Answers
Step-by-step explanation:
5a.
10 white squares
15 shaded squares
5b.
a1 = 1 = 2×1 - 1
a2 = a1 + 2×2 - 1 = 2×1 - 1 + 2×2 - 1 = 2×(1+2) - 2
a3 = a2 + 2×3 - 1 = 2×(1+2+3) - 3
...
an = 2×(1+2+...+n) - n = 2×n×(n+1)/2 - n = n²
so,
a350 = 350² = 122,500
figure350 has 122,500 squares.
5c.
a1 = 1
a2 = a1 = 1
a3 = a2 + 5
a4 = a3 = 6
a5 = a4 + 9
a6 = a5 = 15
a7 = a6 + 13
a8 = a7 = 28
...
a(2n) = a(2n - 1)
a(2n - 1) = a(2(n-1) - 1) + 1 + 4(n - 1) = n×1 + 4(0+1+2+...+n-1) =
= n + 4×(n-1)×n/2 = n + 2×(n² - n) = 2n² - n
therefore,
a350 = a349
a349 = a(2×175 - 1) = 2×175² - 175 = 61,075
figure350 has 61,075 shaded squares.
Related Questions
Pls help asap, have a great day
find, w: x: y: z:
Answers
Answer:
See below ↓
Step-by-step explanation:
Finding w and x [both are equal]
Take the cos function of one of the 45° angles, which is the ratio of the adjacent side to the hypotenusecos(45°) = [tex]\frac{1}{\sqrt{2} } = \frac{w}{6}[/tex]⇒ w = [tex]\frac{6}{\sqrt{2} } = \frac{6}{\sqrt{2} } *\frac{\sqrt{2} }{\sqrt{2} } = \frac{6\sqrt{2} }{2}[/tex]⇒ w = 3√2 and x = 3√2Finding y
Take the cos ratio of the 60° angle to find ycos(60°) = [tex]\frac{1}{2} = \frac{y}{x} = \frac{y}{3\sqrt{2} }[/tex]⇒ y = [tex]\frac{3\sqrt{2} }{2}[/tex]Finding z
Take the sin ratio of 60° angle of the triangle, which is the ratio of the opposite side to the hypotenusesin(60°) = [tex]\frac{\sqrt{3} }{2}= \frac{z}{x} = \frac{z}{3\sqrt{2} }[/tex]⇒ z = [tex]\frac{3\sqrt{6} }{2}[/tex]Help plsss its an emergency
Answers
Answer:
-8.05E14
Step-by-step explanation:
If you arent familiar with E notation it means the same thing as [tex]10^x[/tex] where x is the number proceeding the E
Find the decimal expansion for 5/12
Answers
Answer:
Answer would be 0.4166666667
Step-by-step explanation:
Mr. Sanchez’s class sold fruit pies for $1.73 each and Mr. Kelly’s class sold bottles of fruit juice for $1.44 each. Together, the classes sold 83 items and earned $130.83 for their school. Write and solve a system of equations that models this problem.
Answers
The system of equation that models the problem is as follows;
x + y = 83
1.73x + 1.44y = 130.83
The number of fruit pies sold is 44 and the number of fruit juice sold is 39.
How to solve a system of equation that models a problem?
Mr Sanchez class sold fruit pies for $1.73 each and Mr Kelly's class sold bottles of fruit juice for $1.44 each.
Therefore,
let
x = number of fruit pies sold
y = number of fruit juice sold
Together, the class sold 83 items. Therefore,
x + y = 83
They sold a total of $130.83. Therefore,
1.73x + 1.44y = 130.83
x + y = 83
1.73x + 1.44y = 130.83
1.73x + 1.73x = 143.59
1.73x + 1.44y = 130.83
0.29x = 12.76
x = 12.76 / 0.29
x = 44
Therefore,
y = 83 - 44
y = 39
learn more on system of equation here: https://brainly.com/question/13958134
Stacy is making a scale model of the Eiffel Tower for French class. Her model is 500 times smaller than the actual tower, which is 300 meters tall. How many millimeters tall is Stacy's model?
