Given the triangle below, find the angle θ in radians. Round to four decimal places.
Answer:
θ = 0.9626
Step-by-step explanation:
Hi there!
We're given the hypotenuse and the leg adjacent to θ in this right triangle. To find θ, we can use the cosine ratio:
[tex]\displaystyle cos\theta=\frac{adjacent}{hypotenuse}[/tex]
Plug in the given information
[tex]\displaystyle cos\theta=\frac{4}{7}[/tex]
Use the inverse cosine ratio
[tex]\displaystyle \theta=cos^-^1(\frac{4}{7})[/tex]
Plug this into your calculator (and ensure you're solving for radians instead of degrees in the settings)
[tex]\displaystyle \theta=0.9626[/tex]
Therefore, θ = 0.9626 when rounded to four decimal places.
I hope this helps!
Answer:
theta = 0.9626 radians
Step-by-step explanation:
cos theta = a/h
cos theta = 4/7 = 0.5714
so, the angle theta = arc cos 0.5714 =
55.1520 °
in radians => 55.1520 × π / 180°
= 0.9626 radians
The manager at a computer recycling plant says it takes workers a minimum of 120 seconds to break down a computer monitor. The exact amount of time depends on the number of screws in the computer that must be removed. It takes 10 seconds to remove each screw, and then an additional 30 seconds to sort the computer parts into their appropriate containers for recycling. Write an inequality that determines the minimum number of screws that are in each computer monitor.
Answer: 120 + 10s + 30
Step-by-step explanation:
120 + 10s + 30
let "s" be the amount of screws
Someone please help me with 13 and 14 I’m really struggling
Answer:
Step-by-step explanation:
Twenty is 12% of what number? Round to two decimal places if needed.
Answer:
166,67
Step-by-step explanation:
We want to find a number x which 12% is 20:
x * 0.12 = 20
x = 20 / 0.12
x = 166,67
Calculate the area of this section of floor in square feet.
Answer:
A total= 0.6703125 ft²
Step-by-step explanation:
A1= 3.9× 14.3= 55.77 in²
A2=1/2 × 14.3× ( 9.6-3.9)= 40.755 in²
A total= A1+ A2= 55.77+40.755=96.525 in²
1 ft= 12 in , 1ft²= 144 in²
Atotal= 96.525÷144= 0.6703125 ft²
The median speed at which Dave drove to work was __________. 63 miles per hour 62 miles per hour 58.89 miles per hour 59 miles per hour
Step-by-step explanation:
Dave run with was 63 miles
Question 7 of 10 Which of the following is most likely the next step in the series? A B. C. D.
please help if you can
Answer:
I choose option d it maybe the answer
Answer:
D
Step-by-step explanation:
The number of sides increase by 1 each time
Plzzz helppppp!!!!!!! 20+PTS and brainliest!!!!!!!!!!!!!!!
Please show work!!!!!!!!!!!
Refer to the equation y=mx+c
Kaitlin recorded the results for a sample of 536 candies.
Color Counts Sample Proportion ()
Red 123 23%
Yellow 145 27%
Green 64 12%
Orange 129 24%
Purple 75 14%
The candy company claims that the distribution of each color is exactly 20%.
Select the observed and expected frequencies for the yellow candies.
a.) Observed: 145
Expected: 80.4
b.) Observed: 123
Expected: 80.4
c.) Observed: 107.2
Expected: 14
d.) Observed: 145
Expected: 107.2
Answer:
Observed: 145
Expected: 107.2
Step-by-step explanation:
to get the observed frequency, we simply look at the value in the column. In this case, it is 145 for the yellow group.
To get the expected frequency, we use the formula:
n equals s a m p l e space s i z e equals 536
p equals h y p o t h e s i z e d space p r o p o r t i o n equals 20 percent sign equals 0.2
E x p e c t e d space F r e q u e n c y equals n times p equals 536 times 0.2 equals 107.2
Answer: 104.5
107.2
Step-by-step explanation:
I'm a little stuck on this, could I get some help? C:
How much would you need to deposit in an account each month in order to have $50,000 in the account in 10 years? Assume the account earns 5% annual interest compounded monthly.
