Answer:
A. True
Step-by-step explanation:
Stepwise regression is a variable-selection method for independent variables.
Stepwise regression helps us to recognize and choose the most handy descriptive variables from a list of several reasonable independent variables.
It entails a series of steps that is drafted to locate the most handy X-variable to incorporate in a regression model. During each step of the course of action or method, each X - variable is estimated by applying a set criterion to determine if it is meant to exist in the model.
The basis for selection can be choosing a variable which satisfies the stipulated criterion or removing a variable that least satisfies the criterion. A typical illustration of such criterion is the t value.
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
Heidi bought a machine that throws tennis balls for her dog to fetch. The height of each ball thrown by the machine, in feet, is modeled by the function f(x) = –x2 + x + 2, where x represents time in seconds. How many seconds after the machine throws the ball does it hit the ground?
Answer:
2 seconds
Step-by-step explanation:
Given the equation:
[tex]f(x) = -x^2 + x + 2[/tex]
Where f(x) represents the height of each ball thrown by machine.
and x represents the time in seconds.
To find:
The number of seconds after which the machine throws the balls hits the ground = ?
Solution:
In other words, we have to find the value of [tex]x[/tex] after which the [tex]f(x) = 0[/tex]
(Because when the ball hits the ground, the height becomes 0).
Let us put [tex]f(x) = 0[/tex] and solve for [tex]x[/tex]
[tex]f(x) = -x^2 + x + 2 =0\\\Rightarrow -x^2 + x + 2 =0\\\Rightarrow x^2 - x - 2 =0\\\Rightarrow x^2 - 2x+x - 2 =0\\\Rightarrow x(x - 2)+1(x - 2) =0\\\Rightarrow (x+1)(x - 2) =0\\\Rightarrow x =-1, 2[/tex]
[tex]x=-1[/tex] sec is not a valid answer because time can not be negative.
So, the answer is after 2 seconds, the ball hits the ground.
What is f(0) given f(x) = 5(x + 2)2 – 10?
Answer:
10
Step-by-step explanation:
f(o) is given when x= 0 in f(x)
f(0) = 5 ( 0 + 2 ) 2 - 10
= 20 - 10
= 10
Answer:
[tex] \boxed{ \bold{ \huge{ \sf{f{(0) = 10}}}}}[/tex]
Step-by-step explanation:
Given, f ( x ) = 5 ( x + 2 )² - 10
Let's find f ( 0 ) :
[tex] \sf{f(0) = 5( {0 + 2)}^{2} - 10}[/tex]
Add the numbers
⇒[tex] \sf{f(0) = 5( {2)}^{2} - 10}[/tex]
Evaluate the power
⇒[tex] \sf{f(0) = 5 \times 4 - 10}[/tex]
Multiply the numbers
⇒[tex] \sf{ 20 - 10}[/tex]
Subtract 10 from 20
⇒[tex] \sf{10}[/tex]
Hope I helped !
Best regards !!
According to the Empirical Rule, 99.7% of scores in a normal distribution fall within 2 standard deviations of the mean.
a. True
b. False
Answer:
False
Step-by-step explanation:
Here, we want to check the validity of the given statement. The statement is false.
Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.
Please check attachment for diagrammatic representation of the empirical rule.
8. (01.02)
Given that f(x) = x2 + 2x + 3 and g(x)
X+4.
3
solve for f(g(x)) when x = 2.
2
5
11
33
Answer:
51.
Step-by-step explanation:
f(x) = x^2 + 2x + 3 and g(x) = x + 4.
f(g(x)) = (x + 4)^2 + 2(x + 4) + 3
= x^2 + 4x + 4x + 16 + 2x + 8 + 3
= x^2 + 8x + 16 + 2x + 11
= x^2 + 10x + 27.
x = 2.
f(g(2)) = 2^2 + 10 * 2 + 27
= 4 + 20 + 27
= 31 + 20
= 51.
Hope this helps!
Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 + 4xy − 48y2 = 2(x + By)(x − 4y)
Answer:
B = 6
Step-by-step explanation:
2x^2 + 4xy − 48y^2
Factor out 2
2(x^2 + 2xy − 24y^2)
What 2 numbers multiply to -24 and add to 2
-4 *6 = -24
-4+6 = 2
2 ( x+6y)( x-4y)
Answer:
[tex]\huge\boxed{B=6}[/tex]
Step-by-step explanation:
They are two way to solution.
