The chef needed a) 3¾ cups of lemon juice and b) 20 pints olive oil for the larger batch.
What is mixed fraction?A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like 2 1/3 is one where the remainder is 1 and the quotient is 2. Therefore, a mixed fraction is made up of both a whole number and a correct fraction.
The recipe was for 4 person, but now here are 40
The scale multiple is = 40/4
= 10
a) As 1 cup = 16 tablespoon
The number of tablespoon of lemon required for 40 men = 6 × 10
= 60
Converting to cup = 60/16
= 3¾ cups
b) As 1 cup = 0.5 pints
The number of cups of olive oil required for 40 men = 1 × 10
= 10
Converting to pints = 10/0.5
= 20 pints
Thus, The chef needed 3¾ cups of lemon juice and 20 pints olive oil for the larger batch.
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John Corporation produces widgets. The fixed expenses are $45,000,
and the variable expenses are $9 per widget. Express the total expense E
in terms of q, where q is the quantity of widgets produced. (Hint: E = V + F).
The total cost E expressed as a function of q, wherein q is the number of widgets manufactured= E = 9q + 45,000.
What is fixed expenses?Changes in sales or production volume have no effect on costs or expenses that are constant. They cover costs like rent, insurance, membership dues and subscriptions, equipment leases, loan payments, depreciation, management salaries, and advertising.
What exactly are variable expenses?Variable costs are expenses that alter as the volume of a product or service that a company produces fluctuates. The total of marginal costs over all units produced is what is referred to as variable costs. They may also be regarded as ordinary expenses. The two parts of total cost are fixed costs as well as variable costs.
According to the given information:The fixed expenses = $45,000,
The variable expenses = $9
E = V + F
E = 9q + 45,000
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Cold cabin? The Fathom screen shot below shows the results of taking 500 SRSs of 10 temperature readings from a population distribution that is and recording the sample minimum each time. (a) Describe the approximate sampling distribution. (b) Suppose that the minimum of an actual sample is . What would you conclude about the thermostat manufacturer's claim? Explain.
The sample distribution is approximately normal with a mean of 10 and a standard deviation of 1.
The distribution is slightly skewed to the left, with a slightly higher probability of lower readings than higher readings.
(b) If the sample minimum is lower than 9, this would indicate that the thermostat manufacturer's claim is false. This is because the manufacturer claims that the temperature will not go below 10 degrees, but the sample minimum of 9 suggests that it does. The probability of observing a sample minimum of 9 or lower is 0.25, which indicates that the probability of the temperature dropping below 10 degrees is relatively high.
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At an amusement park, guests have to take either a train or a boat 22 miles from the parking lot to the front entrance and then back when they leave the park. The train goes 10 mph faster than the boat . Abdul takes the train into the park and the boat on his way back. The boat goes an average speed of 20 mph. How long did the round trip take?
Answer:
1 hour 50 minutes
Step-by-step explanation:
Total distance from parking lot to entrance = 22 miles
We will assume that the total distance from entrance to lot is also 22 miles
The average speed of the boat = 20mph
The average speed of the train is 10 mph faster = 20 + 10 = 30 mph
Time taken for travel from parking lot to park by train = 22/30 hours
22/30 hours = 22/30 x 60 minutes = 44 minutes
On the way back, the boat was taken
Distance = 22 miles, speed = 20 mph
Time taken = distance/speed = 22/20 hours
22/20 hours = 22/20 x 60 minutes = 66 minutes
Total round trip time taken = 44 + 66 = 110 minutes
110 minutes = 110/60 hours
= 1 50/60 = 1 hour 50 minutes
GRADES On his first five quizzes, Percy has earned scores of 24, 27, 22, 21, and 18 points. What score must Rachael earn on her sixth and final quiz so that both the mean and median of her quiz scores is 23?
Answer:
26
Step-by-step explanation:
To find the mean score of all six quizzes, you add all the scores and divide by the number of examinations. So if Percy's first five quiz scores are 24, 27, 22, 21, and 18, the total is 112. To find the mean score of all six quizzes, add Rachael's sixth quiz score to the total and divide by 6.
If the mean score of all six quizzes is 23, then the total score of all six examinations is 138 (23 x 6).
