A man has 24 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 345 cents, how many dimes and how many quarters does he have?

Answers

Answer 1

The man has 17 dimes and 7 quarters.

A system of equations was set up, using the total number of coins and their total value, to determine the quantity of each coin type.

Let's denote the number of dimes as d and the number of quarters as q. We are given two facts: (1) the man has a total of 24 coins, and (2) the total value of the coins is 345 cents. Thus we have two equations:

d + q = 24 (since the total number of coins is 24)10d + 25q = 345 (since the value of each dime is 10 cents and each quarter is 25 cents, and their total value is 345 cents)

We can solve this system of equations to find the values of d and q.

Subtracting the first equation from the second (multiplied by 10) to eliminate the variable d:

10d + 25q = 345
-(10d + 10q = 240)
-------------------------
15q = 105

Dividing by 15 to solve for q, we get q = 7. This means the man has 7 quarters. Substituting q = 7 into the first equation:

d + 7 = 24
d = 24 - 7
d = 17

So, the man has 17 dimes.

Therefore, the man has 17 dimes and 7 quarters.


Related Questions

The graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units a)up b)down c)left D) right

Answers


Correct  ansver:  a) translated 3 units up



Answer:

A)up

Step-by-step explanation:

Given : f(x)=log x +3

            g(x)= log x

To Find :

The graph of f(x) = log x + 3 is the graph of  g(x) = log x translated 3 units

a)up

b)down

c)left

d) right

Solution:

Rule: f(x)→f(x)+b

So, the graph f(x) is translated up by b units

So, on comparing given f(x) with rule , we can say that the graph g(x) is translated up by 3 units

Thus option A is correct.

Hence The graph of f(x) = log x + 3 is the graph of  g(x) = log x translated 3 units up

A salesperson makes a base salary of $2000 a month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000. Write a piecewise-defined function to model the salesperson's total monthly salary (in $) as a function

Answers

Answer:

The piecewise-defined function to model the salesperson's total monthly salary (in $) is,

[tex]f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}[/tex]

Step-by-step explanation:

It is given that the salesperson makes a base salary of $2000 a month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000.

Let the x represents the amount of sales and f(x) represents the salary of salesperson.

It means till the sale of $40,000, the salary of the salesperson is constant, i.e., $2000.

[tex]f(x)=2000[/tex]    for   [tex]x\leq 40,000[/tex]

He will get commision of 5% on the amount in sales over $40,000.

[tex]f(x)=2000+\frac{5}{100}(x-40000)[/tex]  for  [tex]x>40,000[/tex]

Therefore the piecewise-defined function to model the salesperson's total monthly salary (in $) is,

[tex]f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}[/tex]

The piecewise-defined function to model the salesperson's total monthly salary (in $) as a functionis [tex]\boxed{f\left( x \right)=\left\{\begin{gathered}2000{\text{ if }}x \leqslant 40000 \hfill\\2000 + 0.05\left( {x - 40000} \right){\text{ if }}x > 40000 \hfill\\\end{gathered}\right.}[/tex].

Further explanation:

The piecewise defined function is defined as a function that takes different values in different interval. It is defined on the sequence of intervals.

Given:

The base salary is [tex]\$ 2000[/tex].

He will earn [tex]5\%[/tex] additional commission on the amount sales over [tex]\$ 40000[/tex].

Explanation:

The base salary of a salesperson in a month is $2000.

If the salesperson reaches to $40000, he will earns 5% additional commission on the amount sales over [tex]\$ 40000[/tex].

The person get [tex]\$ 2000[/tex] if sale less than  [tex]\$ 40000[/tex].

[tex]f\left( x \right) =2000{\text{ for }}x \leqslant 40000[/tex].

The value of the function for less than $40000 is  [tex]f\left( x \right)=2000[/tex].

If he sales over 40000 the amount he will get can be expressed as follows,

[tex]f\left( x \right)=2000+\dfrac{5}{{100}}\left( {x - 40000} \right)[/tex] for[tex]x > 40000.[/tex]

The value of the function for greater than 40000 is  [tex]f\left( x \right)=2000 + \dfrac{5}{{100}}\left({x - 40000} \right)[/tex].

