The first three terms of the number sequence are 1, 1/8, and 1/27. And the tenth term of this sequence is 1/1000.
We have been given the nth value of a number sequence that is,
aₙ = n⁻³
We can find the terms by replacing n with required values.
Thus the first term , a₁ = (1)⁻³
= 1
Second term, a₂ = (2)⁻³
= 1/8
Third term, a₃ = (3)⁻³
= 1/27
Tenth term, a₁₀ = (10)⁻³
= 1/1000
Hence the first three terms of the number sequence are 1, 1/8, and 1/27. And the tenth term is 1/1000.
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Which exponential function bests models the graph below?
A.
B.
C.
D.
D.
Group Activity let U= { 2, 4, 6, 8, 10, 12, 14, 16, 18} A = {4, 10, 12, 14,18} B = { 2,4,6,8,10,14,16} Drow the Venn diagram and Find 1.A' 2.B' 3.(AUB)' 4.A'UB'
We get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.
We are given the sets as:
U= { 2, 4, 6, 8, 10, 12, 14, 16, 18}
A = {4, 10, 12, 14, 18}
B = { 2, 4, 6, 8, 10, 14, 16}
We first will find out A':
A' = U - A
A' = { 2, 4, 6, 8, 10, 12, 14, 16, 18} - {4, 10, 12, 14, 18}
A' = { 2, 6, 8, 16}
Now, we will find B':
B' = U - B
B' = { 2, 4, 6, 8, 10, 12, 14, 16, 18} - { 2, 4, 6, 8, 10, 14, 16}
B' = { 12, 18}
Now, we have to find:
(AUB)' = U - (AUB)
AUB = {4, 10, 12, 14, 18} U { 2, 4, 6, 8, 10, 14, 16}
AUB = { 2, 4, 6, 8, 10, 12, 14, 16, 18} = U
(AUB)' = U - U = ∅.
Now, we will find A' U B':
A' U B' = { 2, 6, 8, 16} U { 12, 18}
A' U B' = {2, 6, 8, 12, 16, 18}
Therefore, we get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.
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22) Larry earns a yearly salary of $35,000 plus 5% commission on his sales. If his total sales for the
aro $260.000 what will be his total earnings ( salary and commission) for the year?
Answer:
48000
Step-by-step explanation:
260000*5%=13000
35000+13000=48000
Factorise C^2 - ( d + 2 )^2
Answer:
Step-by-step explanation:
[tex]\boxed{x^2-y^2=(x+y)(x-y)}[/tex]
[tex]c^2-(d+2)^2=\\(c+(d+2))(c-(d+2))=\\(c+d+2)(c-d-2)[/tex]
f (3/10)= -5 (3/10) -14
Answer: -15.5 or -31/2
Step-by-step explanation:
it may look weird but if that's what the equations says then your gonna do it.
-5(3/10) -> (5/1)(3/10) = 15/10 = -3/2 or -1.5
-1.5 - 14 = -15.5
:
() =-5-14 (=3/10)
(3/10)= -5 (3/10) -14
f(3/10) = -15/10 -14
= -15-140
----------
10
= -195/10
=- 19.5
Will give brainliest.
Answer:
Option 3
Step-by-step explanation:
First tke lcm i.e. 6 then multiply the dinominator to make six.
Multiply tje above no. With the same digit the sub. The numerators
Answer:
c) 7/6
Step-by-step explanation:
The difference will be,
→ (5/3) - (1/2)
→ (10/6) - (3/6)
→ (10 - 3)/6
→ 7/6
So, the answer is 7/6.
Juanita recorded 1 1/2 hours of a school musical concert. during editing, she deleted 1/3 of the recording. what was the length of the recording after editing was completed?
The final length of Juanita recording after editing was completed was 7/6
To solve this exercise, we have to state the equation using the information of the problem:
Information about the problem:
Recorded= 1 1/2 hDeleted= 1/3Final length= ?Transforming the mixed number to fraction, we get:
1 1/2 =
[(2*1) +1] /2
(2+1)/2
3/2
Calculating the final length of the recording, we have:
Final length = Recorded - deleted
Final length = 3/2 - 1/3
Final length = (9-2) / 6
Final length = 7/6
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Chloe and tino have a combined age of 48. three years ago chloe was double the age tino is now. find tinos age
(solve using simultaneous equations)
As given Chole and Tinos age , the present age of Tino is equal to 15 years.
