Cheryl falkowski has a collection of silver spoons from all over the world. she finds that she can arrange her spoons in sets of 77 with 44 left over, sets of 88 with 33 left over, or sets of 1515 with 1414 left over. if cheryl has fewer than 200 spoons, how many are there?
Answers
.. 14, 29, 44, 59, 74, 89, 104, 119, 134, 149, 164, 179, 194 (separated by 15)
Modulo 8, these numbers are
.. 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2
This reduces the numbers of interest to those that are 3 modulo 8:
.. 59, 179 (separated by 8*15 = 120)
Looking at these modulo 7, we have
.. 3, 4
pinpointing 179 as the number of spoons in Cheryl's collection.
_____
The attachment shows a solution via graphing calculator. We simply added the absolute values of the differences of the remainders from the desired values and looked for where that sum was zero. This method, too, pointed to 179 as the solution to the problem.
Related Questions
EXPERTS/ACE/GENIUSES HELP PLZ!!:)
( only #2 )
Explain as well!! Best answer will get brainlist... but make ur answer short and sweet plz.
Answers
(a) Volume of 1st cup = (1/3)pi *(4/2)^2 * 8 = 32/3 pi in^3
scoops = (2000/3)pi / ( 32/3) pi = 2000/32 = 62.5 = 63
(b) Volume of 2nd cup = (1/3)pi *(8/2)^2 * 8 = 128/3 pi in^3
scoops = (2000/3)pi / ( 128/3) pi = 2000/128 = 15.625 = 16
which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9
Answers
[tex]x^2+2x-8=(x+4)(x-2)[/tex]
In the denominator we have a difference of squares:
[tex]x^2-9=x^2-3^2=(x+3)(x-3)[/tex]
Now we can rewrite our function:
[tex]y= \frac{x^2+2x-8}{x^2-9} = \frac{(x+4)(x-2)}{(x+3)(x-3)} [/tex]
From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at [tex]x=3[/tex] and [tex]x-3[/tex]
We can conclude that the graphic of our rational function is:
Consider a game in which a coin will be flipped three times. for each heads you will be paid $100. assume that the coin comes up heads with probability 4/5.
Answers
The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle? A. length = 20 inches, width = 17 inches B. length = 17 inches, width = 14 inches C. length = 10 inches, width = 7 inches D. length = 34 inches, width = 10 inches
Answers
To find the length and width of a rectangle given its area and the relationship between its dimensions, set up and solve an equation by following the step-by-step process.
Explanation:Given: The width of a rectangle is 3 inches less than its length and the area is 340 square inches.
To solve: Let the length be 'x' inches, then the width is 'x - 3' inches. Set up the equation 'x(x - 3) = 340', solve for 'x' to find the length and width.
Step-by-step:
Express the area as a product of the length and width: 'x(x - 3) = 340'.Expand and rearrange the equation: 'x^2 - 3x - 340 = 0'.Factor the quadratic equation: '(x + 17)(x - 20) = 0'.Solve for 'x': 'x = -17' or 'x = 20'. Since length cannot be negative, the length is 20 inches.Calculate the width: '20 - 3 = 17 inches'.what is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6
a. -6
b. 7
c. x+2
d. 2x-3
Answers
Final answer:
The greatest common factor (GCF) of the numerator and denominator in the rational expression (7x+14)/(2x²+x-6) is x+2. Thus, option C is correct.
Explanation:
To find the greatest common factor (GCF) of the numerator and denominator of the given rational expression (7x+14)/(2x²+x-6), we need to factor both the numerator and the denominator separately.
For the numerator 7x+14, we can factor out a 7:
7x + 14 = 7(x + 2)
For the denominator 2x² + x - 6, we need to factor it as a quadratic expression. This can be done by finding two numbers that multiply to give -12 (the product of the coefficient of x² and the constant term) and add up to 1 (the coefficient of x). These numbers are 3 and -4, so the denominator can be factored as:
2x² + x - 6 = (2x - 3)(x + 2)
Now we can see that the common factor between the numerator and the denominator is x + 2. Therefore, the GCF is x + 2, which corresponds to option (c).
There are 100 books in the library. There are non-fiction and fiction books. Write the fraction of the books that are fiction.
