Mathematics College

Keith has p pennies, n nickels, and d dimes in his pocket. The total number of coins is 9. The expression 0.01p+0.05n+0.10d represents the value of the coins, which is equal to $0.44. He has one more dime than nickels. How many pennies does Keith have? Keith has _____ pennies.

Answers

Answer 1

he has 4 pennies

2 nickels=10 cents

3 dime=30 cents

20 cents

40 +4 pennies =44 cents

Answer 2

Answer:

Keith has 4 pennies, 3 dimes and 2 nickels.

Step-by-step explanation:

Let the pennies be = p

Let the nickels be = n

Let the dimes be = d

Total coins Keith has = 9

So, 1st equation form :

[tex]p+n+d=9[/tex] ....(1)

Keith has one more dime than nickels, means [tex]d=n+1[/tex] .....(2)

Total value of these coins is $0.44

So, third equation forms:

[tex]0.01p+0.05n+0.10d=0.44[/tex] .....(3)

Substituting (2) in (1)

[tex]p+n+n+1=9[/tex]

[tex]p+2n=8[/tex] .....(4)

Similarly substitution (2) in (3)

[tex]0.01p+0.05n+0.10(n+1)=0.44[/tex]

[tex]0.01p+0.05n+0.10n+0.10=0.44[/tex]

[tex]0.01p+0.15n=0.34[/tex] ....(5)

Now multiplying (4) by 0.01 and subtracting by (5)

[tex]0.01p+0.02n=0.08[/tex] subtracting this from (5) we get

[tex]0.13n=0.26[/tex]

So, we get n = 2

[tex]p+2n=8[/tex]

[tex]p+2(2)=8[/tex]

[tex]p+4=8[/tex]

p = 4

[tex]p+n+d=9[/tex]

[tex]4+2+d=9[/tex]

[tex]6+d=9[/tex]

d = 3

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

Therefore, Keith has 4 pennies, 3 dimes and 2 nickels.

Related Questions

I keep getting 13. It's supposed to be 3. Can you show me how it's done? 3(a-5) = -6

Answers

First, divide both sides by 3. I think your mistake was that you were multiplying -3. Please note that in order to cancel something out you need to do the reverse operation. The reverse operation of subtraction is addition and the reverse of multiplication is division.

3(a - 5) = -6
a - 5 = -2

Now add 5 to both sides

a - 5 = -2
+5 +5
a = 3

Hope this helps!

3(a-5) = -6

Start by distributing...

3a - 15 = - 6

Add 15 to both sides...

3a = 9

Divide both sides by 3 to get a by its self

a = 3

The driver of a car traveling at 54ft/sec suddenly applies the brakes. The position of the car is s=54t-3t^2, t seconds afyer the driver applies the brakes.
How many seconds after the driver applies the brakes does the car come to a stop

Answers

s = 60t - 3t^2
v = ds/dt = 60 - 6t

when it comes to rest, v = 0,
so t = 10 sec

now distance travelled = time taken x average velocity
= 10 x (60 + 0)/2
= 300 ft

After time [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.

What is time?

" Time is defined as the measurable slot of period in which required action is done."

Formula used

[tex]y = x^{n} \\\\\implies \frac{dy}{dx} = nx^{n-1}[/tex]

According to the question,

Position of the car [tex]'s' = 54t - 3t^{2}[/tex]

[tex]'s'[/tex] represents the distance

[tex]'t'[/tex] is the time in seconds

When driver applies break [tex]v= 0[/tex],

[tex]v = \frac{ds}{dt}[/tex]

Calculate the first derivative with respect to time we get,

[tex]'s' = 54t - 3t^{2}\\\\\implies \frac{ds}{dt} = 54- 6t[/tex]

As [tex]\frac{ds}{dt} =0[/tex] we get the required time as per given condition,

[tex]54-6t =0\\\\\implies 6t =54\\\\\implies t = 9[/tex]

Hence, after time [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.

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What percent of 9.2 is 43.7

Answers

if we take 9.2 to be the 100%, what is 43.7 off of it in percentage then?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 9.2&100\\ 43.7&p \end{array}\implies \cfrac{9.2}{43.7}=\cfrac{100}{p}\implies p=\cfrac{43.7\cdot 100}{9.2}[/tex]

The requried 475% of 9.2 is 43.7, as of the given percentage situation.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
In the question, we are asked to determine the 43.7 is what percent of 9.2.

