The probability of getting 3 heads in 4 coin tosses, given that we get at least 2 heads, is 4/11 or 0.364.
To solve this problem, we can use the conditional probability formula. Let A be the event of getting 3 heads in 4 coin tosses, and let B be the event of getting at least 2 heads in 4 coin tosses. Then we want to find P(A|B), the probability of getting 3 heads in 4 coin tosses given that we get at least 2 heads.
By the definition of conditional probability, we have:
P(A|B) = P(A and B) / P(B)
To find P(B), the probability of getting at least 2 heads in 4 coin tosses, we can use the complement rule and find the probability of getting 0 or 1 heads:
P(B) = 1 - P(0 heads) - P(1 head)
To find P(0 heads), the probability of getting 0 heads in 4 coin tosses, we use the binomial probability formula:
P(0 heads) = (4 choose 0) * (0.5)^0 * (1-0.5)^(4-0) = 1/16
Similarly, we can find P(1 head):
P(1 head) = (4 choose 1) * (0.5)^1 * (1-0.5)^(4-1) = 4/16
So,
P(B) = 1 - P(0 heads) - P(1 head) = 11/16
To find P(A and B), the probability of getting 3 heads in 4 coin tosses and getting at least 2 heads, we can use the binomial probability formula again:
P(A and B) = (4 choose 3) * (0.5)^3 * (1-0.5)^(4-3) = 4/16
Therefore,
P(A|B) = P(A and B) / P(B) = (4/16) / (11/16) = 4/11
So the probability of getting 3 heads in 4 coin tosses, given that we get at least 2 heads, is 4/11 or approximately 0.364.
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One couple and four individuals have been invited to a dinner party where dinner will be served promptly at 8pm. The chance any individual arrives late to the party is 10%. The chance the couple arrives late is 30% (the couple will arrive together) Let X = the number of guests arriving late Note: suppose I wanted to find the probability that 3 people arrive late to the party. This can happen in two ways ° (a) any combination of 3 individuals arive late (all others on time) » (b) any 1 individual and the couple arrive late (all others on time) or We consider in the following table all ways that (a) any combination of 3 individuals are late, the couple is on-time, and the remaining individual is on-time
Probability of 3 people arriving late is 0.34%.
The probability of 3 people arriving late to the party is the probability of a combination of 3 individuals arriving late and the couple and remaining individual arriving on time. This can be expressed mathematically as P(X = 3) = P(3 individuals arrive late)P(Couple arrives on time)P(Individual arrives on time).
We can calculate this probability as follows:
P(X = 3) = (0.1 x 0.1 x 0.1) x (0.7 x 0.7) = 0.00343
This means that there is a 0.34% chance that 3 people arrive late to the party. Probability of 3 people arriving late is 0.34%.
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Find a function whose domain is the set of all integers and whose target is the set of all positive integers that satisfies each set of properties.
(a) Neither one-to-one, nor onto.
(b) One-to-one, but not onto.
(c) Onto, but not one-to-one.
(d) One-to-one and onto.
a) This function maps even integers to the next odd integer, and maps odd integers to themselves. It is not one-to-one
b) This function maps positive integers to even positive integers, and maps negative integers to odd positive integers. It is one-to-one because different inputs always have different outputs.
c) This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs, and it is onto because every positive and negative integer is in its range.
d) This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs
(a) One example of a function that is neither one-to-one nor onto is:
[tex]f(x) = \begin{cases} x+1 & \text{if } x \text{ is even} \ x & \text{if } x \text{ is odd} \end{cases}[/tex]
This function maps even integers to the next odd integer, and maps odd integers to themselves. It is not one-to-one because, for example, f(2) = f(4) = 3. It is not onto because no positive even integer is in the range of f.