Answers
Let
x--------------------- > non-fiction books.------------------ > x=60
y--------------------- > fiction books.
we know that
x+y=100
y=100-x=100-60=40
the fiction books. are y=40
if 100%----------------------- > 100 books
X---------------------------- > 40
X=40*100/100=40%
40%-------------- > 40/100=20/50=2/5
the answer is
the fraction of the books that are fiction is (2/5)
Which graph correctly solves the system of equations below? x2 + y2 = 25 y = x + 1
Answers
x2 + y2 = 25
y = x + 1
using a graph tool
see the attached figure
the solution are the points (3,4) and (-4,-3)
x2 + y2 = 25
It is a circle of radius r = 5 units.
y = x + 1
It is a line of positive slope.
The solution is the cut points of both graphs.
Attached graphic and analytical solution.
Use the graph to find the local minimum and the local maximum for the given function.
Answers
On the interval [-3, 0] the minimum is -16.
On the interval [0, 3] the maximum is 3.75.
On the interval [0, 3] the minimum is -3.
In the interval [-3, 0] the local minimum is -16 and In the interval [0, 3], the local maximum is 4 and local minimum is -3.
What is Local Maxima and Local Minima?
The local maxima and minima are the input values for which the function gives the maximum and minimum output values respectively. The y - coordinate of local maxima is called local maximum and that of local minima is called as local minimum.
Given is a graph of a function.
In the graph the local maximum is the y - coordinate that has maximum value at any specific input. Similarly, local maximum is the y - coordinate that has minimum value at any specific input.
PART A
In the interval [-3, 0], the local minimum is -16
PART B
In the interval [0, 3], the local maximum is 4 and local minimum is -3.
Therefore, in the interval [-3, 0] the local minimum is -16 and In the interval [0, 3], the local maximum is 4 and local minimum is -3.
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How many three-letter codes can we make using only vowels, a, e, i, o, or u?
Answers
Answer: 125 codes
Answer and explanation:
Given : Vowels a,e,i,o or u.
To find : How many three-letter codes can we make using only vowels ?
Solution :
1) If we assume that repetition is allowed then
The three letter code can form
[tex]5\times 5\times 5=125[/tex] ways
Number of three-letter codes can we make using only vowels is 125.
2) If we assume that repetition is not allowed then
The three letter code can form
[tex]5\times 4\times 3=60[/tex] ways
Number of three-letter codes can we make using only vowels is 60.
Diameter of a cylindrical tank is 9 feet and the height of a tank is 25 feet. Find the approximate volume of the cylindrical tank to the nearest hundredth place
C. 1,589.63 cubic feet
D. 2,325.26 cubic feet
E. 6,358.50 cubic feet
F. 3,489.27 cubic feet.
Answers
.. V = π*r^2*h
.. = π*(4.5 ft)^2*(25 ft)
.. ≈ 1590.43 ft^3
The closest choice is C 1589.63 ft^3.
_____
Apparently, someone used the 3-digit approximation 3.14 for π to compute a 6-digit result. That is why it is wrong in the last 3 digits.
Which statements about the opposite of −12 are true? Select each correct answer. −12 and its opposite are on located on the same side of zero on a number line. The opposite of the opposite of −12 is −12 . The opposite of −12 is −112 . −12 and its opposite are located the same distance from zero on a number line.
there's more than 1 answer
Answers
The opposite of the opposite of -12 is -12
The opposite of -12 is 12, and the opposite of 12 is -12.
-12 and its opposite are located the same distance from zero on a number line.-see attached picture
The true statements about the opposite of -12 are that the opposite of the opposite of -12 is -12 and -12 and its opposite are located the same distance from zero on a number line. The opposite of -12 is +12.
Explanation:In mathematics, the opposite of a number is also called its additive inverse, which is the number that, when added to the original number, will result in zero. −12 and its opposite, +12, are indeed located on opposite sides of zero on a number line, not on the same side. The second statement is true, the opposite of the opposite of −12 is indeed −12. The third statement is incorrect, the opposite of −12 is +12, not −112. The fourth statement is also true, −12 and its opposite are both 12 units away from zero on a number line, so they're at the same distance from zero.
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if f(x) = 5x^3-2 and g(x)= 2x+1, find (f+g) (x).
Answers
To start, whenever you are performing (f+g)(x), this means that you are to add the functions f(x) and g(x) together.
In this case, f(x) is equal to 5x^3-2 and g(x) is equal to 2x+1.
Because you are adding the two expressions as according (f+g)(x), you should set up this expression:
(5x^3-2)(2x+1)
Now, combine your like terms (terms of the same variables that are all raised to the same power):
(5x^3-2)(2x+1)
=5x^3+2x-1
Therefore, (f+g)(x)=5x^3+2x-1
Hope this helps and I hope you have a marvelous day! :)
The expression for (f + g)(x) is [tex]\rm 5x^3+2x-1[/tex] and this can be determined by using the arithmetic operations and the given data.
