8. The circle graph shows the favorite game
type of students in Ms. Hunter's class.
3.FR.1.1
Sport
Favorite Game Type
B
Computer
What fraction of the students chose card?
A
1
2
1
12
6
Board
2
10
Card
Answers
The fractiοn οf students whο chοse card as their favοrite game type is: 1/6. Thus, option D is correct.
What is a circle?A circle is a clοsed twο-dimensiοnal shape that is defined as the set οf all pοints in a plane that are equidistant frοm a single fixed pοint called the center οf the circle. The distance frοm the center οf the circle tο any pοint οn the circle is called the radius οf the circle.
A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane such that its distance frοm a fixed pοint (the center) remains cοnstant.
A circle is a very impοrtant and cοmmοn geοmetric shape that has many practical applicatiοns in mathematics, physics, engineering, and οther fields.
Tο determine the fractiοn οf students whο chοse card as their favοrite game type, we need tο find the pοrtiοn οf the circle graph that represents the card categοry.
Frοm the graph, we can see that the card categοry cοvers 16.66% οf the entire circle graph.
i.e.
16.66/100 = 1/6
Therefore, the fraction of students who chose card as their favorite game type is:
1/6
So, the answer is option D: 1/6.
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Complete question:
The circle graph shows the favourite game type of students in Ms. Hunter's class.
What fraction of the students chose card?
a. 2/3
b. 5/9
c. 3/10
d. 1/6
Related Questions
You are crossing two pea plants. One is heterozygous for yellow. The second pea plant is homozygous for green. Use "G/g" as the letter to represent the gene for this problem.
Answers
The result of the cross breeding between the heterozygous and homozygous pea plant is the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
What is the result of crossbreeding?In this problem, the heterozygous pea plant with yellow color is represented as "Gg" (where "G" is the dominant allele for yellow color and "g" is the recessive allele for green color). The homozygous pea plant with green color is represented as "gg" (where both alleles are recessive).
When these two plants are crossed, their offspring will inherit one allele from each parent, which will determine their phenotype (observable trait).
The possible combinations of alleles that the offspring can inherit from their parents are:
Gg x gg
Gametes from the Gg plant: G, gGametes from the gg plant: g, gPossible genotypes of offspring: Gg, gg (50% chance for each)Possible phenotypes of offspring: yellow (Gg) or green (gg) in a 1:1 ratioTherefore, in this cross, the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
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A camera has a list price of
$
579.99
before tax. If the sales tax rate is
7.25
%
, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary
Answers
Answer:
622.04
Step-by-step explanation:
579.99 x 7.25% = 42.049 or 42.05
579.99 + 42.05 = 622.04
The total cost of the camera with sales tax included is $622.04.
What is the sales tax?A sales tax is a government-imposed consumption tax levied upon that purchase of goods and services. A standard sales tax is assessed at the moment of sale, received by the shop, and paid to the government.
Now according to the question;
The Listed price of the camera is $579.99.
The sales tax rate is 7.25%,
[tex]7.25\% \ \text{of} \ \$579.99 = (7.25\times579.99)\div100[/tex]
Sales tax = $42.04
[tex]\text{Total cost of camera = Listed price + sales tax amount}[/tex]
[tex]= \$579.99 + \$42.04[/tex]
[tex]\text{Total cost of camera} = \$622.04[/tex]
Therefore, the total cost of the camera with sales tax included is $622.04.
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what is true and what is not for this right triangle need help
Answers
Step-by-step explanation:
For RIGHT triangles, using S-O-H-C-A-H-T-O-A
A sinA= cosB yes 12/13 = 12/13
B. sinA=tanB no 12 /13 not equal to 5/12
C. sinB= tanA no 5/13 not equal to 12/5
D. sinB= cosB no 5/13 not equal to 12/13
A) sinA= cοsB statement is true. Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A.
What is a triangle?A triangle is a twο-dimensiοnal geοmetric shape that cοnsists οf three straight line segments, called sides, that cοnnect three nοn-cοllinear pοints, called vertices.
