Answer:180
Step-by-step explanation:
100 - 10 is 90
90 x 2 is 180
I did a reverse calculation you can also check this is correct by knowing that half of 180 is 90 and 100 dollars is 10 more than 90 dollars.
Identify the domain and range of each function.
y = 3.52
The domain of this function is
The range of this function is
DONE
The domain and range of each function y = 3.52 is All real numbers and {3.52}.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
We are given that;
The function y=3.52
Now,
For the function y = 3.52, the output (y-value) is always the same, regardless of the input (x-value). Therefore, the domain of this function is all real numbers, and the range of this function is the single value 3.52.
Therefore, the domain and range will be All real numbers and {3.52}
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What is the volume of the following rectangular prism?"
8 units
5- 1/4units
Volume =
Answer: 42
Step-by-step explanation:
convert 5 1/4 to an improper fraction=21/4
then multiply 21/4 • 8 = 42!
hope this helps (:
The volume of the rectangular prism is, 42 units³
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
For a rectangular prism,
Base area = 5 1/4 units
Height = 8 units
We know that;
The volume of the rectangular prism = Base area x Height
Substitute given values, we get;
The volume of the rectangular prism = Base area x Height
The volume of the rectangular prism = 5 1/4 x 8
The volume of the rectangular prism = 21/4 x 8
The volume of the rectangular prism = 42 units³
Thus, The volume of the rectangular prism is, 42 units³
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A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.85 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.
a. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods.
b. What is the probability that in the long run the traffic will not be in the delay state?
c. An important assumption of the Markov process models presented in this chapter has been the constant or stationary transition probabilities as the system operates in the future. Do you believe this assumption should be questioned for this traffic problem? Explain.
Answer:
Check the explanation
Step-by-step explanation:
First define the below events
Delayt : Traffic delay in current period
Delayt-1 : Traffic delay in preceding period
No-Delayt : No traffic delay in current period
No-Delayt-1 : No traffic delay in preceding period
Based on above definitions, define below given probabilities
P(No-Delayt/No-Delayt-1) = Probability of "no delay" in current period given that "no delay" in preceding period
= 0.85
P(Delayt/Delayt-1) = Probability of "delay" in current period given that "delay" in preceding period
= 0.75
and given that one period = 30 minutes
a) Given that motorist already knows that there is a traffic delay, probability of delay in next 60 minutes will be possible if both the consecutive periods is in "delay" state.
Period A Period B
---------------- -----------------
Delay -------> Delay ------> Delay
Since both the delay events should occur together(consecutive) to get the required probability, hence
Probability that next 60 minutes(two consecutive periods) will be in delay state
= P(Delayt/Delayt-1) * P(Delayt/Delayt-1)
= 0.75 * 0.75
= 0.5625 [ANSWER]
b) probability that in the long run the traffic will not be in the delay state is equivalent to proability that all the time in No-delay state.
First calculate the probability of currren period in delay state given that preceding period in No-delay state
P(Delayt/No-Delayt-1) = 1 - P(No-Delayt/No-Delayt-1)
= 1 - 0.85
= 0.15
Now the required probability,
P(All the time No-Delay state) = 1 - P( one period in delay state)
= 1 - ( P(Delayt/Delayt-1) + P(Delayt/No-Delayt-1) )
= 1 - (0.75 + 0.15)
= 0.10 [ANSWER]
c) Yes. Because this assumption assumes that for the 30 minutes traffic will be in delay state and just after 30 minutes, there will be No-delay state which is a hypothetical situation. In general scenario, traffic doesn't behave like this. To make the model more realistic, the probabilities might have been modeled as a function of time, instead of being constant for 30 minutes.
A decorative steel frame is shown below
It is made of a circular section ad 6 stems
The lenght of each stem is 45cm
work out the total lenght of steel used in the frame
Answer:
552.78
Step-by-step explanation:
45 x 6 =270
2πr = r x 2 x 3.142 = 45 x 2 x 3.142 = 282.78
270 + 282.78
The total length of the steel when both the circular section is added would be = 552.6cm.
