The 8 students at the pizza party ate 2 and 2/3 pizzas if each student ate 1/3 of a pizza.
If each of the 8 students ate 1/3 of a pizza, we can find the total number of pizzas by multiplying the number of students by the fraction of a pizza each student ate:
8 students × 1/3 pizza per student = 8/3 pizzas
However, it's more common to express the result as a mixed number or decimal. To convert the improper fraction 8/3 to a mixed number, we can divide the numerator by the denominator:
8 ÷ 3 = 2 with a remainder of 2
Therefore, the students ate 2 and 2/3 pizzas altogether. Alternatively, we can convert the improper fraction to a decimal by dividing the numerator by the denominator:
8/3 = 2.67
Therefore, the students ate approximately 2.67 pizzas altogether.
To recap, if each of the 8 students at the pizza party ate 1/3 of a pizza, they ate 8/3 pizzas altogether, which is equal to 2 and 2/3 pizzas or approximately 2.67 pizzas.
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In 2019 and in 2020, consumers in Dexter purchased only books and pens.
The prices and quantities for 2019 and 2020 are listed in the table.
The reference base period for Dexter's CPI is 2019, and 2019 is also the year of the Consumer Expenditure Survey.
What is the inflation rate in 2020?
The inflation rate in 2020, given the CPI in 2020 and the price in both years, would be 95. 5 %.
How to find the inflation rate ?To find the inflation rate from the CPI (Consumer Price Index), subtract the beginning CPI from the end CPI. This gives you the increase in the price level over the time period.
Divide the increase in the price level by the beginning CPI. Multiply the result by 100 to get the inflation rate as a percentage. Basically, the formula is:
= (CPI in 2020 - CPI in 2019 ) / CPI in 2019
= ( 195.5 - 100 ) / 100
= 95. 5 %
Note : The CPI for 2020 is 195.5 and the assumed CPI for 2019 would be 100 as a base year.
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I dont know how to do this
pls answer if u know with simple working
Answer: 11 in the 5th picture
Step-by-step explanation:
or if you add 5 more then it would be 17
add 2
a certain newspaper provides the net asset value, the year-to-date percent return, and the three-year percent return for 882 mutual funds at the end of 2017. assume that a simple random sample of 12 of the 882 mutual funds will be selected for a follow-up study on the size and performance of mutual funds. use the third column of the table of random numbers, beginning with 71744, to select the simple random sample of 12 mutual funds. begin with mutual fund 744 and use the last three digits in each row of column 3 for your selection process. what are the numbers of the 12 mutual funds in the simple random sample? (enter your answers as a comma-separated list.)
The 12 mutual funds in the simple randοm samples are
714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488
What is a simple randοm sample?A simple randοm sample is a subset οf persοns picked at randοm, all with the same prοbability, frοm a larger set οf individuals. It is a methοd οf chοοsing a sample at randοm.
Here, we have
Given: a certain newspaper prοvides the net asset value, the year-tο-date percent return, and the three-year percent return fοr 882 mutual funds at the end οf 2017. assume that a simple randοm sample οf 12 οf the 882 mutual funds will be selected fοr a fοllοw-up study οn the size and perfοrmance οf mutual funds. use the third cοlumn οf the table οf randοm numbers, beginning with 71744, tο select the simple randοm sample οf 12 mutual funds.
The last three digits in each rοw οf cοlumn 6 less than 882 are
714, 041, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488
Hence, The 12 mutual funds in the simple randοm samples are
714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488.
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Suppose the solution set of a certain system of linear equations can be described as x_1 = 6 + 3x_3, x_2 = -2 - 5x_3, with x_3 free. Use vectors to describe this set as a line in R^3. Geometrically, the solution set is a line through parallel to
The solution set of the given system of linear equations can be expressed as a line in R^3 vector as r = (6, -2) + x_3(3, -5).
To express the solution set of the given system of linear equations as a line in R^3, we first need to express the solution set as a vector equation. We can do this by expressing the equations in terms of x_3 as follows:
x_1 = 6 + 3x_3,
x_2 = -2 - 5x_3
Therefore, the solution set of the given system of linear equations can be expressed as a line in R^3 as follows:
r = (6, -2) + x_3(3, -5).