To find the score Rachael needs on her sixth quiz, you subtract Percy's score (112) from the total score of all six examinations (138)
Rachael needs to score 26 on her sixth quiz (138 - 112) for the mean and median of her quiz scores to be 23
The angle of elevation to a nearby tree from a point on the ground is measured to be
53. How tall is the tree if the point on the ground is 89 feet from the tree? Round
your answer to the nearest hundredth of a foot if necessary.
The height of the tree is approximately 51.4 feet, to the nearest hundredth of a foot.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. Trigonometry is based on the study of the ratios of the sides of a right triangle to its angles, these ratios are called trigonometric functions and are represented by sine, cosine and tangent.
To solve the problem, we can use the tangent function. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle.
Given that the angle of elevation to the tree is 53 degrees, we can use the tangent function to find the height of the tree.
Let h be the height of the tree and x be the distance from the point on the ground to the tree.
tan 53 = h/x
h = x * tan 53
h = 89 * tan 53
= 89*(√3/3) ≈ 89*0.577 ≈ 51.4
Hence, the height of the tree is approximately 51.4 feet, to the nearest hundredth of a foot.
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Which of the following is an appropriate statement about Wilt’s free-throw shooting, based on this dotplot?
a) If Wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0,03.
b) If Wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0,03.
c) If Wilt is now shooting better than 56%, the probability that he would make at least 34 of his shots is about 0,03.
d) If Wilt is now shooting better than 56%, the probability that he would make at least 34 of his shots is about 0,03.
If Wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0,03.The correct option is a
To perform this simulation, we can use a computer program to generate a random number between 0 and 1 for each shot.
If the random number is less than or equal to 0.56, then the shot is counted as a make. We can then repeat this process 50 times and count the number of shots that were made.
We can repeat this process many times, and count the proportion of times that 34 or more makes are achieved. This proportion is the estimated probability that a 56% free-throw shooter would make 34 or more in a sample of 50 shots.
Hence a) If Wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0,03.
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Which graph has infinite solutions
The graph that shows a system of equations with infinite solutions is graph C.
Which graph has infinite solutions?Here we have some systems of equations graphed.
A system of equations has infinite solutions when both equations are equivalent (in this case, both equations represent the same line)
Then we we look at the graph of the system of equations we will see a single graph instead of two, like what we can see on option C.
The graph that shows infinite solutions is graph C (the one in the top right side).
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The function f has the property that as x gets closer and closer to 3, the values of f(x) get closer and closer to 5. Which of the following statements must be true?
A) f(3) = 5
B) f(5) = 3
C) lim f(x) = 5
x-->3
D) lim f(x) = 3
x-->5
The function f has the property that as x gets closer and closer to 3, the values of f(x) get closer and closer to 5.
The function f has the property that as x gets closer and closer to 3, the values of f(x) get closer and closer to 5.
A) f(3) = 5
C) lim f(x) = 5
x-->3
The function f has the property that as x gets closer and closer to 3, the values of f(x) get closer and closer to 5. This means that the limit of f(x) as x approaches 3 is 5, so C) lim f(x) = 5 x-->3 must be true. Additionally, since the values of f(x) approach 5 as x approaches 3, it follows that f(3) must also equal 5, so A) f(3) = 5 must be true as well. D) lim f(x) = 3 x-->5 is not true since the limit of f(x) as x approaches 5 is not 3. Similarly, B) f(5) = 3 is not true since f(5) does not necessarily equal 3.
The statements A) f(3) = 5 and C) lim f(x) = 5 x-->3 must be true for the given function.
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When we have a distribution of a variable, we know or have a sense of two qualities. Select the two qualities: How often we observe each of the possible values of a variable. - The experimental units involved in the study.- The explanatory and response variables of a study. - The possible values the variable can take on.- The observational units involved in the study
The possible values the variable can take on and how often we observe each of the possible values of a variable.
The possible values the variable can take on and how often we observe each of the possible values of a variable.
A distribution of a variable describes the possible values the variable can take on and how often we observe each of the possible values of a variable. It does not describe the experimental units involved in the study or the explanatory and response variables of a study, nor does it describe the observational units involved in the study. The possible values the variable can take on and how often we observe each of the possible values of a variable.
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show that the least squares cost function for linear regression written compactly as in section 3.1.3
The cost function is minimized when the predicted values are as close as possible to the actual values, which is achieved by finding the optimal values of the parameters θ.
