to \: 3 \: sig.figs)[/tex]

Liz wants to buy a shirt for $25. How much will Liz's shirt cost in Springfield(4.1%) Round up to the nearest cent? Show your work

Answers

In order to find the total amount of the shirt including tax, first convert the tax into a decimal:
4.1/100 = 0.041 %
Next multiply the cost of the shirt before tax by the tax in decimal form:
25 * 0.041 = 1.025
After that you will add the tax cost and the shirt cost:
25 + 1.025 = 26.025
Finally round to the nearest cent:
26.03
Hope this helps and let me know if you have more questions!

I think it would be $102.6

The perimeter of a triangle is 29 feet where one side of the triangle is twice the length of the shortest side. the largest side is 13 feet more than the shortest side. how long is the shortest side

Answers

x + 2x + (13 + x) = 29
3x + x + 13 = 29
4x = 29 - 13
4x = 16
x = 16/4
x = 4

The length of the shortest side is 4 ft

Answer:

The shortest side is 4 feet.

Step-by-step explanation:

The perimeter is the border of a geometric figure and corresponds to the sum of the length of all its sides.

So the perimeter in the case of a triangle is the sum of its three sides:

L₁ + L₂ + L₃ =Perimeter

In this case, the perimeter is known and it is necessary to calculate the value of the shortest side. In that case it will be called L₁. So, you know:

L₁= shortest sideL₂=twice the length of the shortest side → L₂=2*L₁L₃=largest side (13 feet more than the shortest side) → L₃=L₁ + 13Perimeter= 29 feet

Replacing:

L₁ + 2*L₁ + L₁ + 13= 29

Solving:

(1+2+1)*L₁ + 13= 29

4*L₁ + 13=29

4*L₁ = 29-13

4*L₁ =16

L₁= 16÷4

L₁=4

The shortest side is 4 feet.

14 minus the product of three and the number has 26

Answers

Assuming “has” means “equals”

14 - 3 (x) = 26
Subtract 14 from both sides
-3x = 12
Divide both sides by -3
X= -4

Segments and angles practice with special angles find the measures of the lettered angles

Answers

IM A BEGINNER SO DONT REALLY BUT I THINKS IT 532181

y=x^2+8x+6 16x-2y=-44

Answers

What? Is that two problems? I'll change my answer, give me my answer.

A market sells bananas for $0.69 per pound. Which expression represents the cost, in dollars, of p pounds of bananas? 1 p/69 2 0.69p 3 p/0.69 4 69p

Answers

Assuming p is the pounds of bananas;

$0.69p would be the correct answer (2) because each pound costs $0.69

Hope I helped :)

Answer:

Option 2. 0.69p

Step-by-step explanation:

A market sells bananas for = $0.69 per pound

The cost, in dollars of p pounds of bananas = 0.69 × p

So the expression represents the cost, in dollars of p pounds of bananas

= 0.69p

Option 2. 0.69p is the right answer.

State the vertex as an ordered pair.

y = -|3x +5|+7

Answers

in plain and short, what value of "x" makes the expression |3x + 5| to 0?

well, we can check by simply setting it to 0 and solving for x.

[tex]\bf 3x+5=0\implies 3x=-5\implies \boxed{x=-\cfrac{5}{3}}\\\\ -------------------------------\\\\ \textit{therefore, the vertex of }y = -|3x+5|\boxed{+7}\textit{ is at }\left(-\frac{5}{3}~,~7 \right)[/tex]

notice, all you do is, get the x-value that makes the expression to 0, and then append the constant outside it as the y-value, and that's the vertex.

You plan to take $450 u.s. on a trip to south africa. how many rands is this if one u.s. dollar equals 3.70 rands?

Answers

$1 = 3.70 rand

$450 is the same as 450 * $1, so multiply both sides of the conversion equation above by 450.

450 * $1 = 450 * 3.70 rand

$450 = 1665 rand

limit as x approaches 0 of csc3x/cotx

Answers

Hello Meggieh821, to find the lim as x approaches 0 we can check this by inserting a number that is close to 0 that is coming from the left and from the right.

