Answer:
The sum of of the polynomials (m + n + 3) + (m + n + 4) is 2m + 2n +7
Step-by-step explanation:
The given expression is (m + n + 3) + (m + n + 4)
we need to find the sum of this expression
so, first we add the similar terms
m + n + 3 + m + n + 4
first write the like term together and then constant,
⇒ m + m + n + n +3 + 4
⇒ 2m + 2n +3 + 4
⇒ 2m + 2n +7
Therefore, The sum of of the polynomials (m + n + 3) + (m + n + 4) is 2m + 2n +7
5 more than twice x (algebraic expression)
Determine the amount of an investment if 5000 is invested at an interest rate of 4.5% compounded monthly for 10 years. Round your answer to the nearest whole dollar
The amount of an investment of $5,000 at an interest rate of 4.5% compounded monthly for 10 years will be $7,847, rounded to the nearest whole dollar.
Explanation:To determine the amount of an investment that starts at $5,000, with an interest rate of 4.5% compounded monthly for 10 years, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per unit t.t is the time the money is invested for in years.Plugging the values into the formula:
A = 5000(1 + 0.045/12)^(12*10)
A = 5000(1 + 0.00375)^(120)
A = 5000(1.00375)^(120)
A = 5000 * 1.569463137
A = $7,847 (rounded to the nearest whole dollar)
The amount of the investment after 10 years, compounded monthly at 4.5% interest, will be $7,847.
Suppose that water is stored in a cylindrical tank of radius 5 m. if the height of the water in the tank is h, then the volume of the water is v = Ïr 2h = (25m2)Ïh = 25Ïh m2. if we drain the water at a rate of 250 liters per minute, what is the rate at which the water level inside the tank drops?
To calculate the rate at which the water level drops, use the formula dh/dt = dV/dt / (25Ï) and the given drainage rate of 250 liters per minute. The resulting rate is -0.01/Ï meters per minute, which represents the speed of the water level decreasing.
Explanation:To determine the rate at which the water level inside the cylindrical tank drops, we use the given volume formula of the cylinder, V = 25Ï h, where V is volume in cubic meters, h is height in meters, and Ï is the constant pi (approximately 3.14159).
Draining the tank at a rate of 250 liters per minute corresponds to a volume rate of 0.25 cubic meters per minute (since 1 cubic meter equals 1000 liters). Using the formula dV/dt = 25Ï dh/dt, we want to find the rate dh/dt at which the height of the water decreases.
Rearranging for dh/dt gives us dh/dt = dV/dt / (25Ï). Substituting the known rate of volume change, dV/dt = -0.25 m³/min (negative because the volume is decreasing), we get dh/dt = -0.25 / (25Ï), which simplifies to dh/dt = -0.01 / Ï meters per minute. Therefore, the rate at which the water level drops is -0.01/Ï meters per minute.
A company is creating a box without a top from a piece of cardboard, but cutting out square corners with side length x.
Which expression can be used to determine the greatest possible volume of the cardboard box?
(x−10)(x−30)x
(10−2x)(30−2x)x
(10−x)(30−x)x
(30x−10)(10x−30)
Answer:
(10−2x)(30−2x)x
Step-by-step explanation:
I know how to explain it, but the other person's answer already has a good explanation. I'm just confirming this to be correct! :D
please help me on math???
A piece of string is 325 centimeters long. You need the string to be 1 1/4 meters long. How many centimeters should you cut off
Emanuel used the calculations below to find the product of the given fractions. In which step did his error occur?
Answer:
Emanuel made huis mistake in first step and step 1 is incorrect.
Step-by-step explanation:
The given expression is
[tex](\frac{3}{5})(\frac{4}{9})(-\frac{1}{2})[/tex]
It can be written as
[tex]\frac{3}{5})(\frac{4}{9})(\frac{-1}{2}[/tex]
Step 1: [tex](\frac{(3)(4)(-1)}{(5)(9)(2)})[/tex]
Emanuel used negative sign with both numbers 1 and 2. Therefore the first step of Emanuel is incorrect.
Step 2: [tex]\frac{-12}{90}[/tex]
Step 3: [tex]\frac{-2}{15}[/tex]
Therefore Emanuel made huis mistake in first step and step 1 is incorrect.