How to calculate the total length of the given steel?The total length of the steel can be calculated following the steps below:
The total length of the 6 stems with 45cm = 45×6 = 270cm
The length of circular section = 2πr
where r = 45cm
C = 2× 3.14×45
= 282.6
The total length = 270+ 282.6
= 552.6cm
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The Louvre Pyramid, designed by the architect I. M. Pei, is a landmark in the city of Paris. The right pyramid has a vertical height of 21.621.621, point, 6 meters (\text{m})(m)(, start text, m, end text, )and a square base with side length 35\,\text{m}35m35, start text, m, end text. The Inverted Pyramid is a skylight in the shape of an upside-down right pyramid located on the ceiling of a mall below the Louvre Pyramid. The Inverted Pyramid has a vertical height of 7and a square top with side length 16. Approximately how much greater is the volume of the Louvre Pyramid than the volume of the Inverted Pyramid, to the nearest cubic meter t, cubed,
Answer:
8223 cubic meter
Step-by-step explanation:
Louvre Pyramid
Vertical Height =21.6 meters
Side Length of Square Base =35 m
Volume of a Pyramid [tex]=\frac{1}{3}*$Base Area X Height[/tex]
Therefore, Volume of Louvre Pyramid[tex]=\frac{1}{3}*35^2 X 21.6[/tex]
=8820 cubic meter.
Inverted Pyramid
Vertical Height =7 meters
Side Length of Square Base =16 m
Volume of a Pyramid [tex]=\frac{1}{3}*$Base Area X Height[/tex]
Therefore, Volume of Louvre Pyramid[tex]=\frac{1}{3}*16^2 X 7[/tex]
=597.33 cubic meter.
Difference in Volume
Difference=Volume of Louvre Pyramid-Volume of Inverted Pyramid
=8820-597.33
=8222.67
=8223 cubic meter (to the nearest cubic meter)
The graph of a hyperbola is shown. What are the coordinates of a focus of the hyperbola?
(−12, 0)
(0, −5)
(0, 0)
(13, 0)
The answer is D.) (13,0)
I remember seeing this question somewhere before... Along with the graph.
Additionally, make sure to add the graph to the question next time!
The coordinates of focus are ( 13, 0)
What is Hyperbola?The hyperbola can be defined as the difference of distances between a set of points, which are present in a plane to two fixed points is a positive constant.
A hyperbola is a set of points whose difference of distances from two foci is a constant value. This difference is taken from the distance from the farther focus and then the distance from the nearer focus. For a point P(x, y) on the hyperbola and for two foci F, F', the locus of the hyperbola is PF - PF' = 2a.
We know,
Foci for hyperbola is : (c,0) and (−c,0)
As, from the attached graph below the focus is:
Focus : ( 13, 0)
Hence, the Focus is: ( 13, 0).
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Sara is 3 years older than Fiona. Paul is 3 years younger than Fiona. If the total of their ages is
60, how old is the youngest of them?
Answer:
Paul is the youngest at 17 years old. Fiona is 20 years old, Sara is 23 years old
Step-by-step explanation:
Assign variables to the ages.
S = sara's age
F = Fiona's age
P = Paul's age.
S + F + P = 60
S = 3 + F
P = F - 3
(3 + F) + F + (F - 3) = 60
3 + 3F - 3 = 60
3F = 60
F = 20
S = 23
P = 17
Q2
Solve for the height (h) of this
triangular prism if the volume is 1080.
The volume of a triangular prism is V =
(B)(h), where B is the area of the
triangle. Remember the area of a
triangle is 1/2(b)(h). BE CAREFUL
BECAUSE THERE ARE TWO HEIGHTS,
ONE FOR THE TRIANGLE AND ONE
FOR THE TRIANGULAR PRISM. *
A
Answer:
(C)18 Units
Step-by-step explanation:
Volume of a Triangular Prism =Base Area X Height
The base is a right triangle of base 8 Units and Height 15 Units.
Area of the Triangle =0.5 x 8 x 15 =60 Square Units
Base Area, B=60 Square Units
Since Volume of the Triangular Prism=1080
1080=60h
Divide both sides by 60
Height of the Prism=18 Units
In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch?
Answer:
16.16 or 16 inch
Step-by-step explanation:
you can use the pythagoras theorem,
h = 19
so, width = [tex]\sqrt{19^2 - 10^2}[/tex]
Answer:
16.16 or 16 inch
What is the volume of a hemisphere with a radius of 61.9 m, rounded to the nearest
tenth of a cubic meter?
Answer:
The volume of the hemisphere is 496741.6 m³
Step-by-step explanation:
The volume of an sphere is given by:
[tex]V_{s} = \frac{4\pi r^{3}}{3}[/tex]
In which [tex]\pi = 3.14[/tex] and r is the radius.
