Answer:
1 , - ( 3x^2/2), + (25x^4/24).
Step-by-step explanation:
We are given the following information:
y = (e^-x^2)cosx.
STEP ONE: Write out the power series out(either by deriving it or otherwise).
If you check the power series table, you will get the power series for the two functions that is cos x and e^-x^2.
e^-x^2 = 1 - (x^2) + ( x^4/2! ) - (x^6/3!) +...
Cos x = 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...
STEP TWO: Multiply both the power series of e^-x^2 and Cos x together because we are to determine or find the first three nonzero terms in the maclaurin series for the given function.
1 - (x^2) + ( x^4/2! ) - (x^6/3!) +... - 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...
= 1 - ( 3x^2/2) + (25x^4/24).
= 1, - ( 3x^2/2) , + (25x^4/24) => comma- separated list.
20 points + brainliest = 30 points!
Answer:
see below
Step-by-step explanation:
Addition and subtraction are both closed under polynomials.
That means that when we add and subtract polynomials, we will end up with a polynomial
f(x) + g(x) will = always be a polynomial when we start with polynomials
f(x) - g(x) will = always be a polynomial when we start with polynomials
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
A polynomial is an expression consisting of variables and coefficients.
[tex]f(x)[/tex] and [tex]g(x)[/tex] are polynomial functions.
Adding polynomials and subtracting polynomials is essentially combining like terms of polynomial expressions.
[tex]f(x)+g(x)[/tex] is always a polynomial
[tex]f(x)-g(x)[/tex] is always a polynomial
If you add, subtract or multiply any two polynomials then the result will be always a polynomial.
WHOEVER ANSWERS FIRST GETS BRAINLIEST:) Which expression represents the surface area of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. S A = pi r l + pi r squared (pi) (6) (10) + (pi) (6 squared) (pi) (8) (10) + (pi) (8 squared) (pi) (12) (10) + (pi) (12 squared) (pi) (10) (12) + (pi) (10 squared)
Answer:
Step-by-step explanation:
The surface area of a cone is:
● Sa = Pi*r^2 +Pi*r*l
r is the radius and l is the slant heigth
The diameter of this cone is 12 inches so the radius is 6 (12/2=6).
●Sa = Pi*36 +Pi*6*10
●Sa = 301.59 in^2
Answer:
pi (6) * 10+ pi ( 6)^2
Step-by-step explanation:
The surface area of a cone is given by
SA = pi rl +pi r^2 where r is the radius and l is the slant height
We know the diameter is 12 so the radius is 12/2 = 6
SA = pi (6) * 10+ pi ( 6)^2
6 2/9 - 5 - 8/9 = ?
Is (-1, -1) a solution of y = 3x + 2?
Answer:
Yes
Step-by-step explanation:
Well the integer (-1, -1) means x = -1 and y = -1
So we can plug this into the equation
-1 = 3(-1) + 2
-1 = -3 + 2
-1 = -1
So yes (-1, -1) is a solution.
3) and
What is the equation, in point-slope form, of the line that
is perpendicular to the given line and passes through the
point (-4, 3)?
O y-3 = -2(x+4)
Oy-3=-{(x + 4)
y-3 = {(x + 4)
O y-3 = 2(x + 4)
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The given line passes through the points (-4, -3) and (4, 1).
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, 3)?
a) y - 3 = -2(x + 4)
b) y - 3= - (x + 4)
c) y - 3 = (x + 4)
d) y - 3 = 2(x + 4)
Answer:
The equation of the line that is perpendicular to the given line and passes through the point (-4, 3) is
a) y - 3 = -2(x +4)
Step-by-step explanation:
First of all, we will find the slope of the given line.