The number of students at Valley View Middle School increased by 10%, to 770 total students. How many students were enrolled at Valley View Middle School before the increase?
There are 700 students were enrolled at Valley View Middle School before the increase.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
The number of students at Valley View Middle School increased by 10%, to 770 total students.
Now,
Since, The number of students at Valley View Middle School increased by 10%,
And, The number student after the increase = 770
So, We can formulate;
The number of students before the increased is calculated as;
= 770 / (1 + 10%)
= 770 / 1.1
= 700
Thus, There are 700 students were enrolled at Valley View Middle School before the increase.
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If p(a|b) = 0.35, p(b) = 0.75 and p(a) = 0.44 are the events a and b independent ?
Final answer:
Two events A and B are considered independent if the probability of A given B (P(A|B)) is equal to the probability of A, and the probability of B given A (P(B|A)) is equal to the probability of B. In this case, events a and b are not independent.
Explanation:
Two events A and B are considered independent if the probability of A given B (P(A|B)) is equal to the probability of A, and the probability of B given A (P(B|A)) is equal to the probability of B.
In this case, if p(a|b) = 0.35, p(b) = 0.75, and p(a) = 0.44, we can determine if events a and b are independent by comparing the given probabilities.
To check if events a and b are independent, we need to find p(a|b) and compare it to p(a), and find p(b|a) and compare it to p(b).
p(a|b) = 0.35 means that the probability of event a occurring given that event b has occurred is 0.35. Since p(a|b) is not equal to p(a), events a and b are not independent.
Which quadrilateral has two pairs of different but equal adjacent sides?
2.Tumford the cats ate 1 5/6 pounds of cat food last week. This week, he ate 3/4 pounds less. How much cat food did he eat this week?
What is the 24th term of the arithmetic sequence where a1 = 8 and a9 = 56 ?
Answer:the answer would be c which is 146
Step-by-step explanation:
The 6 consecutive integers below add up to 447. x − 2 x − 1 x x + 1 x + 2 x + 3 what is the value of x ? f. 72 g. 73 h. 74 j. 75 k. 76
The value of x is 75.
what is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
6 consecutive integers are x − 2, x − 1, x, x + 1, x + 2, x + 3
Now, the integers add up to 447.
So, x-2 + x-1 + x+ x +1 + x+2 + x+3= 447
6x -3 + 6 = 447
6x = 450
x= 75
Hence, the value of x is 75.
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the population pf a city is 2,500. if the number of males is 240 more than the number of females how many males and females are there in the city
You need to represent the number of males in terms of females.
Explanation:Since you know the number of males relative to females, it makes sense to represent the number of females as a variable, let's say f.
So then the number of males is f+240 and we know that the number of males plus the number of females is 2500. Knowing this, we can write an equation: f+(f+240)=2500. I put the number of males in brackets there just to make it easy to recognize.
This equation can be condensed into 2f+240=2500 and then solved:
2f=2500−240
f=2500−2402
f=1130
Then, we know the number of females, and we can solve for the number of males from here using our male formula: males=f+240. You should then get 1370 as the number of males.
Checking this answer, we see that 1130 + 1370 does equal 2500.
What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of -8?
Answer:
The explicit equation for the given geometric sequence is [tex]a_n=4(-2)^{n-1}[/tex]. The domain for the geometric sequence is all positive integers except 0.
Step-by-step explanation:
It is given that the first term of the geometric sequence is 4 and the second term is -8.
[tex]a_1=4,a_2=-8[/tex]
The common ratio for the sequence is
[tex]r=\frac{a_2}{a_1}=\frac{-8}{4}=-2[/tex]
The explicit equation for a given geometric sequence is
[tex]a_n=ar^{n-1}[/tex]
where, a is first term, n is number of term and r is common ratio.
The explicit equation for the given geometric sequence is
[tex]a_n=4(-2)^{n-1}[/tex]
Here n is the number of term. So, the value of n is must be a positive integer except 0.
Therefore the domain for the geometric sequence is all positive integers except 0.
unit 0 algebra review functions graphing linear equations
Let sin a = 12 13 with a in qii and sin b = − 15 17 with b in qiii. find sin(a + b), cos(a + b), and tan(a + b)
The sin(a + b), cos(a + b) and tan(a + b) for angles a and b where sin a = 12/13 and sin b = -15/17 respectively, can be calculated using the formulas for the sine, cosine, and tangent of the sum of two angles. The results are -252/221 for sin(a+b), 56/221 for cos(a+b) and -4.5 for tan(a+b).
