Answer: n = 412
Step-by-step explanation:
If the last two digits of a number are divisible by 4, the whole number is divisible by 4 since any multiple of 100 is divisible by 4. The largest number that can be created is 421 since the largest number is in the hundreds place and then the second largest number is in the tens place, but 21 is not divisible by 4. The second largest number, 412, still has the greatest number as the hundreds place, but the tens place is now smaller. 12 is divisible by 4, so 412 is divisible by 4. We know that 412 is the largest possible number for n because there is only one larger number than 412, which is 421 and it is not divisible by 4.
Answer:
The largest possible n is 9412-----------------------------
Divisibility rule for 4:
If the last two digits of a number are divisible by 4, the number is divisible by 4We have 3 digits and the greatest number can be made by these digits is 421. But it has to be divisible by 4, hence we rearrange it to 412. Since 12 is divisible by 4, the number is divisible by 4.
Now, we choose 9 as the fourth digit. It will be a first digit from left and form the largest possible number n:
n = 9412Find the derivative of f(x) = cot-1(2x + 1).
The first derivative of the inverse trigonometric function is equal to f'(x) = - 2 / [1 + (2 · x + 1)².
How to get the first derivative of an inverse trigonometric function
Herein we find the definition of an inverse trigonometric function, whose first derivative must be found by using derivative rules and especially derivative formulas for inverse trigonometric functions and chain rule. First, write the original function:
f(x) = cot⁻¹ (2 · x + 1)
Second, use derivative rules to determine the derivative:
f'(x) = [- 1 / [1 + (2 · x + 1)²]] · 2
f'(x) = - 2 / [1 + (2 · x + 1)²
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The surface area of a cylinder is 2,285.92 square inches. What is the height?
The height of the cylinder is determined as 36.2 inches.
What is the height of the cylinder?The height of the cylinder is calculated by applying the formula for surface area of a cylinder as shown below;
S.A = 2πr(r + h)
where;
r is the radius of the cylinder h is the height of the cylinderThe height of the cylinder is calculated as follows;
2,285.92 = 2π x 8.2 (8.2 + h)
2,285.92 = 51.52(8.2 + h)
8.2 + h = 2,285.92/51.52
8.2 + h = 44.37
h = 36.2 inches
Thus, the height of the cylinder for the given radius and surface area is determined by using the equation for surface area of a cylinder.
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The complete question is below:
The surface area of a cylinder is 2,285.92 square inches. What is the height? if the radius of the cylinder is 8.2 inches.
The triangular prism below has a height of 13.4 units3 and a volume of 536 units
Find the area of one of its bases.
Answer: 40
Step-by-step explanation:
Divide. (10m8 + 4m6 + 10m5) ÷ 2m2 5m6 + 4m4 + 10m3 5m6 + 2m4 + 10m5 5m6 + 2m4 + 5m3 5m8 + 2m6 + 5m5
The remainder when dividing
[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] is
[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
To find the remainder when dividing
[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3),[/tex] we can use polynomial long division.
The dividend is[tex](10m^8 + 4m^6 + 10m^5)[/tex] and the divisor is [tex](2m^2 + 5m^6 + 4m^4 + 10m^3).[/tex]
Starting with the highest degree term, we divide ([tex]10m^8[/tex]) by ([tex]2m^2[/tex]) which gives us [tex]5m^6[/tex].
Next, we multiply the entire divisor [tex](2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] by [tex]5m^6[/tex], which gives us ([tex]10m^8 + 25m^{12} + 20m^{10} + 50m^9[/tex]).
We then subtract this product from the original dividend:
[tex](10m^8 + 4m^6 + 10m^5) - (10m^8 + 25m^{12} + 20m^{10} + 50m^9)[/tex] =[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
We repeat the process with the new dividend ([tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex]) and the divisor ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]).
Continuing the long division process, we eventually find the remainder to be: [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
Therefore, the remainder when dividing ([tex]10m^8 + 4m^6 + 10m^5[/tex]) by ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]) is [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex].
