Answer:
2ab(3b^2+2a+4)
Step-by-step explanation:
6ab^3 + 4a^2b + 8ab
2*3*a*b*b^2 +2*2*a*a*b +2*2*2*a*b
Factor out the common terms
2ab( 3*b^2 +2*a +2*2)
2ab(3b^2+2a+4)
Devaughn is 6 years older than Sydney. The sum of their ages is 56 . What is Sydney's age?
Answer:
Devaughn = 31, Sydney = 25
Step-by-step explanation:
(56-6)÷2= 25
So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31
ATQ
[tex]\\ \sf\longmapsto x+x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x=56-6[/tex]
[tex]\\ \sf\longmapsto 2x=50[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]
[tex]\\ \sf\longmapsto x=25[/tex]
A forest has 800 pine trees, but a disease is introduced that kills a fourth of the pine trees in the forest
every year.
Which graph shows the number y of pine trees remaining in the forest 2 years after the disease is
introduced?
In a graph
The exponential function that models the number of trees after t years is given by:
[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]
Hence, after 2 years, 450 trees will be remaining, as the graph at the end of this answer shows.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
The forest has 800 pine trees, hence A(0) = 800.Each year, a disease is introduced that kills a fourth of the pine trees in the forest every year, hence [tex]r = \frac{1}{4}[/tex].Then, the equation is:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 800(1 - \frac{1}{4})^t[/tex]
[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]
After 2 years:
[tex]A(2) = 800\left(\frac{3}{4}\right)^2 = 450[/tex]
450 trees will be remaining.
You can learn more about exponential functions at https://brainly.com/question/25537936
a game is played with a fishpond containing 100 fish; 90 white, 9 red, and 1 blue. a contestant randomly catches a fish and receives payments as follows: $0.30 for white, $1.00 for red, and $10.00 for blue. If it cists $0.60 to play this game, how much (on average) does a contestant win on each play
Answer:
loses 14 cents
- $0.14
Step-by-step explanation:
90% $0.30 $(0.30) $(0.27)
9% $1.00 $0.40 $0.04
1% $10.00 $9.40 $0.09
$(0.14)
how many 50 cents coins are there in $10:50
Answer:
21
Step-by-step explanation:
you divide 10.50 by 50
The correlation coefficient, r, between the ages of employees, x, and the number of sick days taken per year, y, equals 0.81.
Complete the statement based on the information provided.
The value of r is
✔ positive
and is relatively close to
✔ 1
, so the variables are
✔ closely
associated. It appears that, as the age of an employee increases, the number of sick days taken
✔ increases
.
Answer:
✔ positive
✔ 1
✔ closely
✔ increases
ED2021
Graphs of the following equations are straight lines except :
A. 3x+2y=8
B. y=x/2-5
C. x=4y
D. y=x^2+3
Answer:
D.
Step-by-step explanation:
D. This contains an x^2 and is called a parabola ( curved line like a U).
Answer:D
Step-by-step explanation: d is the correct answer
the recipe for pumpking pie instructs you to bake the pie at 425∘F, for 15 minutes and then reduce the oven temperature to 350∘F. What is the change in temperature in degrees Celsius?
Answer:
ΔT = -75°F
Step-by-step explanation:
ΔT = T₁ - T₀ = 350 - 425 = -75°F
interest on 600 2 years at rate of paise per rupee per month
What is the slope, m, and the y-intercept of the line that is graphed below?
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
Answer:
Slope: 1
Y-intercept: (0,3)
Step-by-step explanation:
The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.
Y intercept: (0, 3)
For slope, you can use the formula rise over run. [tex]\frac{Rise}{Run}[/tex]
From the picture, I have drawn the rise over run, which is [tex]\frac{3}{3}[/tex], which is also 1.
Slope: 1
Hope this helped.
Answer: 1
Step-by-step explanation: got it right on edge
Please Help with this
Answer:
csc = 6/5= 1.2
cot = √(11)/5= 0.6633
sin = 5÷6= 0.83333
What is the point-slope form of a line with slope -4 that contains the point
(-2, 3)?
