Answer:
A) 90
B) The individuals in the survey will be 11, 101, 191,...., 2621.
Step-by-step explanation:
Tenemos lo siguiente a partir del enuciado:
A) let, a consider a department has an alphabetical list of all 2708 employees at company and wants to conduct a systematic sample. Substitute the value as:
k = N/n
reemplanzado nos queda:
k = 2708/30 = 90.26
Lo que quiere decir que el valor de k es de aproximadamente 90 B) Randomly select the number between I and 90, Suppose the randomly selected sumber is 11. The individuals in the survey will be; need to find 30th team, hence by using the airthmetic perogression nth term formula:
30th term = 11+ (30 - 1) *90
30th term = 2621
The individuals in the survey will be 11, 101, 191,...., 2621.
The random sample is obtained
The arithmetic mean (average) of four numbers is 85. If the largest of these numbers is 97, find the mean of the remaining three numbers. I cannot solve this. Please help on it.
Answer:
81
Step-by-step explanation:
Let's do this systematically:
Four numbers: a, b, c, d
Whose mean is 85: [tex]\frac{a + b + c + d}{4} = 85[/tex]
Whose largest number is 97: [tex]\frac{a + b + c + 97}{4} = 85[/tex]
Lets solve for the other numbers:
a+b+c+97 = 85*4 = 340
340 - 97 = 243
a+b+c = 243
at this point it doesn't matter what the numbers are, they just need to add up to 243.
We can do 243÷3=81, which is our answer
Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+16y=0. Separate your answers by commas. isn't the answer just ±4?
Answer: k = 4, k = -4 and k = 0.
Step-by-step explanation:
If we have y = sin(kt)
then:
y' = k*cos(kt)
y'' = -k^2*son(x).
then, if we have the relation:
y'' - y = 0
we can replace it by the things we derivated previously and get:
-k^2*sin(kt) + 16*sin(kt) = 0
we can divide by sin in both sides (for t ≠0 and k ≠0 because we can not divide by zero)
-k^2 + 16 = 0
the solutions are k = 4 and k = -4.
Now, we have another solution, but it is a trivial one that actually does not give any information, but for the diff equation:
-k^2*sin(kt) + 16*sin(kt) = 0
if we take k = 0, we have:
-0 + 0 = 0.
So the solutions are k = 4, k = -4 and k = 0.
My question is probably obvious but I don't know it. What is the z axis
Answer:
z-Axis. The axis in three-dimensional Cartesian coordinates which is usually oriented vertically. Cylindrical coordinates are defined such that the -axis is the axis about which the azimuth coordinate. is measured.
Step-by-step explanation:
Sal wrote the statement below to represent the inequality 8n - 5 ≥ 25. Which words should Sal use to complete the verbal statement? The product of 8 and n decreased by 5 is _____25. less than greater than less than or equal to greater than or equal to
The symbol [tex]\ge[/tex] can be thought of a greater than sign over top an equal sign, like this [tex]\stackrel{>}{=}[/tex] though the second horizontal line is erased to keep things relatively more simple (in terms of having to write it out).
If you transform x2+ y2 = 25 into 4x2+ 4y2 = 25, which option below describes the effect of this transformation on the
radius?
It multiplies the radius by 2
It multiplies the radius by 4
It divides the radius by 4
It divides the radius by 2
Answer:
It divides the radius by 2, which is the last option in your list of possible answers.
Step-by-step explanation:
Recall that the standard equation of a circle of radius R centered at the origin of coordinates is given by:
[tex]x^2+y^2=R^2[/tex]
so when you have the first equation of the circle:
[tex]x^2+y^2=R^2\\x^2+y^2=25\\x^2+y^2=5^2[/tex]
The radius of the circle was 5
Now, when you work with the second equation, we need to divide both sides by 4 in order to get the standard form of the circle and be able to understand what the radius is:
[tex]4x^2+4y^2=25\\x^2+y^2=\frac{25}{4} \\x^2+y^2=(\frac{5}{2})^2[/tex]
So we see that the initial radius 5 is now divided by 2.