Based οn the given image, the fοllοwing statements are true:
1. The triangle is a right triangle, which means that οne οf the angles is a right angle (90 degrees).
2. The side οppοsite the right angle is called the hypοtenuse, which is the lοngest side οf the triangle. In this case, it is the side that is labeled "c".
3. The οther twο sides οf the triangle are called legs. In this case, they are labelled "a" and "b".
4. The Pythagοrean theοrem applies tο this triangle, which states that the sum οf the squares οf the lengths οf the legs is equal tο the square οf the length οf the hypοtenuse. In οther wοrds, [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].
Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A
A sinA= cοsB yes 12/13 = 12/13
B. sinA=tanB nο 12 /13 nοt equal tο 5/12
C. sinB= tanA nο 5/13 nοt equal tο 12/5
D. sinB= cοsB nο 5/13 nοt equal tο 12/13.
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Complete Question:
In Δ ABC , angle C is right Angle
Which Statement must be True?
A sinA= cosB
B. sinA=tanB
C. sinB= tanA
D. sinB= cosB
Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment..
Answers
The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
Explain about the sample space of an event?A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.
When this happens, we want to give each event—like rolling a two—a number that represents the likelihood of the occurrence and describes how probable it is that it will occur. Similar to this, we would like to give any event or group of outcomes—say rolling an even number—a probability that reflects how possible it is that the occurrence will take place if the experiment is carried out.Martin features a spinner with four compartments marked A, B, C, and D.
To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.
Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
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determine between which two whole numbers lies square root of 20
Answers
Answer:
The square root of 20 is approximately between 4 and 5.
To find this, you can estimate the square root of 20 by finding the square root of the closest perfect squares, which are 16 (4^2) and 25 (5^2):
√16 = 4
√25 = 5
Since 20 is closer to 25 than 16, we know that the square root of 20 must be closer to 5 than to 4. Therefore, the square root of 20 lies between 4 and 5.
Julian Nestor is ready to purchase a new stroller. It is regularly priced at $127.99. The sale price is $88.54. What is the markdown?
Answers
Answer:
$39.45, about 31%
Step-by-step explanation:
You want to know the markdown represented by a sale price of $88.54 on a regular price of $127.99.
MarkdownThe dollar amount of the markdown is ...
88.54 -127.99 = -39.45
The price was marked down $39.45.
The percentage markdown from the original price is ...
-39.45/127.99 × 100% ≈ -30.823% ≈ -31%
The original price was marked down about 31% to get the sale price.
__
Additional comment
The negative price change means the price was marked down. If the change were positive, it would signify a markup.
At a certain instant, the base of a triangle is 5 inches and is increasing at the rate of 1 inch per minute. At the same instant, the height is 10 inches and is decreasing at the rate of 2.5 inches per minute. Is the area of the triangle increasing or decreasing? Justify your answer.
Answers
Using differentiation, the area of the triangle is decreasing at the given time.
Is the area of the triangle increasing or decreasing?The formula for the area of a triangle is:
A = (1/2)bh
where b is the base and h is the height.
Differentiating both sides of the equation with respect to time t, we get:
[tex]\frac{dA}{dt} = (1/2)[(\frac{db}{dt}) h + b(\frac{dh}{dt}) ][/tex]
Substituting the given values, we get:
[tex]\frac{dA}{dt} = (1/2)[(1)(10) + (5)(-2.5)] = (1/2)(10 - 12.5) = -1.25[/tex]
Since the derivative of the area with respect to time is negative (-1.25), the area of the triangle is decreasing at the given instant.
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Determine the following standard normal (z) curve areas. (Round all answers to four decimal places.)
(a) The area under the z curve to the left of 1.73
(b) The area under the z curve to the left of
−0.69
(c) The area under the z curve to the right of 1.3
(d) The area under the z curve to the right of
−2.82
(e) The area under the z curve between −2.22 and 0.52
(f) The area under the z curve between
−1
and 1
(g) The area under the z curve between
−4
and 4
Answers
(a) The area under the standard normal curve to the left of 1.73 is 0.9582.
(b) The area under the standard normal curve to the left of -0.69 is 0.2454.
(c) The area under the standard normal curve to the right of 1.3 is 0.0968.
(d) The area under the standard normal curve to the right of -2.82 is 0.9974.
