Answer:
The answer is option CStep-by-step explanation:
6x³ - 4x² - 16x
To factorize the expression first factor out the GCF out
The GCF in the expression is 2x
That's
2x( 3x² - 2x - 8)
Next Factorize the terms in the bracket
To factorize write - 2x as a difference
that's
2x( 3x² + 4x - 6x - 8)
Factor out x from the expression
2x [ x( 3x + 4) - 6x - 8 ]
Next factor out - 2 from the expression
2x [ x ( 3x + 4) - 2( 3x + 4) ]
Factor out 3x + 4 from the expression
We have the final answer as
2x( 3x + 4)( x - 2)Hope this helps you
According to the local union president, the mean gross income of plumbers in the Salt Lake City area follows a normal distribution with a mean of $48,000 and a population standard deviation of $2,000. A recent investigative reporter for KYAK TV found, for a sample of 49 plumbers, the mean gross income was $47,600. At the 0.05 significance level, is it reasonable to conclude that the mean income is not equal to $47,600? Determine the p value. State the Null and Alternate hypothesis: State the test statistic: State the Decision Rule: Show the calculation: What is the interpretation of the sample data? Show the P value
Answer:
Step-by-step explanation:
Given that:
population mean [tex]\mu[/tex] = 47600
population standard deviation [tex]\sigma[/tex] = 2000
sample size n = 49
Sample mean [tex]\over\ x[/tex] = 48000
Level of significance = 0.05
The null and the alternative hypothesis can be computed as follows;
[tex]H_0 : \mu = 47600 \\ \\ H_1 : \mu \neq 47600[/tex]
Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.
The test statistics can be calculated by using the formula:
[tex]z= \dfrac{\overline X - \mu }{\dfrac{\sigma}{ \sqrt{n}}}[/tex]
[tex]z= \dfrac{ 48000-47600 }{\dfrac{2000}{ \sqrt{49}}}[/tex]
[tex]z= \dfrac{400 }{\dfrac{2000}{ 7}}[/tex]
[tex]z= 1.4[/tex]
Conclusion:
Since 1.4 is lesser than 1.96 , we fail to reject the null hypothesis and that there is insufficient information to conclude that the mean gross income is not equal to $47600
The P-value is being calculate as follows:
P -value = 2P(Z>1.4)
P -value = 2 (1 - P(Z< 1.4)
P-value = 2 ( 1 - 0.91924)
P -value = 2 (0.08076 )
P -value = 0.16152
Please please help :((((
Answer:
y = x-4
Step-by-step explanation:
The y intercept is -4
We have 2 points so we can find the slope
( 0,-4) and(4,0)
m = ( y2-y1)/(x2-x1)
= ( 0- -4)/ (4-0)
= 4/4
=1
The slope intercept form is
y = mx+b
y = 1x-4
y = x-4
a=5,and 5+z=14,so a+z=14
Answer:
Z=9
Step-by-step explanation:
Insert A into A+Z=14
5+z=14
Subtract 5 on both sides, to find Z.
-5 -5
z=9
solve the equation
Answer:
x = 10
Step-by-step explanation:
2x/3 + 1 = 7x/15 + 3
(times everything in the equation by 3 to get rid of the first fraction)
2x + 3 = 21x/15 + 9
(times everything in the equation by 15 to get rid of the second fraction)
30x+ 45 = 21x + 135
(subtract 21x from 30x; subtract 45 from 135)
9x = 90
(divide 90 by 9)
x = 10
Another solution:
2x/3 + 1 = 7x/15 + 3
(find the LCM of 3 and 15 = 15)
(multiply everything in the equation by 15, then simplify)
10x + 15 = 7x + 45
(subtract 7x from 10x; subtract 15 from 45)
3x = 30
(divide 30 by 3)
x = 10
What is the midpoint of the segment below?
A.
(0, 0)
B.
(-1, 1)
C.
(0.5, 0.5)
D.