What is the value of x to the power of 2 to the power of 4 when x = 8 and y =2
Answer:
x is 64 and y is 16 but if you can't comprehend thats 64/16 = 4
Step-by-step explanation:the power is the number multiplied by it self so 8 to the power if 2 is 8 x 8 and 2 to the power of four is 2 x 2 x 2 x 2= 16
ABCD is a kite.
B
O
y = [?]
A 40°
C
Х
Enter the number
that belongs in
the green box.
D
Answer:
50°
Step-by-step explanation:
ABCD is a kite.
Therefore, AB = BC
[tex]\therefore m\angle BCA= m\angle BAC = 40\degree \\
\because BD \perp AC.. (Diagonals \: of\: kite) \\
\therefore y + 90\degree + m\angle BCA = 180\degree \\
\therefore y + 90\degree + 40\degree = 180\degree \\
\therefore y = 180\degree - 130\degree \\
\huge\red {\boxed {y = 50\degree}} [/tex]
Find m^4+(1/m^4) if m-(1/m)=3 Please help with this.
Answer:
m^4+(1/m^4)= 123.4641 or 118.6
Step-by-step explanation:
m-(1/m)=3
m² - 1= 3m
m² -3m -1= 0
m = (3-√13)/2 = -0.3
Or
m =( 3+√13)/2= 3.3
m^4+(1/m^4) for m = -0.3
= (-0.3)^4 + (1/(0.3)^4)
= 0.0081 + 123.456
= 123.4641
m^4+(1/m^4) for m = 3.3
= (3.3)^4 + (1/(3.3)^4)
= 118.5921 + 0.008432
= 118.6
4b • 0.5a 2ab 2a2b 2ab2 2a2b2
Answer:
(4b)•(0.5a) = (4•0.5)(a)(b) = 2ab
Step-by-step explanation:
Assume that the random variable X is normally distributed, with mean 60 and standard deviation 16. Compute the probability P(X < 80). Group of answer choices
Answer:
P(X < 80) = 0.89435.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 60, \sigma = 16[/tex]
P(X < 80)
This is the pvalue of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 60}{16}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.89435.
So
P(X < 80) = 0.89435.
What does csc x cot x (1-cos^2 x) equal
Answer:
Step-by-step explanation:
Please answer this correctly
Answer:
80%
Step-by-step explanation:
The numbers 5 or even are 4, 5, 6, and 8.
4 numbers out of 5.
4/5 = 0.8
Convert to percentage.
0.8 × 100 = 80
P(5 or even) = 80%
Answer:
80% chance
Step-by-step explanation:
There are 4 numbers that fit the rule, 4, 5, 6, and 8. There is a 4/5 chance spinning one of those numbers or 80% chance.
how do you get the answer after you have an equation?
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value t Subscript alpha divided by 2,(b) find the critical value z Subscript alpha divided by 2,or (c) state that neither the normal distribution nor the t distribution applies.Here are summary statistics for randomly selected weights of newborn girls: nequals235,x overbarequals33.7hg, sequals7.3hg. The confidence level is 95%.
Answer:
To construct a confidence interval, Normal distribution should be used since the sample size is quite large (n > 30)
From the z-table, at α = 0.025 the critical value is
[tex]z_{\alpha/2} = 1.96[/tex]
Step-by-step explanation:
We are given the following information:
The sample size is
[tex]n = 235[/tex]
The mean weight is
[tex]\bar{x}= 33.7 \: hg[/tex]
The standard deviation is
[tex]s = 7.3 \: hg[/tex]
Since the sample size is quite large (n > 30) then according to the central limit theorem the sampling distribution of the sample mean will be approximately normal, therefore, we can use the Normal distribution for this problem.
The correct option is (b)
The critical value corresponding to 95% confidence level is given by
Significance level = α = 1 - 0.95 = 0.05/2 = 0.025
From the z-table, at α = 0.025 the critical value is
[tex]z_{\alpha/2} = 1.96[/tex]
What is Normal Distribution?
A Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
Find the surface area of the solid shown or described. If necessary, round to the nearest tenth. A.348m^2 B.484m^2 C.180.7m^2 D.262m^2
Answer: 484m²
Step-by-step explanation: This is a question on solid shape.
The surface area of a cone is the same thing as the perimeter of the cone ie, the materials required to construct the cone.
Formula for the surface area of the cone = πrl + πr², ( the circular base )
From.the diagram,
r = 7.1m , l = 14.6m, π = 3.142
Now substitute for those values in.the formula above
SA = πrl + πr²
= 3.142 × 7.1 × 14.6 + 3.142 × 7.1²
= 325.6997 + 158.388
= 484.09
Now to the nearest tenth meter,
SA = 484m²
Evaluate the function rule for the given value y=12•3x for x=-2
Answer:
-72
Step-by-step explanation:
We just have to plug in -2 for x so the answer is 12 * 3 * (-2) = -72.
a child rolls a 6-sided die 6 times. what is the probability of the child rolling no more than three twos g
Answer:
Pr(Three 2's) = 1/27
Step-by-step explanation:
Let's assume the die is a fair die, on the first roll of the die, the child has a 1/6 chance of getting any number, including 6.
Second roll, the child has a 1/36 chance of getting any two numbers, including two 6's.
And on the third roll, the child has a 1/36×1/6=1/216 chance of getting any three numbers, including three 6's. And this is due to the fact that the rolls are independent, so the total possible outcomes multiply each roll with each roll's probability. Since each roll's probability is 1/6.
The probability of the child rolling no more than three twos will be =2/6×2/6×2/6
=1/3×1/3×1/3
=1/27
Therefore, the chances of three twos will be 1/27
pls help me on this question
Hey there! :)
Answer:
Choice C: x + 8 = 3x.
Step-by-step explanation:
Solve this question by simplifying each answer choice:
a) 4x = 20
Divide both sides by 4:
4x/4 = 20/4
x = 5. This is incorrect.
b) x/2 = 8
Multiply both sides by 2:
x = 16. This is incorrect.
c) x + 8 = 3x
Subtract x from both sides:
8 = 2x
Divide 2 from both sides:
x = 4. This is correct.
d) x = x+5 /2
Multiply both sides by 2:
2x = x + 5
Subtract x from both sides:
x = 5. This is incorrect.
Therefore, choice C is the correct answer.
Answer:
C . x+8=3x
Step-by-step explanation:
[tex]x +8 = 3x\\Collect-like-terms\\8=3x-x\\8=2x\\\frac{2x}{2} =\frac{8}{2} \\x =4[/tex]
suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, remove it from the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble? The multiplication rule says to use P(red) P(blue).
Describe the probability of finding a red marble?
Describe the probability of finding a blue marble?
Describe the process of finding the probability of finding a red marble followed by a blue marble if the first marble was permanently removed?
What affect did removing the first marble from the box have on the problem?
Describe the probability of finding a red marble followed by the blue marble if the first marble is removed?
Answer:
1) 2/9
2)3/9
Step-by-step explanation:
sorry,thats what i know so far
Mary is 5 feet tall and Alice is 1.6 meters tall. Who is taller? By how many inches?
Answer:
Alice
Step-by-step explanation:
5 feet is approximately 1.5 meters so we can say Alice is taller than Mary by 10cm
Answer:
Mary, by 3 inches.
Step-by-step explanation:
Convert the unit to inches.
5 feet = 60 inches
1.6 meters = 63 inches
63 - 60 = 3
Mary is taller than Alice by 3 inches.
The circumference of a circle can be found using the
fortula C=2
Which is an equivalent equation solved for r?
r=CH
r= C(2)
or = 21
Select the correct answer.
The function RX) = 2x + 3x + 5, when evaluated, gives a value of 19. What is the function's input value?
A. 1
B. -1
C. 2
D. -2
E. -3
Answer:
Correct option: C.
