Answer:
The answer is "6.093 years".
Step-by-step explanation:
The rate of decline in sales in [tex]22\%[/tex] per year.
The starting sales is 100 units:
Using compounding formula:
[tex]\to 100 \times (1-\frac{22}{100})^t=22\% \ of \ 100\\\\\to 100 \times (\frac{100-22}{100})^t=\frac{22}{100} \times \ 100\\\\\to (\frac{78}{100})^t=\frac{22}{100}\\\\\to 0.78^t=0.22\\\\\text{taking \log on both the sides}\\\\[/tex]
taking log on both sides
[tex]\to \log_e \ 0.78^t= \log_e\ 0.22\\\\\to t \log_e \ 0.78= \log_e\ 0.22\\\\\to t = \frac{\log_e 0.22}{\log_e 0.78}\\\\[/tex]
[tex]= \frac{-0.6575}{-0.1079}\\\\= \frac{0.6575}{0.1079}\\\\=6.093[/tex]
If A and B are independent events, then it must be true that P(ATB) = P(A).
well, let's take a look at two independent events
A) the potato is hot
B) it's raining
now, the potato could be hot whether is raining or not, A is totally independent of B, so what's the probability of "the potato being hot, GIVEN that it's raining" P(A | B) is the same as if it wasn't raining, or P(A), the fact that B occurred, doesn't affect A at all, the potato is hot regardless, rain or not. So P(A | B) = P(A).
pls answer w explanation!
What is the product of the complex numbers 2 + 6i and 2 - 6i? (Note: i= √-1)
Answer:
10
Step-by-step explanation:
Apply difference of squares.
[tex](x + y)(x - y) = {x}^{2} - {y}^{2} [/tex]
[tex](2 + 6i)(2 - 6i) = {2}^{2} - {6i}^{2} [/tex]
[tex] = 4 + 6[/tex]
[tex] = 10[/tex]
Use the equation of the water level of the river represented by the equation y = −4x + 170, where x represents the number of years and y represents the total feet. What points are located on the line? Check all that apply. (170, 0) (0, 170) (12, 126) (50, 30) (5, 150) (60, –70)
Answer:
(0, 170) (5, 150) (60, -170)
Step-by-step explanation:
Plug each x value into the equation. The point is located on the line if the y values match.
Ex. -4 (170) + 170 = -510 this point is not on the line
-4 (0) + 170 = 170 this point is on the line because it is a "true" statement
Answer:
(0, 170) (5, 150) (60, -170)
Step-by-step explanation:
The 20th term of an arithmetic progression 1,5,9,13......
Answer:
a₂₀ = 77
Step-by-step explanation:
There is a common difference between consecutive terms , that is
5 - 1 = 9 - 5 = 13 - 9 = 4
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 1 and d = 4 , then
a₂₀ = 1 + (19 × 4) = 1 + 76 = 77
After simplification, the value of 1-2/1(1+2)-3/(1+2)(1+2+3)-4/(1+2+3)(1+2+3+4)-...-100/(1+2+...+99)(1+2+...+100)
is a proper fraction in its lowest form. Find the difference of its numerator and denominator.
Answer: no
Step-by-step explanationn. .......................................................w:eorkeok,feoferkeorkoe
Evaluate the expression 42 +6.52 – 33 = 32,
What is the answer to this question
PLEASE HELP ILL GIVE BRAINLIEST
If t< sand s< r what is the relationship between the values tand /?
Answer:
If you are talking about inequalities, t < r.
Step-by-step explanation:
Since s is bigger than t and r is bigger than s,
r should be bigger than t obviously.
PLZ HELPPP!!! whoever answers first with a good answer ill mark as brainliest
This is because the nth term is found by adding the previous two terms
F(n) = nth term
F(n-1) = term just before the nth term
F(n-2) = term before the F(n-1) term
F(n) = F(n-1) + F(n-2)
We can re-index values of n to say this equivalent statement
F(n+2) = F(n+1) + F(n)
Based on either equation mentioned, adding F(51) and F(52) will get us F(53). In other words, the 51st and 52nd terms add to the 53rd term.
Please help ASAP and please explain how you got the answer.