We are given that the line passes through the points (-4, -3) and (4, 1)
[tex](x_1, y_1) = (-4,-3) \\\\(x_2, y_2) = (4,1) \\\\[/tex]
The slope of the equation is given by
[tex]$ m_1 = \frac{y_2 - y_1 }{x_2 - x_1} $[/tex]
[tex]m_1 = \frac{1 -(-3) }{4 -(-4)} \\\\m_1 = \frac{1 + 3 }{4 + 4} \\\\m_1 = \frac{4 }{8} \\\\m_1 = \frac{1 }{2} \\\\[/tex]
Recall that the slopes of two perpendicular lines are negative reciprocals of each other.
[tex]$ m_2 = - \frac{1}{m_1} $[/tex]
So the slope of the other line is
[tex]m_2 = - 2[/tex]
Now we can find the equation of the line that is perpendicular to the given line and passes through the point (-4, 3)
The point-slope form is given by,
[tex]y - y_1 = m(x -x_1)[/tex]
Substitute the value of slope and the given point
[tex]y - 3 = -2(x -(-4) \\\\y - 3 = -2(x +4)[/tex]
Therefore, the correct option is (a)
y - 3 = -2(x + 4)
The equation of the line in point-slope form is y - 3 = -2(x + 4)
What is a linear equation?
A linear equation is in the form:
y = mx + b
Where y,x are variables, m is the rate of change and b is the y intercept.
The line passes through the point (-4, -3) and (4, 1). Hence:
Slope = (1 - (-3)) / (4 - (-4)) = 1/2
The slope of the line perpendicular to this line is -2 (-2 * 1/2 = -1).
The line passes through (-4, 3), hence:
y - 3 = -2(x - (-4))
y - 3 = -2(x + 4)
The equation of the line in point-slope form is y - 3 = -2(x + 4)
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Hi Folks, l have this Rearranging difficult formulae exercise, l have the answer but l dont understand at all the procedure, the method applied, if someone can explain it to me please will be appreciatted thanks 1/a = 1/b+1/c the procedure is: 1= a/b + a/c (x a) b= a+ ab/c (x b) bc= ac +ab ( x c) b (c-a) = ac b= ac/c-a OR b= - ac /a - c Def l dont understand the method thanks for your help
Step-by-step explanation:
1/a = 1/b + 1/c
Multiply both sides by a.
1 = a/b + a/c
Multiply both sides by b.
b = a + ab/c
Multiply both sides by c.
bc = ac + ab
Subtract ab from both sides.
bc − ab = ac
Factor b.
b (c − a) = ac
Divide both sides by c − a.
b = ac / (c − a)
Answer:
see below
Step-by-step explanation:
1/a = 1/b+1/c
Multiply each side of the equation by a
a( 1/a) =a( 1/b+1/c)
1 = a/b + a/c
Then multiply each side of the equation by b
b*1 =b( a/b + a/c)
b = a + ab/c
Then multiply each side of the equation by c
cb = c( a+ ab/c)
bc = ac + ab
We have gotten rid of the fractions
Now we can solve for a
Factor out a on the right side
bc = a( c+b)
Then divide by c+b on each side
bc / ( c+b) = a ( c+b) / ( c+b)
bc / ( c+b) = a
Now we can solve for b
bc = ac + ab
Subtract ab from each side
bc -ab = ac + ab-ab
bc -ab = ac
Factor out b on the left side side
b( c-a) = ac
Then divide by c-a on each side
b( c-a) / ( c-a) = ac / ( c-a)
b = ac/ ( c-a)
We can factor out -1
b = -ac/( a-c)
What is the inverse of the logarithmic function
f(x) = log2x?
f –1(x) = x2
f –1(x) = 2x
f –1(x) = logx2
f –1(x) = StartFraction 1 Over log Subscript 2 Baseline x EndFraction
Answer:
B. edge 2021
B. is correct for the next one too.
Step-by-step explanation:
B. is the correct answer for the first one
B. is also the correct answer for the second one
Which number is an integer? Negative three-fourths 0 2.3 Pi
Answer:
0
Step-by-step explanation:
An integer is colloquially defined as a number that can be written without a fractional component.
