The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule [tex]n^4+1[/tex]. The next number would then be fourth power of 7 plus 1, or 2402.
And the harder way: Denote the n-th term in this sequence by [tex]a_n[/tex], and denote the given sequence by [tex]\{a_n\}_{n\ge1}[/tex].
Let [tex]b_n[/tex] denote the n-th term in the sequence of forward differences of [tex]\{a_n\}[/tex], defined by
[tex]b_n=a_{n+1}-a_n[/tex]
for n ≥ 1. That is, [tex]\{b_n\}[/tex] is the sequence with
[tex]b_1=a_2-a_1=17-2=15[/tex]
[tex]b_2=a_3-a_2=82-17=65[/tex]
[tex]b_3=a_4-a_3=175[/tex]
[tex]b_4=a_5-a_4=369[/tex]
[tex]b_5=a_6-a_5=671[/tex]
and so on.
Next, let [tex]c_n[/tex] denote the n-th term of the differences of [tex]\{b_n\}[/tex], i.e. for n ≥ 1,
[tex]c_n=b_{n+1}-b_n[/tex]
so that
[tex]c_1=b_2-b_1=65-15=50[/tex]
[tex]c_2=110[/tex]
[tex]c_3=194[/tex]
[tex]c_4=302[/tex]
etc.
Again: let [tex]d_n[/tex] denote the n-th difference of [tex]\{c_n\}[/tex]:
[tex]d_n=c_{n+1}-c_n[/tex]
[tex]d_1=c_2-c_1=60[/tex]
[tex]d_2=84[/tex]
[tex]d_3=108[/tex]
etc.
One more time: let [tex]e_n[/tex] denote the n-th difference of [tex]\{d_n\}[/tex]:
[tex]e_n=d_{n+1}-d_n[/tex]
[tex]e_1=d_2-d_1=24[/tex]
[tex]e_2=24[/tex]
etc.
The fact that these last differences are constant is a good sign that [tex]e_n=24[/tex] for all n ≥ 1. Assuming this, we would see that [tex]\{d_n\}[/tex] is an arithmetic sequence given recursively by
[tex]\begin{cases}d_1=60\\d_{n+1}=d_n+24&\text{for }n>1\end{cases}[/tex]
and we can easily find the explicit rule:
[tex]d_2=d_1+24[/tex]
[tex]d_3=d_2+24=d_1+24\cdot2[/tex]
[tex]d_4=d_3+24=d_1+24\cdot3[/tex]
and so on, up to
[tex]d_n=d_1+24(n-1)[/tex]
[tex]d_n=24n+36[/tex]
Use the same strategy to find a closed form for [tex]\{c_n\}[/tex], then for [tex]\{b_n\}[/tex], and finally [tex]\{a_n\}[/tex].