Step-by-step explanation:
(Assuming the correct function is R(x) = 2x^2 + 3x + 5)
To find the input value that gives the value of R(x) = 19, we just need to use this output value (R(x) = 19) in the equation and then find the value of x:
[tex]R(x) = 2x^2 + 3x + 5[/tex]
[tex]19 = 2x^2 + 3x + 5[/tex]
[tex]2x^2 + 3x -14 = 0[/tex]
Solving this quadratic function using the Bhaskara's formula (a = 2, b = 3 and c = -14), we have:
[tex]\Delta = b^2 - 4ac = 9 + 112 = 121[/tex]
[tex]x_1 = (-b + \sqrt{\Delta})/2a = (-3 + 11)/4 = 2[/tex]
[tex]x_2 = (-b - \sqrt{\Delta})/2a = (-3 - 11)/4 = -3.5[/tex]
So looking at the options, the input to the function is x = 2
Correct option: C.
The respiratory rate (in breaths per minute) in newborns varies according to a distribution that is approximately Normal, with a mean of 50 and a standard deviation of 5. Use Excel to answer this question: What is the probability that a randomly chosen newborn has a respiratory rate between 40 and 55 breaths per minute
Answer:
[tex]P(40<X<55)[/tex]
And since we need to use excel the code in order to find the answer would be:
=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)
And the answer would be:
[tex]P(40<X<55)=0.819[/tex]
Step-by-step explanation:
Let X the random variable that represent the respiratory rate of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(50,5)[/tex]
Where [tex]\mu=50[/tex] and [tex]\sigma=5[/tex]
We are interested on this probability
[tex]P(40<X<55)[/tex]
And since we need to use excel the code in order to find the answer would be:
=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)
And the answer would be:
[tex]P(40<X<55)=0.819[/tex]
(matching type) given f(x)= x+4 and g(x) = 2x + 1 match the expression to its simplication operation
choose
x+4 / 2x+1
Answer 1
Choose...
f of g
f/g
f - g
f∙g
g/f
f + g
2x+1 / x+4
Answer 2
Choose...
f of g
f/g
f - g
f∙g
g/f
f + g
3x + 5
Answer 3
Choose...
f of g
f/g
f - g
f∙g
g/f
f + g
2x + 5
Answer 4
Choose...
f of g
f/g
f - g
f∙g
g/f
f + g
-x + 3
Answer 5
Choose...
f of g
f/g
f - g
f∙g
g/f
f + g
2x2 + 9x + 12
pa help po
Answer:
1) [tex]h(x) = \frac{f(x)}{g(x)}[/tex], 2) [tex]h(x) = \frac{g(x)}{f(x)}[/tex], 3) [tex]h(x) = f(x) + g(x)[/tex], 4) [tex]h (x) = f [g (x)][/tex], 5) [tex]h(x) = f(x) - g(x)[/tex]
Step-by-step explanation:
1) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h (x) = \frac{x+4}{2\cdot x + 1}[/tex], then:
[tex]h(x) = \frac{f(x)}{g(x)}[/tex]
2) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = \frac{2\cdot x + 1}{x+4}[/tex], then:
[tex]h(x) = \frac{g(x)}{f(x)}[/tex]
3) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = 3\cdot x + 5[/tex], then:
[tex]h(x) = 3\cdot x + 5[/tex]
[tex]h (x) = (1 + 2)\cdot x + (4+1)[/tex]
[tex]h(x) = x + 2\cdot x + 4 +1[/tex]
[tex]h(x) = (x+4) + (2\cdot x + 1)[/tex]
[tex]h(x) = f(x) + g(x)[/tex]
4) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = 2\cdot x + 5[/tex], then:
[tex]h(x) = 2\cdot x + 5[/tex]
[tex]h(x) = 2\cdot x + 1 + 4[/tex]
[tex]h(x) = (2\cdot x +1)+4[/tex]
[tex]h (x) = f [g (x)][/tex]
5) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = -x + 3[/tex], then:
[tex]h(x) = -x + 3[/tex]
[tex]h(x) = (1 - 2)\cdot x + 4 - 1[/tex]
[tex]h(x) = x - 2\cdot x + 4 - 1[/tex]
[tex]h(x) = x + 4 - (2\cdot x + 1)[/tex]
[tex]h(x) = f(x) - g(x)[/tex]
The U.S. Department of Agriculture guarantees dairy producers that they will receive at least $1.00 per pound of butter they supply to the market. Below is the current monthly demand and supply schedule for wholesale butter (in millions of pounds per month). Wholesale Butter Market
Price (dollars per pound) Quantity of Butter Demanded Quantity of Butter Supplied
(millions of pounds) (millions of pounds)
$0.80 107 63 0
.90 104 71
1.00 101 79
1.10 98 87
1.20 95 95
1.30 92 103
1.40 89 111
1.50 86 119
1.60 83 127
1.70 80 135
1.80 77 143
a. In the butter market, the monthly equilibrium quantity is million pounds and the equilibrium price is $ per pound.