Thank you, and I am eternally grateful.
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Answer:
$321.99
Step-by-step explanation:
Use the annuity formula and solve for P.
A = P(12/r)((1 +r/12)^(12t) -1) . . . . value of a series of deposits P earning rate r compounded monthly for t years.
50,000 = P(12/0.05)((1 +0.05/12)^(12·10) -1) = P(240)(0.64700950)
P = 50,000/155.282279 = 321.99
You would need to deposit $321.99 in the account each month to have $50,000 in 10 years.
How do you find the HCF of 15t and 6s?
Answer:
HCF=3
Step-by-step explanation:
Factors of 15t= 3*5*t
Factors of 6s= 2*3*s
HCF= Common factors
common factor = 3
HCF=3
Find the value of x if
Answer:
C. 4
Step-by-step explanation:
We have the equation [tex]\sqrt[x]{81} =3[/tex] and are asked to find the value of x.
To find x, we need to find how many times 3 can go into 81 but as an exponent, instead of saying 3 * x it would be [tex]3^x[/tex].
So find the value of each exponent by replacing it with each answer choice :
[tex]3^8 = 6561[/tex]
[tex]3^{27} = 7.6255975e+12[/tex]
[tex]3^4 = 81[/tex]
[tex]3^2 = 9[/tex]
Since to the power of 4 equals the cube root in the original equation, therefore B. is the answer.
Subtracting a number is the same as adding its additive inverse. For which elevation do we need to find the additive inverse? What is the additive
inverse of that elevations
Answer:
what elevation there is no elevation
Step-by-step explanation:
pew pew
Answer:duhh
Step-by-step explanation:
Help me pls!!!!!!!!!!!
Answer:
.01 times
Step-by-step explanation:
if the 6th term of an A.p is 11and its first term is 1 find the common diferent
Answer:
[tex]thank \: you[/tex]
5 times some number added to 8 amounts to 10 added to the product of 3 and the number
How do you solve this
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Answer:
the number is 1
Step-by-step explanation:
First of all, you need to know what you're solving. Here, we assume you're trying to find "the number."
__
Let n represent "some number." The given relation can be written using math symbols as ...
5n +8 = 10 +3n
Subtract 3n +8 from both sides to separate the variable and the constant terms.
2n = 2
n = 1 . . . . . . . divide by 2
The number is 1.
__
Check
5 times 1, added to 8 is 13. This amounts to the same thing as 10 added to the product of 3 and 1.
Evaluate the expression 4x + 6 -y^2 when x=-3 and y=4
The expression 4x + 6 -y^2 when evaluated has a value of -22
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
4x + 6 -y^2
Also, we have
x=-3 and y=4
Substitute the known values in the above equation, so, we have the following representation
4x + 6 -y^2 = 4 * -3 + 6 - 4^2
Evaluate
4x + 6 -y^2 = -22
Hence, the solution is -22
Read more about expression at
https://brainly.com/question/30492964
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The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7. Find the probability of observing exactly three accidents on this stretch of road next month.
Select one:
A. 18.147387
B. 2.846161
C. 0.332381
D. 0.052129
Answer:
D
Step-by-step explanation:
hhgxhsbjxkxjebdibfhejx
Derrek wants to find another way to show 6 thousands. Which value is equal to 6 thousands?
Answer:
6,000
Step-by-step explanation:
60 hundreds.
600 tens.
Given log4(3) =0.7925 and log4(5) =1.1610, use log properties to find log4(300).
Answer:
4.1145
Step-by-step explanation:
You can use the following formula to solve this kind of problems,
[tex] log_{a}(b) + log_{a}(c) = log_{a}(bc) [/tex]
So, let's start of with log4_(300). Since the question have already gave log4_(3) =0.7925 and log4_(5) =1.1610. It means that you have to split the 300 into the simplest form where almost all of the numbers are 3 and 5.
