The capacities at which U.S. nuclear power plants are working are shown in table for various years.
Year Percent
1975 56
1980 59
1985 58
1990 70
1995 76
2000 88
2004 89
Let
f
(
t
)
be the capacity (in percent) at which U.S. nuclear power plants are working at t years since 1970. A model of the situation is
f
(
t
)
=
0.027
t
2
+
0.216
t
+
53.296
.
Use a graphing calculator to draw the graph of the model and, in the same viewing window, the scattergram of the data. Does the model fit the data well?
The function is not a good model for the data
The function is a good model for the data.
Estimate at what capacity U. S. nuclear power plants were working in 2014.
% Round to the nearest whole percent.
Predict when U. S. nuclear power plants will be working at full (100%) capacity.
Enter the year this occurs.
Answers
The function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.
Given that the table which shows the capacities at which U.S. nuclear power plants are working and a model of the situation is f(t)=0.027t²+0.216t+53.296.
The Scatter plot for our function and points is shown in attached image and the point are highly related to the curve .
So the function is good model.
The year 2014 means t=2014-1970=44
So to get the population,put t=44 in equation
f(t)=0.027(44)²+0.216(44)+53.296
f(t)=0.027(1936)+0.216(44)+53.296
f(t)=52.272+9.504+53.296
f(t)=115.072
And on rounding it we get 115%.
Now, to find year at which capacity is 100% ,put f(t)=100 and solve for t
f(t)=0.027t²+0.216t+53.296=100
0.027t²+0.216t+53.296=100
0.027t²+0.216t+53.296-100=0
0.027t²+0.216t-46.704=0
Now, we will solve this using quadratic formula for f(x) =ax²+bx+c=0
[tex]\begin{aligned}x&=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end[/tex]
for our function a= 0.027 , b=0.216 ,c=-46.704 substitute this value and we get
[tex]\begin{aligned}t&=\frac{-0.216\pm \sqrt{(0.216)^2-4\times 0.027\times (-46.704)}}{2\times 0.027}\\ &=\frac{-0.216\pm \sqrt{0.046656+5.044032}}{0.054}\\ &=\frac{-0.216\pm \sqrt{5.090688}}{0.054}\\ &=\frac{-0.216\pm 2.256}{0.54}\\ &=37.78, -45.78\end[/tex]
As we all know time cannot be negative so t=-45.78 will be rejected.
So, t=37.78=38
Now, we will find the corresponding year
1970+38=2008
Hence, from the given table the function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.
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Related Questions
Find the distance between each pair of points.
33) (2, 2), (-2, 6)
A) 2√13
C) 8
B) 4√2
D) 2√2
Answers
Answer:
D
Step-by-step explanation:
Applying the distance formula root square x2-x1 +y2-y1
then
let the (x1,y1 )=(2,2)
(x2,y2)=(-2,6)
Select all names that apply
Answers
Answer:
A irrational
B real
Step-by-step explanation:
Given the value π/7, you want to classify it as whole, integer, real, and/or irrational.
Number classificationAny number that does not have an imaginary part is a real number. Real numbers include integers, whole numbers, and natural numbers, none of which have any fractional part.
Any ratio of integers (with a non-zero denominator) is a rational number. All other real numbers are irrational numbers. Pi (π) is an irrational number.
When rational numbers are written as decimal numbers, their fractional part will either terminate or repeat. When the fractional part of a decimal number does not terminate or repeat, but continues indefinitely, the number is irrational.
Pi/7As we said, pi is an irrational number. Multiplying it by a rational number (1/7) does not change its classification.
π/7 is irrational and real
What is the image of the point.
Answers
Answer:they will both negative because the rules are -x,-y
Step-by-step explanation:
During a Brazilian Day celebration, dancers perform in groups to honor Brazil's independence. There are 56 dancers wearing green outfits and 42 dancers wearing yellow outfits. Each group of dancers has the same number of dancers wearing green and the same number of dancers wearing yellow. All of the dancers are in a group. What is the greatest number of groups that can be formed?
Answers
The greatest number of groups that can be formed is 7.
How to calculate the value?
It should be noted that there are 56 dancers wearing green outfits and 42 dancers wearing yellow outfits.