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Find the length of AC in this right-angled triangular
prism.
Give your answer in centimetres (cm) to 1 d.p.
44 cm
A
E
42 cm
B
F
57 cm
с
The length of AC in this right-angled triangular prism is approximately 60.66 cm.
What is Pythagoras theorem?
For right angle triangle,
Hypotenuse² = Height²+Base²
However, we can use the Pythagorean theorem to find the length of AC if we know the lengths of AE and EC and ED.
If we assume that face AEC is the base of the prism and the right angle is at vertex E, then we can use the Pythagorean theorem to find the length of AC:
AC² = AE²+ EC²
We are given that AE = 43 cm, but we don't know the length of EC. However, we can use the fact that the base of the prism is a rectangle to find EC. Since opposite sides of a rectangle are equal, we have:
EC = 51 cm and ED = 45 cm
Substituting this into the equation above, we get:
AC² = 43² + 51²
AC² = 3680
AC ≈ 60.66 cm (to 1 decimal place)
Therefore, the length of AC in this right-angled triangular prism is approximately 60.66 cm.
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Correct question is "Find the length of AC in this right-angled triangular prism. Give your answer in centimetres (cm) to 1 d.p.
Base is ED 51 cm and height is AE 43 cm of the prism."
A rope is 4212 meters long. It is cut into 17 pieces of equal lengths. What is the length of each piece?
Each piece of the rope is 247.76 meters long, approximately.
To find the length of each piece, we need to divide the total length of the rope by the number of pieces it is cut into:
Length of each piece = Total length of the rope / Number of pieces
Length of each piece = 4212 meters / 17
Length of each piece = 247.76 meters (rounded to two decimal places)
The method used to find the length of each piece of rope is division. We divided the total length of the rope by the number of pieces it was cut into, which gives us the length of each piece. This method is based on the fact that the length of each piece is the same, so we can divide the total length equally among the pieces.
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-5 x blank equals 35
Answer:
-7
Step-by-step explanation:
A negative number times a negative number is positive. Because -5 is negative and 35 is positive the other factor must be negative as well.
5 x 7 = 35
So, -5 x -7 also equals 35
please help me please
251^5+8-(9x20+3)=
Answer:
996,250,626,076
Step-by-step explanation:
You want the value of the numerical expression 251^5+8-(9×20+3).
CalculatorYour calculator will evaluate this properly if you enter it as shown. See the attachment.
If you're doing this in parts, the Order of Operations tells you to start with the parentheses, then do the exponentiation.
251^5 +8 -(9·20 +3)
= 251^5 +8 -183
= 996,250,626,251 +8 -183 = 996,250,626,076
__
Additional comment
You can use a spreadsheet (or an on-line calculator) if your calculator only displays 10 digits.
If it takes John 5/12 of an hour to work on a fence, how many minutes will it take him to finish the job?
Answer:
Step-by-step explanation:
Which statement best compares and contrasts the two formats?
The infographic shows the movement of water visually, while the text describes it.
The infographic would be less appealing to visual learners than the text.
It is impossible to understand the infographic without the text.
The text is more accurate than the infographic.
Consider the t distribution with 5 degrees of freedom.
(a) What proportion of the area under the curve lies to the right of t = 2. 015?
(b) What proportion of the area lies to the left of t = −3. 365?
(c) What proportion of the area lies between t = –4. 032 and t = 4. 032?
(d) What value of t cuts off the upper 2. 5% of the distribution?
The cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.
(a) 0.974
(b) 0.998
(c) 0.996
(d) 2.571
(a) To find the proportion of the area under the curve to the right of t = 2.015, we first calculate the cumulative probability of t = 2.015 from the t-distribution table. The cumulative probability of t = 2.015 is 0.974, which means that 0.974 or 97.4% of the area under the curve lies to the right of t = 2.015.
(b) To find the proportion of the area under the curve to the left of t = −3.365, we calculate the cumulative probability of t = −3.365 from the t-distribution table. The cumulative probability of t = −3.365 is 0.998, which means that 0.998 or 99.8% of the area under the curve lies to the left of t = −3.365.