(0.5, -0.5)
Answer:
Step-by-step explanation:
(5+(-4))/2 = 1/2 or 0.5
(-7 + 6)/2 = -1/2 or -0.5
the solution is D
(0.5, -0.5)
Evaluate integral _C x ds, where C is
a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)
b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)
Answer:
a. [tex]\mathbf{36 \sqrt{5}}[/tex]
b. [tex]\mathbf{ \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]
Step-by-step explanation:
Evaluate integral _C x ds where C is
a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)
i . e
[tex]\int \limits _c \ x \ ds[/tex]
where;
x = t , y = t/2
the derivative of x with respect to t is:
[tex]\dfrac{dx}{dt}= 1[/tex]
the derivative of y with respect to t is:
[tex]\dfrac{dy}{dt}= \dfrac{1}{2}[/tex]
and t varies from 0 to 12.
we all know that:
[tex]ds=\sqrt{ (\dfrac{dx}{dt})^2 + ( \dfrac{dy}{dt} )^2}} \ \ dt[/tex]
∴
[tex]\int \limits _c \ x \ ds = \int \limits ^{12}_{t=0} \ t \ \sqrt{1+(\dfrac{1}{2})^2} \ dt[/tex]
[tex]= \int \limits ^{12}_{0} \ \dfrac{\sqrt{5}}{2}(\dfrac{t^2}{2}) \ dt[/tex]
[tex]= \dfrac{\sqrt{5}}{2} \ \ [\dfrac{t^2}{2}]^{12}_0[/tex]
[tex]= \dfrac{\sqrt{5}}{4}\times 144[/tex]
= [tex]\mathbf{36 \sqrt{5}}[/tex]
b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)
Given that:
x = t ; y = 3t²
the derivative of x with respect to t is:
[tex]\dfrac{dx}{dt}= 1[/tex]
the derivative of y with respect to t is:
[tex]\dfrac{dy}{dt} = 6t[/tex]
[tex]ds = \sqrt{1+36 \ t^2} \ dt[/tex]
Hence; the integral _C x ds is:
[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]
Let consider u to be equal to 1 + 36t²
1 + 36t² = u
Then, the differential of t with respect to u is :
76 tdt = du
[tex]tdt = \dfrac{du}{76}[/tex]
The upper limit of the integral is = 1 + 36× 2² = 1 + 36×4= 145
Thus;
[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]
[tex]\mathtt{= \int \limits ^{145}_{0} \sqrt{u} \ \dfrac{1}{72} \ du}[/tex]
[tex]= \dfrac{1}{72} \times \dfrac{2}{3} \begin {pmatrix} u^{3/2} \end {pmatrix} ^{145}_{1}[/tex]
[tex]\mathtt{= \dfrac{2}{216} [ 145 \sqrt{145} - 1]}[/tex]
[tex]\mathbf{= \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]
Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula. A. an=44−6n B. an=41−6n C. an=35−6n D. an=43−6n
Answer:
The answer is option AStep-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 38
d = 32 - 38 = - 6 or 20 - 26 = - 6
Substitute the values into the above formula
A(n) = 38 + (n - 1)-6
= 38 - 6n + 6
We have the final answer as
A(n) = 44 - 6nHope this helps you
Answer:
a
Step-by-step explanation:
you're welcome!
nick used 1 3/4 kg of salt to melt the ice on his sidewalk. He then used another 3 4/5 kg on the driveway. How much salt did he use in all?
Answer:
5 11/20
Step-by-step explanation:
1 3/4 + 3 4/5
Get a common denominator of 20
1 3/4 * 5/5 + 3 4/5 *4/4
1 15/20 + 3 16/20
4 31/20
Rewriting
4 + 20/20 + 11/ 20
4+1 + 11/20
5 11/20
Researchers recorded that a certain bacteria population declined from 450,000 to 900 in 30 hours at this rate of decay how many bacteria will there be in 13 hours
Answer:
30,455
Step-by-step explanation:
Exponential decay
y = a(1 - b)^x
y = final amount
a = initial amount
b = rate of decay
x = time
We are looking for the rate of decay, b.
900 = 450000(1 - b)^30
1 = 500(1 - b)^30
(1 - b)^30 = 0.002
1 - b = 0.002^(1/30)
1 - b = 0.81289
b = 0.1871
The equation for our case is
y = 450000(1 - 0.1871)^x
We are looking for the amount in 13 hours, so x = 13.
y = 450000(1 - 0.1871)^13
y = 30,455
Which function below has the following domain and range?
