y = e is the equation of the tangent line to the given curve at the specified point , y = [tex]e^{x}[/tex] / x , (1, e)
Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.
The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).
thus , y' = [tex]\frac{e^{x}-xe^{x} }{x^{2} }[/tex]
y'(1) = 0 = m
Our slope is indicated by the horizontal line.
y−[tex]y_{1}[/tex]=m(x−[tex]x_{1}[/tex])
Our line will simply be our y-coordinate because our slope(m) is 0:
e
Therefore:
The tangent line's equation is y=e.
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a random sample of 120 students has a test score average with a standard deviation of 9.1. find the margin of error for the 90% onfidence interval.
Therefore, the margin of error for the 90% confidence interval is 1.32. This means that you can be 90% confident that the true population mean falls within a range of 1.32 around the sample mean.
To find the margin of error for a 90% confidence interval, you can use the following formula:
margin of error = z * standard deviation / sqrt(n)
Where z is the z-score for the desired level of confidence (in this case, 90%), standard deviation is the standard deviation of the sample, and n is the sample size (in this case, 120).
Plugging in the values, you get:
margin of error = 1.645 * 9.1 / sqrt(120)
= 1.645 * 9.1 / 11.1
= 14.72 / 11.1
= 1.32
Why is mean the term for average?The middle of the set of values is represented by the mean. This value is the mean of all values in the data collection. In statistics, the middle quantity, referred to as the mean, is known as the average.
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Funky Fro-Yo
The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in
the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes
you can fill your cup with yogurt and toppings for $0.40 per ounce.
1. Write an equation that gives the total cost in dollars, d, of attending the event if you
order z ounces of fro-yo.
2. If your cup weighs 14 ounces, how much would you pay in total for the evening?
1) An equation that gives the total cost in dollars, d, of attending the event if you order z ounces of fro-yo is d = $5 + $0.40z
2) 2. If your cup weighs 14 ounces, you would pay $10.6 in total for the evening.
Define equation.A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts.
Given,
The school jazz band is playing at Sweet Yo's, a frozen yogurt shop. It costs $5 to get in the door for the event and if you'd like to eat fro-yo to eat while listening to their tunes you can fill your cup with yogurt and toppings for $0.40 per ounce.
1) Total cost = d
Total ounces = z
Equation
d = $5 + $0.40z
2) If cup weighs 14 ounces
d = $5 + 0.40(14)
d = $5 + $5.6
Total cost:
d = $10.6
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True or false. When writing a ratio (fraction) in math, it does not matter which value goes in the numerator and which goes in the denominator of the ratio.
Answer:
False
Step-by-step explanation:
The first value given is the numerator even if its greater than the denominator.
Find the volume in question number 12
Answer:
[tex]223093\pi/187500[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3}\pi r^2 h=(\pi/3)(1.31^2)(2.08)=223093\pi/187500[/tex]
In the figure below, mzPQR= 75° and m2 1=28°.
Find m2 2.
P
1
R
2
Q
ma
The measurement of m∠2 = 47°.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given that m∠PQR = 75° and m∠1 = 28°.
From the figure ∠PQS = m∠1 and ∠SQR = m∠2
The angle ∠PQR can be written as the sum of two angles.
∠PQR = ∠PQS + ∠SQR
∠PQR = m∠1 + m∠2
Putting m∠PQR = 75° and m∠1 = 28°:
75° = 28° + m∠2
Subtract 28° from both sides:
m∠2 = 75° - 28°
m∠2 = 47°
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26. Make Sene and Perevere Suppoe x ha the ame value in both of the expreion you wrote for Exercie 25. Are the two expreion you wrote equivalent? Explain
No, The two expression you wrote is not true. Because expression are equivalent when values are substituted in for variables. So, both expression gave same answer. Then we can say equivalent expression.
What is expression?
Expression is a finite of symbols that are formed in accordance with dependent rule. It is a number, a variable and combination of variables or symbols. It can be possible by multiply, divide, subtraction and addition.
What is equivalent expression?
Equivalent expression that always work same but look different. When equivalent expression simplified they give same answer. If all the terms in the two expression are identical then we can expression are equivalent.
NOW we have expression
ax +3b
3b+xc
ax+3b=3b+xc
ax=xc
The two expression can only be equivalent if ax=xc it mean that a is equal to c. which is not true. So, they are not equivalent.
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if a mixture has an ee of 90%, what is the percentage of each enantiomer? a) 65% : 35% b) 55% : 45% c) 80% : 20% d) 95% : 5% like 0
Percentage for each enantiomer is 95%, 5%. Option (d) is Correct.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages. %, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
% ee = % enantiomer A - % ensarstomer B
wheee ee is enantiomeric excess.
ee = 90%.
