The sum of the cubes of first 15 natural numbers.
Solution:[tex]( \frac{(15 \times 16)}{2} {)}^{2} [/tex]
[tex] = (15 \times 8 {)}^{2} [/tex]
=14400
Hence, the sum of the cubes of first 15 natural numbers is 14400
Martin had 100 trees in his orchard the first year. Each year after that, he
increased the number of trees in his orchard by 10%, rounded to the nearest
whole number. How many trees did he have in his orchard in the sixth year?
So trees after 1 year
100+10=110Trees after 2 years
110+0.1(110)=121Trees after 3 years
121+0.1(121)133(Whole no)Trees after 4years
133+0.1(133)146Trees after 5 years
146+0.1(146)161Trees after 6 years
161+0.1(161)177treesAnswer:
177
Step-by-step explanation:
This scenario can be modeled as an exponential function.
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
If the number of trees increase by 10% each year, then the number of trees each year will be 110% of the number of trees the previous year. Therefore, the growth factor is 110%.
Given:
a = 100 treesb = 110% = 1.10 (in decimal form)x = time (in years)y = number of trees in the orchardSubstituting the given values into the function:
[tex]\implies y=100(1.10)^x[/tex]
(where x is time in years and y is the number of trees in the orchard)
To find how many trees are in the orchard in the 6th year, input x = 6 into the found equation:
[tex]\implies 100(1.10)^6=177.1561=177\: \sf (nearest\:whole\:number)[/tex]
Therefore, Martin had 177 trees in his orchard in the sixth year.
PLEASE HELP!! NEED THIS TO PASS!
Answer:
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Step-by-step explanation:
njfdhnnmidf shmdf no d DJ NJ haven't bag kid NC b njfdhnnmidf
How can I solve this:
Simplify
Answer:
see the attachment photo!
Answer:
the answer is 7! hope this helps
Step-by-step explanation:
Which of the following is the product of the rational expressions shown
below?
x+2/X-4 * 3X/X+4
Answer: x = 0; x=10
Step-by-step explanation:
[tex]\frac{x+2}{x-4} *\frac{3x}{x+4}\\ \\x+2(x+4) = x-4(3x)\\x^{2} +2x+ 4x + 8 = 3x^{2} -12x\\2x+4x+12x =3x^{2} - x^{2} \\20x= 2x^{2} \\10x = x^2\\x=0\\x=10[/tex]
Hope this helps!
In the diagram, ΔGEF and ΔHEF are congruent. What is the value of x?
Similar triangles are triangles that has all sides and angles to be equal. The value of x if , ΔGEF and ΔHEF are congruent is 28
Similar trianglesSimilar triangles are triangles that has all sides and angles to be equal. From the given diagram;
<GFE = <EFH
Given
<GFE = 60 degrees
<EFH = 2(x+2)
Substitute
2(x+2) = 60
2x + 4 = 60
2x = 60 - 4
2x = 56
x = 28
Hence the value of x if , ΔGEF and ΔHEF are congruent is 28
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A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
to determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
The correlation coefficient between the student's height and the distance they were able to jump is 0.86.
What is the correlation coefficient?The correlation coefficient is a number that ranges from -1 to 1. It shows the strength of the relationship between two variables. It also shows the direction of the relationship.
Positive correlation is when the two variables move in the same direction. If one variable increases, the other variable also increases. Negative correlation is when two variables move in different direction. If one variable increases, the other variable decreases. Zero correlation is when there is no relationship between the variables.
The correlation coefficient is calculated using a financial calculator.
Here is the complete question:
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.
Enter the correlation coefficient. Round your answer to the nearest hundredth.
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Answer:
It's 0.92
Step-by-step explanation:
I took the test already
Simplify this expression.
(2-5√6)-3√2
6√2-15√6
6√2-15√/12
6√2-8√6
6√2-30√
Answer: [tex]2-5\sqrt{6}-3\sqrt{2}[/tex]
Step-by-step explanation:
= [tex](2-5\sqrt{6} )-3\sqrt{2}[/tex]
= [tex]2-5\sqrt{6}-3\sqrt{2}[/tex]
This expression is simplified already
For the quadrilateral on the grid, the slope of WX is 0, the slope of XY is , the slope of YZ is 0, and the slope of ZW is .
Which statement verifies that quadrilateral WXYZ is a parallelogram?
The difference of the slope of adjacent sides is .
The slopes of adjacent sides are opposite reciprocals.
The opposite sides have the same slope.
XY and YZ have the same slope.