Given :
[tex]\rm f(x) = 5x^3-2[/tex][tex]\rm g(x) = 2x + 1[/tex]The following steps can be used in order to determine the value of (f + g)(x):
Step 1 - Write the given functions.
[tex]\rm f(x) = 5x^3-2[/tex] --- (1)
[tex]\rm g(x) = 2x + 1[/tex] --- (2)
Step 2 - Now, to determine the value of (f + g)(x), add both function f(x) and g(x).
f(x) + g(x) = (f + g)(x)
Step 3 - Substitute the value of f(x) and g(x) in the above expression.
[tex]\rm (f + g)(x) = 5x^3-2+2x+1[/tex]
Step 4 - Simplify the above expression.
[tex]\rm (f + g)(x) = 5x^3+2x-1[/tex]
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The population of a small town decreased from 983 to 901. What is the percent decrease, to the nearest tenth of a percent?
Answers
Well first there's 82 less ppl
That would be 82/100 so .82
And mutlypy by 100% is 8.20 so it's 8%
Have a nice day
The population of the small town percent decreased by approximately 8.4%.
To find the percent decrease in the population of the small town, we can use the formula for percent decrease:
Percent Decrease = [(Initial Value - Final Value) / Initial Value] * 100
Given that the initial population was 983 and the final population was 901, we can plug these values into the formula:
Percent Decrease = [(983 - 901) / 983] * 100
Now, calculate the numerator:
Percent Decrease = [82 / 983] * 100
Divide and multiply:
Percent Decrease = 0.0835 * 100
Now, calculate the percent decrease to the nearest tenth of a percent:
Percent Decrease ≈ 8.4%
So, the population of the small town decreased by approximately 8.4%.
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True or False 68oz < 4lb 6oz
Answers
Answer:true!!!
Step-by-step explanation:
A basketball player makes 60% of his shots from the free throw line. suppose that each of his shots can be considered independent and that he throws 4 shots. let x = the number of shots that he makes. what is the probability that he makes all 4 shots?
Answers
Using the binomial distribution, it is found that there is a 0.1296 = 12.96% probability that he makes all 4 shots.
-------------------------------
For each throw, the player either makes it or misses it. The probability of making each throw is the same, independent of other throws, thus, the binomial distribution is used to solve this question.
Binomial probability distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, with X having two possible outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success on a single trial.
Makes 60% of the shots, thus [tex]p = 0.6[/tex]4 shots, thus [tex]n = 4[/tex].The probability of making all of them is P(X = 4), thus:[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]
0.1296 = 12.96% probability that he makes all 4 shots.
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Two secant segments intersect outside a circle as shown. What is the value of x?
Answers
Thanks Darriennichole
How do you solve 7(2-j)-5??
Answers
You can simplify the expression by making use of the distributive property and collecting like terms.
.. 7(2 -j) -5
.. = 7*2 -7*j -5
.. = 14 -7j -5
.. = 9 -7j
The game called lotto sponsored by the louisiana lottery commission pays its largest prize when a contestant matches all 4 of the 41 possible numbers. assume there are 41 ping-pong balls each with a single number between 1 and 41. any number appears only once, and the winning balls are selected without replacement.
a. the commission reports that the probability of matching all the numbers are 1 in 101,270. what is this in terms of probability
Answers
[the probability of matching all the numbers]=1/101270
[the probability of matching all the numbers]=0.00000987-------> (0.000987%)
the answer is
1 in 101,270-------> means that the probability is 0.00000987
Final answer:
The reported probability of 1 in 101,270 for matching all four lotto numbers is equivalent to a decimal probability of approximately 0.00000987.
Explanation:
The Louisiana Lottery Commission's lotto game entails participants matching all 4 numbers out of a pool of 41. The reported probability of achieving this feat is 1 in 101,270. To express this probability, we utilize the ratio of successful outcomes to total possible outcomes. Consequently, the probability of matching all four numbers is 1/101,270, equivalent to approximately 0.00000987 in decimal form. This minute probability underscores the challenging nature of the lotto game, highlighting the rarity of successfully predicting and matching the specified set of numbers within the given range.
The volume of a rectangular prism is (x3-3x2+5x-3), and the area of its base is (x -2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
Answers
To find the height of the rectangular prism, divide the volume by the area of the base.