An hemisphere is half of an sphere, so it's volume is half the sphere's volume. So
[tex]V_{h} = \frac{V_{s}}{2} = \frac{2\pi r^{3}}{3}[/tex]
In this question:
[tex]r = 61.9[/tex]. So
[tex]V_{h} = \frac{2\pi (61.9)^{3}}{3} = 496741.6[/tex]
The volume of the hemisphere is 496741.6 m³
Answer:
The volume of the hemisphere = 496741.6 m³
Step-by-step explanation:
Volume of a sphere is= (4/3) × π × r³
r is the radius
π is 22/7
hemisphere is half of an sphere,
so the volume of henisphere is (2/3) × π × r³
Given that ;
r = 61.9 m
[tex]V = \frac{2\pi (61.9)^{3}}{3} = 496741.6[/tex]
therefore, the volume of the hemisphere is 496741.6 m³
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome. What is the probability that the random variable has an outcome of 3?
The correct answer is that the probability of the random variable having an outcome of 3 is 0.
To solve this problem, we need to understand that the random variable assigns the number of blue marbles drawn to each outcome of the experiment. Since the experiment consists of two independent draws with replacement, there are four possible outcomes:
1. Draw a blue marble, then draw another blue marble.
2. Draw a blue marble, then draw a red marble.
3. Draw a red marble, then draw a blue marble.
4. Draw a red marble, then draw another red marble.
The probability of drawing a blue marble in a single draw is given as 3/8. Therefore, the probability of drawing a red marble is the complement of this, which is 1 - 3/8 = 5/8.
Now, let's calculate the probability of each of the four outcomes:
1. The probability of drawing two blue marbles (BB) is (3/8) * (3/8), because the draws are independent.
2. The probability of drawing a blue marble followed by a red marble (BR) is (3/8) * (5/8).
3. The probability of drawing a red marble followed by a blue marble (RB) is (5/8) * (3/8).
4. The probability of drawing two red marbles (RR) is (5/8) * (5/8).
Since the random variable assigns the number of blue marbles to each outcome, the only way to have an outcome of 3 is to draw a blue marble, then draw another blue marble. This is the first outcome listed above.
The probability of drawing two blue marbles (BB) is (3/8) * (3/8) = 9/64.
However, the question asks for the probability of the random variable having an outcome of 3. Since the maximum number of blue marbles that can be drawn in two draws is 2, it is impossible to have an outcome of 3. Therefore, the probability of the random variable having an outcome of 3 is 0.
In conclusion, the probability that the random variable has an outcome of 3 is 0, because it is not possible to draw more than 2 blue marbles in two independent draws with replacement from a bag where the probability of drawing a blue marble is 3/8.
Steve order plaster cases for storing his baseball cards. Each case has a length of 12 centmeters a width of 6.5 centmeters and a height of 1.25 centmeters. What is the volume in cubic centmeters of one baseball card?
plzzzzzz hellpppp !!!!!!!!!!!!
listen yeah
plot the points on the graph and join up dots
then draw a line x = 4 so 4 on x axis draw a vertical line as its line of symmetry
then reflect the shape
for the x co ordinates, say that they are different because the x values are not the same
for the y co ordinates, say thay they are the same because the y values did not change
plot points on 2nd graph and join up dots
then draw a line y = 2 so 2 on y axis draw a horizontal line as its line of symmetry
then reflect shape
for the x co ordinates, say that they are the same because the x values did not change
for the y co ordinates, say that they are different because the y values are not the same
Someone pls pls pls help me!!
In 2002, there were 972 students enrolled at Oakview High School. Since then, the number of students has increased by 1.5% each year. Write an exponential function to model the situation, then find the number of students enrolled in 2014. Is this considered growth or decay?
Answer:
n(t) = 972×1.015^t1162 studentsgrowthStep-by-step explanation:
The growth factor is 1 added to the growth rate of 1.5%, so is 1.015. This factor is applied each year. So the number of students will be the original number multiplied by this factor as many times as there are years (after 2002).
Repeated multiplication is signified using an exponent. The function can be written as ...
n(t) = 972×1.015^t
In 12 years after 2002, the number of students is modeled as ...
n(12) = 972×1.015^12 ≈ 1162 . . . students in 2014
__
When the change is described as "increased by ...", it means the function is modeling growth. If the population were to decrease, it would be considered decay. That is, the "growth factor" is greater than 1 for growth, and less than 1 for decay. 1.015 is greater than 1, so this is considered growth.
