Answers
Answer:
S₁₂ = - 654
Step-by-step explanation:
there is a common difference between consecutive terms , that is
- 14 - (- 5) = - 23 - (- 14) = - 32 - (- 23) = - 9
this indicates the series is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = - 5 and d = - 9 , then
S₁₂ = [tex]\frac{12}{2}[/tex] [ (2 × - 5) + (11 × - 9) ]
= 6(- 10 - 99 )
= 6 × - 109
= - 654
Related Questions
Explain why the following form linearly dependent sets of vectors. (solve this problem by inspection.)
u1 = (3, -l), u2 = (4, 5), u3 = (-4, 7) in r2
Answers
A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution
x1 = x2 = .... = xk =0. Then the set {v1,v2,...,vk} is linearly dependent otherwise.
So putting in the formula we get
x1u1 + x2u2 + x3u3 = 0
x1u1 + x2u2 = -x3u3
au1 + bu2 = u3 ∵ (-x1/x3 = a & -x2/x3 = b)
On putting in the values
a(3,-1) + b(4,5) = (-4,7)
(3a+4b,-a+5b) = (-4,7)
On comparing we get
3a + 4b = -4 -(1)
-a + 5b = 7 -(2)
on solving these equations we get
b = 17/19 and a= -48/19
which is non trivial.
Thus the following form linearly dependent sets of vectors.
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A triangular face of the roof of the garage has two sides
that are √93 feet in length each and a base of length
186 feet. Is the roof a right triangle? Explain the steps
to take to determine whether the roof forms a right
triangle.
Answers
Answer:
The roof does form a right triangle.
Step-by-step explanation:
If it is a right triangle then it will obey the Pythagoras Theorem.
Now (√186)^2 = (√93)^2 + (√93)^2
186 = 93 + 93 = 186
So it obeys the theorem and is therefore a right triangle.
Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using LA Theorem.
Answers
Given the parameters in the diagrams, we have;
4. ∆ABC ≈ ∆DEF by ASA
5. UW ≈ XZ by CPCTC
6. QR ≈ TR by CPCTC
How can the relationship between the triangles be proven?4. The given parameters are;
<B = <E = 90°
AB = DE Definition of congruency
<A = <D Definition of congruency
Therefore;
∆ABC ≈ ∆DEF by Angle-Side-Angle, ASA, congruency postulate5. Given;
XY is perpendicular to WZ
UV is perpendicular to WZ
VW = YZ
<Z = <W
Therefore;
∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate
Which gives;
UW is congruent to XZ, UW ≈ XZ, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC6. Given;
PQ is perpendicular to QT
ST is perpendicular to QT
PQ ≈ ST
From the diagram, we have;
<SRR ≈ <PRQ by vertical angles theorem;
Therefore;
∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate
Which gives;
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The design of a building that has a square pyramid roof as a roof is shown. The cost of material for the outside of the building and for the roof
ranges from $25 per square foot to $50 per square foot. The budget for this material is $500,000. The rectangular front of the building has a
length twice as long as its height. The slant height of the roof is the same as the height of the rectangular front of the building.
What is the maximum possible length of the rectangular front of the building to the nearest foot?
feet
The maximum possible length of the rectangular front of the building is
A. 164
B. 41
C. 82
D. 29
Answers
The maximum possible length of the rectangular front of the building is 23 feet
How to determine the maximum possible length?The complete question is attached
Let the length of the rectangular front be x and the height be y.
So, we have:
x = 2y
The building has 4 congruent sides.
So, the area of the 4 sides is
A = 4 * (x * y)
This gives
A = 4 * (x * 2x)
Evaluate
A = 8x²
For the triangular roof, we have:
Slant height, l = y
Base, b = x
So, the area of the 4 triangular faces is
A = 0.5 * 4 * xy
This gives
A = 2xy
Recall that:
x = 2y
Make y the subject
y = 1/2x
So, we have:
A = 2x * 1/2x
A = x²
The cost of designing the buildings is
C = 25 * 8x² + 50 * x²
C = 200x² + 50x²
C = 250x²
This gives
250x² = 500000
Divide both sides by 250
x² = 2000
Square both sides
x = 45
Recall that:
y = 1/2x
This gives
y = 1/2 * 45
y = 23
Hence, the maximum possible length of the rectangular front of the building is 23 feet
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The line plot (shown in the attached image) shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Please help!! show all work and be sure to give final responses in complete sentence form in context of the problem, and explain your reasoning.
Answers
a. Mean is 70.8, median is 70, and mode is 60
b. Mean describes the data best
c. Mean can be a misleading central measure in case of outliers
Calculating Mean, Median and Mode
Mean = Total sum of pries / Total number of sunglasses
Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25
Mean = 70.8
Median = (n/2 + 1)th term
Here, n is the number of sunglasses.
