Answer:
3/10
Step-by-step explanation:
6+3+1=10
since there are 3 blue marbles, we put the 3 into the place of the numerator
and since there is 10 marbles in total it goes into the denominator
The probability that a randomly selected marble is not blue will be 0.70.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
A bag contains 6 red marbles, 3 blue marbles and 1 green marble.
The total number of the event will be
Total event = 6 + 3 + 1
Total event = 10
Then the probability that a randomly selected marble is not blue will be
Favorable event = 7 {red, green}
Then the probability will be
P = 7 / 10
P = 0.70
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ2
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.1 degrees. Low Temperature (◦F) 40−44 45−49 50−54 55−59 60−64 Frequency 3 6 13 7
Answer:
[tex]Mean = 53.25[/tex]
Step-by-step explanation:
Given
Low Temperature : 40−44 || 45−49 || 50−54 || 55−59 || 60−64
Frequency: --------------- 3 -----------6----------- 1-----------3--- -----7
Required
Determine the mean
The first step is to determine the midpoints of the given temperatures
40 - 44:
[tex]Midpoint = \frac{40+44}{2}[/tex]
[tex]Midpoint = \frac{84}{2}[/tex]
[tex]Midpoint = 42[/tex]
45 - 49
[tex]Midpoint = \frac{45+49}{2}[/tex]
[tex]Midpoint = \frac{94}{2}[/tex]
[tex]Midpoint = 47[/tex]
50 - 54:
[tex]Midpoint = \frac{50+54}{2}[/tex]
[tex]Midpoint = \frac{104}{2}[/tex]
[tex]Midpoint = 52[/tex]
55- 59
[tex]Midpoint = \frac{55+59}{2}[/tex]
[tex]Midpoint = \frac{114}{2}[/tex]
[tex]Midpoint = 57[/tex]
60 - 64:
[tex]Midpoint = \frac{60+64}{2}[/tex]
[tex]Midpoint = \frac{124}{2}[/tex]
[tex]Midpoint = 62[/tex]
So, the new frequency table is as thus:
Low Temperature : 42 || 47 || 52 || 57 || 62
Frequency: ----------- 3 --||- -6-||- 1-||- --3- ||--7
Next, is to calculate mean by
[tex]Mean = \frac{\sum fx}{\sum x}[/tex]
[tex]Mean = \frac{42 * 3 + 47 * 6 + 52 * 1 + 57 * 3 + 62 * 7}{3+6+1+3+7}[/tex]
[tex]Mean = \frac{1065}{20}[/tex]
[tex]Mean = 53.25[/tex]
The computed mean is greater than the actual mean
Little bit more math hw
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
For these kind of problems, simply take the denominator and compare it to zero. Then solve the equation.
[tex]x+2=0\\\\\Rightarrow x=-2[/tex] By subtracting 2 from both sides!
Best Regards!
find x, if sq.root(x) +2y^2 = 15 and sq.root(4x) - 4y^2=6
Answer:
Example: solve √(2x−5) − √(x−1) = 1
isolate one of the square roots:√(2x−5) = 1 + √(x−1) square both sides:2x−5 = (1 + √(x−1))2 ...
expand right hand side:2x−5 = 1 + 2√(x−1) + (x−1) ...
isolate the square root:√(x−1) = (x−5)/2. ...
Expand right hand side:x−1 = (x2 − 10x + 25)/4. ...
Multiply by 4 to remove division:4x−4 = x2 − 10x + 25.
Answer:
Step-by-step explanation:
ewrerewrwrwerrwer
Use parenthesis to make each number sentence true.
