==============================================
Explanation:
Let n be the number we want to find. We want n to be as small as possible, but also be a positive integer. Intuitively, we can see that n cannot be smaller than 16; otherwise, we don't meet the remainder requirements.
Divide n over 12 and we get some quotient x and remainder 3
So,
n/12 = (quotient) + (remainder)/12
n/12 = x + 3/12
Multiply both sides by 12 to end up with
n = 12x + 3
Similarly, if we divide over 16 we get some other quotient y and remainder 7
n/16 = y + 7/16
which turns into
n = 16y + 7
after multiplying both sides by 16
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We have these two equations
n = 12x+3n = 16y+7Apply substitution and do a bit of rearranging like so
12x+3 = 16y+7
12x-16y = 7-3
4(3x-4y) = 4
3x-4y = 4/4
3x-4y = 1
The goal from here is to find the smallest positive integers x and y that make that equation true. We have a few options here and they are
Guess and check: We have a small sample size to work with so it shouldn't take too long. Make a table of xy values where you have x along the top row and y along the left column. Then plug each x,y pair into the equation above to see if you get a true statement or not. Again, keep in mind that x and y are positive integers. Graphing: Graph the line 3x-4y = 1, which is the same as y = (3/4)x - 1/4 and note where the line lands on a lattice point. Focus on the upper right quadrant of the graph. This quadrant is above the x axis and to the right of the y axis.Extended Euclidean Algorithm: This method is the most efficient, but it's only useful if your teacher has gone over it.Whichever method you use, you should find that (x,y) = (3,2) is the point we want.
Note how:
3x-4y = 1
3(3)-4(2) = 1
9-8 = 1
1 = 1
So that verifies (3,2) is on the line 3x-4y = 1.
Because x = 3 and y = 2, we know that
n = 12x + 3
n = 12*3 + 3
n = 39
and we can see that
n = 16y + 7
n = 16*2 + 7
n = 39
So 39 is the smallest such integer such that when we divide it over 12 and 16, we get remainders 3 and 7 respectively.
Here's a quick verification that we've fit the requirements.
39/12 = 3 remainder 3
39/16 = 2 remainder 7
We know we hit the smallest value of n because (x,y) was made to be the smallest positive integer solution to 3x-4y = 1. There are infinitely many positive integer (x,y) solutions to 3x-4y = 1, which in turn means there are infinitely many numbers n that satisfy the remainder conditions (but n is not the smallest possible in those cases).
y
is directly proportional to
x
2
.
If
y
=
12
when
x
=
2
find
y
when
x
=
6
Answer:
y=54+7
Step-by-step explanation:
Please!!!!! help!!!!!
Answer:
유퓨요ㅛㅜㅑㅑㅅ재 내 8 ㅓㅕ를펴 16 ㅐㅏ?
Step-by-step explanation:
Choose Yes or No to tell if the expression is equal to 8 x 40.
Help me plzzzzzzzzzz.z.z.z.z.z.z..z.z.z.z
Answer:
Area of rectangle = 10 in.²
Area of triangle = 0.5 in.²
Square inches of plastic in bookmark = 9.5 in.²
Step-by-step explanation:
✔️Area of rectangle = Length × Width
Length = 5 in.
Width = 2 in.
Area of rectangle = 5 × 2 = 10 in.²
✔️Area of Triangle = ½*bh
b = 1 in.
h = 1 in.²
Area of triangle = ½*1*1
Area of triangle = 0.5 in.²
✔️Square inches of plastic in bookmark = area of rectangle - area of triangle
= 10 - 0.5 = 9.5 in²
The temperature changes from 9°F to -5°F. Which of the following expressions model the distance on thermometer between 9°F and -5°F? Choose all the correct answers
A I -5 -9 I
B I 9 -5 I
C I 9- (-5) I
D I -5 (-9) I
E I -9 - (-5) I
Answer:
[tex]d = |- 5- 9|[/tex]
Step-by-step explanation:
Given
[tex]Initial = 9^\circ F[/tex]
[tex]Final = -5^\circ F[/tex]
Required
Determine the difference
Represent this with d.
d is calculated using
[tex]d = |Final - Initial|[/tex]
The equation becomes
[tex]d = |- 5- 9|[/tex]
2 to the third power minus the quantity of (2x3) +(-4) =
could show the step by step process of working this problem
An organization published an article stating that in any one-year period, approximately 10.2% of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, nine of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country.
