A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.
Define polynomial function.In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Given,
As stated, the polynomial's leading coefficient is equal to 1.
The function's zeroes are also listed as -2, 3, and 6.
For root 3: ( x - 3)
for root 6: (x - 6)
As a result, the polynomial function is
f = 1(x+2)(x-3)(x-6) (x-6)
f = (x+2)(x² - 6x - 3x + 18)
f = (x+2)(x² - 9x + 18)
f = x³ - 9x² + 18x + 2x² - 18x + 36
f = x³ - 7x² + 36
A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.
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sweet-fit jeans has a factory that makes two styles of jeans; super-fit and super-hug. each pair of super-fit takes 20 minutes to cut and 30 minutes to sew and finish. each pair of super-hug takes 20 minutes to cut and 55 minutes to sew and finish. the plant has enough workers to provide at most 18,999 minutes per day for cutting and at most 40,999 minutes per day for sewing and finishing. the profit on each pair of super-fit is $6.50 and
The profit earned per day is $6674.695 at point (449.93,500.02).
Let the number of pair of super-fit jeans = x
Let the number of pair of super-hug jeans = y
We know that x,y≥0.
Total time provided for cutting per day = 18,999 minutes
Total time provided for sewing and finishing per day = 40,999 minutes
Therefore, the inequalities are:
20x+20y ≤ 18,999
30x+55y ≤ 40,999
The shaded region is the feasible region and the point of intersection is (449.93,500.02).
The profit on Super-fit jeans = $6.50
The profit on super-hug jeans = $7.50
To maximise the profit in a day, we maximize z = (6.50 x x) + (7.50 x y)
The maximum profit is obtained at (449.93,500.02).
Therefore, z = (6.50 x 449.93) + (7.50 x 500.02)
z = 2924.545 + 3750.15
z = 6674.695
The profit earned per day is $6674.695.
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28. For any of the vehicles listed in the table,
how many days can you rent the vehicle
before it would be less expensive to rent
for the week?
Answer:
small car: 2
medium car: 2
luxury car: 2
Small van: 2
Large van: 3
Step-by-step explanation:
just multiply the amount per day by numbers increasing from 1 till you get a number that is larger than the week. I swear whoever made this car rental will not be in business much longer lol.
For 2 days, vehicle can be given to rent before it would be less expensive to rent.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
Given that,
Rent for small car,
For 1 day = $100.
For 1 week = $250
The maximum days in which small car could be given to rent,
= 250 / 100 = 2.5 ≅ 2 days.
Similarly, for medium car = 290 / 110 = 2.7 ≅ 2 days.
For luxury car = 325 / 120 = 2.54 ≅ 2 days.
For small van = 350 / 150 = 2.3 ≅ 2 days.
And for large can = 390 / 170 = 2.28 ≅ 2 days.
Each car can be rented for 2 days before it would be less expensive for the week.
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find the arc length?
The length of the Arc of the circle is 17.00 units
How to find the length of arc?We should know that the arc of the circle is part of the circumference of the circle cut off by the radii of the circle.
The length of the arc is given by
L=[tex]\frac{A}{360} *2*\pi *r[/tex] where A= angle made by the radii
[tex]\pi[/tex]=3.14, radius =10, L-length of arc = x
Applying the values in the formula we have
x=(x/3*2*3.14*10)÷360
Simplifying the expression
62.8x=1080x
Taking the ratio of both sides we have
62.8x:1080x
= 17.00 units
Therefore the length of the arc is 17.00 units
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-3x^2-6x+24 factor this equation by any means
Step-by-step explanation:
-3x² - 6x + 24
this is an expression, not an equation.
for an equation this would have to look like e.g.
-3x² - 6x + 24 = 0
anyway, yes, we can factor this expression :
-3x² - 6x + 24 = -3(x² + 2x - 8) = -3(x + 4)(x - 2)
why ?
x² + 2x - 8 corresponds to
(x + a)(x + b) = x² + (a+b)x + ab
so which factors a and b multiply to ab = -8 and add to (a+b) = 2 ?
-8 has the factors
4, -2
-4, 2
8, -1
-8, 1
only (4, -2) covers the both criteria.
therefore, the correct factorization is
-3(x + 4)(x - 2)
use the factor theorem to determine whether is a factor of . specifically, evaluate at the proper value, and then determine whether is a factor.
