[tex]\\ \Large\sf\longmapsto h(t)[/tex]
[tex]\\ \Large\sf\longmapsto 2+8t-3t^2+\dfrac{1}{5}t^3[/tex]
[tex]\\ \Large\sf\longmapsto 2+8(3)-3(3)^2+\dfrac{1}{5}(3)^3[/tex]
[tex]\\ \Large\sf\longmapsto 2+24-3(9)+\dfrac{27}{5}[/tex]
[tex]\\ \Large\sf\longmapsto 26-27+5.4[/tex]
[tex]\\ \Large\sf\longmapsto -2+5.4[/tex]
[tex]\\ \Large\sf\longmapsto h(t)=3.4m[/tex]
HELP ASAP PLEASE!!!!!!!!
Answer:
1
Step-by-step explanation:
1 : 1 :sqrt(2)
The legs are in the ratio of 1 to 1
tan 45 = opp side / adj side
tan 45 = 1/1
tan 45 =1
Answer:
Step-by-step explanation:
What value of x makes the equation 3x +7=22
Answer:
x = 5
Step-by-step explanation:
Your goal is to isolate x
3x + 7 = 22
Subtract 7 from both sides and you are left with
3x = 15
In order to isolate x divide both sides by 3
x = 5
How many solutions will each system of linear equation have?
Answer:
The top system of equations has one solution, the middle system has infinitely many, and the bottom system has no solution.
Step-by-step explanation:
We can immediately see the top system has one solution because the two equations have different slopes.
For the middle system, we can rearrange terms and multiply by 3 to get that the equations are the same line, so there are infinitely many solutions.
Finally, we can move the -2x to the other side in the first equation of the bottom system to get 2x+y=5. But it also equals -7 from the second equation! This is impossible, so there are no solutions to the bottom system.
PLz help!!
What is the degree of the polynomial
Answer:
3 maybe I'm just guessing.
now thats room for an answer again: yeah, 3 is right. its the x³ that defines the degree, its just the biggest power.
Need help! Thank you :)
Answer:
The value of [tex]x[/tex] is 10.
Step-by-step explanation:
Both angles ABC and CBD are complementary, that is, the sum of the measures of both angles equals 90°, that is:
[tex]\angle ABC + \angle CBD = 90^{\circ}[/tex] (1)
If we know that [tex]\angle ABC = 5\cdot x[/tex] and [tex]\angle CBD = 4\cdot x[/tex], then the value of [tex]x[/tex] is:
[tex]5\cdot x + 4\cdot x = 90^{\circ}[/tex]
[tex]9\cdot x = 90^{\circ}[/tex]
[tex]x = 10[/tex]
The value of [tex]x[/tex] is 10.
What is the maximum amount of a loan you can get if you pay $700 each month at a yearly rate of 0.89% for 10 years?
Answer:
$785.17
Step-by-step explanation:
Given data
PV is the loan amount
PMT is the monthly payment
i is the interest rate per month in decimal form (interest rate percentage divided by 12)
n is the number of months (term of the loan in months)
PMT =$700
n = 10 years
i = 0.89%
The formula for the loan amount is
what is the solution for this equation?
In(x+6)-in(2x-1)=0
answers in the image!
Answer:
x=7
Step-by-step explanation:
ln(x+6)-ln(2x-1)=0
add ln(2x-1) to each side
ln(x+6) = ln(2x-1)
Raise each side to the base e
e^ln(x+6) = e^ln(2x-1)
x+6 = 2x-1
Subtract x from each side
x+6-x = 2x-1-x
6 = x-1
Add 1 to each side
6+1 = x-1+1
7=x
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{gold}{Answer \red{:)}}}}}}}}[/tex]
[tex]\sf ln(x+6)-ln(2x-1)=0\\\\\tt ln(x+6)=ln(2x-1)\\\\ \sf e^{ln(x+6)}=e^{ln(2x-1)}\\\\ \tt x+6=2x-1\\\\\sf 2x-1=6+1\\\\\bold x=7[/tex]
Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the region bounded by the curve y = 2x - x^2 and the line y = x about the y-axis.