(c) To find the proportion of the area under the curve between t = –4.032 and t = 4.032, we calculate the cumulative probability of t = 4.032 and subtract the cumulative probability of t = −4.032. The cumulative probability of t = 4.032 is 0.995 and the cumulative probability of t = −4.032 is 0.003. Subtracting the two gives us 0.996, which means that 0.996 or 99.6% of the area under the curve lies between t = –4.032 and t = 4.032.
(d) To find the value of t that cuts off the upper 2.5% of the distribution, we calculate the cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.
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Help I got logged out of my account and forgot the password and the email I used to sign up is not an real to receive the code
If locked out of an account due to forgotten password and invalid email, try password recovery options or contact customer support, or create a new account.
If you've been locked out of your account. If you've forgotten your password and the email you used to sign up is not valid, it can be difficult to regain access to your account. Few steps you can try to recover your account:
Check if there's any password recovery option: Depending on the website or platform you've signed up for, there may be a password recovery option that doesn't rely on email verification. For example, some sites may allow you to answer security questions or use your phone number to reset your password.Contact customer support: If there's no password recovery option or it's not working for you, try contacting the customer support team for the website or platform. Explain the situation and provide any relevant information you can. They might be able to assist you in getting your account access back.Create a new account: If all else fails, you may need to create a new account with a valid email address. Make sure to choose a strong, unique password and consider enabling two-factor authentication to help secure your account in the future.It's important to note that in some cases, it may not be possible to regain access to your account. Always be cautious about the information you provide when signing up for online services and make sure to keep your login credentials in a safe and secure location.
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John has 10 apples he gives Janet 8 how many does he have
Answer:
2
Step-by-step explanation:
John had 10 and he gave Janet 8, which means that he remained with 2
The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?
6
20
27
30
[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{"y" varies}\\ \textit{directly with "x"}\\ \textit{inversely with "z"} \end{array}\qquad y=\cfrac{kx}{z}\hspace{5em}\textit{we also know that} \begin{cases} x=10\\ z=4\\ y=15 \end{cases} \\\\\\ 15=\cfrac{k(10)}{4}\implies \cfrac{4}{10}\cdot 15=k\implies 6=k\hspace{8em}\boxed{y=\cfrac{6x}{z}} \\\\\\ \textit{when x = 20 and z = 6, what's "y"?}\qquad y=\cfrac{6(20)}{6}\implies y=20[/tex]
Answer:
I think is 500 hope it helps
The number of bacteria in a culture is given by the function
0. 3t
n(t) = 920e
where t is measured in hours.
(a) What is the relative rate of growth of this bacterium population?
Your answer is
percent
(b) What is the initial population of the culture (at t=0)?
Your answer is
(c) How many bacteria will the culture contain at time t=5?
Your answer is
a) The continuous rate of growth of this bacterium population is 45%
b) Initial population of culture at t = 0 is 950 bacteria
c) number of bacterial cultures contain at t = 5 is 9013 bacteria
The number of bacteria in a culture is given by the function n(t) =950[tex]e^{0.450t}[/tex] Where t is measured in hours
what is the continuous rate of growth of this bacterium population
The number of bacteria in a culture is given by
n(t) = 950[tex]e^{0.45t}[/tex]
a) rate of growth is
Bacteria growth model N(t) = no[tex]e^{rt[/tex]
Where r is the growth rate
hence r = 0.45
= 45%
b) Initial population of culture at t = 0
n(0) = 950[tex]e^0[/tex]
= 950
= 950 bacteria
c) number of bacterial culture contain at t = 5
n(5) = 950[tex]e^{0.45*5}[/tex]
= 9013.35
= 9013 bacteria
the complete question is-
The number of bacteria in a culture is given by the function n(t) =950e^0.45t Where t is measured in hours A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent B) what is the initial population of the culture (at t=0) your answer is __ C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria
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Question in photo
!!!!!
Answer:
Binomial
Step-by-step explanation:
A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials.
