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Calculus Examples
Popular Problems Calculus Find the Domain and Range f(x)=5x-3
f
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x
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=
5
x
−
3
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
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−
∞
,
∞
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Set-Builder Notation:
{
x
|
x
∈
R
}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
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−
∞
,
∞
)
Set-Builder Notation:
{
y
|
y
∈
R
}
Determine the domain and range.
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
(
−
∞
,
∞
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,
{
y
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y
∈
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}
Help please!! I will mark brainilist and give a lot of points.
This is Pythagorean theorem.
Formula: a^2+b^2=c^2
When I say ^2 I mean to the power of 2.
The question is asking me to solve for a.
Then give me b and c which is b = 17 1/3 and c = 16.
How do I solve for a when b is greater than c? Won’t that give me a negative a? You can’t have a negative a right?
Unless I’m wrong.
Please help my solve this!!!!! :D
Hello there,
I just looked into the question and you are absolutely right whatever you inferred.I think the question might be wrong.The value of c should be greater than b.I guess it will like this:[tex]b = 16 \: \: \: c = 17 \frac{1}{3} [/tex]The values should be like this.I am solving the equation by this:[tex] {a}^{2} = {c}^{2} - {b}^{2} \\ = > {a}^{2} = {(17 \frac{1}{3}) }^{2} - {(16)}^{2} \\ = > {a}^{2} = {( \frac{52}{3} )}^{2} - {(16)}^{2} \\ = > {a}^{2} = ( \frac{52}{3} - 16)( \frac{52}{3} + 16) \\ = > {a}^{2} = ( \frac{52 - 48}{3} )( \frac{52 + 48}{3} ) \\ = > {a}^{2} = \frac{4}{3} \times \frac{100}{3} \\ = > {a}^{2} = \frac{400}{9} \\ = > a = \sqrt{ \frac{400}{9} } \\ = > a = \frac{20}{3} \\ = > a = 6 \frac{2}{3} [/tex]So, the value of a is[tex]a = 6 \frac{2}{3} [/tex]
Hope you could get an idea from it.
Doubt clarification - use comment section.
A submersible is a type of underwater vessel. Suppose a submersible starts at a depth of 40 feet below sea level, represented by –40 feet. The table shows the submersible's change in depth from one minute to the next. Time and Depth of Submersible
2:15 p. m. 2:16 p. m. 2:17 p. m. 2:18 p. m.
–40 feet 180 feet lower 175 feet lower 185 feet lower
Answer the questions to find the depth of the submersible after 3 minutes.
1. Write and evaluate a subtraction expression to find the depth of the submersible at 2:16 p. m.
Write your answer in the space below.
2. Write and evaluate a subtraction expression to find the depth of the submersible at 2:17 p. m.
Write your answer in the space below.
3. Write and evaluate a subtraction expression to find the depth of the submersible at 2:18 p. m.
Write your answer in the space below.
4. If the submersible dove straight down, what is the distance between the submersible's starting position at 2:15 and its position at 2:18? Show your work.
Write your answer in the space below.
Step-by-step explanation:
1. -40 - 180 = -220
2. - 40 - 180 - 175 = -395
3. -395 - 185 = -580
4. starting position of submersible at 2:15 = -40
position at 2:18 = -580
therefore, their distance = -580 -(-40) = -540.
HOPE THIS ANSWER HELPS YOU!
geomtry plzzzz help 15 points
Answer:
True.
Step-by-step explanation:
The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side. this makes it possible for the triangle to be formed.
The hourly median power (in decibels) of received radio signals transmitted between two cities
follows a lognormal distribution with parameter values u = 3.5 and o2 = 1.22.
(5 points) What is the 90th percentile of this distribution?
(5 points) What is the probability that received power for one of these radio signals is
less than 150 decibels?
(5 point) Consider a random sample of 10 radio signals. What is the probability that for
6 of these signals, the received power is less than 150 decibels?