Answers
Answer: 600 mm
Step-by-step explanation:
Let height of her model be x meters
So,
500x = 300
[tex]\begin{aligned}&\rightarrow x=\frac{300}{500} \\&\rightarrow x=\frac{3}{5}=0.6 \text { meters } \\&\rightarrow x=0.6 \times 1000 \text { millimeters } \\&\rightarrow x=600 \text { millimeters }\end{aligned}[/tex]
Therefore, Stacy's model is 600 millimeters tall
Help with tthis photo pls T.T
Answers
Answer:
1. False
2. Not sure
3. True
Statement A
A = bh/2
34 = (10)h/2
68/10 = h
h = 6.8
FALSE The actual height of the triangle is the hypotenuse of the fake outer triangle. 6.8 is not used to calculate the area.
Statement B
A = (d1 + d2)/2
56 = (d1 + d2)/2
112 = d1 + d2
I have no idea for this one. There is no way that I know of to verify the area if I don't have at least one diagonal.
Statement C
A = (a + b)(h)/2
24 = (7 + 9)(3)/2
48 = (7 + 9)(3)
16 = 7 + 9
16 = 16
TRUE Area of the trapezoid = 24 in².
CAN SOMEONE HELP ME PLEASE
Answers
Answer:
the answer is -4
Step-by-step explanation:
you take the points (0,6) and (4,-10), then you subtract -10 by 6 and you get -16. then you take 4 subtracted by 0 and you get 4. -16 divided by 4 is -4.
Toni is 30 inches less than twice Jordan's height. Toni is 66 inches tall. How tall is Jordan?
Answers
Answer:
96 inches
Step-by-step explanation:
66 + 30 = 96
3. Evaluate the following:
a.) What value of Syields the coordinate point (1, 3)?
b.) What value of Syields the coordinate point (3, 1)?
c.) x(710)=
d.) y(V10+ V5)= = B С
e.) x(2)=
f.) y(2.5)=
Answers
Answer: See below
Step-by-step explanation:
Question 3:
[tex]a) \ $S=1$ \ yields \ $(1,3)$ \\ \\b) \ $S=3$ \ yields \ $(3,1)$ \\ \\ c) \ $x(\sqrt{10})=\sqrt{10}$ \\ \\d) $y(\sqrt{10}+\sqrt{5})=1$ \\ \\e) $x(2)=2$ \\ \\f) $y(2,5)=1$ \\[/tex]
Challenge:
[tex]\begin{aligned}&x(s)=s \quad ,s \in[0,4] \\&y(s)=\left\{\begin{array}{cc}3 s & , s \in[0,1] \\5-2 s &, s \in[1,2] \\1 & s \in[2,4]\end{array}\right.\end{aligned}[/tex]
Historians have commonly believed that paint used before the year 1500 did not contain copper. However, lab techniques have shown that copper is present in the paint of both the Mona Lisa painted by Leonardo da Vinci (1452-1519), a widely-renowned and timeless piece that is one of the most valuable pieces in the Louvre today, and in that of another painting known as the Sine Nomine, also from the same time period, whose painter is unknown—but not found in the paint of any other Renaissance painting analyzed. This is strong evidence that the Sine Nomine was painted by da Vinci, as well as evidence that the presence of copper in the paint of a recently resurfaced map by Fra Mauro, ostensibly from the year 1450, cannot be used as an argument against the map's authenticity.
The reasoning in the passage is vulnerable to criticism on the grounds that:
A) both the Sine Nomine and the Fra Mauro Map are objects that can be appreciated on their own merits whether or not the precise date of their creation or the identity of the person who made them is known
B) it is unreasonable to suppose that determination of the date and location of an art piece’s painting or drawing can be made solely on the basis of the presence or absence of a single element in the paint used in the document
C) the results of the analysis are interpreted as indicating that the use of copper as an ingredient in fifteenth-century paint both was, and was not, extremely restricted
D) the discovery of copper in the paint of the Fra Mauro Map must have occurred before copper was discovered in the paint of the Sine Nomine and Mona Lisa
E)if the technology that makes it possible to detect copper in paint has only recently become available, it is unlikely that cartographers or artists in the fifteenth century would know whether their paint contained copper or not
Answers
The reasoning in this text is vulnerable to criticism because works such as Sine Nomine and the map can be appreciated on their own (option A).