(b) One example of a function that is one-to-one but not onto is:
[tex]f(x) = \begin{cases} 2x & \text{if } x > 0 \ -2x+1 & \text{if } x \leq 0 \end{cases}[/tex]
This function maps positive integers to even positive integers, and maps negative integers to odd positive integers. It is one-to-one because different inputs always have different outputs. However, it is not onto because no odd positive integer is in the range of f.
(c) One example of a function that is onto but not one-to-one is:
[tex]f(x) = \begin{cases} x/2 & \text{if } x \text{ is even} \ -(x+1)/2 & \text{if } x \text{ is odd} \end{cases}[/tex]
This function maps even integers to positive integers, and maps odd integers to negative integers. It is onto because every positive and negative integer is in the range of f. However, it is not one-to-one because, for example, f(2) = f(-2) = 1.
(d) One example of a function that is both one-to-one and onto is:
f(x) = x
This function simply maps every integer to itself. It is one-to-one because different inputs always have different outputs, and it is onto because every positive and negative integer is in its range.
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Coral runs down 23rd street. Each block is 1/4 mile long. She runs 2/3 of a block before she gets tired. What part of a mile does she run?
Answer:
1/6
Step-by-step explanation:
1/4x2/3 = 2/12 = 1/6
Find the mean 12, 13, 15, 16, 24, 15, 22, 10, 9, 13, 13, 18, 16, 25, 23, 24
Round to two decimals
Answer:24
Step-by-step explanation:
because
The Smith family is selling their home for $250,000 with a required down payment of 5%. Find the amount of the required down payment and the mortgage.
Down Payment:
Mortgage:
Answer:
Down payment is $12,500.
Mortgage = $237,500
Step-by-step explanation:
The required down payment is 5% of the selling price of the house, which is $250,000.
Down payment = 5% of $250,000 = 0.05 x $250,000 = $12,500
Therefore, the required down payment is $12,500.
To find the amount of the mortgage, we need to subtract the down payment from the selling price of the house.
Mortgage = Selling price of the house - Down payment
Mortgage = $250,000 - $12,500
Mortgage = $237,500
Therefore, the amount of the mortgage is $237,500.
Given the function below, find p (-2).
p(x) = x² - 7x
Answer:
18
Step-by-step explanation:
to find p(-2), substitute it into the equation!
you can make this easier by factoring x out, so p(x) = x(x-7)
then, plug -2 in
p(-2)=-2(-2-7)
p(-2)=-2(-9)
p(-2)=18
Answer:
Step-by-step explanation:
p(x)=[tex]x^{2}-7x\\[/tex]
=>p(-2)=[tex](-2)^{2} -7.(-2)[/tex]
= 4+14=18
1.
Solve for x. Round to one
decimal place (nearest
tenth).
X
48°
1
15
The length of the hypotenuse or the value of 'x' is 60.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjacent/hypotenuse and
tan = opposite/adjacent.
From the given diagram respect to the reference angle of 37°,
Hypotenuse is 'x' and adjacent is 48.
And we know, cos = adjacent/hypotenuse.
Therefore, cos37° = 48/x.
x = 48/0.8.
x = 60.
Q. A right-angle triangle is shown, Find the value of x.
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create a matrix of dimension 300 x 7, called `bin.matrix`, whose columns contain the 7 vectors we've created, in order of the success probabilities of their underlying binomial distributions (0.2 through 0.8). hint: use `cbind()`.
The creation of the bin.matrix using cbind() allows us to organize and manipulate our data in a way that is conducive to statistical analysis.
A binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, with a constant probability of success.
First, let's define what a binomial distribution is. For example, if we toss a fair coin 10 times, the number of heads that come up is described by a binomial distribution.
Now, let's talk about the cbind() function. cbind() is short for "column bind". It is used to combine vectors or matrices into a single matrix, where each input vector or matrix becomes a column in the final matrix.
In this exercise, we have created 7 vectors, each with a different success probability for a binomial distribution, ranging from 0.2 to 0.8. We will use cbind() to combine these vectors into a matrix called bin.matrix.