According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
The factor theorem states
[tex]$(x-a)$ is a factor of $f(x) \Leftrightarrow f(a)=0$[/tex]
f(x)=4 x^3-3 x^2-8 x+4
we have (x-2)[tex]\Rightarrow a=2[/tex]
& [tex]f(2)=4 \times 2^3-3 \times 2^2-8 \times 2+4 \\& f(2)=4 \times 8-3 \times 4-16+4 \\& f(2)=32-12-16+4 \\& f(2)=8 \neq 0\end{aligned}[/tex]
[tex]$\therefore x-2$ is not a factor of $4 x^3-3 x^2-8 x+4$[/tex]
however by the remainder theorem when
[tex]$f(x)=4 x^3-3 x^2-8 x+4$[/tex] is divided by [tex]$(x-2)$[/tex] the remainder is 8
the factor theorem being a special case of the remainder theorem
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Answer:
Step-by-step explanation:
Use the factor Theorem to determine whether x =3 is a factor of P (x)=x-2x2-6. Specifically, evaluate P at the proper value, and then determine whether X-3 is a factor. P (UI) - 0 P 0 1 - 3 is a factor of P (*) O +- 3 is not a factor of P (x) This problem has been solved!
A box starts with 2 balls: 1 black and 1 white. We draw one of these balls uniformly at random, then replace it with 2 of the same color (so that the box will have 3 balls now). The process repeats. For each i = 1,2,3,..., let X; = 1 if we draw a white ball on trial i. You may use any property of the X;'s to help you answer the following questions, you just have to name the property you are using and how you are using it. Compute the...(a) probability that X, = 1. How about probability that X, = 1 instead? (b) probability that X, = 1 given X, = 1. (c) probability that in the first 4 trials you get (at least) three white balls in a row. (d) expected value of the number of white balls in 4 trials. (e) variance of the number of white balls in 4 trials.
(a) The probability that X, = 1 will be =1/2
(b) The probability that X, = 1 given X,= 1 will be =2/3
(c) The probability that in the first 4 trials you get (at least) three white balls in a row will be=2/5
(d) The expected value of the number of white balls in 4 trials will be=2
(e) The variance of the number of white balls in 4 trials will be=2
A box starts with 2 balls; [ black and 1 white, x draw on these balls are supposed to be uniformly at random then we will replace it with 2 of the same colour. The Process repeats for Each i=1,2,3..........
Let x_1=1, if we draw a white ball on trial 1
The Property of the x_1 is
The Event where The drawn fall is white =A
Let the number of white balls in 4 trials is denoted by 'x'.
[tex]P(x=0) P\left(A^c A^c A^c A^c\right) . \\=1 / 2 \times 3 / 3 \times 3 / 4 \times 4 / 5=1 / 5 . \\P(x-1)=P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right) \\=1 / 2 \times 1 / 3 \times 1 / 4 \times 3 / 5+1 / 4 \times 1 / 3 \times 2 / 3 \times 3 / 5+1 / 2 \times 2 / 3 \times 1 / 4 \times 3 / 5+1 / 2 \times 2 / 3^2 \times 3 / 4 \times 1 / 5 . \\=\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20} . \\=4 \times \frac{1}{20}=1 / 5 . \\[/tex]
[tex]\therefore P(x=2)=1 / 2 \times 2 / 3 \times 1 / 4 \times 2 / 5 \times 4 / 2=6 \times 1 / 3=1 / 5 .[/tex]
[tex]$\begin{aligned} \therefore P(x=2) & =1 / 2 \times 2 / 3 \times 1 / 4 \times 2 / 5 \times 4 / 2=6 \times 1 / 3=1 / 5 . \\ P(x=3) & =1 / 2 \times 2 / 3 \times 3 / 4 \times 1 / 5 \times 4 / 3 . \\ & =1 / 20 \times 4=1 / 5 . \\ P(x=4) & =1 / 2 \times 2 / 3 \times 2 / 4 \times 4 / 5=P(\text { AAAA })=1 / 5 .\end{aligned}$[/tex]
(a)
[tex]P\left(X_2=1\right) & =P(A A)+P\left(A^C A\right) . \\& =1 / 2 \times 2 / 3 \times 1 / 2 \times 1 / 3 . \\& =2 / 6+1 / 6=3 / 6=1 / 2 . \\P\left(X_4=1\right)= & P(A A A)+P\left(A A A A^{\prime} A\right)+P\left(A^C A A\right)+P\left(A^{\prime} A^{\prime} A\right)+P \\& \left.\quad\left(A^{\prime} A A A\right)+P\left(A^{\prime} A^{\prime} A\right)+P\left(A^A A A\right)\right) \\[/tex]