For instance, we can find the lim by using the number -.00001 for x and solve
csc(3x) / cot(x)
csc(3*-.00001) / cot(-.00001) = .333333... = 1 /3

We also need to check coming from the right. We will use the number .00001 for x
csc(3x) / cot(x)
csc(3*.00001) / cot(.00001) = .333333... = 1 /3

So since we are getting 1/3 from the left and right we can say as x approaches 0 the limit is 1/3

[tex]\lim_{x\to 0} \frac{csc(3x)}{cot(x)} = \frac{1}{3}[/tex]

Final answer:

The limit of csc(3x)/cot(x) as x approaches 0 is 1, after applying trigonometric identities and the properties of limits.

Explanation:

The student is asking for the limit of the function csc(3x)/cot(x) as x approaches 0. This is a limit problem in calculus, which is a part of mathematical analysis that deals with the behavior of functions near certain points. To find the limit as x approaches 0 for the function csc(3x)/cot(x), we need to apply trigonometric identities and the properties of limits. The function csc(3x) can be rewritten as 1/sin(3x) and cot(x) as cos(x)/sin(x). So the original limit becomes:

lim(x → 0) [csc(3x)/cot(x)] = lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))].

Using the trigonometric limit lim(x → 0) (sin(x)/x) = 1 and lim(x → 0) (cos(x)) = 1, we can simplify the expression by substituting 3x for x in the limit sin(x)/x. We get:

lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))] = lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x).

As x approaches 0, cos(x) approaches 1 and 3x/x approaches 3, hence:

lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x) = lim(x → 0) (sin(x)/x) × lim(x → 0) 1/cos(x) × lim(x → 0) (3x/3sin(3x)) = 1 × 1 × (3/3) = 1.

The final limit of csc(3x)/cot(x) as x approaches 0 is 1.

Help?

Simplify. 9√56x^7y^12 Assume x and y are nonnegative.

Answers

Applying the product property of square roots to the expression 9 * √(56) * √(x^7) * √(y^12), we simplify to 18y^6 * √(14x) * |x^3|.

Apply the product property of square roots:

9 * √(56) * √(x^7) * √(y^12)

Evaluate the square root:

9 * 2 * √(2 * 7) * √(x^7) * √(y^12)

Multiply the numbers:

9 * 2 * √(14) * √(x^7) * √(y^12)

Simplify the square root of an exponential expression:

9 * 2 * √(14) * |x^3| * √(x) * √(y^12)

Simplify the square root of an exponential expression:

9 * 2 * √(14) * √(x) * |x^3| * y^6

Apply the product property of square roots to the product of square roots is equal to the square root of the product:

9 * 2 * y^6 * |x^3| * √(14x)

Multiply the numbers:

18 * y^6 * √(14x) * |x^3|

Help me solve this plzz!!Simplify:

Answers

a.

You can use the rule:
[tex](a^b)^c=a^{b*c} [/tex]

So, let's do it:
[tex](27x^6)^ \frac{1}{3} = 27 x^{6* \frac{1}{3} } [/tex]

Simplify:
[tex](27x)^2[/tex]

And there you have it. If you need it one step further, then square 27, but take the parenthesis out.

If you need further help, feel free to ask for it.

A couch and coffee table cost a total of $1017. The cost of the couch is two times the cost of the coffee table. Find the cost of each item.
cost of couch:
cost of coffee:

Answers

Answer:

Using the concept of linear equations, we made two equations. Solving those two equations, we find that the cost of couch is $678 and that of coffee is $339.

Step-by-step explanation:

Concept: Let the cost of couch be $x and that of coffee be $y. The total cost is $1017, so,

x + y = 1017

Also, the cost of couch is two times that of coffee. So,

x = 2y

Substitute the value of x in first equation

2y + y = 1017

3y = 1017

y = 339

And, x + y = 1017

x + 339 = 1017

x = 678

Using the two equations, we find that y = $339 and x = $678.

So, the cost of couch is $678 and that of coffee is $339.

For more explanation, refer the following link:

https://brainly.com/question/22052132

#SPJ10

Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?