1. Calculate the following.
a. x =
b. p' =
c. n =
2. Calculate σx.
3. Find the p-value.
Answer:
W21221
Step-by-step explanation:
please help i need help
Answer:
(9×3÷4)+y
Step-by-step explanation:
(9×3÷4)+y = y+9 × 3/4
3/4 = 3:4
9× 3/4 = 9×3÷4
there is y+ (9× 3 ÷ 4)
what is the answer to 3/4 x 5/6
Answer:
[tex] \frac{3}{4} \times \frac{5}{6} [/tex]
[tex] \frac{3 \times 5}{4 \times 6} [/tex]
[tex] \frac{15}{24} [/tex]
[tex] \frac{5}{8} [/tex]
Answer:
5/8
Step-by-step explanation:
Sorry for the messy handwriting.
Hope this helps! Have a great day!
There are 85 sixth grade students in Mr. Green’s math class. This makes up 34% of the students in 6th grade in the school. What is the total amount of students in 6th grade?
Answer:
250
Step-by-step explanation:
Take the part (85) and put it over 34% like a fraction.
85 x
34 100
Then do 85 times 100
8500
Then divide it by your percent (34)
8500/34=250
Because of bad weather, the number of days next week that the captain of a charter fishing boat can leave port is uncertain. The following probability distribution for the number of days that the boat is able to leave port per week was determined based on historical data when the weather was poor: The number of days the boat can leave port per week Probability 0 0.20 1 0.05 2 0.05 3 0.05 4 0.15 5 0.10 6 0.15 7 0.25 Based on the probability distribution, what is the expected number of days per week the captain can leave port. Group of answer choices 3.55 4.00 3.50 4.05 2.85
Answer:
The expected number of days per week the captain can leave port is 4.05.
Step-by-step explanation:
We are given the following distribution:
[tex]P(X = 0) = 0.2[/tex]
[tex]P(X = 1) = 0.05[/tex]
[tex]P(X = 2) = 0.05[/tex]
[tex]P(X = 3) = 0.05[/tex]
[tex]P(X = 4) = 0.15[/tex]
[tex]P(X = 5) = 0.1[/tex]
[tex]P(X = 6) = 0.15[/tex]
[tex]P(X = 7) = 0.25[/tex]
What is the expected number of days per week the captain can leave port.
We multiply each outcome by its probability. So
[tex]E = 0*0.2 + 1*0.05 + 2*0.05 + 3*0.05 + 4*0.15 + 5*0.1 + 6*0.15 + 7*0.25 = 4.05[/tex]
The expected number of days per week the captain can leave port is 4.05.
What is the equation of the circle with a radius of 4 and a center at (3, 2) ?
Answer:
(x - 3)^2 + (y + 2)^2 = 16
Step-by-step explanation:
(x - h)^2 + (y - k)^2 = r^2
r = radius
(h, k ) is center of circle.
The center of the circle is (3, 2) and r is 4.
(x - 3)^2 + (y + 2)^2
16
Best of luck :3
•) Zeeshaan bought 12 kilograms of wheat seeds and 18 kilograms of rice seeds. How many kilograms of seeds did he buy ?
PLEASE HELP WITH THE FOLLOWING. WILL GIVE BRAINLIEST. THANK YOU
Answer:
50.8°Step-by-step explanation:
First, we need to use the Pythagorean Theorem to find the third side. We will then use the law of cosines to find the angle.
2√15² = 2√6² + b²
60 = 24 + b²
Subtract 24
36 = b²
b = 6
Now, that we have all three sides, we will use the law of cosines to figure out the angle.
c² = a² + b² - 2abCosC°
Substitute the values in.
6² = 2√15² + 2√6² - 2(2√15)(2√6)CosC°
36 = 60 + 24 - 2(37.947331922)CosC°
36 = 60 + 24 - 75.894663844CosC°
36 = 84 - 75.894663844CosC°
Subtract 84
-48 = -75.9CosC°
0.63241106719 = CosC°
Arccos (0.63241106719) = 50.77176844°
The largest acute angle is approximately 50.8°
what is the shape and direction of f(x)=(x+7)(x+11)
Given:
The function is
[tex]f(x)=(x+7)(x+11)[/tex]
To find:
The shape and direction of the given function.
Solution:
We have,
[tex]f(x)=(x+7)(x+11)[/tex]
It can be written as
[tex]f(x)=x^2+11x+7x+77[/tex]
[tex]f(x)=x^2+18x+77[/tex]
It is a quadratic function and the power of [tex]x[/tex] is 2 so the graph of this function is a vertical parabola.
The leading coefficient is positive so the parabola opens upward.