[tex]= & 1 / 5+1 / 20+1 / 20+1 / 20+1 / 20+1 / 30+1 / 30+1 / 20 . \\= & 1 / 5+4 / 20+3 / 20 .=2 / 5+1 / 10 . \\= & \frac{4+1}{10}=5 / 10=1 / 2 .[/tex]
[tex]$\therefore$[/tex] Probability that x_2=1 is equal with probability that x_4 >1
(b) Probability that x_2=1 given x_4=1
[tex]$$\begin{aligned}& =P\left(x_2=1 / x_{4=1}\right)=\frac{P\left(x_2=1 \& x_4=1\right)}{P\left(x_4=1\right) .} \\& =\frac{P(A A A A)+P\left(A A A^{\prime} A\right)+P(A A A A)+P\left(A^C A A^C A\right)}{1 / 2} \\& =2 \times(1 / 5+1 / 20+1 / 20+1 / 30] \\& =2 \times[1 / 5+1 / 10 \times 1 / 30] \\& =2 \lambda\left[\frac{6+30+1}{30}\right] \\& =2 \times \frac{10}{30} .=2 / \mathrm{3} .\end{aligned}$$[/tex]
(c) Probability that in that the nuts is 3 which is P(x=3)+P(x=4) is [tex]=1 / 5+1 / 5=2 / 5[/tex]
(d) Expected volume of number of white ball is 4 trial is,
[tex]$$\begin{gathered}{[0 \times 1 / 5+1 \times 1 / 5+2 \times 1 / 5+3 \times 1 / 5+3 \times 1 / 5+4 \times 1 / 5]} \\=\frac{1+2+3+4}{5}=10 / 5=2 .\end{gathered}$$[/tex]
(e)
[tex]E\left(x^2\right) & =0^2 \times 1 / 5+1^2 \times 1 / 5+2^2 \times 1 / 5+3^2 \times 1 / 5 .+4^2+1 / 5 . \\& =\frac{1+4+9+16}{5 .} \\& =30 / 51=6 . \\\therefore var/x =E\left(x^2\right)-E[(x)]^2 . \\& =6-2^2 =6-4=2[/tex]
[tex]$\therefore$[/tex] The variance of the number of white balls in 4 trails =2
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Linear function k has a zero at 3 and a y-intercept of 9 . Which graph best represents k ?
In the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.
In the given question, linear function k has a zero at 3 and a y-intercept of 9.
We have to choose which graph best represents k.
As we know that;
The link between the two unknown variables is represented by a linear equation. The linear equation have one degree.
The most basic linear equation demonstrates the relationship between (x,y), which can be used to create a table, a graph on the coordinate plane, or to perform an assessment at a particular x or y value.
We represent linear function in the form of y=mx+c.
where m is the slope of the line, c is the y intercept of the line, x is independent variable and y is the dependent variable.
As we see the y intercept in the graph crosses the y axis.
Here y intercept is 9.
The zeros of the linear function is that where y value is zero.
As in the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.
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the ration of hugs to kisses at the family reunion was 4:1 if there were 148 hugs how many kisses were there
There were 37 kisses at the family reunion. Probability is used to make predictions and inform decision-making.
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.
To find the number of kisses at the family reunion, you can set up the ratio 4 hugs : 1 kiss as a proportion and solve for the number of kisses. Here's how you can do this:
First, cross-multiply to find the total number of hugs and kisses:
4 hugs * 1 kiss = 148 hugs
4 kisses = 148 hugs
Then, divide both sides of the equation by 4 to find the number of kisses:
4 kisses / 4 = 148 hugs / 4
1 kiss = 37 hugs
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Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers.
f(x)=sqrt(x)+8 , g(x)=x^2+1
f(g(x))=
g(f(x))=
The solution to the given composite functions are;
f(g(x)) = √(x² + 1) + 8
g(f(x)) = [√(x) + 8]² + 1
How to solve composite functions?
Composite functions are usually formed when one function is used as the input of another function.