So, let the percent be x,
x % of 9.2 = 43.7
x/100 × 9.2 = 43.7
x = 43.7/9.2 × 100%
x = 475%

Thus, the requried 475% of 9.2 is 43.7, as of the given percentage situation.

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the weight of an object on the moon is about .167 of its weight on Earth. How much does a 180 lb astronaut weigh on the moon?

Answers

[tex]\bf \begin{array}{ccll} \stackrel{lbs}{earth}&\stackrel{lbs}{moon}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&0.167\\ 180&x \end{array}\implies \cfrac{1}{180}=\cfrac{0.167}{x}\implies x=\cfrac{180\cdot 0.167}{1}[/tex]

The astronaut will weigh less on the moon. Determine how much the scale will indicate by multi. 180 lb by 0.167: (180 lb)(0.167) = 30.06 lb.

If f(x) = 3x + 6, which of the following is the inverse of f(x)?

A. f –1(x) = 3x – 6
B. f –1(x) =
C. f –1(x) =
D. f –1(x) = 6 – 3x

Answers

Final answer:

To determine the inverse of the function f(x) = 3x + 6, you need to switch 'x' and 'f(x)', isolate f-1(x) on one side of the equation, then solve for f-1(x). The resulting inverse function is f-1(x) = (x - 6)/3.

Explanation:

The function given is f(x) = 3x + 6. To find the inverse of this function, we first need to switch 'x' and 'f(x)', giving us: x = 3f-1(x) + 6. Next, we want to isolate f-1(x) on one side of the equation. To do this, we subtract 6 from both sides of the equation resulting in: x - 6 = 3f-1(x). Finally, we divide all terms by 3 to solve for f-1(x), which gives us f-1(x) = (x - 6)/3. So, the correct answer from the options given is not listed.

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Find all values of x that are simultaneously a solution to the congruences x ≡ 2 (mod 3), x ≡ 1 (mod 5), x ≡ 3 (mod 29).

Answers

[tex]\begin{cases}x\equiv2\pmod3\\x\equiv1\pmod5\\x\equiv3\pmod{29}\end{cases}[/tex]

Let's start by supposing [tex]x=2+3+3=11[/tex]. Modulo 3, we end up with 2 as needed.

But modulo 5, we want to get 1, so we'd need to multiply the first and last terms by 5 and the second term by the inverse of 3 modulo 5. We have [tex]3\times2\equiv6\equiv1\pmod5[/tex], so we multiply by 2:

[tex]x=2\times5+3\times2+3\times5=31[/tex]

But now modulo 3, the first term gives a remainder of 1, so simply multiply by 2:

[tex]x=2\times5\times2+3\times2+3\times5=41[/tex]

Next, modulo 29, we can force the first two terms to vanish by multiplying them by 29, but the last term still yields 15. We want to get 3 on its own, so we could just multiply the third term by the inverse of 5 modulo 29. We have [tex]5\times6\equiv30\equiv1\pmod{29}[/tex].

[tex]x=2\times5\times2\times29+3\times2\times29+3\times5\times6=844[/tex]

Now, [tex]844\equiv1\pmod3[/tex], so we need to multiply the first term by 2 one more time; [tex]844\equiv4\pmod5[/tex], so we need to multiply the second term by the inverse of 4 modulo 5, which would be 4 since [tex]4^2\equiv16\equiv1\pmod5[/tex]; and [tex]844\equiv3\pmod{29}[/tex], so the last term is okay.

[tex]x=2\times5\times2\times29\times2+3\times2\times29\times4+3\times5\times6=1946[/tex]

We know 1946 is a possible solution because we engineered it that way, but it's not the smallest positive solution. We have

[tex]1946\equiv206\pmod{3\times5\times29}\equiv206\pmod{435}[/tex]

The general solution to the system is then [tex]x=206+435n[/tex], where [tex]n\in\mathbb Z[/tex].

If s = {r, u, d} is a set of linearly dependent vectors. if x = 5r + u + d, determine whether t = {r, u, x} is a linearly dependent set

Answers

Consider any arbitrary linear combination of the vectors [tex]\mathbf r,\mathbf u\,\mathbf x[/tex]. We have

[tex]c_1\mathbf r+c_2\mathbf u+c_3\mathbf x=c_1\mathbf r+c_2\mathbf u+c_3(5\mathbf r+\mathbf u+\mathbf d)[/tex]
[tex]=(c_1+5c_3)\mathbf r+(c_2+c_3)\mathbf u+c_3\mathbf d[/tex]
[tex]=c_4\mathbf r+c_5\mathbf u+c_6\mathbf d[/tex]

We know [tex]\mathbf r,\mathbf u,\mathbf d[/tex] are linearly dependent, which means there must exist some choice of not all zero constants [tex]c_4,c_5,c_6[/tex] such that the combination above gives the zero vector. So [tex]T=\{\mathbf r,\mathbf u,\mathbf x\}[/tex] is a set of linearly dependent vectors.

