Answer:
7.35 years
Step-by-step explanation:
Given that :
mean = 8.4
standard deviation = 0.6
From the negative z tables, the corresponding data for 0.04 = -1.75
So, using the z-score formula:
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
[tex]-1.75 = \dfrac{x - 8.4}{0.6}[/tex]
-1.75 × 0.6 = x - 8.4
- 1.05 = x - 8.4
x = -1.05 + 8.4
x = 7.35 years
the shortest lifespan will last less than 7.35 years
∴ the longest 4% will have lifespans longer than x = 8.4 + 1.75(0.6)
= 9.45 years
What is the greatest common factor of 28, 34, and 42?
Answer:
28 (0,2,4,14,28)
34 (0,2,17,34)
42 (0,2,6,7,21,42)
the greatest common factor is 2 because it's the greatest number that can be divided by 28, 34 and 42
What is the value of 30-2(7+2)-1?
O 11
0 14
017
019
Find the modulus of the following |9+40i|
Answer:
modulus of |9+40i| is 41
Step-by-step explanation:
Let z = 9+40i
then
|z| = [tex]\sqrt{9^{2}+40^{2} }[/tex]
= [tex]\sqrt{81+1600}[/tex]
= [tex]\sqrt{1681}[/tex]
= 41
|z| = 41
Answer:
Step-by-step explanation:
1. |9+40i| = 41
2. |-10+24i| = 26
Express each vector as a product of its length and direction.
16–√i−16–√j−16–√k
Question:
Express each vector as a product of its length and direction.
[tex]\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]
Answer:
[tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
Step-by-step explanation:
A vector v can be expressed as a product of its length and direction as follows;
v = |v| u
Where;
|v| = length/magnitude of v
u = unit vector in the direction of v
---------------------------------------------------------------------------------------
Let the given vector be v, i.e
[tex]v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]
(i) The length/magnitude |v| of vector v is therefore,
|v| = [tex]\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2[/tex]
|v| = [tex]\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})[/tex]
|v| = [tex]\sqrt{(\frac{3}{6})[/tex]
|v| = [tex]\sqrt{(\frac{1}{2})[/tex]
|v| = [tex]\frac{1}{\sqrt{2}}[/tex]
(ii) The unit vector u in the direction of vector v, is therefore,
u = [tex]\frac{v}{|v|}[/tex]
[tex]u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}[/tex]
[tex]u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)[/tex]
[tex]u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)[/tex]
[tex]u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
Therefore, the vector can be expressed as a product of its length and direction as:
|v| u = [tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
Help I am stuck on this.
Answer:
i think is the second one
Step-by-step explanation:
2. Kevin drives to the pizza place for lunch.
He walks 5 km east, then 5 km south, then 5
km east again.
Distance:
Displacement:
Answer: Distance = 15km ; Displacement ≅ 11'2km
Step-by-step explanation:
In Physics when we speak of distance we refer to the space traveled that is always measured on the trajectory, while displacement refers to the space from an initial position to a final position regardless of the path. When the path is a straight line, the space traveled is equal to the module of the displacement.
Distance: 5km + 5km + 5km = 15km (Red lines)
Displacement² : (10km)² + (5km)² = 100km² + 25km² = 125km²
Displacement : √125km² ≅ 11'2km (Blue line)
(See attached image)SpymoreWhat is the slope of the line on the graph?
We can use the points (-4, 0) and (0, 2) to solve.
Slope formula: y2-y1/x2-x1
2-0/0-(-4)
2/4
1/2
Best of Luck!
What is the common ratio of the Fibonacci sequence called
Answer:
1.618
The Fibonacci sequence is significant because of the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number, ignoring the first few numbers.
Step-by-step explanation:
Plz Mark me as brainliest
[tex]\Large \boxed{\sf golden \ ratio}[/tex]
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
In the figure points A B C D and E are collinear. If AE = 38 and BD = 15
Answer:
D. 30.5
Step-by-step explanation:
Given that A, B, C, D, and E are collinear,
AE = 38,
BD = 15, since segment BC = CD = DE, therefore
BD = ⅔ of BE
15 = ⅔*BE (substitution)
Solve for BE
Multiply each side by 3
15*3 = ⅔*BE*3
45 = 2*BE
Divide both sides by 2
45/2 = BE
22.5 = BE
BE = 22.5
Find AB:
AB + BE = AE (segment addition postulate)
AB + 22.5 = 38 (Substitution)
AB = 38 - 22.5 (Subtracting 22.5 from each side)
AB = 15.5
Find length of segment AD:
AB + BD = AD (segment addition postulate)
15.5 + 15 = AD (Substitution)
30.5 = AD
AD = 30.5
this is easy but im hella lazy and dont feel like doing this pls help me, i mark brainliest! ty ❤️
Answer:
D. It is a decimal that terminates after 3 decimal places
I hope this helps!