Using the lognormal and the binomial distributions, it is found that:
The 90th percentile of this distribution is of 136 dB.There is a 0.9147 = 91.47% probability that received power for one of these radio signals is less than 150 decibels.There is a 0.0065 = 0.65% probability that for 6 of these signals, the received power is less than 150 decibels.In a lognormal 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{\ln{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.In this problem:
The mean is of [tex]\mu = 3.5[/tex].The standard deviation is of [tex]\sigma = \sqrt{1.22}[/tex]Question 1:
The 90th percentile is X when Z has a p-value of 0.9, hence X when Z = 1.28.
[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{\ln{X} - 3.5}{\sqrt{1.22}}[/tex]
[tex]\ln{X} - 3.5 = 1.28\sqrt{1.22}[/tex]
[tex]\ln{X} = 1.28\sqrt{1.22} + 3.5[/tex]
[tex]e^{\ln{X}} = e^{1.28\sqrt{1.22} + 3.5}[/tex]
[tex]X = 136[/tex]
The 90th percentile of this distribution is of 136 dB.
Question 2:
The probability is the p-value of Z when X = 150, hence:
[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]
[tex]Z = \frac{\ln{150} - 3.5}{\sqrt{1.22}}[/tex]
[tex]Z = 1.37[/tex]
[tex]Z = 1.37[/tex] has a p-value of 0.9147.
There is a 0.9147 = 91.47% probability that received power for one of these radio signals is less than 150 decibels.
Question 3:
10 signals, hence, the binomial distribution is used.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.For this problem, we have that [tex]p = 0.9147, n = 10[/tex], and we want to find P(X = 6), then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{10,6}.(0.9147)^{6}.(0.0853)^{4} = 0.0065[/tex]
There is a 0.0065 = 0.65% probability that for 6 of these signals, the received power is less than 150 decibels.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
what is 7 1/2 inches as a decimal of 1 foot
Answer:
7 1/2 inches as a decimal of 1 foot is 0.625ft
Answer:
7 1/2 inches = 0.625 ft
Step-by-step explanation:
7 1/2 inches = 7.5 inches
1 ft = 12 inches
7.5/12 = 0.625
7 1/2 inches = 0.625 ft
A side of the triangle below has been extended to form an exterior angle of 165º. Find
the value of x.
Answer:
x = 120°
Step-by-step explanation:
the 165 degree obtuse angle forms a straight line with the upper left angle inside the triangle, therefore this angle measures 15 degrees
we know two of the three angle measures so we add all three together to find the unknown angle
x + 15 + 45 = 180
x + 60 = 180
x = 120°
Rodolfo has 15 toys in a toy box, and he adds 2 new toys every month. Based on this information , which representation best shows this relationship between the number of toys Rodolfo has in his toy box, y, and the number of months that have passed, x?
Answer: The image listed below. It's the only valid answer that best shows the numbers of toys Roldlfo has in his toy box, y, and the number of months that have passed, x.
4(x - 4) + 2x -10 and what the answer
Answer:
Expression: 6x - 26. Equation: 3
Step-by-step explanation:
EXPRESSION
4x - 16 + 2x - 10
6x - 26
EQUATION 1
4x - 16 = 2x - 10 (Seems reasonable. Sorry if this isn't it)
4x = 2x + 6
2x = 6
x = 3
EQUATION 2
4x - 16 + 2x = - 10
6x - 16= -10
6x = 6
x = 1
If Lauren can run
150 feet in 1/3 of
a minute. What
is her unit rate in
feet per minute?
Answer:
450
Step-by-step explanation:
150* 3
hope this helps
Answer:
450
Step-by-step explanation:
150 feet in 1/3 min
? ----- 1 min
150 * 1 = x * 1/3
x = 150 * 3
= 450
Which quadratic equation has roots-8 + 3i and -8 - 3i?