Median = (25/2 + 1)th term
Median =13th term
Median = 70
Mode = Most occurring data
Mode = 70
Why is mean the best central measure to describe the data?
When your data distribution is continuous and symmetrical, such as when your data are normally distributed, the mean is typically the best measure of central tendency to utilize. Thus, mean describes the average price of the sunglasses here
Mean Being Misleading
In case there are outliers, the mean of the data gets highly affected. Hence, it can be misleading for analyzing average price of the data.
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PLRASE HELPPP PLS IM STUCK
Answers
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
What is 3/4 divided 1/6
Answers
Answer:
Fraction form: 9/2
Mixed number form: 4 1/2
Decimal form: 4.5
Step-by-step explanation:
To divide the two number, follow these steps.
3/4÷1/6
3/4×6/1=18/4
Reduce.
18/4=9/2 or 4 1/2
Hope this helps!
Answer:
[tex]\dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]
Step-by-step explanation:
[tex] \dfrac{3}{4} \div \dfrac{1}{6} = [/tex]
To divide a fraction by a fraction, rewrite the first fraction and multiply it by the reciprocal of the second fraction. To get the reciprocal of a fraction, flip it. The reciprocal of 1/6 is 6/1.
[tex] = \dfrac{3}{4} \times \dfrac{6}{1} [/tex]
[tex] = \dfrac{3 \times 6}{4 \times 1} [/tex]
[tex] = \dfrac{18}{4} [/tex]
[tex]= \dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]
The number of people in the world was 2.5 billion in 1950. The population has grown by 1.2% each year since then. Create a equation to model this situation using P to represent population (in billions) and y to represent years.
Answers
The equation which correctly models the situation in discuss is; P = 2.5(1.012)^y.
Which equation best models the situation?If follows from the task content that the situation given is that The number of people in the world was 2.5 billion in 1950.
Afterwards, The population has grown by 1.2% each year since then. Hence it follows that the function is an exponential one whose factor is; (100+1.2)%= 1.012.
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2. The lengths in centimeters of four line segments
are shown below.
3.12, 3.24, 31, √10
Write the lengths in order from least to greatest.
Answers
Answer:
I'm pretty sure it is √10, 3.12, 3.24, 31
Step-by-step explanation:
I don't know if you messed up but I got a question similar that is the length 31 in your quesion is actually 3 1/4 in my question. but i did the math and 31 is still the greatest number.
The image point of A after a translation right 4 units and up 2 units is the point B(1,−3). Determine the coordinates of the pre-image point A.
Answers
The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The point A = (1 - 4, -3 - 2) = (-3, -5)
The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)
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OUICK PLEASE
Find the equation of the line
Answers
Answer:
y = 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = ( 0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-2)}[/tex] = [tex]\frac{4}{0+2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 2x + 4 ← equation of line
Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters. What is the volume of the space filled with tissue paper in the packaging box? 81.84 cubic centimeters 105.84 cubic centimeters 198.264 cubic centimeters 222.264 cubic centimeters
Answers
The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters
VolumeVolume if small, Vs = 24 cubic inchesConstant = k
= 2.1³
= 9.261
Volume of large : volume of small = k
Vl / Vs = k
Vl = Vs × k
= 24 × 9.261
= 222.264 cubic inches
Therefore,
Volume of tissue paper = volume of large - volume of small
= 222.264 cubic inches - 24 cubic inches
= 198.261 cubic inches
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A printing company charges a fixed rate to set up the printing press, plus a cost of $3.50 for every 100 copies. If 800 copies cost $64.00, how much will it cost to print 1500 copies?
Answers
Answer:
88.5
Step-by-step explanation:
3.5 * 8 = 28, this is how much was spent on copies printed. If 800 copies cost $64 and 28 of that was on the 3.5 fee per 100, then the flat rate must be:
64-28 = 36.
Now, let's do 1500. For 1500 copies, you will get charged $3.5 15 times. This amounts to 52.5, then adding the fixed fee of 36 dollars, you get
88.5
Multiply the following numbers. Reduce the answer to lowest terms.
Answers
Answer:
B 4 1/3
Step-by-step explanation:
SOMEONE PLEASE HELP!!! Instructions: Find the length of the arc. Round your answers to the nearest tenth.
Answers
The length of the arc is 15.70 km
Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).
The formula is given by
s = ϴ × r,
where
s is the arc length
r is the radius of the circle
θ is the central angle of the arc in radians
Given :- Radius = 10km
Angle = 90 ° = [tex]\pi[/tex]/2 radians (1 radian = 180°/[tex]\pi[/tex])
By using formula we get
Length of arc = 10 x[tex]\pi[/tex]/2 = 5[tex]\pi[/tex] km ([tex]\pi[/tex] = 3.14)
= 15.70 km
Thus the length of the arc is 15.70 km
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Figure TUVS is a parallelogram.