[tex]\begin{cases}c_1=50\\c_{n+1}=c_n+24n+36&\text{for }n>1\end{cases}[/tex]
[tex]c_2=c_1+24\cdot1+36[/tex]
[tex]c_3=c_2+24\cdot2+36=c_1+24(1+2)+36\cdot2[/tex]
[tex]c_4=c_3+24\cdot3+36=c_1+24(1+2+3)+36\cdot3[/tex]
and so on, up to
[tex]c_n=c_1+24(1+2+3+\cdots+(n-1))+36(n-1)[/tex]
Recall the formula for the sum of consecutive integers:
[tex]1+2+3+\cdots+n=\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2[/tex]
[tex]\implies c_n=c_1+\dfrac{24(n-1)n}2+36(n-1)[/tex]
[tex]\implies c_n=12n^2+24n+14[/tex]
[tex]\begin{cases}b_1=15\\b_{n+1}=b_n+12n^2+24n+14&\text{for }n>1\end{cases}[/tex]
[tex]b_2=b_1+12\cdot1^2+24\cdot1+14[/tex]
[tex]b_3=b_2+12\cdot2^2+24\cdot2+14=b_1+12(1^2+2^2)+24(1+2)+14\cdot2[/tex]
[tex]b_4=b_3+12\cdot3^2+24\cdot3+14=b_1+12(1^2+2^2+3^2)+24(1+2+3)+14\cdot3[/tex]
and so on, up to
[tex]b_n=b_1+12(1^2+2^2+3^2+\cdots+(n-1)^2)+24(1+2+3+\cdots+(n-1))+14(n-1)[/tex]
Recall the formula for the sum of squares of consecutive integers:
[tex]1^2+2^2+3^2+\cdots+n^2=\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}6[/tex]
[tex]\implies b_n=15+\dfrac{12(n-1)n(2(n-1)+1)}6+\dfrac{24(n-1)n}2+14(n-1)[/tex]
[tex]\implies b_n=4n^3+6n^2+4n+1[/tex]
[tex]\begin{cases}a_1=2\\a_{n+1}=a_n+4n^3+6n^2+4n+1&\text{for }n>1\end{cases}[/tex]
[tex]a_2=a_1+4\cdot1^3+6\cdot1^2+4\cdot1+1[/tex]
[tex]a_3=a_2+4(1^3+2^3)+6(1^2+2^2)+4(1+2)+1\cdot2[/tex]
[tex]a_4=a_3+4(1^3+2^3+3^3)+6(1^2+2^2+3^2)+4(1+2+3)+1\cdot3[/tex]
[tex]\implies a_n=a_1+4\displaystyle\sum_{k=1}^3k^3+6\sum_{k=1}^3k^2+4\sum_{k=1}^3k+\sum_{k=1}^{n-1}1[/tex]
[tex]\displaystyle\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}4[/tex]
[tex]\implies a_n=2+\dfrac{4(n-1)^2n^2}4+\dfrac{6(n-1)n(2n)}6+\dfrac{4(n-1)n}2+(n-1)[/tex]
[tex]\implies a_n=n^4+1[/tex]
Find the value of x. A: 15 B: 12 C: 10 D: 8
Answer:
[tex]\boxed{\sf C. \ 10}[/tex]
Step-by-step explanation:
[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]
[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]
[tex]NH \times HT = MH \times HY[/tex]
[tex](x+20) \times 8=12 \times 20[/tex]
[tex]\sf Expand \ brackets \ and \ multiply.[/tex]
[tex]8x+160=240[/tex]
[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]
[tex]8x+160-160=240-160[/tex]
[tex]8x=80[/tex]
[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]
[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]
[tex]x=10[/tex]
The value of x is 10.
We have a circle and inside it two chords MY and NT intersect at point H.
We have to find the value of x in the figure.
What is intersecting chord theorem?According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then
AO x OB = CO x OD
Applying the chord intersecting theorem to the figure in the question, we get -
MH x HY = NH x HT
12 x 20 = (x+20) x 8
240 = 8x + 160
8x = 80
x = 10
Hence the value of x is 10.
To solve more questions on Circles and chords, visit the link below -
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A quiz has 4 multiple-choice questions with 4 possible answer choices each. For each question, there is only 1 correct answer.
A student guesses each answer at random. What is the probability of getting exactly 3 questions correct, to the nearest percent?
(3 correct and 1 incorrect)
Answer:
5%
Step-by-step explanation:
so, for 3 questions he has a 1 in 4 chances to get it right.
4³ chances, so a 1/4³ probability.
and he has one other question with a 3 in 4 chance to get it wrong.
a 3/4 probability.
that is in total
1/4³ × 3/4 = 3/4⁴
and now we have 4 over 3 combinations as possibilities to get 3 right and 1 wrong.
that is 4! / (3! × (4-3)!) = 4
so our total probability is
4 × 3/4⁴ = 3/4³ = 3/64 ≈ 0.05 = 5%
in other words, the expected quote for him to achieve that result is in 5 out of 100 (or 1 out of 20) attempts.