For the function f(x)=3x2 +3x+8, evaluate and fully
simplify each of the following.
f(x+h)= ?
f(x+h)-f(x) / h = ?
By evaluating and simplifying f(x)=3x2 +3x+8, we get f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8 and (f(x + h) - f(x))/h = 6x + 3h + 3.
Given function is, f(x) = 3x² + 3x + 8
Evaluate f(x + h)
Expanding f(x + h) => f(x) + hf′(x) + h²/2f″(x)
Applying formulae in the given function f(x + h) = 3(x + h)² + 3(x + h) + 8=> 3x² + 6xh + 3h² + 3x + 3h + 8Now, f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8
Evaluate (f(x + h) - f(x))/h
Expanding both the terms f(x + h) and f(x) and simplifying, (f(x + h) - f(x))/h = [3x² + 6xh + 3h² + 3x + 3h + 8 - (3x² + 3x + 8)]/h=> [3x² + 6xh + 3h² + 3x + 3h + 8 - 3x² - 3x - 8]/h=> [6xh + 3h² + 3h]/h=> 6x + 3h + 3
Therefore, the required value is f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8and (f(x + h) - f(x))/h = 6x + 3h + 3.
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please help if you can
Using variation, the model for F = 42(m/p)
What do you mean by variation?There is a direct variation between the two variables whenever one quantity directly influences the other, such as when one quantity increases relative to the other and vice versa. There is a connection between two variables when one of them is a constant multiple of the other. Because of their immediate connection, the two variables are referred to as directly proportional.
Inverse variation establishes a proportionality between two quantities that are inversely related. There are two separate proportionalities. They are the direct variation and inverse variation. The two quantities are said to be directly proportional if an increase or decrease in one generates an equal increase or decrease in the other. In an inverse variation, on the other hand, one quantity increases while the other falls.
Now as F is directly proportional to m and inversely to p, so we can form a model as:
F = 42(m/p)
So that F=36 when m =6 and p =7.
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Unit 8 Right Triangles & Trigonometry Homework 3: similar Right triangles & geometric mean
In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
A right-angled triangle ABC with drawn with angle B = 90°.
A line BD is drawn which is perpendicular to AC.
The angle BDC is also 90 degrees.
The measure for line segment AD = 12 and CD = 40.
The measure for line segment BD is x.
The side BD is common for triangle ABC and BDC.
So, by the formula of indirect measurement we have -
DC / BD = BD / AD
Substitute the values in the equation -
40 / x = x / 12
x² = 480
x = 21.908
x = 21.91
Therefore, the value of x is obtained as 21.91.
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The frequency table shows Sam's record in swimming
Year
Number of medals
2008
2009
2010
2012
2013
Based on this record, what is the probability of picking up a medal won by him in the years 2009 or 2012
The probability of picking a medal won by Sam in the years 2009 or 2012 is 5/6.
The probability of picking a medal won by Sam in the years 2009 or 2012 can be calculated using the formula P(A∪B) = P(A) + P(B) - P(A∩B). In this case, P(A) equals the probability of picking a medal won by Sam in 2009, which is 1/3, and P(B) equals the probability of picking a medal won by Sam in 2012, which is 1/2. P(A∩B) would be the probability of picking a medal won by Sam in both years, which is 0, since he did not win a medal in both years. Therefore, the probability of picking a medal won by Sam in the years 2009 or 2012 is P(A∪B) = P(A) + P(B) - P(A∩B) = 1/3 + 1/2 - 0 = 5/6.
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which expression is equivalent to 6 divided by 2/5
Answer:15
Step-by-step explanation:
Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, 6 divided by 2/5 is the same as multiplying 6 by 5/2, which equals 15.
Explanation:The expression 6 divided by 2/5 is equivalent to 6 multiplied by 5/2. This is because dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/5 is 5/2. Therefore, 6 divided by 2/5 is the same as 6 multiplied by 5/2, which gives you the result 15.
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(10 POiNTS!!!)Find the value of x that makes this a true statement.