What is the reasoning behind this text?The author of this text explains copper has been found in the Mona Lisa painting by Da Vinci that dates back to 1450. This evidence is used to conclude a similar painting known as the Sine Nomine belongs to the same painting and that a similar map belongs to the same period.
What is the problem with this reasoning?The reasoning fails at considering each artwork is unique and can be appreciated on its own without jumping to conclusions about the period and author of them.
Learn more about reasoning in: https://brainly.com/question/11478756
Classify each of the following lines as parallel, transversal or perpendicular.
Answers
Answer:
5. Perpendicular
6. Parallel
7. Transversal
8. Perpendicular
9. Parallel
10.Transversal
Step-by-step explanation:
|x+3/4|= 5 6/7 please help with this question from 6.2 russian mathemetics school
Answers
Answer:
143/28 or -185/28
Step-by-step explanation:
Negative case
-(x+3/4))=(41/7)
-x-(3/4)=(41/7)
-x=(185/28)
x=-(185/28)
Positive case
(x+(3/4))=(41/7)
x=(143/28)
lol this was easy r u sure its 6 grade?
Answer:
143/28 or -185/28
help me please
I couldn't solve it
Answers
[tex]\text{L.H.S}\\\\=\dfrac{\sin^4 A - \cos^4 A}{ \sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A)^2-(\cos^2 A)^2}{\sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A + \cos^2 A)(\sin^2 A-\cos^2 A)}{\sin A + \cos A}\\\\\\=\dfrac{1\cdot(\sin A+\cos A)(\sin A - \cos A)}{\sin A +\cos A}\\\\\\=\sin A - \cos A\\\\\\=\text{R.H.S}~~~ \\\\\text{Proved.}[/tex]
Answer:
heya! ^^
[tex] \\ \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } = ( \: sin \: A\: - \: cos \: A \: )\\[/tex]
[tex] \\LHS = \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } \\ \\ \frac{( \sin {}^{2} \: A + \cos {}^{2} \: A)( \sin {}^{2} A - \cos {}^{2} A) }{ (\sin \: A + \cos \: A) } \\ \\ we \: know \: that \: - \: sin {}^{2} A + cos {}^{2} A = 1 \\ \\ \therefore \: \frac{(1)(\sin {}^{2} \: A - \cos {}^{2} \: A)}{(\sin \: A + \cos \: A)} [/tex]
now , we're well aware of the algebraic identity -
[tex]a {}^{2} - b {}^{2} = (a + b)(a - b)[/tex]
using the identity in the equation above ,
[tex]\dashrightarrow \: \frac{(sin \:A - \: cos \: A)\cancel{(sin \:A + \: cos \: A )}}{\cancel{(sin \: A\: + \: cos \: A)}} \\ \\ \dashrightarrow \: (sin \: A \: - \: cos \: A) = RHS[/tex]
hence , proved ~
hope helpful :D
The basketball team has four players who can play the center position. Their heights (in
inches) are 78, 80, 77, and 80.
a) List all 6 possible SRSs of size n = 2, calculate the mean height for each sample.
b) Display the sampling distribution of the sample mean on a dotplot.
c) If the sample size was increased to n = 3, what would happen to the sampling distribution?
(statistics)
Answers
The mean height for each sample from the basketball team will be 79, 77.5, 79, 78.5, 80, and 78.5
How to calculate mean?For sample 1, the mean will be:
= (78 + 80)/2 = 79.
For sample 2, the mean will be:
= (78 + 77)/2 = 77.5
For sample 3, the mean will be:
= (78 + 80)/2 = 79
For sample 4, the mean will be:
= (80 + 77)/2 = 78.5
For sample 5, the mean will be:
= (80 + 80)/2 = 80
For sample 6, the mean will be:
= (77 + 80)/2 = 78.5
When the sample size was increased to n = 3, the shape of the sampling distribution becomes bell shaped on the population mean.