We are given the functions;
f(x) = √(x) + 8
g(x) = x² + 1
1) f(g(x)); This simply means we will put the entire g(x) function for x in f(x) to get;
f(g(x)) = √(x² + 1) + 8
2) g(f(x)); This simply means we will put the entire f(x) function for x in g(x) to get; g(f(x)) = [√(x) + 8]² + 1
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help meeeee last question
The number of cubical boxes that can contain in the rectangular box is 36.
What is the volume of a cuboid?Volume is defined as the space occupied by an object.
The volume of a cuboid is (length×width×height).
Given, Length of the rectangle box is 16 cm and the width of the box is
12 cm.
We know the volume of a cube is (side)³.
Therefore, given that the volume of a cubical 64 cm³ and we know (4)³ is 64.
Hence the height of the rectangular box is 3 layers so (4×3) = 12 cm
So, the volume of the rectangular box is (16×12×12) cm³ = 2304 cm³.
Therefore, The maximum number of boxes that can be contained is
= (2304/64)
= 36.
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write an equation of the line that is parallel to the graph of 3x-5=y and whose y intercept is (0,7).
Parallel lines always have the same slope and different y-intercepts.
Slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptSolving the QuestionWe're given:
[tex]3x-5=y[/tex]b = (0,7)We can see that in [tex]y=3x-5[/tex] that the slope of the line is 3. Parallel lines have the same slope, so therefore:
m = 3
We're also given that the y-intercept is (0,7).
b = 7
Plug m and b into slope-intercept form:
[tex]y=3x+7[/tex]
Answer[tex]y=3x+7[/tex]
Last year the depth of the river was 4.2 feet deep. This year it dropped 24%. Find the depth of the river this year to cross it.
The depth of the river is 3.192 feet.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Since last year the depth of the river was 4.2 feet deep and year it dropped 24%. The depth will be:
= 4.2 - (24% × 4.2)
= 4.2 - 1.008
= 3.192 feet
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an fda representative randomly selects 8 packages of ground chuck from a grocery store and measures the fat content (as a percent) of each package. assume that the fat contents have an approximately normal distribution. the resulting measurements are given below.fat contents (%)12 15 16 1315 13 15 13step 1 of 2 : calculate the sample mean and the sample standard deviation of the fat contents. round your answers to two decimal places, if necessary.
We calculated sample mean 14 and standard deviation 1.32
What is sample mean?A sample mean refers to the average of all values included in the data list.
How to calculate sample mean and standard deviation from the list of data?When we have a list of data set, we can calculate the mean value of the data set by adding all the values and divided by the amount of data.
We are given, 8 packages of ground chuck
number of samples, N = 8
fat contents (%) for 8 packages, X= 12, 15, 16, 13, 15, 13, 15, 13
Sum of X= ∑X= 112
sample mean= sum of all data values/ number of data items in the sample
X= ∑X/N
sample mean X = 112/8 =14
we calculate X² for 8 sample = 144, 225, 256, 169, 225, 169, 225, 169
∑X² = 1582
standard deviation is calculated by using the formula bellow
√[∑X²/N-(∑X/N)²] = √[1582/8-(112/8)²]
standard deviation = 1.32
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Match the inequality on the left with the appropriate graph on the right
Answer:
i got the last two but i am confused on the first two
Step-by-step explanation:
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The price of an item has been reduced by 95%. The original price was $65
The new price of the item is equivalent to $3.25.
What is percentage?In mathematics, a percentage is a number or ratio that represents a fraction of 100. A percentage is a dimensionless number i.e. it has no unit of measurement.Given is that the price of an item has been reduced by 95%. The original price was $65
Assume the new price to be $[x]. So, we can write -
x = 65 - {95% of 65}
x = 65 - {(95/100) x 65}
x = 65 - {6175/100}
x = 65 - 61.75
x = 3.25
Therefore, the new price of the item is equivalent to $3.25.
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displayed the factor tree on the board. complete the factor tree to find the number that has a prime factorization of 2(4) x 2
Answer: 2
Step-by-step explanation:
If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows from this?
answer choices
O If you flip three coins 1000 times, you will get three heads exactly 125 times.
O If you flip 3 coins 10 times and never get three heads, the probability of getting three heads in the next set of 10 flips is slightly greater than 0.125.
O If you have 20 sets of three coin flips, then at least one set of flips will be three heads.
