Answer:
1584
Step-by-step explanation:
The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.
__
series of partial sumsThe partial sums, taken 3 terms at a time, are
1+2-3 = 0
4+5-6 = 3
7+8-9 = 6
...
97+98-99 = 96
So the original series is equivalent to ...
0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)
That is, the sum is 3 times the sum of the consecutive integers 1..32.
__
consecutive integersThe sum of integers 1..n is given by the equation ...
s(n) = n(n+1)/2
__
series sumUsing this to find the sum of our series, we find it to be ...
series sum = 3 × (32)(33)/2 = 1584
_____
Alternate solution
The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...
1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)
Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).
Computed that way, we find the sum to be ...
(99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584
What is the slope of the line y=3-x/8?
5/6 of all the money in Salma's bank account is ₹55,000. how much money does Salma have in her bank account?
please answer
Answer:
₹66,000
Step-by-step explanation:
If 5/6 is 55,000 then just multiply 55,000 by the reciprocal 6/5 to get 66,000
Which of the following are solutions to the equation below?
Check all that apply. x^2 + 6x + 9= 20
Sketch the graph of y = –1.5(4)x. Then state the function’s domain and range.
The plot of the graph y = –1.5(4)^x is shown below of which its domain and range exist on all real values
Exponential equationThe standard exponential function is expressed as y = ab^x
where
a is the base valuex is the exponentThe exponential function shows an increase along the y-axis and towards the x-axis
According to the equation, we are to plot the graph y = –1.5(4)^x of which its domain and range exist on all real values
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An airplane flight has 374 seats. The probability that a person who buys a ticket actually goes on that flight is about 85%. If the airline wants to fill all the seats on the flight, how many tickets should it sell?
Taking into account the definition of ratio and proportion, the airline should sell 440 tickets.
What is ratio and proportionThe ratio is the comparison of two quantities and is measured from the division of two values.
The relationship of equality that exists between two ratios, that is, between two comparisons between two determined quantities, is known as a proportion. So if [tex]\frac{a}{b}[/tex] corresponds to the ratio, then [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex] equals a proportion.
Amount of tickets soldAn airplane flight has 374 seats. The probability that a person who buys a ticket actually goes on that flight is about 85%. The airline wants to fill all the seats (100%) on the flight.
This can be represented by the proportion:
[tex]\frac{374}{85}[/tex] = [tex]\frac{amount of tickets}{100}[/tex]
Solving:
amount of tickets= 100×[tex]\frac{374}{85}[/tex]
amount of tickets= 440
Finally, the airline should sell 440 tickets.
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Combine like terms to simplify the expression:
-50 m+ 10-3 m+ (-13) =
[tex] - 50m + 10 - 3m + ( - 13) \\ - 50m + 10 - 3m - 13 \\ - 53m - 3[/tex]
Hope it helps
please give brainliest
tn=2(n-1)
Given the formula for the nth term, state the first 5 terms of each sequence.
Answer:
0, 2, 4, 6, 8
Step-by-step explanation:
substitute 1 for n in first term, 2 for n in second term, 3 for n in third term, 4 for n in fourth term, 5 for n in fifth term
2 (1) -2 = 0 first term
2 (2)-2 = 2 second
2 (3)-2 = 4 third
2 (4)-2 =6 fourth
2 (5)-2 =8 fifth
1 what is sum of the interior angles of ABCD what is the sum of the exterior angles of CHFE 3 which sides are parallel to CE 4 whicl side id perpendoicular to CE 5 what is the of the measure of
Given that ABCD is a parallelogram, the sum of its interior angles is:
360°
A parallelogram is a rectilinear two-dimensional figure with four sides whose opposite sides are parallel. See the image attached.
What is the sum of the exterior angles of CHFE?The sum of the exterior angles of any Triangle or any polygon is 360°. Hence, the sum of the exterior angles of CHFE (a polygon) is 360°.
Which sides are parallel to CE?The sides that are parallel to CE are:
FH
AD and
IJ.The side that are perpendicular to CE is side side HH, hence we can state that:
CE ⊥ EH, because both lines intersect each other at right angles.
Because the sum of angles in a triangle is 180° and we already have ∠CEH to be equal to ∠90° hence,
∠C + ∠H? = 180° - 90°
= 90°
What is the measure of the exterior angles of a Regular Pentagon?The measure of the exterior angles of a regular pentagon is 72°
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!!
