Answer:
Goldbach’s Conjecture precipitated from letters in 1742 between German mathematician Christian Goldbach and legendary Swiss mathematician Leonhard Euler, considered one of the greatest in math history. As Euler put it, “I regard [it] as a completely certain theorem, although I cannot prove it.”
Euler may have sensed what makes this problem counterintuitively hard to solve. When you look at larger numbers, they have more ways of being written as sums of primes, not less. Like how 3+5 is the only way to break 8 into two primes, but 42 can broken into 5+37, 11+31, 13+29, and 19+23. So it feels like Goldbach’s Conjecture is an understatement for very large numbers.
Still, a proof of the conjecture for all numbers eludes mathematicians to this day. It stands as one of the oldest open questions in all of math.
Answer:
dividing and multiplying decimals
Step-by-step explanation:
Robert recently discovered a forgotten student loan bill. The amount due after 10 years is
now $10,819.33. He found some old statements and determined that after 7 years the bill
was $8831.80 and after 5 years he owed $7714.03.
1. How much did Robert borrow initially?
2. Robert is planning to pay the loan in full next year. How much will he owe then?
3. What is the interest rate on Robert’s loan?
Answer:
1.Robert borrowed $ 5,500.00
2.The amount Robert would repay next year is $ 11,576.69
3.The interest rate on the loan is 7%
Step-by-step explanation:
The interest on the loan can be computed using compound annual growth
rate
CAGR=(EB/BB)^1/n-1
EB is ending balance of $8831.80 in year7
BB is the balance of year 5 $7714.03
n=7-5=2
CAGR=(8831.8/7714.03)^(1/2)-1
CAGR==1.070000427-1
CAGR=0.070000427
CAGR=7%
The amount borrowed can be computed using the PV formula
At year 0 year 5 amount of $7714.03 is the future value
rate of interest is 7%
number of years is 5
PV=$7714.03*(1+7%)^-5
PV=$ 5,500.00
The amount Robert would pay next year is :
FV=$10,819.338(1+7%)^1
FV=$ 11,576.69
A soup can, shaped like a cylinder, has a diameter of 3.5 inches and a height of 5 inches. Each serving of soup is 15 cubic inches. If a can of soup this size costs $1.99, what is the cost of each serving of soup? Round to the nearest cent.
Answer:
The answer to your question is Cost of a serving = $0.62
Step-by-step explanation:
Data
diameter = 3.5 in
height = 5 in
each serving = 15 in³
Cost of the can = $1.99
Process
1.- Calculate the volume of the can
Volume = πr²h
-Substitution
Volume = (3.14)(3.5/2)²(5)
-Simplification
Volume = (3.14)(3.062)(5)
-Result
Volume = 48.08 in³
2.- Use proportions and cross multiplication to find the cost of a serving.
48.08 in³ ---------------- $1.99
15 in³ ---------------- x
x = (15 x 1.99)/48.08
x = 29.85/48.08
x = $0.62
What is the range of the function represented by this graph?
Answer:
wheres the graph and it would be match easier if I can see it
Step-by-step explanation:
....
Answer:
where is the graph
Step-by-step explanation:
please give a image next time
Jan is trying to increase her water intake to meet recommended guidelines. She currently consumes 2 (24 oz. each) bottles of water per day, and 2 cups (8 oz. each) of low-fat milk. Assuming that she will obtain 15% of her fluid needs from foods, how many cups of water does she still need to drink?
Answer:
Extra 4 cups to make up 11 cups a day
Step-by-step explanation:
Here we have that Jan obtains 15% of her fluid needs from food, therefore, she gets the remaining 85 % from drinking water
If the recommended daily intake = 2.7 liters or 91.3 oz
And she already consumes 48 oz of water and 16 oz of milk
Note milk is equivalent to 0.87 water therefore total intake = 48 + 16*0.87= 61.92 oz
She needs to take additional (91.3 - 61.92) = 29.4 oz or 3.68 ≈ 4 cups extra to meet her recommended daily dosage.
An angle measures 49.4° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
40.6
Step-by-step explanation:
Pretty sure a complementary angle is 90 so 90-49.4=40.6
There are 2 brown marbles, 3 black marbles, and 4 gold marbles in a bag. What is the probability of drawing 2 brown marbles if the first is replaced after it is drawn?
Answer:
.049 (2sf)
Step-by-step explanation:
[tex] \frac{2}{9} \times \frac{2}{9} = 0.4938[/tex]
Answer & explanation:
The correct answer is 4/81. The probability of each marble drawn being brown is 2/9 because there are two brown marbles in a bag of nine total marbles. So, the probability that both marbles drawn will be brown is 2/9 times 2/9 or 4/81!