What is the least squares cost function?
The least squares cost function for linear regression is used to measure the difference between the predicted values and the actual values of the target variable. It is defined as the sum of the squared differences between the predicted values and the actual values.
The compact form of the cost function is given by:
J(θ) = (1/2m) * Σ(i=1 to m) (hθ(x^i) - y^i)^2
where:
hθ(x^i) is the predicted value of the target variable for the ith sample, given by the hypothesis function hθ(x^i) = θ^T * x^i
y^i is the actual value of the target variable for the ith sample
θ is the vector of parameters for the linear regression model
m is the number of samples in the dataset
Hence, The cost function is minimized when the predicted values are as close as possible to the actual values, which is achieved by finding the optimal values of the parameters θ.
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Four students used the same meter stick to measure an edge of the same wooden cube four times. They obtained the following results
Which student'$ measurements represent the greatest precision? A Student I B Student II C. Student III D Student IV
the standard deviation of 2nd student data is least so the measurement of 2nd student is more precise.
In this problem we have four sample of four students which measure by same meter stick. Average of all student's data is 12.4 which is same. we have to check whose measurement is precision. according to least standard deviation is least which data is more precision.
the standard deviation=[tex]\sqrt{\frac{\sum(xn-x')^2}{n-1} }[/tex] ,where x' is average of data .
by the above formula.
We have standard deviation for first student is 0.40.
2nd student is 0.23, 3rd student is 0.52 and 4th student is 0.36.
after examining the standard deviation of all data 2nd student measurement is more precision.
The complete question is,
Four students used the same meter stick to measure an edge of the same wooden cube four times. They obtained the following results:
Student I II III IV
11.90 cm 11.95 cm 11.90 cm 11.95 cm
12.25 cm 12.35 cm 12.15 cm 12.30 cm
12.70 cm 12.60 cm 12.45 cm 12.55 cm
12.75 cm 12.70 cm 13.10 cm 12.80 cm
Average 12.40 cm 12.40 cm 12.40 cm 12.40 cm
Which student’s measurements represent the
greatest precision?
A. Student I
B. Student II
C. Student III
D. Student IV
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50 POINTS!!! Simplify each expression by combining like terms. NO SPACES in your answer.
−5.2t+8.2−7.8t
What is the answer in simpelest form?
Answer: -13t+8.2
Step-by-step explanation:
When combining like terms, only the same terms can be combined. In this case, it is -5.2t and -7.8t are the same. If we add them together, we got -13, unfortunately, 8.2 is different, so our simplest form is
-13t+8.2.
Then Venn diagram shows sets shade (A n B) ‘U C’
Venn diagram you mentioned illustrates the connection between A, B, and C, three sets. set (A n B), which is the intersection of two sets, is represented as region where A and B overlap. Scroll down for more detail.
What Is A Venn Diagram?A Venn Diagram is a pictorial representation of the relationships between sets.
The relationship between the three sets A, B, and C is depicted in the Venn diagram you are referring to. The set (A n B), which is the intersection of the two sets, is represented as the region where A and B overlap. The set (A U C) or the union of the sets A and C is represented by the region outside of this intersection but inside the larger circles. In the universal set, this is sometimes referred to as the complement of (A n B).
The following figures show how to shade regions of Venn Diagrams for two sets:
A intersect B, A union B, A’, A intersect B’, A’ intersect B, A union B’,
A’ union B, A’ union B’ = (A intersect B)’, A’ intersect B’ = (A union B)’.
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in one or two well-crafted paragraphs, summarize how neurons communicate at the synapse. your paragraph must include each of the following terms. underline each term in your paragraph. synapse action potential neurotransmitters vesicles axon dendrites axon terminal receptors
Dendrites first receive electrical signals from other neurons, after which an action potential is sent down the axon until it reaches the axon terminal. The vesicles then set the neurotransmitters in motion. Neurotransmitters will then travel to the synapse, where receptors will begin to transmit the signal.
What is neurotransmitters?A neurotransmitter is a signaling molecule that a neuron secretes to affect another cell across a synapse. The cell receiving the signal, which could be any major body part or target cell, could be another neuron or a gland or muscle cell. Neurotransmitters are chemical messengers required by your body to function. They are in charge of moving chemical signals (called "messages") from one neuron (nerve cell) to the next target cell. The next target cell might be another nerve cell, a muscle cell, or a gland.