b. What is the monthly surplus created in the wholesale butter market due to the price support (price floor) program? 22 million pounds 79 million pounds Zero 11 million pounds Suppose that a decrease in the cost of feeding cows shifts the supply schedule to the right by 40 million pounds at every price.
Answer:
a. In the butter market, the monthly equilibrium quantity is 95 million pounds and the equilibrium price is $1.2 per pound.
b. The correct option is zero.
c. See the attached excel file for the new supply schedule.
d. The monthly surplus created by the price support program is 18 million pounds given the new supply of butter.
Step-by-step explanation:
Note: This question is not complete. A complete question is therefore provided in the attached Microsoft word file.
a. In the butter market, the monthly equilibrium quantity is million pounds and the equilibrium price is $ per pound.
At equilibrium, quantity demanded must be equal with the quantity supplied.
In this question, equilibrium occurs at the price of $1.20 per pound and quantity of 95 million pounds.
Therefore, in the butter market, the monthly equilibrium quantity is 95 million pounds and the equilibrium price is $1.2 per pound.
b. What is the monthly surplus created in the wholesale butter market due to the price support (price floor) program?
Price floor refers to a government price control on the lowest price that can be charged for a commodity.
It should be noted that for a price floor to be binding, it has to be fixed above the equilibrium price.
Since the price floor of $1 per pound is lower than the equilibrium price of $1.2 per pound, the price floor will therefore not be binding. As a result, the market will still be at the equilibrium point and the monthly surplus created in the wholesale butter market due to the price support (price floor) program will be zero.
Therefore, the correct option is zero.
c. Fill in the new supply schedule given the change in the cost of feeding cows.
Since a decrease in the cost of feeding cows shifts the supply schedule to the right by 40 million pounds at every price, this implies that there will be an increase in supply by 40 million at each price.
Note: Find attached the excel file for the new supply schedule.
d. Given the new supply of butter, what is the monthly surplus of butter created by the price support program?
Since the price floor has been fixed at $1 per pound by the price support program, we can observe that the quantity demanded is 101 million pounds and quantity supplied is 119 million pounds at this price floor of $1. The surplus created is then the difference between the quantity demanded and quantity supplied as follows:
Surplus created = Quantity supplied - Quantity demanded = 119 - 101 = 18 million pounds
Therefore, the monthly surplus created by the price support program is 18 million pounds given the new supply of butter.
Simplify the expression where possible. (6 3) -3
Answer:
-189
Step-by-step explanation:
(63) -3
Calculate the product
-3(63)
Multiply both numbers
-3 × 63
= -189
In the figure, ABC is a quarter circle and CDEF is a square.
(a) The length of DF is 38 cm. Find the area of the square CDEF.
(b) Find the area of the shaded parts. Give your answer correct to
2 decimal places.
Answer:
a). 722 cm²
b). 412.11 cm²
Step-by-step explanation:
ABC is a quarter circle with radius CE,
Area of a quarter circle = [tex]\frac{1}{4}\pi r^{2}[/tex]
Since CDEF is a square, diagonals CE and FD will be equal.
