The solution is, (a/2) ^4 or a^4/16 is in Simplest Form of (8a^3)^-4/3.
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here , we have,
(8a^-3)^-4/3
split into two parts
8^ -4/3 * (a^-3)^-4/3
using the power to the power rule we can multiply the exponents
8^(-4/3) *a^(-3*-4/3)
8^ (-4/3) * a^(4)
replace 8 with 2^3
(2^3)^(-4/3) * a^(4)
using the power to the power rule we can multiply the exponents
2^(3*-4/3) * a^(4)
2 ^ (-4) * a^4
the negative exponent means it goes in the denominator if it is in the numerator
a^4/2^4
make a fraction
(a/2) ^4
or a^2/16
Hence, The solution is, (a/2) ^4 or a^4/16 is in Simplest Form of (8a^3)^-4/3.
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the radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.6 in/s. at what rate is the volume of the cone changing when the radius is 144 in. and the height is 138 in.?
Answer:
Let's use the formula for the volume of a right circular cone to solve this problem:
V = (1/3)πr^2h
We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.
Using the chain rule of differentiation, we can express the rate of change of the volume as follows:
dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)
To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:
dV/dr = (2/3)πrh
dV/dh = (1/3)πr^2
Substituting the given values and their rates of change, we have:
dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)
dV/dt = 55,742.4 - 1,994,598.4
dV/dt = -1,938,856 in^3/s
Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.
Step-by-step explanation:
Does someone mind helping me with this problem? Thank you!
the answer to the problem that you need to is 1024
Education Planning For the past 15 years, an employee of a large corporation has been investing in an employee sponsored educational savings plan. The employee has invested $8,000 dollars per year. Treat the investment as a continuous stream with interest paid at a rate of 4.2% compounded continuously.
a. What is the present value of the investment?
b. How much money would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the amount found in part a?
The amount that would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the present value is $37,537.19.
The investment can be treated as a continuous stream with the interest paid at a rate of 4.2% compounded continuously.The present value of the investment can be calculated using the formula:P = C/e^(rt)Where,P = Present ValueC = Cash Flowsr = Interest Rate Per Periodt = Number of Periodse = Euler’s numberThe given values are as follows:C = $8,000 per yearr = 4.2% compounded continuously for 15 years.
C = $8,000e = 2.71828t = 15 yearsNow, we need to calculate the present value using the above formula.P = 8000/e^(0.042 x 15) = $82,273.24.The formula to calculate the amount that would have been invested 15 years ago is:A = P x e^(rt)Where,A = Future Value of the investmentP = Present Value of the investmentr = Rate of Interest Per Periodt = Number of Periodse = Euler’s numberThe present value of the investment is $82,273.24.
The rate of interest is 4.2% compounded continuously.t = 15 yearsNow, we need to calculate the amount that would have been invested 15 years ago.A = 82,273.24 x e^(0.042 x 15) = $37,537.19
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Joan has a credit limit of $900. Her new balance is $450. What is Joan's available credit?
Hi!
Let's write this out.
Her limit is $900, and she's used $450. So, we subtract 450 from 900.
900-450 = 450.
So, she has $450 available credit left.
Hope this helps!
~~~PicklePoppers~~~
Answer: your credit utilization ratio on that card would be 50% but the answer is 450
Step-by-step explanation:
900-450 = 450
when calculating confidence intervals in this class the product of a constant times a margin of error is added and subtracted to what value to obtain the ci range? group of answer choices mean standard deviation alpha median
The confidence interval is calculated by adding and subtracting the product of a constant (usually 1.96), the margin of error, and the mean.
The constant times the margin of error is added and subtracted from the sample mean to obtain the confidence interval range.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
The constant is determined by the confidence level of your analysis (typically 95%) and the margin of error is determined by the standard deviation and the size of your sample.
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find the derivative of y equals 5 x squared sec to the power of short dash 1 end exponent (2 x minus 3 )
The derivative of the given function [tex]y = 5x^2 sec^{(-1)(2x-3)^2}[/tex] is [tex]dy/dx=-20x\sqrt{((2x-3)^2-1)}[/tex]
It can be derived as:
We can use the chain rule and the derivative of [tex]sec^{(-1)x}[/tex] which is [tex]-1/(x*\sqrt{(x^2-1)})[/tex]
First, we apply the chain rule to the function.