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the sine of the angle at a is equal to side bc divided by side ab. the sine of angle a is therefore equal to:
sin(a) = bc/ab. is the angle of a is therefore the sine of angle at a is equal to side bc divided by side ab.
this is explained as below as :
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse. In this case, the angle at "a" is opposite side "bc" and the hypotenuse is side "ab". Therefore, the sine of angle "a" is equal to the ratio of side "bc" divided by side "ab", or sin(a) = bc/ab.
The sine of an angle in a triangle is a trigonometric function that is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The hypotenuse is the side of a right triangle that is opposite the right angle.
In this particular case, the statement "the sine of the angle at a is equal to side bc divided by side ab" is referring to a right triangle where angle "a" is one of the angles, side "bc" is the side opposite angle "a" and side "ab" is the hypotenuse.
This is known as the sine ratio and it is used in trigonometry to calculate the sine of an angle in a right triangle. It is important to note that the sine ratio is only valid for right triangles, and the measure of the angle must be in radians.
It's also worth mentioning that this relationship holds true for any angle in a triangle, not only in right triangles, but in non-right triangles sine, cosine and tangent ratios are defined differently.
So, the sine of angle "a" is calculated as the ratio of side "bc" to side "ab" (bc/ab).
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In the figure below, the segments HI and HJ are tangent to the circle centered at O. Given that OI=8 and OH=11.6, find HJ.
Answer:
HJ = 8.4
Step-by-step explanation:
tangents to a circle from an external point are congruent , then
HJ = HI
the angle between a tangent and a radius of the circle at the point of contact is a right angle.
so Δ OHI is right with ∠ OIH = 90°
using Pythagoras' identity in the right triangle
HI² + OI² = OH² , that is
HI² + 8² = 11.6²
HI² + 64 = 134.56 ( subtract 64 from both sides )
HI² = 70.56 ( take square root of both sides )
HI = [tex]\sqrt{70.56}[/tex] = 8.4
Then
HJ = HI = 8.4
6.
Simplify. Write in scientific notation. (9 × 10-3)2
08.1 x 10-5
081 x 104
081 × 10-3
08.1 x 10-6
[tex]$\left(9 \times 10^{-3}\right)^2$[/tex] can be wrltten in sclentlflc notation as[tex]$8.1 \times 10^{-5}$[/tex]
What is scientific notation?If a number is too big or too small to be conveniently represented in decimal form, it can be expressed using scientific notation. It might also be known as standard form in the UK, scientific form, or standard index form. A simple approach to write numbers is in scientific notation. Since it is shorter, more efficient, and clearly indicates magnitude, it is particularly helpful when expressing extremely big or extremely small values. Every real number can be expressed as the product of two elements, a decimal portion and an integer power of ten. The default base value ought to be 10. The exponent must be an integer that is not zero; therefore, it may be either positive or negative.A number is written in scientific notation if it can be written as [tex]$p \times 10^x$[/tex]where p has value greater than or equal to 1 and less than 10 and x is an integer.
Given[tex]- $\left(9 \times 10^{-3}\right)^2$[/tex]
Flrst applying [tex]$(a b)^2=a^2 b^2$[/tex]
We get, [tex]$\left(9 \times 10^{-3}\right)^2=9^2 \times\left(10^{-3}\right)^2$[/tex]
using property of exponents [tex]$\left(a^n\right)^m=a^{n m}$[/tex]
[tex]$9^2 \times\left(10^{-3}\right)^2=81$[/tex] times [tex]$10^{-6}$[/tex]
Thus, we have to write 81 times[tex]$10^{-6}$[/tex]In scientific notation,
Multiply and divide by 10 , we get
81 times [tex]$10^{-6}=8.1 \times 10^{-5}$[/tex]
Thus, [tex]$\left(9 \times 10^{-3}\right)^2$[/tex]can be written in scientific notation as [tex]$8.1 \times 10^{-5}$[/tex]
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Cola Root Beer Lemon-line
Under 21 years of age 40 25 20
Between 21 and 40 35 20 30
Over 40 years of age 20 30 35If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
The probability of the person over 40 years of age who drinks root beer is equal to 0.1176.
