Solution:
Array means arrangement of numbers in terms of rows and columns.
The conjecture is not True.
So, the conjecture made by chloe that given any two numbers, the greater number can always be arranged into more arrays is not true.
For example ,
1.(2,3)
2→(2×1),(1×2)
3→(3×1),(1×3)
This pair has same number of arrays because both of them are prime.
2. (3,4)
Here, 4>3
3→ (3 × 1),(1×3)
4→(4×1),(1×4),(2×2)
The pair of numbers are Co-prime, one of them is not prime. So Composite number has more number of arrays.
4. (6,11)
6→(1×6),(6×1),(2×3),(3×2)
11→(1×11),(11×1)
The number 6 is smaller, but it has more number of arrays.
5. (6,8)
6→(1×6),(6×1),(2×3),(3×2)
9→(1×9),(9×1),(3×3)
Both the numbers are composite.Smaller number 6 has more arrays.
These examples disprove the Conjecture made by Chloe, which states that given any two numbers, the greater number can always be arranged into more arrays.
You decide to market your own custom computer software. You must invest $3255 for computer hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, write a system of equations at determine how many copies you must sell to break even
Translate the following sentence into math symbols. Then solve the problem y is more than 4 is –36
Answer:
y = 32
Step-by-step explanation:
4 + y = 36
to work out y you need to make it by itself
so take the 4 to the other side
36 - 4 = y
so y equals 32
How do you write 4xy + 2y + 6x^2 in ascending order
Answer: 6x² + 4xy + 2y
Step-by-step explanation:
Polynomials are written in the order of the highest degree to the lowest degree.
x² has a degree of 2 because the exponent is 2 so it is the first term.xy has a degree of 2 --> x has a degree of 1 and y has a degree of 1. The sum of their degrees is 2 so this is the second term.y has a degree of 1 which is the lowest degree so it is the last term.Which of the following numbers is irrational
Answer:
A) -7.888
Step-by-step explanation:
The answer is A because it is an never ending number, which means it is irrational
The following numbers is irrational D) √0.025, which is an irrational number.
To determine which of the given numbers is irrational, we need to understand what an irrational number is. An irrational number is a real number that cannot be expressed as a fraction (i.e., it cannot be written as a ratio of two integers). Irrational numbers have non-repeating, non-terminating decimal expansions.
Let's evaluate each of the given options:
A) -7.8: This is a rational number because it can be expressed as -78/10 or -39/5, which is a ratio of two integers.
B) √25: This is a rational number because it is equal to 5, which can be expressed as 5/1. It's a ratio of two integers.
C) 25.8125: This is a rational number because it can be expressed as 258125/10000, which is a ratio of two integers.
D) √0.025: This is an irrational number. To see why, we can simplify it. √0.025 is the same as √(25/1000), which simplifies to √(1/40). The square root of 1 is 1, and the square root of 40 is a non-repeating, non-terminating decimal, making √0.025 an irrational number.
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What equation is equal to 1+4(6p-9)
Answer:
24p -35
Step-by-step explanation:
Simplify. Remember to follow PEMDAS. First, distribute 4 to all terms within the parenthesis
4(6p - 9) 4(6p) - (4)(9) = 24p - 36
Next, simplify. Add 1 to the constant
24p - 36 + 1
24p - 35
24p - 35 is your answer
~
Andrew and Mark make 4 gallons of ice tea for their ice tea stand.How many quarts will they will be able to sell? If they charge $4.00 per quart,how much money will they make if they sell it all?
The sum of two polynomials is 8d^5-3c^3d^2+5c^2d^3-4CD^4+9. If one added is 2d^5-c^3d^4+8CD^4+1, what is the other added
The other added polynomial is 6d^5-3c^3d^2+5c^2d^3-12CD^4+8.
Explanation:To find the other polynomial, we need to subtract the given polynomial from the sum of the two polynomials. The sum of the two polynomials is 8d5-3c3d2+5c2d3-4CD4+9. The polynomial that is added is 2d5-c3d4+8CD4+1.
Subtracting the given polynomial from the sum, we get:
8d5-3c3d2+5c2d3-4CD4+9 - (2d5-c3d4+8CD4+1)
Simplifying the polynomial, we get:
6d5-3c3d2+5c2d3-12CD4+8
What construction tool would be used to measure an angle?
Answer:
A protractor.
Step-by-step explanation:
What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is the length of the line segment from A to B?
(1, 5)
(0, 3)
(–4, –5)
(–5, –7)
The correct answer is:
C: (-4, -5)
Hope it helps!
Answer:(-4,-5)
Step-by-step explanation:
A farm tree is going out of business. It has 45 maple trees and 27 pine trees left for sale. How much money would the owners make if they sell all the trees?
first to answer will be the brainliest
What is the solution to the system of equations?