Explanation:To find the height of the rectangular prism, we need to divide the volume by the area of the base. The formula for the volume of a rectangular prism is V = lwh, where l, w, and h represent the length, width, and height, respectively. The formula for the area of the base is A = lw.
In this case, the volume is given as (x3-3x2+5x-3) and the area of the base is (x -2). So, we need to divide the volume by the area of the base, which gives us:
(x3-3x2+5x-3)/(x -2).
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If a student scored 82 points on a test where the mean score was 78.2 and the standard deviation was 6.7. the student's z score is .
Answers
x = data value
m= mean
sd = standard deviation
z= (82-78.2) / 6.7
=0.567
=0.57
A chord of a circle is a line segment connecting any point on the circle to the center of the circle.
Answers
Answer:
FALSE
Step-by-step explanation:
A chord of a circle is a line segment that connects two points on the circle.
Answer:
FALSE
Step-by-step explanation:
Please help me with questions 26 and 27
Answers
This is the horizontal line that cuts the figure into two congruent pieces.
--------------------------------------------------------------
27) Answer is choice A: AB = 24 and DE = 12
CA/DF = 12/6 = 2
CB/FE = 20/10 = 2
The ratio of the larger to smaller corresponding sides is 2:1 or just 2
So AB needs to be twice as long as DE
That only happens with choice A
how can you be able to find an area
Answers
Ming says that 0.24 > 14 because 0.24 = 24. Which best explains Ming's error?
Answers
Answer:
Ming says that 0.24 > 14
1
4
because 0.24 = 24
2
4
. Which best explains Ming's error?
Step-by-step explanation:
Two years ago Carol's living expenses were $ 1200 $ 1200 per month. This year the same items cost Carol $ 1400 $ 1400 per month. What was the annual inflation rate for the past two years?
Answers
= ((200 / 1200) x 100) / 2
= 8.33%
2 years ago - consumer price index 1,200 per month
current year - consumer price index 1,400 per month
Inflation rate = [(Consumer price index current - Consumer price index previous) / Consumer price index previous ] * 100%
Inflation rate = [(1400 - 1200) / 1200] * 100% = (200 / 1200) * 100% = 16.67%
Since 2 years has passed, the 16.67% inflation rate is good for 2 years. We simply divide the inflation rate by 2 to get the annual inflation rate.
16.66% / 2 = 8.33%
The annual inflation rate for the past two years is 8.33%
A right triangle has legs that are 15 feet and 25 feet long. What is the length of the hypotenuse? Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
Answers
Hope this helps!
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24 cubic units what is the height of the cylinder
Answers
.. V = π*r^2*h
.. 24 = π*(h/3)^2*h
.. 24 = π/9*h^3
.. 9*24/π = h^3
.. ∛(216/π) = h
.. h = (6/π)√(π^2) ≈ 4.097 . . . . units
The height of the cylinder is about 4.097 units.
the answer is c.6 i just took the test.
How many numbers must be selected from the set $\{1, 3, 5, 7, 9, 11, 13, 15\}$ to guarantee that at least one pair of these numbers add up to 16?
Answers
1+15=16
3+13=16
5+11=16
7+9= 16
IF YOU ANSWER WITHOUT A PROPER ANSWER AND YOU JUST WANT POINTS YOUR ANSWER WILL BE REPORTED! 99 POINT QUESTION! So I want a full explanation, best answer gets to be the brainliest. How much is 457 - (-54) + 7700 * 325 = ? I feel generous today so I'm making this 99 points. Btw, this is my first question asked here on brainly.
Answers
457 + 54 + 7700 * 325 = x
So then you multiply 7700* 325 which would be 2502500
Then it is 457 + 54 + 2502500
So , 457 + 54 = 511
And 511 + 2502500 = 2503011
Did this help ?
So for this question you have to use PEMDAS, in other words, order of operations. PEMDAS means you have to do parentheses first, then exponents, then multiplication and division, and them addition and subtraction.
You have to to start with the multiplication first since that is what comes first in this question.
457 - (-54) + 7700 * 325 turns into
457 - (-54) + 2502500
Afterwards you continue with addition and subtraction.
So, 457 - (-54) + 2502500 turns into
511+2502500
The reason 457 - (-54) equaled 511 is because negatives cancelled out and became a addition sign.
You finish off by 511+2502500
Your final answer would be 2503011
The cost for a pack of 4 padlocks is $17.60 . Find the unit price in dollars per padlock. If necessary, round your answer to the nearest cent.
Answers
Answer:
18.00
Step-by-step explanation:
60+40=100