(e) The area under the standard normal curve between -2.22 and 0.52 is 0.6851.
(f) The area under the standard normal curve between -1 and 1 is 0.6826.
(g) The area under the standard normal curve between -4 and 4 is 0.9998.
(a) Using a standard normal table, the area under the standard normal curve to the left of 1.73 is 0.9582.
(b) Similarly, the area under the standard normal curve to the left of -0.69 is 0.2454.
(c) The area to the right of 1.3 is the same as the area to the left of -1.3. Using a standard normal table, this area is 0.0968.
(d) The area to the right of -2.82 is the same as the area to the left of 2.82. Using a standard normal table, this area is 0.9974.
(e) To find the area under the standard normal curve between -2.22 and 0.52, we need to find the area to the left of 0.52 and subtract the area to the left of -2.22. Using a standard normal table, we find that the area to the left of 0.52 is 0.6990 and the area to the left of -2.22 is 0.0139. Therefore, the area between -2.22 and 0.52 is 0.6990 - 0.0139 = 0.6851.
(f) To find the area under the standard normal curve between -1 and 1, we need to find the area to the left of 1 and subtract the area to the left of -1. Using a standard normal table, we find that the area to the left of 1 is 0.8413 and the area to the left of -1 is 0.1587. Therefore, the area between -1 and 1 is 0.8413 - 0.1587 = 0.6826.
(g) The area under the standard normal curve between -4 and 4 is the same as the area to the left of 4 minus the area to the left of -4. Using a standard normal table, we find that the area to the left of 4 is 0.9999 and the area to the left of -4 is 0.0001. Therefore, the area between -4 and 4 is 0.9999 - 0.0001 = 0.9998.
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Find the center and radius of the circle whose equation is x^2+y^2+4y=32
Answers
Answer:
center: (0, -2)
radius: 6
Step-by-step explanation:
You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.
see image.
BRAINEST IF CORRECT! 25 POINTS.
What transformation of Figure 1 results in Figure 2?
Select from the drop-down menu to correctly complete the statement.
A ______ of Figure 1 results in Figure 2.
Answers
Answer:
its reflection
Step-by-step explanation:
a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Answer:
It is Reflection. Check if it is in the list.
The area of a trapezium is 156cm2, the parallel sides are 17cm and 35cm respectively. What is the height of the trapezium
Answers
Answer:
6 cm
Step-by-step explanation:
You want the height of a trapezium with bases 17 cm, 35 cm and area 156 cm².
Area formulaThe formula for the are of a trapezium is ...
A = 1/2(b1 +b2)h
Filling in the given values, we have ...
156 = 1/2(17 +35)h = 26h
6 = h . . . . . . . . . . divide by 26
The height of the trapezium is 6 cm.
Answer:
6cm
Step-by-step explanation:
To find:-
The height of the trapezium.Answer:-
We are here given that the area of the trapezium is 156cm² and two of the parallel sides are 17cm and 35cm .We are interested in finding out the height of the trapezium.
The area of the trapezium is given by the formula,
[tex]:\implies \sf Area =\dfrac{1}{2}\times (s_1+s_1)\times h \\[/tex]
where s1 and s2 are the || sides of the trapezium and h is the height of the trapezium.
Now on substituting the respective values in the given formula, we have;
[tex]:\implies \sf 156cm^2 =\dfrac{1}{2} (17cm+35cm)\times h \\[/tex]
[tex]:\implies \sf 156cm^2(2) = 52cm (h) \\[/tex]
[tex]:\implies \sf h =\dfrac{156(2)}{52} cm\\[/tex]
[tex]:\implies \sf \pink{ height = 6 cm }\\[/tex]
Hence the height of the trapezium is 6cm .
HELP PLEASEEE 30 POINTS!!