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Note the full question is:
Divide. (10m8 + 4m6 + 10m5) ÷ 2m2 5m6 + 4m4 + 10m3 5m6 + 2m4 + 10m5 5m6 + 2m4 + 5m3 5m8 + 2m6 + 5m5
What is the reminder
A school of 800 students has 60% girls.
Of them, 50% go to music classes. 10% of those music students are into volleyball. If the team is
32 Girls, how many are not into music?
Answer:
8
Step-by-step explanation:
I will just calculate the population of every detail for ease.
800 total students.
800 * 60% or 0.6 = 480
480 girls.
480 * 50% or 0.5 = 240
240 music class girls.
240 * 10% or 0.1 = 24
24 music class girls.
so 24 music class girls that are into volleyball and 32 team girls.
32-24 = 8
8 of the team girls are not into music.
Suppose that an individual has a body fat percentage of 17.8% and weighs 173 pounds how many pounds of his weight is made up of fat round you answer to the nearest tenth
30.8 pounds of the individual's weight is made up of fat, rounded to the nearest tenth.
To calculate the pounds of body fat, we need to multiply the body weight by the body fat percentage in decimal form:
173 pounds x 0.178 = 30.794 pounds
Therefore, approximately 30.8 pounds of his weight is made up of fat.
To find out how many pounds of an individual's weight is made up of fat, you can use the following formula:
Total weight x Body fat percentage = Fat weight
In this case:
173 pounds x 0.178 (17.8%) ≈ 30.8 pounds
So, approximately 30.8 pounds of the individual's weight is made up of fat, rounded to the nearest tenth.
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You roll a 6-sided die.
What is P(odd or less than 2)?
Answer:
50%.
Step-by-step explanation:
If the die is perfectly balanced, the probability of rolling an odd number is 3 out of 6, or 50%.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B)
Step-by-step explanation:
Geometric mean:
[tex]\sf 5 , a_2,a_3, a_4, a_5,1215[/tex]
[tex]\bf a_1 = first \ term = 5[/tex]
n = number of terms = 6
r = common ratio
[tex]\boxed{\bf a_n = a_1 * r^{n-1}}[/tex]
[tex]a^{6} = 5 *r^{6-1}\\\\1215 = 5*r^5\\\\ \dfrac{1215}{5}=r^5\\\\243=r^5\\\\3^5=r^5[/tex]
As powers are same, compare the bases,
r = 3
Each term is obtained by multiplying the previous term by the common ratio. r = 3
[tex]\sf a_2 = 5*3 = 15\\\\a_3= 15*3 = 45\\\\a_4 = 45 *3 =135\\\\ a_5 = 135*3 = 405[/tex]
The price of a home is $170,000. The bank requires a 15% down payment. The buyer is offered two mortgage options: 15-year fixed at 10% or 30-year fixed at 10%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 15-year option? Use the following formula to determine the regular payment amount.
Answer:36000
Step-by-step explanation:
He saves 36000 dollars
what the answer for this?
Can someone help me pleaseeee
The solution to the system of equations, using the Gauss-Jordan method, is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]
How to solve the system of equations?The matrix representing the system of equations is given as follows:
[tex]\left[\begin{array}{cccc}-5&-3&-4&-12\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]
First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1/5, that is:
R1 -> -1/5R1
Hence:
[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]
First we want a value of 1 at line 2, column 2, hence we multiply the second line by -1/2, that is:
R2 -> -1/2R2
Hence:
[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&1&4&-22\end{array}\right][/tex]
We want an element of zero at line 3, column 2, hence:
R3 -> R3 - R2
Hence:
[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&2.5&-3\end{array}\right][/tex]
First we want a value of 1 at line 3, column 3, hence we multiply the third line by 2.5, that is:
R3 -> 1/2.5R3
Hence:
[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&1&1.2\end{array}\right][/tex]
Then the solution to the system of equations is given as follows:
z = 1.2.y = -19 - 1.5z = -21.4.x = 2.4 - 0.6y - 0.8z = 14.28.Hence the row-echelon form is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]
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A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 58° and AB = 9.3.