As given in the question,
Total number of people is equal to 255
From the given table :
Number of people who drinks root beer and over 40 years of age is
= 30
Required probability who drinks root beer and over 40 years of age is given by :
= ( Number of favourable outcomes ) / ( total number of outcomes )
= ( 30 / 255 )
= 0.1176
Therefore, the required probability of the people over the age of 40 years and drinks root beer is given by 0.1176.
The above question is incomplete , the complete question is :
Cola Root Beer Lemon-line
Under 21 years of age : 40 25 20
Between 21 and 40 : 35 20 30
Over 40 years of age : 20 30 35 If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
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The numeric components of the electric field in a region of space can be calculated using the equations E; fzy and Ey (0, Y) and (X,Y) ? Which of the following expressions vields the potentia difference between the points (0,y) and (x,Y)a. -6yb. 6yc. -3x^2yd. 3x^2ye. 3x^2y-6
The potential difference between the points (0, y) and (x, y) is given by the equation V = 3x^2y - 6yx.
e. 3x^2y-6y
The potential difference between two points (x, y) and (0, y) is given by the equation V = -E⋅x. The electric field in the region is given by the equations E; fzy and Ey (0, Y) and (X,Y). Using these equations, the electric field in the region can be calculated as E = 3x^2y - 6y. Therefore, the potential difference between the points (0, y) and (x, y) is given by V = -(3x^2y - 6y)⋅x = 3x^2y - 6yx.
The potential difference between the points (0, y) and (x, y) is given by the equation V = 3x^2y - 6yx.
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Write an equation in the form y = a(x-r)(x-s) to represent the parabola shown.
On solving the provided question, we can say that from the graph we have a equation [tex]y = x^2 - 3x - 4[/tex] => y= x(x+1) - 4(x+1) => y = (x+1)(x-4)
What is graphs?Mathematicians use here graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
from the graph we have a equation
[tex]y = x^2 - 3x - 4[/tex]
y= x(x+1) - 4(x+1)
y = (x+1)(x-4)
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Let f: X - Y, where X and Y are the set of all real numbers, and x and h are real numbers. a. Find a function f such that the equation / (x + h) = / (x) + f (h) is not true for all values of x and h. Justify your reasoning. b. Find a function / such that equation / (x + h) = / (x) + / (h) is true for all values of x and h. Justify your reasoning. c. Let /(x) = 2*. Find a value for x and a value for h that makes f(x + h) = f(x) + / (h) a true number sentence.
Answer:
a. A function f such that the equation f(x + h) = f(x) + f(h) is not true for all values of x and h is a function that is not linear. For example, a function f(x) = x^2 is not linear because it does not satisfy the equation f(x + h) = f(x) + f(h).
b. A function f such that the equation f(x + h) = f(x) + f(h) is true for all values of x and h is a linear function. For example, a function f(x) = mx + b, where m and b are constants, is a linear function because it satisfies the equation f(x + h) = f(x) + f(h).
c. Let f(x) = 2x. If we choose x = 3 and h = 2, then f(x + h) = f(3 + 2) = f(5) = 2(5) = 10, and f(x) + f(h) = f(3) + f(2) = 2(3) + 2(2) = 6 + 4 = 10. Therefore, the equation f(x + h) = f(x) + f(h) is true in this case.
Use the Remainder Estimation Theorem and the method of Example 1 to prove that the Taylor series for sinx about x=π/4 converges to sinx for all x.
We know that,
f(x) = ∑[tex]\frac{f^{k} (x_{0} ) }{k!} (x-x_{0} )^{k}[/tex]
We know that,
f(x) = ∑[tex]\frac{f^{k} (x_{0} ) }{k!} (x-x_{0} )^{k}[/tex]
holds at a point x if and only if
[tex]\lim_{n \to \infty} R_n(x) = 0[/tex]
Let f(x) = sin x. The Taylor series for f(x) is
f(x) = sin x = ∑ [tex](-1)^{k}[/tex] [tex]\frac{x^{2k+1} }{(2k+1)!}[/tex]
According to the above theorem, we must show that [tex]R_{n}[/tex] ⇒0 or all x as n ⇒ infinity. For all x we have
[tex]f^{n+1} (x) =[/tex] ± sin x
or, [tex]f^{n+1} (x)[/tex] = ± cosy
and in all cases we have [tex]| f^{n+1} (x) |\leq 1.[/tex]
We need to conclude that
[tex]0\leq |R_{n}(x) | \frac{|x|^{n+1} }{(n+1)!}[/tex]
Furthermore, it follows that
[tex]\lim_{n \to \infty} \frac{|x|^{n+1} }{(n+1)!} = 0[/tex]
Using this result, it follows that [tex]|R_{n}|[/tex] ⇒0 and hence that [tex]R_{n}[/tex] ⇒0 is n⇒infinity.