Answers
Answer:
m<1 = 63° (Exterior alternating Angles)
m<2 = 62°
m<3 = 118°
Step-by-step explanation:
[tex]{ \tt{m \angle 2 + 63 \degree + 55 \degree = 180 \degree}} \\ { \sf{(exterior \: corresponding \: angles)}} \\ { \tt{m \angle 2 = 180 - (63 + 55)}} \\ { \tt{ \underline{ \: m \angle 2 = 62 \degree \: }}}[/tex]
[tex]{ \tt{m \angle 3 = m \angle 1 + 55 \degree}} \\ { \tt{m \angle 3 = 63 + 55}} \\ { \tt{ \underline{ \: m \angle 3 = 118 \degree \: }}}[/tex]
Which of the following quotients are true? Select all that apply. A. 1 2 ÷ 2 = 4 B. 1 3 ÷ 4 = 4 3 C. 1 2 ÷ 6 = 1 12 D. 1 5 ÷ 2 = 10 E. 1 8 ÷ 3 = 1 24
Answers
Answer:
A. 1/2 ÷ 2 = 1/4 is true.
B. 1/3 ÷ 4 = 1/12 is true.
C. 1/2 ÷ 6 = 1/12 is true.
D. 1/5 ÷ 2 = 1/10 is true.
E. 1/8 ÷ 3 = 1/24 is true.
Therefore, all the quotients are true.
(please mark my answer as brainliest)
Using the set of data below, which statements are true?
13, 11, 16, 12, 42, 8
The mean of this data set is 17.
The median is 12.5.
The median is 14.5.
The mean is more affected by the outlier.
The median is more affected by the outlier.
The mean of this data set is 12.
Answers
Statements 1,2 and five are correct.
Explanation:
Statement one:
To calculate the mean we must add all the numbers first
13+11+16+12+42+8= 102
Now we must divide the total by the amount of numbers, which in this case will be 6
102/6 = 17
Mean= 17
Statement 2:
First we should organize the numbers from smallest to biggest
8,11,12,13,16,42
Now since there is no middle number, we must find the average
12+13=25
25/2=12.5
Statement 5:
We know the median is an outlier as it’s the only number with a decimal
ne al Compute the derivative of the given function. TE f(x) = - 5x^pi+6.1x^5.1+pi^5.1
Answers
The derivative of f(x) is
[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].
What is derivative?The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.
In this case, the function f(x) is a polynomial, which means it is a combination of terms of the form [tex]ax^b[/tex], where a and b are constants. The derivative of f(x) can be calculated by taking the derivative of each term in the function and then combining them together.
The derivative of a term [tex]ax^b[/tex] is [tex]abx^(b-1)[/tex]. For the first term of f(x),[tex]-5x^pi[/tex], the derivative is [tex]-5pi x^(pi-1)[/tex]. For the second term, [tex]6.1x^5.1[/tex] the derivative is[tex]6.1 * 5.1x^(5.1-1)[/tex]. For the third term, [tex]pi^5.1[/tex], the derivative is [tex]5.1pi^(5.1-1)[/tex].
Combining these terms together, the derivative of f(x) is
[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].
This answer is the derivative of the given function. This is how the function changes as its input changes.
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The derivative of f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is [tex]-5\pi x^{\pi -1}[/tex]+ [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex] which can be calculated with the power rule.
What is derivative?The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.
The derivative of the given function f(x) = [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] can be calculated with the power rule, which states that the derivative of xⁿ is nx⁽ⁿ⁻¹⁾
To calculate the derivative of the given function, we begin by applying the power rule to each term.
The first term is [tex]-5^{\pi }[/tex] which has a derivative of [tex]-5\pi x^{\pi -1}[/tex].
The second term is [tex]6.1x^{5.1}[/tex] which has a derivative of [tex]6.1*5.1x^{5.1-1}[/tex].
The third term is [tex]\pi^{5.1}[/tex], which has a derivative of 5.1[tex]\pi^{5.1-1}[/tex].
Therefore, the derivative of the given function
f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is [tex]-5\pi x^{\pi -1}[/tex]+ [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex].
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Question:
Compute the derivative of the given function.
f(x) = - [tex]5x^{\pi }[/tex]+[tex]6.1x^{5.1}[/tex]+[tex]\pi^{5.1}[/tex]
The weight of a miniature Tootsie roll is normally distributed with a mean of 3.30 grams and standard deviation of .13 gram
Answers
We can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams for standard deviation of 0.13 gram.