A x^2 - 16x + 73 = 0
B x^2 - 16x + 79 = 0
C x^2 + 16x + 79 = 0
D x^2 + 16x + 73 = 0
The two roots are
[tex]\alpha = -8+3i,~~~ \beta = -8-3i\\\\\\x^2 - (\alpha + \beta)x + \alpha \beta = 0\\\\\implies x^2 - (-8+3i-8-3i)x + (-8+3i)(-8-3i)=0\\\\\implies x^2 +16x + (-8)^2+3^2 =0\\\\\implies x^2 +16x +64+9=0\\\\\implies x^2 +16x +73[/tex]
Hence the answer is D.
Barack is saving up his money to buy a television that costs $395.50. Right now he has $85.00 and can save $29.00 each week. How many weeks will it take for Barack to have enough money to buy the television?
Answer:
11 weeks
Step-by-step explanation:
Its easy
For every 0.3048 meters, there is one foot. Determine the number of feet in 7.9248 meters. Use paper to support your answer.
There are ??
feet in 7.9248 meters.
Triangle ABC is similar to triangle DEF.
Side AB is the longest side of ABC. It measures 12 centimeters.
Side DE is the longest side of DEF. It measures 8 centimeters.
What is the scale factor that takes triangle ABC to triangle DEF?
Answer:
1.5
Step-by-step explanation:
12 / 8 = 1.5
Two hundred fifty tickets are sold at a fund raiser. If Sarah buys 15 tickets, the probability that she will win the prize quilt is
.
Answer:
6%
Step-by-step explanation:
15/250=3/50 or 6%
The probability that Sarah would win the prize quilt given the tickets she bought is 6%.
What is the probability?
Probability is how likely it is that a stated event would happen. The probability of the event happening lie between 0 and 1.
The probability that Sarah would win the prize quilt = number of tickets bought / total number of tickets
(15 / 250) x 100 = 6%
To learn more about probability, please check: https://brainly.com/question/13234031
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What decimal is 0.77 %
Answer:
0.0077
Step-by-step explanation:
Can someone please help me
Answer:
Q14. Percentage decrease in price of TV
= (1100-1034)r1100×100%
= 66r1100×100%
= 6%
Q15. 450r9000 × 100% = 5% discount
Answer:
Q14 - 6% decrease
Q15 - 5% decrease
Step-by-step explanation:
how to get your answers;
subtract starting value with final value
divide the sum with the starting value
multiply by 100 and round if needed
hope that helps. ♥️
ASAP please!! What is the best approximation for one of the relative minimums of the
polynomial function graphed below?
Answer: C
Step-by-step explanation: Brainliest please
pls answer fast
Write an equation of the line that passes through (0, -5) and is perpendicular to the line y =-4/5x
Answer:
I am pretty sure its y={5}/{4}x-5
Step-by-step explanation:
What integer is equivalent to 25 3/2?
Answer:
[tex]25\frac{3}{2} =26.5[/tex]
Step-by-step explanation:
This mixed number can be separated into 25 and [tex]\frac{3}{2}[/tex]. Convert the fraction to a decimal by plugging it into a calculator, then add 25.
If you meant what whole number is equivalent, that does not exist.
Jamal cut a piece of wood that is 2 1/3 feet long into 1/6 foot sections. How many sections will he get
Answer:
14 sections
Step-by-step explanation:
2 1/3=7/3
7/3 divided by 1/6 is nothing but 7/3*6, which is just 14
33. Due to some error in a weighing scale, it shows the following reading when at rest (no weight is placed on it). Neerja measured her weight on this scale. The weight shown on the scale was 28 kg. What should she do to find out her correct weight?
(A) Add 2 kg to the weight shown. (B) Subtract 2 kg from the weight shown.
(C) Subtract 28 kg from the weight shown. (D) Add 4 kg to the weight shown
Answer:
The traditional scale consists of two plates or bowls suspended at equal distances from a fulcrum. One plate holds an object of unknown mass (or weight), while known masses are added to the other plate until static equilibrium is achieved and the plates level off, which happens when the masses on the two plates are equal. The perfect scale rests at neutral. A
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What is the end behavior of the polynomial function?