Which of the following graphs represents a one-to-one function? On a coordinate plane, a function has two curves connected to a straight line. The first curve has a maximum of (negative 6, 4) and a minimum of (negative 4.5, negative 1). The second curve has a maximum of (negative 3.5, 2) and a minimum of (negative 2.5, 0.5). The straight line has a positive slope and starts at (negative 2, 1) and goes through (1, 2). On a coordinate plane, a circle intersects the x=axis at (negative 2, 0) and (2, 0) and intercepts the y-axis at (0, 4) and (0, negative 4). On a coordinate plane, a v-shaped graph is facing up. The vertex is at (0,0) and the function goes through (negative 4, 4) and (4, 4). A coordinate plane has 7 points. The points are (negative 4, 1), (negative 3, 4), (negative 1, 3), (1, negative 3), (3, negative 4), (4, negative 2), (5, 3). Mark this and return
Answer:
d. this graph
Step-by-step explanation:
Find the volume of this composite figure. Show all work.
Please!!!!!
Answer:
718.75ft³
Step-by-step explanation:
Rectangular Prism=5x5x17.5=437.5
Cube=5x5x5=125
Triangular Prism=5x5x12.5x.5=156.25
437.5+125+156.25=718.75ft³
Needs to be done using the Pythagorean Theorem
Answer:
11.3 ft high
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
4² + b² = 12²
16 + b² = 144
b² = √128
b = 11.3
A random sample of size results in a sample mean of and a sample standard deviation of . An independent sample of size results in a sample mean of and sample standard deviation of . Does this constitute sufficient evidence to conclude that the population means differ at the level of significance?
Answer:
A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.
Step-by-step explanation:
Find the measure of c.
Answer:
149 degrees
Step-by-step explanation:
This shape is a cyclic, so opposite angles add up to 180 degrees.
180-31 = 149
Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.
Answer:
The resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].
Step-by-step explanation:
The distributive property of multiplication is:
[tex]a\times (b+c)=(a\times b)+(a\times c)[/tex]
The two polynomials provided are:
[tex](2x+3)\\(x^{2}+x-2)[/tex]
Determine the final expression by multiplying the two polynomials as follows:
[tex](2x+3)\times (x^{2}+x-2)=[2x\times(x^{2}+x-2)]+[3\times(x^{2}+x-2)][/tex]
[tex]=[(2x\times x^{2})+(2x\times x)-(2x\times 2)]+[(3\times x^{2})+(3\times x)-(3\times 2)]\\\\=[2x^{3}+2x^{2}-4x]+[3x^{2}+3x-6]\\\\=2x^{3}+2x^{2}+3x^{2}-4x+3x-6\\\\=2x^{3}+5x^{2}-x-6[/tex]
Thus, the resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].
If ‘BOXES’ is OBXSE, then BOARD is
9514 1404 393
Answer:
OBADR
Step-by-step explanation:
The first two letters are swapped, and the last two letters are swapped.
BOARD . . . becomes
OBADR
Please help!!
A) In a movie, a mad scientist enlarges a cow to 100 times its normal size. How much stronger would its legs be than a normal cow?
B) How many times more would it weigh than a normal cow?
C) Can you see how results A and B would yield a cow that would collapse under its own weight?
Answer:
100 times everything.
Step-by-step explanation:
If the cow is 100 times larger than its normal size, obviously everything else should be 100 times stronger and heavier.
Pimeter or area of a rectangle given one of these...
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 48 cm, find its area.