What is a normal distribution?A normal distribution is a symmetric, bell-shaped continuous probability distribution that is defined by its mean and standard deviation. The majority of the data in a normal distribution is located close to the mean, and the number of data points decreases as you deviate from the mean in either direction. Because many real-world events, like human height or test scores, have a tendency to follow a normal distribution, the normal distribution is frequently utilised in statistics. A helpful technique for determining the range of values within a normal distribution based on the mean and standard deviation is the empirical rule, commonly known as the 68-95-99.7 rule.
Given that, the mean of 3.30 grams and standard deviation of 0.13 gram.
Using the empirical formula the range that falls in 95% is associated to two standard deviations.
Mean + 2 standard deviations = 3.30 + 2(0.13) = 3.56 grams
Mean - 2 standard deviations = 3.30 - 2(0.13) = 3.04 grams
Hence, we can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams.
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Solve using the correct order of
operations.
P
E
MD
AS
15-(4-3) 2= [?]
Enter
Help
Answers
Here using the correct order of operations that is PEMDAS, we get the value to be 13.
Define PEMDAS?PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.
The letters stand for:
P stands for parentheses.
Exponents are shown as E.
D stands for division.
The letter M stands for multiplication.
A stand for addition.
S stands for subtraction.
Now in the given question,
15 - (4-3)2
First the parentheses
15 - (1)2
Next is exponents.
15 - 2
At last, after subtracting, we get:
13
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awaite
Find the Factors of 24 less than 24.
Answers
Answer: Factors of 24 include: 1 and 24, 2 and 12, 3 and 8, 4 and 6
Step-by-step explanation:
20/8as a mixed number in its simplest form
Answers
Answer:
2 1/2
Step-by-step explanation:
20/8=2r4
2r4= 2 4/8
2 4/8 = 2 1/2
Answer:
2 1/2
Step-by-step explanation:
Step 1:
We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
20/8= 2.5 = 2
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numerator
To work this out we'll use the whole number we calculated in step one (2) and multiply it by the original denominator (8). The result of that multiplication is then subtracted from the original numerator:
20 - (8 x 2) = 4
Step 3: Our mixed fraction
We've now simplified 20/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
2 4/8
Step four: Convert it by simplifying
2 4/8 = 2 1/2
can anyone help with this triangle question
Answers
Step-by-step explanation:
Set it up as a ratio:
14 is to (14 +6) as 21 is to ?
14/20 = 21/?
? = 21 * 20 / 14 = 30 units
In a survey of 124 pet owners, 44 said they own a dog, and 58 said they own a cat. 14 said they own both a dog and a cat. How many owned neither a cat nor a dog?
Answers
Step-by-step explanation:
See Venn diagram below
Find the surface area of the figure on the right.
Answers
The fig's right side of total surface = 42yds.
What is surface area?
A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
According to our question-
(17+17+8)yds
42yds
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 9 feet. Container B has a diameter of 8 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Answers
Step-by-step explanation:
the volume of container B is Travers from A to B.
so, the volume of the empty space in A is exactly the volume of container B.
the volume of a cylinder is
base area × height = pi×r² × height.
the reside is as always half of the diameter.
r = 8/2 = 4 ft
the volume of the empty space in A = the volume of container B =
= pi×4² × 20 = pi×16 × 20 = 320pi = 1,005.309649... ≈
≈ 1,005.3 ft³
If a + b = 3 and ab = 2, find the value of a² + b²
Answers
Answer:
Through observation, a=2, b=1 or vice versa .
Step-by-step explanation:
If a=2 and b=1
a² +b²=?
2² +1² =4+1=5
a²+b²=5
a falling stone takes 0.31 s to travel past a window 2.2 m tall (fig.). from what height above the top of the window did the stone fall?
Answers
The stone fell from a height of 1.75 m above the top of the window.
We can use the kinematic equation for the vertical motion of an object in free fall to solve this problem:
y = vi*t + (1/2)at^2
where y is the initial height above the top of the window, vi is the initial velocity (which is zero since the stone is dropped), t is the time it takes for the stone to fall past the window (0.31 s), a is the acceleration due to gravity (-9.8 m/s^2).