The piecewise-defined function to model the salesperson's total monthly salary (in $) as a functionis [tex]\boxed{f\left( x \right)=\left\{\begin{gathered}2000{\text{if }}x \leqslant 40000\hfill\\2000 + 0.05\left( {x - 40000}\right){\text{if }}x > 40000 \hfill \\\end{gathered}\right.}[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear Equation

Keywords: solving equation, inverse operation, isolate, variable, addition property, good guess, solution, order of operations, reverse order, two solution, linear equation.

Convert 1/3 and 4/5 to a decimal. Are both of them repeating or terminating?

Answers

1/3 = 0.33333 ( repeating)

4/5 = 0.8 (terminating)

How do I solve this equation? I need a refresher on Algebra.

Answers

These equations seem tricky, but aren't as hard as you think. Just solve it like you are regularly adding fractions.

Your common denominator is 9x + 9, so

1/(9x+9)  =  36/(9x + 9)   -    (5x + 5)/9

1 - 36 + 5x + 5 / 9x - 9
30x - 30/9x - 9
10x-10/3x - 3
10(x-1)/3(x-1)
10/3

Hope this helped!

1.5x - 3y = 6 (solve for y)

Answers

hello : 
1.5x - 3y = 6
3y = 1.5x - 6
y = (1.5x - 6)/3

An equation is formed of two equal expressions. The value of y for the given equation is (1.5x - 6)/3.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

1.5x - 3y = 6

Subtract 1.5x from both the sides of the equation,

1.5x - 3y - 1.5x = 6 - 1.5x

-3y = 6 - 1.5x

Divide both the sides of the equation by -3,

-3y/(-3) = (6 - 1.5x)/(-3)

y = (1.5x - 6)/3

Hence, the value of y for the given equation is (1.5x - 6)/3.

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some hot dogs come in packages of 8.Why would a baker of hot dog buns packages 7 hot dog buns to a package

Answers

The reason as to why the baker had package hotdogs of seven and not eight because they are making consumers buy another package because other people will likely buy eight and if it is only comprise with seven, they will likely buy another package, to have eight hotdogs and not just seven.

Identify the expressions and the value that are equivalent to 6 times 5 squared.

Answers

Six * five squared
6*5^2
=6*25
=150

The value that is equivalent to 6 times 5 squared is 150.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a mathematical relationship or a quantity.

Expressions in mathematics can be evaluated or simplified to produce a single value or to represent a more simplified form of the original expression.

6 times 5 squared can be written in a few different ways:

6 x 5²

6 x 25

150

So the expressions that are equivalent to 6 times 5 squared are:

6 x 5²

6 x 25

The value that is equivalent to 6 times 5 squared is 150.

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How do I write 19.4 in expanded form

Answers

Final answer:

To write 19.4 in expanded form, you can break down the number into its place values. The digit 1 is in the tens place, the digit 9 is in the ones place, and the digit 4 is in the tenths place. Therefore, 19.4 in expanded form is 10 + 9 + 0.4.

Explanation:

To write 19.4 in expanded form, we break down the number into its place values. The digit 1 is in the tens place, the digit 9 is in the ones place, and the digit 4 is in the tenths place. So, we can write 19.4 in expanded form as 10 + 9 + 0.4.

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Find the next three terms in the patter 9, 4, -1, -6, -11....then describe the pattern

Answers

you can notice that each time you subtract 5
9-5=4
4-5=-1
-1-5=-6
-6-5=-11
following the same pattern, the next term would be:
-11-5= -16
this is a linearily decreasing pattern (decreases with constant linear rate)

The number n(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation. initially, n(0) = 500, and it is observed that n(1) = 1000. solve for n(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 50,000. (round all coefficients to four decimal places.)