124 - 6 x 0 + 15 = 34
Answer:
12 - 6 x (0 + 15) = 34
How I got my answer
First, how i got my answer was that I had to solve the equation first, ignoring the answer. I got 0 x 6 = 0, then I did 124 - 0 = 124, then I did 124 - 15 = 109, which clearly isn't 34. I figured that we have to put the parentheses around the zero because if we don't, we are going have to multiply something by zero, which always gets zero. After that, I decided that I should put the parentheses around either the 6, or the 15. I did both, and saw which one was correct. If we put it around the 6, we get, 124 - (6 x 0) + 15 = 124 - 0 - 15 = 124 - 15 = 109, which isn't 34. Then I checked 124 - 6 x (0 + 15) = 124 - 6 x 15 = 124 - 90 = 34, and we just got the answer.
P.S. Sorry if it was confusing, I didn't really know how to explain it
The first side of a triangle measures 3 in. less than the second side, the third side is 2 in. more than the first side, and the perimeter is 20 in. Set up an equation that relates the sides of the triangles in terms of the perimeter of the triangle.
Answer:
P = 3x - 4
Step-by-step explanation:
Side 1 = x - 3
Side 2 = x
Side 3 = 2 + (Side 1) = 2 + x - 3 = x - 1
Perimeter = 20 in
Perimeter = Side 1 + Side 2 + Side 3
Perimeter = (x - 3) + (x) + (x - 1)
Perimeter = x - 3 + x + x - 1
Perimeter = 3x - 3 - 1
Perimeter = 3x - 3 - 1
Perimeter = 3x - 4
P = 3x - 4
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
A normal curve with a peak at 0 is shown. The area under the curve shaded is 1 to 2.
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.14
0.16
0.86
0.98
Answer:
0.14
Step-by-step explanation:
The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14
The area under the curve shaded is 1 to 2 is 0.14
What are probabilities?Probabilities are used to determine the chances of an event
The shaded region represents the probability of the z-scores
The shaded region 1 to 2 is represented as:
P(1 < z < 2) =
Using the probability of z-score, we have the formula
P(1 < z < 2) = P(z < 2) - P(z < 1)
From the given standard normal table:
P(z < 2) = 0.9772
P(z < 1) = 0.8413
So, we have:
P(1 < z < 2) = 0.9772 - 0.8413
P(1 < z < 2) = 0.1359
Approximate
P(1 < z < 2) = 0.14
Hence, the area under the curve shaded is 1 to 2 is 0.14
Read more about normal distribution at:
https://brainly.com/question/4079902
About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.a. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.b. In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximatly normal, we need random samples where the sample size is at least 40.c. A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.d. A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.e. Tripling the sample size will reduce the standard error of the sample proportion by one-third.
Answer:
a. True
b. true
c. false
d. false
e. false
Step-by-step explanation:
a. true
polutation = 25% = 0.25
sample = n= 12
n x p
= 12 x o. 25 = 3 and 3 is less than 10
12(1 - p)
= 12 x 0.75
= 9 and is less than 10
b. True
the sample distribution of the population is normal when
sample size x population > or equal to 10
40 x 0.75
= 30 and 30 is greater than 10
c. false
50 x 0.25 = 12.5
50 x 0.20 = 10
z = 10 - 12.5/sqrt(12.5)
= -2.5/3.54
= -0.70
H0: Young american family who delayed
H1: young american family who did not delay
p(z = -0.70)
0.2420>0.005
therefore we accept the null hypothesis
d. false
150 x 0.20 = 30
150 x 0.75 = 37.5
z = 30 - 37.5/sqrt(37.5) = -7.5/6.12 = -1.22
p(z = -1.22) = 0.1112 > 0.05
therefore we do not reject the null hypothesis
e. false
se1 = sqrt(p(1-p)/n
se2 = sqrt(p(1-p)/3n
se2 = 1/sqrt(3)se2
!2,19,26 what comes nxt
Answer:
12 , 19 , 26 , 33
Explaination:Here, n+7
12+7=19
19+7=26
So,
26+7=33
Hope you understand ❣
Step-by-step explanation:
12 , 19 , 26 , ?
Given
___________
a1= 12
a2= 19
a3 = 26
d= ?
a4 = ?
––——————
we can solve this by using formula from Ap .