Answers

y=-3x+14 I hope this helps!

Answer:

[tex]y=-3x+14[/tex], slope intercept form

[tex]3x+y =14[/tex], standard form

Step-by-step explanation:

[tex]y + 1 = -3(x - 5)[/tex]

We need to write the given equation in slope intercept form or standard form

slope intercept form is [tex]y=mx+b[/tex]

To get slope intercept form , we need to get y alone

[tex]y + 1 = -3(x - 5)[/tex] ( multiply -3 inside the parenthesis )

[tex]y+1=-3x+15[/tex] , subtract 1 on both sides

[tex]y=-3x+14[/tex]

Standard form is [tex]Ax + By = C[/tex]

To get standard form we keep x term and y term on the left hand side

[tex]y=-3x+14[/tex]

Add 3x on both sides

[tex]3x+y =14[/tex]

Yori has 14.25 cups of cupcake batter if each cupcake used 0.75 cup of batter how many cups cakes can yori make?

Answers

14.25 / 0.75 = 19 <=== Yori can make 19 cupcakes

First, compare the statements
0.75=1 cupcake
14.25=Y cupcakes
I represented the unknown with Y.
Next, cross and multiply. 14.25 will multiply 1 to give 14.25 and 0.75 will multiply Y to give 0.75Y. That will be;
0.75Y=14.25
Divide both sides by 0.75
Y=14.25/0.75
Y=19
She can make 19 cupcakes. Hope that helped. Have a nice day

Anna has 5 muffins but 8 friends coming over. How much will each friend get

Answers

Hello! To solve this question, all we have to do is 5/8. You can basically leave it like it is, because that’s your answer. Each friend will get 5/8 of a muffin.

For a car rental, the rental agency charges $21.00$⁢21.00 per day, plus $0.23$⁢0.23 for each additional mile above 125125. find a function for the cost of a rental where x is the number of miles driven.

Answers

21d+.23x (d being per day) (x being every mile above 125)

Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.

A. 6 cm by 1.5 cm
B.10 cm by 2 cm
C. 13 cm by 4 cm
D.18 cm by 4.5 cm
E.80 cm by 20 cm

Answers

Answer:

Step-by-step explanation:

The scale copy of a shape is the resulting shape when the original shape is dilated. Possible scaled rectangles of rectangle A are:

A. 6cm by 1.5cm because

D. 18cm by 4.5cm because

E. 80cm by 20cm because

Given that

[tex]Length = 12cm[/tex]

[tex]Width = 3cm[/tex]

Divide the length and the width of the rectangle

[tex]k = Length \div Width[/tex]

[tex]k = 12cm \div 3cm[/tex]

[tex]k = 4[/tex]

This means that a scaled copy of rectangle A must have a value of 4 when the dimensions are divided.

Possible rectangles are:

A. 6cm by 1.5cm because [tex]6cm \div 1.5cm = 4[/tex]

D. 18cm by 4.5cm because [tex]18cm \div 4.5cm = 4[/tex]

E. 80cm by 20cm because [tex]80cm \div 20cm = 4[/tex]

Answers

Your equation would be y = 2/5x + 4 because 2/5 is your constant and 4 is what you get when x=0

Hope this helps!

A clydesdale drinks about 120 gallons of water every 4 days.At this rate,about how many gallons of water does a clydesdale drink in 28 days

Answers

A clydes dale can drink up to 840 gallons of water in 28 days

b) Imagine that you earned $8,425 in one year. If the government enforces a 15% income tax, how much money would you owe in taxes at the end of the year? Show your work.

Answers

$1,263.75 is how much would be taxed
Take 8425 multiply it by 0.15 to get your answer

Answer:

The tax would be $ 1,263.75

Step-by-step explanation:

Given,

Total earning in one year = $ 8,425,

Income tax percentage per year on earning = 15%

Hence, the amount of tax at the end of one year

= 15% of the total earnings

= 15% of 8425

[tex]=\frac{15\times 8425}{100}[/tex]

[tex]=\frac{126375}{100}[/tex]

= $ 1,263.75

The areas of: FGHM is 12, MHIJ is 36, EFNL is 24, LNJK is 48. EGIK is a rectangle cut into the rectangles with given areas. What is the area of the shaded quadrilateral EMIN?