METHOD 1:Factor the polynomial on the left side of the equation:
[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]
Therefore:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]
METHOD 2:Multiply everything on the right side of the equation using the distributive property and FOIL:
[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]
Compare polynomials:
[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]
From here we have two equations:
[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]
[tex]1)\\2B-8=4[/tex] add 8 to both sides
[tex]2B=12[/tex] divide both sides by 2
[tex]B=6[/tex]
[tex]2)\\-8B=-48[/tex] divide both sides by (-8)
[tex]B=6[/tex]
The results are the same. Therefore B = 6.
Please help. I’ll mark you as brainliest if correct! Thank you
Answer:
8 pounds of cheaper candy,
17.5 pounds of expensive candy
Step-by-step explanation:
Let's define some variables. Let's say the amount of pounds of candy that sells for $2.20/lb is x, and the $7.30 is y. Now we can write some equations!
x + y = 25.5
[tex]\frac{2.2x + 7.3y}{25.5} = 5.7[/tex]
We can start substitution. We can say that x = 25.5 - y. Plugging this into our second equation, we get:
y = 17.5
Plugging this in, we find that:
x = 8.
Kevin's total payroll deductions are 30% of his earnings. If his deductions add up to $369 for a two week period, how much were his earnings for the period?
Answer:
His earnings for the period= $123
Step-by-step explanation:
Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.
If 30% of his earnings = $369
His earnings = x
30/100 * x= 369
X= 369*100/30
X= 123*10
X=$ 1230
His earnings for the period= $123
A 160-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top
Weight of man and paint = 160 + 5 = 165 total pounds.
Gravitational force is independent of the path taken so we can ignore the radius of the silo.
Work done = total weight x height
The problem says he climbs to the top so overall height is 90 feet
Work = 165 lbs x 90 ft = 14,850 ft-lbs
Assume a random sample of size n is from a normal population. Assume a single sample t test is used to for hypothesis testing. The null hypothesis is that the population mean is zero versus the alternative hypothesis that it is not zero. If the sample size is decreased, and the Type I error rate is unchanged, then the Type II error rate will increase.a. Trueb. False
Answer:
true
Step-by-step explanation:
type 1 and type 2 are not independent of each other - as one increases, the other decreases
What is 2 cm converted to feet?
Answer:
0.065617 ft
Step-by-step explanation:
Answer:
0.0656168 feet.
Step-by-step explanation:
Which system of linear inequalities has the point (3, –2) in its solution set?
Answer:
see below
Step-by-step explanation:
We want where both inequalities are true
y > -3
-2 >-3 this is true
y ≥ 2/3x -4
-2≥ 2/3*3 -4
-2 ≥ 2 -4
-2≥ -2
This is true
This is is the graph
Answer:
[tex]\boxed{\sf Option \ 3}[/tex]
Step-by-step explanation:
[tex]\sf The \ values \ must \ be \ true \ for \ both \ inequalities.[/tex]
[tex]x = 3\\y = -2[/tex]
[tex]y>-3\\-2>-3\\ \sf True[/tex]
[tex]y\geq \frac{2}{3}x-4 \\ -2\geq \frac{2}{3}(3)-4\\2\geq 2-4\\-2\geq-2 \\ \sf True[/tex]
Raul tried to evaluate an expression step by step.
Answer:
(B) Step 2
Step-by-step explanation:
In step 2, Raul should have had one of these results:
8 -7 . . . . according to the order of operations
or
3 -2 . . . . properly adding 5 -7
Raul's step 2 is not either of these (or 5-4), so is incorrect.
Answer:
step 2 i did it on khan yall
Step-by-step explanation:
What is the value of x?
Answer:
58
Step-by-step explanation:
By the property of intersecting secants outside of a circle, we have:
x° = 1/2( 141° - 25°) = 1/2 * 116° = 58°
Therefore, x = 58
what would be the answer for f(0) = -3x+7?
Answer: 7
Step-by-step explanation:
f(0) means that x is equal to zero and so you substitute all the x's for zeros which means -3 times 0 plus 7 is equal to 7
Answer:
[tex]x=\frac{7}{3}[/tex]
Step-by-step explanation:
Since any number multiplied by zero equals zero, our equation is really:
0 = -3x+7
First, we'd have to subtract the 7 from both sides:
-7 = -3x
Now we need to divide the negative three from both sides to isolate the x.