Answer:
The third one
Step-by-step explanation:
All show complementary angles ( angles that add up to 90 degrees ) except for the third one
First one: shows a square within the two angles which indicates that the angles form a right angle ( 90 degree angle ) meaning that they are complementary angles
Second: the angles add up to equal 90 ( 50 + 40 = 90 ) hence they are complementary angles
Third one: the angles form a straight line. Angles that form a straight line add up to equal 180 and are known as supplementary angles
Fourth: the angles shown add up to 90 ( 65 + 25 = 90) hence they are complementary angles
All are complementary but the third one
Can someone help me with this math homework please!
Answer:
1/2
8
Step-by-step explanation:
When its talking about the result or output, look at the range, and then follow the line(s) back to the number(s) in the domain. Do the opposite when it's talking about the function of a certain number, e.g. f(4).
please help i don’t have much time left !!!
Answer:
8.5
Step-by-step explanation:
QR is 10
PQRS AREA is 45
10 times 4.5 is 45
meaning BC and PQ is 4.5
4.5 plus 4.5 is 9
26 minus 9 is 17
17 divided by two is 8.5
AB is 8.5
On a Venn diagram, shade the region:
1. AnB
2. (BnC)nA
Answer:
hope it will be helpful to you
Step-by-step explanation:
anb shade and anbnc shade
Drag each condition to the correct location on the table.
Match each condition to the number of triangles that can be constructed to fit the condition.
condition A: one side
measuring 4 inches,
another side measuring
8 inches, and a third
side measuring 10 inches
condition B: one angle
measuring 60°, another
angle measuring 40°, and
a third angle measuring 90°
condition C: one side
measuring 4 inches,
another side measuring
8 inches, and the angle
between them measuring 70°
condition D: one side
measuring 5 inches,
another side measuring
7 inches, and a third
side measuring 12 inches
condition E: one angle
measuring 30°, another
angle measuring 80°,
and the length of the
included side measuring
8 inches
condition F: one angle
measuring 40°, another
angle measuring 80°, and
a third angle measuring 60° I don't know how to do a pic, but it is no triangle one triangle and many triangle
Answer:
Condition A= 320 inches
Condition B= 190 Degrees F
Condition C= 2240 inches
Condition D= 350 inches
Condition E= 110 Degrees F 8 inches
Condition F= 180 Degrees F
Step-by-step explanation:
4 inches
8 inches
70 inches
60 D
40 D
90 D
4 inches
8 inches
70 D
5 inches
7 inches
12 inches
30 D
80 D
8 inches
40 D
80 D
60 D
Answer:
Condition A= 320 inches
Condition B= 190 Degrees F
Condition C= 2240 inches
Condition D= 350 inches
Condition E= 110 Degrees F 8 inches
Condition F= 180 Degrees F
Step-by-step explanation:
In a school of 50 pupils,15 study English only and 20 study French only. 5 students do not study any of the two subjects. (i)illustrate the information on a Venn diagram
Answer:
48
Step-by-step explanation:
2-6$83737463363+77#7#+#++;#+#73737363644646464672727282939
Answer:
10
Explanation:
n(U)= 50
n०(E)= 15
n०(F)= 20
number of (E U F) whole complement= 5
NOW,
n(U)= 15+20+5+n(E intersection F)
or, 50= 40+n(E intersection F)
.•. n( E intersection F) = 10
c) What should be subtracted from 5m - 3n to get 2m + 5n?
What she hechosomoce 2-59
Answer:
3m-8n
Step-by-step explanation:
Set up an equation:
(5m-3n)-(2m+5n) = ?
Solve:
5m-3n
- 2m+5n
3m-8n
Hope this helps!
Find the equation of a quadratic function in general form whose graph has points: (-2, 3) (0, 3) and (-4,-5).
Try your best to show complete work & explain your strategy.
Answer:
-x²-2x+3
Step-by-step explanation:
The first thing I noticed is that the first and second point has the same y intercept despite being only 2 x coordiantes away. This must mean that the vertex's x coordiante is probably (-1,4)
Because the vertex is probably (-1,4) the graph must also be concave down because the point (-4,-5) is below it
writing this in vertex form we get
-a(x+1)²+4
Where a is some constant
solve for a by plugging in (0,3)
3= -a(0+1)²+4
3= -a+4
-1= -a
a=1
therefore the equation looks like
-(x+1)²+4
expanding this so that it's in stantard form...