Learn more about the mean on:
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Find the simple Intrest for
$ 2000 at 4% for 3 months
Answers
Answer:
Simple interest: 240, Final amount: 2240
hope im right
Step-by-step explanation:
can anyone help with this?
Answers
Answer:
It's a 270 degree rotation or -90 degree rotation there the same thing all the other answer choices are wrong besides 270 degree rotation.
Step-by-step explanation:
Traveling in a fried-out Kombi
On a hippie trail, head full of zombie
I met a strange lady, she made me nervous
She took me in and gave me breakfast
And she said
Do you come from a land down under?
Where women glow and men plunder?
Can't you hear, can't you hear the thunder?
You better run, you better take cover
Buying bread from a man in Brussels
He was six-foot-four and full of muscle
I said, "Do you speak-a my language?"
He just smiled and gave me a Vegemite sandwich
And he said
I come from a land down under
Where beer does flow and men chunder
Can't you hear, can't you hear the thunder?
You better run, you better take cover, yeah
Lyin' in a den in Bombay
With a slack jaw, and not much to say
I said to the man, "Are you trying to tempt me
Because I come from the land of plenty?"
And he said
Oh, you come from a land down under? (Ooh, yeah, yeah)
Where women glow and men plunder?
Can't you hear, can't you hear the thunder?
You better run, you better take cover ('cause we are)
Living in a land down under
Where women glow and men plunder
(Can't you hear thunder) can't you hear, can't you hear the thunder?
You better run, you better take cover
Living in a land down under
Where women glow and men plunder
Can't you hear, can't you hear the thunder? (Ooh yeah)
Better run, you better take cover (we are)
Living in a land down under (ooh yeah)
Where women glow and men plunder
Can't you, can't you hear the thunder?
Better run, you better take cover
Living in a land down under (living in a land down under)
Where women glow and men plunder
Can't you, can't you hear the thunder?
To measure the height of the Washington Monument, a student 5.5 ft tall measures his shadow to be 4.25 ft. At the same time of day, he measured the shadow of the Washington Monument to be 430 ft
long. Use a calculator to estimate the height of the monument to the nearest foot.
The Washington Monument is approximately ________ft tall?
Answers
Answer:
OK, Well to solve this first,
Set up a ratio:
height of the student/student shadow length = height of the monument/monument shadow length
height of the monument = x
6ft./4.75ft = x/435ft.
cross multtiply
6 * 435 = 4.75x
2610 = 4.75x
divide by 4.75 to both sides
2610/4.75 = 4.75x/4.75
549.47 = x
There you go Slide Brainliest Please
Step-by-step explanation:
Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 3.
On = 31/2,w=
- 3/2
On - 3√2, w = 3/2
Oh = 12, w = 312
W
Oh=312. W = 2
Answers
The dimensions to maximize the area must be:
length = (√3)/2width = (√3)/2How to get the dimensions of the rectangle?The rectangle with the largest area that can be inscribed on a circle of radius 3, will be a rectangle whose diagonal is equal to the diameter of the circle, so we have:
√(x + y) = 6 units.
Where x and y are the dimensions of the rectangle. We also must have that:
x < 6 unitsy < 6 units.Now, because we have limits, the largest area (which is the product of x and y) happens when x and y have the same value x = y, then we have:
√(x + x) = 6 units.
√(2x) = 6 units.
x = (√3)/2 = y
So the rectangle is actually a square of side length = (√3)/2
If you want to learn more about rectangles, you can read:
https://brainly.com/question/17297081
Select the correct answer.
What are the roots of this quadratic equation?
help
Answers
Answer:
A
Step-by-step explanation:
I took the test it was right
Out-of-pocket spending in a country for health care increased between 2003 and 2008. The function f(x) = 2573e^0.0359x models average annual expenditures per household, in dollars. In this model, x represents the year, where x = 0 corresponds to 2003 .