O If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
O If you get 3 heads two times in a row, the probability of getting 3 heads again on the next toss of 3 coins is nearly zero.
Using the given provided probability value of getting three heads, The statement which best follow the given condition is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close to 12.5%.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
According to the given question:
Assume you have a fair coin, which means it will likely land tails up 50% of the time and heads up 50% of the time. Let's say you flip it three times, each time independently. What is the likelihood that it will land heads up first, followed by a tails up landing?
The solution is 1/8, or 12.5%.
coin flipped = 3 times.
probability of getting three heads = 0.125
Since, This probability explains the chances of landing three heads which is 0.125 which in terms of percentage is 12.5% .
So, The statement is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
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F.ds = 4 pi, F.ds = 9 pi Use Green's Theorem to determine the circulation of F around C1, assuming that curl (F) = 2 on the shaded region. F. ds =
F.ds = 4 pi, F.ds = 9 pi
circulation of F around C1, assuming that curl (F) = 2 on the shaded region. F. ds =
c1-9 (52-12-12) π+9л+4л=(207+12)л=219л
Green's Theorem =Green's Theorem states that a line integral around the boundary of the plane region D can be computed as the double integral over the region D. where the path integral is traversed anti-clockwise. Green's Theorem Area
Therefore, the line integral defined by Green's theorem gives the area of the closed curve. Therefore, we can write the area formulas as: A = − ∫ c y d x. A = ∫ c x d y. Green's theorem relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C. The theorem is useful because it allows us to translate difficult line integrals into more simple double integrals, or difficult double integrals into more simple line integrals.
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Find the length of the triangle.
The height of the triangle that has an area of 7 ⁷/₈ square cm will be 3 cm.
What is the area of the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Assume 'h' is the height of the triangle and 'b' be the base of the triangle.
Then the area of the triangle is given as,
A = (1/2) × h·b
The area of the triangle is 7 ⁷/₈ cm² and the base length of the triangle is 5 ¹/₄ cm.
Convert the mixed fraction number into a fraction number. Then we have
7 ⁷/₈ = 63/8
5 ¹/₄ = 21/4
The height of the triangle is given as,
63/8 = (1/2) x h x (21/4)
Simplify the equation, then we have
63/8 = (1/2) x h x (21/4)
63/8 = (21/8)h
21h = 63
h = 3 cm
The height of the triangle that has an area of 7 ⁷/₈ square cm will be 3 cm.
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in non-degenerate cases of the logistic regression model, the maximum likelihood estimator always exists and is always unique. assume the design matrix is of full rank.
For regression and classification predictive modeling, the Maximum Likelihood Estimation framework can be used as a foundation for estimating the parameters of numerous machine learning models.
The logistic regression model is a part of this.
Is MLE always present?For species distribution models, maximum likelihood is a common parameter estimation method. A popular species distribution model, the Poisson point process, does not always have maximum likelihood estimates.
In logistic regression, how is the maximum likelihood determined?At the end of the day, the most extreme probability gauge for p is the mean of the y variable from the N draws. According to the result, p=n1/N=y is the value of p that maximizes the above log-likelihood function.
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tara has 5/8 gallons of glue. She uses 2/5 of the glue to make blue slime, 1/5 of the glue to make green slime, and the rest of the glue to make purple slime. How many gallons of glue does tara use to make purple slime
Answer:
We can say that he used a total of 5/8 gallons of glue
let x - glue to make purple slime
5/8 = 2/5 + 1/5 + x
5/8 = 3/5 + x (LCD of 5 and 8 is 40)
25/40 = 24/40 + x
25/40 - 24/40 = 24/40 - 24/40 + x (subtract 24/40 both sides)
x = 1/40
CHECKING:
5/8 = 2/5 + 1/5 + 1/40
5/8 = 3/5 + 1/40
25/40 = 24/40 + 1/40
25/40 = 25/40
Therefore, the glue to make purple slime is 1/40 gallons.
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Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Please help will mark Brainly
Answer:
120 children
Step-by-step explanation:
c=children
a=adults
c+a=237
1.75c+2a=444
(c+a=237)*2 ==> make a in the equation equal to 2a
2c+2a=474
- (1.75c+2a=444) ==> eliminate a from the equation
2c-1.75c + 2a-2a = 474-444
2.00c-1.75c = 30
0.25c = 30
4 * 0.25c = 4 * 30 ==> remove decimals by multiplying each side by 4
c = 120 children
Let Sn be the number of lattice paths in the Cartesian plane that start at (0,0), end at (n,n), contain no points above the line y = x, and are composed only of steps (0, 1), (1,0), and (1, 1), i.e. 1, +, and /. So = 1. Consider the generating function S(x):=∑_(n=0)^[infinity]▒〖SnX^n〗. Prove that 1 + (x – 1)S(x) + xS(x)2 = 0.