Since this, is true for all x, we have proved that the Taylor series for sin x converges to sin x for all x.
Holds at a point x if
[tex]\lim_{n \to \infty} R_n(x) = 0[/tex]
Let f(x) = sin x. The Taylor series for f(x) is
f(x) = sin x = ∑ [tex](-1)^{k}[/tex] [tex]\frac{x^{2k+1} }{(2k+1)!}[/tex]
According to the above theorem, we must show that [tex]R_{n}[/tex] ⇒0 or all x as n ⇒ infinity. For all x we have
[tex]f^{n+1} (x) =[/tex] ± sin x
or, [tex]f^{n+1} (x)[/tex] = ± cosy
and in all cases we have [tex]| f^{n+1} (x) |\leq 1.[/tex]
We need to conclude that
[tex]0\leq |R_{n}(x) | \frac{|x|^{n+1} }{(n+1)!}[/tex]
Furthermore, it follows that
[tex]\lim_{n \to \infty} \frac{|x|^{n+1} }{(n+1)!} = 0[/tex]
Using this result, it follows that [tex]|R_{n}|[/tex] ⇒0 and hence that [tex]R_{n}[/tex] ⇒0 is n⇒infinity.
Since this, is true for all x, we have proved that the Taylor series for sin x converges to sin x for all x.
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There are 80 pupils in a group. The only languages available for the group to study are Russian and Spanish. 50 pupils study Russian. 31 pupils study Spanish. 23 pupils study neither Russian nor Spanish. Find the probability to select a pupil that studies Spanish and Russian. Probability
3/10
Explanation
The total number of people that are studying neither Russian nor Spanish will be subtracted from the total number of people
i.e 80-23=57
Now let's calculate those that studies both languages (x)
50+31-x=57
-x=57-50-31
-x=-24
x=24
probability of choosing those that studies both Spanish and Russian is
24/80=3/10
Answer:
33 out of 80 pupils
Step-by-step explanation:
Total = 80 pupils
Studying Russian and Spanish = 80 - 23;
= 57 pupils
Out of 57 pupils, 50 pupils study Russian = 7 diff.
Out of 57 pupils 31 pupils study Spanish = 26 diff.
دین
-10
26. The drama club is selling tickets for the upcoming play. Each student ticket costs $5.50 and each adult
ticket costs $9.50. If the Drama Club sold 98 tickets and raised $703, write a system of equations to figure out
how many of each ticket was sold. Find how many of each ticket was sold.
A total of 57 student tickets and a total of 41 adult tickets were sold to generate a total revenue of $703.
What is the definition of an equation?A mathematical statement known as an equation is composed of two expressions joined together with the equal sign. A formula would've been 3x - 5 = 16, for illustration.. When this equation is solved, we discover that the quantity of the variables x is 7.
The following response has been produced in a straightforward, step-by-step manner.
Step: 1
Price of each student ticket = $ 5.50
Price of each adult ticket = $ 9.50
If x Equals the quantity of student tickets sold
If y Equals the quantity of adult tickets sold,
Step: 2
(i). It is given that a total of 98 tickets were sold.
Therefore, we can write as -
(Number of student tickets sold) + (Number of adult tickets sold) = 98
x+y =98 -----------equation (1)
Step: 3
(ii). The total revenue earned from the sale of tickets was $703.
Therefore, we can write as -
(Revenue earned from selling student tickets) + (Revenue earned from selling adult tickets) = 703
(Price of each student ticket×Number of student tickets sold) + (Price of each adult ticket ×Number of adult tickets sold) = 703
(5.50 × x)+ (9.50 × y) =703
5.50x+9.50y =703 ----------equation 2
Step: 4
System of Equations :
1) x+y =98
2) 5.50x + 9.50y =703
On performing (eq 2) - 5.50(eq 1), we get -
(5.50x +9.50y) - 5.50(x+y)=703-5.50(98)
5.50x + 9.50y - 5.50x-5.50y=703-539
4y=164
y=164/4
y=41
The operation was performed to reduce the equation in a single variable.