7/3 = x
So, our answer is x=7/3
Hope this helps!! <3 :)
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
solve 27 to the power of (2/3)
Answer:
9Step-by-step explanation:
[tex]27^{\frac{2}{3}}\\\mathrm{Factor\:the\:number:\:}\:27=3^3\\=\left(3^3\right)^{\frac{2}{3}}\\\mathrm{Apply\:exponent\:rule}:\\\\\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\\\left(3^3\right)^{\frac{2}{3}}=3^{3}\times \frac{2}{3}}\\\\3\=times \frac{2}{3}=2\\\\=3^2 \\\\=9[/tex]
[tex]27^{2/3}=(3^3)^{2/3}=3^2=9[/tex]
22/25of a number is what percentage of that number?
Answer:
88%.
Step-by-step explanation:
Multiply the fraction by 100:
(22/25) * 100
= 22 * 4
= 88%.
Find an equation for the line tangent to the curve at the point defined by the given value of d²y/dx².
At this point. x = 2 cos t, y = 2 sin t, t=π/4
Answer:
Step-by-step explanation:
Given:
x = 2cost,
t = (1/2)arccosx
y = 2sint
dy/dx = dy/dt . dt/dx
dy/dt = 2cost
dt/dx = -1/√(1 - x²)
dy/dx = -2cost/√(1 - x²)
Differentiate again to obtain d²y/dx²
d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)
At t = π/4, we have
(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)
A random sample of 1003 adult Americans was asked, "Do you think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without. Construct and interpret a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without out.
Answer:
The 95% confidence interval is [tex]0.503 < p < 0.535[/tex]
The interpretation is that there is 95% confidence that the true population proportion lie within the confidence interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 1003
The number that indicated television are a luxury is k = 521
Generally the sample mean is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
[tex]\r p = \frac{521}{1003}[/tex]
[tex]\r p = 0.519[/tex]
Given the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{ \frac{ 0.519 (1- 0.519 )}{1003} }[/tex]
=> [tex]E = 0.016[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.519 - 0.016 < p < 0.519 + 0.016[/tex]
=> [tex]0.503 < p < 0.535[/tex]
HCF of x minus 2 and X square + X - 6
Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{x - 2}}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]
To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F
Let's solve
First expression = x - 2
Second expression = x + x - 6
Here, we have to find the two numbers which subtracts to 1 and multiplies to 6
= x + ( 3 - 2 ) x + 6
Distribute x through the parentheses
= x + 3x - 2x + 6
Factor out x from the expression
= x ( x + 3 ) - 2x + 6
Factor out -2 from the expression
= x ( x + 3 ) - 2 ( x + 3 )
Factor out x+3 from the expression
= ( x + 3 ) ( x - 2 )
Here, x - 2 is common in both expression.
Thus, H.C.F = x - 2
Hope I helped!
Best regards!!!
Answer:
x - 2
Step-by-step explanation:
by factorization method
1) x - 2
2) x^2 + x - 6
by splitting method
x^2 + 3x - 2x - 6
taking separate common from the first two terms and last two terms
x(x + 3) - 2(x + 3)
now writing x+3 once and the other term to get the right answer
(x + 3)(x - 2)
in both parts just see the similar term and write it as HCF
HCF= x - 2
and the second method by which you can get this answer is division method
Use the graph of f to estimate the local maximum and local minimum. Local maximum: (0,1); local minimum: three pi over two, negative 1 and negative pi, negative 1 Local maximum: (0,0) and approx (0,1); local minimum: negative three pi over two, negative 1 Local maximum: (0,0); local minimum: three pi over two, negative 1 Local maximum: (0,1); local minimum: approx. (0,0) and three pi over two, negative 1
Answer:
The answer is A.
Step-by-step explanation:
Local maximums are whenever the graph reaches it's highest y value.
Local minimums are whenever the graph reaches it's lowest y value.
From the graph, we can see that the maximum y-value the graph reaches is y=1. And this happens when x=0.
This only happens once (from the graph shown). Thus, the local maximum would be:
[tex](0,1)[/tex]
The minimum values we can see from the graph is at y=-1. This happens twice from the graph, once at -π and again at 3π/2.
Thus, the local minimums are:
[tex](-\pi,-1), (3\pi/2,-1)[/tex]
(2²)³+(2³)²/4
Simplificar
━━━━━━━☆☆━━━━━━━
▹ Answer
80
▹ Step-by-Step Explanation
(2²)³ + (2³)² ÷ 4
Rewrite:
2⁶ + 2⁶ ÷ 2²
Divide:
2⁶ + 2⁴
Factor:
(2² + 1) * 2⁴
Evaluate:
(4 + 1) * 2⁴
Calculate:
5 * 16
= 80
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Find the minimum and maximum values of 3 sin^2x – 2 cos^2x + 9
There are 8 books needing re-shelving in a library where 65% of the library's collection consists of reference books. Let X be the number of reference books a student helper re-shelves out of the 8 on her cart. a) What is the probability that all 8 of them are reference books
Answer:
0.0319
Step-by-step explanation:
To approximate this probability, we shall be using the Bernoulli approximation of the Binomial distribution.