Let [tex]u = (2x-3)^2[/tex], then:
[tex]y = 5x^2 sec^{(-1)u}[/tex]
[tex]dy/dx = d/dx [5x^2 sec^{(-1)u}][/tex]
[tex]dy/dx = d/dx [5x^2 sec^{(-1)[(2x-3)^2]}][/tex]
[tex]dy/dx= 5x^2 d/dx[sec^{(-1)u}][/tex] (Using the chain rule)
Now, let [tex]v = u^{(1/2)} = (2x-3)[/tex].
Then:
[tex]dy/dx = 5x^2 d/dv [sec^{(-1)v}] dv/dx[/tex] (Using the chain rule again)
We have:
[tex]d/dv [sec^{(-1)v}] = -1/(v*\sqrt{(v^2-1)}) = -1/[(2x-3)*\sqrt{((2x-3)^2-1)}][/tex]
Also, [tex]dv/dx = 2[/tex]
Substituting these back into the equation:
[tex]dy/dx = 5x^2 d/dv [sec^{(-1)v}] dv/dx[/tex]
[tex]dy/dx= 5x^2 (-1/[(2x-3)*\sqrt{((2x-3)^2-1)}] (2)[/tex]
Simplifying this expression gives:
[tex]dy/dx = -20x (2x-3)/[(2x-3)*\sqrt{((2x-3)^2-1)}][/tex]
[tex]dy/dx = -20x\sqrt{((2x-3)^2-1)}[/tex]
Therefore, the derivative of y with respect to x is:
[tex]dy/dx = -20x\sqrt{((2x-3)^2-1)}[/tex]
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Tickets for the school play cost $5 for students and $8 for adults. For one performance, 128 tickets were sold for $751. How many tickets were for adults and how many were for students?
91 student tickets were sold and 37 adults tickets were sold whose total 128 tickets were sold.
What is elimination method?The elimination method is a technique for solving a system of linear equations, which involves adding or subtracting the equations to eliminate one of the variables, and then solving for the other variable.
According to question:Let x be the number of student tickets sold, and y be the number of adult tickets sold. Then we can set up a system of two equations to represent the information given:
x + y = 128 (1) (the total number of tickets sold is 128)
5x + 8y = 751 (2) (the total revenue from ticket sales is $751)
We can solve for one of the variables in terms of the other in the first equation:
x = 128 - y
Substituting this expression into the second equation to eliminate x, we get:
5(128 - y) + 8y = 751
Expanding and simplifying:
640 - 5y + 8y = 751
3y = 111
y = 37
Therefore, 37 adult tickets were sold. Substituting this value back into equation (1) to solve for x, we get:
x + 37 = 128
x = 91
Therefore, 91 student tickets were sold.
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PLEASE HELP FIRST CORRECT WILL GET BRAINLIEST
Answer: Felipe has walked 25.1 meters.
Step-by-step explanation:
Felipe walks the length of his living room, which is 9.1 meters. He then turns and walks the width of his living room, which is 3.5 meters. Finally, he walks back to the corner he started from, which is another 9.1 meters.
The total distance that Felipe has walked is the sum of the distances he covered in each of these three parts of his walk. So, we need to add up 9.1 meters, 3.5 meters, and 9.1 meters to get the total distance.
9.1 m + 3.5 m + 9.1 m = 21.7 m
Therefore, Felipe has walked 21.7 meters so far. However, he still needs to walk back to the corner he started from. This distance is equal to the diagonal of the rectangle formed by his living room.
We can use the Pythagorean theorem to find the length of this diagonal. The length and width of the rectangle are 9.1 meters and 3.5 meters, respectively. Let d be the length of the diagonal, then:
d² = 9.1² + 3.5²
d² = 83.06
d ≈ 9.11 meters
Therefore, the total distance that Felipe has walked is approximately:
21.7 m + 9.11 m ≈ 25.1 m
So, Felipe has walked about 25.1 meters.
Answer:
Felipe has walked 25.2 meters in total.
Step-by-step explanation:
To find out how far Felipe has walked, we need to calculate the perimeter of his living room. The perimeter is the distance around the outside of a shape.
The formula for the perimeter of a rectangle is:
perimeter = 2(length + width)
Given that the length of Felipe's living room is 9.1 meters and the width is 3.5 meters, we can substitute these values into the formula and get:
perimeter = 2(9.1 + 3.5)
perimeter = 2(12.6)
perimeter = 25.2 meters
1(1/2)= 1 1/2 draw number line and represent this
|-----|-----|-----|----|-----|-----|--│--|-----|----|-----|
-5 -4 -3 -2 -1 0 1 │ 2 3 4 5
1 1/2
On this number line, the tick mark labeled "1 1/2" is located halfway between the integer values of 1 and 2.