-(x²+x+x+1)+4
-x²-2x+3
which is the final answer
My teacher keeps saying it’s wrong pls help, it’s question number 5
Which is an irrational number?
9514 1404 393
Answer:
A √2 is an irrational number
Step-by-step explanation:
A: √2 ≈ 1.4142135623730950488... an infinite non-repeating decimal (irrational)
B: √4 = 2 (rational)
C: ∛8 = 2 (rational)
D: √16 = 4 (rational)
Explain what the construction does and list the steps to creating the construction. Be as detailed as possible :D
Step-by-step explanation:
This construction bisects the pqr angle.
This is done by placing a compass on the pqr angle and marking construction lines at the points c and a.
Then at where the construction lines at points c and a meet the lines qr and qp draw 2 more from that placement.
Then draw a line running through angle pqr and where the construction lines meet at point b.
Hope this helps and good luck!
I would appreciate the help on all of these :)
Answer:
Pythagoras theorem states that c²=a²+b²
14²=12²+x²
14²-12²=x²
196-144=x²
52=x²
√52=√x²
7.2111025509279785=x
rounded up to the nearest hundredth=7.21
Please help ASAP! D,:
What are the dimensions of the rectangle shown below? Remember to use the axes on the coordinate grid to help you.
Answers:
14 units × 4 units
16 units × 8 units
24 units × 14 units
64 units × 4 units
please help me it’s urgent
Answer:
600g of Flour
Step-by-step explanation:
According to the question every 15 biscuits is 50g it need 50g of sugar and flour is 3 times the amount it needs for 15 biscuits so 50*3=150 now we know 15 biscuits need 150g of flour so 30 requires 300 and 300g +300g is equal to 600g of flour.
Answer:
600 g of flour.
Step-by-step explanation:
If Deon needs 50 g of sugar to make 15 biscuits, and she is going to make 60 biscuits, then she will need 200 g of sugar, since 60/15 is 4.
If the amount of flour she needs is equal to the amount of sugar multiplied by three, or 3x, if x is the amount of sugar, then she will need 200 x 3 g of flour.
Therefore, she will need 600 g of flour.
Can someone help me solve this problem please
Thankyouuuu
Answer:
in picture
Step-by-step explanation:
Brainliest please
Answer:
this is the best way for the question
What is the probality of rolling a 6-sided die on a getting a 1 or a prime number?
Answer:
1/12
Step-by-step explanation:
Chances of getting a 1 are 1/6 and chances of getting a prime number excluding 1 is 3/6. 3/6 x 1/6= 3/36 or 1/12 chance.
The price of an item decreased by 20% to $200. Then later the price decreased again from $200 to $150. What is the percent of decrease from the original price to the final price $150?
Answer:
40%
Step-by-step explanation:
ok so first find the og price:
100% - 20% = 80%
so 80% = 200
let the 100% be x:
x * 0.8 = 200
x= 250
100% = 250
(difference/ og price) * 100% = the percentage decrease/ increase
(250-150/250)* 100% = 40%
OR
((the final price/ og price) * 100%) - 100%
((150/250)*100%) - 100% = 40%
There was a 40% decrease from the og price to the final price of 150.
What is the equation of the line that passes through the given point and is perpendicular to the given line?
Point: (1,1)
Line: y=15x+45
Answer:
y= -1/15x + 16/15
Step-by-step explanation:
When two lines are perpendicular to each other that means their slopes are the negative reciprocals of each other.
So that means if a line has has a slope of 6, a line perpendicular to that line will have a slope of -1/6.
(a reciprocal is when the fraction is flipped over)
In this case, the negative reciprocal of 15 would be -1/15. So the slope of the line that is perpendicular would be -1/15.
The equation we would have so far for that line would be: y=-1/15x+b
Now we have to find the 'b' or the y intercept, which we can get by plugging in the point that was given (1,1), which is on that line.
Which gives us 1=-1/15(1)+b.
1=-1/15+b
1+1/15=b
Then you solve for b and get b= 16/15.
The equation of the line that is perpendicular to the given line is y= -1/15x + 16/15.
The equation of the line that passes through the point (1, 1) and is perpendicular to y = 15x + 45 is
y = 15x - 14.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Let the equation of a line is y = mx + c.