Answers

Rounding the coefficients to four decimal places:

[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]

The logistic equation governing the number of people exposed to the advertisement in the community is given by:

[tex]\[ \frac{{dn}}{{dt}} = kn \left(1 - \frac{n}{M}\right) \][/tex]

Where:

n(t)  is the number of people exposed to the advertisement at time t

k  is the growth rate constant

M  is the limiting number of people who will see the advertisement

Given:

[tex]\( n(0) = 500 \)[/tex]

[tex]\( n(1) = 1000 \)[/tex]

[tex]\( M = 50000 \)[/tex]

We first need to find the growth rate constant \( k \):

[tex]\[ 1000 = 500 \times \left(1 - \frac{500}{50000}\right) \times k \][/tex]

[tex]\[ 1000 = 500 \times \left(1 - \frac{1}{100}\right) \times k \][/tex]

[tex]\[ 1000 = 500 \times \frac{99}{100} \times k \][/tex]

[tex]\[ k = \frac{1000 \times 100}{500 \times 99} \][/tex]

[tex]\[ k = \frac{2000}{99} \][/tex]

Now, we integrate to find [tex]\( n(t) \)[/tex]:

[tex]\[ \int \frac{{dn}}{{n(1 - \frac{n}{50000})}} = \int \frac{{2000}}{{99}} dt \][/tex]

[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t + C \][/tex]

Using the initial condition [tex]\( n(0) = 500 \)[/tex], we find[tex]\( C \)[/tex]:

[tex]\[ -\ln|1 - \frac{500}{50000}| = 0 + C \][/tex]

[tex]\[ -\ln\left(\frac{99}{100}\right) = C \][/tex]

So, the equation becomes:

[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t - \ln\left(\frac{99}{100}\right) \][/tex]

Solving for n(t) :

[tex]\[ |1 - \frac{n}{50000}| = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ 1 - \frac{n}{50000} = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ \frac{n}{50000} = 1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ n(t) = 50000 \times \left(1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)}\right) \][/tex]

This is the solution for [tex]\( n(t) \)[/tex]. Now, rounding the coefficients to four decimal places:

[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]

If a coin is tossed 4 times, and then a standard six-sided die is rolled 2 times, and finally a group of four cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?

Answers

[tex]\(1138368400\)[/tex] different outcomes possible when considering all the events together.

Coin Toss: Since each toss is independent of the others, the total number of outcomes for 4 tosses is:

[tex]\(2 \times 2 \times 2 \times 2 = 2^4 = 16\)[/tex].

Die Roll: A standard six-sided die has 6 faces, each with a different number from 1 to 6. When the die is rolled once, there are 6 possible outcomes. If the die is rolled 2 times, the number of different outcomes is:

[tex]\(6 \times 6 = 6^2 = 36\)[/tex]

Card Draw: When drawing a card from the deck, there are 52 possible outcomes. If a second card is drawn without replacing the first, there are now 51 possible outcomes for the second card (since one card has already been drawn). Continuing this pattern, for the third card, there are 50 possible outcomes, and for the fourth card, there are 49 possible outcomes.

The number of different outcomes for drawing 4 cards without replacement is: [tex]\(52 \times 51 \times 50 \times 49\)[/tex].

[tex]\[ \text{Total Outcomes} = (\text{Coin Toss Outcomes}) \times (\text{Die Roll Outcomes}) \times (\text{Card Draw Outcomes}) \][/tex]

[tex]\[ \text{Total Outcomes} = 16 \times 36 \times (52 \times 51 \times 50 \times 49) \][/tex]

[tex]\[ \text{Total Outcomes} = 6^2 \times 52 \times 51 \times 50 \times 49 \][/tex]

[tex]\[ \text{Total Outcomes} = 36 \times 52 \times 51 \times 50 \times 49 \][/tex]

[tex]\[ \text{Total Outcomes} = 36 \times 31625400 \][/tex]

[tex]\[ \text{Total Outcomes} = 1138368400 \][/tex]

Find the distance between the points on a number line -7, -54

Answers

the answer to the question is 47

since they are both negative numbers just subtract 7 from 54

54-7 = 47

how many more kilometers in 4320 than 7200

Answers

2880 more kilometers

highest common factor of 92 and 42

Answers

To get the Greates Common Factor (GCF) of 92 and 42 we need to factor each value first and then we choose all the copies of factors and multiply them: 

92:   22  2342:   2 37 GCF:   2    

The Greates Common Factor (GCF) is:   2

 

You can always share this solution
The correct answer is going to be 2



glad to help anytime

Ned has scored 84 points in the first 6 games of the basketball season. How many points per game has Ned scored?