The greatest number of groups that can be formed will the highest common factor between the numbers.
It should be noted that the highest common factor between 42 and 56 is 7.
Therefore, the greatest number of groups that can be formed is 7.
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A truck costing $56,000 has accumulated depreciation of $50,000. The truck is sold for $8,500. What is the journal entry for this transaction?
Answers
Answer: debit Cash for $8,500, debit Accumulated Depreciation− Truck for $50,000, credit Truck for $56,000, and credit Gain on Disposal for $2,500.
Help pls and thanks
Answers
The products of the matrices are
[-4 19]
ST = [8 -21]
and
[-12 -8]
TS = [-25 -10]
How to determine the product of the matrices?The matrices are given as
[4 1]
S = [-3 -2]
[0 4]
T = [-4 3]
The product of the matrices is then calculated as
[4 * 0 + 1 * -4 4 * 4 + 1 * 3]
ST = [-3 * 0 - 2 * -4 -3 * 4 - 3 * 3]
Evaluate the sum or difference of products
So, we have
[-4 19]
ST = [8 -21]
Also, we have
[0 * 4 + 4 * -3 0 * 1 + 4 * -2]
TS = [-4 * 4 + 3 * -3 -4 * 1 + 3 * -2]
Evaluate the sum or difference of products
So, we have
[-12 -8]
TS = [-25 -10]
Hence, the products of the matrices are
[-4 19]
ST = [8 -21]
and
[-12 -8]
TS = [-25 -10]
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A polling company reported that 98% of 2,330 surveyed adults said that they play football. What is the exact value that is 98% of 2,330?
Answers
The exact value that is 98% of 2330 is 2283
The value is 98% of 2330
98% of 2330 is 98/100×2330=2283.4≅2283
The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.Percentage is a fraction or a ratio in which the value of whole is always 100. Percent is another name for indicating hundredths.The percentage formula is used to find the share of a whole in terms of 100To learn more about percentages visit:
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Riley weighs something and records it to the nearest tenth of a gram as 8.6. Is it possible for the actual weight to be 8.549 grams?
Answers
Answer:
no
Step-by-step explanation:
it would have to be 8.55 to be rounded up not 8.549... there is a rule of if it is 4 and lower go down and if 5 and higher go up
What is the area of the circle shown below?
A circle with radius 8 centimeters.
a.
8 pi cm2
c.
StartFraction 16 Over 3 EndFraction pi cm2
b.
16 pi cm2
d.
64 pi cm2
Answers
Answer:
Step-by-step explanation:
64 pi cm2
Answer:
201.1 = 8^2 pi cm2 = 64 pi cm2
Step-by-step explanation:
The area of a circle with a radius 8 is 201.1
Hope it helps!!!
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Tamara’s shopping bill comes up to $750. How much does she have to pay after a VAT of 15% is added to all the items?
Answers
$750 + $112.5 = $862.50
5m+n=10 solve for m I give extra point
Answers
Given, 5m+n = 10
5m = 10-n
[tex]m = \frac{10 - n}{5} [/tex]
Hope this helps :)
Answer:
5m = 10- n
m = (10 - n) /5
I used bracket around 10-n because they're both being divided by 5.
Find an equation of the line that satisfies the given conditions.
Through (-2, 2); perpendicular to the line y = -1/2x + 2
Answers
Answer:
y=2x+6
Step-by-step explanation:
First find the gradient of the perpendicular line. We can do this by turing the given gradient into a negative reciprocal.
-1/2 -> 2 (new gradient)
substitute new gradient into y=mx+c as well as the values for x and y from the given coordinate (-2,2)
y=mx+c
2=2(-2)+c
then solve for c
2=-4+c
c=6
therefore the formula for the line is y=2x+6
The revenues and expenses of Up-in-the-Air Travel Service for the year ended April 30, 20Y7, follow:
Fees earned $742,000
Office expense 308,000
Miscellaneous expense 10,000
Wages expense 490,000
Prepare an income statement for the year ended April 30, 20Y7. Be sure to complete the statement heading. Refer to the lists of Accounts in the information given, Labels, and Amount Descriptions for the exact wording of the answer choices for text entries. Enter amounts as positive numbers unless the amount is a calculation that results in a negative amount. For example: Net loss should be negative. Expenses should be positive. A colon (:) will automatically appear if it is required.