As given,
Let x and y be the present age of Chole and Tino. respectively.
Combined age = 48
Given condition,
x + y = 48 _______(1)
Three years ago
x - 3 = 2y
⇒x =2y +3 _______(2)
Substitute the value of x in (1),
2y+3 +y =48
⇒ 3y = 45
⇒ y = 15years
Therefore , as given Chole and Tinos age , the present age of Tino is equal to 15 years.
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(Type exponential notation with positive exponents.)
The correct answer to the exponential expression which is as given in the task content is; 8³.
Based on the given task content, Gina's error from her workings is dividing the bases of the exponent.
Exponential notationThe bases of exponential expression, if same, should be taken as one.If the bases of exponential notation are entirely different, then it should be simplified.In indices, Division between two different expressions simply means Subtraction of powers.Multiplication means addition of powersGina's working:
8^12 / 8^9
= 0^12 / 0^9
The Correct workings:
8^12 / 8^9
= 8^(12-9)
= 8³
So therefore, the correct answer to the exponential expression which is given in the above expression is 8³.
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An isosceles triangle has a base of 14cm and sides of 50cm. calculate its height
A triangle is a 2-dimensional shape that has 3sides and 3 interior angles. The height of the isosceles triangle is approximately 49.5cm
Pythagoras theoremThe theorem states that the square of the hypotenuse is equal to the sum of the square of other two sides.
From the given question, the hypotenuse is 50cm and the base of the triangle is 14cm
Determine the height using the expression
h² = 50² - (14/2)²
h² = 2500 - 7²
h² = 2500 - 49
h = √2451
h = 49.5cm
Hence the height of the triangle is approximately 49.5cm
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If point A is located at (5, –3) and point B is located at (–4, –6). Find AB A B rounded to the nearest tenth.
The distance between the point A and point B is 9.5 units
Distance between two pointsThe formula for calculating the distance between two points is expressed according to the formula shown below;
AB = √(x₂-x₁)²+(y₂-y₁)²
Using the given coordinates points A(5, -3) and B (-4, -6)
Substitute to have:
AB = √(5-(-4))²+(-3-(-6))²
AB = √(5+4)²+(-3+6))²
AB = √81+9
AB = √90
AB = 9.5 units
Hence the distance between the point A and point B is 9.5 units
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The position of a car is given, for positive t, by x = 9t - 3t3. x is in meters and t is in seconds. when (in seconds) it its velocity zero?
When the velocity of the car is zero. Then the time will be 1 second.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The position of a car is given, for positive t, by x = 9t - 3t³. x is in meters and t is in seconds.
We know that velocity is the rate of change of displacement. Then we have
v = dx / dt
v = 9 - 9t²
When the velocity of the car is zero. Then the time will be
v = 0
9 - 9t² = 0
1 - t² = 0
(1 - t)(1 + t) = 0
t = 1, -1
When the velocity of the car is zero. Then the time will be 1 second.
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At a cross-country track meet, Alicia ran 8 mph for the first part of the race, then increased her speed to 12 mph for the second part. If the race was 21 miles long and Alicia finished in 2 hours, how far did she run at the faster pace?
She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.
What is the justification for the above result?The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.
Since the race is 21 miles in total, x and y together must add up to 21.
Hence,
x + y = 21
The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation
d = st, or t = d/s.
Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:
x/8 + y/12 = 2
Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24
3x + 2y = 48
And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:
3x + 2(21 - x) = 48
3x + 42 - 2x = 48
x = 6
Use y = 21 - x again:
y = 21 - (6) = 15.
Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.
Obviously, 15 + 6 = 21, thus the overall distance is correct.
In terms of time, 6 miles at 8 mph takes
6/8 =.75 hours = 45 minutes, whereas
15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.
As stated in the question, the total time to complete would be.
75 + 1.25 = 2 hours.
As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.