Write this number
7 ones, 2, tens, 3 hundreds
Answer:
327
Step-by-step explanation:
7 ones = 7*1 = 7
2 tens = 2*10 = 20
3 hundreds = 3 * 100 = 300
300 +20 +7 = 327
a, = - 9n - 7.
What’s the first five terms
Answer:
-16, -25, -34, -43, and -52
Step-by-step explanation:
a, = - 9n - 7.
Sequence given by
a_n, = - 9n - 7.
a_1 = -9*1 - 7 = -16
a_2 = -9*2 - 7 = -18 - 7 = -25
a_3 = -9*3 - 7 = -27 - 7 = -34
a_4 = -9*4 - 7 = -36 - 7 = -43
a_5 = -9*5 - 7 = -45 - 7 = -52
A new kind of rocket takes off along an exponential trajectory, with height, in miles, represented by 3x, where x is the time, in seconds. Find the time when the height of the rocket is 8 miles.
What is the exact solution written as a logarithm?
What is an approximate solution rounded to the nearest thousandth?
We have been given that a new kind of rocket takes off along an exponential trajectory, with height, in miles, represented by [tex]3^x[/tex], where x is the time, in seconds. We are asked to find the time when the height of the rocket id 8 miles.
To find the time, we will equate height function with 8 and solve for x as:
[tex]3^x=8[/tex]
To solve for x, we will take natural log on both sides as:
[tex]\ln(3^x)=\ln (8)[/tex]
We can rewrite 8 as [tex]2^3[/tex].
[tex]\ln(3^x)=\ln (2^3)[/tex]
Using natural log property [tex]\ln(a^b)=b\cdot \ln(a)[/tex], we will get:
[tex]x\cdot \ln(3)=3\cdot\ln (2)[/tex]
[tex]\frac{x\cdot \ln(3)}{ \ln(3)}=\frac{3\cdot\ln (2)}{ \ln(3)}[/tex]
[tex]x=\frac{3\cdot\ln (2)}{ \ln(3)}[/tex]
Therefore, exact solution will be [tex]\frac{3\cdot\ln (2)}{ \ln(3)}[/tex].
[tex]x=\frac{2.0794415416798359}{1.0986122886681097}[/tex]
[tex]x=1.892789260714[/tex]
Upon rounding to nearest thousandth, we will get:
[tex]x\approx 1.89[/tex]
Therefore, the height of the rocket will be 8 miles after approximately 1.89 seconds.
What is the value of the expression below?
(121/4)4
Answer:
121
Step-by-step explanation:
Answer:
if the 1/4 is supposed to be small and above the 12, the answer should be 12
Step-by-step explanation:
test
I need of help ASAP please
Drag the numbers to the correct locations on the table. Not all numbers will be used.
Alexis performed an experiment by drawing equal-sized colored balls from a box. She randomly drew a ball 50 times and recorded the color in the frequency table.
Answer:
Red-5-0.1
Blue-0.26
White-10
Green-22
Step-by-step explanation:
In the experiment, Alexis drew colored balls and you need to organize the results in a frequency table. The numbers given represent frequency counts for each color. Keep in mind that the total draws were 50, so no frequency count should exceed this number.
The question is about Alexis' experiment involving drawing colored balls from a box. The results of the 50 trials are recorded in a frequency table. As the student, you are expected to correctly assign certain numbers to their respective places in this table. These numbers represent the total counts per color across the 50 trials.
To accomplish this, you must first understand what a frequency table is. A frequency table is a method of organizing raw data in a compact form by displaying a series of data values in ascending order, along with their corresponding frequencies.
In this scenario, the frequencies are the number of times Alexis drew a ball of a specific color. For example, if she drew a red ball 15 times, we would put 'Red' in the color column and '15' in the frequency column.
Please note that not all the provided numbers will be used, and there should be no number in the table higher than 50 since that was the maximum number of trials Alexis performed.
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is {(4, 8), (8, 4), (4, 12), (20, 16), (12, 16)} a function
Answer:
no
Step-by-step explanation:
Look at the first numbers of each ordered pair:
4, 8, 4, 20, 12
If any are repeated, the relation is NOT a function. Here, 4 is repeated.