In the provided options, 90%. the difference is given by subtracting 95%, 5%
95% - 5% = 90%
4th option is 5%, 90% correct.
Percentage of each enantiomer is 95%, 5%.
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if $0.\overline{1331}$ is written as a fraction $\frac{a}{b}$ with $a$ and $b$ being positive integers with a greatest common divisor of 1, what is $a b$?
The value of a is 133 and b is 999.
A vinculum is a horizontal line that serves a variety of functions in mathematical notation. In decimal numbers, a bar across one or more consecutive digits indicates that the pattern of digits beneath the bar repeats indefinitely.
Given [tex]0.\overline{1331}[/tex]. This means that 1331 repeats many times in this expression. This expression is the same as 1330/9990.
1, 7, 19, and 133 are factors of 133, and 1, 3, 9, 27, 37, 111, 333, and 999 are the factors of 999. From this, the GCD is found to be 1.
Therefore, by simplifying, we get 1330/9990 = 133/999. The answer to a is 133 and b is 999.
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Help meeeee please !!!!
Answer: seth made 3 banana bread and 2 bananas where left over
Step-by-step explanation:
so draw 11 bananas circle three until you are left with less than three
count how many circles have three bananas which is 3 circles
now count how many bananas are not in a circle which is 2
i have adhd so i'm not good at explaining things so yeah hope this helps
:)
HELPPP Emma had to finish her 249-page novel by Friday. She had already read 166 pages. Write and solve an equation to show how many pages Emma had left to read by Friday. p + 166 = 249; p = 83 pages
p − 166 = 249; p = 415 pages
p over 166 equals 2; p = 332 pages
83p = 166; p = 2 pages
Answer:
[tex]p+166=249[/tex]; [tex]p=83[/tex] pages
Step-by-step explanation:
The number of pages that need to be read plus the 166 pages already read must add to 249.
At her health club, Lauren ue a treadmill every 2 day and the weight machine every 8 day. She ued a treadmill on march 8. Lauren ay that the firt time he will ue both a treadmill and the weight machine in march i march 16 becaue the lcm of 2 and 8 i 16. Doe Lauren reaoning make ene? Ue an example or counterexample to explain your analyi
Lauren’s reasoning does not make sense, as the lcm of 2 and 8 is 8.
In this question we have been given Lauren uses a treadmill every 2 days and the weight machines every 8 days.
She used a treadmill on March 2 and will use the weight machines on March 8.
But she says that the first time she will use both a treadmill and the weight machines in March is March 16 because the LCM of 2 and 8 is 16.
First we find and list multiples of each number until the first common multiple is found. And that would be the least common multiple.
Multiples of 2:
2, 4, 6, 8, 10, 12
Multiples of 8:
8, 16, 24
Therefore, LCM(2, 8) = 8 and Lauren is incorrect.
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Write a word problem for the following linear function y = 2x + 14
Delilah is baking cupcakes for her brother's birthday party. She has already made 14 cupcakes and is making 2 cupcakes per hour. How many cupcakes will she have in 10 hours? How many hours does it take to make 20 cupcakes?
Solve for x. Figures are not necessarily drawn to scale.
Check the picture below.
[tex]\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x[/tex]
please show your work please
Answer:
A.
Step-by-step explanation:
5 x 14 = 70
x^1 x x^7 = 8
y^0 x y^5 = 5
please help really struggling!
Answer:
Step-by-step explanation:
First, they want you to recall that in a right triangle, that you know the angle y, because you know two of the angles already. and you know the total is 180° around a triangle. There is a lot you're supposed to remember. Anyway,
180 = y + 62+90
180-62-90 = y
28 = y
see??
z = the same length, as triangle IHK on the same segment
z= 1
Laine read 200 page in 240 minute. If Laine read 25 page at thi ame rate, how long will it take her?
It would take Laine 20.83 minutes to read 25 pages at the same rate.
Assuming that Laine was able to read 200 pages in 240 minutes at a consistent rate, it would take her 25 minutes to read 25 pages. To figure out how long it would take Laine to read 25 pages, we need to use a proportion.
Let x represent the time it will take Laine to read 25 pages.
200/240 = 25/x
Cross multiply to solve for x:
240x = 5000
Divide both sides by 240:
x = 20.83 minutes
Therefore, it would take Laine 20.83 minutes to read 25 pages at the same rate.
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Cheter hope to earn $1200 in interet in 3. 5 year time from $60,000 that he ha available to invet. To decide if it' feaible to do thi by inveting in an account that compound quarterly, he need to determine the annual interet rate uch an account would have to offer for him to meet hi goal. What would the annual rate of interet have to be? Round to two decimal place
The annual interest rate would have to be about 0.57% in order to earn $1200 in interest in 3.5 years. Rounded to two decimal places, the annual interest rate would have to be about 0.57%.
What is an annual interest rate?