Parallelogram T U V S is shown. Angle U is (4 x + 9) degrees and angle V is (6 x minus 29) degrees.
Which angles equal 91°?
angles T and V
angles S and U
angles U and V
angles S and T
Answers
Angles T and V of the parallelogram are equal to 91°.
Calculating the Value of x
In the parallelogram TUVS, adjacent angles U and V are given as,
U = 4x+9
V = 6x-29
Since U and V are adjacent angles, and as per the properties of a parallelogram, sum of adjacent angles is equal to 180°.
4x+9 + 6x-29 = 180
10x - 20 =180
10x = 200
x = 20
Calculating the Angles of the Parallelogram
∠U = 4x + 9
∠U = 4(20) + 9
∠U = 80 + 9
∠U = 89°
∠V = 6x - 29
∠V = 6(20) - 29
∠V = 120 - 29
∠V = 91°
According to the properties of a parallelogram, opposite angles are of equal measure.
∴ ∠T = ∠V and ∠S = ∠U
⇒ ∠T = 91° and ∠S = 89°
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Answer:
angles t and v
Step-by-step explanation:
edge
Find the quotient: look at pic
Answers
Answer:
2y+6
Step-by-step explanation:
first, pull out the 2 from the top to separate the equation
second, factor out y
third, cancel out the common factor of y-1
fourth, remove the parenthesis from 2(y+3)
answer = 2y+6
Ilean works as a welder and
web designer. As a welder, she earns $18 per hour. Last week she
worked x hours as a welder and her friend paid her $75 to design a web page. Write an
expression to represent the total amount llean earned last week.
Answers
The expression which can be used to represent the total amount llean earned last week is 75 + 18x
EquationAmount llean earns per hour welding = $18Number of hours worked as welder = xAmount earned as a web page designer = $75An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)
= 75 + (18 × x)
= 75 + 18x
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Tickets for a concert were \$5$5dollar sign, 5 for each child and \$8$8dollar sign, 8 for each adult.
Answers
Answer:
What exactly is the question
Step-by-step explanation:
There's no clear question.
The length of tr is 17 units. what are the lengths of sv and qt? sv = units qt = units
Answers
Applying the properties of kite, the measures are: SV = 41 units; QT = 21 units.
What is a kite?A kite is a quadrilateral that has 2 pairs of congruent adjacent sides, and has two diagonals where the longest one bisects the shorter one and divides it into equal segments.
The diagram given is a kite. Where TR = 17 units. Thus we would solve for x using the equation as shown below:
TR = RV [congruent adjacent sides of the kite]
Plug in the values
17 = 3x + 2
17 - 2 = 3x
15 = 3x
15/3 = x
x = 5
SV = TS = 9x - 4 [congruent adjacent sides of the kite]
Plug in the value of x
SV = 9(5) - 4
SV = 41 units
The length of segment QT is 41 units.
QT = QV = 4x + 1 [congruent adjacent sides of the kite]
Plug in the value of x
QT = 4(5) + 1
QT = 21 units
The length of segment QT is: 21 units.
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Answer:
SV: 41
QT:21
Step-by-step explanation:
The number of bacteria in a certain population increases according to a continuous exponential growth model with a growth rate parameter of 4.9% per hour how many hours does it take for the size of the sample to double
Answers
Answer:
14.5 hours to the nearest tenth.
Step-by-step explanation:
4.9% = 0.049.
If the original number is 50 it will double to 100 so
100 = 50(1.049)^t
1.049^t = 2
t * log 1.049 = log 2
t = log 2 / log 1.049
= 14.49 hours,
A potato was launched in the air using a potato gun. the function for the situation was h(t) = -16t2 + 100t + 10, where t was the time in seconds and h(t) was the height in feet. (3 points each) a. what was the maximum height of the potato? b. what was the lowest height of the potato? c. what was the lowest time that applies to the actual situation? d. what is the greatest time that applied to the actual situation? e. using your answers to parts a through d, what are the domain and range of the function, as they apply to this situation? use set builder notation.
Answers
The answers to all the parts are given below.
To find the answers using a function:The height equation is:
h(t) = - 16t^2 + 100t + 10
A) To find the maximum height, we must find the time where the velocity is 0, so we must derive it with respect to the time.
v(t) = - 2 * 16 * t + 100 = 0
t = 100/(2*16) = 3.125s
Now we put this time in our height equation:
h(3.125s) = -16*3.125^2 + 100*3.125 + 10 = 166.25 ft.
B) The lowest height of the potato will be h = 0ft when the potato hits the ground.
C) the lowest time that works for that function is t = 0s when the potato is fired by the gun.