Write the equation of a line, in general form , that has an slope of zero and a y-intercept of (0, -6).

Answers

Use the slope-intercept form.
y = mx + b,

where m = slope and b = y-intercept.
Your y-intercept is -6, so b = -6.
The slope is zero, so m = 0

y = mx + b

y = 0x + (-6)

y = -6

PLEASE HELP 15 POINTS WILL GIVE BRAINLIEST The following formula, F = ma, relates three quantities: Force (F), mass (m), and acceleration (a). A: Solve this equation, F = ma for a. B If F = -24 units and m = 10 units, what is the acceleration, a? Use the equation from Part (a) to answer the question. C: If F = 24 units and a = 12 units, what is the mass, m? Use the equation, F = ma, to plug in the known values and solve for m

Answers

Part A

The expression "ma" is the same as "m*a" (m times a). To isolate 'a', we divide both sides by m. Division is the inverse operation of multiplication. Think of it as undoing multiplication

F = ma
F = m*a
F/m = m*a/m
F/m = a
a = F/m

Answer: a = F/m
Note: the slash "/" without quotes means "divide"

===========================================
Part B

Use the result from part A. We will plug F = -24 and m = 10 into that equation

a = F/m
a = -24/10
a = -2.4

Answer: -2.4

===========================================
Part C

We will use the equation F = m*a

F = m*a
24 = m*12 ... plug in F = 24 and a = 12
24/12 = m*12/12
2 = m
m = 2

Answer: 2

Toby exercises 14 hours a week. John exercises 20% more than Toby and Jenny exercises two more hours than John. Which expression represents how much Jenny exercises? (w represents weeks)

Answers

John exercised 20% more than Toby. So the number of hours that John exercises per week is 14 + 0.2(14) = 14 + 2.8 = 16.8.

Jenny exercises two more hours than John. So the number of hours that Jenny exercises per week is 16.8 + 2 = 18.8.

So an expression representing the number of hours that Jenny exercises after w weeks is 18.8w.

the answer is 18.8w

Toby 14w

John 14(1.2)w

Jenny 14(1.2)w + 2w

thus, Jenny exercise

14(1.2)w + 2w

16.8w + 2w

18.8w

Suppose 8 out of every 20 students are absent from school less than 5 days a year.Predict how many students would be absent less than 5 days a year out of 40,000 students.

Answers

Answer:
8/20 * 40,000 = 16,000

12 PTS!!!

John ordered two kinds of pizza for a party: sausage pizzas and veggie pizzas. He ordered three pizzas of each kind. The pizzas cost a total of $99. If the cost of each veggie pizza is $18, what is the cost of a sausage pizza?

Answers

99-18= 81/3=27
Answer: 27

1 veggie pizza cost 18 so 3 cost 18*3 = 54

99-54 = 45 for the 3 sausage pizzas

45/3 = 15 dollars each for sausage

explain how you could find 3/8% of 800

Answers

3/8 of 800 is 300.. 3/8 of 800 is really 300.To check, take 3/8 and convert it to .375. Then, find what .375 of 800 is... 300!
Also, you can see that 3/8 and 800 can easily be converted to a common denominator... 800. So, just add 2 zeros to 3, and you get 300!

First turn 3/8 into a decimal, which would be .375 Next the key word of in 3/8% of 800 tells us to multiply 3/8% and 800 so since we know 3/8% = .375 in decimal form, lets multiply .375 x 800 = 300 so 3/8% of 800 is 300

a construction crew Must build 4 miles of road in one week on Monday they build 1/2 mile of road in one week on Tuesday they build 1/3 mile of road how many more miles of road are left to build

Answers

To solve this, you need to make the amount they built on Monday and the amount they built on Tuesday compatible with each other so you can add them together to subtract that amount from 4.

Start by multiplying 1/2 by 3, and 1/3 by 2.

This gives you 3/6 and 2/6. Now add them together:

3/6 + 2/6 = 5/6

Finally, subtract this amount from 4:

4 - 5/6 = 3 1/6 (19/6 works too)

Hope this helps! :)

4 - 1/2 - 1/3
24/6 - 3/6 - 2/6 = 19/6 = 3 1/6

what is the least common denominator for 5/6 and 3/8

Answers

The least common denominator is 24.