Mum spent 3/5 of her money and put 1/8 of the remainder in the bank. If she had $750 left, how much did she start with?
Answer:
$2142.86
Step-by-step explanation:
The remaining part of her money, after spending 3/5 of it and depositing 1/8 of it is equal to $750.
===============================================================
Retracing the steps :
⇒ She put 1/8 of the remainder in the bank, which gives $750
⇒ R - R/8 = 750
⇒ 7R/8 = 750
⇒ R = 750/7 × 8
⇒ R = 107.142857 × 8
⇒ R = 857.142856
* Don't worry, we'll simplify at the end of the answer *
=============================================================
Now, this remainder is what was left after spending 3/5 of it.
⇒ T - 3/5T = 857.142856
⇒ 2/5T = 857.142856
⇒ T = 857.142856/2 × 5
⇒ T = 428.571428 × 5
⇒ T = $2142.86 (nearest cent)
HELP WITH THE RIGHT ANSWER FOR BRAINLIEST!!!
Answer: this is the wrong answer
Step-by-step explanation:
Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used.
Answer:
The answer is below :
Solve the system of equations by substitution.
-3x - 2y + 2z = 19
2x + y + 3z = -20
Z = -2
Answer:
Step-by-step explanation:
-3x - 2y + 2(-2) = 19
-3x -2y - 4 = 19
-3x - 2y = 23
2x + y - 6 = -20
2x + y = -14
-3x -2y = 23
2x + y = -14
-3x - 2y = 23
4x + 2y = -28
x = -5
-10 + y = -14
y = -4
x= -5, y = -4, z= -2
The angle measures of quadrilateral RSTU are shown.
m∠R = (2x)°
m∠S = (3x – 35)°
m∠T = (x + 35)°
The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?
Yes, opposite angles R and T are congruent to each other if x = 35.
Yes, consecutive angles R and S are congruent to each other if x = 35.
No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.
No, if x = 35, the three given angle measures make it impossible for the figure to be a quadrilateral.
The quadrilateral RSTU be a parallelogram if opposite angles R and T are congruent to each other if x = 35 option first is correct.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners.
We have:
The angle measures of quadrilateral RSTU are shown.
m∠R = (2x)°
m∠S = (3x – 35)°
m∠T = (x + 35)°
If R and T are congruent:
2x = x + 35
x = 35 degree
Opposite angles R and T are congruent to each other if x = 35.
Thus, the quadrilateral RSTU be a parallelogram if opposite angles R and T are congruent to each other if x = 35 option first is correct.
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Answer:
It's c
Step-by-step explanation:
On edge 2023
Need help ASAP
Stuck on this question and need help
Answer:
Factory A = 1200
Factory B= 1350
Factory C= 1050
Factory D = 1100
Step-by-step explanation:
Factory B as the fastest rate of production
Which expression is not a polynomial?
Answer:
the first choice is not a polynomial because you can't divide by a variable.
m || n, find the value of x.
m
n
(6x+16)⁰
(8x-18)°
Please help! I’ll give good review
Step-by-step explanation:
please mark me as brainlest
im lost can someone help?
Round your answer to the nearest tenth if necessary. Use 3.14 for .
A building can be approximated by a cylinder that is 100 meters in diameter and 30 meters in height. Find
its volume.
Its volume is approximately
m³.
OMG THIS IS SO HARD!!
Answer:
235500m3
Step-by-step explanation:
Volume of Cylinder= πr^2h
π=3.14, D=100m, r=D/2, r=100/2, r=50m, h=30m
πr^2h= 3.14×50×50×30
=3.14×75000
=235500m3
Each statement describes a transformation of the graph of y = ln x. Which statement correctly describes the graph of y = ln(x - 7) + 3?
The statement correctly describes the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.
what is the graph of logarithmic function?The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right
if 0 < b < 1. And if the base of the function is greater than 1, b > 1, then the graph will increase from left to right.
Given graph : y = ln(x), has a vertical and horizontal translation.
As we know, y = ln(x - h) + k | where h is the vertical shift, and k is the horizontal shift.
If ln(x - k), then the graph is translated right k units.If ln(x + k), then the graph is translated left k units.If ln(x) + h, then the graph is translated up h units.If ln(x) - h, then the graph is translated down h units.Therefore, comparing y = ln(x - 7) + 3 it with different function we can write the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.