A. y + 3 = 4(x + 2)
B. y - 3 = -4(x + 2)
c. y + 3 = -4(x - 2)
D. y - 3 = 4(x + 2)
Answer:
y-3 = -4(x+2)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y-3 = -4(x --2)
y-3 = -4(x+2)
The circle below is centered at (2, 3) and has a radius of 4. What is its
equation?
A. (x-3)2 + (y - 2)2 = 16
O B. (x-3)2 + (y-2)2 = 4
C. (x - 2)2 + (y - 3)2 = 16
O D. (x-2)2 + (y-6)2 = 4
The equation of the circle is [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] . The option C is the correct option.
Given that the centre of the circle is (2,3) and circle has radius 4.
To find the equation of the circle, use the general equation of the circle as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the centre of the circle and r is the radius of the circle.
Since, h = 2, k = 3 and radius r = 4.
Therefore, the equation of the circle:
[tex](x-h)^2+(y-k)^2=r^2\\(x-2)^2+(y-3)^2=4^2\\(x-2)^2+(y-3)^2=16[/tex]
The equation of the circle cantered at (2,3) and has a radius of 4 is [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .
Therefore, The equation of the circle cantered at (2,3) and has a radius of 4 is [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .
Learn more about Diameter here:
https://brainly.com/question/32968193
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A sequence is defined by the recursive function f(n + 1) = f(n) – 2.
If f(1) = 10, what is f(3)?
1
6
8
30
Answer:
f(3) = 6
Step-by-step explanation:
If f(1)=10, then f(1+1)=f(1)-2
f (2) = 10 - 2 = 8
Therefore f(3) = f(2) - 2 = 8 - 2 = 6
Need help ASAP no links pls
Answer:
y = 6
I hope this helps you out!
Please answer ASAP will be greatly appreciated!!
Look at photo and answer.
Answer:
h.
[tex] \frac{9 {x}^{10}(y. {x}^{3}) {}^{2} }{y.x(3 {x}^{3}) {}^{3} } \\ \\ = \frac{9 {x}^{10}(y {}^{2} )( {x}^{6} ) }{3y. {x}^{10} } \\ \\ = \frac{ {3}^{2} {x}^{16} {y}^{2} }{3y {x}^{10} } \\ \\ = 3y {x}^{6} [/tex]
j.
[tex] \frac{(3x. {y}^{7} ) {}^{2}. {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{3 {x}^{2} . {y}^{14} . {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{ {3x}^{7} {y}^{14} }{3 {x}^{7} {y}^{4} } \\ \\ = {y}^{10} [/tex]
What is the volume of a cone with a height of 6m and a diameter of 12m? Nearest meter.
Answer:
0.0005m^3
Step-by-step explanation:
V=1/3hπr²
h=6m
d=12m
r=12÷2=6m
V=1/3×6×(3.14)×36
V=1/2034.72
V=0.0005m^3
Which graph represents the equation x2 = 8y? On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 8), and a directrix at y = negative 8. On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 2), and a directrix at y = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (2, 0), and a directrix at x = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (8, 0), and a directrix at x = negative 8.
Answer:
The parabola x²=8y has,
vertex: (0,0)
focus: (0,2)
directrix: y=-2
so that option is the answer,
btw, the parabola opens up to the top and axis of symmetry is x=0
Answer:
It's A!
Step-by-step explanation:
Got it correct on my test! :)
Solve each system by graphing.
Answer:
(2,-1)
Step-by-step explanation:
Solved using math.
Answer:
The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.
Step-by-step explanation:
Write the sum using summation notation, assuming the suggested pattern continues. 6, -18, 54, -162, +… Is this sequence arithmetic or geometric? Explain your answer.
Answer:
Hello,
This sequence is geometric with a ratio of -3
the first term is 6
Step-by-step explanation:
[tex]u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\[/tex]
serie does not converge.
equation that passes 1,3 and slope of 2 in point slope form
Answer:
y-3 = 2(x-1)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-3 = 2(x-1)
Answer:
3=2x+1
Step-by-step explanation:
Use the equation y=mx+b
where y is the y component, x is the variable and b is the x intercept
A triangle is rotated 90° about the origin. Which rule describes the transformation?