(a) Estimate out-of-pocket household spending on health care in 2008 .
(b) Determine the year when spending reached $2783 per household.
Answers
Answer:
(a) The total expenditures per household in the year 2008 were approximately $3,080.
(b) The spending reached $2875 per household in 2006.
Step-by-step explanation:
Note: This question is not complete, and the part c is not another question but the same question as part a. The complete question is therefore provided before answering the question as follows:
Out of-pocket spending in a country for health care increased between 2003 and 2008. The function f(x) = 2574e^(0.0359x) models average annual expenditures per household, in dollars. In this model, x represents the year, where x = 0 corresponds to 2003.
(a) Estimate out-of-pocket household spending on health care in 2008.
(b) Determine the year when spending reached $2875 per household
The explanation to the answer is now given as follows:
(a) Estimate out-of-pocket household spending on health care in 2008.
Given;
f(x) = 2574e^(0.0359x) ........................ (1)
Since x = 0 corresponds to 2003; by counting from 2003 to 2008, it implies that x = 5 corresponds to 2008.
Substituting x = 5 into equation (1) to estimate out-of-pocket household spending on health care in 2008, we have:
f(6) = 2574e^(0.0359 * 5)
f(6) = 2574 * 1.19661890406748
f(6) = 3,080.09705906969
Rounding to the nearest dollar as needed, we have:
f(6) = $3,080
Therefore, the total expenditures per household in the year 2008 were approximately $3,080.
(b) Determine the year when spending reached $2875 per household
This can be determined using equation (1) in part a by equating f(x) to $2875 solve for x as follows:
2875 = 2574e^(0.0359x)
2875 /2574 = e^(0.0359x)
1.11693861693862 = e^(0.0359x)
Taking the natural log of both sides, we have:
ln(1.11693861693862) = ln(e^(0.0359x))
0.110591565075382 = 0.0359x
x = 0.110591565075382 / 0.0359
x = 3.0805449881722
Approximating to a whole number, we have:
x = 3
Since x = 0 corresponds to 2003; by counting from 2003, x = 3 corresponds to 2006.
Therefore, the spending reached $2875 per household in 2006.
The sum of squares of lengths of the two sides of a rectangular field is 25m2.Their difference is 1m .what is the length of each side of the field
Answers
Answer:
Perimeter of a rectangle = 2×(Length+Breadth)
(i) Length = 16.8 cm
Breadth = 6.2 cm
Perimeter = 2×(Length+Breadth)
= 2×(16.8+6.2) =46 cm
(ii) Length = 2 m 25 cm
=(200+25) cm (1 m = 100 cm )
= 225 cm
Breadth =1 m 50 cm
= (100+50) cm (1 m = 100 cm )
= 150 cm
Perimeter = 2×(Length+Breadth)
= 2×(225+150) =750 cm
(iii) Length = 8 m 5 dm
= (80+5) dm (1 m = 10 dm )
= 85 dm
Breadth = 6 m 8 dm
= (60+8) dm (1 m = 10 dm )
= 68 dm
Perimeter = 2×(Length+Breadth)
= 2×(85+68) =306
) Find the value of b for which 50y +150 is a factor of y3 – by2 +by+3b.
Answers
[tex]f(y) = y^3-by^2+by+3b\\\\\text{Since 50y+150 is a factor of f(y), }\\\\~~~~~f\left ( -\dfrac{150}{50}\right) = 0 \\\\\implies f(-3)=0 \\\\\implies (-3)^3 -b(-3)^2+b(-3)+3b =0\\\\\implies -27-9b-3b+3b=0\\\\\implies -27-9b =0\\\\\implies 9b = -27\\\\\implies b = -\dfrac{27}9\\\\\implies b = -3[/tex]
A spherical balloon has a 16-in diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.
a. Find the volume of the fully-inflated balloon.
b. Find the volume of the half-inflated balloon
c. What is the radius of the half-inflated balloon?