Answer:
A=108 cm²
Step-by-step explanation:
length (l)=3w
perimeter=2l+2w
P=2(3w)+2w
48=6w+2w
width=48/8
w=6
l=3w=3(6)=18
l=18 cm , w=6 cmArea=l*w
A=18*6
A=108 cm²
Use Taylor series to evaluate
limx→0(tan x − x)/x^3
Recall that
tan(x) = sin(x)/cos(x)
and
sin(x) = x - x ³/6 + x ⁵/120 - x ⁷/5040 + …
cos(x) = 1 - x ²/2 + x ⁴/24 - x ⁶/720 + …
Truncate the series to three terms. Then
[tex]\displaystyle \lim_{x\to0}\frac{\tan(x)-x}{x^3} = \lim_{x\to0}\frac{\frac{x-x^3/6+x^5/120}{1-x^2/2+x^4/24}-x}{x^3} \\\\ = \lim_{x\to0}\left(\frac{x-x^3/6+x^5/120}{x^3-x^5/2+x^7/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2-x^4/2+x^6/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac{1-x^2/2+x^4/24}{x^2\left(1-x^2/2+x^4/24\right)}\right) \\\\ = \lim_{x\to0}\frac{x^2/3-x^4/30}{x^2\left(1-x^2/2+x^4/24\right)} \\\\ = \lim_{x\to0}\frac{1/3-x^2/30}{1-x^2/2+x^4/24} = \boxed{\frac13}[/tex]
Which of the following graphs is the inverse of f(x) = x2 + 4?
Answer:
Step-by-step explanation:
Can someone help me with this?
Answer:
183.3 in^3
Step-by-step explanation:
Find the volume of the rectangular bottom
V = l*w*h
V = 5*5*6 =150 in^3
Find the volume of the triangular pyramid
V = 1/3 Bh where B is the area of the base and h is the height
V = 1/3 ( 5*5) * 4 = 100/3
Add the two volumes together
150 + 100/3
150 +33.3
183.3 in^3
Find all real solutions of the equation: x 2 + 3x − 10 = 0
Answer: x=8/3 or x= 2.6666....
Step-by-step explanation:
[tex]2+3x-10=0[/tex]
[tex]2-10=-8[/tex]
[tex]3x-8=0[/tex]
add 8 on both sides
[tex]3x-8+8=0+8[/tex]
[tex]3x=8[/tex]
divide 3 on both sides
[tex]x=\frac{8}{3}[/tex]
Answer:
8/3
Step-by-step explanation:
2 +3x + 10 = 0
2-10 +3x = 0
-8 + 3x = 0
3x = 8
x = 8/3
For a closed rectangular box, with a square base x by x cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 18 cm3.
Answer:
∛18 * ∛18 * 18/(∛18)²
Step-by-step explanation:
Let the surface area of the box be expressed as S = 2(LB+BH+LH) where
L is the length of the box = x
B is the breadth of the box = x
H is the height of the box = h
Substituting this variables into the formula, we will have;
S = 2(x(x)+xh+xh)
S = 2x²+2xh+2xh
S = 2x² + 4xh and the Volume V = x²h
If V = x²h; h = V/x²
Substituting h = V/x² into the surface area will give;
S = 2x² + 4x(V/x²)
Since the volume V = 18cm³
S = 2x² + 4x(18/x²)
S = 2x² + 72/x
Differentiating the function with respect to x to get the minimal point, we will have;
dS/dx = 4x - 72/x²
at dS/dx = 0
4x - 72/x² = 0
- 72/x² = -4x
72 = 4x³
x³ = 72/4
x³ = 18
[tex]x = \sqrt[3]{18}[/tex]
Critical point is at [tex]x = \sqrt[3]{18}[/tex]
If x²h = 18
(∛18)²h =18
h = 18/(∛18)²
Hence the dimension is ∛18 * ∛18 * 18/(∛18)²
How do you compress this?
[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=2x\\b=3\\r+1=4\Rightarrow r=3\\n=5\\T_4=\binom{5}{3}\cdot (2x)^{5-3}\cdot3^3\\T_4=\dfrac{5!}{3!2!}\cdot 4x^2\cdot27\\T_4=\dfrac{4\cdot5}{2}\cdot 4x^2\cdot27\\\\T_4=1080x^2[/tex]
PLEASE ANSWER ASAP!!!