Answers

84/6 = 14

Ned scored ~14 points a game

hope this helps

Answer:

84/6=14

Step-by-step explanation:

read the answer

Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. Using the tables in the Business Math Handbook that accompanies the course textbook, determine which one of the following is the best deal.
A. Four Rivers
B. Mystic
C. Mystic for last two years
D. Four Rivers for first two years

Answers

The answer to this question would be B. Mystic


Since the rate should be constant, option C and D wouldn't be true.
If the Four Rivers bank gives 12% per year and Mystic Bank gives 14% per year, it will be 3% per quarter year for Four Rivers Bank and 7% semiannually for Mystic Bank. 
The total rate would become:
Four rivers 103%^4= 1.125
Mystic : 107%^2= 1.145

17 - 8.63 find the sum please thank you

Answers

subtract the numbers. You should get 8.37.

1. Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Draw a ray with endpoint C.
Step 2: Open the compass to the length of AB.
Step 3: With the same compass setting, put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D.
a. a perpendicular bisector
b. a congruent segment
c. an angle bisector
d. a congruent angle

2. Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Put the compass point on A and draw a long arc. Be sure the opening is grater than 1/2 AB.
Step 2: With the compass on the same setting, put the compass point on B and draw another long arc. Label the points where the two arcs meet as X and Y.
Step 3: Draw XY. Label the point of intersection of AB and XY as M, the midpoint of AB.
a. a perpendicular bisector
b. a congruent segment
c. an a

Answers

number one is c. an angle bisector i think number 2 is b. a congruent segment i think

1. For that accurate reason, CD and AB will be congruent. the answer here is B) A congruent segment. 2. Option (A) is the right answer. We can construct a perpendicular bisector usind the given steps.

How to find the correct steps?

1. Form opening the compass to the length of AB you are setting the radius of the circle the compass could create to the same length of AB then by intersecting with the ray C, we have to copied the length of AB to ray C.

For that accurate reason, CD and AB will be congruent.

Therefore, The answer here is B) A congruent segment.

2. Given a segment with endpoints A and B.

By using the construction step we will draw the following figure that  represents a perpendicular bisector XY of line segment AB.

Hence, Option (A) is the right answer. We can construct a perpendicular bisector usind the given steps.

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63 POINTS!!!!!
Please help fast 1.4t-0.4(t-3.1)=5.8

t= what

Answers

1.4t - 0.4t - 1.24 = 5.8

1t -1.24 + 1.24 = 5.8 + 1.24

1t = 5.8 + 1.24

t = 7.04

hope this helps

Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot. Find the geometric mean of the pair of numbers. A. 20 ft B. 38.4 ft C. 55 ft D. 25 ft

Answers

Refer to the diagram below for the sketch of the position of the mirror, Michelle, and the flagpole.

Using similar triangle concept, to find the height of the flagpole, we first need to find out the scale factor of the horizontal distance. 
We write this as ratio
Mirror to Michelle : Mirror to Flagpole
            12ft             :             48ft
             1                :               4

So the ratio of the height is
Michelle : Flagpole
     1         :       4
    5ft       :      20ft

Answer: A

How many liters of a 10% alcohol solution must be mixed with 90 liters of a 60% solution to get a 30% solution?