The dimension of the bin.matrix is
=> 300 x 7.
This means that the matrix has 300 rows and 7 columns. Each row represents a trial, and each column represents a different success probability. For example, the first column might represent a trial with a success probability of 0.2, while the second column might represent a trial with a success probability of 0.3, and so on.
By creating this matrix, we can easily perform statistical analyses on the data contained within it. We can calculate summary statistics, such as the mean and variance, for each column, or we can compare the distributions of the different columns to see if there are any significant differences between them.
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This scale drawing shows a reduction in a figure.
What is the value of x?
Enter your answer as a decimal in the box.
x =
Two rectangles of different sizes. The first rectangle has a longer side labeled 6.4 inches and a shorter side labeled 3.6 inches. The second rectangle has a longer side labeled 1.6 inches and a shorter side labeled x inches.
Answer: 0.9 is the answer hope I helped.
Step-by-step explanation:
The require value of side of rectangle(x) is equal to 0.9 in.
What is rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
According to question:We have;
length of longer side = 6.4 in and loneger side of small rectangle = 1.6 in.
Then,
Scale factor = 6.4/1.6 = 4
It means Sides of big rectangle is 4 times of small rectangle.
We also have smaller side of big rectangle = 3.6 in
3.6 = 4x
x = 3.6/4
x = 0.9
Thus, required value of x is 0.9 in.
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Evaluate sec2 (pi/5) - tan2 (pi/5).
The value of sec2(pi/5) - tan2(pi/5) is equals to 1.
What is trigonometric identity ?
A trigonometric identity is a mathematical equation that relates the values of trigonometric functions of an angle. These identities are true for all values of the angle for which both sides of the equation are defined.
We can use the trigonometric identities to simplify this expression. Recall that:
sec(x) = 1/cos(x)
tan(x) = sin(x)/cos(x)
sin2(x) + cos2(x) = 1
Using these identities, we can rewrite the expression as:
sec2(pi/5) - tan2(pi/5)
= (1/cos2(pi/5)) - (sin2(pi/5)/cos2(pi/5))
= (1 - sin2(pi/5))/cos2(pi/5)
= cos2(pi/5)/cos2(pi/5) (using the identity sin2(x) + cos2(x) = 1)
= 1
Therefore, sec2(pi/5) - tan2(pi/5) = 1.
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Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5, y=1,
and the y-axis about the line y=−2
.
The volume of the solid obtained by rotating the region in the first quadrant bounded by [tex]$y=x^5$[/tex], y = 1, and the y-axis about the line y = −2 is 29.0359321.
The region is bounded in the xy plane and is said to be bounded in between the curve, line and y-axis as given by
Curve: [tex]$y=x^5$[/tex]
Line: y = 1
y-axis: x = 0
The curve and line intersect at [tex]x^5=1[/tex] and x = 1
The region bounded can be expressed as
[tex]x^5 \leq y \leq 1 \\[/tex]
0 ≤ x ≤ 1
Here we have to determine the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5, y=1
Now if the solid is obtained by the rotation of the region about the line y = -2 then the volume of the solid is evaluated by the method of the rings/washers as
Volume [tex]$=\int_{\mathrm{a}}^{\mathrm{b}} \mathrm{A}(\mathrm{x}) \mathrm{dx}[/tex]
Volume [tex]$=\int_{\mathrm{a}}^{\mathrm{b}} \pi\left[\text { (outer radius) }^2-\text { (inner radius }^2\right] \mathrm{dx}[/tex]
Volume [tex]$=\pi \int_0^1\left[(1-(-5))^2-\left(x^5-(-5)\right)^2\right] d x[/tex]
Volume [tex]$=\pi \int_0^1\left[(1+5)^2-\left(x^5+5\right)^2\right] d x[/tex]
Volume [tex]$=\pi \int_0^1\left[(6)^2-\left(x^5+5\right)^2\right] \mathrm{d} x[/tex]