(x, y) (-x, -y)
O(x,y) (-y, x)
(x, y) (-), -x)
(x,y) →ly, -x)
Answer:
(x,y) -> (-y,x), second option.
Step-by-step explanation:
Rotation of 90 degrees about the origin:
The rule for a rotation of a point (x,y) 90 degrees about the origin is given by:
(x,y) -> (-y,x)
This is that the question asks, and so, this is the answer, which is the second option.
Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? Use a level of significance of 0.05. Table shows the results of the survey. Has there been a change in the distribution of voter preferences since the earthquake?
Peter Alan Sui
Before 1838 418 1475
After 1420 329 1140
What is the chi-square test-statistic for this data?
χ2=_____.
Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
Devy likes to learn! Could someone please tell me how to answer this question?
If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?
On a coordinate plane, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).
On a coordinate plane, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).
On a coordinate plane, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).
On a coordinate plane, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).
Answer:
B
Step-by-step explanation:
Recall that if two functions, f and g, are inverses, then by definition:
[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]
Hence, the graph of f(g(x)) should be simply y = x.
Therefore, our answer is B, as both coordinates are equivalent for all three points.
To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used
Answer:
Cluster Sampling
Step-by-step explanation:
Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.
If the volume of the expanding cube is increasing at the rate 24 cm3 / min , how fast is its surface area increasing when the surface area is 216 cm2 ?
Answer:
16 cm^2/min
Step-by-step explanation:
dV/dt=24
V=a^3, differentiate with respect to t
dV/dt=3a^2*da/dt, a^2*da/dt=8
S=6a^2, 216=6a^2. a=6. da/dt=(8/36)
dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min
I are these orders pairs a function
х,у
0,9
2,8.
4,7
6,6
8,5
10,4
9514 1404 393
Answer:
yes
Step-by-step explanation:
No x-value is repeated, so these ordered pairs do represent a function.
An adult can lose or gain two pounds of water ina course of a day. Assume that the changes in water weight isuniformly distributed between minus two and plus two pounds in aday. What is the standard deviation of your weight over a day?
Answer:
The standard deviation of your weight over a day is of 1.1547 pounds.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b, and the standard deviation is:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
Assume that the changes in water weight is uniformly distributed between minus two and plus two pounds in a day.
This means that [tex]a = -2, b = 2[/tex]
What is the standard deviation of your weight over a day?
[tex]S = \sqrt{\frac{(2 - (-2))^2}{12}} = \sqrt{\frac{4^2}{12}} = \sqrt{\frac{16}{12}} = 1.1547[/tex]
The standard deviation of your weight over a day is of 1.1547 pounds.
find the supplement of 158 degrees and 17 minutes
Answer:
supplement of 158 degree
x+158=180
x=180-158
x=22 degree.
Step-by-step explanation:
Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows.
Before 13 22 65 123 56 63
After 14 21 43 84 75 72
1. The article included the statement "A paired t-test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs." Carry out such a test. (Note: The relevant normal probability plot shows a substantial linear pattern.)
a. State and test the appropriate hypotheses. (Use α = 0.05.)
b. Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t = _____
p-value = _____
c. State the conclusion in the problem context.
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
B. Reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
C. Fail to reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
D. Reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
2. If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in the number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)
Answer:
Test statistic = 0.63
Pvalue = 0.555
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
Step-by-step explanation:
Given :
Before 13 22 65 123 56 63
After_ 14 21 43 84 75 72
To perform a paired t test :
H0 : μd = 0
H1 : μd ≠ 0
We obtain the difference between the two dependent sample readings ;
Difference, d = -1, 1, 22, 39, -19, -9
The mean of difference, Xd = Σd/ n = 33/6 = 5.5
The standard deviation, Sd = 21.296 (calculator).
The test statistic :
T = Xd ÷ (Sd/√n) ; where n = 6
T = 5.5 ÷ (21.296/√6)
T = 5.5 ÷ 8.6940555
T = 0.6326
The Pvalue : Using a Pvalue calculator ;
df = n - 1 = 6 - 1 = 5
Pvalue(0.6326, 5) = 0.5548
Decision region :
Reject H0 ; If Pvalue < α; α = 0.05
Since 0.5548 > 0.05 ; we fail to reject the Null and conclude that the data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