To represent the number 1 1/2 on a number line, we need to draw a horizontal line with evenly spaced tick marks. Each tick mark represents a specific value on the number line. Since 1 1/2 is a mixed number that includes a whole number (1) and a fraction (1/2), we need to locate it between the integer values of 1 and 2. The tick mark for 1 1/2 should be halfway between these two integers, which means it would be located at the midpoint of the line segment that connects the tick marks for 1 and 2. By placing the tick mark for 1 1/2 in the correct position on the number line, we can accurately represent this number visually.
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Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.x2+y2=100a) Find dy/dt when x=6, y=8 given that dx/dt=4.b) Find dx/dt when x=8, y=6 given that dy/dt=-2.
a) When x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.
Using implicit differentiation, we have:
2x(dx/dt) + 2y(dy/dt) = 0
Solving for dy/dt, we get:
dy/dt = -(x/y)(dx/dt)
Substituting x = 6, y = 8, and dx/dt = 4, we get:
dy/dt = -(6/8)(4) = -3
Therefore, when x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.
b) Using implicit differentiation again, we have:
2x(dx/dt) + 2y(dy/dt) = 0
Solving for dx/dt, we get:
dx/dt = -(y/x)(dy/dt)
Substituting x = 8, y = 6, and dy/dt = -2, we get:
dx/dt = -(6/8)(-2) = 1.5
Therefore, when x = 8 and y = 6, and dy/dt = -2, the value of dx/dt is 1.5.
To find the values of dy/dt and dx/dt, we used implicit differentiation, which is a technique used to find the derivative of an equation that is not expressed in the form y = f(x).
In this case, we had the equation x^2 + y^2 = 100, and we differentiated both sides of the equation with respect to t. Then, we solved for the required derivative using the given values of x, y, and the other derivative.
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Please simplify the following expression while performing the given operation.
(-3+1)+(-4-i)
Answer:
To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:
(-3+1)+(-4-i) = -2 + (-4-i)
Next, we can simplify the addition of -2 and -4 by adding their numerical values:
-2 + (-4-i) = -6 - i
Therefore, (-3+1)+(-4-i) simplifies to -6-i.
Step-by-step explanation:
how to check 2(a+3)=-12
Answer:
a = -9
Step-by-step explanation:
2(a+3) = -12
2a + 6 = -12
2a = -18
a = -9
Let's Check
2(-9 + 3) = -12
2(-6) = -12
-12 = -12
So, a = -9 is the correct answer.
if a watch costs $40 and you must pay 6.5% sales tax how much will the tax be ?
Answer:$2.60
Step-by-step explanation:40*0.065
Answer:42.06
Step-by-step explanation:
Please help!
The object above is symmetrical through Z. If Y = 11 inches, Z = 13 inches, and H = 6 inches, what is the area of the object?
A. 6.5 square inches
B. 78 square inches
C. 31 square inches
D. 156 square inches
the correct area of the symmetrical object is option (B). 78 square inches.
Definition of SymmetryIf two more identical parts can be separated from a form and arranged in an orderly fashion, the shape is said to be symmetrical. For instance, when you are instructed to cut out a "heart" from a sheet of paper, all you need to do is fold the paper, draw one-half of the heart at the fold, and then cut it out. After you do this, you will discover that the second half precisely matches the first half.
In the first part of the object
Area of the object=½×H×Z
=½×13×6
=39 square inches
Given that object above is symmetrical through Z.
So, the area of 2nd part of object will also be 39 square inches
Hence total area is 78 square inches.
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This was an exceptionally dry year for portions of the southwestern United States. Monthly precipitation in Phoenix, Arizona, was recorded in the table and is modeled by y = –0.04088x2 + 0.4485x + 1.862. In what month did Phoenix receive the lowest amount of precipitation? Month (x) Precipitation January 2.27 inches February ? March ? April ? May ? June ? July ? August ? September 2.59 inches October ? November ? December ? Sketch a graph or fill in the table to answer the question. January February November December
the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.
Why it is and how to form a graph?
To find the month with the lowest amount of precipitation, we need to find the minimum value of the quadratic equation y = –0.04088x²2 + 0.4485x + 1.862.