Calculate the length of BC rounded to 3 SF.
Answer:
To calculate the length of BC in the triangle ABC, we can use the trigonometric functions sine and cosine.
Given that ∠CAB = 90° and ∠ABC = 58°, we can determine that ∠BCA = 180° - 90° - 58° = 32°.
Using the sine function, we can find the length of BC:
sin(∠BCA) = BC / AB
Rearranging the formula, we have:
BC = AB * sin(∠BCA)
Substituting the given values:
BC = 9.3 * sin(32°)
Using a calculator or trigonometric table, we find:
BC ≈ 9.3 * 0.529 = 4.917
Rounding to three significant figures (SF), the length of BC is approximately 4.92 units.
Step-by-step explanation:
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 105 months, with a variance of 81 . If he is correct, what is the probability that the mean of a sample of 70 computers would differ from the population mean by less than 1.9 months? Round your answer to four decimal places.
The requried probability that the mean of a sample of 70 computers would differ from the population means by less than 1.9 months is 0.8671, rounded to four decimal places.
The mean of the sampling distribution of the sample means is:
u = 105
and the variance of the sampling distribution of the sample means is:
σ² = 81/70
We can standardize the distribution of the sample means by using the z-score formula:
z = (x - u) / (σ/ √(n))
where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
We want to find the probability that the sample mean differs from the population mean by less than 1.9 months, or |x - u| < 1.9. This is equivalent to finding the probability that the standardized sample mean falls within the range:
-1.9 / (σ/ √(n)) < z < 1.9 / (σ/ √(n))
Substituting the values we have, we get:
-1.9 / (9 / √(70)) < z < 1.9 / (9 / √(70))
Simplifying, we get:
-1.1158 < z < 1.1158
Using a standard normal distribution table, we can find the probability that the z-score falls within this range:
P(-1.1158 < z < 1.1158) = 0.8671
Therefore, the probability that the mean of a sample of 70 computers would differ from the population means by less than 1.9 months is 0.8671, rounded to four decimal places.
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5. Sketch rectangles with whole number dimension with perimeters that range from 12 to 16 units. a) For each perimeter, what are the dimensions of the rectangle that give the greatest area? b) For each perimeter, what are the dimensions of the rectangle that give the least area? 6. Draw a figure made from square tiles where adding an additional tile decreases the perimeter. 7. A student claims that perimeter is a 2-dimensional measure because one needs to know length and width (or base and height) in order to measure it. How would you respond to this student? 8. Compare a square, equilateral triangle, and circle that each have perimeter of 12 cm. Which has the greatest area? Which has the least area?
The solution to all parts are shown below.
a) For a rectangle with a perimeter of 12 units, the dimensions that give the greatest area are 3 units by 3 units.
For a perimeter of 13 units, the dimensions are 3 units by 3.5 units.
For a perimeter of 14 units, the dimensions are 3.5 units by 3.5 units.
For a perimeter of 15 units, the dimensions are 3.5 units by 4 units.
For a perimeter of 16 units, the dimensions are 4 units by 4 units.
b) For a rectangle with a perimeter of 12 units, the dimensions that give the least area are 1 unit by 5 units.
For a perimeter of 13 units, the dimensions are 1 unit by 6 units.
For a perimeter of 14 units, the dimensions are 2 units by 5 units.
For a perimeter of 15 units, the dimensions are 2 units by 6 units.
For a perimeter of 16 units, the dimensions are 2 units by 7 units.
6. One possible figure made from square tiles where adding an additional tile decreases the perimeter is a "U" shape.
If you arrange 9 square tiles in the shape of a "U", the perimeter is 12 units. If you add another tile to the middle of the "U", the perimeter will decrease to 10 units.
7. Perimeter is a 1-dimensional measure because it only involves adding up the lengths of the sides of a shape. The student's claim that perimeter is a 2-dimensional measure is incorrect.