[tex] log_{4}(300) = log_{4}(4 \times 5 \times 3 \times 5) \\ = log_{4}(4) + log_{4}(5) + log_{4}(3) + log_{4}(5) \\ = 1 + 1.1610 + 0.7925 + 1.1610 \\ = 4.1145[/tex]
Write 7 hundred in standard form
Answer:
700
Step-by-step explanation:
Answer:
700
Step-by-step explanation:
7 hundred in standard form is 700.
ii) Ramesh asked me where I lived. (into direct speech)
Answer:
Ramesh asked me,"where do you live?"
Ramesh said to me," where do you live".
Ruben is driving along a highway that passes through Barstow. His distance d, in miles, from Barstow is given by the equation
d = |210 − 60t|,
where t is the time, in hours, since the start of his trip and
0 ≤ t ≤ 5.
When will Ruben be exactly 90 miles from Barstow? (Enter your answers as a comma-separated list.)
The absolute value of a number returns the positive value of the given number. Ruben will be at exactly 90 miles in 2 hours or 5 hours
Given that:
[tex]d = |210 - 60t|[/tex]
To calculate t when [tex]d = 90[/tex], we have:
[tex]90 = |210 - 60t|[/tex]
Rewrite as:
[tex]|210 - 60t| = 90[/tex]
Remove absolute bracket
[tex]210 - 60t = 90 \ or\ 210 - 60t = -90[/tex]
Collect like terms
[tex]- 60t = -210 + 90 \ or\ - 60t = -210 -90[/tex]
[tex]- 60t = -120 \ or\ - 60t = -300[/tex]
Divide through by -60
[tex]t = 2 \ or\ t = 5[/tex]
Hence, Ruben will be at exactly 90 miles in 2 hours or 5 hours
Read more about absolute values at:
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Sarah, Bob and Nellie are cousins. Sarah is half the age of Bob. In three years time Nellie will be twice as old as Sarah. Their ages at the moment add to 38 years. Determine the ages of Sarah, Bob and Nellie
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Answer:
Sarah is 7Bob is 14Nellie is 17Step-by-step explanation:
Let s, b, n represent the current ages of Sarah, Bob, and Nellie, respectively.
s = b/2 . . . . . . Sarah is half Bob's age
2(s+3) = n+3 . . . . in 3 years, Nellie will be twice Sarah's age
s + b + n = 38 . . . . . their ages now add to 38
__
We can rearrange the first two equations to find Bob and Nellie's age in terms of Sarah's. Then we can substitute into the third equation to find Sarah's age.
b = 2s . . . . . . multiply the first equation by 2
2s +3 = n . . . . subtract 3 from the second equation and simplify
s +(2s) +(2s+3) = 38 . . . . substitute for b and n
5s = 35 . . . . . . . . . . . . subtract 3, collect terms
s = 7 . . . . . . . . . . . . divide by 5
b = 2(7) = 14
n = 2(7) +3 = 17
Sarah is 7, Bob is 14, and Nellie is 17.
Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a face card or an Ace.
Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a percentage, rounded to the nearest whole number.
31%
8%
4%
25%
Answer:
8%
Step-by-step explanation:
Ok, there is 52 cards per deck, 13 per suit ( club, diamond, heart, and spade)
if you multiply 13 by 4 ( 4 is dependent on the number of suit, and 4 will always be the number of suit )
The probability is 8%.
Why, because 25 would be pulling a random card and your saying you want the suit to be diamond the probability of you getting a random diamond card would be 25%. But were not doing that. So cross out 31% and 25%.
Also, 4% would be as your counting 100 cards. So that leaves me with 8%.
x ^ 2 − 17x − 60
Which expression is equivalent to the expression above?
(Please explain in simple terms cause, it's usually hard for me to understand)
[tex] {x}^{2} - 17x - 60 \\ (x + 3)(x - 20)[/tex]
First we put parentheses and in each bracket we put (X) and then we put the signs x² is positive and the 17X before it is a negative q is positive with negative —> negative, and negative before 17X and negative before the 60 —> positive. And then the number that does not have (x) where did it come from, for example 60 came from 20 x 3 or 30 x 2...etc. We can verify this by multiplying the parentheses together and the same number comes out .