Therefore, the given function is a vertical parabola that opens upward.
Which figures always have right angles
Answer:
rectangles, squares, and right triangles
help me please
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Joel had a coin collection. He had two hundred coins,
which were dimes and quarters. The total value of his
collection was worth $32.
Remember to define your variables.
Create 2 equations
(Each equation should have a "common theme" for
example in this problem one equation will be the the
total number of coins and the other will be the total
value of the coins)
The next step is to solve the problem. Remember to
think of the best method for problem solving
Answer:
Joel's coin collection had 120 dimes and 80 quarters.
Step-by-step explanation:
Given that Joel had a coin collection of two hundred coins, which were dimes and quarters, and the total value was worth $32, to determine how many coins of each type he had, the following equations must be performed:
0.25 - 0.10 = 0.15
200 x 0.10 = 20
32 - 20 = 12
12 / 0.15 = 80
200 - 80 = 120
(80 x 0.25) + (120 x 0.1) = X
20 + 12 = X
32 = X
Therefore, Joel's coin collection had 120 dimes and 80 quarters.
What is 14 2/7 x 4 3/10=
Answer:
430/ 7
Step-by-step explanation:
yess this is the correct answer
Is 17—6x a expression or Equation
Answer:
expression because an equation has to have a plus +×÷ or divsion sign to be an equation
Find the area of this figure around your answer to the nearest 100. use 3.14 to approximate 3.14 as pi
Answer:
Area = 49.12 ft²
Step-by-step explanation:
The area of the figure = area of triangle + area of half of a circle
= ½*bh + ½(πr²)
b = 6 ft
h = 8 ft
r = ½ of 8 ft = 4 ft
π = 3.14
Plug in the values
Area of the figure = ½*6*8 + ½(3.14*4²)
Area = 24 + 25.12
Area = 49.12 ft²
Answer:
49.12
Step-by-step explanation:
Twenty-five less than the product of three and ten and five tenths.
Answer:
On the left side is "13", that is the whole number part. There are two digits on the right side, the 7 is in the "tenths" position, and the 6 is the "hundredths" position. So, 13.76 is "13 and 7 tenths and 6 hundredths".
Step-by-step explanation:
Answer:
3 x 10 x .5 - 25
Step-by-step explanation:
Is your expression
What is 3 divided by 1/3?
Answer:
It will be 9
hope this helps
Answer:
9
Step-by-step explanation:
3/1 ÷ 1/3 = 3/1 · 3/1 = 9
9.85xs;s=4
help me. please
Answer:
39.4
Step-by-step explanation:
9.85 * (4) = 39.4
What is the slope of the line X=-3?
Answer:
undefined
Step-by-step explanation:
Answer:
The slope is undefined
Step-by-step explanation:
The relationship is “hours multiplied by
equals the number of dogs.”
Answer:
3
Step-by-step explanation:
Answer:
The relationship is “hours multiplied by
3
equals the number of dogs.”
Step-by-step explanation:
there are only two lines of symmetry in a circle true or false
Answer:False
Step-by-step explanation: a circle has infinite lines of symmetry an oval has two
Allison had 310 rocks in the rock collection after three months, her collection increases by 40% how many rocks does she have now?
Answer:
434
Step-by-step explanation:
310 times .4 (percentage) = 124 which is how much she gained, then you add that onto the original amount to find how many she has now, which is 434
Due Now
How do matter and energy move through an ecosystem?
Step-by-step explanation:
How Matter Moves Through Ecosystems
Decomposers release nutrients when they break down dead organisms. The nutrients are taken up by plants through their roots. The nutrients pass to primary consumers when they eat the plants. The nutrients pass to higher-level consumers when they eat lower-level consumers. When living things die, the cycle repeats.How Energy Moves Through Ecosystems
Energy is transferred between organisms in food webs from producers to consumers. The energy is used by organisms to carry out complex tasks. The vast majority of energy that exists in food webs originates from the sun and is converted (transformed) into chemical energy by the process of photosynthesis in plants. A small proportion of this chemical energy is transformed directly into heat when compounds are broken down during respiration in plants. The majority of the chemical energy stored in plants is transformed into other forms by an assortment of consumers, such as cows, rabbits, horses, sheep, caterpillars, and other insects eating plants.what fraction is 15 minutes of 1 hour
Answer:
1/4
Step-by-step explanation:
Convert 1 hour to minutes
1 hour = 60 minutes
Then you can find the fraction
15/60
simplifies to 1/4
15 minutes is 1/4 of 60 minutes/1 hour