Answers

Since 10% = 0.10 by moving the decimal two spots to the left, we can say that 0.10L is the amount of alcohol with 10% concentration in L liters. Similarly, 0.60L is 60% for L liters and 0.30L is the amount of liters with 30%. If the amount of 10% alcohol solution in liters is x and the 60% in y, we get 0.10x+0.60y=0.30L due to that the liters add up to get a 30% amount of alcohol (this equation represents the amount of alcohol). Next, x+y=L. Since we know that we have 90 liters of 0.60, y=90 and we have 
0.10x+54=0.30L 
x+90=L. Plugging x+90 for L, we get 0.10x+54=0.3(x+90)=0.3x+27. Subtracting 27 and 0.1x from both sides, we get 0.2x=27. Next, we can multiply both sides by 5 (since 1/0.2=5) to get x=135 liters

A number changed to 12.6 after it was rounded to what place was the number rounded what would the answer be




Answers

Answer:  "to the nearest tenths place" .
__________________________________________

two different ways to find the value of the expression 5.4 * 1.17 * 100 that do not require you to First multiply 5.4 X 1.17

Answers

Using the commutative property of multiplication, we get that 5.4*1.7*100=
5.4*100*1.7, so we could multiply 5.4 and 100 first, then by 1.7. In addition, we have 1.7*100*5.4 in where we multiply 1.7 and 100, then by 5.4

Solve formula please

Answers

c=PI*d

divide both sides by PI to get d by itself

d = c/PI

 . Which is equivalent to a drink made with 3 ounces of 80-proof vodka?

Answers

Omg frat part y lsolldlddld

Suppose there are two full bowls of cookies. bowl #1 has 10 chocolate chip and 30 plain cookies, while bowl #2 has 20 of each. our friend stacy picks a bowl at random, and then picks a cookie at random. we may assume there is no reason to believe stacy treats one bowl differently from another, likewise for the cookies. the cookie turns out to be a plain one. how probable is it that stacy picked it out of bowl #1?

Answers

its an even probability that she picked it out of either bowl, theyre trying to trick you by saying which bowl has more plain lol.

The that stacy picked it out of bowl #1 is 0.6

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Bowl 1 has 10 chocolate chip and 30 plain cookies, while Bowl #2 has 20 of each.

So, P[tex](H_1|E)[/tex]

= P( E| [tex]H_1[/tex]) P([tex]H_1[/tex]) / [  P( E| [tex]H_2[/tex]) P([tex]H_2[/tex] )+  P( E| [tex]H_1[/tex]) P([tex]H_1[/tex])  

= (0.75 x 0.5) / (0.75 x 0.5 + 0.5 x 0.5)

= 0.375 / (0.375 + 0.25)

= 0.6

Hence, the probability is 0.6

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which of the following is a solution set to 4|x+3|

Answers

It is absolute value. We also need more info because their is no solution set.

if f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?

Answers

Sent a picture of the solution.
Final answer:

To find (g-f)(3), evaluate g(3) and f(3), then subtract f(3) from g(3).

Explanation:

To find (g-f)(3), we need to subtract the function f(x) from g(x) and then evaluate the result at x = 3. Let's first simplify the expressions for f(x) and g(x):

f(x) = 4 - x^2

g(x) = 6x

Now substitute these into (g-f)(3) and simplify:

(g-f)(3) = g(3) - f(3)

= 6(3) - (4 - 3^2)

= 18 - (4 - 9)

= 18 - (-5)

= 23

Therefore, (g-f)(3) is equivalent to 23.

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What does information meanins

Answers

It's similarly to message.

What is the approximate base area of the resulting figure?
Area of a circle: A = πr2

Answers

Answer:   [tex]78.5\ cm^2[/tex]

Step-by-step explanation:

From the given we can see that there is a  rectangle is rotated about a line bisecting its length in segment of 5 cm in each.

Since the base will be a circle, then the area of the base will be :-

[tex]\text{Area of base}=\pi r^2\\\\\\\Rightarrow\text{Area of base}=3.14\times(5)^2\\\\\\\Rightarrow\text{Area of base}=78.5\ cm^2[/tex]

Hence, the base area of the resulting figure = [tex]78.5\ cm^2[/tex]

The approximate base area of the rectangle is rotated about a line bisecting its length in segments of 5 cm in each is 78.5.

From the given, we can see that there is a  rectangle is rotated about a line bisecting its length in segments of 5 cm in each.

Since the base will be a circle, then the area of the base will be

What is the area of the base?

A=pir^2

Where r is the radius of the circle.

A=3,14(5)^2

A=78.5.

Therefore, the approximate base area of the resulting figure is 78.5.

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