−3(x − 100) = −5(x − 100) + 6
Answer: x = 100
Step-by-step explanation:
mpho takes 140 km trip to visit his unclevon his motorbike.THE motorbike has a fuel capacity of 16 litres.He stops for lunch break after 5/7 of the journey.how many kilometers did he travel before he stopped for lunch?
Answer:
40Km
Step-by-step explanation:
Total Distance of Journey = 140KM
5/7 of the journey:
[tex]\frac{5}{7 } * 140 = 100km[/tex]
Distance travelled before stopping: Total Distance - 5/7 of Total Distance
= 140 - 100KM = 40KM
The box-and-whisker plots show the speed, in miles per hour, for each of 10 fish and 10 mammals. Speed of 10 F 30 50 D 60 Speed of 10 Mammals + 60 70 30 40 50 70 Letecia wants to predict the speeds of one additional fish and one additional mammal. She notices that the box-and-whisker plots show that about 75% of the fish were faster than 40 mph and that about 75% of the mammals were slower than 50 mph. Based upon this information, which prediction about the speeds of the additional fish and the additional mammal is justified? A The speed of the fish will be less than 40 mph, and the speed of the mammal will be greater than 50 mph. The speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph. The speed of the fish will be greater than 40 mph, and the speed of the mammal will be greater than 50 mph. The speed of the fish will be less than 40 mph, and the speed of the mammal will be less than 50 mph.
Based on the information, the only prediction that is justified is that the speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph.
Therefore option B is correct.
How do we know this?Based on the given information above, we were able to deduct that about 75% of the fish were faster than 40 mph and about 75% of the mammals were slower than 50 mph.
We can go ahead and use this information to make predictions about the speeds of one additional fish and one additional mammal.
Note that the median speed is around 50 mph, and the upper quartile (75th percentile) is around 60 mph and we know that about 75% of the fish were faster than 40 mph, we can predict that the additional fish will have a speed greater than 40 mph. However, since the upper quartile is only at 60 mph, we cannot predict that the additional fish will have a speed greater than 60 mph. Therefore, the only prediction that is justified is that the speed of the fish will be greater than 40 mph, which eliminates options A and D.the only prediction that is justified is that the speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph, which is option BLearn more about speed at:
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Gloria traveled a total of
8
88 miles to get from school to her apartment. Gloria took the bus from school and then walked the remaining
880
880880 yards home
Gloria traveled a distance of 7.5 miles on the bus.
Why is unit conversion crucial while addressing problems?The process of translating a measurement from one unit to another is known as unit conversion. Since multiple units are frequently used to measure the same quantity and because unit conversion is required to carry out calculations and solve issues, it is significant in problem solving. Moreover, unit conversion is crucial since it enables us to compare measurements and present them in a uniform manner. For instance, measurements in science and engineering are frequently stated in SI units.
Given that, Gloria traveled a total of 8 miles.
8 x 1760 = 14080 yards.
The distance walked is 880 yards.
So the distance she traveled on the bus is:
14080 - 880 = 13200 yards
13200 / 1760 = 7.5 miles
Hence, Gloria traveled 7.5 miles on the bus.
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The complete question is:
town A is 60 km from town B and 61km from town C a road connects town B and C directly find the length of the road for class 7 ncert
Answer:Using the triangle inequality, we can conclude that the distance between towns B and C must be less than 121 km (the sum of the distances between towns A and B, and between towns A and C).
To find the exact length of the road connecting towns B and C, let's use the Pythagorean theorem.
Let x be the length of the road connecting towns B and C. Then we have:
x^2 = 61^2 + 60^2
x^2 = 3721 + 3600
x^2 = 7321
x ≈ 85.6 km
Therefore, the length of the road connecting town B and C is approximately 85.6 km.
Step-by-step explanation:
The two charges q are fixed at the vertices of an equilateral triangle with sides of length
a. If k = 1/4π ε0, the work required to move q from the other vertex to the center of the line joining the fixed charges is:
The work required to move q from the other vertex to the center of the line joining the fixed charges is (1/4π ε0) x 2 x q 2/a.
To solve this problem, we can use the principle of superposition to calculate the potential at the center of the equilateral triangle due to each of the two fixed charges, and then add them up to get the total potential.