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Which clock shows 11:22?
A.
A clock shows the hour hand slightly past 11 and the minute hand at one mark past the 3.
B.
A clock shows the hour hand slightly past 11 and the minute hand at 6.
C.
A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.
D.
A clock shows the hour hand slightly past 11 and the minute hand at one mark past the 2.
Answer:
Option C
Step-by-step explanation:
A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.
What is the area of this rectangle? (4 points)
A rectangle completely covered in square units is partitioned into two rectangles. The first rectangle has a measurement of four centimeters along the top and seven centimeters along the side. The second rectangle has a measurement of two centimeters along the top and seven centimeters along the side.
Answer:
42 cm
Step-by-step explanation:
The first rectangle has a length of 4 and a Width of 7. the second rectangle has a length of 2 and a width of 7.
The formula for area of a rectangle is A=l*w
SO,
Rectangle 1: A= L*W
A=4*7
A=28
Rectangle 2:
A=L*W
A=2*7
A=14
Now, add both areas since they are both part of one whole recatngle.
28+14
= 42
What is the permimeter of a 4’ square
Answer:
16'
Step-by-step explanation:
4'
4 equal sides
4+4+4+4=16
Answer: Permimeter of a 4’ square is 16.
Step-by-step explanation:
given that:
• length = 4
∴ Perimeter of Square = 4 x length
⇒ P = 4 × 4
⇒ P = 16 units ...answer...
hope that helps...
What is the volume of this rectangular
pyramid?
3 m
4 m
Submit
5 m
cubic meters
The volume of the given rectangular pyramid.
Solution:[tex]\large\boxed{Formula:V=\frac{1}{3}lbh}[/tex]
First, multiply the length (5), breadth (4) and height (3).
[tex]5×4×3[/tex]
[tex]= 60 \: cm [/tex]
Now, divide 60 by 3.
[tex]\frac{60}{3}[/tex]
[tex]\large\boxed{V= 20 \: {m}^{3}}[/tex]
Therefore, the volume of the given rectangular pyramid is 20 cubic meters.
sanjana wrote the cross multiplication property for her proportion: xt=uy
Answer:
what does this mean. oh wAit iM dematerializinG mvxhkgd
hdgxmgxmgxkgzkgsktxktdktdktdktdtdkgd
rotation 180° about the origin
Answer:
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y).
Step-by-step explanation:
The rotation of angle 180 degree about origin is described below.
Rotation 180° about the origin is a geometric transformation that involves rotating a figure or shape around the point (0,0),
Also known as the origin, by an angle of 180 degrees.
This means that every point on the shape is moved to an equal distance away from the origin but on the opposite side of the origin.
This transformation is a reflection where the shape is flipped along,
the x-axis or y-axis or both, depending on the shape's orientation.
The rotation 180° about the origin is a common transformation in various geometrical applications, such as computer graphics, engineering, and physics.
It is a simple transformation that can be easily represented and performed using matrices or complex numbers.
Therefore,
rotation 180° about the origin is a geometric transformation that is important in various applications and involves rotating a shape around the origin by an angle of 180 degrees, resulting in a reflection of the shape across the x or y-axis.
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Use the drop downs to determine which symbols
would complete the inequality for the domain.
-4 _(a)_x__(b) 4
(a)
less than or equal to O
(b)
less than or equal to
less than
greater than or equal to
greater than
-5
5
ty
5
x
The domain of the graph is x ≥ -4
How to determine the domain?From the given graph, we have the following highlights:
The x values start from -4The x value moves to the right of the graph (this means greater than)There is a closed circle at the smallest x value (this means equal to)Greater than and equal to are represented by ≥.
This means that the symbol that completes the domain of the graph is ≥
Hence, the domain of the graph is x ≥ -4
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let me know asap PLEASE
Answer:
the correct answer is B
Step-by-step explanation:
A function g is the inverse for the function f if for y-f(x), x-g(y)
y=7x-6
Replace x with y
x=7y-6
Solve for y in x=7y-6
Switch sides
7y-6=x
Add 6 to both sides
7y-6+6=x+6
Simplify
7y=x+6
Divide both sides by the coefficient of y, which is 7. We have:
7y/7 = x/7+6/7
7y & 7 are cancelled out and we're left with: x/7 & 6/7
Now we find the LCM of the denominators which is 7.