Domain: { -6, -5,1,2,6}
Range: {2,3,8)
{(2,3), (-5,2), (1,8), (6,3), (-6, 2)
{(-6,2), (-5,3), (1,8), (2,5), (6,9)}
{(2,-5), (8, 1), (3,6), (2, - 6), (3, 2)}
{(-6,6), (2,8)}
Answer:
{(2,3), (-5,2), (1,8), (6,3), (-6, 2)
Step-by-step explanation:
The domain is the input and the range is the output
We need inputs of -6 -5 1 2 6
and outputs of 2 3 and 8
Which one is correct? in need of large help
Answer:
Option C. x + 12 ≤ 2(x – 3)
Step-by-step explanation:
From the question, we obtained the following information:
x + 12 ≤ 5 – y .......(1)
5 – y ≤ 2(x – 3) ....... (2)
To know which option is correct, do the following:
From equation 2,
5 – y ≤ 2(x – 3)
Thus, we can say
5 – y = 2(x – 3)
Now, we shall substitute the value of 5 – y into equation 1 as shown below:
x + 12 ≤ 5 – y
5 – y = 2(x – 3)
x + 12 ≤ 2(x – 3)
From the above illustration, we can see that if x + 12 ≤ 5 – y and 5 – y ≤ 2(x – 3), then x + 12 ≤ 2(x – 3) must be true.
Option C gives the correct answer.
Tonya and Leo each bought a cell phone at the same time. The trade-in values, in dollars, of the cell phones are modeled by the given functions, where x is the number of months that each person has owned the phone.
Answer:
The answer is: Leo's phone had the greater initial trade-in value. Tonya's phone decreases at an average rate slower than the trade in value of Leo's phone.
Step-by-step explanation:
I got it right. Hope this helps.
The initial trade-in value of Tonia's phone is greater when compared with Leo's
There is a decrease in the trade-in value of Leo's phone at an average slower rate
[tex]f(x) = 490\times 0.88[/tex]
[tex](x)[/tex] ⇒ [tex]g(x)[/tex]
[tex]0[/tex] ⇒ [tex]480[/tex]
[tex]2[/tex] ⇒ [tex]360[/tex]
[tex]4[/tex] ⇒ [tex]470[/tex]
Now we will solve with the greater initial value
The initial value is when x = 0. So, we have
[tex]f(x) = 490 \times o.88^x\\\ f(o) = 490 \times 0.88 ^0\\f(0 =490 \times 1 \\f(o) = 490[/tex]
From leos table
[tex]g(0) = 480\\f(0) > g(o)\\i.e \\490 > 480[/tex]
So Tonia had a greater initial value
Solving (b): The phone with a lesser rate
y [tex]y = a b ^ x[/tex]
An exponential function is:
where [tex]b \rightarrow rate[/tex]
For Tonia
[tex]b = o.88[/tex]
For Leo we have
[tex](x_{1} , y_{1} )= (0,480)\\(x_{1}, y_{1} ) = (2, 360)[/tex]
So the equation becomes
[tex]y = ab ^x \\480 = ab ^0 \\and \\360 = ab ^2[/tex]
On solving
[tex]480 = a \times 1\\a = 480[/tex]
[tex]360 = ab ^ 2[/tex]
so it becomes
[tex]480 = 360 \times b ^2 \\[/tex]
On dividing both sides by [tex]480[/tex] we get
[tex]b ^ 2 = 0.87[/tex]
[tex]b ^ 2 = 0.75[/tex]
On taking square root we get
[tex]b = 0.87[/tex]
In comparison, we get Leo's rate is slower.
Learn more about Equation here:
https://brainly.com/question/14686792
# SPJ2
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (k)left parenthesis, k, right parenthesis she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional.
How many kilometers can Pamela drive with 12 liters of fuel?
Answer:
132 kilo meters
Step-by-step explanation:
Pro por tions:
9 lite rs ⇒ 99 km
12 lite rs ⇒ P km
P = 99*12/9
P = 132 km
Answer:
132
Step-by-step explanation:
give person above brainliest :))
NEED ASAP! Given: AB = 12 AC = 6 Prove: C is the midpoint of AB. A line has points A, C, B. Proof: We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments. Answer choices: Congruence Symmetric Reflexive Transitive
Answer:
It’s symmetric property
Answer:
Symmetry
Step-by-step explanation:
The guy above me
A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.