But for this we have to find d
As we know that
common difference(d) = a2-a1 = 19 -12
= 7
so difference after every no is 7 so
a4 = a3 + d
= 26 +7
= 33
So 33 is ur answer mate
Hope it helps
while jeff was replacing the obstruction of light on a cell tower, he accidentally dropped his cell phone. If he was 150 ft up at the time, approximately how long did it take the phone to reach the ground
Answer:
3.19 seconds
Step-by-step explanation:
Given:
Phone gets dropped from a Height = 150 ft
To find:
Time taken for the phone to reach the ground = ?
Solution:
First of all, let us learn about the formula of distance in terms of Initial speed u; Time t and Acceleration a:
[tex]s=ut+\dfrac{1}{2}at^2[/tex]
Here the phone is dropped from a height so a = g m/[tex]s^2[/tex] i.e. acceleration due to gravity.
g = 9.8 m/[tex]s^2[/tex]
s = 150 ft
Initial velocity, u = 0
Putting all the values in the formula:
[tex]150=0 t+\dfrac{1}{2}gt^2\\\Rightarrow 50=\dfrac{1}{2}\times 9.8 \times t^2\\\Rightarrow t^2=\dfrac{50}{4.9 }\\\Rightarrow t^2=10.20\\\Rightarrow t = 3.19\ sec[/tex]
So, the time taken is 3.19 seconds.
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of million cells per microliter and a standard deviation of million cells per microliter. (a) What is the minimum red blood cell count that can be in the top % of counts? (b) What is the maximum red blood cell count that can be in the bottom % of counts?
Answer:
(a) Minimum red blood cells 5.744 million cells per micro liter
(b) Maximum red blood cells 5.068 million cells per micro liter.
Step-by-step explanation:
Z-score formula is = [tex]\frac{x-u}{Standard deviation}[/tex]
Z-score = [tex]\frac{x-5.5}{0.4}[/tex]
The value of z-score is 0.61 so then x will be;
x = 5.744
The minimum red blood cells count that can in top is 27% of count which is 5.744 million cells per micro liter.
Z-score = [tex]\frac{x-5.5}{0.4}[/tex]
The value of z-score is 0.14 so then x will be;
x = 5.068
The maximum red blood cells count that can be in top is 14% of count which is 5.068 million cells per micro liter.
You are an urban planner assessing the growth of a city. Ten years ago, the city's population was 250,823. Its current population is 325,823. By about what percentage has the city grown over the past ten years? Round to the nearest percent.
Answer:
Here is the answer i got-
Step-by-step explanation:
325823-250823=75000
325823’s 244367250percent is 75000
There are 47 contestants at a national dog show. How many different ways can contestants fill the first place, second place, and third place positions?
Answer:
97290
Step-by-step explanation:
47 different people can win first
47
Now there are only 46 people left
46 different people can win second
46
45 different people can win third
47*46*45
97290
Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = 5 + ln(t), y = t2 + 2, (5, 3)
Answer:
Step-by-step explanation:
Given that:
[tex]x = 5 + In (t)[/tex]
[tex]y = t^2+2[/tex]
At point (5,3)
To find an equation of the tangent to the curve at the given point,
By without eliminating the parameter