P(t) = 520/1+5e^-0.2t
Find the initial population size
A machine was able to make 32 bags of Hot Cheetos in 8 seconds. What is
the rate made per second? *
Answer: 32÷8=4
Please brainliest
Select the correct answer.
Angela uses 3 cup of strawberries to make 6 of a liter of smoothie. What is the unit rate in cups of strawberries per liter of smoothie?
OA. cups per liter
B. cups per liter
OC. cups per liter
OD. cups per liter
If there are 3 cups of strawberries per 6 liters of smoothie, that means that there is [tex]\frac{1}{2}[/tex] cups of strawberries per liter of smoothie.
[tex]\frac{3}{6}=\frac{1}{2}[/tex]
Hope this helps.
頑張って!
What percent is equivalent to 2/3?
A.) 66 1/3% B.) 66 3/5% C.) 66 2/3% D.) 66 7/10%
Answer:
C
Step-by-step explanation:
2/3=66 therefore it also equals 2/3%
Answer: C
Step-by-step explanation:
First find the decimal of 2/3
Divide it 2/3 = 0.6666666
Now multiply it by 100 to convert it to a percent
You get 66.66..% which is the same as 66 2/3%
what is the slope and the g intercept ? ( i added the picture )
Step-by-step explanation:
A straight line graph is of the form:
y = mx+b
So we get our equation in this form:
9=2x+3y
or, 9-2x=3y
or, -2x+9 = 3y
or, y= (-2x+9)/3
or, y = -2/3x + 3
So,
Slope(m)=−2/3
y-intercept (b) = 3
Therefore, slope(m) is -2/3x and y-intercept(b) is 3.
Dimensional analysis. How many seconds are in a year?
Answer:
31536000
Step-by-step explanation:
365 days x 24 hours x 60 minutes x 60 seconds = 31536000
I need help! Please. Justify answer using Intermediate value theorem (IVT)
Step-by-step explanation:
N(t) is continuous at t = 6, so f(6) = 25(6) + 150 = 300.
f(0) = 80.
f(t) is continuous, so by Intermediate Value Theorem, f(t) must equal 250 at some point between t=0 and t=6.
r+4r-1=24
Be quick please :)
Step-by-step explanation:
r+4r=24+1
5r=25
r=25/5
r=5
Answer:
r = 5
Step-by-step explanation:
r + 4r - 1 = 24
r + 4r = 25
5r = 25
r = 5
solve the equation
[tex] 5 = \frac{z}{4} - 3[/tex]
Answer:
z=32Step-by-step explanation:
[tex]5=\frac{z}{4}-3[/tex]
[tex]\frac{z}{4}-3=5[/tex]
[tex]\frac{z}{4}=5+3[/tex]
[tex]\frac{z}{4}=8[/tex]
[tex]z=8\cdot \:4[/tex]
[tex]z=32[/tex]
determine if the interval is increasing or decreasing
*
True or False? Natural Numbers are closed under division.
Answer: False
Natural numbers are not closed under division
Some natural numbers divide to get another natural number. For example, divide 10 over 2 to get 10/2 = 5.
However, there are infinitely many natural numbers that divide to get something that isn't a natural number. Example: 10/7 = 1.43 approximately. All we need is one counterexample to contradict the original statement.
A set is considered closed under division if dividing any two values in that set leads to another value in the set. More formally, if a & b are in some set then a/b must also be in the same set for that set to be closed under division.
If we changed "natural numbers" to "rational numbers", then that set is closed under division. If p, q are rational numbers then p/q is also rational. Basically, dividing any two fraction leads to some other fraction. The value of q cannot be zero.
bfnskalalalallsmsmsm help
Answer:
x>18
Step-by-step explanation:
simplify
4( 2u - 2) - 3(u + 5)
Answer:
5u - 23
Step-by-step explanation:
Answer:
4( 2u - 2) - 3(u + 5)
(4*2u + 4*-2)-(3*u + 3*5)
8u-8-3u+15
8u-3u-8+15
5u+7
Step-by-step explanation:
I hope this helped you.