Expressions and answer options in picture
If you were asked to subtract in the following pair of expressions, what you use as the least common denominator?
any unrelated answers will be reported
Answer:
C=x (x+3)
Step-by-step explanation:
x cannot divide x+3 definitely so the denominators must be multiplied to get the least common denominator.
The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
h = –21.962x + 114.655
As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.
Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
Learn more about the line of best fit here:
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An ‘in shuffle’ is a perfect shuffle on a standard deck of 52 playing cards that splits the deck in half, then interleaves cards starting with the top half.
Required:
a. What is the position of the first card after the 7th shuffle?
b. How many times must one perform the shuffle so that the top card becomes the bottom card?
c. When do the first and last cards in the deck touch?
Answer:
a) position 22
b) 26
c) shuffle 25
Step-by-step explanation:
Assuming the shuffling occurs so that the bottom card of the top half of the deck (card 26) becomes the bottom card (card 52), while the top card of the bottom half (card 27) becomes the top card (card 1), the sequence of card 1 positions with successive shuffles is ...
{2, 4, 8, 16, 32, 11, 22, 44, 35, 17, 34, 15, 30, 7, 14, 28, 3, 6, 12, 24, 48, 43, 33, 13, 26, 52, 51, 49, 45, 37, 21, 42, 31, 9, 18, 36, 19, 38, 23, 46, 39, 25, 50, 47, 41, 29, 5, 10, 20, 40, 27, 1}
That is, after the first shuffle, card 1 is at position 2; after the second shuffle, it is at position 4; and so on.
(a) Hence the position of card 1 after the 7th shuffle is 22.
__
(b) The top card is in position 52 after 26 shuffles.
__
(c) The top card is in position 26 after 25 shuffles; the bottom card is in position 27 after 25 shuffles. That is when they first touch. (They touch again after 51 shuffles.)
Simone invests $2,000 in an account that compounds interest quarterly and earns 9%. How many years will it take for his money to double? (Round your answer to one decimal place.)
no te puedo contestarte yo no hablo inglés
What best explains whether a triangle with side links 5 cm 13 cm and 12 cm is a right triangle
Step-by-step explanation:
Pythagoras Theorem
If the sum of the squares of the smaller two sides is equal to the square if the third side then it is a right triangle
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
So, (5)^2 + (12)^2
is 25 + 144 = 169
Which is equal to (13)^2 which is also 169
The sides of the given triangle follows pythagoras theorem, therefore it is a right triangle
Hope it helps:)
Answer:
Pythagorean theorem
Step-by-step explanation:
We can explain it using the Pythagorean theorem. Right triangles always have a hypotenuse which is the longest side. That means 13 must be the hypotenuse of the triangle. The Pythagorean theorem is a^2+b^2=c^2
We already know all the values since every side is given so we just fill it in.
5^2+12^2=13^2
25+144=169
169=169
It is a right triangle
The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly.Monthly Sales Salesperson After Before1 94 902 87 853 90 844 86 815 80 806 85 80
Answer:
it is clear that at 95% confidence that the bonus plan has increased the sales significantly, because if we observe you will notice that sales after is greater than sales before in all six cases.
Step-by-step explanation:
A 95% confidence interval as we have above is the range of values that we can say with utmost certainty and confidence that 95% chance it contains the true mean of the population. in other words we can say that a 95% confidence interval defines a range of values that you can be 95% certain contains the population mean.
Write the polar form of a complex number in standard form for [tex]8[cos(\frac{\pi}{2}) + isin(\frac{\pi}{2})][/tex]
Answer:
Solution : 8i
Step-by-step explanation:
We can use the trivial identities cos(π / 2) = 0, and sin(π / 2) = 1 to solve this problem. Let's substitute,
[tex]8\left[cos\left(\frac{\pi }{2}\right)+isin\left(\frac{\pi \:}{2}\right)\right][/tex] = [tex]8\left(0+1i\right)[/tex]
And of course 1i = i, so we have the expression 8(0 + i ). Distributing the " 8, " 8( 0 ) = 0, and 8(i) = 8i, making the fourth answer the correct solution.
