Answer:
part 1: After one year, the cost of the refrigerator modeled by f(x) is cheaper.
part 2: 14 years
part 3: g(x)
part 4: 51
hope this helps :)
To find the cheapest refrigerator in the long run, calculate the limit of the cost per year as x approaches infinity for both given functions and compare the results. The cost of the refrigerator modeled by f(x) will be the cheapest, averaging $62 per year.
Explanation:The average annual costs for owning two different refrigerators for x years can be calculated using the given functions: f(x) = 850 + (62x / x) and g(x) = 1004 + (51x / x). To determine which refrigerator will be cheaper in the long run, we need to find the limit of the cost per year as x approaches infinity for both functions. Taking the limit as x approaches infinity for f(x), we get 62. Therefore, the cost of the refrigerator modeled by f(x) will be the cheapest, averaging $62 per year.
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Can you help me answer this question?
Answer:
674.2 lb
Step-by-step explanation:
(5 ft)·(8 ft)·(1.2 in)·(12 in/ft)²·(2.54 cm/in)³·(2.7 g/cm³)/(453.592 g/lb) ≈ 674.2 lb
_____
Comment on units conversion
Units conversion is easily done using conversion factors that have a value of 1. That is, the value of the numerator is equal to the value of the denominator. (12 in = 1 ft, for example). The numerator units are chosen to match units you want, while the denominator units are chosen to match units you want to cancel.
Here, we convert in³ to cm³ to lb using conversion factors given and ones we know.
Given f(x) = 2x^2 + 3x and g(x) = 5x^2 - 2x - 6
What is (f+g)(x)?
A. -3x^2 + 5x + 6
B. 10x^2 + x + 6
C. 7x^2 + x - 6
D. 3x^2 - 5x - 6
Answer:
C. 7x^2 + x - 6
Step-by-step explanation:
f(x) = 2x^2 + 3x and g(x) = 5x^2 - 2x - 6
(f+g)(x) = 2x^2 + 3x + 5x^2 - 2x - 6
(f+g)(x) = 7x^2 + x - 6
According to the Substitution Property of Equality: If y = -5 and 7x + y = 11, then _______ . Question 9 options: 7(-5) + y = 11 7x - 5 = 11 7x + 5 = 11 -5 + y = 11
Answer:
7x - 5 = 11
Step-by-step explanation:
To solve for x, substitute y = -5 into the equation 7x + y = 11.
This becomes 7x + (-5) = 11 or 7x - 5 = 11.
In the same circle, chord AB determines a 115° arc and chord
AC determines a 43° arc. Find m∠BAC.
Answer:
101 degrees
Step-by-step explanation:
- A circle with two chords
- The two cords have common start point A on the circle
- The chord AB subtended arc AB with measure 115°
- The chord AC subtended arc AC with measure 43°
- The measure of any circle is 360°
* These two cords divide the circumference of the circle into
three arcs, arc AB , arc AC and arc BC
∵ The measure of arc AB = 115°
∵ The measure of arc AC = 43°
∵ The measure of the circle is 360°
∴ The measure of arc BC = 360 - (115 + 43) = 360 - 158 = 202°
- In the circle, the angle whose vertex is on the circle is
called inscribed angle and subtended by the opposite arc,
its measure is half the measure of the subtended arc
∵ ∠BAC is an inscribed angle subtended by arc BC
∴ m∠BAC = 1/2 measure of arc BC
∵ The measure of arc BC = 202°
∴ m∠BAC = 202 ÷ 2 = 101°
On average, how long does it take for each person to throw away 100 pounds of garbage?
Answer: About 22.73 days.
Step-by-step explanation: Each person throws away about 4.4 pounds of trash daily. So the way to calculate this is to divide 100 pounds by 4.4 to find out how many days it would take for a person to throw away 10 pounds of trash.
A store is having a sale where everything is discounted 30%. Find the discount and the sales price if a customer buys an item they normally sells for $365
Answer:
$255.50
Step-by-step explanation:
✯Hello✯
↪ Alright so the item is originally 365 dollars
↪ you have to work out 30% of this which is 109.50
↪ then do 365- 109.50
↪ thats $255.50
❤Gianna❤
Please answer this multiple choice question!
Answer:
C. 48
Step-by-step explanation:
If you cut the circle in half through the points M and C it splits 96 in half which is 48 which is the same size as M
Answer:
c. 48°Step-by-step explanation:
Look at the pictures.
(the picture 1)
Inscribed angle and central angle.
(the picture 2)
In a circle, central angle is two times larger than inscribed angle that intercept the same arc.
We have the central angle C. m∠C = 96°.