-3/4 ---- It is a fraction itself, so it is a fractional component
0 ---- Has no fractional component
2.3 Pi ---- Pi is irrational and is a decimal, so is 2.3. Most of this is a fractional component already.
The only one we can't eliminate using just the definition is 0.
Hope that helps, tell me if you need a further explanation
From the given numbers the number that is an integer is 0. The correct option is B.
What is an integer?An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.
Given the following numbers -(3/4), 0, 2.3, and π. Therefore, from the given numbers the number that is an integer is 0.
Hence, From the given numbers the number that is an integer is 0.
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please answer me question 3 solving part
Answer:
1. D
2. B
3. A
Step-by-step explanation:
Question 1:
The pair of <JKL and <LKM can be referred to as linear pairs. They are two adjacent angles that are formed from the intersecting of two lines.
Question 2:
Given that <KLM = x°
<KML = 50°
<JKL = (2x - 15)°
According to the exterior angle theorem, exterior ∠ JKL = <KLM + KML.
2x - 15 = x + 50
Solve for x
2x - x = 15 + 50
x = 65
Therefore, <KLM = 65°
QUESTION 3:
<JKL = 2x - 15
Plug in the value of x
<JKL = 2(65) - 15
= 130 - 15
<JKL = 115°
A contractor originally estimated the total cost of a job including labor and materials at $ 57,000. In reviewing the costs, a new estimate of $ 48,000 is made, reducing the labor cost by 15% and the material cost by 18%. What is each cost, labor and material, of the new estimate?
Answer:
shadow cow
Step-by-step explanation:
In new estimate cost of labor and material is 35,700 and 12,300 respectively.
What is reducing factor?Reduction Factor means the percentage obtained by dividing the Net Worth Shortfall Amount by the Required Net Worth Amount.
According to the question
A contractor originally estimated the total cost of a job including labor and materials at $ 57,000.
let Labor cost = l
Material cost = m
Now ,
l + m = 57000 ----------(1)
A new estimate of $ 48,000 is made, reducing the labor cost by 15% and the material cost by 18%.
i.e,
[tex]\frac{(100-15)}{100} l + \frac{(100-18)}{100} m = 48000[/tex]
[tex]\frac{(85)}{100} l + \frac{(82)}{100} m = 48000[/tex]
0.85l + 0.82m = 48000 --------------------------------(2)
multiplying equation (1) from 0.85
0.85l + 0.85m = 48450 -------------------------------(3)
subtracting equation (1) and (3)
0.85l + 0.85m = 48450
-0.85l -0.82m = -48000
0.03m=450
m = 15000 (old cost )
new cost of m is = 0.82 * 15000 =12,300
putting value of m in equation (1)
l + m = 57000
l + 15000 = 57000
l = 42000 (old cost)
new cost of l is = 0.85l = 0.85*42000
new cost of l is = 35,700
Hence, The new cost of labor is 35,700 and new cost of material is 12,300 .
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Drag each tile to the correct box.
Match each equation with its solution.
x = -0.4
x= 10
x = 2
x = -10
Answer:
1). x = 2
2). x = -10
3). x = [tex]-\frac{2}{5}[/tex]
4). x = 10
Step-by-step explanation:
1). x - 6 = -4
(x - 6) + 6 = -4 + 6 [By adding 6 to both the sides of the equation]
x = 2
2). x + 3 = -7
(x + 3) - 3 = -7 - 3 [By subtracting 3 to both the sides of the equation]
x = -10
3). 5x = -2
[tex]\frac{5x}{5}=\frac{-2}{5}[/tex] [By dividing with 5 from both the sides of the equation]
x = [tex]-\frac{2}{5}[/tex]
4). 0.5x = 5
[tex]\frac{0.5x}{0.5}=\frac{5}{0.5}[/tex] [By dividing with 0.5 from both the sides of the equation]
x = 10
Complete the table.PLSSS HELP ILL GIVE BRAINLIEST.PLS PLS PLS PLS
Answer:
0, 22, 44, 66
Step-by-step explanation:
Given the equation for the model, [tex] d = 11t [/tex] , you can complete the table above by simply plugging in each value of "t" has given in the table to solve for "d".