Tom and Jerry had a race. Tom started at 0200 running at 4.5km per hour. Jerry started
later at 6:30am running at 6.5km per hour. After five hours, who was ahead, and by how
much (answer in kilometres)
Answer:
Tom, 10.25
Step-by-step explanation:
Distance covered by Tom=4.5*(4 1/2+5)=81/4=42.75km
Distance covered by Jerry=6.5*(5)=32.5km
Tom is ahead from Jerry by 10.25km
Ava placed the point of her pencil on the origin of a regular coordinate plane. She marked a point after moving her pencil 4 units to the left and 7 units up. Which ordered pair identifies where Ava marked her point?
[tex] \Large{ \boxed{ \bold{ \color{lightgreen}{Solution:}}}}[/tex]
So, Let's solve this question by using cartesian plane.
Here, Origin is shown by (0, 0)Ava moves 4 units left from origin. On the left side of origin, negative x axis begins. So, she reached (-4, 0) now.Then, from that point she moved 7 units upwards. On the upper side, there is positive y axis. So, Finally she will reach point (-4, 7).(-4, 7) is the coordinate of point which is 4 units left from y axis and 7 units up from x axis.It lies on the second quadrant.Well, What is cartesian plane?
A - A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
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How many 1/8 servings can I get from 3/4
Answer:
6 1/8th cups in 3/4 cups
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
you convert 3/4 into 8ths which will be 6/8
A carpenter is making doors that are 20582058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 1010 doors is made, and it is found that they have a mean of 20462046 millimeters with a standard deviation of 1515. Is there evidence at the 0.050.05 level that the doors are too short and unusable
Answer:
Z= 0.253
Z∝/2 = ± 1.96
Step-by-step explanation:
Formulate the null and alternative hypotheses as
H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test
Here ∝= 0.005
For alpha by 2 for a two tailed test Z∝/2 = ± 1.96
Standard deviation = s= 15
n= 10
The test statistic used here is
Z = x- x`/ s/√n
Z= 2058- 2046 / 15 / √10
Z= 0.253
Since the calculated value of Z= 0.253 falls in the critical region we reject the null hypothesis.
There is evidence at the 0.05 level that the doors are too short and unusable.
Variable g is 8 more than variable w. Variable g is also 2 less than w. Which pair of equations best models the relationship between g and w? g = 8w g = w + 2 w = g + 8 w = g − 2 w = 8g w = g + 2 g = w + 8 g = w − 2
Answer: g = w + 8 g=w-2
Step-by-step explanation:
We could represent the word phrases by the equations.
g = w + 8
g = w - 2
Answer:
g = w + 8
g = w - 2
Step-by-step explanation:
Assuming that g and w exists, then we can show the relation as described:
"Variable g is 8 more than variable w."
g = w + 8
"Variable g is also 2 less than w."
g = w - 2
These are the two equations of the described relationship between g and w.
Note that g could not actually exist in the real number system:
g = w + 8
g = w - 2
w + 8 = w - 2
w - w = -2 - 8
0 != -10
This is impossible within the real number system.
Cheers.
The number of weekly hours spent on a smart device varies inversely with the person's age. If a 20-year-old person spends 52 hours on their smart device each week, how many hours does a 50-year-old person spend on their smart device?
Answer:
20.8 hours
Step-by-step explanation:
Given that hours (h) varies inversely with age (a) then the equation relating them is
h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation
To find k use the condition h = 52 when a = 20, thus
52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )
1040 = k
h = [tex]\frac{1040}{a}[/tex] ← equation of variation
When a = 50, then
h = [tex]\frac{1040}{50}[/tex] = 20.8 hours