The inscribed angle M: m∠M = 96° : 2 = 48°
Help a need ma grade up
To answer this we must know BIDMAS
Brackets) Let's do 8-6 as (2*3 is 6 as we substitute X with 3) and that gives us 2
Indices) Let's do 2 square which gives 4
Addition) Then finally add 4 to 4 giving us 8
The answer is 8
Please help. I think I know the answer but I am not 100 percent sure.
Answer: 105°
Step-by-step explanation:
∠U and ∠S are supplementary angles, so
∠U + ∠S = 180°
x + 75° = 180°
x = 105°
Answer:
x = 105 degrees.
Step-by-step explanation:
RS is parallel to TU so x + 75 = 180
x = 105 degrees.
As its is isosceles y is also = 105 degrees.
I REALLY NEED HELP!
What is the future value of the 10% savings from earnings of $1,470 if it earns 3.5% annual interest,
compounded monthly for 25 years?
Use the compound interest formula to estimate the future value.
A = P (1+r/n)^nt
A.
$295.72
B.
$352.19
C.
$419.43
D.
$523.89
What is the future value of the 10% savings from earnings of $36,000 if it earns 6.25% annual interest, compounded quarterly for 15 years?
Use the compound interest formula to estimate the future value.
A = P (1+r/n)^nt
A.
$912.65
B.
$9,126.53
C.
$1,825.31
D.
$18,253.31
Justin contributes $208 each month to a savings account that earns 5% annual interest. Calculate his annuity savings over the course of 25 years.
Use
S = P ((1+r^n)-1/r)
A.
$9.927.23
B.
$65,520.00
C.
$62,660.00
D.
$123,866.02
Answer:
B
Step-by-step explanation:
The compound interest formula is [tex]A = P (1+r/n)^nt[/tex] where:
P is the starting amount called the principler is the rat written as a decimaln is the number of times compounded in a yeart is the number of yearsSubstitute a value into each variable to solve.
P = $147 since 10% of 1,470 is being invested which makes P = 0.10(1470) = 147.The rate is 3.5% or r = 0.035.n = 12 because it is compounded monthly meaning 12 times a year.t = 25 since it will earn for 25 years.[tex]A = P (1+r/n)^{nt}\\A = 147(1 + \frac{0.035}{12})^{12*25}\\A = 147 ( 1 + 0.002916)^{300}\\A = 147(1.002916)^{300}\\A = 352.19[/tex]
Repeat this process for each formula.
Answer:
B. $352.12
B. $9,126.53
D. $123,866.02
Step-by-step explanation:
Hope this helps! Have an awesome day/night!
How do you do this problem? SImple and concise answer please! PLEASE HELPPPPPPPPP
Answer:
b^(6c) = 3a is the only answer
Step-by-step explanation:
There is only one answer that works, and you put a check by it.
b is the base
When it is raised to the 6c power, you get 3a.
b^(6c) = 3a is the only answer
=========================
The only other possible answer would be
a = (1/3) b^(6c) which isn't there.
Find the percent increase from 9.56 to 9.65
Round your answer to the nearest tenth of a percent
Can someone explain how to do this? ive tried to look online but it doesnt get the correct answer i guess.
Answer:
Step-by-step explanation:
9.65-9.56=0.09
0.09/9.56=0.009414
0.009414*100=0.94%
9.56 increased by 0.94% to 9.65
Victoria can make 8 necklaces in four days. How long does it take to make one necklace?
it takes her half a day to make one necklace
Answer:
1/2 day
Step-by-step explanation:
4/8=1/2
The function below has been transformed from f(x) = x2. Describe the transformation. h(x) = 4x2 + 12
Answer:
vertically expanded by a factor of 4then, translated upward 12 unitsStep-by-step explanation:
If f(x) = x² and g(x) = 4x² = 4f(x), the function g(x) represents a vertical expansion of f(x) by a factor of 4.
If h(x) = g(x) +12, the function h(x) represents a translation of g(x) by 12 units upward.
Together, these transformations on f(x) are ...
vertical expansion by a factor of 4translation upward by 12 units_____
Please be aware that there are alternate transformations that will do the same thing:
h(x) = 4(f(x) +3) . . . . is a translation upward by 3, then a vertical expansion by a factor of 4
h(x) = f(2x) +12 . . . . is horizontal compression of f(x) by a factor of 2, then a translation upward by 12.
There is a 70% chance that your car will get stuck in the snow during the next big snow fall. Given that you are already stuck in the snow with your car, the chance that you will require a tow truck to pull you out is 90%. What is the chance that you will get stuck in the snow with your car AND require a tow truck to pull you out?