The relation is not a function.
g For a specific location in a particularly rainy city, the time a new thunderstorm begins to produce rain (first drop time) is uniformly distributed throughout the day and independent of this first drop time for the surrounding days. Given that it will rain at some point both of the next two days, what is the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days
Answer:
The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.
Step-by-step explanation:
The random variable X is defined as the time a new thunderstorm begins to produce rain.
The random variable X is uniformly distributed throughout the day, i.e. between the 24 hours a day or 1440 minutes.
[tex]X\sim Uniform\ [0, 1440][/tex]
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]
It is provided that it will rain at some point both of the next two days.
Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM as follows:
9:10 AM = (9 × 60) + 10 = 550 minutes.
3:30 PM = 15:30 = (15 × 60) + 30 = 930 minutes.
Compute the value of P (550 < X < 930) as follows:
[tex]P(550<X<930)=\int\limits^{930}_{550}{\frac{1}{1440-0}}\, dx\\\\=\frac{1}{1440}\times \int\limits^{930}_{550}{1}\, dx\\\\=\frac{1}{1440}\times [x]^{930}_{550}\\\\=\frac{930-550}{1440}\\\\=0.2639[/tex]
The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM is 0.2639.
Then the complement of this event is:
The probability that the first drop of rain will not be felt between 9:10 AM and 3:30 PM is:
P (Not between 9:10 AM and 3:30 PM) = 1 - 0.2639 = 0.7361
Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days as follows:
P (At least 1) = 1 - P (Less than 1)
= 1 - P (None)
= 1 - P (Not between 9:10 AM and 3:30 PM)
= 1 - 0.7361
= 0.2639
Thus, the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.
It's too short. Write at least 20 characters to get a great answer.It's too short. Write at least 20 characters to get a great answer.
Answer:
143°
Step-by-step explanation:
We know that the two lines are parallel, which means that since ∠A and ∠B are same-side angles, they are equal. That means we can set the expressions equal:
7x + 24 = 3x + 92
4x = 68
x = 17
Plug this into the expression for A:
∠A = 7x + 24 = 7 * 17 + 24 = 143
The answer is 143°.
Since both lines are parallel, both equations are equal.
7x + 24 = 3x + 92
Solve for x.
~Subtract 24 to both sides
7x + 24 - 24 = 3x + 92 - 24
~Simplify
7x = 3x + 68
~Subtract 3x to both sides
7x - 3x = 3x - 3x + 68
~Simplify
4x = 68
~Divide 4 to both sides
4x/4 = 68/4
~Simplify
x = 17
Substitute 17 with x in ∠A
∠A = 7x + 24
∠A = 7(17) + 24
∠A = 119 + 24
∠A = 143
Best of Luck!
Please help!!!!
And thank you in advance!
Answer:
282.7431 cm^2 (Lateral Surface Area)
Step-by-step explanation:
If you didn't need Lateral Surface Area let me know and I'll see what I can do :3
A machine randomly dispenses a pink, orange, blue, or yellow golf ball to each customer at a miniature golf course. If is the probability of receiving a blue golf ball from the machine, what are the odds in favor of receiving a blue golf ball?
Estimation is best defined as: a. both a process of inferring the values of unknown samples statistics from those of known population parameters and any procedure that views the parameter being estimated not as a constant, but, just like the estimator, as a random variable b. a sampling procedure that matches each unit from population A with a "twin" from population B so that any sample observation about a unit in population A automatically yields an associated observation about a unit in population B c. any procedure that views the parameter being estimated not as a constant, but, just like the estimator, as a random variable d. a process of inferring the values of unknown samples statistics from those of known population parameters e. a process of inferring the values of unknown population parameters from those of known sample statistics
Answer:
Option D is the correct answer - Estimation is best defined as a process of inferring the values of unknown samples statistics from those of known population parameters
Step-by-step explanation:
Estimation involves the usage of the value of a statistic derived from a sample to estimate the value of a corresponding population parameter.
The sample provides information that can be extended, through several formal or informal processes, to determine a range most suitable to describe the missing information.
An estimate that turns out to be incorrect would either be termed as over-estimation or under-estimation. If the estimate exceeds the actual result, it is termed as an over-estimation, and as an under-estimation, if the estimate came short of the actual result.
Thus, option D is correct.
The best definition of estimation will be E. process of inferring the values of unknown population parameters from those of known sample statistics.