The annual interest rate is the percentage of the principal (the initial amount of money invested or borrowed) that is charged as interest on a loan or earned on an investment over a period of one year. It is used to calculate the amount of interest that will be earned or charged over a given period of time.
To determine the annual interest rate that an account would have to offer in order to earn $1200 in interest in 3.5 years, we need to use the following formula:
rate = (interest / principal) * (1 / time)
Where the rate is the annual interest rate, interest is the amount of interest earned, the principal is the amount of money invested, and time is the length of time in years.
Plugging in the given values, we get:
rate = ($1200 / $60000) * (1 / 3.5)
= 0.02 * (1 / 3.5)
= 0.00571428571
Hence, the annual interest rate would have to be about 0.57% in order to earn $1200 in interest in 3.5 years. Rounded to two decimal places, the annual interest rate would have to be about 0.57%.
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AIR CONDITIONING A commercial air conditioner can cool a large room with a volume of up to 40,000 cubic feet. A rectangular room in a
warehouse is designed to have a length of 75 feet, a width of 50 feet, and a height of 8 feet. The builder wants to make the room larger by
increasing the length and the width by the same amount.
By how many feet can the length and width be increased and still not exceed the capacity of the air conditioner? Round to the nearest tenth of
a foot if necessary.
The maximum length or width we can increase so that it will not exceed the capacity of AC is 100 feet.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
The volume AC can cool, v = 40000 feet³,
The dimensions of the room are 75 feet × 50 feet × 8 feet.,
Calculate the volume of the room as shown below,
Volume = 75 feet × 50 feet × 8 feet
Volume = 30000 feet³
The remaining margin of volume = 40000 - 30000
The remaining margin of volume = 10000 feet³
Thus, the maximum dimension we can increase in length and width is 100 feet.
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Please helpppppp!!! Find the equation of direction given that y varies directly with x and y is 2 when x is 4
Answer:
y= 1/2x
Step-by-step explanation:
If y is 2 and x is 4
2= 1/2 (4)
2 = 2
the probability distribution shows the weights x, in kilograms, of boxes being shipped from a certain factory. a shipped box is randomly chosen. what is the probability that it weighs less than 27 kilograms?
The probability that the weight of the box less than 27 kilogram is 0.375
The figure shows the probability distribution shows the weights x, in kilograms, of boxes being shipped from a certain factory.
Then a shipped box is randomly chosen
The probability is the ratio of the number of favorable outcomes to the total number of outcome
The probability = Number of favorable outcomes / Total number of outcomes
Number of possible weights = 8 weights
Number weights less than 27 kilogram = 3
Substitute the value in the equation of probability
The probability = 3/8
Divide the numbers
= 0.375
Therefore, the probability is 0.375
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A group of data items and their mean are given.
27, 45, 63, 108, 162, 243; Mean = 108
a. Find the deviation from the mean for each of the data items.
b. Find the sum of the deviations in part (a).
a. Type the deviation from the mean for each of the data items.
27
45
63
108
b. The sum of the deviations in part (a) is
162
243
□
a) The deviation from the mean for each term is given as follows:
27: 81.45: 63.63: 45.108: 0.162: 54.243: 135.b) The sum of all deviations obtained in part a is of 378.
How to calculate the deviation from the mean?The deviation from the mean of each term is given by the absolute value of the difference between each term and the mean.
Hence, for example, the absolute deviation of 27 from the mean of 108 is given as follows:
|27 - 108| = |-81| = 81.
(the absolute value of a number is the number without the signal).
For a number greater than the mean of 108, the deviation of 243 from the mean is given as follows:
|243 - 108| = |135| = 135.
Then the sum of all deviations obtained in part a is given as follows:
81 + 63 + 45 + 0 + 54 + 135 = 378.
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Greg earned $45 dollars for washing cars this month. He earned twice as much for washing cars than he did for mowing lawns. Write an equation to determine how much he earned for mowing lawns. m over
m over 2 equals 45
2m = 45
m + 2 = 45
m − 2 = 45
Answer:
[tex]2m=45[/tex]
Step-by-step explanation:
He earned twice as much washing cars, which is [tex]2m[/tex]. This is given to be equal to 45.
a group of students played a game in which they earned points for answering questions correctly. the following dotplot shows the total number of points earned by each student.
The best description of the distribution is bimodal with a gap.
Here in the plot, we can see that there are two peaks and it implies that there are two modes.
This can be seen in a histogram as a distinct gap between two cohesive groups of bars. When two clearly separate groups are visible in a histogram, you have a bimodal distribution. Literally, a bimodal distribution has two modes, or two distinct clusters of data
We can see that there is a gap between the two modes. So the best description of the distribution is bimodal with a gap.
The following dot-Plot shows the bimodal with a gap.