Let p = probability of selecting a reference book = 65% = 0.65
Let q = probability of selecting other books= 1-p = 1-0.65 = 0.35
Now, we want to find the probability that all of these 8 books to be re-shelved are reference book.
We set up the probability as follows;
P(X = 8) = 8C8 •p^8•q^0
P(X = 8) = 1 * (0.65)^8 * (0.35)^0
P(X = 8) = 0.031864481289 which is 0.0319 to 4 decimal places
What is the probability that a randomly selected individual on this campus weighs more than 166 pounds? (express in decimal form and round final answer to 4 decimal places)
Answer:
hello attached is the missing part of your question and the answer of the question asked
answer : 0.2951
Step-by-step explanation:
Given data:
number of persons allowed in the elevator = 15
weight limit of elevator = 2500 pounds
average weight of individuals = 152 pounds
standard deviation = 26 pounds
probability that an individual selected weighs more than 166 pounds
std = 26 , number of persons(x) = 15, average weight of individuals(u) = 152 pounds
p( x > 166 ) = p( x-u / std, 166 - u/ std )
= p ( z > [tex]\frac{166-152}{26}[/tex] )
= 1 - p( z < 0.5385 )
p( x > 166 ) = 1 - 0.70488 = 0.2951
Given the two functions, which statement is true?
fx = 3^4, g(x) = 3^x + 5
Answer:
third option
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Given
g(x) = [tex]3^{x}[/tex] + 5 ← this represents a shift up of 5 units
Thus g(x) is the graph of f(x) translated up by 5 units
Answer:
[tex]\boxed{\sf{Option \: 3}}[/tex]
Step-by-step explanation:
g(x) is translated up 5 units compared to f(x). In a vertical translation, when the graph is moved 5 units up, 5 is added to the function. When the graph is moved 5 units down, 5 is subtracted from the function. The graphs are shifted in the direction of the y-axis.
A box is 1 m high, 2.5 m long, and 1.5 m wide, what is its volume?
Answer:
3.75
Step-by-step explanation:
[tex]v = lbh \\ 2.5 \times 1.5 \times 1 \\ = 3.75[/tex]
The volume of the rectangular prism will be 3.75 cubic meters.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
A box is 1 m high, 2.5 m long, and 1.5 m wide.
Then the volume of the rectangular prism will be
V = L x W x H
V = 1 x 2.5 x 1.5
V = 3.75 cubic meters
Thus, the volume of the rectangular prism will be 3.75 cubic meters.
More about the volume of the rectangular prism link is given below.
https://brainly.com/question/21334693
#SPJ2
Which is the simplified form of (StartFraction 2 a b Over a Superscript negative 5 Baseline b squared EndFraction) Superscript negative 3? Assume a not-equals 0, b not-equals 0. StartFraction b cubed Over 8 a Superscript 18 Baseline EndFraction StartFraction b squared Over 8 a Superscript 45 Baseline EndFraction StartFraction a Superscript 6 Baseline Over 4 b EndFraction StartFraction 2 a Superscript 6 Baseline Over b Superscript 5 Baseline EndFraction
Answer:
[tex]\dfrac{b^3}{8a^{18}}[/tex] matches the first choice
Step-by-step explanation:
[tex]\left(\dfrac{2 a b}{a^{-5}b^2}\right)^{-3}=(2a^{1-(-5)}b^{1-2})^{-3}=(2a^6b^{-1})^{-3}\\\\=2^{-3}a^{6(-3)}b^{-1(-3)}=8^{-1}a^{-18}b^3=\boxed{\dfrac{b^3}{8a^{18}}}[/tex]
__
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^-b = 1/a^b
Answer:
A
Step-by-step explanation:
just took the pretest! good luck!
Theresa bought 2 pineapples for $6. She be wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part A
Using the diagram, find the constant of proportionality in terms of dollars per pineapple.
Answer:
$3 per pineapple
Step-by-step explanation:
Hey there!
If 2 pineapples are $6,
6 / 2 = 3
So 1 pineapple is $3.
Hope this helps :)
Answer:
3 dollars for 1 pineapple
Step-by-step explanation:
well 2 pinapples is 6 bucks. so 2x=6, and to get x, just divide each side by 2. 6/2=3.