(a) If the initial distribution for states A, B, and C is P0 = ( 1／3 , 1／3 , 1／3 ), find the distribution of X2
(b) Find the steady state distribution by solving πP = π.
Answer:
A) distribution of x2 = ( 0.4167 0.25 0.3333 )
B) steady state distribution = [tex]\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}[/tex]
Step-by-step explanation:
Hello attached is the detailed solution for problems A and B
A) distribution states for A ,B, C:
Po = ( 1/3, 1/3, 1/3 ) we have to find the distribution of x2 as attached below
after solving the distribution
x 2 = ( 0.4167, 0.25, 0.3333 )
B ) finding the steady state distribution solving
[tex]\pi p = \pi[/tex]
below is the detailed solution and answers
Which graph shows the polar coordinates (-3,-) plotted
During the 2014 season, the Los Angeles Dodgers won 58% of their games. Assuming that the outcomes of the baseball games are independent and that the percentage of wins this season will be the same as in 2014: What is the probability that the Dodgers will win at least one of their next seven games
Answer: 0.98
Step-by-step explanation:
given data:
probability they won a game = 58% = 0.58
since outcome of games are independent, and percentage would remain same as 2014.
probablility that Dodgers wins atleast 1 of their next 7 games
= 1 - p
= 1 - ( 0.58 )^ 7
= 1 - 0.02208
= 0.98
probabikotun that Dodgers would win one of their next seven games is 0.98
A raffle offers one $8000.00 prize, one $4000.00 prize, and five $1600.00 prizes. There are 5000 tickets sold at $5 each. Find the expectation if a person buys one ticket.
Answer:
The expectation is [tex]E(1 )= -\$ 1[/tex]
Step-by-step explanation:
From the question we are told that
The first offer is [tex]x_1 = \$ 8000[/tex]
The second offer is [tex]x_2 = \$ 4000[/tex]
The third offer is [tex]\$ 1600[/tex]
The number of tickets is [tex]n = 5000[/tex]
The price of each ticket is [tex]p= \$ 5[/tex]
Generally expectation is mathematically represented as
[tex]E(x)=\sum x * P(X = x )[/tex]
[tex]P(X = x_1 ) = \frac{1}{5000}[/tex] given that they just offer one
[tex]P(X = x_1 ) = 0.0002[/tex]
Now
[tex]P(X = x_2 ) = \frac{1}{5000}[/tex] given that they just offer one
[tex]P(X = x_2 ) = 0.0002[/tex]
Now
[tex]P(X = x_3 ) = \frac{5}{5000}[/tex] given that they offer five
[tex]P(X = x_3 ) = 0.001[/tex]
Hence the expectation is evaluated as
[tex]E(x)=8000 * 0.0002 + 4000 * 0.0002 + 1600 * 0.001[/tex]
[tex]E(x)=\$ 4[/tex]
Now given that the price for a ticket is [tex]\$ 5[/tex]
The actual expectation when price of ticket has been removed is
[tex]E(1 )= 4- 5[/tex]
[tex]E(1 )= -\$ 1[/tex]
Simplify . 7+ the square root of 6(3+4)-2+9-3*2^2 The solution is
Answer:
7+sqrt(37)
Step-by-step explanation:
7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)
The expression (x - 4)2 is equivalent to which expression
Answer:
8-2x
Step-by-step explanation:
2 distributed over the entire expression equals 8-2x
Answer:
the answer is b
Step-by-step explanation:
Brainliest! Jared uses the greatest common factor and the distributive property to rewrite this sum: 100 + 75 Drag one number into each box to show Jared's expression. Brainliest!
Answer:
25(4 + 3)
Step-by-step explanation:
100 = 2^2 + 5^2
75 = 3 * 5^2
GCF = 5^2 = 25
100 + 75 =
= 25 * 4 + 25 * 3
= 25(4 + 3)
Please Solve
F/Z=T for Z
Answer:
F /T = Z
Step-by-step explanation:
F/Z=T
Multiply each side by Z
F/Z *Z=T*Z
F = ZT
Divide each side by T
F /T = ZT/T
F /T = Z
Answer:
[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]
Step-by-step explanation:
[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]
Please help 1-7 questions
Answer:
25= q+20
25 - 20 =q
5 = q
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------
Answer: q = 5.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]25 = q + 20[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]q + 20 = 25[/tex]
Subtract 20 from both sides.