Volume = [tex]$\pi \int_0^1\left[(36)-\left(x^{10}+10 x^5+25\right)\right] d x$$[/tex]
Volume = [tex]$\pi \int_0^1\left(36-x^{10}-10 x^5-25\right) d x[/tex]
Volume [tex]$=\pi \int_0^1\left(11-x^{10}-10 x^5\right) d x[/tex]
Volume [tex]$=\pi\left[11 x-\frac{1}{11} x^{11}-10\left(\frac{x^6}{6}\right)\right]_0^1$$$$[/tex]
Volume [tex]$=\pi\left[11 x-\frac{1}{11} x^{11}-\frac{5}{3} x^6\right]_0^1$$$$[/tex]
Volume [tex]$=\pi\left(11(1-0)-\frac{1}{11}\left(1^{11}-0\right)-\frac{5}{3}\left(1^6-0\right)\right)[/tex]
Volume [tex]=\pi\left(11(1)-\frac{1}{11}(1)-\frac{5}{3}(1)\right)[/tex]
Volume [tex]=\pi\left(11-\frac{1}{11}-\frac{5}{3}\right)$$[/tex]
Volume = [tex]$\frac{305}{33} \pi[/tex]
Therefore the volume of the solid is
V [tex]=\frac{305}{33} \pi \approx[/tex] 29.0359321
Therefore the volume of the solid is 29.0359321
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y=2x-1 (2,3) (5,11)(-1,-3) determine which of the following points work for the given information algebraically
The law of sines states that the ratio of the ____ of an angle to the length of the side ________ that angle is ________ in any triangle.
The law of sines states that the ratio of the Sine of an angle to the length of the side opposite that angle is constant in any triangle.
The Law of Sines is defined as a relationship that applies to all triangles, not just right triangles.
The law states that the ratio of length of side of a triangle to sine of angle opposite that side is constant for all sides and angles in the triangle.
So , for any triangle, ratio of length of one side to the sine of angle opposite that side is = ratio of length of any other side to the sine of the angle opposite that side.
The Sine Law is also useful for solving problems which involves the angles and sides of triangles, especially when not all sides and angles are known.
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A new battery’s voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 90% of all batteries have acceptable voltages. Let Y denote the number of batteries that must be tested.
a. What is p(2), that isP ( Y = 2), ?
b. What is p(3)? [Hint: There are two different outcomes that result inY = 3 .]
c. To have Y=5, what must be true of the fifth battery selected? List the four outcomes for which Y= 5 and then determine p(5).
d. Use the pattern in your answers for parts (a)–(c) to obtain a general formula for p(y).
a) Probability, P(y = 2) = P(AA) is equals to the 0.81.
b) Probability, P(y = 3), is equals to the 0.162.
c) For P(y=5), 5ᵗʰ battery must be an A. four outcome for which Y= 5 , probability is equals to the 0.00324.
d) General formula for p(y) is P(y)= (y-1)(0.1)⁽ʸ⁻²⁾(0.9)².
A new battery’s voltage may be acceptable (A) or unacceptable (U). Assume that 90% of all batteries have acceptable voltages. So, probability of acceptance = 0.90 and
probability of unacceptance = 1 - 0.9 = 0.1
Let the number of batteries that must be tested be "Y". A particular flashlight requires two batteries, that is batteries will be independently selected.
a) For P(y = 2), both the batteries must be acceptable. Hence probability, P(y = 2)
= P(AA) = 0.90× 0.90 = 0.81
b)For P(y = 3 ) = P(AUA) + P(UAA)
=0.9× 0.1×0.9 + 0.1× 0.9× 0.9 = 0.162
C) For any(Y = n), nᵗʰ batterry should be acceptable, as search for two acceptable batteries will complete once second acceptable battery gets selected. Hence for P(y=5), 5ᵗʰ battery must be an A. four outcome for which Y
= 5 are (AUUUA) ,(UAUUA),(UUAUA),(UUUAA)
P(y=5) = P(AUUUA) + P(UAUUA) + P(UUAUA) + P(UUUAA)
= 4× 0.9² × 0.1³
= 0.00324
d) From above probabilities we conclude, the general formula for p(y) is p(y) =(y- 1)(0.1)⁽ʸ⁻²⁾(0.9)².