[tex]\dfrac{dx}{dt}= \dfrac{1}{t}[/tex]
[tex]\dfrac{dy}{dt}= 2t[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{ \dfrac{dy}{dt} }{\dfrac{dx}{dt} }[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{ 2t }{\dfrac{1}{t} }[/tex]
[tex]\dfrac{dy}{dx}= 2t^2[/tex]
[tex]\dfrac{dy}{dx}_{ (5,3)}= 2t^2_{ (5,3)}[/tex]
t² + 5 = 4
t² = 4 - 5
t² = - 1
Then;
[tex]\dfrac{dy}{dx}_{ (5,3)}= -2[/tex]
The equation of the tangent is:
[tex]y -y_1 = m(x-x_1)[/tex]
[tex](y-3 )= -2(x - 5)[/tex]
y - 3 = -2x +10
y = -2x + 7
y = 2x - 7
By eliminating the parameter
x = 5 + In(t)
In(t) = 5 - x
[tex]t =e^{x-5}[/tex]
[tex]y = (e^{x-5})^2+5[/tex][tex]y = (e^{2x-10})+5[/tex]
[tex]\dfrac{dy}{dx} = 2e^{2x-10}[/tex]
[tex]\dfrac{dy}{dx}_{(5,3)} = 2e^{10-10}[/tex]
[tex]\dfrac{dy}{dx}_{(5,3)} = 2[/tex]
The equation of the tangent is:
[tex]y -y_1 = m(x-x_1)[/tex]
[tex](y-3 )= -2(x - 5)[/tex]
y - 3 = -2x +10
y = -2x + 7
y = 2x - 7
If 6x +3= 2x+ 19, then x =
Answer:
x = 4
Step-by-step explanation:
6x + 3 = 2x + 19 ------ subtract 3 both sides
6x + 3 - 3 = 2x + 19 - 3 simplify
6x = 2x + 16 ------ subtract 2x both sides
6x - 2x = 2x + 16 - 2x simplify
4x = 16
x = 16 / 4
x = 4
Answer: x = 4
Step-by-step explanation: If the variable appears on both sides of the equation, we put the variables together on one side of the equation and the numbers together on the other side of the equation.
So let's put our variables on the left side by first subtracting
2x from both sides of the equation to get 4x + 3 = 19.
Next, we subtract 3 from both sides to get 4x = 16.
Finally, we divide both sides by 4 to get x = 4.
GIVING OUT BRAINLIEST TO THE FIRST PERSON TO ANSWER!!
One circle has a diameter of 6 inches. A second, larger circle has a diameter that is four times the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?
A. 2:3
B. 1:6:4
C. 1:16
D. 1:64
Please include ALL work! <3
Answer:
The answer is option CStep-by-step explanation:
To find the ratio first find the diameter of the larger circle
Diameter of first circle = 6 inches
Diameter of second circle = 4 × diameter of the first circle
Which is
Diameter of second circle
= 4 × 6 = 24 inches
Area of a circle = πr²
r is the radius
Area of smaller circle
Diameter = 6 inches
Radius = 6 / 2 = 3 inches
Area = (3)² π = 9π in²
Area of larger circle
Diameter = 24 inches
Radius = 24 / 2 = 12 inches
Area = (12)²π = 144π in²
The ratio of the smaller circle to the larger circle is
[tex] \frac{9\pi}{144\pi} [/tex]
Reduce the fraction by 9π
That's
[tex] \frac{1}{16} [/tex]
We have the final answer as
1 : 16Hope this helps you
Answer:
C. 1:16
Step-by-step explanation:
Area of a circle is:
[tex]\pi \times {r}^{2} [/tex]
Small circle Area:
radius = diameter/2
radius = 6/2 = 3
[tex]area \: of \: a \: circle \: = \pi {3}^{2} [/tex]
a = 28.27
Large circle 4 times larger diameter
6*4 = 24
diameter = 24
r = 24/2
r = 12
[tex]a \: = \pi {12}^{2} [/tex]
a = 452.39
area of large circle/ area of small circle
452.39/28.27 = 16.00
ratio is 1:16
what is the least number to be added to 1500 to make it a perfect square?