What is the value of the expression StartAbsoluteValue negative 7 EndAbsoluteValue + StartAbsoluteValue negative 4 EndAbsoluteValue?
Answer:
11
Step-by-step explanation:
|-7|+|-4|
-|-7|-|-4|
Answer 11
Answer:
11
Step-by-step explanation:
can i pls have brainlist i really need it to level up plss
A zoo has some new exhibits.
In a survey, 2400 zoo attendants are asked to choose their favorite.
The results are shown in the following table.
(a) find the percentage for each type of animal.
Answer:
Elephant 14%
Panda 18%
Tiger 29%
Bonobo 39%
Step-by-step explanation:
Divide each number by 2400 then multiply the answer by 100.
The percentage of elephants, pandas, tigers, and bonobos are 14%, 18%, 29%, and 39% respectively.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
The zoo has some new exhibits.
In a survey, 2400 zoo attendants are asked to choose their favorite.
From the table:
The total number of animals = 336 + 432 + 696 + 936 = 2400
Percentage of Elephant = (336/2400)x100 = 14%
Percentage of Panda = (432/2400)x100 = 18%
Percentage of Tiger = (696/2400)x100 = 29%
Percentage of Bonobo = (936/2400)x100 = 39%
Thus, the percentage of elephants, pandas, tigers, and bonobos are 14%, 18%, 29%, and 39% respectively.
Learn more about the percentage here:
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The value for √10 is approximately between 3 and 4. Approximate further to find the values to the tenths place that √10 is between.
a less-than StartRoot 10 EndRoot less-than b
a =
b =
Answer:
a = 3.1
b = 3.2
Step-by-step explanation:
I did the quiz
Answer:
a =
✔ 3.1
b =
✔ 3.2
Step-by-step explanation:
What is the equation of the line that passes through the point
(−3,5) and has a slope of -2?
Answer:
y = -2x-1
Step-by-step explanation:
y = -2x+b
5 = -2(-3)+b
5 = 6+b
-1 = b
Coordinates (-3, 5), ( -3, 8), and (2, 5). The triangles was dilated by a scale favtor of 3. What is the area of the dilated triangle, in square units?
Answer:
The area of the triangle is 7.5 unit²
Step-by-step explanation:
Here we have the coordinates given as
(-3, 5) (-3, 8) and (2, 5)
Let us call the points A = (-3, 5)
B = (-3, 8) and
C = (2, 5)
Therefore the lengths of the sides of the triangle are
AB = a = [tex]\sqrt{(-3-(-3))^2+(5-8)^2} = 3[/tex]
AC = b = [tex]\sqrt{(-3-2)^2+(5-5)^2} = 5[/tex]
BC = c = [tex]\sqrt{(-3-2)^2+(8-5)^2} = \sqrt{34}[/tex]
Therefore the Area can be derived from Heron's formula which is
A = [tex]\sqrt{s\times (s-a)\times (s-b)\times (s-c)}[/tex] where s = semi perimeter or (a + b + c)/2
Therefore, plugging the values, we get
s = (3 + 5 + √34)/2 = 6.9155≈6.92
A = [tex]\sqrt{6.92\times (6.92-3)\times (6.92-5)\times (6.92-\sqrt{34} )}[/tex] = 7.499≈7.5.
Answer:
67.5 square units
Step-by-step explanation:
The points (-3, 5) and ( -3, 8) form a vertical segment, and the points (-3, 5) and ( 2, 5) form a horizontal segment, so the triangle has a right angle.
The base of the triangle is the segment formed by the points (-3, 5) and ( 2, 5), and their distance is:
D1 = sqrt((-3-2)^2 + (5-5)^2) = 5
The height of the triangle is the segment formed by the points (-3, 5) and ( -3, 8), and their distance is:
D2 = sqrt((-3+3)^2 + (5-8)^2) = 3
If the triangle is dilated by a scale of 3, so the base is D1*3 = 15 and the height is D2*3 = 9, then the area is:
The area of a triangle is Base * Height / 2, so we have that:
Area = 15 * 9 / 2 = 67.5 square units
Write down the value of x = 65 give your reason for your answer
Please help me idk this ?!?!?
Using the formula given in the question, we can solve for the area.
h = 10
b1 = 20
b2 = 8
Now, solve with the given values.
1/2(10)(20 + 8)
5(28)
140
Therefore, the area is 140 square feet.
Best of Luck!
Calculate the simple interest on
N650.00 for 2 years at 6% per
annum.
Answer:
N78
Step-by-step explanation:
The explanation is in the picture
please rate and mark as brainliest
Find the solutions of the quadratic equation Choose 1 answer:
Answer:
B
Step-by-step explanation:
The cost of an entry ticket to an amusement park is $5 for a child and $8 for an
adult. During a given 15 minute period, 120 people entered the park, and the total
revenue from ticket sales was $810. During that 15 minute period, how many adults
entered the amusement park?