8. For a square, equilateral triangle, and circle each with a perimeter of 12 cm, the circle has the greatest area and the equilateral triangle has the least area.
To see this, we can use the formulas for the perimeter and area of each shape:
A square with a perimeter of 12 cm has side length 3 cm.Its area is (3 cm)² = 9 cm².
An equilateral triangle with a perimeter of 12 cm has side length 4 cm.Its area can be calculated using the formula A = (√(3)/4) x s², where s is the side length of the triangle.
Thus, the area is (√(3)/4) x (4 cm)² = 4sqrt(3) cm², which is approximately 6.9 cm².
A circle with a perimeter of 12 cm has circumference 12 cm.Its radius can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle.
Thus, r = 6/(2π) cm, which is approximately 0.955 cm.
The area of the circle is πr², which is approximately 2.87 cm².
Therefore, the circle has the greatest area, followed by the square, and the equilateral triangle has the least area.
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Nam asked his mother's permission to go buy toys to give to Tuan's friend on the occasion of his birthday. Men buy two toys with list prices of VND 45,000 and VND 25,000 respectively and receive a 10% discount. how much does the male have to pay to buy those two toys?
Answer:
The total cost of the two toys before the discount is VND 45,000 + VND 25,000 = VND 70,000.
Step-by-step explanation:
The discount is 10% of the total cost, which is 0.1 x VND 70,000 = VND 7,000.
Therefore, the final cost after the discount is VND 70,000 - VND 7,000 = VND 63,000.
Nam will have to pay VND 63,000 to buy the two toys after the discount.
determine unkown side length in a right triangle. round to nearest tenth.
side 1= 9
side 2= 3
Step-by-step explanation:
If side 1 and side 2 are LEGS of the triangle, then hypotenuse is found by
hyp^2 = 9^2 + 3^2 using pythagorean theorem
hyp^2 = 90
hyp = sqrt 90 = 3 sqt 10 =9.5 units
If hyp is 9 and 3 is one leg:
9^2 = 3^2 + L^2
L = 6 sqrt 2 =8.5 units
Please help me with these questions
The value of each angle 6x + 7 and 4x + 3 will be 55° and 35°, respectively.
Given that:
Angles, ∠1 = 6x + 7 and ∠2 = 4x + 3
Two angles are said to be complementary angles if their sum is 90 degrees.
The equation is given as,
∠1 + ∠2 = 90°
6x + 7 + 4x + 3 = 90°
10x + 10 = 90°
10x = 80°
x = 8
The value of each angle is calculated as,
∠1 = 6 * 8 + 7
∠1 = 55°
∠2 = 4 * 8 + 3
∠2 = 35°
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A math quiz has 3 multiple choice questions and 2 true/false questions. Each multiple choice questions has 4 answer options: A, B, C, D.
Find the number of possible outcomes.
Answer:
The total number of possible outcomes for the math quiz is 16
Step-by-step explanation:
What is the mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs?
The mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population of GPAs.
The mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population. This is due to the central limit theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Therefore, if we were to take all possible samples of size 81 from the population of GPAs and calculate the mean of each sample, the distribution of these means would be approximately normal with a mean equal to the population mean of GPAs. This means that if we take a large number of samples of size 81 and calculate the mean of each sample, the average of these means will be very close to the population mean of GPAs.
In conclusion, the mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population of GPAs.
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PLEASE SEE IMAGE TO SOLVE PROBLEM
Answer:
r(x) = x(x - 7)
Step-by-step explanation:
given the roots of a parabola x = a , x = b , then
the corresponding factors are (x - a) and (x - b)
from the graph the roots are where the graph crosses the x- axis
the graph crosses the x- axis at x = 0 and x = 7 , then
the corresponding factors are (x - 0) and (x - 7) , that is x and (x - 7)
the equation is then the product of the factors , that is
r(x) = x(x - 7)
Whats the probability either event will occur?
Answer: 0.68
Step-by-step explanation:
Help pleaseee is just one problem
The matrices after the row operations are given as follows:
a) [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
b) [tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]
How to obtain the resultant matrices?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]
When we multiply a matrix row by a constant, each element of the row is multiplied by the constant.