*When t (seconds) = 0, distance (feet) would be:
[tex] d = 11(0) [/tex]
[tex] d = 0 [/tex]
*When t (seconds) = 2, distance (feet) would be:
[tex] d = 11(2) [/tex]
[tex] d = 22 [/tex]
*When t (seconds) = 4, distance (feet) would be:
[tex] d = 11(4) [/tex]
[tex] d = 44 [/tex]
*When t (seconds) = 6, distance (feet) would be:
[tex] d = 11(6) [/tex]
[tex] d = 66 [/tex]
What is the value of x?
Answer:
54
Step-by-step explanation:
x is half the difference of the two arcs:
x = (136 -28)/2 = 54
The value of x is 54.
If a 5 ft tall man cast an 8 ft long shadow at the same time a tree cast a 24 ft long shadow, how tall is the tree?
Answer:
15 feet
Step-by-step explanation:
We have 2 similar right triangles with legs height and length of shadows.
height of men : length of shadows of the man = height of tree : length of shadows of the tree
5 : 8 = x : 24
8x = 5* 24
x = 5*24/8 = 15 (feet)
Answer:
15ft
Step-by-step explanation:
5 ft is to 8 ft
A ft is to 24 ft
A = 24*5/8
A = 15ft
15ft
how many pairs of matching surfaces does a cereal box have
Answer:
3 pairs
Step-by-step explanation:
Top and Bottom
Front and Back
Side and Side.
Cereal Boxes have 6 sides
Aracely can spend up to a total of $20 on streamers
and balloons for a party. Streamers cost $1.49 per
pack, and balloons cost $4.39 per pack. Which of
the following inequalities represents this situation,
where is the number of packs of streamers Aracely
can buy, and b is the number of pack of balloons
Aracely can buy? (Assume there is no sales tax.)
Answer:
[tex]1.49S + 4.39B \leq 20[/tex]
Step-by-step explanation:
The options are not given; However, the question can be solved without the list of options
Given
Let S represent packs of Streamers
Let B represent packs of Balloons
Required
Represent this with an inequality
From the question, we understand that;
[tex]1S\ =\ \$1.49\ and\ \ 1B\ = \ \$4.39[/tex]
Also, it's stated that Aracely can't spend more than $20;
This mean that the maximum Aracely can spend is $20 and it can be represented with the inequality sign [tex]\leq 20[/tex]
Bringing them together;
[tex]1.49S + 4.39B \leq 20[/tex]
The function h(t) = –16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot. What does h(3.2) represent? the height of the rock 3.2 seconds before it reaches the ground the time it takes the rock to reach the ground, or 3.2 seconds the time it takes the rock to reach a height of 3.2 meters the height of the rock 3.2 seconds after it is propelled
Answer:
The answer is d
Step-by-step explanation:
h(3.2) represents the height of the rock 3.2 seconds after it is propelled.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given a function,
h(t) = -16t² + 28t + 500
Here t represents the time after it is propelled.
h(t) represents the height of the rock t seconds after it is propelled.
So, h(3.2) represents the height of the rock 3.2 seconds after it is propelled.
Hence the correct option is D.
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The diagram shows the floor plan for Harry's new tree house. The entry terrace on the tree house is shaped like an isosceles trapezoid.
Answer:
what do you need help with its not really clear
Answer
1. 48 2. 308
Step-by-step explanation:
Let x stand for the length of an individual screw. 100 screws were sampled at a time. The population mean is 2.5 inches and the population standard deviation is 0.2 inches.