Answer:
70 adults
Step-by-step explanation:
because there is 70 adults and 50 kids
f(x) = 4x2 + 7x - 18
Find f(-9)
Answer:
f(-9)= 243
Step-by-step explanation:
f(x) = 4x²+7x -18
f(-9) = 4(-9)²+7(-9)-18
= 4(81) -63-18
= 324- 81
= 243
Answer:279
Step-by-step explanation:
Bc
s the interquartile range of this data?
6
8
9
20
Box-and whisker plot titled Number of Coins in Collection with five-number summary from left to right 7, 16, 30, 36, 38.
We have been given the 5-number summary of a box plot that represents Coins in Collection. The five-number summary from left to right is 7, 16, 30, 36, 38.
We are asked to find the inter-quartile range of the given data.
We know that interquartile range is difference of upper quartile and lower quartile.
We know that the 5-point summary represents the lower data point, lower quartile, median, upper quartile and upper data point respectively.
We can see from our given 5 point-summary that lower quartile is 16 and upper quartile is 36.
[tex]\text{Interquartile range}=\text{Upper quartile}-\text{Lower quartile}[/tex]
[tex]\text{Interquartile range}=36-16[/tex]
[tex]\text{Interquartile range}=20[/tex]
Therefore, the interquartile range of the given data is 20 and last option is the correct choice.
Answer:
here is my answers, it is just my test....
The model represents the factorization of 2x2+5x+3.
What are the factors of the polynomial?
'O
tx
+X
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)
AX
Answer:
(2x+3)(x+1)
Step-by-step explanation:
Porque si lo factorizas da ese resultado.
The factors of the polynomial are (2x + 3) and (x+1)
Factorizing quadratic expressionsGiven the quadratic equation expressed as:
2x^2+5x+3
We are to find the factors of the given quadratic function as shown:
2x^2+5x+3
2x^2+2x +3x +3
2x(x+1)+ 3(x+ 1)
(2x + 3)(x + 1)
Hence the factors of the polynomial are (2x + 3) and (x+1)
Learn more on factors of the polynomial here:https://brainly.com/question/527031
Which value of x makes the equation true?
x + 7 = -9
Answer:
x = -16
Step-by-step explanation:
x + 7 = -9
x = -9 - 7
x = -16
Answer:
X=-16
Step-by-step explanation:
If you add -16 Then add a positive 7 you will end up with a -9
Have a great day
Tell which set or sets the number below belongs to natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
614
Select all sets in which the number 614 is an element.
A. whole numbers
B. rational numbers
C. integers
D. irrational numbers
E natural numbers
F. real numbers
The number 614 belongs to the sets of natural numbers, whole numbers, integers, rational numbers, and real numbers. It does not belong to the set of irrational numbers.
Explanation:The number 614 belongs to multiple sets of numbers, including natural numbers, whole numbers, integers, rational numbers, and real numbers. It does not belong to the set of irrational numbers.
Natural Numbers: This set includes the positive integers starting from 1, so 614 is a natural number.Whole Numbers: This set includes all natural numbers plus zero. Since 614 is a positive integer and natural number, it is also a whole number.Integers: This set includes all whole numbers and their negatives. As 614 is a whole number, it is also an integer.Rational Numbers: This set consists of numbers that can be expressed as a fraction with integers in both the numerator and denominator, where the denominator is not zero. Since 614 can be expressed as 614/1, it is a rational number.Irrational Numbers: These numbers cannot be expressed as a simple fraction; 614 is not an irrational number since it can be expressed as a fraction.Real Numbers: This set includes all rational and irrational numbers. Because 614 is a rational number, it is also a real number.
The number 614 belongs to the sets: Whole Numbers, Rational Numbers, Integers, Natural Numbers, and Real Numbers.
A. Whole Numbers: Whole numbers include all natural numbers and zero. Since 614 is a positive integer, it is a whole number. So, A is correct.
B. Rational Numbers: Rational numbers include integers and fractions. Since 614 is an integer, it is also a rational number. So, B is correct.
C. Integers: Integers include all positive and negative whole numbers along with zero. Since 614 is a positive integer, it is an integer. So, C is correct.
D. Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Since 614 can be expressed as the fraction 614/1, it is not irrational. So, D is incorrect.
E. Natural Numbers: Natural numbers include all positive integers starting from 1. Since 614 is a positive integer, it is a natural number. So, E is correct.
F. Real Numbers: Real numbers include all rational and irrational numbers. Since 614 is a rational number, it is also a real number. So, F is correct.
In summary, the correct sets for the number 614 are A, B, C, E, and F.