Explanation:The given sin values represent the sides of the right triangles in terms of opposite/hypotenuse. Given we are in the second and third quadrants, where cos values are negative, we can use Pythagoras' Theorem, for example, to find cos a = -√(1 - sin²a) = -√(1 - (12/13)²) = -5/13 and analogously, we obtain cos b = -√(1 - sin²b) = 8/17.
Using the formulas for the sine, cosine, and tangent of the sum of two angles:
sin (a + b) = sin a cos b + cos a sin b, we obtain sin(a + b) = 12/13*(-8/17) + 5/13*(-15/17) = -252/221.For cos (a + b) = cos a cos b - sin a sin b, cos(a + b) = -5/13*-8/17 - 12/13*-15/17 = 56/221.And lastly for tan (a + b) = sin (a + b) / cos (a + b), tan(a + b) = -252/221 / 56/221 = -4.5.
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A rectangle has perimeter 74 cm and length 28. What is its width?
Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x –
What are the solutions of –x2 + 4x = x – 4?
The solutions of the equation [tex]-x^2+4x=x-4[/tex] is:
x= -1 and x=4
Step-by-step explanation:The solution of the graphs of the equation is equal to the x-value of the point of intersection of the graph of two functions i.e. the function on the left side of the equality on the right side of the equality.
Here, the expression is:
[tex]-x^2+4x=x-4[/tex]
Hence, we will see at which point the graph of:
[tex]y=-x^2+4x[/tex]
and [tex]y=x-4[/tex] meet.
The point of intersection of the graph is: (-1,-5) and (4,0).
Hence, the solution of the graph is: x= -1 and x=4
How do you factor 8x^2+18x+9=0
3a+20=-25 what is the value of a?
Four subtracted from the reciprocal of a number
a carpenter is measuring a board with which he is working. because one end of the measuring tape is unreadable, the carpenter places the measuring tape so that one end of the board is at 3 inches and the other is at 15 inches. how long is the board?
Answer:
12 inches
Step-by-step explanation:
15 - 3 = 12
The board is 12 inches long.
_____
A measuring tape is like a number line. To find the distance between two numbers on the number line, you subtract the smaller one from the larger one. The tape measure works the same way. Subtract the number at one end of the board from the number at the other end of the board to find the length of the board.
The system of inequalities and graph the solution on the graph.
The perimeter, P, of a rectangle is the sum of twice the length and twice the width.
P = 2(l+w) units
P = 2(5)+2(9) units
P = 4x units
P = (l+l)+(w+w) units
P = 2(x+3) units
Answer:
P=2(l+w)
Step-by-step explanation:
It is given that perimeter, P, of a rectangle is the sum of twice the length and twice the width.
Let length of rectangle is l and width of the rectangle is w.
Perimeter = 2 × Length + 2 × Width
[tex]P=2\times l+2\times w[/tex]
[tex]P=2l+2w[/tex]
Taking out common factors.
[tex]P=2(l+w)[/tex]
[Note: (l+l)+(w+w) units is also true but according to the statement only option 1 is true]
Therefore, the correct option is 1.
Subtracting 3xy2 from 8xy2 gives the same result as the expression
A.7xy^2-2xy^2
B.-7xy^2-2xy^2
C.3xy^2-8xy^2
8-3 = 5
7-2 = 5
so the answer would be A
A football team loses 4 yards on each of three plays. Then they complete a pass for 9 yards. What is the change in yardage after this four plays?
A comuter has $245 in his commuter savings account b. How much must he add to his account if he wants to have 20 weeks worth of tickets in his account
The membership of a committee consists of 3 english teachers, 4 mathematics teachers, and 2 social studies teachers. if 2 committee members are to be selected at random to write the committee's report, what is the probability that the two members selected will both be english teachers?
Isaac read a total of 20 books over 5 months. After belonging to the book club for 7 months, how many books will Isaac have read in all? Assume the relationship is directly proportional.
(easy question i just forgot how to do it lol)
20 books / 5 months = 4 books per month
4 books * 7 months = 28 books total