What is the mean of the sampling distribution of sample means?
Answer:
The mean is defining the average length(2.5in) of the 100 measured screws.
Step-by-step explanation:
The mean is usually calculated in order to determine the average of a set of values.
Leslie buys a large circular pizza that is divided into eight equal slices. She measures along the outer edge of the crust from one piece and finds it to be 5.5 inches. What is the diameter of the pizza to the nearest inch?
Answer:
i believe it's 4.5
Step-by-step explanation:
Answer:
14 in. hope this helps!!:)
Step-by-step explanation:
nineteen multiplied by twenty five
Answer:
19*25= 475
Step-by-step explanation:
You can either use a calculator or use the standard operation
Find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 7.
Answer:
The height of the right circular cylinder is 14/√3 and its radius is 7√6/3.
Step-by-step explanation:
Check the attachment for the diagram.
The volume of a right circular cylinder = πr²h
r is the radius of the cylinder
h is the height of the cylinder
V = πr²h... 1
From the diagram, we can use Pythagoras theorem on the right angled triangle to get r². From the triangle P² = r²+(h/2)²
P is the radius of the sphere.
P = 7
7² = r²+(h/2)²
r² = 49-(h/2)²... 2
Substituting equation 2 into 1:
V = π(49-(h/2)²)h
V = π(49h-h³/4)...3
To get the height h of the cylinder, we need to differentiate the volume of the cylinder with respect to h and equate to zero. i.e dV/dh = 0 since it's the maximum volume.
dV/dh = π(49-3h²/4)
0 = π(49-3h²/4)
Dividing both sides by π
0/π = π(49-3h²/4)/π
49-3h²/4 = 0
49 = 3h²/4
3h² = 49×4
3h² = 196
h² = 196/3
h = √196/√3
h = 14/√3
To get the radius of the cylinder, we will substitute h = 14/√3 into equation 2
r² = 49-(h/2)²
r² = 49-{(14/√3)/2}²
r² = 49-{14/2√3}²
r² = 49-(7/√3)²
r² = 49 - 49/3
r² = (147-49)/3
r² = 98/3
r = √98/√3
r = √49× √2/√3
r = 7√2/√3
r = 7√2/√3 × √3/√3
r = 7√6/3
The height of the right circular cylinders is 14/√3 and its radius is 7√6/3.
How many games are played in a 4 team round robin tournament? (Each team
plays every other team only once.)
Answer: 6
Step-by-step explanation:
If we call each team, A, B, C and D, each team has to play each other team once. Let's call each pairing between 2 teams the 2 teams' letters next to each other, e.g. AB is A playing against B. A has to play against B, C and D so we have AB, AC and AD. So we have 3 so far.
We have already counted that B is playing A but we haven't counted B playing C and D yet so we also have BC and BD. So we have 5 in total
Lastly, C needs to play D, we have already counted C playing B and C playing A so we have CD left. In total that gives 6.
Now we have already included D playing every other team so we don't include any other pairings.
In total, now every team has played every other team giving a total of 6.
(another way of solving this is doing "3!2 but if you haven't learnt factorials yet stick to the first method.
Answer:
6 games.
Step-by-step explanation:
The answer is the number of combinations of 2 from 4
= 4*3 / 2*1
= 6.
A formal hypothesis test is to be conducted using the claim that the mean AC thermostat setting in restaurants is equal to 74degrees°F. What is the null hypothesis and how is it denoted?