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) You are deciding between two landscaping companies to work on your backyard renovation. Company A charges a $50 fee to come out to your house plus $10 an hour to work. Company B charges $15 per hour and $30 to show up. How many hours will it take for both companies to equal the same price, and how much money will it cost at that time?
Considering the definition of an equation and the way to solve it, it will take 4 hours for both companies to equal the same price and it will cost $90 at that time.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseFirst, you define the variable "t" as the time for the landscaping company to work on the backyard renovation. You know that:
Company A charges a $50 fee to come out to your house plus $10 an hour to work. Company B charges $15 per hour and $30 to show up.So the price of each company is:
Price of company A=50 + 10tPrice of company B=30 + 15tIf both companies equal the same price, the equation in this case is:
Price of company A= Price of company B
50+ 10t= 30 + 15t
Solving
50 - 30= 15t - 10t
20= 5t
20÷5= t
4=t
At this time, the price of both companies is
Price of company A= 50+ 10t= 50 + 10×4= 90Price of company B= 30 + 15t= 30 + 15×4= 90In summary, it will take 4 hours for both companies to equal the same price and it will cost $90 at that time.
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i am equivalent to 5/6 the sum of my numerator and my denominator is 44 the sum of the digits in my denominator is 6 what fraction am i
Step-by-step explanation:
a/b = 5/6
a + b = 44
a = 44 - b
so, the first equation is
(44 - b)/b = 5/6
44 - b = 5b/6
264 - 6b = 5b
264 = 11b
b = 24
a = 44 - b = 44 - 24 = 20
the fraction is a/b = 20/24.
Also 2+4 as sum of the digits of the denominator = 6 is correct.
Mercury has a freezing point of -38. Water has a freezing point of 32. What is the difference
B ABCD is a parallelogram and angle A< 90°. The height through the vertex D intersects the diagonal AC at point M. The height through vertex B intersects the diagonal AC at point N. Prove that MBND is a parallelogram.
MBND is a parallelogram as BN=MD and BN║MD.
A parallelogram is a quadrilateral whose both pair of opposite side are equal and parallel. Few examples of parallelograms are square, Rhombus and rectangle.
Given ABCD is a parallelogram and ∠A=90°
Now we have to prove that MBND is a parallelogram
Given BN⊥AC and DM⊥AC
Since BN and DM are both perpendicular to the same straight line AC then we cam say that BN║DM.
Again we know from the properties of parallelogram that the diagonal divides a parallelogram into two equal triangles.
Therefore the diagonal AC divides the parallelogram into two equal triangles ΔABC and ΔADC.
Now we know that the area of a triangle is given by [tex]\frac{1}{2}[/tex] ×base ×height .
Area of ΔABC =Area of ΔADC
Since BN⊥AC and DM⊥AC
∴[tex]\frac{1}{2}[/tex]×BN×AC=[tex]\frac{1}{2}[/tex]×DM×AC
This above equation can be simplified as
BN=MD
Hence BMND is a parallelogram as we know from the properties of parallelogram that when a pair of opposite sides are equal and parallel in a quadrilateral it is a parallelogram.
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Which probability value indicates that there is statistical significance? 0.9756 0.015 0.9078 0.2356
The probability value indicates that there is statistical significance in 0.015 option (b) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
The p-values are:
0.9756 0.015 0.9078 0.2356As we know,
Statistical significance is commonly defined as a probability value of 0.05 or even less. P-value can be used in replacement of or in additional to preset levels of confidence when testing the claim.
Thus, the probability value indicates that there is statistical significance in 0.015 option (b) is correct.
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Find the slope of the line passing through the points (7, -2) and (7,5).
slope:
Answer: the slope=0
Step-by-step explanation:
[tex]\displaystyle\\(7,-2)\ and\ (7,5)\\[/tex]
[tex]\displaystyle\\\boxed {the \ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]
[tex]x_1=7\ \ \ \ \ x_2=7\ \ \ \ y_1=-2\ \ \ \ \ y_2=5\\Hence,\\\displaystyle\\the slope=\frac{7-7}{5-(-2)} \\\\the\ slope=\frac{0}{5+2} \\\\the\ slope=\frac{0}{7}\\\\ the\ slope=0[/tex]
use this to find the equation of the tangent line to the curve at the point and write your answer in the form: , where is the slope and is the y-intercept.