The line is perpendicular to y = 15x + 45.
y = 15x + 45 is in the form of y = mx + c
This means,
Slope = 15
m = 15
The line passes through the point (1, 1) = (x, y).
This means,
y = mx + c
1 = 15 x 1 + c
1 = 15 + c
c = 1 - 15
c = -14
The equation of the line is y = 15x - 14.
Thus,
The equation of the line that passes through the point (1, 1) and is perpendicular to y = 15x + 45 is
y = 15x - 14.
Learn more about equation of a line here:
https://brainly.com/question/23087740
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A paintball park charges an entrance fee, and fee per game played. On saturday, Jesse plays 19 games and pays a total of 62.50 dollars. Paula plays 10 games and pays a total of 40 dollars. Find the entrance fee and then fee per games played
Answer:
Entrance fee=15, fee per games played=2.50
Step-by-step explanation:
x=fee per games played, y=entrance fee
19x+y=62.50 equation 1
10x+y=40 equation 2
y=40-10x isolate y in equation 2
19x+40-10x=62.50 substitute y value from equation 2 into equation 1
9x=22.50
x=2.50
solve for y by substituting x value in either equation
10x+y=40
10(2.50)+y=40
25+y=40
y=15
Check answer:
19x+y=62.50
19(2.50)+15=62.50
47.50+15=62.50
62.50=62.50
1. In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at least one of the number cubes.
(a) Make a list of all the different possible outcomes when two number cubes are rolled.
(b) What fraction of the possible outcomes is favorable?
(c) Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain. Answer:
Answer:
34
Step-by-step explanation:
You should not expect more than 34 times to be favorable, because favorable outcomes are about 28% of outcomes, and 28% of 100 is 28, which is less than 34.
6/21 outcomes will be favorable.
Here is a list of all possible :
1 - 1
1 - 2
1 - 3
1 - 4
1 - 5
1 - 6
2 - 2
2 - 3
2 - 4
2 - 5
2 - 6
3 - 3
3 - 4
3 - 5
3 - 6
4 - 4
4 - 5
4 - 6
5 - 5
5 - 6outcomes29 out of every 100 outcomes will likely
6 - 6
One or two of the underlined outcomes have a three. The total number of outcomes is 21, and six of them include 3's. Therefore, when we multiply 6/21 by .286, we get 28.6%. be favorable.
Hope this helps! : )
Having some difficulty with this test, can you please help?
Answer:
y = 3/2x +1
Step-by-step explanation:
The y int = is 1 by observation
To calculate the slope it is rise over run
3/2 as for every 3 up the line moves 2 across
HELP PLS ITS ALGEBRA 1
Answer:
[tex] - \frac{2}{6} [/tex]
Step-by-step explanation:
Use distributive property to simplify both sides.
[tex] \frac{1}{6} (1 - 6x) = - \frac{1}{3} ( 6x + \frac{1}{2} )[/tex]
Use the Golden Rule of Algebra: (What we do to one side, we must do to the other).
[tex] \frac{1}{6 } - x = - 2x - \frac{1}{6} [/tex]
[tex] \frac{1}{6} = - x - \frac{1}{6} [/tex]
[tex] \frac{2}{6 } = - x[/tex]
[tex]x = - \frac{2}{6} [/tex]
Answer:
Step-by-step explanation:
[tex]\frac{1}{6}[/tex](1-6x) = - [tex]\frac{1}{3}[/tex](6x+[tex]\frac{1}{2}[/tex])
distribute in the fractions
[tex]\frac{1}{6}[/tex] - 1x = -2x - [tex]\frac{1}{6}[/tex]
subtract [tex]\frac{1}{6}[/tex] from both sides
-[tex]\frac{1}{6}[/tex]+[tex]\frac{1}{6}[/tex]-1x = -2x -[tex]\frac{1}{6}[/tex]-[tex]\frac{1}{6}[/tex]
-1x = -2x -[tex]\frac{2}{6}[/tex]
-x = -2x - [tex]\frac{1}{3}[/tex]
[tex]\frac{1}{3}[/tex] = -2x + x
[tex]\frac{1}{3}[/tex] = -x
- [tex]\frac{1}{3}[/tex] = x
x = - [tex]\frac{1}{3}[/tex]
see? :/