Please mark Brainliest.
Have a great day!!!!!!!!!
E Solve for x 6(x - 1) = 9(x + 2) x = -8 x= 3 x = 8
Answer:
x = -8
Step-by-step explanation:
[tex]6(x - 1) = 9(x + 2)[/tex]
Expand :
[tex]6(x - 1) = 6x - 6 \\ 9(x + 2) = 9x + 18[/tex]
[tex]6x - 6 = 9x + 18[/tex]
Collect like terms and simplify
[tex]6x - 9x = 18 + 6 \\ - 3x = 24[/tex]
Divide both sides of the equation by -3
[tex] \frac{ - 3x}{ - 3} = \frac{24}{ - 3} \\ x = - 8[/tex]
Answer:
Step-by-step explanation:
6x - 6 = 9x + 18
-3x - 6 = 18
-3x = 24
x = -8 is the solution
Rachael gets 94 marks in her exams.these are 47% of the total marks.find the maximum number of mark
Answer:
200 is the maximum amount
Step-by-step explanation:
94x100=9400
9400/47=200
can i have brainliest?
Question
of 27
Which of the following shows an element of the sample space for first
tossing a coin and then rolling a number cube?
Α.Τ, Η
B. T, 2
C. 6,1
D. 4, H
The sample space for first tossing a coin and then rolling a number cube is (T, 2).
What are Outcomes of Probability?An outcome is a possible result of an experiment or trial in probability theory. Each experiment's possible outcomes are distinct, and alternative outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment).
As, the outcomes for tossing a coin is Head (H) and Tail (T).
and, the outcome for rolling a die
{1, 2, 3, 4, 5, 6}.
So, the sample space for first tossing a coin and then rolling a number cube
= ( T, 2)
Learn more about Outcome of Probability here:
https://brainly.com/question/30661698
#SPJ5
On a road map, the locations A, B and C are collinear. Location C divides the road from location A to B, such that AC:CB = 1:2. If location A is at (5,16) and location C is at (3,10). Find the coordinates of location B. A. (1,4) B. (4,13) C. (-1,-2)
Answer:
C. (-1,-2)
Step-by-step explanation:
Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.
Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)
So x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Substituting the values of the coordinates, we have
x = (mx₂ + nx₁)/(m + n)
3 = (1 × x₂ + 2 × 5)/(2 + 1)
3 = (x₂ + 10)/3
multiplying through by 3, we have
9 = x₂ + 10
x₂ = 9 - 10
x₂ = -1
y = (my₂ + ny₁)/(m + n)
10 = (1 × y₂ + 2 × 16)/(2 + 1)
10 = (x₂ + 32)/3
multiplying through by 3, we have
30 = y₂ + 32
y₂ = 30 - 32
y₂ = -2
So, the coordinates of B are (-1, -2)
41 2/3 divined by 4 1/4
Answer:
Exact form: [tex]9 \frac{41}{51}[/tex]
Decimal form: [tex]9.80392156[/tex]
Step-by-step explanation:
[tex]41\frac{2}{3}[/tex] ÷ [tex]4\frac{1}{4}[/tex]
Let's put everything into a fraction.
[tex]\frac{41\frac{2}{3} }{4\frac{1}{4} }[/tex]
Now we have an answer.
Exact form: [tex]9\frac{41}{51}[/tex]
Decimal form: [tex]9.80392156[/tex]
Hope this helps!
I need help with this please
Answer:
C
Step-by-step explanation:
PLS HELP! 10 POINTD ILL MARK BRAINLIEST
l=3w
3w(4)=48
12w=48
w=4
l=12
hope it helps
comment if u have any questions
Answer:
Length is 18; width is 6.
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
We are given that the perimeter is 48 feet. We are also told that the length is 3 times the width. In other words:
[tex]l=3w[/tex]
So, substitute this for l and 48 for P. Thus:
[tex]48=2(3w)+2w[/tex]
Distribute:
[tex]48=6w+2w[/tex]
Combine like terms:
[tex]48=8w[/tex]
Divide both sides by 8:
[tex]w=6[/tex]
So, the width is 6.
The length as we know is 3 times the width, so the length is 3(6) is 18.
And we are done!