A formal power series that encodes the coefficients of a sequence of numbers is a generating function.
Here, the coefficients of the sequence {Sₙ} are encoded by the generating function S(x). where Sₙ is the number of lattice paths as described above.
Here we will use the fact that the generating function for a sequence satisfies a functional equation that relates the generating function to the sequence itself to prove that 1 + (x – 1)S(x) + xS(x)² = 0,
Here, the functional equation is
S(x) = 1 + xS(x) + xS(x)²
This equation implies that
The term 1 on the right-hand side corresponds to the fact that to reach the point (0,0) (the starting point), there is exactly one way which is to stay at the starting point.
The term xS(x) corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-1, n-1) we can reach any point (n,n)
The term xS(x)² corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-2, n-2), and then taking another step in the positive x-direction and following a path to (n-1, n-1) we can reach any point (n,n)
Thus, 1 + (x – 1)S(x) + xS(x)² = 0. Hence proved.
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Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. y = 12+ 1.8x n=17 SSR = 225 SSE = 75 S_01 = 0.2683 Refer to Exhibit 12-3. The t statistic for testing the significance of the slope is a. 1.96 b. 0.555 c. 6.709 d. 1.80
The t statistic used to determine whether the slope is significant is 6.709 when applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).
Given that,
The following information was discovered after applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).
y=12+1.8x
n=17
SSR=225
SSE=75
S₀₁=0.2683
We have to find what is the t statistic used to determine whether the slope is significant.
We know that,
Given by, the t test is used to determine whether the slope is significant.
t= b1/s.e
Where b1= slope of the given regression line
s.e= standard error of the line ( Sb1)= 0.2683
The regression line is given by
Y=12+1.8X
X is the independent variable here, and Y is the dependent variable.
Intercept = 12
Slope = 1.8
The t test is used to determine whether the slope is significant.
t= b1/s.e=1.8/0.2683= 6.7089=6.709
Therefore, The t statistic used to determine whether the slope is significant is 6.709 when applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).
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Consider the following statement. (Assume that all sets are subsets of a universal set U.)
For all sets A, B, and C, if A ⊆ B and B ∩ C = ∅ then A ∩ C = ∅.
Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set.
Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C.
Then (A ∩ C)c = U.
Hence x ∈ B ∩ C by definition of intersection.
Then by definition of intersection and complement A = U.
By definition of intersection x ∈ A and x ∈ C.
Therefore A ⊈ B.
Thus B ∩ C ≠∅ by definition of ∅.
Proof by contradiction:
Suppose that there exists sets A, B, and C such that A ⊆ B, and B ∩ C = ∅ and A ∩ C ≠∅. Then there exists an element x such that x ∈ A ∩ C.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠∅ by definition of ∅.
---Select--- Then x ∈ B because A ⊆ B. In addition, we know that x ∈ C. Then (A ∩ C)ᶜ = U. Hence x ∈ B ∩ C by definition of intersection. Then by definition of intersection and complement A = U. By definition of intersection x ∈ A and x ∈ C. Therefore A ⊈ B. Thus B ∩ C ≠∅ by definition of ∅.
But this contradicts the supposition. Hence the supposition is false, and so A ∩ C = ∅.
The correct order of the given statements is- 1, 2, 3, 4, 5, 6, followed by 7.
Here, we are given the following statement-
For all sets A, B and C if A ≤ B and B∩C = Φ
then A∩C = Ф
We can use the proof-by-contradiction method to prove the given statement as shown below-
Suppose that there exist 3 sets, that are- A, B, and C
Such that A ≤ B, B∩C = Φ
and A∩C ≠ Φ
Then, there must exist an element x such that x ∈ A∩C
Now, by the definition of intersection, we have- x ∈ A and x ∈ C
Then x ∈ B because A ≤ B. Additionally, we know that x ∈ C
Hence, by the definition of intersection, x ∈ B∩C
Thus, B∩C ≠ Φ by definition of null set (Φ)
But this contradicts the supposition. Hence, our assumption is false and so A∩C = Ф.