Hint: P(A|B)= P(A∩B) / P(B)
66%
63%
78%
29%
Answer:
63%
Step-by-step explanation:
This is a problem of conditional probability.
The two events that are given are:
Car stuck in the snow - Let it be event S. P(S) = 70% = 0.70Require a tow truck - Let it be event T.We have to find the probability of being stuck in the snow AND requiring a tow truck which can be given as P(S and T)
We are also given the conditional probability, which is P(T | S) = 90% = 0.90
Using the given formula for our case we can modify the formula as:
[tex]P(T|S)=\frac{P(S \cap T)}{P(S)}[/tex]
[tex]0.90=\frac{P(S \cap T)}{0.70}\\\\ P(S \cap T)=0.90 \times 0.70\\\\ P(S \cap T)=0.63[/tex]
Therefore, there is 63% (0.63) chance that you will get stuck in the snow with your car AND require a tow truck to pull you out
The probability of getting stuck in the snow and requiring a tow truck is found by multiplying the individual probabilities, resulting in a 63% chance.
The question asks for the probability that you will get stuck in the snow with your car AND require a tow truck to pull you out. To calculate this combined probability (P(A AND B)), we use the rule of multiplication for dependent events, which states P(A AND B) =[tex]P(B|A) imes P(A).[/tex] Here, P(A) is the probability of getting stuck in the snow, and P(B|A) is the probability of requiring a tow truck given that you are stuck.
In numbers, this becomes P(A AND B) = [tex]0.90 imes 0.70 = 0.63 or 63%[/tex]. Therefore, the chance that you will get stuck in the snow and require a tow truck to pull you out is 63%.
The complement of an angle is one-fourth the measure of the supplement of the angle. What is the measure of the angle to the nearest whole degree?
Answer:
the answer is 60
Step-by-step explanation:
Which type of graph would be best for displaying the frequencies of ages of runners in a race, according to five-year age groups?
a bar graph
a circle graph
a histogram
a line graph
A Histogram would be best
Victoria's favorite cookie recipe uses 170 grams of butter for every 250 grams of flour. Victoria's daughter made cookies using 340 grams of butter for every 400 grams of flour. What will Victoria think of her daughter's cookies?
Victoria's daughter's cookies will have more butter. Victoria uses 0.68g of butter per gram of flour, whereas her daughter uses 0.85g of butter per gram of flour.
Answer:
Daughter is using 0.17 gram more butter for each gram flour.
Step-by-step explanation:
Victoria's favorite cookie recipe uses 170 grams of butter for every 250 grams of flour = [tex]\frac{170}{250}[/tex] = 0.68
Therefore, this recipe needs 0.68 grams of butter for every gram flour.
Her daughter made cookies using 340 grams of butter for every 400 grams of flour = [tex]\frac{340}{400}[/tex] = 0.85
She is using 0.85 grams of butter for every gram flour.
Victoria's daughter is using 0.17 gram of butter more on every gram flour.
Identify the range of the function shown in the graph.
Answer:
C
Step-by-step explanation:
The range is the set of ALLOWED y-values of the function (graph). Also, the range is the y-values for which the function is defined.
Looking at the graph, we see that the graph is defined between y = 1 and y = 7. So the range is 1 ≤ y ≤ 7
the correct answer is C
A plane veered off its course at an angle of 11 degrees. If the plane ended up 170 miles due west of its planned destination, how far did it fly? Estimate your answer to two decimal places.
Answer:
890.99
Step-by-step explanation:
170/x=sin11
Which graph has the most appropriate scales and units for this situation ?
Answer:
your answer is A HOPE THIS HELPS!!!
Step-by-step explanation:
Answer:
The graph B is the most appropriated
Step-by-step explanation:
Due to we need to know the charging of the company as a function of miles, it is practical to enter into the graph with the miles into the horizontal axis and obtain the charge over the vertical axis. In fact, the common usage, it is by entering the unknown quantity (independent variable) into the x-axis (horizontal axis) and looking function calculated value into the y-axis (vertical axis).
Taking the previous into account, we chose the graph from option B.
let f(x)=x+3 and g(x)=x^2. find (gf)(5)
Answer:
[tex]g(f(5))=64[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x+3[/tex]
[tex]g(x)=x^{2}[/tex]
we know that
[tex]g(f(x))=(x+3)^{2}[/tex]
so
[tex]g(f(5))=(5+3)^{2}=64[/tex]
n article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 15 of 19 repairs were successful while for shorter tears, 21 of 29 repairs were successful. (a) Is there evidence that the success rate is greater for longer tears? Use . What is the -value? (b) Calculate a one-sided 95% confidence bound on the difference in proportions that can be used to answer the question in part (a). (a) There evidence that the success rate is greater for longer tears. The -value is Round your answer to four decimal places (e.g. 98.7654). (b) The one-sided 95% confidence bound is . Round your answer to three decimal places (e.g. 98.765).