Use the substitute method
Y=3x-4
9x-3y=14
A. There is no solution
B. (12,14)
C. (14,12)
D. There are infinite solutions
Answer:
A: There is no solution
Step-by-step explanation:
This is not a very likable question.
Y=3x-4
9x-3y=14
Put the y value from the first equation into the second.
9x - 3(3x - 4) = 14 Remove the brackets
9x - 9x + 12 = 14 Combine like terms on the left
12 = 14 When you get this kind of conclusion, that means there is no solution. I'll graph these two for you.
Blue: y =3x - 4
Green: 9x - 3y = 14
They never touch they never meet: they are parallel. They don't give a solution.
At the beginning of year 1, Sam invests 700 at an annual compound interest rate of 5%, he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account's balance at the beginning of year 4? what is the balance?
a) 805.
b) 825.42
c) 850.85
d) 810.34
Answer:
(d) 810.34
Step-by-step explanation:
The explicit formula used for calculating the account's balance is given by:
A= P(1+R)^T
where: A= Amount (account's balance)
P= Principal (700)
R= Rate (5%)
T= Time (3 years) [since, the balance is calculated in the beginning of the forth year]
A= P(1+R)^T
A = 700(1+0.05)^3
= 700(1.05)^3
= 700*1.157
= 810.34
a reciepe for 1 1/4 dozen cupcakes calls for 1 2/3 cups of flour, but Rashida has only 1 cup of flour. How many cupcakes can she make?
let's firstly convert the mixed fractions to improper fractions.
now, 1¼ dozen of cupcakes.... well, let's keep in mind that a dozen has 12 units, so 1¼ dozen is then 12(1¼) cupcakes total.
[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{how many cupcakes in }\frac{5}{4}\textit{ of a dozen?}}{12\cdot \cfrac{5}{4}\implies \cfrac{12}{4}\cdot 5\implies 15} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} cupcakes&\stackrel{cups}{flour}\\ \cline{1-2}\\ 15&\frac{5}{3}\\[1em] c&1 \end{array} \implies \cfrac{15}{c}=\cfrac{~~\frac{5}{3}~~}{1}\implies \cfrac{15}{c}=\cfrac{5}{3} \\\\\\ 45=5c\implies \cfrac{45}{5}=c\implies \boxed{9=c}[/tex]
In the given case, Rashida can make approximately 9 cupcakes with 1 cup of flour.
To determine how many cupcakes Rashida can make with the 1 cup of flour she has, we need to calculate the conversion factor between the given measurement of 1 2/3 cups of flour and the available 1 cup of flour.
The conversion factor is found by dividing the available amount by the required amount
(1 cup ÷ 1 2/3 cups).
We can simplify the fraction to obtain a decimal,
1 ÷ (5/3) = 3/5 ≈ 0.6.
So, Rashida can make approximately
0.6 × 1 1/4 dozen = 0.6 × 15 = 9 cupcakes.
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For every 20 litres of petrol a car can run for 75 km.
How much petrol do you need (to 1 DP) to ensure the car has enough petrol of a trip that is 196 km?
Answer:
52.3 litres.
Step-by-step explanation:
The car consumption is 75/20 = 3.75 km/litre.
Volume of petrol needed to travel 196 km
= 196 / 3.75 = 52.3 litres.
which of the following numbers must be added to complete the square in the equation below? x^2+6x-19=23 A. 19 B. -9 C. 3 D. 9
Answer:
the answer is D
Step-by-step explanation:
Answer:
D. 9
Step-by-step explanation:
Alonzo takes 12 minutes to run 6 times around a 400-meter track. Assuming he runs at a constant speed, how long does he take to run 1-kilometer?
Answer:
5 minutes to run 1 kilometer
Step-by-step explanation:
Alonzo takes 12 minutes to run 6 times around a 400-meter track.
6 times around a 400 m track
400 * 6 = 2400 meters
It take 12 minutes to run 2400 meters
2400 meters = 2400/1000 = 2.4km
distance = 2.4 km and time = 12 minutes
Now we find our constant speed
[tex]Distance = speed * time[/tex]
2.4 = speed * 12
divide by 12 on both sides
speed = 0.2
so speed is 0.2 km per minute
Now we find out time when distance = 1km
Distance = speed * time
1 = 0.2 * t
divide by 0.2 on both sides
5 = t
So it take 5 minutes to run 1 kilometer
for what values of t on the interval [-2pi,2pi] is sint=1?
Hello from MrBillDoesMath!
Answer:
pi/2, - 3pi/2
Discussion:
The solutions of sin(t) = 1 are (pi/2) + 2*pi*n, where n = 0, -1,1, -2,2,-3,3, etc.