CE ≅ FD ≅ 38cm
(a). Measure of a side of the square CDEF = [tex]\sqrt{\frac{1}{2} (\text {Diagonal})^2}[/tex]
Side = [tex]\sqrt{\frac{(38)^2}{2} }[/tex]
= 26.87
Area of the square CDEF = (Side)²
= (26.87)²
= 722 cm²
b). Area of the shaded part = Area of the quarter circle - Area of the square
Area of the quarter circle = [tex]\frac{1}{4}\pi (38)^{2}[/tex]
= 1134.11495 cm²
Area of the shaded area = 1134.11495 - 722
= 412.11495 cm²
≈ 412.11 cm²
Type the correct answer in each box. If necessary, use/for the fraction bar(s).
In this triangle, the product of Sin B and tan C is_____, and the product of sin C and tan B is_____.
please view picture at the top
Answer:
1). sinB × tanC = [tex]\frac{c}{a}[/tex]
2). sinC × tanB = [tex]\frac{b}{a}[/tex]
Step-by-step explanation:
From the figure attached,
A right triangle has been given with m∠A = 90°, m(AC) = b, m(AB) = c and m(BC) = a
SinB = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{\text{AC}}{\text{BC}}[/tex]
= [tex]\frac{b}{a}[/tex]
tanB = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{\text{AC}}{\text{AB}}[/tex]
= [tex]\frac{b}{c}[/tex]
SinC = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{\text{AB}}{\text{BC}}[/tex]
= [tex]\frac{c}{a}[/tex]
tanC = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{c}{b}[/tex]
Now sinB × tanC = [tex]\frac{b}{a}\times \frac{c}{b}[/tex]
= [tex]\frac{c}{a}[/tex]
And sinC × tanB = [tex]\frac{c}{a}\times \frac{b}{c}[/tex]
= [tex]\frac{b}{a}[/tex]
Simplify the expression.
(7-6)(-1)
-7 +0
-7-
7-6
7+ c
Answer:
7+c or 6
Step-by-step explanation:
Answer:
-89+c
Step-by-step explanation:
I'm assuming
"(7-6)(-1)
-7 +0
-7-
7-6
7+ c"
Is the whole equation.
(7-6)(-1) -7+0 -7- 7-6 7+c=
(1)(-1)-7+0-7-7-67+c=
-1-7+0-7-7-67+c=
-8+0-7-7-67+c=
-8-7-7-67+c=
-15-7-67+c=
-22-67+c=
-89+c
A piggy bank contains pennies, nickels, and dimes. The number of dimes is 15 more than the number of nickels, and there are 140 coins altogether totaling $7.17. Find the number of nickels in the bank.
Answer:
Option D is correct.
There are 34 nickels in the piggy bank.
Step-by-step explanation:
A piggy bank contains pennies, nickels and dimes.
Let the number of pennies be p
Let the number of nickels be n
Let the number of dimes be d
Also, note that 1 penny = $0.01
1 nickel = $0.05
1 dime = $0.10
- The number of dimes is 15 more than the number of nickels.
d = 15 + n
- There are 140 coins altogether totaling $7.17.
p + n + d = 140
0.01p + 0.05n + 0.1d = 7.17
Bringing the 3 equations together
d = 15 + n (eqn 1)
p + n + d = 140 (eqn 2)
0.01p + 0.05n + 0.1d = 7.17 (eqn 3)
Substitute (eqn 1) into (eqn 2)
p + n + d = 140
p + n + (15 + n) = 140
p + 2n + 15 = 140
p = 140 - 15 - 2n = 125 - 2n
p = 125 - 2n (eqn 4)
Substitute (eqn 1) and (eqn 4) into (eqn 3)
0.01p + 0.05n + 0.1d = 7.17
0.01(125 - 2n) + 0.05n + 0.1(15 + n) = 71.7
1.25 - 0.02n + 0.05n + 1.5 + 0.1n = 7.17
0.1n + 0.05n - 0.02n + 1.5 + 1.25 = 7.17
0.13n + 2.75 = 7.17
0.13n = 7.17 - 2.75 = 4.42
0.13n = 4.42
n = (4.42/0.13) = 34
d = 15 + n = 15 + 34 = 49
p = 125 -2n = 125 - (2×34) = 125 - 68 = 57
Hence, there are 57 pennies, 34 nickels and 49 dimes in the piggy bank.
Hope this Helps!!!