[tex]q = 25 - 20[/tex]
Subtract 20 from 25 to get, you guessed it, 5!how do I write 1/2 in a from of a decimal?
Answer:
0.5
1 divide by 2 = 0.5
You are going to your first school dance! You bring $20,
and sodas cost $2. How many sodas can you buy?
Please write and solve an equation (for x sodas), and
explain how you set it up.
Answer:
10
Step-by-step explanation:
Let the no. of sodas be x
Price of each soda = $2
Therefore, no . of sodas you can buy = $2x
2x=20
=>x=[tex]\frac{20}{2}[/tex]
=>x=10
you can buy 10 sodas
Answer: 10 sodas
Step-by-step explanation:
2x = 20 Divide both sides by 2
x = 10
If I brought 20 dollars and I want to by only sodas and each sodas cost 2 dollars, then I will divide the total amount of money that I brought by 2 to find out how many sodas I could by.
evaluate the expression 4x^2-6x+7 if x = 5
Answer:
77
Step-by-step explanation:
4x^2-6x+7
Let x = 5
4* 5^2-6*5+7
4 * 25 -30 +7
100-30+7
7-+7
77
I'm not sure about this one please I need someone to help me.
Answer:
The corresponding graph is Graph A.
Step-by-step explanation:
Part 1: Rewriting the inequality and solving for d
To start, the inequality will need simplified.
[tex]9-4d\geq -3\\\\-4d\geq -12\\\\\frac{-4d}{-4} \geq \frac{-12}{-4} \\\\d \leq 3[/tex]
Because simplifying the inequality involved dividing by a negative number, the sign must be flipped.
Part 2: Determining the graph for the inequality
Now, refer to the rules for graphing inequalities.
If the sign is simply < or >, the graph will start at the number that it begins at and the circle will be open.If the sign is ≤ or ≥, the graph will start at the number that it begins at and the circle will be closed.Therefore, because [tex]d \leq 3[/tex], the graph will start at 3 as a closed dot. Then, it will go left because values must be equal to 3 or less than 3.
Therefore, the graph that represents this is Graph A.
Answer:
Graph A
I hope this helps!
Factor completely 6x - 18.
6(x + 3)
6(x-3)
6X (-18)
Prime
Answer:
6(x-3)
Step-by-step explanation:
the common number for 6 and 18 is 6 so if you extract that from the expression then it turns to 6(x-3) which cannot be factored further
Answer:
Option B: 6(x - 3)
Step-by-step explanation:
��2222 is the diameter of a circle. The coordinates are �(−2, −3) and �(−12, −5). At what coordinate is the center of the circle located? A. (5, 1) B. (−5, −1) C. (−4, −7) D. (−7, −4)
Answer:
D ). (-7,-4)
Step-by-step explanation:
To locate the position or the location of the centre of the circle we have to bear in mind that the center of the circle is the midpoint of the diameter line.
Formula for midpoint of a line is given below
Midpoint= (X1+x2)/2 ,(y1+y2)/2
Where X1= -2,y1= -3
X2= -12, y2= -5
The midpoint= (-2+(-12))/2,(-3+(-5))/2
Midpoint= (-2-12)/2,(-3-5)/2
Midpoint= (-14)/2,(-8)/2
Midpoint=( -7,-4)
The center of the circle is located at the point (-7,-4)
Two fraction have the same denominator, 8.the some of two fraction is 1/2.if one of the fraction is added to five times the order, the result is 2,find the number.
Answer:
1/8, 3/8
Step-by-step explanation:
Let x and y represent the two fractions. Then we are given ...
x + y = 1/2
x + 5y = 2
Subtracting the first equation from the second, we get ...
(x +5y) -(x +y) = (2) -(1/2)
4y = 3/2 . . . . . simplify
y = 3/8 . . . . . . divide by 4
x = 1/2 -3/8 = 1/8
The two numbers are 1/8 and 3/8.