Using calculus, we can find the minimum point of the quadratic function by taking its derivative and setting it equal to zero:
y' = -0.08176x + 0.4485
0 = -0.08176x + 0.4485
x = 5.484
This means that the minimum value of the function occurs at x = 5.484. Since x represents the month number (with January being 1), we can conclude that the month with the lowest amount of precipitation is February (the second month in the table).
To verify this, we can plug in x = 2 into the quadratic equation:
y = –0.04088(2)²2 + 0.4485(2) + 1.862
y = 2.31752
Therefore, the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.
To graph the function, we can plot the points given in the table and connect them with a smooth curve. Here is a completed table with the missing values:
Month (x) Precipitation
January 1 2.27 inches
February 2 2.32 inches
March 3 2.57 inches
April 4 2.94 inches
May 5 3.43 inches
June 6 3.94 inches
July 7 2.72 inches
August 8 2.86 inches
September 9 2.59 inches
October 10 2.03 inches
November 11 1.46 inches
December 12 1.03 inches
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Answer:
D: December
The given model for precipitation in Phoenix, Arizona is y = –0.04088x2 + 0.4485x + 1.862, where x is the month number (1 for January, 2 for February, and so on) and y is the precipitation in inches. We can use this model to fill in the missing values in the table:
| Month (x) | Precipitation |
|-----------|---------------|
| January | 2.27 inches |
| February | 2.27 inches |
| March | 2.24 inches |
| April | 2.18 inches |
| May | 2.09 inches |
| June | 1.98 inches |
| July | 1.84 inches |
| August | 1.68 inches |
| September | 2.59 inches |
| October | 1.50 inches |
| November | 1.30 inches |
| December | 1.08 inches |
According to the table, Phoenix received the lowest amount of precipitation in **December** with **1.08 inches** of precipitation, so the correct answer is **D. December**.
WILL YOU CRACK THE CODE ? 8 2 One number is correct and well placed One number is correct but wrong place Two numbers are correct but wrong places 3 8 Nothing is correct CODE 8 One number is correct but wrong place
Cracking the code: 8 2One number is correct and well placed One number is correct but in the wrong placeTwo numbers are correct but in the wrong place38Nothing is correctCODE8One number is correct but in the wrong placeCracking the code of this sequence of numbers can be a bit tricky, but let's do it step by step. We are given the following clues about the sequence of numbers:
One number is correct and well placed: Since the sequence of numbers is 8 2, we know that the number 8 is in the first position. So the code is either 8 _ _ _ or _ _ _ 8.One number is correct but in the wrong place: This clue tells us that the number 2 is not in the second position of the code, but it is somewhere else.
Therefore, we know that the code is not 8 2 _ _ or _ _ 2 8.Two numbers are correct but in the wrong places: This clue tells us that the code contains the numbers 3 and 8, but they are in the wrong position. Since the code cannot be 8 2 _ _ or _ _ 2 8, we know that the two correct numbers are not in the last two positions. Therefore, the code must be _ 3 8 _ or _ 8 3 _.Nothing is correct: This clue tells us that the code cannot be 3 8 _, 8 3 _, or _ 3 8 because they all contain at least one correct number. Therefore, the code must be _ _ 3 8 or 3 8 _ _.One number is correct but in the wrong place: This clue tells us that the code cannot be 3 8 _, so it must be 8 3 _. Therefore, the code is 8 3 _ _.I hope this helps you crack the code!
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Can i get assistance with this?
Answer:
see attached
Step-by-step explanation:
You want the given triangle dilated by a factor of -3 about point A.
DilationTo find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.
In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.
This same process can be used to locate the other vertices of the triangle's image.
Brittany needed new tires for her truck. She went to the auto shop and bought 4 tires on sale for $85.95 each. The salesman told her that she saved a total of $96.16. If Brittany saved the same amount on each tire, what was the original price of each tire?
The best solution gets brainlist
Answer:
$109.99
Step-by-step explanation:
The original price of each tire is [tex]\[/tex][tex]109.99[/tex]
Solution:Take the amount saved and divide by 4 to find the amount saved on each tire
[tex]96.16\div4 =24.04[/tex]
Add that to the sale price of each tire to find the original price
[tex]85.95+24.04 =109.99[/tex]
Therefore, The original price is $109.99.
If 140 men working 10 hours a day can build a house in 16 days, find out how many men will build same kind of house in 12 days by working 13 hours a day?
We need 144 men to build the house in 12 days working 13 hours a day.
Let M be the number of men needed to build the house in 12 days working 13 hours a day.