Answers

5

Overall area of quadrilateral EGIK is 12+36+24+48 = 120. I'll call the length of EK to be w, and EG to be h, representing width and height.

The line FJ splits EGIK into EFJK and FGIJ which have areas of 72 and 48 respectively. Since EFJK and FGIJ have the width, their heights have to be in the ratio of 72/48 = 3/2. So GF = 2h/5 and EF = 3h/5

Now FGHM and MHIJ share the same height, so their widths have to be in the ratio 12/36 = 1/3, so GH = w/4 and HI = 3w/4

And EFNL and EMIN also share the same height, so their widths have to be in the ratio 24/48 = 1/2, so EL = w/3 and LK = 2w/3.

So the length of MN will be FN - FM. And FN is the same as EL which is w/3, and FM is the same as GH which is w/4. So
w/3 - w/4 = 4w/12 - 3w/12 = w/12

If you look at quadrilateral EMIN, you'll see that it's area is the sum of triangles MNI and MNE. And the area of a triangle is 1/2 bh. And conveniently, we have MN as the base with a length of w/12 for both triangles.

area MNI = 1/2 MN * GF = 1/2 * w/12 * 2h/5 = 2hw/120
area MNE = 1/2 MN * EF = 1/2 * w/12 * 3h/5 = 3hw/120

And their sums are 2hw/120 + 3hw/120 = 5hw/120.
And hw is the total area of EGIK which is 120. So we get:
5 * 120/120 = 5 * 1 = 5

So the area of quadrilateral EMIN is 5.

Area of EMIN = 5 The shaded quadrilateral EMIN is composed of two triangles MNI and MNE. Since the area of a triangle is 1/2bh where b is the base and h the height, the area of the quadrilateral is A = 0.5 * MN * MH + 0.5 MN * EF A = 0.5 MN (MH + EF) Now the large rectangle GIKE has an area of 12+36+24+48 = 120. We'll call the overall width "w" and the overall height "h", so wh = 120. (1) Consider that rectangle GIKE has been divided into 2 rectangles by line FJ. The area above the line is 12+36 = 48, and the area below the line is 24+48 = 72. So the ratio of their heights is 2/3. Therefore we'll call the height of the top rectangle 2h/5 and the bottom rectangle 3h/5. (2) Considering rectangles FGHM and MHIJ, their heights are the same and their areas are in the ratio 12/36=1/3. So we'll consider the width of FGHM to be w/4 and the width of MHIJ to be 3w/4. (3) Now consider rectangles EFNL and LNJK. They also share the same height, so their ratios of width is 24/48 = 1/2. So their widths will be w/3 and 2w/3 respectively. (4) This means that the line segment MN will be w/3 - w/4 = 4w/12 - 3w/12 = w/12 (See (2) and (3) above) Now taking the formula at the very beginning for the area of the quadrilateral EMIN, we have A = 0.5 MN (MH + EF) MN = w/12 ; See (4) above MH = 2h/5 ; See (1) above EF = 3h/5 ; See (1) above So A = 0.5 MN (MH + EF) A = 0.5 w/12 (2h/5 + 3h/5) A = 0.5 w/12 (5h/5) A = 0.5 w/12 h A = w/24 h A = wh/24 And since the overall area of the entire rectangle is wh = 120, we get A = wh/24 A = 120/24 A = 5 As for the actual width and height of the overall rectangle? Don't know and don't care. Any value of w and h will work as long as their product is 120. But regardless of the actual dimensions, the area of quadrilateral EMIN will be 5.

find the value of x

Answers

180 - 44 = 136
136 / 2 = 68

x = 68 + 44 = 112

Describe the transformation.
A) translation 6 units down
B) translation 2 units down
C) reflection across the x-axis
D) reflection across the y-axis

Answers

C) reflection across the x-axis

Answer: C is the answer

Step-by-step explanation:

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