Answer:
Step-by-step explanation:
let present age of father=y
present age of son=x
then y=3x
after 15 years age of father=y+15
and age of son=x+15
∴y+15=2(x+15)
y+15=2x+30
y-2x=30-15
y-2x=15
∴3x-2x=15
x=15
y=3x=15×3=45
father's present age=45 years
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.
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.
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
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.
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
For
90° < 0 < 270°
, which of the primary trigonometric functions may have positive values?
Answer:
sine and tangent
will be positive.
Complete the equation describing how x
and y are related.
Х у
y = [? ]x +
07
1 9
2 11
3 13
4 15
5 17
Enter the answer that
belongs in [?]
Answer:
Hello,
Answer 2
Step-by-step explanation:
7=2*0+7
9=2*1+7
11=2*2+7
13=2*3+7
15=2*4+7
17=2*5+7
y=2*x+7
An other way:
[tex]points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\[/tex]
The complete equation is [tex]y = 2x+7[/tex].
What is equation?An equation is a condition on a variable such that two expressions in the variable should have equal value.
What is substitution?Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
[tex]y = ax + b[/tex]
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
[tex]\implies 7 = a(0) + b\\\implies b = 7[/tex]
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
[tex]\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2[/tex]
substitute the value of a and b in the equation y = ax + b.
[tex]\implies y = 2x+ 7[/tex]
Therefore, the complete equation is [tex]y = 2x+7[/tex].
Find out more information about equation and substitution here:
https://brainly.com/question/2581775
#SPJ2
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
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.
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
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
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
Find the intersection point for the following liner function f(x)= 2x+3 g(x)=-4x-27
Answer:
( -5,-7)
Step-by-step explanation:
f(x)= 2x+3 g(x)=-4x-27
Set the two functions equal
2x+3 = -4x-27
Add 4x to each side
2x+3+4x = -4x-27+4x
6x+3 = -27
Subtract 3
6x+3 - 3 = -27-3
6x = -30
Divide each side by 6
6x/6 = -30/6
x =-5
Now we need to find the output
f(-5) = 2(-5) +3 = -10+3 = -7
Answer:
Step-by-step explanation:
big burgewr
What's the simplified expression of -2a-3 bº?
Answer:
-2a - 3
Step-by-step explanation:
bº equals 1 due to the zero exponent.
Thus, -2a-3 bº simplifies to -2a - 3.
Answer:
−2/a^3
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
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]
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.)
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
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]
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:
prove that 2^n+1>(n+2).sin(n)
Step-by-step explanation:
F(n)=|sin(n)|+|sin(n+1)|
then
F(n+π)=|sin(n+π)|+|sin(n+π+1)|=|sin(n)|+|sin(n+1)|=F(n)
and
F(π−n)=|sin(π−n)|+|sin(π−n+1)|=|sinn|+|sin(n−1)|≠F(n)
so we must prove when n∈(0,π), have
F(n)>2sin12
when n∈(0,π−1),then
F(n)=sinn+sin(n+1)=sinn(1+cos1)+sin1cosn
and n∈(π−1,π),then
F(n)=sinn−sin(n+1)
How prove it this two case have F(n)>2sin12? Thank you
and I know this well know inequality
|sinx|+|sin(x+1)|+|sin(x−1)|≥2sin1,x∈R
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
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
A sample contains 61 pairs of values. Find the critical value for the linear correlation coefficient from Table A-6 corresponding to a 0.05 significance level.
0.236
0.254
0.279
0.330
Answer:
0.254
Step-by-step explanation:
Table A-6 will be shown below for reference. Since none of the answer choices contain the critical value for 61, we can just round that number to 60. We will see that the critical value is 0.254. If you're having trouble reading the table below, look at the columns to find the corresponding significance level you are working with then find the sample value.
Best of Luck!
B is the midpoint of line segment AD, and C is the midpoint of line segment BD. If AD = 12, what is BC?
A. 1.5
B. 3
C. 4
D. 6
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
a polynomial p has zeros when x=1/5,x=-4, andx=2 what could be the equation of p?
Answer:
x^3 + (9/5)x^2 -(42/5)x + (8/5)
Step-by-step explanation:
since 1/5, -4, and 2 are all zeroes, (x-1/5)(x+4)(x-2) must be a factor of p. if you distribute the statement, you get
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
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.
Can someone please help I don't understand. Determine the domain and range of the following function. Record your answers in set notation.
Look at the screenshot!!!