The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
What do we mean by equations?An equation is a mathematical declaration composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To find the equation:
When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:
[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]
The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:
[tex]y^{\prime}\left(\frac{\pi}{3}\right)=6 \sec \left(\frac{\pi}{3}\right) \tan \left(\frac{\pi}{3}\right)+12 \sin \left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex]The general equation y applies to the tangent line passing through the point [tex](a, y(a))[/tex] on the curve [tex]y(x)-y(a)=y^{\prime}(a)(x-a)[/tex].The tangent line in this case passes through the point [tex]\left(\frac{\pi}{3}, y\left(\frac{\pi}{3}\right)\right)=\left(\frac{\pi}{3}, 6\right)[/tex] and has the slope [tex]y^{\prime}\left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex].As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]
Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
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The correct question is given below:
Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.
HEEYYY PLEASE ANSWER THIS I GOT COVID SO I DONT UNDERSTAND IT SINCE I CANT BE IN CLASS
You can just try out all the answers but I'll give you a solution.
We will expand out the middle term to 5x^2 - 30x - 6x + 36, then we group the first 2 terms together, and the last 2 terms together.
= 5x (x - 6) - 6(x - 6)
And we put x-6 out : (x-6)(5x-6) = 0
Now, we can just set the value of one bracket to 0 and find out the value of x, and do the same for the other one
x - 6 = 0 -> x = 6
5x - 6 = 0 -> x = 6/5
Because 6 is not a possible option, the answer is x = 1.2
Kenzie runs at an average speed of 6.25mi/h. The length of her typical run is within one mile of 6 miles long.
Write an absolute value equation to represent the situation. Find the shortest or longest amount of time for Kenzie’s run. Round to the nearest minute.
Answer: 13512
100332
Step-by-step explanation:
The shortest time for her run is approximately 36 minutes and the longest time is approximately 67 minutes.
To represent Kenzie's situation, we can use an absolute value equation. Let x represent the length of her run in miles.
The equation would then be |x - 6| ≤ 1, which means the distance between x and 6 is less than or equal to 1.
To find the shortest or longest amount of time for Kenzie's run, we need to consider the speed.
The time can be found by dividing the distance by the speed, so the minimum time would be (6 - 1)/6.25 hours,
which is approximately 0.6 hours or 36 minutes.
The maximum time would be (6 + 1)/6.25 hours,
which is approximately 1.12 hours or 67 minutes.
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is anybody good at maths
15times15 divide by 20 takeway 5 add100
[tex]111.2[/tex]
Step-by-step explanation:
As per the question, 15 times 15 i.e. 225
[tex]15 \times 15 = 225[/tex]
225 divide by 20 i.e. 11.25
[tex] \frac{225}{20} = 11.25[/tex]
take away five from the 11.25 then it will be 11.2
Add 100 to 11.2 i.e
[tex]11.2 + 100 = 111.2[/tex]
Answer: 115
Step-by-step explanation:
[tex]\displaystyle\\\frac{15*15}{20-5} +100=\\\\\frac{15*15}{15} +100=\\\\15+100=\\\\115[/tex]
Volume of cone if height is 18 and diameter is 10,
Answer:
150pi
Step-by-step explanation:
The formula for the volume of a cone is one-third the volume of a cylinder.
It is [tex]V=\frac{1}{3} Bh[/tex] where B is the area of the circle base and h is the height of the cone.
To find the base of the cone, use the formula for the area of a circle. So, the radius is 5. So, the area of the base is pi × radius².
[tex]5^{2} =25[/tex]
[tex]\frac{1}{3}[/tex] × 25pi × 18 = 150pi
Solve the quadratic equation by completing the square.