Answer:
The answer is "[tex]\frac{5\pi}{6}[/tex]"
Step-by-step explanation:
Please find the graph file.
[tex]h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\[/tex]
The jury pool for the upcoming murder trial of a celebrity actor contains the names of 100,000 individuals in the population who may be called for jury duty. The proportion of the available jurors on the population list who are Hispanic is .40. A jury of size 12 is selected at random from the population list of available jurors. Let X = the number of Hispanics selected to be jurors for this jury.
a. What is the expected number of hispanic jurors being on the jury?
b. What is the expected value (or theoretical mean) of a great earthquake off the coast of Oregon in two years?
c. Use the poisson distribution to appropriate the probability that there will be at least one major earthquake in the next two years.
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Have a Spanish Jury possibility[tex]= 0.40[/tex]
Jury member No. to be chosen[tex]= n= 12[/tex]
Hispanic Juror Expected [tex]= np = 12\times 0.40 = 4.8[/tex]
The jury group will be constituted by Hispanic Jurors [tex]4.8[/tex]
OR
The binomial distribution defines the behavior of a count variable X, provided:
There are a set number of data points n.
Set [tex]n=12[/tex]
Each perception is independent. This will not affect others if your first juror is selected
One of two results is that each observation ("success" or "failure"). English or not
Each result has the same chance of "success" p. for every [tex]p=0.40[/tex]
Well by the binomial distribution. Mean[tex]=E(x)=np=4.8[/tex]
Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
I think the area is 60 but i couldn't figure out the perimeter, sorry.
Step-by-step explanation:
Answer:
perimeter = 36 m
area = 60 m²
Step-by-step explanation:
there is some missing information. for example about the types of the shapes. e.g. if the triangle on the top is an isosceles triangle (2 equal sides). or if the rectangle at the bottom is actually a square with 6 m on all sides. in order to make the sloped side of the top triangle a round, whole number, i assume that the bottom part is a square.
so, the area of this combined shape is the area of the bottom square plus the area of the top triangle.
area square As = 6×6 = 36 m²
so, one side of the triangle is also 6 m, the other is 14-6 = 8 m.
the area of such a right-angled triangle is half of the full rectangle of 6×8.
area triangle At = 6×8/2 = 48/2 = 24 m²
total area = As + At = 36 + 24 = 60 m²
the perimeter of the total shape is the sum of all sides.
so, 14, 6, 6 and ... the baseline/ Hypotenuse of the top triangle.
for that r need the mentioned Pythagoras :
c² = a² + b²
where a and b are the sides, and c is the Hypotenuse (the side opposite of the 90 degree angle).
so, in our case of an isosceles triangle with a 90 degree angle :
c² = 8² + 6² = 64 + 36 = 100
c = 10 m
so, the perimeter is
14+6+6+10 = 36 m
Can you please help me
Answer:
you will type your answers and send
Answer:
Step-by-step explanation:
⅔-2/5 = 4/15
Given the coordinates of two points on a line, explain two methods to determine the slope of the line.
Answer:
Step-by-step explanation:
1. Use the slope formula (y2 - y1 / x2 - x1)
2. Use the graph. Take two points and count the rise over the run.
I’m so confused. Need the help
1.621 kN
Step-by-step explanation:
Let the centerline of the canal be the x-axis. Because the forces exerted by the horses are symmetric to the centerline, only the x-components of these forces contribute to the resultant force on the barge, i.e., the y-components cancel out. Each x-component is equal to [tex]F_x = 839\cos 15[/tex] = 810.4 N. Therefore, the resultant force on the barge is twice this:
[tex]F_{net} = 2(839\:\text{N})\cos 15 = 1620.8\:\text{N}[/tex]
[tex]= 1.621\:\text{kN}[/tex]
The pie chart shows student participation in fundraisers
at Mountain View Middle School.
Mountain View Middle School
Fundraisers
Which describes a bar diagram showing the percent of
students who participated in dances?
1 shaded square out of 10 squares
2 shaded squares out of 10 squares
3 shaded squares out of 10 squares
4 shaded squares out of 10 squares
20
Carnival
Car Wash
Bake Sale
Talent Show
10
50
5
15
Dances
Answer:
Step-by-step explanation:
If you add all of the numbers up, you get 100. Dances are colored purple, and that is 20. 20/100 simplified is 1/5. 1/5 is equivalent to 2/10. Therefore, the answer is 2 shaded squares out of 10 squares.
Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2935 mm with a standard deviation of 0.000924 mm.
(a) A certain shipment has a diameter of 0.2963. Find the standardized z-score for this shipment.
Answer:
Step-by-step explanation:
the formula attached
I really need help
Dz,2 of X is
(0-4)
(2,-2)
(6,2)
9514 1404 393
Answer:
(6,2)
Step-by-step explanation:
As is often the case with multiple-choice problems, you don't actually need to know the detailed working. You just need to know what the answer looks like.
When point X is dilated by a factor of 2 with point Z as the center of dilation, it will move to a location twice as far from Z. You can tell by looking at the graph that X' will be in the first quadrant, above and to the right of the location of X. The only sensible answer choice is ...
X' = (6, 2)
_____
Additional comment
X is a distance of X-Z = (4, 0) -(2, -2) = (2, 2) from Z Doubling that will put the image point a distance of 2(2, 2) = (4, 4) from Z. When this is added to Z, we find ...
X' = Z + (4, 4) = (2+4, -2+4) = (6, 2)
Write expression with two terms that is equivalent to the expression shown. 4(2x + 11 - x)
What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?
1
–1
i
–i
Answer:
B. -1 should be the answer
Step-by-step explanation:
Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.
Part 1: You can simplify [tex]a_n[/tex] to
[tex]\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}[/tex]
Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.
(a) So, the sequence is bounded above by its first value,
[tex]|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}[/tex]
(b) And because both fractions in [tex]a_n[/tex] converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,
[tex]|a_n| \ge \boxed{0}[/tex]
(c) Finally, [tex]a_n[/tex] is bounded above and below, so it is a bounded sequence.
Part 2: Yes, [tex]a_n[/tex] is monotonic and strictly decreasing.
Part 3:
(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.
(b) Since [tex]a_n[/tex] is decreasing and bounded below by 0, its limit as n goes to infinity is 0.
Part 4:
(a) We have
[tex]\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10[/tex]
and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.
(b) Taking the limit gives
[tex]\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty[/tex]
so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.
For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".
(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge
(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.
(e) does : this is true and is known as the monotone convergence theorem.
What is the quadratic regression equation that fits these data?
9514 1404 393
Answer:
D. y = -0.32x² -1.26x +15.81
Step-by-step explanation:
This is one of those multiple-choice questions where you only need a vague idea of what the answer is supposed to look like.
In this case the answer must be a quadratic equation with a negative leading coefficient. (The parabola opens downward.)
The only answer choice that is a 2nd degree polynomial with a negative leading coefficient is choice D.
__
A: linear equation
B: exponential equation
C: quadratic that opens upward (positive leading coefficient)
D: quadratic that opens downward -- the answer you're looking for
2) Consider the quadratic sequence 72, 100, 120, 132
2.1.1) Determine Tn the nth term of the quadratic.
Answer:
Tn = -4n²+40n+36
Step-by-step explanation:
A general quadratic sequence, Tn = an²+bn+c, where n is the term of the sequence.
So, when n = 1, Tn = 72, which means T1 = a+b+c=72.
when n = 2, Tn = 100, which means T2= 4a+2b+c = 100
when n = 3, Tn = 132, which means T3 = 9a+3b+c = 132.
Now, use a calcaulatot to solve the 3 variable simultaneous equation. According to my calculator, a = -4, b = 40, c = 36.
Hence, you a, b, and c in the Tn equation given above.
Therefore, Tn = -4n²+40n+36
Find the y-intercept from the line passing through (1, 3) and having slope m=2.
Answer:
The y intercept is 1
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Substitute the point into the equation and solve for y
3 = 2(1)+b
3 =2+b
1 = b
The y intercept is 1
What is the difference between the temperature - 7 Celsius and - 12 Celsius on a scatter diagram
Answer:
Sự khác biệt giữa nhiệt độ - 7 độ C và - 12 độ C trên biểu đồ phân tán là gì
Step-by-step explanation:
What is the scale factor of the dilation?