Hence the resulting matrix after we multiply row 3 by 2 is given as follows:
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
We can also exchange rows of the matrix, hence the resulting matrix after rows 1 and 3 are exchanged is given as follows:
[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]
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A line has a slope of 7 and includes the points (-5,-5) and (-3,w). What is the value of w?
The value of w is 9.
We can use the slope formula to find the value of w.
The slope formula is:
m =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]
where m is the slope of the line and [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are two points on the line.
We know that the slope of the line is 7, and the two points on the line are (-5, -5) and (-3, w). So we can plug in these values into the slope formula and solve for w:
7 = (w - (-5)) / (-3 - (-5))
Simplifying the right-hand side, we get:
7 = (w + 5) / 2
Multiplying both sides by 2, we get:
14 = w + 5
Subtracting 5 from both sides, we get:
w = 9
Therefore, the value of w is 9.
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Find the area of the regular polygon. Round your answer to the nearest hundredt
7
square units
Answer: A ≈ 127.31 units²
Step-by-step explanation:
We can use the given formula for the area of a regular hexagon, where a is equal to a given side (here, that is 7).
[tex]\displaystyle A=\frac{3\sqrt{3} }{2} a^2[/tex]
We will substitute known values and solve by computing and simplifying.
[tex]\displaystyle A=\frac{3\sqrt{3} }{2} a^2[/tex]
[tex]\displaystyle A=\frac{3\sqrt{3} }{2} (7)^2[/tex]
[tex]\displaystyle A=\frac{5.1961524}{2} 49[/tex]
[tex]\displaystyle A=(2.59807621)(49)[/tex]
[tex]\displaystyle A=127.3057[/tex]
[tex]\displaystyle A\approx 127.31[/tex]
how do i solve these types of problems?
Tick the box to show where the hyphen is needed in the sentence below.
Answer:
I’m sorry but I don’t see any sentence below. Could you please provide me with the sentence?
3.the diameter of a drum is 150 cm. What is the area of the space where the drum stands
4.Rachel is making a circular table cloth with a radius of 48 dm. How much area of the wall did it occupy?
5.A circular clock with a circumference of 75 cm is attached on a wall. How much area of the wall did it occupy?
Please answer it and do not please joke around
Answer:
All you have to do is to find the area of a circle to know the area it will contain.
Step-by-step explanation:
3. d=150cm= 150/100m=1.5m
r= 1.5/2= 0.75m
since a drum is circular under it will take a circular area
Area of a circle=πr^2
=π×(0.75)^2
=0.5625π = 1.77m^2
4. r=48dm=48/10=4.8m
since the clock is circular it will contact a circular area
Area of a circle= πr^2
=π(4.8)^2
=23.04π= 72.38m^2
5. since it's circular
C=75cm=75/100m=0.75m
Circumference of a circle=2πr
0.75=2πr
r=0.75/2π
r=0.119m
Area of a circle= πr^2
=π×(0.119)^2
=0.045m^2
I hope it helps.
Can someone please help me with this? I’ll give brainlist!!
Answer:
12) x = 6. 13) not tangent
Step-by-step explanation:
12) x² - 5 = 31 (since they are both tangents)
x² = 31 + 5 = 36
x = ±6
x = +6 (has to be positive since it's a length).
13) if it was tangent, angle BAC would be 90°.
that would also mean AB² = BC² - AC²
= 15² - 5²
= 225 - 25
= 200
AB = √200 ≠ 14.
Since the values are different, AB is not a tangent to the circle
Can you Please calculate this:
Answer:
14
Step-by-step explanation:
used a calculator to check the answer
A truck driver travels 400 miles on day one and 215 miles on day two. The driver spent a total of 10 hours and 12 minutes driving on the two days. What was the truck driver's average speed in miles per hour (mph)? (Round to the nearest tenth.)
Answer:37.5 average
Step-by-step explanation:I think