Using this number cube and spinner, which simulation would help you answer this question? Over the past 50 years, records for one northwest city show that snow fell on the first day of winter 16 of the time. If you choose a year at random, what are the chances that the first day of winter will be a snowy Monday?
Answer:
0.045714286
Step-by-step explanation:
The chance of it being snowy is 16/50, or 0.32. And the chance of that day being Monday out of 7 days over the week is 1/7, or 0.143. Then the chances that the first day of winter will be a snowy Monday is 0.32*0.143 = 0.045714286
Answer:
A- roll and spin 50 times. Roll on a 3 AND land on red
Step-by-step explanation:
I need help please?!!!
Answer: (3)/(4)(3x+8), x^(2)-4, 3^(2+)x, -5(x-3)
Step-by-step explanation: Those are the right answers, trust me, this took a while.
Have a good day, brainliest wouldn't be bad :)
Select the correct answer.
In which direction must the graph of f(x) = 7* be shifted to produce the graph of g(x) = 7* + 7?
O A.
up
OB. right
0
C. down
0
D.
left
Reset
Next
Answer:
Maybe A hopefully its the correct answer
Make the x the subject of the formula y= 7x + 4
Answer:
[tex]y = 7x + 4 \\ y - 4 = 7x \\ \frac{y - 4}{7} = \frac{7x}{7} \\ x = \frac{y - 4}{7} [/tex]
hope this helps you....
Answer:
x = y-4
7
Step-by-step explanation:
y = 7x + 4
y- 4 = 7x
[tex]\frac{y-4}{7}[/tex] =x
Dave determines the meal he ordered at the restaurant contains 22% of his daily sodium intake. If the meal contains 260 mg of sodium, how many mg of sodium are in Dave's daily diet? Round your answer to the nearest whole mg
Answer:
1182 mg to the nearest mg.
Step-by-step explanation:
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 * (100/22)
= 1181.82 mg.
what is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Examples of percentages are:
10% is equal to 1/10 fraction
20% is equivalent to ⅕ fraction
25% is equivalent to ¼ fraction
50% is equivalent to ½ fraction
75% is equivalent to ¾ fraction
90% is equivalent to 9/10 fraction
Given,
Dave determines the meal he ordered at the restaurant contains 22% of his daily sodium intake
Meal contains 260 mg of sodium
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 x ([tex]\frac{100}{22}[/tex])
= 1181.82 mg.
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 * (100/22)
= 1181.82 mg.
Learn more about percentage here:
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the wheels of a bicycle are 0.6 m in diameter. If I go around the bike block, each wheel will perform 346 full turns. What distance, to the tenth of a meter ready, that represents it
Answer:
The distance that represents it is 651.9 m.
Step-by-step explanation:
In order to calculate the distance that the wheel travelled we need to find the length of the circumference of the wheel. This is given by the following formula:
length = 2*pi*r = pi*d
Since the diameter of the wheel is 0.6 m we can find the length of the wheel that is:
length = 3.14*0.6 = 1.884 m
The wheel made 346 full turns, that means that the total distance is the number of turns multiplied by the length of the wheel.
distance = 346*1.884 = 651.9 m
The distance that represents it is 651.9 m.
Find four solutions of the equation. Write the solutions as ordered pairs.
y = x+5
Answer:
when x=1, y=6. etc.
Step-by-step explanation:
x y
1 6
2 7
3 8
4 9
Yolanda reads 24 chapters of a book in 6 hours. What is her rate in chapters per hour?
Answer:
4 chapters an hour
Step-by-step explanation:
24 / 6 = average of 4 chapters an hour
Answer:
4 chapters per hour
Step-by-step explanation:
[tex]rate \: of \: reading \\ = \frac{total \: chapters}{total \: time} \\ \\ = \frac{24}{6} \\ \\ = 4 \: chapters \: per \: hour[/tex]
Two number cubes each have sides that are labeled 1 to 6. Iris rolls the 2 number cubes. What is the probability that the sum of the numbers on the number cubes will equal 4?
1/36
1/18
1/6
1/12
Given:
Two cubes are rolled together.
To find the probability that the sum of the numbers on the number cubes will equal 4.
Formula
P(A) = [tex]\frac{x}{y}[/tex]
where, A be any event.
x be the number of successful outcomes
y be the total number of outcomes
Now,
If the two cubes are rolled together, total number of outcomes = 36
In total outcomes, the sum of the numbers of cube will be 4 for (1,3),(3,1) and (2,2)
So, the number of successful outcomes = 3
Now,
Putting x=3 and y = 36 we get,
[tex]P(A) = \frac{3}{36}[/tex]
or, [tex]P(A) = \frac{1}{12}[/tex]
Hence,
The probability that the sum of the numbers on the number cubes will equal 4 is [tex]\frac{1}{12}[/tex]. Option D.