7 divide the denominators equal 1, we use the to multiply the numerators, x & 6
our final answer= x+6/7
I hope this helps.
for each circle , work out
Answer:
Formulas
[tex]\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Area of a semicircle}=\dfrac{1}{2}\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]
[tex]\textsf{Radius of a circle}=\sf \dfrac{1}{2}d\quad\textsf{(where d is the diameter)}[/tex]
[tex]\textsf{Perimeter of a semicircle}=r(\pi +2) \quad \textsf{(where r is the radius)}[/tex]
Use the above formulas to calculate the various measurements, remembering to calculate the radius first when given the diameter.
Question 9a) Radius = 2.7 cm
[tex]\implies \textsf{Area}=\sf \pi (2.7)^2=22.9\:\:cm^2\:(1\:d.p.)[/tex]
[tex]\implies \textsf{Circumference}=\sf 2 \pi (2.7)=17.0\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
b) Diameter = 45 mm
[tex]\sf \implies Radius =\dfrac{45}{2}=22.5\:\:mm[/tex]
[tex]\implies \sf Area= \pi (22.5)^2=1590.4\:\:mm^2\:(1\:d.p.)[/tex]
[tex]\implies \sf Circumference= 2 \pi (22.5)=141.4\:\:mm\:(1\:d.p.)[/tex]
Question 10a) Radius = 8.5 cm
[tex]\implies \sf Area=\dfrac{1}{2}\pi (8.5)^2=113.5\:\:cm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=8.5(\pi +2)=43.7\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
b) Radius = 24 mm
[tex]\implies \sf Area=\dfrac{1}{2}\pi (24)^2=904.8\:\:mm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=24( \pi +2)=123.4\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
c) Diameter = 32 cm
[tex]\sf \implies Radius =\dfrac{32}{2}=16\:\:cm[/tex]
[tex]\implies \sf Area=\dfrac{1}{2}\pi (16)^2=402.1\:\:cm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=16( \pi +2)=82.3\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
d) Diameter = 15 m
[tex]\sf \implies Radius =\dfrac{15}{2}=7.5\:\:m[/tex]
[tex]\implies \sf Area=\dfrac{1}{2}\pi (7.5)^2=88.4\:\:m\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=7.5( \pi +2)=38.6\:\:m\:(1\:d.p.)[/tex]
Please help. Trigonometric ratios
Question 2.1.1
Answer: 5 unitsReason:
Use the distance formula to find the distance from the origin (0,0) to the terminal point (-3, 4)
[tex](x_1,y_1) = (0,0) \text{ and } (x_2, y_2) = (-3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-(-3))^2 + (0-4)^2}\\\\d = \sqrt{(0+3)^2 + (0-4)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
The pythagorean theorem is a similarly related alternative path you can take.
This triangle is a 3-4-5 right triangle.
====================================================
Question 2.1.2
Answer: 1/5Reason:
r = distance from origin to terminal point
r = 5, calculated back in the previous problem above.
sin(alpha) = y/r = 4/5
cos(alpha) = x/r = -3/5
sin(alpha)+cos(alpha) = (4/5)+(-3/5) = 1/5
====================================================
Question 2.1.3
Answer: 1Reason:
Recall that tangent is the ratio of sine over cosine
tan = sin/cos
Therefore,
[tex]\tan(\alpha) *\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)*\cos(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\1[/tex]
This assumes that neither sin(alpha) nor cos(alpha) are zero. Otherwise, we have a division by zero error.
The graph of function g (x) predicts the profit of jimmy's famous Jer*y for a week. The x-axis represents the number of employees earning overtime for the week. The y-axis is the business's profit for the week in hundreds of dollars.
By identifying the maximums, we see that in each blank we need to write:
1) 2
2) 2
3) greater.
How to complete the given statement?
First, we need to find the maximum of the function g(x).
You can see that for x = 2 we have the maximum of the parabola, which gives y = 9.
Then the maximum profit is got when 2 employees earn overtime.
We also need to find the maximum for the table. Notice that the maximum value of the table also happens for x = 2, and this time the maximum is y = 16.
So we can see that the maximum of Cathy's cupcakes is larger than the maximum of Jimmy's.
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