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11.9 A cube has edge lengths that are each 100 centimeters. What is the volume of
the cube?
A
B
1 cubic centimeter
1 cubic meter
100 cubic centimeters
100 cubic meters
The volume of the cube is 1 cubic meter.
Option B is the correct answer.
What is a cube?It is a polygon having six faces.
The volume of a cube is side³.
Example:
The volume of a cube of 3 cm in length is 27 cm³.
We have,
Side length = 100 cm
Now,
Volume.
= Side³
= 100³
= 1000000 cm³ _____(1)
Now,
1 m = 100 cm
1 m³ = 1000000 cm³ _____(2)
From (1) and (2),
Volume = 1 cubic meter.
Thus,
The volume of the cube is 1 cubic meter.
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A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failed beams are randomly selected and the type of failure is determined for each one. Let X = the number of beams among the three selected that failed by shear. List each outcome in the sample space for the original random experiment of selecting three failed beams and denoting the type of failure along with each outcome's associated value of x.
The probability of each outcome can be calculated using basic probability formulas, such as the multiplication rule and the addition rule is 1/2
Probability is the branch of mathematics that deals with the likelihood of events occurring. In this scenario, we are looking at the probability of a concrete beam failing by shear or flexure.
When three failed beams are randomly selected, the type of failure is determined for each one. We want to find the probability of each possible outcome, where X represents the number of beams among the three selected that failed by shear.
To list the outcomes in the sample space, we can use the following notation: S for shear failure and F for flexure failure. The possible outcomes are:
SSS, where all three beams failed by shear. In this case, X = 3.
SSF, where two beams failed by shear and one by flexure. In this case, X = 2.
SFS, where two beams failed by shear and one by flexure. In this case, X = 2.
FSS, where two beams failed by shear and one by flexure. In this case, X = 2.
SFF, where one beam failed by shear and two by flexure. In this case, X = 1.
FSF, where one beam failed by shear and two by flexure. In this case, X = 1.
FFS, where one beam failed by shear and two by flexure. In this case, X = 1.
FFF, where all three beams failed by flexure. In this case, X = 0.
Each outcome has a different value of X, which represents the number of beams that failed by shear.
Then the probability is calculated as,
=> 1/2
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in a sample of 28 cups of coffee at the local coffee shop, the temperatures were normally distributed with a mean of 182.5 degrees with a sample standard deviation of 14.1 degrees. what would be the 95% confidence interval for the temperature of your cup of coffee? homework help: 5ve. confidence intervals with sample standard deviation links to an external site.(1:37) group of answer choices (177.03, 187.97) (168.40, 196.60) (177.28, 187.72) (148.40, 176.60)
The Confidence interval starts at 177.28 and the Confidence interval ends at 187.72. Thus option c is correct.
The given data is as follows:
Number of coffee, N = 28
Mean, µ = 182.5
Standard deviation, α = 14.1
Confidence Level, CL = 95%
z-value for 95% confidence interval = 1.96
The confidence interval is calculated by using the formula,
Confidence interval = μ ± Ζ (α/√n )
Confidence interval = 182.5 ± 1.96*(14.1/√28)
Confidence interval = 182.5 ± 5.22
Confidence interval = (177.28, 187.72)
Therefore we can conclude that the Confidence interval starts at 177.28 and the Confidence interval ends at 187.72.
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Please tell me the answer and explain how
The value of x is 60.
We can use the fact that the opposite angles of a parallelogram are equal to find the value of x. Angle BCD is therefore equal to angle ABD, and angle CBD is equal to angle CAD.
