For point M, we have x-coordinate cos( 5π/ 6) ≈0.5 y- match sin( 5π/ 6) =0.9
Since thex-coordinate is positive and the y- match is negative, we know that the angle lies in the alternate quadrant.
We can find another angle in the alternate quadrant that has the same sine and cosine values by abating 2π from the angle. thus, the two real figures that determine point M are 5π/ 6 and 5π/ 6- 2π = -7 π/ 6 Simplifying, we get
Two real figures that determine M 5π/ 6,-7 π/ 6 For the other points, we can use the same system
Two real figures that determine N π, π Two real figures that determine P 5π/ 4, 5π/ 4- 2π = -3 π/ 4 Two real figures that determine Q 7π/ 6, 7π/ 6- 2π = -5 π/ 6 .
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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
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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If a + b = 3 and ab = 2, find the value of a² + b²
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
Which of the following statements is true about an angle drawn in standard position?
Positive angles are measured clockwise.
The vertex of the angle is at point (1,1).
One side is always aligned with the positive y-axis.
One side is always aligned with the positive x-axis.
Answer:
Step-by-step explanation:
The statement that is true about an angle drawn in standard position is that one side is always aligned with the positive x-axis. The other side of the angle can be aligned with either the positive y-axis or the negative y-axis. The vertex of the angle does not necessarily have to be at point (1,1) and positive angles are measured counterclockwise.
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..
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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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?
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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ne al Compute the derivative of the given function. TE f(x) = - 5x^pi+6.1x^5.1+pi^5.1
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]
An initial deposit of $800 is put into an account that earns 5% interest, compounded annually. Each year, an additional deposit of $800 is added to the account.
Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the seventh deposit is __________.
The balance of the account after the seventh deposit can be calculated using the formula below:
A = P (1 + r/n)ⁿ
where:
A = the balance of the account
P = The initial deposit of $800
r = the interest rate of 5%
n = the number of times the interest is compounded annually
n = 1
Therefore, the balance of the account after the seventh deposit is:
A = 800 (1 + 0.05/1)⁷
A = 800 (1.05)⁷
A = 800 (1.4176875)
A = 1128.54
Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.
20/8as a mixed number in its simplest form
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
HELP PLEASEEE 30 POINTS!!
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]
what is true and what is not for this right triangle need help
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
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.
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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Find the surface area of the figure on the right.
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?
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
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.
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.
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.
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?
Answer:
A. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
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.
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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If F1 =(3,0), F2 =(−3,0) and P is any point on the curve 16x^2 + 25y^2 = 400, then PF1 + PF2 equals to:861012
The value of PF1 + PF2 equals to 10 for any point P on curve ellipse of equation 16x^2 + 25y^2 = 400. So, the correct answer is B).
We can start by finding the coordinates of the point P on curve of the ellipse. We can write the equation of the ellipse as:
16x^2 + 25y^2 = 400
Dividing both sides by 400, we get:
x^2/25 + y^2/16 = 1
So, the center of the ellipse is at the origin (0,0) and the semi-axes are a=5 and b=4.
Let the coordinates of point P be (x,y). Then, we can use the distance formula to find the distances PF1 and PF2:
PF1 = sqrt((x-3)^2 + y^2)
PF2 = sqrt((x+3)^2 + y^2)
Therefore, PF1 + PF2 = sqrt((x-3)^2 + y^2) + sqrt((x+3)^2 + y^2)
We can use the property that the sum of the distances from any point on an ellipse to its two foci is constant, and is equal to 2a, where a is the semi-major axis. So, we have:
PF1 + PF2 = 2a = 2(5) = 10
Therefore, PF1 + PF2 equals to 10 for any point P on the ellipse 16x^2 + 25y^2 = 400. So, the correct option is B).
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The area of a trapezium is 156cm2, the parallel sides are 17cm and 35cm respectively. What is the height of the trapezium
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 .
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?
Step-by-step explanation:
See Venn diagram below
can anyone help with this triangle question
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
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.
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?
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.
awaite
Find the Factors of 24 less than 24.
Answer: Factors of 24 include: 1 and 24, 2 and 12, 3 and 8, 4 and 6
Step-by-step explanation:
The weight of a miniature Tootsie roll is normally distributed with a mean of 3.30 grams and standard deviation of .13 gram
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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The definition of differentiable also defines an error term E(x,y). Find E(x,y) for the function f(x,y)=8x^2 − 8y at the point (−1,−7).E(x,y)=
The value of error term E(x,y) = 8x^2 - 8x - 56.
The definition of differentiability states that a function f(x,y) is differentiable at a point (a,b) if there exists a linear function L(x,y) such that:
f(x,y) - f(a,b) = L(x,y) + E(x,y)
where E(x,y) is an error term that approaches 0 as (x,y) approaches (a,b).
In the case of the function f(x,y) = 8x^2 - 8y, we want to find E(x,y) at the point (-1,-7).
First, we need to calculate f(-1,-7):
f(-1,-7) = 8(-1)^2 - 8(-7) = 56
Next, we need to find the linear function L(x,y) that approximates f(x,y) near (-1,-7). To do this, we can use the gradient of f(x,y) at (-1,-7):
∇f(-1,-7) = (16,-8)
The linear function L(x,y) is given by:
L(x,y) = f(-1,-7) + ∇f(-1,-7) · (x+1, y+7)
where · denotes the dot product.
Substituting the values, we get:
L(x,y) = 56 + (16,-8) · (x+1, y+7)
= 56 + 16(x+1) - 8(y+7)
= 8x - 8y
Finally, we can calculate the error term E(x,y) as:
E(x,y) = f(x,y) - L(x,y) - f(-1,-7)
= 8x^2 - 8y - (8x - 8y) - 56
= 8x^2 - 8x - 56
Therefore, the error term E(x,y) for the function f(x,y) = 8x^2 - 8y at the point (-1,-7) is E(x,y) = 8x^2 - 8x - 56.
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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?
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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Find the center and radius of the circle whose equation is x^2+y^2+4y=32
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.
Alberto believes that because all squares can be called
rectangles, then all rectangles must be called squares.
Explain why his reasoning is flawed. Use mathematical
terminology to help support your reasoning.
Alberto's statement is flawed because all squares can be called rectangles, but not vice versa
Reason why Alberto's statement is flawedAlberto's reasoning is flawed because all squares can be called rectangles, but not all rectangles are squares.
While it is true that squares meet the definition of rectangles, not all rectangles meet the definition of squares.
A square is a special type of rectangle with all sides equal in length.
Therefore, Alberto's argument violates the logical concept of implication, where the truth of one proposition (squares can be called rectangles) does not necessarily imply the truth of the converse (all rectangles must be called squares).
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if A is 20% more than B, by what percent is B less than A?
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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