After solving the equations, it is found that there are 32 pennies in the jar.
To solve the problem of determining the number of pennies in the jar, first we establish two variables: let's denote P for the number of pennies and N for the number of nickels.
According to the problem, there are 56 coins in total, which gives us the equation P + N = 56. Also, we know that the total value of the coins is $1.52, and because each penny is worth 1 cent and each nickel is worth 5 cents, we have another equation, which is P + 5N = 152 (since there are 100 cents in a dollar).
Now we have a system of two equations to work with:
P + N = 56
P + 5N = 152
To find P, we can subtract the first equation from the second equation to eliminate P and solve for N:
0P + 4N = 96
N = 96 / 4
N = 24
Now that we know there are 24 nickels, we can find the number of pennies by substituting N back into the first equation:
P + 24 = 56
P = 56 - 24
P = 32
Therefore, there are 32 pennies in the jar.
If the odds of the steelers beating the chiefs are 7 to 4, what is the probability of this event happening?
How many ounces are there in a gallon?
and how would I come about solving this?..
The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. if you select a random sample of 9 tennis balls, what is the probability that the sample mean is between 2.62 and 2.64 inches
Final answer:
The probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%, calculated using the Central Limit Theorem to find the standard error and z-scores.
Explanation:
To calculate the probability that the sample mean diameter of the tennis balls is between 2.62 and 2.64 inches, we can use the Central Limit Theorem since we are dealing with a sample of tennis balls rather than just one. The Central Limit Theorem tells us that the sampling distribution of the sample mean will be normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is called the standard error (SE).
Given that the population mean (μ) is 2.63 inches, the population standard deviation (σ) is 0.03 inch, and the sample size (n) is 9, we first calculate the standard error (SE) as follows:
SE = σ / √n = 0.03 / √9 = 0.03 / 3 = 0.01 inch.
Next, we convert the sample mean range (2.62, 2.64) to z-scores, which are measures of how many standard deviations an element is from the mean.
Z for 2.62 = (2.62 - μ) / SE = (2.62 - 2.63) / 0.01 = -0.01 / 0.01 = -1
Z for 2.64 = (2.64 - μ) / SE = (2.64 - 2.63) / 0.01 = 0.01 / 0.01 = 1
Using a standard normal distribution table or calculator, we find the probabilities corresponding to these z-scores. The probability of a z-score being between -1 and 1 is approximately 0.6827 (68.27%).
Therefore, the probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%.
how to write 293,805 in standard and expanded form
Add (11a + 4b) + (a +4b - 2)
A) 12a + 8b - 2
B) 12a - 2
C) 11a - 2
D) 11a + 8b - 2
I need help with a homework assignment:
Write each series in summation notation beginning with k = 1.
1/2 + 2/3 + 3/4 + 4/5 + 5/6
−11 + 12 − 13 + 14 − 15 + 16
9 − 16 + 25 − 36 + 49 − 64
3 + (3/2) + 1 + (3/4) + (3/5)
I get the numbers that go under and on top of the sigma, I need help deriving the explicit value for the sequence that goes on the right of the sigma.
Thanks
The assembly department started the month with 17,500 units in its beginning work in process inventory. an additional 288,000 units were transferred in from the prior department during the month to begin processing in the assembly department. there were 29,250 units in the ending work in process inventory of the assembly department. how many units were transferred to the next processing department during the month?
A 8.5
B 8.1
C 12.5
D 12.9
Let f(x) = -10x-18 and g(x) = -3x, find (f-g)(x)
karens penny bank is 1/5 full. after she adds 280 pennies it is now 7/10 full how many pennies can karens bank hold?
7/10-1/5 = 7/10-2/10 = 5/10 = 1/2
so 280 pennies fills 1/2 of her piggy bank
so 280*2 = 560
her piggy bank can hold 560 pennies
Which is a correct first step for solving this equation?
2x−1(5−3x)=4x+2
Y=0, what is x when y=x^2-6x+9
Simplify 2(f^4)^2 f^3 divided by 6f^9
Final answer:
The expression 2(f^4)^2 f^3 divided by 6f^9 simplifies to 1/3 f^2, after applying the properties of exponents and dividing coefficients.
Explanation:
To simplify the expression 2(f^4)^2 f^3 divided by 6f^9, we need to use the properties of exponents. First, we simplify (f^4)^2 by multiplying the exponents, which gives us f^8.