Answers
If the revenues and expenses of Up-in-the-Air Travel Service for the year ended April 30, 20Y7, follow: Fees earned $742,000, Office expense 308,000. The income statement has a net loss of: $66,000.
Income statementIncome statement for the year ended April 30, 20Y7
Revenue:
Fees earned $742,000
Expenses:
Office expense $308,000
Miscellaneous expense $10,000
Wages expense $490,000
Total expenses $808,000
Net loss $66,000
($742,000-$808,000)
Therefore if the revenues and expenses of Up-in-the-Air Travel Service for the year ended April 30, 20Y7, follow: Fees earned $742,000, Office expense 308,000. The income statement has a net loss of: $66,000.
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How to solve the equation
Answers
Answer:
x = -26
Step-by-step explanation:
[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]
This is in the domain of the equation, and is thus a solution.
what is the equation for x=3, y=27 pls due tomorrow ASAP
Answers
Find the perimeter and area of a rectangle with side length of 12 cm and width of 6 cm.
Answers
perimeter would be 30 when you add all sides together
Given g(t)= -t+5, what is the value of g(-15)?
Answers
We have that [tex]g(t)=-t+5[/tex], and we are asked to evaluate [tex]g(-15)[/tex] . In notation of functions like this, the number inside the parentheses is the value of the variable. Or, to be more clear, this is essentially telling us that [tex]t=-15[/tex] for our expression [tex]g(t) = -t+5[/tex]. So we can evaluate it as follows:
[tex]g(-15) = -15 + 5 = -10[/tex]
The ratio of zebras to monkeys in a circus is 1 to 4. If there are 7 zebras in the circus, then how many zebras and monkeys are there altogether?
Answers
Answer:
Step-by-step explanation:
1:4 Ratio on zebras to monkeys.
Can be expressed 1x:4x
7 zebras total.
7 x 4 = 28
7 x 1 = 7
(28 + 7 = 35).
So, there for a ratio of 1:4 equals 28 monkeys and 7 zebras leaving a total of 35 monkeys and zebras together.
all answers needed please help i’ll give brainliest !! this is due tmr
Answers
Answer: See below
Step-by-step explanation:
a. 3(4)= 12
b. 4+11+(-4)
=15+(-4)
Answer=11
c. 3.2(2)= 6.4
d. I (-2)+(-2)+(-2) I= 6
e. I 2(-7.5) I = 15
f. [tex]10\frac{1}{5}[/tex](-5)= -51
a rectangle with a diagonal of length x is twice as long as it is wide. what is the area of the rectangle?
Answers
The area of the rectangle whose diagonal is twice its width is (x²√3)/4 square units.
What is the Area of Rectangle?The area of rectangle is defined by the product of its length and width. Mathematically-
Area [A] = Length [L] x Width [W]
Given is a rectangle whose diagonal is twice as long as it's width. From this, we can write -
Width = w
Length of diagonal = x = 2w
Assume that the length of the rectangle is L. Using the Pythagoras theorem in the triangle ΔABC, we get -
AC² = AB² + BC²
x² = L² + w²
(2w)² = L² + w²
4w² = L² + w²
L² = 3w²
L = w√3
Now, the width of rectangle is 'w' and its length is 'w√3'. Its area will be-
Area = length x width
A = w√3 × w
A = w²√3
Now, length of diagonal → x = 2w. So, we can write -
w = x/2
Therefore, the area will be -
A = (x/2)²√3 = (x²√3)/4
Therefore, the area of the rectangle whose diagonal is twice its width is (x²√3)/4 square units.
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(-10) + ( -2 ) + ( -7 )
Please
Answers
-10-2-7= -19
Hello...! :)
Very easy, we must eliminate the Parentheses and then we must use the Law of Signs and in this case we will use this which is:
[tex]\green{\underline{\blue{\bold{Law\: of \: signs:}}}} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - × + = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times + = + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times - = + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times - = - [/tex]
Once we know we must add but since we know that it is a minus sign (-) we will add it as if it were a simple sum but the minus sign just stays there
We start to solve:
[tex] \: \: \: \: \: \: \sf \red{(-10) } \pink+ \blue{ ( -2 ) } \purple+ \green{( -7 )}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{-10} \blue{ -2 } \green{-7}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \blue{-12} \green{ -7}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \green{-19}[/tex]
And in conclusion, the result of our problem is 19
¿Doubts? in the comments Greetings :D
PLEASE HELP!!!