Based on the given angles, we can construct two equations:
Angle ABD + angle CBD = 100 (because angle BCD = angle ABD) Angle ABD + angle ACD = 80 (because angle CAD = angle CBD)
When we substitute the given values, we get:
x + 40 = 100 x + 20 = 80
When we solve for x in both equations, we get:
x = 60 x = 60.
We can be confident that our answer is correct because both equations give us the same value for x. As a result, the value of x is 60.
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Please subtract and simplify.
Subtract (9x+8)-(3x + 5)
6x + 13
2x + 13
6x + 3
6x - 3
Answer:
The expression (9x+8)-(3x + 5) simplifies to 6x + 3. Therefore, the answer is option C: 6x + 3.
What is the area of this composite shape?
Enter your answer in the box.
in²
The combined area of the given figure will be 40 square inches.
What is an area?The area is defined as the space covered by the object in two-dimensional space.
The area of a rectangle with a length of 7 inches and a width of 5 inches is given by:
Area of rectangle = length x width = 7 in x 5 in = 35 square inches
The area of a triangle with a base of 5 inches and a height of 2 inches is given by:
Area of triangle = (1/2) x base x height = (1/2) x 5 in x 2 in = 5 square inches
Therefore, the combined area of the rectangle and triangle is:
35 square inches + 5 square inches = 40 square inches
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Please help me bro.
Answer:
b
Step-by-step explanation:
jaly has 241 times greater of gummys than deens who has 463 but jaly gave 50 away than recived 3542 write this in a sentence in fraction and decimal useing these fractions
6/2 and 4/8
WILL MARK AS BRAINLEST PLSSS HELP
This final result as a fractiοn and a decimal 115075 using the given fractiοns 6/2 and 4/8
What is fractiοn?A fractiοn is a mathematical representatiοn οf a part οf a whοle οr a ratiο between twο quantities. It is typically represented as a tοp number (numeratοr) divided by a bοttοm number (denοminatοr), separated by a hοrizοntal line.
Fοr example, the fractiοn 3/4 represents three parts οut οf fοur equal parts οf a whοle. The numeratοr (3) represents the number οf parts, while the denοminatοr (4) represents the tοtal number οf parts that make up the whοle.
Accοrding tο the questiοn:
Let's first find hοw many gummys Jaly has:
Jaly has 241 times greater number οf gummys than Deens, whο has 463. Sο Jaly has:241 x 463 = 111583 gummys Jaly then gave 50 away and received 3542 gummys.
Therefοre, the tοtal number οf gummy's Jaly nοw has is:111583 - 50 + 3542 = 115075We can express this final result as a fractiοn and a decimal using the given fractiοns 6/2 and 4/8.
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Emily parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded annually. What will be the total balance after 2 years?
(A) $1,314.08
(B) $2,385.72
(C) $3,273.50
(D) $1,757.71
Answer:(A) 1.314.08
Step-by-step explanation:
Inflation
in exercises 9 and 10, (a) for what values of h is v3 in span {v 1, v2}, and (b) for what values of h is {v 1, v2, v3 } linearly dependent? justify each answerV1 = (1 -3 2)V2 = (-3 9 6)V3 = (5 -7 h)
9. a)The required value of h is 4
9.b) The required value of h is 4
10.a)The required value of h is -6
10.b) They are linearly dependent for all values of h.
How to find the vector?Here the given vectors are:
v1 = [tex]\left[\begin{array}{ccc}1\\-3\\2&\end{array}\right][/tex]
v2 = [tex]\left[\begin{array}{ccc}-3\\10\\-6&\end{array}\right][/tex]
v3 = [tex]\left[\begin{array}{ccc}2\\-7\\h&\end{array}\right][/tex]
The vectors v1 and v2 are not scalar multiples of one another so they are not linearly dependent.