Answer:
21
Step-by-step explanation:
√1500 ≈ 38.7
round that up to 39 and square it:
39² = 1521
given that f(x)=x^2-4x -3 and g(x)=x+3/4 solve for f(g(x)) when x=9
Answer:
f(g(9)) = 945/16
Step-by-step explanation:
To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).
g(x) = x + 3/4
f(x) = x² - 4x - 3
f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3
f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3
f(g(x)) = x² - 5/2x + 9/16 + 3 - 3
f(g(x)) = x² - 5/2x + 9/16
Now, put a 9 wherever there is an x in f(g(x)).
f(g(9)) = (9)² - 5/2(9) + 9/16
f(g(9)) = 81 - 5/2(9) + 9/16
f(g(9)) = 81 - 45/2 + 9/16
f(g(9)) = 117/2 + 9/16
f(g(9)) = 945/16
24. After a vertical reflection across the x-axis, f(x) is
Options:
A. –f(x)
B. f(x – 1)
C. –f(–x)
D. f(–x)
Answer:
A. –f(x)
Step-by-step explanation:
The transformation of a reflection about the x-axis is
f(x) -> -f(x).
So the answer is
A. –f(x)
*please help* If multiple forces are acting on an object, which statement is always true?
The acceleration will be directed in the direction of the gravitational force.
The acceleration will be directed in the direction of the applied force.
The acceleration will be directed in the direction of the net force. <-- MY ANSWER
The acceleration will be directed in the direction of the normal force.
Answer: You are correct. The answer is choice C.
The sum of the vectors is the resultant vector, which is where the net force is directed.
An example would be if you had a ball rolling on a table and you bumped the ball perpendicular to its initial velocity, then the ball would move at a diagonal angle rather than move straight in the direction where you bumped it.
Acceleration is the change in velocity over time, so the acceleration vector tells us how the velocity's direction is changing.
The direction of the acceleration on a body upon which multiple forces are applied depends on the direction of the netforce acting on the body.
When multiple forces acts on a body, such that the different forces acts in different directions. The acceleration will be in the direction of the netforce. This is the direction where the Cummulative sum of the forces is greatest. Acceleration due to gravity is always acting downward, if the upward force is greater than the Gravitational force, then the acceleration won't be in that direction.Therefore, acceleration will be due in the direction of the netforce.
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CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already
announced that when he slices the cake, your slice will have a perimeter of 16 inches, because you're his favorite friend, and
that's his favorite number. Since you're helping his mom with the baking, what diameter cake will you recommend she makes
so that you end up with the most possible cake at weird Spud's party? (Hint: you can ignore the thickness df the cake, since
this will be the same, regardless of its diameter.)
10.1
in
Answer:
15.7 in
Step-by-step explanation:
A slice of a round pie is a sector of a circle.
The perimeter of a slice is the arc length s plus twice the radius r.
P = s + 2r
s = rθ = r(16/360) = r/22.5. So,
16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5
16 × 22.5 = 46r
360 = 46r
r = 7.826
D = 2r = 2 × 7.826 = 15.7 in
The diameter of the cake should be 15.7 in.
Check:
[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]
It checks.
Evaluate b h for b = 12 and h = 2 . Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.
Answer:63
Step-by-step explanation:
A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale? a.3.8 grams b.120.01 grams c.800.0 grams d.54 milligrams
Answer:
Step-by-step explanation:
The answer is b
120.01 grams
1. Quadratics: The path of the longest shot put by the Women’s track team at Sun Devil U is modeledby h(x) = -0.015x2 + 1.08x + 5.8, where x represents the horizontal distance from the start and h(x) isthe height of the shot put above the ground. (Both x and h(x) are measured in feet.)a. [3 pts] Determine h(24). Round your answer to 2 decimal places.
Answer:
23.08 feetStep-by-step explanation:
If the path of the longest shot put by the Women’s track team at Sun Devil U is modeled by h(x) = -0.015x² + 1.08x + 5.8 where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground, to determine h(24), we will have to substitute x = 24 into the modeled equation as shown;
[tex]h(x) = -0.015x^2 + 1.08x + 5.8\\\\if \ x = 24;\\\\h(24) = -0.015(24)^2 + 1.08(24) + 5.8\\\\h(24) = -0.015(576)+25.92+5.8\\\\h(24) = -8.64+31.72\\\\h(24) = 23.08\\[/tex]
Hence the value of the height at the horizontal distance of 24 feet is 23.08 feet to 2 decimal place.