Find the measure of the angle indicated in black (top angle).
6x+4
F. 70
G. 55
H. 95
J. 80
Answers
Answer:
F. 70
Step-by-step explanation:
[tex]{ \tt{(6x + 4) = (5x + 15)}}[/tex]
[Alternate angles]
[tex]{ \tt{(6x - 5x) = (15 - 4)}} \\ { \tt{x = 11}}[/tex]
Therefore;
[tex]{ \tt{angle = 6(11) + 4}} \\ = 66 + 4 \\ = 70 \degree[/tex]
perpendicular to y=-1/3x-6 through (-2,8)
Answers
Answer:
y = 3x + 14
See the work below.
Step-by-step explanation:
please help with this i m lost! what formula do i use???
Answers
Answer:
I think it's c I haven't done those formulas in while
i dont know what the answer is anyone help?What is the integer value of (2)3(2)4(2)5?
Answers
Answer:
e=mc2
Step-by-step explanation:
69 ballz = 43= e=mc2
Use the map shown below to find the distance between cities A and B to the nearest tenth.
Answers
Answer:
Use the Pythagorean theorem
Step-by-step explanation:
Based on the histogram above, what is the class width?
Class width =
What is the sample size?
Sample size =
Answers
Based on the histogram above, the class width is equal to 4.
Based on the histogram above, the sample size is equal to 37.
What is a class width?In a frequency distribution table, a class width can be defined as the difference between the upper (maximum) and lower (minimum) boundaries of any class in a data set. This ultimately implies that, all classes must all have the same width in a frequency distribution table.
Mathematically, the class width of a data set can be calculated by using this formula:
Class width = (max - min)/n
Where:
max represents the maximum value in a data setmin represents the minimum value in a data set.n represents the number of desired classes.In this context, the class width of this histogram can be calculated as follows;
Class width = max - min
Class width = 5 - 1
Class width = 4.
Furthermore, the sample size can be computed by adding all the frequencies of the corresponding rectangular bars of the histogram as follows;
Sample size = 6 + 10 + 4 + 2 + 7 + 8
Sample size = 37.
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An image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor. The actual book is 10.5 inches wide.
Answers
The book in real life is 7 times larger than the one on the website. When you divide 10.5/1.5 you get 7. So multiplying 3 by 7 will get you 21.
Therefore, the real book is 21 inches tall
& PHO
The ratio of boys to girls on the
school bus is 2 to 5. If there are 12
boys on the bus, then how many
girls are there?
Answers
Step by step
2 boys to 5 girls is 2/5
2/5 = 12/x Cross multiply
60= 2x
Divide both sides by 2 to solve for x
60/2 = 2/2 x
30 = x amount of girls
Answer: 30
Step-by-step explanation:
Think of each number in the ratio of 2:5 as a group. Each group has to be the same. 2 groups of boys : 5 groups of girls. There are 12 boys on the bus. So the 12 boys are split into 2 groups. 12/2=6. 6 boys are in each group. Since we now know that each group had 6 kids we just need to find the number of girls. There are 5 groups of 6 girls. 5x6=30. There are 30 girls on the bus.
. Read the following statement.
AABC is not an acute triangle.
What is the first step of indirectly proving this statement?
O
Assume AABC is not a scalene triangle.
Assume AABC is an acute triangle.
Assume AABC is not a right triangle.
Assume AABC is not an acute triangle.
Answers
The required step of indirect proving is to assume AABC is an acute triangle. Option B is correct.
Given that,
AABC is not an acute triangle.
What is the first step of indirectly proving this statement is to be determined.
The angle can be defined as the one line inclined over another line.
Here,
Indirect proving implies proving with contradictions,
So in order to prove AABC is not an acute triangle, we have first assumed that AABC is an acute triangle.
Thus, the required step of indirect proving is to assume AABC is an acute triangle. Option B is correct.
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