Or it can be checked by multiplying the first bracket 3 with x from the second parenthesis comes out 3X and negative 20 from the second parenthesis with X from the first parenthesis and subtract 3X from –20xcomes out –17X .
I hope I helped you^_^
A CD with a diameter of 120 millimeters rotates a rate of 45 revolutions per minute. Find the linear speed of the CD in millimeters per minute. And find the angular speed of the CD in radians per minute
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Answer:
16,965 mm/min90π ≈ 282.7 radians/minStep-by-step explanation:
The circumference of the CD is ...
C = πd
C = π(120 mm) ≈ 376.99 mm
This is the distance a point on the edge of the CD will travel when making one revolution. It will travel 45 times this far when making 45 revolutions:
(376.99 mm/rev)(45 rev/min) ≈ 16,965 mm/min
__
There are 2π radians in each revolution, so the angular speed is ...
(2π rad/rev)(45 rev/min) = 90π rad/min ≈ 282.7 rad/min
Which describes the relationship between the distance and the difference?\
Answer:
The distance is always the opposite of the difference.The distance is the absolute value of the difference.
Hope it helps you.Have a nice day!!Answer:
The distance is the absolute value of the difference
Step-by-step explanation:
Sum is the when 2 or more numbers are added . Difference is the quantity at which 2 numbers differ i.e difference between 9 and 7 is 2. If you are talking about distance in reference to segment the distance ishow far apart two points are.
Help please! What is the length of the highlighted side? (Show work)
Answer:
7
Step-by-step explanation:
15ft - 8ft
Several probability expressions for a normal distribution are provided below. Drag the correct percentage to each probability expression.
Items
a. 68%
b. 47.5%
c. 13.5%
d. 2.5%
Category
1) P(?-2??x??)
2) P(?-??x??+?)
3) P(?+2??x)
4) P(?-2??x??-?)
The appropriate distribution of the percentages are :
P(μ-2σ≤x≤μ) = 47.5%
P(μ-σ≤x≤μ+σ) = 68%
P(μ-2σ≤x) = 2.5%
P(μ-2σ≤x≤μ-σ) = 13.5%
For a normal distribution :
The mean, μ = 0
The mean, μ = 0The standard deviation, σ = 1
Therefore :
P(μ-2σ≤x≤μ) = P(x≤μ) - P(x≤μ-2σ)
P(x≤μ) - P(x≤μ-2σ)
P(Z ≤ μ) - P(Z ≤ 2(1))
P(Z ≤ 0) - P(Z ≤ 2)
Using the normal distribution table :
0.5 - 0.02275 = 0.47725 = 47.725% (approximately 47.5%)
P(μ-σ≤x≤μ+σ) = P(x≤μ-σ) - P(x≤μ+σ)
P(x≤μ+σ) - P(x≤μ-σ)
P(Z ≤ μ+σ) - P(Z ≤ μ-σ)
P(Z ≤ (0+1) - P(Z ≤ 0-1)
P(Z ≤ 1) - P(Z ≤ - 1)
Using the normal distribution table /
0.84134 - 0.15866 = 0.68268 = 68.268% = (approximately 68%)
P(μ-2σ≤x) = P(μ-2σ)
P(Z ≤ μ-2σ) = P(Z ≤ (0 - 2(1))
P(Z ≤ - 2) = 0.02275 = 2.275% = (approximately 2.5%)
P(μ-2σ≤x≤μ-σ) = P(x≤μ-σ) - P(x≤μ-2σ)
P(x≤μ-σ) - P(x≤μ-2σ)
P(Z ≤ μ-σ) - P(Z ≤ μ-2σ)
P(Z ≤ (0-1) - P(Z ≤ 0-2(1))
P(Z ≤ -1) - P(Z ≤ -2)
From normal distribution table :
0.15866 - 0.02275 = 0.13591 = 13.59% = approximately 13.5%
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