Answer:
[tex]A. H_o: \mu = 74 ^{\circ} F[/tex]
Step-by-step explanation:
A null hypothesis refers to the hypothesis in which there is no important difference taken place and it is used in statistics and it also does not have any relation between the two measured events or variables or group association
It can be denoted by
[tex]A. H_o: \mu = 74 ^{\circ} F[/tex]
Therefore the above null hypothesis is the correct answer
0.3% of a country has a certain disease. The test for the disease has a sensitivity of 92% (i.e., of those we know have the disease, the test comes back positive 92% of the time.) It has a specificity of 96% (i.e., of those who do NOT have the disease, the test comes back negative 96% of the time.) Determine the ACCURACY of this test (round to 5 decimals) Remember, ACCURACY is correct values (i.e. true positives true negatives)
Answer:
0.95988 (Accuracy of the test )
Step-by-step explanation:
To determine the accuracy of this test we have to list out the given values
Prevalence rate of the disease = 0.3% = 0.003
sensitivity rate of the disease = 92% = 0.92
specificity rate for the test = 96% = 0.96
The accuracy of the test can be found using this equation
Accuracy = sensitivity * prevalence + specificity ( 1 - prevalence )
= 0.92 * 0.003 + 0.96 ( 1 - 0.003 )
= 0.00276 + 0.95712
= 0.95988
Set up a rational equation and then solve the following problems. A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/18. Find the two integers.
Answer:
9 and 18
Step-by-step explanation:
2x and x are the numbers
1/x-1/2x=1/18
2/2x-1/2x=1/18
1/2x=1/18
2x=18X=9,
2x=18
The two integers are 9 and 18
(6/7)^2 times (1/2)^2
Answer:
9/49 or 0.184
Answer:
9/49
Step-by-step explanation:
(6/7)² × (1/2)²
Distribute the square to the fractions.
6²/7² × 1²/2²
36/49 × 1/4
Multiply.
36/196
Simplify.
9/49
Dr. Gongol, a sleep specialist, predicts that the proportion of snoring events compared to other events during a sleep study is more than 35%. To test this prediction, he evaluates 200 random sleep studies and found that 140 studies showed that more than 35% events were snores. The following is the setup for this hypothesis test: H0:p=0.35 Ha:p>0.35 The p-value for this hypothesis test is 0.03. At the 5% significance level, should he reject or fail to reject the null hypothesis?
Answer:
Reject the null hypothesis
Step-by-step explanation:
The claim is H0:p=0.35 Ha:p>0.35
At a significance level of 0.05, if the p value observed is less than 0.05, then we reject the null hypothesis, but if the p value observed is greater than the null hypothesis, then we fail to reject the null hypothesis.
In this case study: the p value is 0.03 which is less than the significance level, this we will reject the null hypothesis and conclude that there is enough statistical evidence to prove that the proportion of snoring events compared to other events during a sleep study is more than 35%.
Find the volume o the sphere.
Answer:
The volume of sphere is 267.95 units³.
Step-by-step explanation:
Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :
[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
[tex]let \: r = 4[/tex]
[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]
[tex]v = \frac{4}{3} \times \pi \times 64[/tex]
[tex]v = \frac{256}{3} \times 3.14[/tex]
[tex]v = 267.95 \: {units}^{ 3} [/tex]
Shane has a bag of marbles with 4 blue marbles, 3 white marbles, and 1 red marbles. Find the following probabilities of Shane drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn. (Give your answer as a fraction)
Answer: A). A Blue, then a Red.
= 4/8 * 1/7
= 1/14
B). A Red, then a White.
= 1/7 * 3/8
= 3/56
C). A Blue, then a Blue, then another Blue.
= 4/8 * 3/7 * 2/6
= 1/14
Step-by-step explanation:
had to complete the question first.
Find the following probabilities of Derek drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn.
(a) A Blue, then a Red =
(b) A Red, then a White =
(c) A Blue, then a Blue, then a Blue =
given data:
blue marble = 4
white marble = 3
red marble = 1
total marble = 8
solution:
probability of drawing
A). A Blue, then a Red.
= 4/8 * 1/7
= 1/14
B). A Red, then a White.
= 1/7 * 3/8
= 3/56
C). A Blue, then a Blue, then another Blue.
= 4/8 * 3/7 * 2/6
= 1/14