Answers
Answer:
a. 2144.66 cubic inches
b.1072.33 cubic inches.
c. 16 inches
Step-by-step explanation:
hello, to answer this question we have to calculate the volume of sphere:
Volume of sphere: 4/3 π r³
Since diameter (d) = 2 radius (r)
Replacing with the value given:
16 =2r
16/2=r
r= 8 in
Back with the volume formula:
V = 4/3 π r³
V =4/3 π (8)³
V = 2144.66 cubic inches
The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.
2144.66/2 = 1072.33 cubic inches.
To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=1072.33
1072.33 = 4/3 π r³
Solving for r
1072.33 / (4/3 π)= r³
256= r³
16 = r
r = 16 inches
Simplify the expression. Write your answer as a power.
The simplified expression is
Answers
therefore
8^14
Allowing 20% discount on the marked price if a watch, the value of the watch will be Rs. 2376. If the VAT of 10% is added, find its marked price.
Ans: Rs. 2700
Answers
original price be x
x-0.2x=23760.8x=2376x=2970VAT 10%
So new price is 10% less
2970-0.10(2970)2970-297Rs 2673≈27007
.
Marisela wants to create a trophy in the shape of a rectangular
pyramid with volume 0.1875 cubic foot. Complete the descriptions
by writing in the missing measurements. 7.6.6
Design #1: pyramid height = 1.5 ft; base width = 0.75 ft;
Answers
Answer:
Volume of a rectangular pyramid:
[tex]V=\dfrac13lwh[/tex]
where:
[tex]V[/tex] = volume[tex]l[/tex] = length of base[tex]w[/tex] = width of base[tex]h[/tex] = heightGiven:
[tex]V[/tex] = 0.1875 ft³[tex]w[/tex] = 0.75 ft[tex]h[/tex] = 1.5 ftSubstitute given values into the formula and solve for [tex]l[/tex]:
[tex]\implies 0.1875=\dfrac13 \cdot l \cdot 0.75 \cdot 1.5[/tex]
[tex]\implies 0.1875=\dfrac{1.125}{3} l[/tex]
[tex]\implies 0.1875=0.375 l[/tex]
[tex]\implies l=\dfrac{0.1875}{0.375}[/tex]
[tex]\implies l=0.5[/tex]
Therefore, the base length is 0.5 ft
When a certain number is divided by 20, the result is same when number is decreased by 361. What is the number?
Answers
Answer:
The number is 380
Step-by-step explanation:
Let the number be 'x'
[tex]\sf \dfrac{x}{20}=x-361\\\\\text{multiply the entire equation by 20}\\\\20*\dfrac{x}{20}=20*(x-361)[/tex]
x = 20x - 20*361
x = 20x - 7220
Now subtract '02x' from both sides
x - 20x = -7220
-19x =-7220
Divide both sides by (-19)
x = (-7220) ÷ (-19)
x = 380
I WILL GIVE BRAINLY
Rectangle ABCD is plotted on a coordinate plane. The coordinates of A are (2, 3) and the coordinates of B are (– 2, 3). Each unit on the coordinate plane represents 3 centimeters, and the perimeter of Rectangle ABCD is 48 centimeters. Find the coordinates of Points C and D given these conditions:aPoints C and D are below Points A and B.bPoints C and D are above Points A and B.7Rectangle PQRS is plotted on a coordinate plane.
Answers
mark as brainliest please :)
A workplace gave an “Employee Culture Survey” in which 500 employees rated their agreement with the statement, “I feel respected by those I work for.”The relative frequency of people who strongly agree with the statement is
Answers
Supposing that 400 people agree with this sentiment, the relative frequency is of 0.8.
What is a relative frequency?A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we suppose that out of 500 employees, 400 agree with the sentiment, hence the relative frequency is given by:
p = 400/500 = 0.8.
More can be learned about relative frequencies at https://brainly.com/question/14398287
Estimate the sum of the decimals below by rounding to the nearest whole
number. Enter your answer in the space provided.
3.145
1.824
+ 7.769
Answers
Answer:
12.738
rounded to the nearest hundred is 12.74