Help me solve this!!!
Answer:
54°
Step-by-step explanation:
Let ∠CYX=x
AB║CD
∠AXE=∠CYX (corresponding angles)
∠AXE=3∠CYX-108
x=3x-108
3x-x=108
2x=108
x=108/2=54°
∠AXE=∠CYX=x=54°
∠BXY=∠AXE=54° (Vertically opposite angles)
What number is equivalent to 9 1/2?
Answer:
the answer is going to be 2/4
Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product by first multiplying the coefficients...then adding your "like term" angles...for instance, cos (2pi/5) + cos (-pi/2) = cos (2pi/5 + -pi/2)...then use the calculator in RADIAN mode to evaluate." Doing those steps, I got the correct constant but a coefficient that was completely off. For the second one, I was told "Good effort...express the quotient by first dividing the coefficients...then subtract your "like term" angles...for instance, cos (2pi/5) - cos (-pi/2) = cos (pi/6 - pi/3)...Finally, use the calculator (in radian MODE) to evaluate."
Answer:
Solution ( Second Attachment ) : - 2.017 + 0.656i
Solution ( First Attachment ) : 16.140 - 5.244i
Step-by-step explanation:
Second Attachment : The quotient of the two expressions would be the following,
[tex]6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,
( 1 ) cos(x) = sin(π / 2 - x)
( 2 ) sin(x) = cos(π / 2 - x)
If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,
( 1 ) [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]
( 2 ) [tex]\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}[/tex]
These two identities makes sin(π / 10) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and cos(π / 10) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex].
Therefore cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]. Substitute,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex]
And now simplify this expression to receive our answer,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex] = [tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i[/tex],
[tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}[/tex] = [tex]-2.01749\dots[/tex] and [tex]\:\frac{3\sqrt{3-\sqrt{5}}}{4}[/tex] = [tex]0.65552\dots[/tex]
= [tex]-2.01749+0.65552i[/tex]
As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.
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First Attachment : We know from the previous problem that cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex], cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,
[tex]6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}[/tex]
We know that [tex]6\sqrt{5+\sqrt{5}} = 16.13996\dots[/tex] and [tex]-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots[/tex] . Therefore,
Solution : [tex]16.13996 - 5.24419i[/tex]
Which rounds to about option b.
Solve for y: 1/3y+4=16
Hey there! I'm happy to help!
We want to isolate y on one side of the equation to see what it equals. To do this, we use inverse operations to cancel out numbers on the y side and find the correct value.
1/3y+4=16
We subtract 4 from both sides, canceling out the +4 on the right but keeping the same y-value by doing the same to the other side.
1/3y=12
We divide both sides by 1/3 (which is multiplying both sides by 3) which will cancel out the 1/3 and tell us what y is equal to.
y=36
Now you know how to solve basic equations! Have a wonderful day! :D
HELP ME ILL GIV ROBUX Identify the property shown by the equation. 14 × 6 = 6 × 14 A. Commutative Property B. Associative Property C. Identity Property D. Distributive Property PLEASE HELP ME
Answer:
Its commutative property..
Step-by-step explanation:
Commutative property says A×B=B×A
Explanation is attached below.
200,000=2x10 to the power of 6
False.
2x10^6 you move the decimal point 6 places to the right. ( add 6 zeros after the 2)
2x 10^6 = 2,000,000
What is the approximate value of x in –2 ln (x + 1) − 3 = 7?
Answer:
x = 1/e^-5 - 1
Step-by-step explanation:
–2 ln (x + 1) − 3 = 7
–2 ln (x + 1) = 10
ln (x + 1) = –5
x + 1 = e^-5
x = e^-5 - 1
x = 1/e^-5 - 1
the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:
1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.
2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.
3. Simplify: -2 ln(x + 1) = 10.
4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.
5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.
6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.
7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.
8. Simplify: x ≈ -0.9933.
Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
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