140 x 10 x 16 = M x 13 x 12
Simplifying the equation, we get:
22400 = 156M
Dividing both sides by 156, we get:
M = 144.1
An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.
Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.
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The population of a town is given by the equation p = 200,000 3/4t where t is the number of years since the population was first recorded in the year 2010 Fill in the table below.
The population increase according to the given years will be 27500, 23750 and 20833.
What is multiplication?Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the number.
In this question,
p = 200,000 3/4t
When t=0
p=0
When t=1
p= 20000 3/4= 27500
when t=2
p= 20000 3/8 = 23750
When t=3
p= 20000 3/12 = 20833
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Below is a list of all possible outcomes in the experiment of rolling two die. 1.2 1,3 14 15 1,6 21 22 23 24 25 2,6 34B2 33 3,4 3 5 3.6 41 4 2 43 4,4 4 5 4,6 5 52 33 5 4 5,5 56 6,1 6,2 6.3 6 4 6,5 6.6 Determine the following probabilities. Write your answers as reduced fractions_ P(sum is odd) P(sum is 5) P(sum is 7) = P(sum is 7 and at least one of the die is a 1) = 18 P(sum is 7 or at least one of the die is 1) = 36
Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, 15, 52, 25, 34, and 43Therefore, the probability of the sum being 7 or at least one die being 1 is:P(sum is 7 or at least one die is 1) = 15/36 = 5/12
Hence, P(sum is odd) = 7/36, P(sum is 5) = 1/9, P(sum is 7) = 1/6, P(sum is 7 and at least one die is 1) = 5/18, and P(sum is 7 or at least one die is 1) = 5/12.
In the given experiment of rolling two dice, the following probabilities are to be determined:
P(sum is odd), P(sum is 5), P(sum is 7), P(sum is 7 and at least one of the die is 1), and P(sum is 7 or at least one of the die is 1).The sum of two dice is odd if one die has an odd number and the other has an even number. The possibilities of odd numbers are 1, 3, and 5, while the possibilities of even numbers are 2, 4, and 6. Therefore, the following outcomes satisfy the condition:
1, 22, 24, 36, 42, 44, and 66Thus, the probability of the sum being odd is: P(sum is odd) = 7/36The sum of two dice is 5 if one die has 1 and the other has 4, or one die has 2 and the other has 3. Thus, the following outcomes satisfy the condition:1, 42, 3Therefore, the probability of the sum being 5 is: P(sum is 5) = 4/36 = 1/9The sum of two dice is 7 if the dice show 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.
Thus, the following outcomes satisfy the condition:1, 63, 54, 45, 36, and 2Therefore, the probability of the sum being 7 is: P(sum is 7) = 6/36 = 1/6The sum of two dice is 7 and at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, or 1 and 5. Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, and 15
Therefore, the probability of the sum being 7 and at least one die being 1 is:P(sum is 7 and at least one die is 1) = 10/36 = 5/18The sum of two dice is 7 or at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, 1 and 5, 2 and 5, 5 and 2, 3 and 4, or 4 and 3.
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what is the z-score for the 75th percentile of the standard normal distribution is: 0.67 1.645 1.28 -0.67 -1.28
The z-score for the 75th percentile of the standard normal distribution is given by 0.67 that is option A.
The most significant continuous probability distribution is the Normal Distribution, often known as the Gaussian Distribution. It is also known as a bell curve. The normal distribution represents a large number of random variables either nearly or exactly.
I found one that shows the following:
Z value Table entry
0.67 0.7486
0.68 0.7517
As a result, the Z value for 0.75 is between 0.67 and 0.68.
Interpolation yields the z value of 0.6745.
If you have a TI-84 calculator, you may calculate the z value as follows:
VARS - 2nd (this will show the DISTR menu)
To select invNorm, press 3.
Enter the value for the area/table (0.75)
If you press enter, it will return the z value.
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Complete question:
what is the z-score for the 75th percentile of the standard normal distribution is:
0.67 1.645 1.28 -0.67 -1.28first 6 terms of n² + 7
Answer:
8, 11, 16, 23, 32, and 43.
Step-by-step explanation:
When n = 1:
n² + 7 = 1² + 7 = 8
When n = 2:
n² + 7 = 2² + 7 = 11
When n = 3:
n² + 7 = 3² + 7 = 16
When n = 4:
n² + 7 = 4² + 7 = 23
When n = 5:
n² + 7 = 5² + 7 = 32
When n = 6:
n² + 7 = 6² + 7 = 43
Therefore, the first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.