Step: 5
On substituting the value of y=41 in eq 1 , we get-
x+41 =98
x= 98-41
x=57
Thus, a total of 57 student tickets and a total of 41 adult tickets were sold to generate a total revenue of $703.
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explain precisely why we cannot apply the mean value theorem to function f(x) on the provided interval:
The Mean Value Theorem states that there exists a point c in the interval (a,b) such that f'(c) equals the function's average rate of change throughout [a,b] if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b).
Describe the mean value theorem.The Mean Value Theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then at some point c on the interval (a, b), f'(c) must equal the function's average rate of change over [a, b].
There is at least one point on a planar arc between two endpoints where the tangent to the arc is parallel to the secant between its ends.
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The complete question is: Explain why the Mean Value Theorem does not apply to the function on the interval [0,6].
Two times the interior angle of a regular polygon is equal to seven times is exterior angle. Find the interior angle of the polygon and the number of sides in it.
The interior angle of a regular polygon with n sides is (n-2) times 180 degrees divided by n.
The exterior angle of a regular polygon with n sides is 360 degrees divided by n.
A polygonal shape is what?
A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.
Given that 2 * interior angle = 7 * exterior angle, we can set up the following equation:
2 * ( (n-2) * 180 / n ) = 7 * ( 360 / n )
Solving for n, we get:
n = (1440 / (2*(7-180)) ) = 9
So the polygon has 9 sides. To find the interior angle, we substitute n back into the formula:
(n-2) * 180 / n = (9-2) * 180 / 9 = 160
So the interior angle of the polygon is 160 degrees.
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you are given a vector in the xy plane that has a magnitude of 90.0 units and a y component of -45.0 units. there are two possibilities for the x component - one positive and one negative. please provide the positive possibility.
The positive possibility of the [tex]x[/tex] component in a vector in the XY plane that has a magnitude of 90 units and the [tex]y[/tex] component is -45 units is [tex]+77.94[/tex].
Given,
The magnitude of the vector, [tex]M[/tex] = 90 units
The y component of the vector, [tex]y[/tex] = -45 units
We know that,
The magnitude of the vector can be expressed as:
[tex]M^{2} = x^{2} +y^{2}[/tex]
[tex]x^{2} =M^{2} -y^{2}[/tex]
Substitute the values in the above equation, and we get :
[tex]x^{2} = (90)^{2} - (-45)^{2}[/tex]
[tex]x^{2} = 8100 - 2025[/tex]
[tex]x^{2} = 6075[/tex]
[tex]x=[/tex] ±[tex]77.94[/tex]
Hence, the Positive possibility of [tex]x[/tex] the component is 77.94
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What is one plus sixety-four
Answer:
65
Step-by-step explanation:
Answer:
like 149
Step-by-step explanation:
big brain
show that the least squares residuals e are heteroskedastic and correlated, even if the disturbance vector e is homoskedastic and uncorrelated.
The least squares residuals e are heteroskedastic and correlated, even if the disturbance vector e is homoskedastic and uncorrelated.
The least squares residuals e are heteroskedastic and correlated even if the disturbance vector e is homoskedastic and uncorrelated because the variance of the observed errors, Var(e) = Var(X'e) = X'Var(e)X. As X'e is not a vector of independent random variables, the variance-covariance matrix of the errors is not diagonal and therefore the errors are correlated and heteroskedastic. This can be calculated by the formula Var(X'e) = X'Var(e)X. This formula shows that the variances of the least squares residuals e depend on the parameters of the model, and that the errors are therefore correlated and heteroskedastic.
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If (5,-4) is a point on f(x), write an ordered pair that must be on the graph of y=f(x-2)-3
I already tried plugging 5 and -4 in for x, but that didn't work.
Answer:
(3,0)
Step-by-step explanation:
x - 2
5 - 2 = 3
3 would be our x value or our input value.
When the input is 3, the output is
3 - 3 = 0
This gives us the ordered pair
(3,0)