PLEASE BE CORRECT
In the figure, L1 || L2. 2x=174º. Find Za+Zb.
9514 1404 393
Answer:
12°
Step-by-step explanation:
We assume you mean ...
∠x = 174°
Angle a is supplementary to angle x, so is ...
∠a = 180° -174° = 6°
Angle b is a vertical angle with respect to angle 'a', so is the same measure.
∠a +∠b = 6° +6° = 12°
Find a fraction equivalent to
that has a denominator of 10.
Answer:
1/10
Step-by-step explanation:
any number (1-9) as the number above the fraction line (numerator) with the number 10 below the fraction line is a fraction with a denominator of 10.
if it was 10/10, it will = 1
Annie bought a 2 3/4 pound roast for the family dinner. A total of 9 people will be at dinner. How many pound of roast will each person get if the roast is divided up equally?
Answer:
11 /36 of a pound
Step-by-step explanation:
Take the pounds and divide by the number of people
2 3/4 ÷ 9
Change the mixed number to an improper fraction
(4*2+3)/4 ÷9
11/4 ÷9
Copy dot flip
11/4 * 1/9
11/36
A number is chosen at random from 1 to 50. What is the probability of selecting
multiples of 10.
Answer: 25
Step-by-step explanation:
The length of a rectangle is 2 centimeters less than three times its width. Its area is 21 square centimeters. Find the dimensions of the rectangle. Use the formula, area=length*width.
Area = length x width
Area = 21 square cm
Width = x
Length = 3x + 2
21 = 3x+ 2 * x
21 = 3x ^2 + 2x
Subtract 21 from both sides:
3x^2 + 2x -21 = 0
Use the quadratic formula to solve for x:
-2 +/- sqrt(2^2-4*3(-21))/(2*3)
X = 7/3 and -3
A dimension can’t be a negative value so x needs to be 7/3
Width = x = 7/3 = 2 1/3 cm
Length = 3(7/3) + 2 = 9 cm
Check: 9 x 2 1/3 = 21
Dimensions: width 2 1/3 cm length 9 cm
Answer:
The dimensions of the rectangle are 7 by 3 centimeters.
Step-by-step explanation:
We are given that the length of a rectangle is two centimeters less than three times its width. In other words:
[tex]\displaystyle \ell = 3w-2[/tex]
Given that the area of the rectangle is 21 square centimeters, we want to determine the dimensions of the rectangle.
Recall that the area of a rectangle is given by:
[tex]A= w\ell[/tex]
Substitute:
[tex](21)=w(3w-2)[/tex]
Solve foro the width. Distribute:
[tex]3w^2-2w=21[/tex]
Isolate the equation:
[tex]3w^2-2w-21=0[/tex]
Factor. Find two numbers that multiply to 3(-21) = -63 and add to -2.
-9 and 7 suffice. Hence:
[tex]3w^2-9w+7w-21=0 \\ \\ 3w(w-3)+7(w-3) = 0 \\ \\ (3w+7)(w-3)=0[/tex]
Zero Product Property:
[tex]3w+7=0\text{ or } w-3=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle w = -\frac{7}{3}\text{ or } w=3[/tex]
Since width cannot be negative, we can ignore the first solution.
Therefore, our width is three centimeters.
And since the length is two less than three times the width, the length is:
[tex]\ell = 3(3) - 2 = 7[/tex]
The dimensions of the rectangle are 7 by 3 centimeters.
if one half of a number is 5 more than 6, what is the value when the number is tripled
Answer:
66
Step-by-step explanation:
let's use x to represent the unknown number
1/2x is 5 more than 6:
↓
1/2x=5+6
solve to find x
1/2x=11
x=22
next, it asks us what is the value of the number when the number is tripled
since we already found what x is equal to, we can multiply that by 3 to figure out its value when it's tripled
3(22)=66
Using mathematical equation to model the scenario, the value of the number when tripled is 66
Let the number = n
0.5n = 5 + 6
0.5n = 11
Divide both sides by 0.5
n = 22
When n is tripled :
n = 22 × 3
n = 66
Hence, the value of the number when tripled is 66
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