The statement that verifies that quadrilateral WXYZ is a parallelogram is C)The opposite sides have the same slope.
What is a Parallelogram?This refers to a four-sided figure that is used in geometry and has parallel opposite sides.
Hence:
Remember that the opposite sides of a parallelogram are parallel.
We would solve:
Slope WX = 0
Slope XY= 5/2
Slope XZ= 0
Slope ZW= 5/2
The next step would be:
Slope WX= Slope YZ
Slope XY = Slope ZW
Based on the fact that the opposite sides have the same slopes, we can conclude that quadrilateral WXYZ is a parallelogram
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which two ratios represents quantities that are proportional? A. 15/10 and 10/15 B. 20/25 and 16/20 C. 5/6 and 17/12 D. 15/21 and 20/24
Select the pair of numbers that have a sum of 7and a difference of 1
Answer:
3,4 is the pair of numbers that have a sum of 7 and a difference of 1
answer?..............
Step-by-step explanation:
please mark me as brainlest
(0.6.01) The probability that an event will occur is 2/3. Which of these best describes the likelihood of the event occurring?
A. Likely
B. Certain
C. Unlikely
D. Impossible
Answer:
Likely
Step-by-step explanation:
It is not guaranteed, but it is not impossible. There is a higher chance of it happening compared to it not happening, so it it likely.
Find the value of the angle θ rounded to 1 DP.
Answer:
35
Step-by-step explanation:
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Question 3
the three straight paths, ab, bc, and ac meet each other at three points, a, b, and how do these points of intersection differ from each
other? explain the differences in terms of the angles that you see. also look at the length of the side opposite each angle. what pattern do you see
regarding the measurements? in what situation would all the points of intersection resemble one another modify the triangle in geogebra to
help you with your answers
b
ux
x
font sizes
aaeeen
characters used: 0 / 15000
submit
airfax county public schools
To find differences in the angles of the intersections we must know how many degrees each angle corresponds to. We must also take into account that the sum of the internal angles must equal 180°.
What is a triangle?A triangle is a polygon that is characterized by having three sides, three vertices, and three angles. An indispensable rule of the interior angles of the triangles is that they must add up to 180º.
Triangles are classified according to their characteristics as shown below:
Equilateral triangle: It is a type of triangle that is characterized by having all equal sides. Consequently, all the angles of an equilateral triangle are 60º. The equilateral triangle is a regular polygon.Isosceles triangle: It is a type of triangle that is characterized by having two equal sides and one different. Consequently, it also has two equal angles.Scalene triangle: A scalene triangle is one that is characterized by having all its sides and angles unequal, that is, different from each other.According to the above, depending on the measurements of the length of the sides and the angles of a triangle, its characteristics and classification change.
Note: This question is incomplete because the image is missing. However I can answer it based on my general prior knowledge.
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Solve- x/x+1 - 1/2 = -1/x+1
Answer:
Step-by-step explanation:
Remark
x/(x+1) - 1/2 = -1 /(x + 1) is the equation to be solved. Add 1/(x + 1 to both sides
x/(x+1) + 1/(x+1) - 1/2 = -1/(x + 1) + 1/(x + 1) Combine
x/(x+1) + 1/(x + 1) - 1/2 = 0 Combine x/(x+1) + 1/(x+1)
(x + 1)/(x + 1) - 1/2 = 0 Cancel (x+1)/(x+1) = 1
1 - 1/2 = 0 No solution
Answer: No solution
Which equation can be simplified to find the inverse of y = 5x² + 10?
Answer:
See below
Step-by-step explanation:
Here is how to start....you didn't include the equations in question, so I do not know what the answer may be
solve for x
y-10 = 5 x^2 divide thru by 5
(y-10)/5 = x^2 'sqrt' both sides
± sqrt( (y-10) / 5 = x change x's and y's
± sqrt ((x-10)/5) = y
A bag contains 7 red marbles, 6 blue marbles and 4 green marbles. If three marbles
are drawn out of the bag, what is the probability, to the nearest 1000th, that all three
marbles drawn will be blue?
Step-by-step explanation:
7red marbles,3 blue marbles,4 green marbles
Please Help I Don't Understand!
Answer:
a reduction
Step-by-step explanation:
this is because its growing smaller
What is the mean absolute deviation of 1,1,1,1,1,1,1,1,2,2,2,2,2,3,4,4,5,6
Answer:
8
Step-by-step explanation:
step 1.
1,1,1,1,1,1,1,1 = 2 + 2 + 2 + 2 = 8
2 + 2 + 2 + 2 + 2 = 10
3 + 0 = 3
4 + 4 = 8
5 + 0 = 5
6 + 0 = 6
Step 2.