It should be noted that estimation doesn't automatically yield an associated observation about a unit in population. Rather, estimation is the process of inferring the values of unknown population parameters from those of known sample statistics.In conclusion, the best option is E.
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A box with a square base and open top must have a volume of 48668 cm3. We wish to find the dimensions of the box that minimize the amount of material used.First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base.[Hint: use the volume formula to express the height of the box in terms of x.]Simplify your formula as much as possible.
Answer:
x=46 gives us the minimum value
Step-by-step explanation:
Let us have the height of the box to be y. Since the box has a square base, let us call the side of the base as x. So, the volume of the box is given by
[tex]x^2\cdot y = 48668[/tex]. From here, we know that [tex]y=\frac{48668}{x^2}[/tex]
Now, we will find the area of the box. Since the box has an open top, then we only have the 4 sides of the box and the base. The base is a square of side x, so its area is [tex]x^2[/tex]. Recall that each side is a rectangle of base x and height y. So, the are of one side is [tex]x\cdot y[/tex]. Then, the area of the box is given by the function
[tex]A(x,y) = x^2+4xy[/tex]. Since we can relate y to x through the volume, this can be a function of one variable. Namely
[tex]A(x) = x^2+4x\cdot \frac{48668}{x^2}= x^2+4\cdot \frac{48668}{x} = x^2+48668x^{-1}[/tex]
If we want to find the mininum value, we should derive the function A and find the value of x for which A'(x) is zero. REcall that the derivative of a function of the form [tex]x^n[/tex] is [tex]nx^{n-1}[/tex]. Then, applying the properties of derivatives, we have
[tex] A'(x) = 2x-4\cdot \frac{48668}{x^2} = \frac{2x^3-4\cdot 48668}{x^2}[/tex]
So, we want to solve the following equation
[tex]2x^3-4\cdot 48668 =0[/tex]
which implies [tex]x^3 = 97336[/tex]. Using a calculator we get the value [tex] x= 46[/tex]
REcall that to check if the point is a minimum, we use the second derivative criteri. It states that the point x is a mininimum if f'(x) =0 and f''(x)>0
Note that [tex]A''(x) = 2+8\cdot\cdot 48668}{x^3}[/tex], note that A''(46) = 6>0, so x=46 is the minimum value of the area.
To find the formula for the surface area of the box in terms of only the length of one side of the square base, express the height of the box in terms of x. The formula for the surface area is S = 194672 / x + x².
Explanation:To find the formula for the surface area of the box in terms of only the length of one side of the square base, we need to express the height of the box in terms of x. The volume of the box is given as 48668 cm³, which is equal to the base area (x²) multiplied by the height (h). So, we have the equation x² * h = 48668. Solving for h, we get h = 48668 / x².
The surface area of the box consists of the area of the four sides of the box (4 * x * h) and the area of the square base (x²). We can substitute the value of h in terms of x into this expression to get the simplified formula for the surface area: S = 4 * x * (48668 / x²) + x². Simplifying further, we get S = 194672 / x + x².
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The amount of gas consumed by a car varies directly with the miles driven. The car traveled 180 miles and used 6 gallons of gas. If the car traveled 1,,260 miles, how many gallons of gas would be used?
A 7 gallon
B 30 gallon
C 42 gallon
D 210 gallon
Answer:
The correct answer is A
Step-by-step explanation:
1,260 divided by 180 = 7
180 times 6 = 1,080
180 times 7 = 1,260
If the car traveled 1260 miles, then 42 gallons of gas would be used.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have the amount of gas consumed by a car varies directly with the miles driven.
Using the formula for direct proportionality -
y₁/x₁ = y₂/x₂
180/6 = 1260/x₂
x₂ = (1260 x 6)/180
x₂ = (126 x 6)/18
x₂ = (21 x 2)
x₂ = 42
Therefore, If the car traveled 1260 miles, then 42 gallons of gas would be used.
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Choose the correct answer.
1. What selid figure has a shape
like a box of cereal?
A rectangular prism
B cylinder
C sphere
Dcone
Answer:
A
Step-by-step explanation:
the solid figure that has the shape like a cereal box is a rectangular prism
On circle OOO below, \overline{SE} SE start overline, S, E, end overline is a diameter. What is the measure of \angle ISE∠ISEangle, I, S, E?
Answer:
Step-by-step explanation:
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