Answer:
When n = 1, n² + 7 = 1² + 7 = 8
When n = 2, n² + 7 = 2² + 7 = 11
When n = 3, n² + 7 = 3² + 7 = 16
When n = 4, n² + 7 = 4² + 7 = 23
When n = 5, n² + 7 = 5² + 7 = 32
When n = 6, n² + 7 = 6² + 7 = 43
The first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.
Step-by-step explanation:
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Select the correct solution for the expression. 2 5 + 3 8 2 5 + 3 8 A. 2 5 + 3 8 = 5 13 2 5 + 3 8 = 5 13 B. 16 40 + 15 40 = 31 40 16 40 + 15 40 = 31 40 C. 10 40 + 24 40 = 34 40 10 40 + 24 40 = 34 40 D. 2 5 + 3 8 = 6 40
In response to the stated question, we may state that As a result, the equation proper answer is: B. 16/40 + 15/40 = 31/40
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
We must identify a common denominator for the two fractions in order to solve the formula 2/5 + 3/8. Because 40 is the lowest common multiple of 5 and 8, we can transform both fractions to have a denominator of 40:
2/5 = 16/40
3/8 = 15/40
We can now sum the two fractions:
16/40 + 15/40 = 31/40
As a result, the proper answer is:
B. 16/40 + 15/40 = 31/40
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At which values in the interval [0, 2π) will the functions f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ intersect?
a: theta equals pi over 3 comma 4 times pi over 3
b: theta equals pi over 3 comma 5 times pi over 3
c: theta equals 2 times pi over 3 comma 4 times pi over 3
d: theta equals 2 times pi over 3 comma 5 times pi over 3
The values in the interval [0, 2π) for which the two points would intersect as required is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.
What values of θ make the two functions intersect?Recall from the task content; the given functions are;
f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ
Therefore, for intersection; f (θ) and g(θ):
2 cos²θ = −1 − 4cos θ − 2cos²θ
4cos²θ + 4cosθ + 1 = 0
let cos θ = y;
4y² + 4y + 1 = 0
y = -1/2
Therefore; -1/2 = cos θ
θ = cos-¹ (-1/2)
θ = 2π/3, 4π/3.
Ultimately, the correct answer choice is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.
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All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the sixth grade?
The number of students that are in the sixth grade is given as follows:
250 students.
How to obtain the number of students?The number of students is obtained applying the proportions in the context of the problem.
We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.
190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:
0.76n = 190
n = 190/0.76
n = 250 students.
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Find the value of x.
Answer:
x=1.9
Step-by-step explanation:
[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]
[tex]11x=21.16[/tex]
[tex]X=1.9[/tex]
Shade in the regions represented by the inequalities
Answer:
Step-by-step explanation:
see diagram
HELP!!
Write a quadratic equation in standard form that has solutions of -3 and -4.
Answer:
If a quadratic equation has solutions of -3 and -4, then it can be written in factored form as:
(x + 3)(x + 4) = 0
To convert this to standard form, we can multiply out the factors:
x^2 + 7x + 12 = 0
Therefore, the quadratic equation in standard form that has solutions of -3 and -4 is:
x^2 + 7x + 12 = 0
a ball is dropped from a height of 6 ft. assuming that on each bounce, the ball rebounds to one-third of its previous height, find the total distance traveled by the ball.
A ball is dropped from a height of 6 ft. assuming that on each bounce, the ball rebounds to one-third of its previous height, the total distance traveled by the ball is approximately 11.926 feet.
How do we calculate the total distance?We have to calculate the distance traveled by the ball with the help of the given data, as shown below;The first height of the ball is 6 feet. Distance traveled by the ball at the first instance = 6 feet.The ball rebounds to one-third of its previous height, and the ball goes to a height of:6/3 = 2 feet.
Distance traveled by the ball after the first bounce = 6 + 2 + 2 = 10 feet.The ball rebounds again to one-third of its previous height, and the ball goes to a height of:2/3 = 0.6667 feet. Distance traveled by the ball after the second bounce = 10 + 0.6667 + 0.6667 = 11.3334 feet.
The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.6667/3 = 0.2222 feet. Distance traveled by the ball after the third bounce = 11.3334 + 0.2222 + 0.2222 = 11.7778 feet. The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.2222/3 = 0.0741 feet.
Distance traveled by the ball after the fourth bounce = 11.7778 + 0.0741 + 0.0741 = 11.926 feet. Therefore, the total distance traveled by the ball is approximately 11.926 feet.
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