Then, we multiply f^8 by f^3 to get f^11. Next, we divide our new expression 2f^11 by 6f^9. This can be done by dividing the coefficients (2 divided by 6) and subtracting the exponents of f (11 minus 9), resulting in f^2 over 3, or 1/3 f^2.
A computer printer can print a 800-word document in 32 seconds. At this rate, how many seconds are required to print a document that contains 880 words?
Explain why the functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.
Please see attached document for the graphs:
The functions with the given graphs can't be solutions of
the differential equation dy dt = et(y − 1)2.
(a) won’t work, since it has negative slope on portions of its solutions. The
slope, e t (y − 1)2 , is a nonnegative function.
(b) won’t work, since it has positive slope at y = 1, where the slope must be flat.
Functions with given graphs cannot be solutions to the differential equation dy / dt = e^t(y-1)^2 because their graphs don't satisfy the conditions imposed by the equation, such as non-oscillatory behavior and non-linear variation with time.
Explanation:The question pertains to why certain functions represented by their graphs cannot be solutions to the differential equation dy / dt = et(y-1)2. The explanation lies in the structure of the given differential equation and the properties of function graphs.
Equation dy / dt = et(y-1)2 is a non-linear first order differential equation. To be a solution to this equation, a function's graph must satisfy certain conditions imposed by the equation. However, if certain function graphs represent an undefined curve or if their graphs demonstrate oscillatory behavior, they do not satisfy these criteria.
For instance, the differential equation demands non-oscillatory behavior as seen in the general solution provided in the reference: Yn(x) = Ce-Bx +De+Bx. This form describes a gradual attenuation of y(x), i.e., it does not oscillate. Similarly, if a graph represents a function that varies non-linearly with time (like In[A] vs. Time), it does not represent a solution to the differential equation as well.
Thus, the inability of certain function graphs to satisfy the conditions required by the given differential equation is the reason they cannot be its solutions.
Learn more about Differential Equations here:https://brainly.com/question/33433874
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A _____ is the composition of a translation and a reflection across a line parallel to the direction of translation. glide reflection tessellation rotation dilation
Answer:
Glide reflection
Step-by-step explanation:
A glide reflection is a composition of a translation and a reflection across a line parallel to the direction of translation. A glide reflection requires a translation on a figure, which is then reflected over a line. This is a symmetry operation that requires a translation rule and a line to reflect over. A common example of this are footsteps in the sand.
Ellen has $75 in her savings account. She deposits $25 every week. Her father also deposits $35 into the account every time Ellen mows the lawn. Her savings account balance can be shown with the following expression: 75 + 25w + 35m Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points) Part B: If Ellen saves for 8 weeks and mows the lawn 2 times, how much will she have in her account? Show your work to receive full credit. (4 points) Part C: If Ellen had $95 in her savings account, would the coefficient, variable, or constant in the expression change? Why?
Simplify 1/3(9a+b)-1/2(4a+2b)
3x+17-5x=12-(6x+3) can someone help
A can in the shape of a right cylinder is filled with 10W-40 oil. The weight of 10W-40 oil is 0.857 gram per cubic centimeter. If the cylinder has a radius of length 5 cm and a height of 10 cm, calculate the weight of the oil (in grams) in the can. Round your answer to the nearest tenth. Use 3.14 for pi
Answer: Weight of the oil is 672.74 grams.
Step-by-step explanation:
Since we have given that
Radius of cylinder = 5 cm
Height of cylinder = 10 cm
Volume of cylinder would be
[tex]\pi r^2h\\\\=3.14\times 5\times 5\times 10\\\\=785\ cm^3[/tex]
Weight of 10W-40 oil = 0.857 grams per cubic cm
So, Weight of the oil in the can would be
Volume × Weight per cm³
[tex]=785.71\times 0.857\\\\=672.74\ grams[/tex]
Hence, Weight of the oil is 672.74 grams.
If Q is directly proportional to P and Q = 28 when P = 4
i) express Q in terms of P
ii) find the value of Q when P=5
iii) calculate the value of P when Q = 42
Answer:
May be !
i> Q = 7P
ii> when p =5 then from above eqn we can find Q = 7p and = 7×5=35
iii> from eqn i we can write p = Q/7 So when Q=42 then P=Q/7=42/7=6
A triangle is dilated by a scale factor of n = 1/3 . Which statement is true regarding the dilation?