1
8
B
4
2
6
2
2
8
B
X
-4
6
o As X->-co, then Y---
As X-→-00, then y0
As X-0, then y →-00
ne X -> then V -> 0
Answer:
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity
Step-by-step explanation:
hope this help
dont know if this is correct
The end behavior of the polynomial function is as x -> ∞, y -> -∞
How to determine the end behavior?From the graph of the polynomial, we have the following highlight:
As x approached infinityThe function approaches negative infinityThe above highlights mean that:
As x -> ∞, y -> -∞
Hence, the end behavior of the polynomial function is as x -> ∞, y -> -∞
Read more about end behavior at:
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In the board game Clue, the object of the game is to determine the which character is the murderer, which weapon was used and in which room the murder took place (e.g., “Colonel Mustard with the Candlestick in the Library”). There are 6 different characters, 6 weapons, and 9 rooms. How many different outcomes are possible?
Answer: 324 different outcomes
Step-by-step explanation: Multiply all of the possibilities together to get the total amount of outcomes. 6 * 6 * 9 = 324
Would appreciate a brainly <3
Which represents discrete data? Question 17 options: A) The price of hamburger meat per pound B) The volume of water in a swimming pool C) The number of pens in a package D) The speed of a train
Answer: C
Step-by-step explanation:
The Number Of pen in a package.
Answer:
B
Step-by-step explanation:
The number of pins in package
Are the two ratios that make up a proportion
always, sometimes, or never equivalent
Answer:
Always
Step-by-step explanation:
In mathematics, when we say that two ratios form a proportion, we mean that the two ratios are equal.
Ex: Ratios and Proportions - Proportions - In Depth. A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."
A proportion is two ratios which have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 105 equals 21 .
The two ratios sometimes that make up a proportion.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
We know that;
Two ratios that make up a proportion when both ratios are equal to each other.
And, When two ratios are not equal then it cannot make a proportion.
Hence, The two ratios sometimes that make up a proportion.
Learn more about the proportion visit:
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Add. 4 7/12 plus 2 3/4 plus 7 5/12 =
Answer:
12 9/12
Step-by-step explanation:
Answer:
exact form- 59/4
mixed numbers- 14 3/4
decimal- 14.75
What is x
5x + 5 = 40
These tables of ordered pairs represent some points on the graphs of lines s and t.
Which system of equations is represented by lines s and t?
5x−2y=−157x+4y=20
3x+5y=−185x−9y=25
x+4y=−89x−y=21
2x−y=−142x+y=6
The equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.
A linear equation is in the form:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
For line s, using the points: (-5, 4) and (4, 22). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-4=\frac{22-4}{4-(-5)} (x-(-5))\\\\y-4=2(x+5)\\\\ y=2x+14[/tex]
Line T passes through the points (-4, 14) and (5, -4). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-14=\frac{-4-14}{5-(-4)} (x-(-4))\\\\y-14=-2(x+4)\\\\ y=-2x+6[/tex]
Hence the equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.
Find out more at: https://brainly.com/question/13911928
In a garden 30% of the plants are carrots. If 63 plants are not carrots, how many of the plants are carrots.
Must show each step.
Answer: 27 see my work
Step-by-step explanation:
1. We know that 30% are carrots, meaning that 70% are not carrots (30% + 70% = 100%)
2. Since 70% and 63 of the plants are not carrots, we know that 63 = 70%
3. We need to find 30% of the plants (all of the carrots) so let’s divide 63 by 7
63 = 70%
*divide both by 7*
9 = 10%
4. We know that 9 plants is equivalent to 10% of the plants, so let’s multiply by 3 to get the number of carrots
9 = 10%
*multiply by 3*
27 = 30%
There are 27 carrots
Identify the sampling technique used. Every 17th person in line to buy tickets to a concert is asked his or her age.
Answer:
systematic sampling
Step-by-step explanation:
This is when you start at a person (using a number that is randomly generated) and go up in intervals to select a sample.
Hope this helps!