D) the maximum time can be found when the potato hits the ground, after that point the equation does not work anymore, let's find it,
h(t) = 0 = -16t^2 +100t+10
we can solve it using Bhaskara's equation:
[tex]t=\frac{-100+-\sqrt{100^{2} +4*16*10} }{-2*16} =\frac{-100+-103.2}{-32}[/tex]
So the two solutions are:
t = 6.3s
t = -0.1s
We need to choose the positive time, as we already discussed that the minimum time that works for the equation is t = 0s.
so here the answer is t = 6.3s
E) the domain is 0s ≤ t ≤ 6.3s
The range is 0ft ≤ h ≤ 166.25 ft.
Therefore, the answers to all the parts are shown.
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Given the following formula, solve for a. 8=a+b+c/2
Answers
Making "a" the subject of the formula would give us: a = 8 - b - c/2
How to Solve for the Subject of Formula?Given the formula, 8 = a+b+c/2, to make a the subject of the formula, we would isolate a in the equation.
8 = a+b+c/2
8 = (2a + 2b + c)/2
2(8) = 2a + 2b + c
16 = 2a + 2b + c
16 - 2b - c = 2a
Divide both sides by 2
16/2 - 2b/2 - c/2 = 2a/2
8 - b - c/2 = a
a = 8 - b - c/2
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What’s 1/6 to 3 dp does anyone know?
Answers
❄ Hi there,
[tex]\sf{\dfrac{1}{6}\approx0.167}[/tex], rounded to 3 DP (decimal places)
[tex]\left\vert\textsf{Decimal Places = Number of digits after the decimal point}\vert[/tex]
Why round? Because the entire number goes on for ever and ever.
So, we need to round. 1/6 rounded to 3 decimal places is 0.167. We have 3 numbers after the decimal point.
❄
What is the domain of the following set of ordered pairs?
{(-2,-5), (-3,8), (12,6), (8, -3), (4,0), (-5, -7)}
○ a. {-5, 8, 6, -3, 0, -7}
O b. {-2, -5, -3, 8, 12, 6}
○ c. {8, −3, 4, 0, − 5, −7}
O d. {-2, -3, 12, 8, 4, −5}
Answers
Answer:
D. {-2, -3, 12, 8, 4, −5}
Step-by-step explanation:
The domain is the set of x coordinates, so the answer is {-2, -3, 12, 8, 4, −5}.
Which of the following statements about the scatter plot and the line of best fit are accurate? Select all that apply.
Answers
Answer:
- There are more points above the line than below
- This is not a line of best fit
Step-by-step explanation:
If we count the data points above and below the line, we can see there are about 4 below and 11 above. This means there are more points above the line than below. Since there are more points above the line than below, this is not a line of best fit.
I keep getting (10,5) or (0,5) someone pls help
Answers
Answer:
(4,-3)
Step-by-step explanation:
Multiplying the bottom equation by -6, we get -6x+12y=-60.
Adding this to the first equation gives 15y=-45, and thus y=-3.
So, it follows that 6x+3(-3)=15, and thus x=4.
The scatter plot below represents the amount of dog food a brand recommends based on the weight of the dog.
A
B
Amount of Food per Day (cups)
6
80
no association
negative linear association
● •
20
·
•
6
6
40
60
Weight of Dog (lb)
6
•
80
Which best describes the type of association shown in the scatter plot?
100
Answers
The best that describes the type of association shown in the scatter plot is positive linear association.
Given the scatter plot below represents the amount of dog food a brand recommends based on the weight of the dog.
Amount of Food per day cups:
20
40
60
No
We are required to find the type of association shown in the given scatter plot.
It is a positive linear association. The slope is positive so the linear association is also positive and linear mean generally in a line not on a curve like a nonlinear association.
Hence the given graph is of positive linear association.
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PLEASE I NEED HELP SO BADLY
Answers
Answer:
[tex]3y^{2} -3y-5[/tex]
3) angle of an isosceles triangle is 70°, find the value of If one remaining angles. a) 40°, 40° b) 45°, 45° c) 40°70° d)50⁰, 50⁰
Answers
The remaining two angles of the given isosceles triangle is Option(C) 40°,70° .
What are the remaining two angles in the isosceles triangle ?For an isosceles triangle, the two sides of the triangle are congruent and equal in length . Also the angles subtending the adjacent equal sides of the isosceles triangle are of same measure.
We also know that the sum of the three interior angles of any triangle is always equal to 180° .
In the options given, in Option(C) the angles measure 40° and 70° .
Thus as one angle of the isosceles triangle is given to be 70°, the other angle of its adjacent side is also 70° .
The sum of the interior angles of the triangle is equal to -
70° + 40° + 70° = 180° which satisfies the property.
Therefore, the remaining two angles of the given isosceles triangle is Option(C) 40°,70° .
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