It is a reduction because n > 1.
It is a reduction because 0 < n < 1.
It is an enlargement because n > 1.
It is an enlargement because 0 > n > 1
Answer: The second statement is true. It is a reduction because 0 < n < 1.
Step-by-step explanation:
Given: A triangle is dilated by a scale factor of n = 1/3 .
as n is less than 1 but greater than 0.
A dilation is a rigid transformation that forms an image that is the same shape as of the original figure, but with a different size. A dilation transform a figure by scalar factor 'n' about the center of dilation is a fixed point in the plane which never change.
A dilation that forms a larger image is known as enlargement. A dilation that forms a smaller image is known as reduction.
• If n is greater than 1, then the image is an enlargement.
• If n is between 0 and 1, then the image is a reduction .
• If n is 1, the figure and then the image are exactly same.
Answer:
2nd statement
Step-by-step explanation:
A parachutist's rate during a free fall reaches 165 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Answer: [tex]250\ m[/tex]
Step-by-step explanation:
Assuming that:
[tex]1\ m=3.3\ ft[/tex]
We can make the conversion from feet per second to meters per second with this procedure:
[tex](165\ \frac{ft}{s})(\frac{1\ m}{3.3\ ft})=50\ \frac{m}{s}[/tex]
Let be "x" the amount of meters the parachutist will fall during 5 seconds of free fall
Knowing that in 1 second the parachutist falls 50 meters, we can calculate "x" by solving the following multiplication:
[tex]x=(50\ \frac{m}{s})(5\ s)\\\\x=250\ m[/tex]
The parachutist's rate of free fall is 165 feet per second, which is equivalent to 50 meters per second. The parachutist will fall approximately 250 meters during 5 seconds of free fall.
Explanation:To convert the rate of 165 feet per second to meters per second, we need to use the conversion factor of 1 meter equals 3.3 feet. So, the rate in meters per second is 165 feet per second divided by 3.3 feet per meter, which equals 50 meters per second.
To find how many meters the parachutist will fall during 5 seconds of free fall, we can multiply the rate of 50 meters per second by the time of 5 seconds. This gives us 250 meters of free fall during 5 seconds.
you are dealt one card from a standard 52 card deck. Find the probability of being dealt a heart
13 hearts
a 13/52 probability.
that reduces to a 1/4 probability of getting a heart
Lebron scored a basket 72 times out of 150 shots. what percent of his shots did he score?
a. 42%
b. 50%
c. 48%
d. 63%
1 gallon of paint pour the paint into a paint tray that measures 10 inch wide 10 inch long and 7 cm deep what will happen
1 gallon = 231 cubic inches
7cm = 2.75591 inches ( round to 2.76 )
10 x 10 x 2.76 = 276 cubic inches
there will be more than enough room for the gallon of paint
276-231 = 45 cubic inches of space left over
05.01)A company makes triangular plates for individual slices of pizza. For each plate, the base is 5 inches and the height is 16 inches. The area of the top of the plate is ____ inches squared
Answer: 40 inches squared
Step-by-step explanation:
1. first, you multiply, do 5*16 what does that give you? (80)
2. then, divide your answer by 2 what do you get? (40)
3. lastly, it should look like this: 5*16=(answer)/2=(answer)
hope this helps
If a pitcher strikes out 5 batters in 4 innings how many batters is it likely he will strike out in, 9 innings round to the nearest whole number
The Darnells are having a swimming pool installed. The pool has a radius of 14 feet and a height of 4 feet. What is the volume of the pool? Use 3.14 for pi .
volume = pi x r^2 x h
3.14 x 4 x 14^2 = 2461.76 cubic feet
Fixed the typo I had in my answer.
Answer:
So volume of the swimming pool is 2461.76 feet³.
Step-by-step explanation:
The Darnells are having a swimming pool installed.
The pool has a radius of 14 feet and height of 4 feet.
Since pool is in the form of a cylinder so volume of cylinder
= πr²h
= π (14)² × 4
= (3.14) (196) × 4
= 2461.76 cubic feet.
So volume of the swimming pool is 2461.76 feet³.
square root of 4 plus 45 over 4 plus 125 over 25