8 + 10 = 18
18 + 3 = 21
21 + 8 = 29
29 + 5 = 34
34 + 6 = 40
40/6 = 8
This is because if you added 6 + 6 eight times, you would get 40.
What is the slope of the line containing (-3, 1) and (1, -2)?
O A
OB.
O C.
O D.
314
413
-
314
43
Slope:-
m=y2-y1/x2-x1m=-2-1/1+3m=-3/4The slope of the given function is -3/4.
What is a slope?Slope is a value that describes the steepness and direction of a line.
Given are the points that lie on line, we need to find the slope of the line,
So,
m = y₂ - y₁ / x₂ - x₁
The ordered pairs are :-
(-3, 1) and (1, -2)
So, the slope (m) = -2-1 / 1+3 = -3/4
Hence, the slope of the given function is -3/4.
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1. Marc and Julian are considering the following investments for their portfolio. Help
them evaluate each one by weighing the risk versus return. Rank each as low,
moderate, or high in each category. (12 points)
The risk versus return of the investments that Marc and Julian are considering are:
Money Market savings account - Low.IRA - Moderate. Stock in new high tech company - High. Mutual Fund - Moderate. Five year CD (2% interest) - Low.High-yield five-year bond - High. How risky are these investments?Money Market savings accounts are offered by commercial banks and are quite safe which is why they have low returns. The same is true of a Five year CD.
IRAs and Mutual funds are considered moderate because they offer higher rates than CDs but with higher risk as well.
Stock and high-yield bonds are quite risky but they have a chance of a high return as well.
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In how many ways can the letters of the word COMPUTER be arranged in a row if the letters C and O can not stand next to each other
Answer:
35280ways
Step-by-step explanation:
let X be the number of ways the letters can be arranged with no restriction,
let M be the number of ways they can be arranged if the letters C and O must stand together,
and let the number of ways the letters C and O can be arranged if they can not stand together.
X=8!
M= 7!
N=X–M=8!–7!=35280 ways
Consider the expression 5/6(1/2x+6)-3x
What is the value of the expression evaluated for x=
12?
-26
-25
12
46
The value of the expression if x is equivalent to 12 is - 26
Functions and valuesGiven the expression
f(x) = 5/6(1/2x+6)-3x
If the value of x is 12, then;
f(12) = 5/6(1/2(12)+6)-3(12)
f(12) = 5/6(6+6) - 36
Simplify
f(12) = 5/6(12) - 36
f(12) = 10 - 36
f(12) = -26
Hence the value of the expression if x is equivalent to 12 is - 26
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help help help help help help help
Answer:
V = 56,448 cm³
Step-by-step explanation:
the volume (V) is calculated as
V =Ah ( A is the area of the base and h the height )
here A = 2,352 and h = 24 , then
V = 2,352 × 24 = 56,448 cm³
what is the answer for 0.32+12.965+1.1 and could you explain how you got the answer
answer: 14.385
Add the numbers as if they were whole numbers.Place the decimal point in the sum so that it lines up vertically with the numbers being added.
hope this helps:)
PLEASE HELPPPPPPPPPPPP!!!
Identify the type of function represented by
f(x) = 4.2x
OA. Decreasing linear
OB. Exponential growth
OC. Exponential decay
OD. Increasing linear
The function is an increasing linear function
How to determine the function type?The function is given as:
f(x) = 4.2x
The above function is a linear function, because linear functions are represented as:
f(x) = mx + b
Where m represents the slope.
A positive slope represents an increasing linear function.
By comparison;
m = 4.2
4.2 is positive
Hence, the function is an increasing linear function
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(72 divided by 8-x2x3+1
Answer: -2(3x-5)
Step-by-step explanation: first you divide 72 and 8 then do the rest
4 dolares
2. Un carro consume 6.8 litros de gasolina por cada 102 kilómetros
viajados. ¿Qué distancia puede viajar el auto con 24 litros de
gasoling?
Porfa urge
Doy corona
The car can travel 360 km with 24 liters of gasoline.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A car consumes 6.8 liters of gasoline for every 102 kilometers traveled.
6.8 liters of gasoline = 102 km
1 liters of gasoline = 102 km/ 6.8
= 15
24 liters of gasoline = 24 x 15 = 360
Hence, The car can travel 360 km with 24 liters of gasoline.
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Simplify using BODMAS rule :
60÷6[{32÷4(7×2-15+5)}+3]
Step-by-step explanation:
the right answer is 1.714