To answer the question, a statistical hypothesis test comparing the proportions of successful repair attempts is needed. This involves calculating a Z-score and referencing Z-tables or statistical software for the p-value. Also, a one-sided 95% confidence interval needs to be calculated for the proportion differences using the Z-test.
Explanation:To answer this question, we need to perform a statistical hypothesis test which involves the comparison of proportions. Let's denote p1 as the proportion of successful repairs for tears greater than 25 mm (15 successful out of 19 trials), and let p2 for tears shorter (21 successful out of 29 trials).
To find the p-value, we need to implement a Z-test using the formula Z = (p1 - p2) - 0 / sqr((p(1-p)(1/n1 + 1/n2)) where p = (x1 + x2) / (n1 + n2). By substituting the values in the formula we get our z-score, which is used to find the p-value from the Z-tables or by using statistical software.
As for the 95% confidence interval, we will also use the Z-test formula, but this time the Z-value for the 95% one-sided confidence level which is approximately 1.645. Substituting the values in we can calculate our confidence bound. Please remember that to make accurate calculations you need to use calculated Z-score and confidence interval in the Z distribution method.
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(a) The p-value is 0.1814, and we do not have evidence that the success rate is significantly greater for longer tears.
(b) The one-sided 95% confidence bound on the difference in proportions is 0.184.
To answer your question regarding the success rates of arthroscopic meniscal repair for varying tear lengths, let's break it down into two parts: (a) the p-value and the evidence regarding the success rates, and (b) calculating a one-sided 95% confidence bound on the difference in proportions.
Part (a): Evidence and p-value Calculation:-
Define Success Rates:
For tears greater than 25 mm:
Number of successful repairs (x1) = 15Total repairs (n1) = 19Success rate (p1) = x1/n1 = 15/19 ≈ 0.7895For shorter tears:
Number of successful repairs (x2) = 21Total repairs (n2) = 29Success rate (p2) = x2/n2 = 21/29 ≈ 0.7241Hypotheses:
Null Hypothesis (H0): There is no difference in success rates, i.e., p1 ≤ p2.Alternative Hypothesis (H1): The success rate for longer tears is greater, i.e., p1 > p2.Calculate the z-statistic:
The formula for the z-statistic comparing two proportions is:
[tex]z = \frac{p_1 - p_2}{\sqrt{p(1 - p)(\frac{1}{n_1} + \frac{1}{n_2})}}[/tex]
where [tex]p = \frac{x_1 + x_2}{n_1 + n_2}[/tex] is the combined proportion.
Combined proportion (p):
[tex]p = \frac{15 + 21}{19 + 29} = \frac{36}{48} = 0.75[/tex]
Z-statistic calculation:
[tex]z = \frac{0.7895 - 0.7241}{\sqrt{0.75 \times (1 - 0.75) \times \left(\frac{1}{19} + \frac{1}{29}\right)}}[/tex]
Upon performing the necessary computations:
Using values,Find the p-value:
This represents the probability of observing a value as extreme (or more extreme) than the z-statistic under the null hypothesis. Using z-tables or a calculator for a right-tailed test:
Decision:
If we use an alpha (α) level of 0.05, since the p-value (0.1814) is greater than α, we fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude that the success rate is greater for longer tears.Part (b): One-sided 95% Confidence Bound:-
Confidence Interval for the Difference in Proportions:
The formula for the confidence interval is given by:
[tex](p_1 - p_2) \pm z_{\alpha} \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
Differences in proportions:
[tex]p_1 - p_2 = 0.7895 - 0.7241 = 0.0654[/tex]
Calculate the margin of error:
[tex]ME = z_{\alpha} \times \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
Confidence Bound:
The one-sided confidence bound:Result:
The one-sided 95% confidence bound on the difference in proportions is approximately 0.184.A survey found that women's heights are normally distributed with mean 63.9 in. and standard deviation 3.6 in. The survey also found that men's heights are normally distributed with mean 69.7 in. and standard deviation 3.6 in. Consider an executive jet that seats six with a doorway height of 55.9 in. Complete parts (a) through (c) below. a. What percentage of adult men can fit through the door without bending? The percentage of men who can fit without bending is 0.02%. (Round to two decimal places as needed.) b. Does the door design with a height of 55.9 in. appear to be adequate? Why didn't the engineers design a larger door?