[tex]\left[\begin{array}{ccc}1&-3&2\\-3&10&-7\\2&-6&h\end{array}\right][/tex]= 0
1(10h -42) -3(-14 +3h) +2 (18-20) =0
10h -9h-4 =0
h = 4
Hence the value of h is 4 so that the vector v3 is in span{v1,v2}
b) The given vectors will be linearly dependent if h =4
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how do these each of these coefficients (a, b, c) theoretically relate to quantities position x, velocity v and acceleration a?
The coefficients (a, b, c) in a polynomial equation is relate to the position x, velocity v, and acceleration a of an object.
Position (x): The position of the object can be represented by the x-coordinate of its position in space. This can be related to the coefficients in the equation by setting the x-coordinate equal to x and solving for the corresponding y-coordinate.
Velocity (v): The velocity of an object is the rate at which its position is changing. This can be related to the coefficients in the equation by taking the first derivative of the equation with respect to time. The result is a linear equation that represents the velocity as a function of time.
Acceleration (a): The acceleration of an object is the rate at which its velocity is changing. This can be related to the coefficients in the equation by taking the second derivative of the equation with respect to time. The result is a constant value that represents the acceleration of the object.
In summary, the coefficients (a, b, c) can be related to the position, velocity, and acceleration in equation for x, taking derivatives of the equation with respect to time, and interpreting the results as the position, velocity, and acceleration of the object.
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Describe the translation needed to obtain the graph of g(x) = 7^x-4 from the graph of (x) = 7^x
The translation needed to obtain the graph of g(x) = 7^x-4 from the graph of (x) = 7^x is 4 units right
How to determine the translation from the functionFrom the question, we have the following parameters that can be used in our computation:
g(x) = 7^x-4
f(x) = 7^x
Using the above as a guide, we have the following:
g(x) = f(x - 4)
This represents a translation to the right by 4 units
Hence, the translation is 4 units right
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If f(x) = ln(x), what is the transformation that occurs if g(x) = ln(x + 2)
The transformation from ln ( x ) to ln ( x + 2 ) is horizontal transformation or shift.
What kinds of functions can be transformed?
Transformations can be divided into three categories: translations, reflections, and dilations. There are two types of transformations that can be done to a function: vertical (which affects the y-values) and horizontal (affects the x-values).
The four transformation variables are included in the equation of a function that is shown below (a, b, h, and k).
f(x) = ln(x)
if g(x) = ln(x + 2)
Then,
The transformation from ln(x) to ln(x+2) is horizontal transformation or shift. As 2 units are added in g(x) the function is horizontally shifted by 2 units in left-hand direction.
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Find the slope of the line that passes through each par of points(4,-4)(2-4)
pls help on these questions, im stuck on them. do 2-6 pls.
The area of each circle, to the nearest tenth is:
1. 19.6 cm²
2. 379.9 in.²
3. 28.3 mm²
4. 78.5 in.²
5. 132.7 cm²
6. 162.8 yd²
What is the Area of a Circle?The area of a circle is calculated as:
A = πr², where, r is the radius of the circle, and π is a constant.
1. r = 5/2 = 2.5 cm
Area = πr² = 3.14 * 2.5²
= 19.6 cm²
2. r = 11 in.
Area = πr² = 3.14 * 11²
= 379.9 in.²
3. r = 3 mm
Area = πr² = 3.14 * 3²
= 28.3 mm²
4. r = 10/2 = 5 in.
Area = πr² = 3.14 * 5²
= 78.5 in.²
5. r = 13/2 = 6.5 cm
Area = πr² = 3.14 * 6.5²
= 132.7 cm²
6. r = 7.2 yd
Area = πr² = 3.14 * 7.2²
= 162.8 yd²
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#7
An insect population after x months can be modeled by
the function g(x) = 11(1.2). Which statement is the
best interpretation of one of the values in this function?
The insect population increased by 12 insects each month
The insect population decreased by 12 insects each month
The insect population increased at a rate of 20% each month
The insect population decreased at a rate of 20% each
month
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