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A section of roller coaster can be modeled by the function:
F(x) = x5 - 5x4 - 31x3 + 113x2 + 282x - 360.
A walkway bridge will be placed at one of the zeros. What are the possible
locations for the walkway bridge?
The possible locations for the walkway bridge are 1, 5, and 6.
What is factorization?
Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.
Here, we have
Given
The function can model a section of a roller coaster:
F(x) = x⁵ - 5x⁴ - 31x³ + 113x² + 282x - 360.
We have to find the possible locations for the walkway bridge.
Now, we factorize the given function
F(x) = x⁵ - 5x⁴ - 31x³ + 113x² + 282x - 360
F(x) = (x-1)(x+3)(x+4)(x-5)(x-6)
then, x - 1 = 0, x+3 = 0, x+4 = 0, x-5 = 0, x-6 = 0
x = 1, -3, -4, 5, 6, becausex>0
s0, x = 1, 5, 6
Hence, the possible locations for the walkway bridge are 1, 5, and 6.
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whats the coefficient 5.4 ×10^8
The coefficient of the equation A = 5.4 x 10⁸ is c = 5.4
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the coefficient of the equation be c
A = 5.4 x 10⁸ be equation (1)
On simplifying the equation , we get
Group coefficients together and exponents together to multiply the numbers in the scientific notation
So , A = c x bˣ
where c is the coefficient
Substituting the values in the equation , we get
The value of c = 5.4
Therefore , the value of c is 5.4
Hence , the coefficient is 5.4
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Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15.
Find the z-score to the nearest tenth for the following blood pressure readings.
A. 142 ________
B. 130________
C. 103________
To find the z-score for a given systolic blood pressure reading, we need to use the z-score formula:
z = (x - mu) / sigma
where z is the z-score, x is the raw score, mu is the mean, and sigma is the standard deviation.
In this case, we are given that mu = 121 and sigma = 15. We can use this information to find the z-score for each of the given blood pressure readings:
A. For a blood pressure reading of 142, we have:
z = (142 - 121) / 15
= 21 / 15
= 1.4
Therefore, the z-score for a blood pressure reading of 142 is approximately 1.4, to the nearest tenth.
B. For a blood pressure reading of 130, we have:
z = (130 - 121) / 15
= 9 / 15
= 0.6
Therefore, the z-score for a blood pressure reading of 130 is approximately 0.6, to the nearest tenth.
C. For a blood pressure reading of 103, we have:
z = (103 - 121) / 15
= -18 / 15
= -1.2
Therefore, the z-score for a blood pressure reading of 103 is approximately -1.2, to the nearest tenth.
Which of the following is not a congruence rule of triangle.
a)SAS rule
b)ASA rule
c)SSS rule
d)AAA ruleâ
Which of the following terms represents the situation in the graphic below?
a glide a reflection a glide reflection
None of these choices are correct.
Answer:
A glide.
Step-by-step explanation:
The image is a shift or a glide.
Reflection is either changes the arrow direction the other direction.
A glide reflection is both.
the smallest angle of an isosceles triangle measures 36 degrees. the other two angles are larger, what is the measure of each of the other two angles?
The measure of each of the other two angles is 72° and 36°.
What is vertex angle?
The angle created by two lines or rays intersecting at a location is known as the vertex angle. The sides of the angle are formed by these two rays. In other terms, vertex angle refers to the angle contained within a certain vertex and is expressed in degrees.
let the vertex angle is 36°
the other two angles are equal
let the angle be x
sum of angle in triangle is 180
x + x + 36 = 180
2x = 180 - 36
2x = 144
x = 144/2
x = 72
largest angle is 72°
smallest angle is 36°
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number of bacteria double every 20 minutes. if the initial population is 20 how many are there after 3 hours
There are 10240 bacteria after 3 hours.
Initial population = 20
Time period = 3 hours
Time period in minutes = 3 hours x 60 minutes = 180 minutes
Number of doublings = 180 minutes / 20 minutes = 9 doublings
Final population = 20 x 2^9
Final population = 20 x 512
Final population = 10240
Bacteria doubling is the process in which one bacterial cell divides into two identical daughter cells. This process is known as binary fission and is the primary way bacteria reproduce. During this process, a single bacterium first replicates its single chromosome, which is then partitioned into two identical parts. The single cell then divides into two daughter cells, each containing one of the replicated chromosomes. This process is incredibly fast and can occur in as little as twenty minutes.
Bacterial doubling is an important process, as it allows bacteria to rapidly increase in number and spread. In optimal conditions, a single bacterial cell can divide into two daughter cells every twenty minutes, and this can continue for many generations. For this reason, bacteria can quickly become abundant in a given environment and pose a potential threat to human health. Fortunately, antibiotics are often able to help control bacterial doubling and limit the spread of certain bacteria.
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