In particular, sin(pi/2) = 1 ( n = 0) and sin(-3pi/2) -1 ( n = -1) and those argument values lie in the interval [-2pi, 2pi]
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
Final answer:
The value of t on the interval [-2π,2π] for which sin(t)=1 is only at t=π/2, since this is where the sine function reaches its maximum value within the given range.
Explanation:
The question asks: For what values of t on the interval [-2π,2π] is sin(t)=1? To answer this, we must understand when the sine function reaches its maximum value of 1. In the unit circle, θ represents the angle in radians from the positive x-axis. The sine function reaches its maximum value of 1 at an angle of θ=π/2 radians. Therefore, within the interval [-2π,2π], sin(t)=1 only at t=π/2. However, the function is periodic with a period of 2π, meaning it repeats every 2π intervals. Even though the question's range allows for multiple cycles of sine's period, only π/2 falls within those bounds with the value of sin(t) exactly equal to 1.
State which of the following ordered pairs is a function. Set A: (-1, 0), (-2, 1), (4, 3), (3, 4) Set B: (1, 4), (2, 3), (3, 2), (4, 1) Set C: (2, 1), (3, 2), (2, 3), (1, 4) a. Set A b. Set B c. Both Set A and Set B d. Set C Please select the best answer from the choices provided
Answer:
Both set A and B.
Step-by-step explanation:
Set A: (-1, 0), (-2, 1), (4, 3), (3, 4)
Set B: (1, 4), (2, 3), (3, 2), (4, 1)
Set C: (2, 1), (3, 2), (2, 3), (1, 4)
In order for (x,y) to be a function, only one x get the value of y, but many x'es can get the value y.
Looking at the set A and B, and the definition above, we can say that they are functions.
What about set C? It is not a function, as x = 2 is equal 1 or 3, which does not meet the condition from the definition.
Final answer:
Both Set A and Set B are functions because each member of the domain in these sets maps to a unique value in the range. Set C is not a function because the same first element maps to different values in the range. Both set A and B are the answers.
Explanation:
To determine which set(s) represent a function, we need to ensure that each element of the domain maps to one and only one value in the range. By examining each set:
Set A: (-1, 0), (-2, 1), (4, 3), (3, 4): Every first element is unique, indicating a function.
Set B: (1, 4), (2, 3), (3, 2), (4, 1): Similarly, all first elements are unique, indicating a function.
Set C: (2, 1), (3, 2), (2, 3), (1, 4): The number 2 appears twice as a first element with different second elements, violating the definition of a function.
Therefore, both sets A and B represent functions since they each map every member of the domain to a unique member of the range, while set C does not.
The answer is b. Both Set A and Set B are functions.
PLEASE HELP!!
type the integer that makes the following addition sentence true
+ -6 = 1
It would be 7.
Here's why:
7 + - 6 = 1
1 = 1
It's a TRUE statement!
Hope this helps you!!!! :)
The integer value that makes the sentence true is 7, as in mathematics, adding a negative number 6 to a number, to yield 1, equates deducting 6 from that number to yield 1.
Explanation:This is a mathematics problem involving the concept of integer addition. In mathematics, adding a negative number is equivalent to subtracting that number's absolute value. Therefore, to find the integer that makes the addition sentence true, you would need to identify the number that, when subtracted by 6, equals 1.
So, the equation can be rewritten as X - 6 = 1. If you add 6 on both sides of the equation to isolate the variable X on one side, the equation becomes X = 1 + 6. As a result, it is clear that the integer value X that would make the equation + -6 = 1 true is 7.
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Find the midpoint between the complex numbers. Show all work for full credit. z1= -8 + 3i z2= 7 - 4i
Answer:
[tex]z_m=-\frac{1}{2}-\frac{1}{2}i[/tex]
Step-by-step explanation:
The given complex numbers are;
[tex]z_1=-8+3i[/tex]
and
[tex]z_2=7-4i[/tex].
The midpoint of any two complex numbers,
[tex]z_1=a_1+a_1i[/tex] and [tex]z_2=a_2+a_2i[/tex] is
is given by,
[tex]z_m=\frac{a_1+a_2}{2}+\frac{a_1+a_2}{2}i[/tex].
The midpoint of the complex numbers can be found by adding the corresponding real parts and imaginary parts and then dividing each by 2.
This is the same as;
[tex]z_m=\frac{z_1+z_2}{2}[/tex]
[tex]\Rightarrow z_m=\frac{-8+3i+7-4i}{2}[/tex]
[tex]\Rightarrow z_m=\frac{-8+7+3i-4i}{2}[/tex]
[tex]\Rightarrow z_m=\frac{-1-i}{2}[/tex]
[tex]\Rightarrow z_m=-\frac{1}{2}-\frac{i}{2}[/tex]
or
[tex]\Rightarrow z_m=-\frac{1}{2}-\frac{1}{2}i[/tex]
Students in band are selling oranges and grapefruit to earn money for a trip. Mrs.Whitten purchased three boxes of oranges and two boxes of grapefruit from a student for a total of $22.50. Mr. Rutig purchased one bag of oranges and four boxes of grapefruit, spending a total of $28.50. How much is one box of oranges?