The correct order of the given statements is- 1, 2, 3, 4, 5, 6, followed by 7.
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Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50. How many dimes are in his collection? How many nickels are in his collection?
Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50. We can infer that he has 60 nickels and 35 dimes.
Define equation.In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.
Given,
Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50.
Set d and n to the appropriate numbers.
Timmy has 95 coins in total, all of which are dimes and nickels, as far as we know.
Equation,
So d + n = 95
His bank is worth a total of $6.50.
A nickel is worth $0.05, while a dime is worth $0.10.
So
0.10d + 0.05n = $6.50
Take note that we have just produced an equation system that we can solve.
The two equations exist.
D + n = 95
and
0.10d + 0.05n = 6.50.
The replacement approach is probably going to be the simplest way to solve this problem out of all the options available to us.
First, we'll want to change the second equation's terms so that one of the variables is defined.
d+ n = 95
Take d off on both sides.
n = 95 - d
Now, let's define "n."
After defining one of the variables, we can now enter (or replace) its value in the other equation. After replacing it, we can find a solution for the other variable.
0.10d + 0.05n = 6.50
n = 95 - d
0.10d + 0.05(95 - d) = 6.50
We now determine d.
0.10d + 0.05(95 - d) = 6.50
distribution of the 0.05 in step 1
0.05 × 95 = 4.75
and
0.05 × -d = -0.05d
0.10d + 4.75 - 0.05d = 6.50
Step 2: Add like terms together (0.10 - 0.05) to get 0.05
0.05d + 4.75 = 6.50
step 3: Take 4.75 off of each side.
0.05d = 1.75
step 4: Subtract 0.05 from both sides.
0.05d / 0.05 = d and 1.75 / 0.05 = 35
d = 35
Now that we know the value of one variable, we can use it to solve for the second variable by plugging it into one of the equations ( note that the equation that we use does not matter, we will acquire the same answer )
d + n = 95
d = 35
35 + n = 95
Take 35 off both sides.
n = 60
We can infer that he has 60 nickels and 35 dimes.
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A marina is in the shape of a coordinate grid. Boat A is docked at (4.2, −2) and Boat B is docked at (−5.2, −2). The boats are ____ units apart. (3 points)
6.2
7.2
9.4
13.4
Answer:
so (-5.2,-2) and (4.2,-2) are 9.4 units apart away from each other
Step-by-step explanation:
so (4.2,-2) and (-5.2,-2) add together and get 9.4
You bought 12 red apples and 15 green apples to make some pies.
What is the ratio of the number of red apples to the total number of apples?
Answer:
4.9
Step-by-step explanation:
Review of logarithms (logs)
For each of the following equations, write down the
name of the operation that occurs in the equation and
the name of the inverse operation that helps you
solve the equation.
Equation
x+10=25
2x=28
4²=64
Name of operation
Name of inverse
operation
The operations, along with their inverses are given as follows:
x + 10 = 25: Operation of addition, the inverse is of subtraction.2x = 28: Operation of multiplication, the inverse is the division.4^x = 64: The operation is the exponential, the inverse is the logarithm.How to solve the operations?The operations are solved applying the inverse operations.
The first operation is solved as follows:
x + 10 = 25
x = 25 - 10
x = 15.
Hence the addition operation was solved applying the subtraction operation, which is the inverse operation of the addition.
The second operation is solved as follows:
2x = 28
x = 28/2
x = 14.
Hence the multiplication operation was solved applying the division operation, which is the inverse operation of the multiplication.
The third operation is given as follows:
4^x = 64.
log4(4^x) = log4(64)
x = 3. (as 4³ = 64, hence log4(64) = 3).
Hence the exponential operation was solved applying the logarithm operation, which is the inverse operation of the exponential.
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Aid!! It's for today
Using theory about stereotypes and different associated thoughts, we have to:
''A girl who has a boy-friend cannot have frie-nds'', this affe-cts us because the thought promotes restrictions on the freedoms of a woman when she has a boy-friend. ''A boy should not show his affection or be tender'', this affects us because it is a thought that promotes stereotypes that do not allow the proper development of people. ¿What is a stereotype?A stereotype, basically, can be defined as an idea that is already pre-established and accepted, it is applied to different individuals.
¡Hope this helped!