How many different 4-digit sequences can be formed using the digits 0, 1,..., 6 if repetition of digits is allowed

Answers

0 through 6 is 7 total numbers

1st digit can be 0-6 = 7 numbers

2nd digit can be 0-6 = 7 numbers

3rd digit can be 0-6 = 7 numbers

4th digit can be 0-6 = 7 numbers

7 * 7 *7 *7 = 2401 different combinations

Two small fires are spotted by a ranger from a fire tower 60 feet above ground. The angles of depressions re 11.6° and 9.4°. How far apart are the fires? (The fires are in the same general direction from the tower.)

Answers

The two fires are about 70 feet from each other. The assumption is that the ground is relatively level and that a right triangle will be made with the three points of the triangle being the ranger, the spot on the ground directly beneath the ranger, and the fire itself. So the distance to the first fire will be: Calculate the angle. That will be 90° - 11.6° = 78.4° The distance will be tan(78.4) = X/60 60 tan(78.4) = X 60 * 4.871620136 = X 292.2972082 = X And that's how far the 1st fire is from the ranger's station. Now for the 2nd angle = 90° - 9.4° = 80.6° 60 tan(80.6) = X 60 * 6.040510327 = X 362.4306196 = X And the distance between the two fires will be the difference in distance from the tower, so 362.4306196 - 292.2972082 = 70.13341146 Rounding to 2 significant figures gives 70 feet.

five friends went to a local restaurant and all had the buffet at $6.75 each. the following is the restaurant bill. does it seem reasonable 5($6.75) =&67.50

Answers

No I think not really to sure

Yes because your food had cost $6.75 each for 5 people, so if you had a bill of $67.50 and your concern about is it reasonable just budget it out.

A car manufacturer claims that, when driven at a speed of 50 miles per hour on a highway, the mileage of a certain model follows a normal distribution with mean μ = 30 miles per gallon and standard deviation σ= 4 miles per gallon.

Answers

84 miles per gallon maybe

Find the rate of change of the area of a square with respect to the length z , the diagonal of the square. what is the rate when z=2?

Answers

The diagonal of a square is equal to the side x times square root of 2, xSqrt(2)
z = xSqrt(2), its rate of change is just Sqrt(2)

The rate of change of Area, A with respect to the diagonal length, z and the rate of change when z = 2 is :

[tex]\frac{dA}{dz} = z [/tex]

[tex]\frac{dA}{dz} = 2 \: when \: z = 2 [/tex]

The area of a square is rated to its diagonal thus :

Area of square = A

Length of diagonal = z

The relationship between Area and diagonal of a square is : [tex]A \: = 0.5 {z}^{2} [/tex]

The rate of change of area with respect to the length, z of the square's diagonal ;

This the first differential of Area with respect to z

[tex] \frac{dA}{dz} = 2(0.5)z \: = z[/tex]

Therefore, the rate of change of area, A with respect to the length, z of the diagonal is [tex]\frac{dA}{dz} = z [/tex]

The rate of change [tex]\frac{dA}{dz} [/tex] when z = 2 can be calculated thus :

Substitute z = 2 in the relation [tex]\frac{dA}{dz} = z [/tex]

Therefore, [tex]\frac{dA}{dz} = 2 [/tex]

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Find the difference: 16.25 - 7.92

Answers

Your answer is going to be 8.33

the difference is 8.33.
give me the best plz

Mr. Carandang sold a total of 1,790 prints of one of his drawings. Out of all 1,273 unframed prints that he sold, 152 were small and 544 were medium-sized. Out of all of the framed prints that he sold, 23 were small and 42 were extra large. Of the large prints that he sold, 188 were framed and 496 were unframed. Small Medium Large Extra Large Total Framed 23 264 188 42 ? Unframed 152 544 496 81 1,273 Total 175 808 684 123 1,790 Which number is missing from the two-way table?'

Answers

framed unframed total
small 23 152 175
medium 264 544 808
large 188 496 684
ex-large 42 81 123
total 517 1273 1790

The missing number in the two-way table is the total number of framed prints, which is 517. This is calculated by subtracting the total unframed prints from the total prints sold and then summing the known framed prints.