Using the normal distribution, it is found that:
a) The percentage of men who can fit without bending is 0.02%.
b) A very small percentage of people can fit through the door, thus the dimensions are not adequate. Possible, the engineers did not design a large door because of engineering constraints.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.Item a:
Men have mean of 69.7 in, thus [tex]\mu = 69.7[/tex]Standard deviation of 3.6 in, thus [tex]\sigma = 3.6[/tex]The proportion is the p-value of Z when X = 55.9, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.9 - 69.7}{3.6}[/tex]
[tex]Z = -3.83[/tex]
[tex]Z = -3.8[/tex] has a p-value of 0.0002.
0.0002 x 100% = 0.02%
The percentage of men who can fit without bending is 0.02%.
Item b:
A very small percentage of people can fit through the door, thus the dimensions are not adequate. Possible, the engineers did not design a large door because of engineering constraints.
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A carnival charges a $5 admission fee plus $1 per ride. What does it cost to ride 6 rides, including the admission fee?
Answer:
the answer is 11 dollars
Step-by-step explanation:
Answer:
11 dollars
Step-by-step explanation:
given sec theta=-4/3 and 90°
Answer:
Option A.
Step-by-step explanation:
It is given secθ = - [tex]\frac{4}{3}[/tex]
then cosθ = -[tex]\frac{3}{4}[/tex]
Now we know the identity
sinθ = [tex]\sqrt{1-cos^{2}\theta }[/tex]
= [tex]\sqrt{1-(-\frac{3}{4} )^{2}}[/tex]
= [tex]\frac{\sqrt{7} }{4}[/tex]
Now sin2θ = 2sinθcosθ
Now we put the values of cosine and sine in the formula
sin2θ = 2×(-[tex]\frac{3}{4}[/tex])([tex]\frac{\sqrt{7}}{4}[/tex])
= -[tex]\frac{3\sqrt{7}}{8}[/tex]
Therefore, option A. is the answer.
18-3n+2=n+20-4n which is the solution 0 (0) or all reals
Answer:
that is a true statment.
20 - 3n = -3n + 20
Step-by-step explanation:
add the numbers, collect the like terms.
Which of the following statements is true according to the measurements in the diagram?
A man who is 6 feet tall casts a shadow thaty is 11 feet long at the same time a tree casts a shadow that is 33 feet long what is the height of the tree
Answer:
The height of the tree is 18 feet tall
Step-by-step explanation:
Set up a proportion:
6 feet over 11 feet long equals x feet over 33 feet long
6/11 = x/33
198 = 11x
x = 18
The height of the tree is 18 feet tall
In the chinese symbol for yin and yang, the dash shows two semicircles formed by the curve seperating yin(dark) and yang(light). Is the circumference of the entire yin and yang symbol, less than, greater than, or equal to the perimeter of the yin?
The perimeter of the yin is bigger than the circumference of the full yin and yang symbol. This is due to the fact that the yin and yang symbol is made up of two semicircles which extend beyond the boundaries of the separate yin and yang halves.
What is Yin and yang Symbol?The Yin and Yang symbol is a Chinese symbol that represents complementary characteristics found in all things, such as light and dark, hot and cold, good and evil, and so on. A circle is divided into two sections, one black and one white, containing a smaller circle of the opposing color in each section.
Yin is represented by the black portion, which is connected with feminine traits, passivity, darkness, or coldness. Yang is represented by the white part, which is connected with masculine attributes such as activity, brightness, and warmth. The symbol is intended to reflect the harmony and balance of both of these opposing energies.
Therefore, the perimeter of the yin is bigger than the circumference of the full yin and yang symbol.
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Final answer:
The circumference of the entire yin and yang symbol is greater than the perimeter of the yin semicircle, as the full symbol represents a complete circle while the semicircle includes only half the circumference plus its diameter.
Explanation:
The question about the Chinese symbol for yin and yang essentially asks about the relationship between the circumferences of two geometric shapes. If we consider the yin and yang symbol as a whole to be a circle, and the yang (or yin, since they are symmetrical) as a semicircle, then we can infer the following regarding circumferences and perimeters:
The circumference of a circle is 2πr, where r is the radius of the circle. The perimeter of a semicircle (half of the full circle and including the diameter) is πr + 2r. If we take the full yin and yang symbol to have a circumference of 2πr (since the full symbol is also circular), then the perimeter of the yang semicircle (which includes the straight edge boundary of the yin) would be less than the circumference of the full symbol, as it lacks the other semicircle's curved edge. In mathematical terms, πr + 2r is less than 2πr for any positive value of r.