Let's first find the potential due to one of the fixed charges at the center of the triangle. We can use the formula for the electric potential due to a point charge q at a distance r from it, which is given by:
V = k x q/r
In this case, the distance from one of the fixed charges to the center of the triangle is: r = a/2
So the potential due to one fixed charge at the center of the triangle is:
V1 = kq/r = kq/(a/2)
Next, let's find the potential due to the other fixed charge at the center of the triangle. Since the triangle is equilateral, the distance from the other fixed charge to the center of the triangle is also a/2. So the potential due to the other fixed charge at the center of the triangle is:
V2 = k x q/(a/2)
Now, the total potential at the center of the triangle due to the two fixed charges is simply the sum of the individual potentials:
V_total = V1 + V2 = kq/(a/2) + kq/(a/2) = 2kq/a
The work required to move a charge q from infinity to the center of the triangle is equal to the change in potential energy of the charge, which is given by:
W = q x (V_final - V_initial)
In this case, the initial potential is zero (since the charge is at infinity), and the final potential is 2kq/a (which we just calculated). So the work required is:
W = q x (2kq/a - 0) = 2kq 2/a
Substituting the given value of k, we get:
W = (1/4π ε0) x 2 x q2/a
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the position (in thousands of feet) of a car driving along a straight road at time t in minutes is given by the function y
The position of a car driving along a straight road at time t in minutes is given by the function y = f(t).
The function y represents the position of the car in thousands of feet, while the variable t represents the time in minutes.
To find the position of the car at any given time, you simply need to plug in the value of t into the function and solve for y. For example, if you wanted to find the position of the car at 2 minutes, you would plug in 2 for t and solve for y:
y = f(2)
Once you have solved for y, you will have the position of the car in thousands of feet at 2 minutes. You can repeat this process for any value of t to find the position of the car at any given time.
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Evaluate. (3. 5−2/3)⋅(−2. 8+4 3/5) Enter your answer as a decimal or mixed number in simplest form in the box
Answer:
5.1, 5 1/10
Step-by-step explanation:
(3.5 − 2/3) ⋅ (−2.8 + 4 3/5) =
= (7/2 - 2/3)(-14/5 + 23/5)
= (21/6 - 4/6)(9/5)
= (17/6)(9/5)
= (17 × 9)/(6 × 5)
= 51/10
= 5.1 = 5 1/10
What’s the first step in evaluating the expression 6-(4/2X5)2?
The first step in evaluating the expression 6 - (4/2 x 5)² is to simplify the expression inside the parentheses first.
What is an expression?An expression is a mathematical phrase that consists of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that are combined according to certain rules to represent a mathematical calculation.
Following the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), as shown below:
4/2 = 2, so we can replace 4/2 with 2:
6 - (2 x 5)²
2 x 5 = 10, so we can replace 2 x 5 with 10:
6 - 10²
10² means 10 multiplied by itself, which equals 100:
6 - 100
Therefore, the expression simplifies to -94.
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a side of an apartment building is shaped like a steep staircase. the windows are arranged in columns. the first column has 3 windows, the next has 6, then 12 and so on. how many windows are on the side of the apartment building if it had 10 columns
Answer:
3069 windows on the side of the apartment building if it has 10 columns.
Step-by-step explanation:
We can notice that the number of windows in each column is double the number of windows in the previous column. So, we can write down the number of windows in each column as a sequence of powers of 2:
3, 6, 12, 24, 48, 96, 192, 384, 768, 1536
We can see that this is a geometric sequence with a common ratio of 2. We can use the formula for the sum of a geometric sequence to find the total number of windows:
Sn = a(1 - r^n)/(1 - r)
where
a = 3 (the first term)
r = 2 (the common ratio)
n = 10 (the number of terms we want to sum)
Substituting these values into the formula, we get:
Sn = 3(1 - 2^10)/(1 - 2)
= 3(1 - 1024)/(-1)
= 3(1023)
= 3069
Therefore, there are 3069 windows on the side of the apartment building if it has 10 columns.