To find the missing number of prints in the table, we need to determine the total number of framed prints sold by Mr. Carandang. We know the following from the table:

Total prints sold: 1,790Unframed prints: 1,273

To find the total number of framed prints:

Total framed prints = Total prints - Total unframed prints

Total framed prints = 1,790 - 1,273 = 517

Now we need to sum the known framed prints:

Framed small: 23Framed medium: 264Framed large: 188Framed extra large: 42

The total of known framed prints is:

23 + 264 + 188 + 42 = 517

Thus, the total framed prints value was missing and it is 517.

Express 9.21212121212... as a rational number, in the form pq

Answers

[tex]x=9.212121\ldots=9.\overline{21}[/tex]
[tex]100x=921.212121\ldots=921.\overline{21}[/tex]
[tex]99x=921.\overline{21}-9.\overline{21}=921-9=912[/tex]
[tex]\implies x=\dfrac{912}{99}=\dfrac{304}{33}[/tex]

The GCF of any two even numbers is always even. true or false?

Answers

your answer is false.

True because if you use prime factorization of even numbers you will always get a 2. If a number has 2 as a factor then it is even.

Please need help as quick as you can . What is the slope of the line that passes through the points (16, –1) and (–4, 10)? A. -20/11 B. -11/20 C. 11/20 D. 20/11

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 16}}\quad ,&{{ -1}})\quad % (c,d) &({{ -4}}\quad ,&{{ 10}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-(-1)}{-4-16}\implies \cfrac{10+1}{-4-16} \\\\\\ -\cfrac{11}{20}[/tex]

Use an algebraic rule to describe a translation right 4 units and down 2 units.

Answers

In the conventional Cartesian plane, horizontal coordinates increase to the right and vertical coordinates increase up. Hence the described translation adds 4 to each horizontal coordinate and -2 to each vertical one:
(x, y)⇒(x+4, y-2)

What is the value of |−25|?

Answers

Hi there!!

The answer to this is |-25| = 25.

Hope this helped!! ☺♥

the answeeeeerrrr is positive 25!!,!

Given e(x + 4) = 10 and e[(x + 4) 2 ] = 116, determine (a) var(x + 4), (b)μ= e(x), and (c)σ 2 = var(x).

Answers

a. [tex]\mathbb V(X+4)=\mathbb E((X+4)^2)-\mathbb E(X+4)^2=116-10^2=16[/tex]

b. [tex]\mathbb E(X+4)=\mathbb E(X)+\mathbb E(4)=\mathbb E(X)+4=10\implies\mathbb E(X)=6[/tex]

c. [tex]\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2[/tex]

[tex]\mathbb E((X+4)^2)=\mathbb E(X^2+8X+16)=\mathbb E(X^2)+8\mathbb E(X)+\mathbb E(16)[/tex]
[tex]\implies116=\mathbb E(X^2)+48+16\implies\mathbb E(X^2)=52[/tex]

[tex]\implies\mathbb V(X)=52-6^2=16[/tex]

Final answer:

In the given statements, first 'x' is derived from the equation e(x + 4) = 10, then it is plugged into e(x) to find μ and the variance formula to obtain σ².

Explanation:

The question presents a scenario with two equations: e(x + 4) = 10 and e[(x + 4) 2 ] = 116 .To solve these equations, you would need to employ various algebraic and statistical concepts. Given this information, let's procede as follows:

To find (a) var(x + 4), we first need to determine the value of 'x' which can be derived from the given e(x + 4) = 10. After calculating 'x', we can work out (b)μ= e(x) by inserting our calculated 'x' into the e(x) formula. Finally, σ 2 = var(x) can be computed by applying 'x' in the variance formula.

Please note, this solution requires a good understanding of the properties of exponential functions and the statistical representation of variance (var), mean (μ), and standard deviation (σ²). Due to the complexity of these equations, I recommend using a calculator to accurately work out each part.

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Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 128 meters

Answers

P = 128 meters = 2W + 2L. We want to maximize the area: A = L*W

Solve 128 meters = 2W + 2L for either W or L:

64 meters = W + L, so W = 64-L
and subst. your result into

A = L*W: A = L*(64-L). Then A(L) = 64L - L^2. You could graph this and find the approx value of L at which A(L) is at its max.

Or, if you know calculus, differentiate A(L) and set the result = to 0. Solve for L.

L + W = 64, so you can subst. your value for L into this eqn to find W.

In Miss Marshalls classroom 6/7 of the students play sports of the students who play sports for fifth also play instruments if there are 35 students in her class how many play sports and instruments

Answers

6/7 time 4/5 = 24/35
24 students do both.

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