2
x² - 10x+10=0
Answer: x=5+[tex]\sqrt{15}[/tex]
Step-by-step explanation:
x² - 10x+10=0
x² - 5x - 5x+10=0
x² - 5x - 5x+25-15=0
(x-5)^2 -15=0
(x-5)^2=15
x-5=[tex]\sqrt{15}[/tex]
x=5+[tex]\sqrt{15}[/tex]
10. Determine whether the inequality is always, sometimes, or never true. (1 point)
4x-8>1 + 4(x+3)
always
sometimes
Onever
Answer: onever
Step-by-step explanation:
4x-8>1+4(x+3)
4x-8>1+4(x)+4(3)
4x-8>1+4x+12
4x-8>4x+13
4x-8-4x>4x+13-4x
-8>13
Hence, inequality is never true
b) The angle of elevation of a tower at a distance of 27 meter from the foot of the tower is 60°, find the height of the tower. Speedy Additional Mathematics - Book VIII 98
The height of the tower is approximately 46.765 feet
Step-by-step explanation:
The given parameters are;
The distance from the foot of the tower where the angle of elevation is
measured = 27 feet
The angle of elevation to the top of the tower from a point 27 feet from the foot of the tower, θ = 60°
Therefore, by trigonometric ratio, we have;
tan 60= the height of tower / distance from foot of tower
[tex]\sqrt{3}[/tex]= height of tower /27
1.73205 *27 = height of tower
46.765 feet is the height of tower
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Use technology to c ompute the standard deviation for the following sample data. 32, 41, 36, 24, 29, 30, 40, 22, 25, 37
The standard deviation is provided by this. = 6.7528
What role does standard deviation play?Because it aids in comprehending measurements whenever the data is distributed, the standard deviation is significant. The standard deviation of the data will be higher the more evenly distributed the data is.
According to the given data:sample data = ( 32, 41, 36, 24, 29, 30, 40, 22, 25, 37)
To find mean of the given data:
Mean = Sum of items/ Count items
Mean = (32 + 41 + 36 + 24 + 29 + 30 + 40 + 22 + 25 + 37 / 10)
= 31.6
now finding the variance:
First we Add All the sample:
32 + 41 + 36 + 24 + 29 + 30 + 40 + 22 + 25 + 37 = 316
make Square of the solution:
316*316 =99856
and multiply by how many items there are. We have 10 items.
=99856/10
= 9985.6
For the time being, put this number aside.
Take your original set of numbers from Step 1 and square each one this time on its own.
32² + 41² + 36² + 24² + 29² + 30² + 40² + 22² + 25² + 37² = 10396
Subtract the sum from Step 2 from of the sum from Step 3.
10396 - 9985.6 = 410.4
The items in someone data set is reduced by 1 by.10 - 1 = 9
Divide the result of Step 4 even by result of Step 5. You get the variation from this.
410.4 / 9 = 45.6
Your response from Step 6 should be squared. The standard deviation is provided by this.
6.7528
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I understand that the question you are looming for is:
For the following sample data, compute the variance and the standard deviation. 32, 41, 36, 24, 29, 30, 40, 22, 25, 37
Evaluate the function.
ƒ(x) = −3x² − x – 15
Find f(−8)
Given ~
[tex] \: [/tex]
[tex] \tt \: f(x) = −3x² − x – 15[/tex]
[tex] \: [/tex]
now , put x= -8 in the function ~
[tex] \: [/tex]
[tex] \tt \: f( - 8) = −3( - 8)² − ( - 8) – 15[/tex]
[tex] \: [/tex]
[tex] \tt f(-8) = −3(64) − (-8) – 15[/tex]
[tex] \: [/tex]
[tex]\tt f(-8) = −192 − (-8) – 15[/tex]
[tex] \: [/tex]
[tex] \tt f(-8) = −192 − (-8) – 15[/tex]
[tex] \: [/tex]
[tex]\tt f(-8) = −184 – 15 [/tex]
[tex] \: [/tex]
[tex] \underline{\boxed{\red {\tt f(-8) = - 199}}}{\green ✓} [/tex]
[tex] \: [/tex]
hope helps ~
2x - 1 = 3x + 8
i ended up getting -7 but i know it’s wrong i just don’t know what i did wrong
Answer:
2x-1=3×+8
Step-by-step explanation:
2×-3x=8+1
-x=9
x=-9