Since the stone falls past a window that is 2.2 m tall, the final height of the stone is 2.2 m. Substituting these values into the equation, we get:
2.2 m = 0 + (1/2)(-9.8 m/s^2)(0.31 s)^2 + y
Simplifying and solving for y, we get:
y = 2.2 m - (1/2)(-9.8 m/s^2)(0.31 s)^2
y = 2.2 m - 0.45 m
y = 1.75 m
Therefore, the height from stone fell is 1.75 m.
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A brand new stock is called an initial public offering or IPO. Remember that in this model the period immediately after the stock is issued offers excess returns on the stock(ie it is selling for more than its actually worth). One such model for a class of internet IPOS predicts the percentage overvaluation of a stock as a function of time, as R(t)=2501^2/e^3t where R(t) is the overvaluation in percent and t is the time in months after issue. Use the information provided by the first derivative and second derivate, and asymptotes to prepare advice for clients as to when they should expect a signal to buy or sell (Inflection point), the exact time when they should buy or sell(max/min) and any false signals prior to an as- ymptote. Explain your reasoning. Make a rough sketch of the function.
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The Function of maximum or minimum for t is infinity.
What is first and second subsidiary test?While the principal subordinate can let us know if the capability is expanding or diminishing, the subsequent subsidiary. tells us in the event that the primary subsidiary is expanding or diminishing. On the off chance that the subsequent subsidiary is positive, the first.
To analyze the function R(t) = 2501² / e(3t), we can take the first and second derivatives:
R'(t) = -7503 * 2501² / e(3t)
R''(t) = 22509 * 2501² / e(3t)
To find the inflection point, we can set R''(t) = 0 and solve for t:
22509 * 2501² / e(3t) = 0
t = ln(0) / -3 = undefined
Since there is no real solution to this equation, there is no inflection point for this function.
To find the maximum or minimum, we can set R'(t) = 0 and solve for t:
-7503 * 2501² / e(3t) = 0
t = infinity
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What is the slope of the line in the following graph?
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Answer:
A. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Synthetic Division to Find Zeros
if f(x)=x^3−3x^2+16x+20 and x+1 is a factor of f(x), then find all of the zeros of f(x) algebraically.
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Answer:
Step-by-step explanation:
Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.
We set up synthetic division as follows:
-1 | 1 -3 16 20
| -1 4 -20
|_____________
1 -4 20 0
The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:
x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))
= (4 ± sqrt(-64)) / 2
= 2 ± 2i√2
Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.
if A is 20% more than B, by what percent is B less than A?
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Answer:
Jika A adalah 20% lebih banyak dari B, maka dapat dituliskan sebagai:
A = B + 0.2B
Dalam bentuk sederhana, hal ini dapat disederhanakan menjadi:
A = 1.2B
Kita dapat menggunakan persamaan ini untuk mencari persentase B yang lebih kecil dari A. Misalnya, jika kita ingin mengetahui berapa persen B lebih kecil dari A, maka kita dapat menggunakan rumus persentase sebagai berikut:
(B lebih kecil dari A) / A x 100%
Substitusikan nilai A = 1.2B dan kita dapatkan:
(B lebih kecil dari 1.2B) / 1.2B x 100%
Maka:
0.2B / 1.2B x 100%
= 0.1667 x 100%
= 16.67%
Jadi, B adalah 16.67% lebih kecil dari A.
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The lunch special at Maria's Restaurant is a sandwich and a drink. There are 2 sandwiches and 5 drinks to choose from. How many lunch specials are possible?
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Answer:
the question is incomplete, so I looked for similar questions:
There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.
the answer = 3 x 4 x 2 = 24 possible combinations
Explanation:
for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich
since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24
If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.
For this question's answer, there are 2 x 5 = 10 lunch specials are possible.
The number of lunch specials possible are 10.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
We are given that;
Number of sandwiches=2
Number of drinks=5
Now,
To find the total number of lunch specials, we need to multiply the number of choices for sandwiches by the number of choices for drinks.
Number of sandwich choices = 2
Number of drink choices = 5
Total number of lunch specials = 2 x 5 = 10
Therefore, by combinations and permutations there are 10 possible lunch specials.
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