Answer:
The cost of one box of oranges = $3.3
Step-by-step explanation:
Let x be cost of one box of oranges and y be the cost of one box of grapefruit.
We have been given that Mrs. Whitten purchased 3 boxes of oranges and 2 boxes of grapefruit from a student for a total of $22.50. We can represent this information as:
[tex]3x+2y=22.50...(1)[/tex]
Mr. Rutig purchased 1 box of oranges and four boxes of grapefruit, spending a total of $28.50. We can represent this information as:
[tex]x+4y=28.50...(2)[/tex]
We will solve our system of linear equations using substitution method.
From equation (1) we will get,
[tex]y=\frac{22.50-3x}{2}[/tex]
Substituting y's value in equation (2) we will get,
[tex]x+4*(\frac{22.50-3x}{2})=28.50[/tex]
[tex]x+2*(22.50-3x)=28.50[/tex]
Upon distributing 2 we will get,
[tex]x+45-6x=28.50[/tex]
[tex]x-6x=28.50-45[/tex]
[tex]-5x=-16.5[/tex]
[tex]x=\frac{-16.5}{-5}[/tex]
[tex]x=3.3[/tex]
Therefore, the cost of one box of oranges is $3.3.
Solve w^3=15 where w is a real number
How to solve for x and y
Answer:
x = 26.4 y= 17
Step-by-step explanation:
Set up proportions.
To find x:
Set 12 over x is equal to 10 over 22.
12 times 22 = 264
264 / 10 =x
x = 26.4
To find y:
Set y over 37.4 is equal to 10 over 22.
37.4 times 10 = 374
374 / 22
y = 17
Please help me. How do you do this.
Use the Pythagorean theorem:
[tex]x^2+4^2=10^2[/tex]
[tex]x^2+16=100[/tex] subtract 16 from both sides
[tex]x^2=84\to x=\sqrt{84}\\\\x=\sqrt{4\cdot21}\\\\x=\sqrt4\cdot\sqrt{21}\\\\\boxed{2\sqrt{21}}[/tex]
WILL GIVE BRAINLIEST
graph f(x) = -0.5x + 3
please tell me the points to put on the graph
thanks :)
Answer:
- 1/5
Step-by-step explanation:
the answer is the one highlighted #1
but to do this you must first change the decimal to a fraction. Personally i use a decimal calculator.
then you go to where the 3 is on the Y axes. since its positive 3 it would be 3 up instead of down.
then you count over how ever many the X is. this is 1/2 so you go over 1 time then up 2 times.
Personally I like the triangle method where u plot the +3 then draw on the line 1 over then 3 up
if u need to find out what the plot line u can keep doing that all the way up and just reverse it when u go down.
Find x, using SOHCAHTOA?
Answer:
x = 57.22754579
Step-by-step explanation:
We know cos 63 = adjacent/ hypotenuse
cos 63 = 15 sqrt(3)/x
Multiply each side by x
x cos 63 =15 sqrt( 3 )
Divide each side by cos 63
x cos (63)/ cos (63) = 15 sqrt(3)/cos (63)
x = 15 sqrt(3)/ cos 63
x = 57.22754579
An animal shelter has 12 cats. Of these cats, 5 weigh no more than 7 lbs. What is the approximate percentile rank of the cats that weigh 7 lbs?
Answer:
84 lbs
Step-by-step explanation:
am i correct for this math question
Answer:
Step-by-step explanation:
Hammers and Wrenches
I have included the graph to the first one. C is the best answer, but I don't think it is quite correct, although it is true. The actual fact is that there is no y intercept as near as I can get. That's an unusual occurrence for this kind of graph. There is no other answer that will satisfy or rectify that condition. I think you are likely to answer C, but be careful. It could turn out to be another answer.
f(x) and g(x)
I agree with your answer
NEED HELP WITH ALL THESE PROBLEMS !!
Answer:
1) ASA 2) In explanation 3) I cant see all of the problem
Step-by-step explanation:
For Number 1 you need one more thing to prove that the triangles are congruent. You could see that there is a pair of vertical angles and vertical angles are congruent so you could use that. Angle DEA is congruent to Angle CEB. When there is a side in between two congruent angles, that is ASA.
For Number 2 it really is almost the same as number 1. First you write the given, then you write that angle DEA is congruent to angle CEB and the reason for that is that vertical angles are congruent. Lastly, you say that triangle ADE is congruent to triangle CBE.