Answer: 72
Step-by-step explanation: First step that I did was to subtract 12 and 4 to get 8. I then subtracted 3 and 2 to get 1. Then since 8 and 1 are in the parenthesis, I multiplied 8 and 1 to get 8. 8 to the 2nd power then comes out to 64. 64 adding the square root of 64 which is 8 then comes out to 64 plus 8 because the square root of 64 is 8. 64 plus 8 equals 72.
Find a cofunction equivalent to sin
5π
12
Cofunction equivalent to [tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex].
You use the formula for the sine of a sum:
[tex]$$\sin (a+b)=\sin a \cos b+\cos a \sin b$$[/tex]
Think of a pie divided into twelve slices. Three of them form one quarter, two more form one sixth of the pie. So, thinking of the "pie" as [tex]$\pi$[/tex]:
[tex]\frac{5 \pi}{12}=\frac{\pi}{4}+\frac{\pi}{6}[/tex]
With that in mind, put [tex]$a=\frac{\pi}{4}, b=\frac{\pi}{6}$[/tex] into the sine formula given above:
[tex]$$\sin \left(\frac{5 \pi}{12}\right)=\sin \left(\frac{\pi}{4}\right) \cos \left(\frac{\pi}{6}\right)+\cos \left(\frac{\pi}{4}\right) \sin \left(\frac{\pi}{6}\right)$$[/tex]
Plug in the familiar values [tex]$\sin \left(\frac{\pi}{4}\right)=\cos \left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}, \cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}$[/tex], [tex]$\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}$[/tex], and you get the answer given above. And, yes, putting that expression into a calculator gives [tex]$0.9659$[/tex] (four significant digits).
The cofunction of an angle θ is the trigonometric complement of an angle. It shows the relationship between trignometric functions:
List the cofunction formula for [tex]$\sin$[/tex]
[tex]$$\sin (\theta)=\cos (\pi / 2-\theta)$$[/tex]
Plug in [tex]$\theta=5 \pi / 12$[/tex] for our cofunction formula:
[tex]$$\sin (5 \pi / 12)=\cos (\pi / 2-5 \pi / 12)$$[/tex]
Determine common denominator in radians
We use a common denominator of [tex]$(12 \div 2)=6$[/tex]
[tex]$\sin (5 \pi / 12)=\cos (6 \pi / 12-(5 \pi / 12))$[/tex]
[tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex]
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please help asap and explain how you got it so i can understand.
Answer:
q = 6
Step-by-step explanation:
|q - 8| = 14
The negatives within an absolute value turn positive so it's really:
q + 8 = 14
q = 6
recipe says that 3 2/5 cups of flour are needed to make 1 batch of biscuits. How many cups of flour are needed to make 2 1/2 batches of biscuits?
Answer: 8 1/2 cups of flour
Step-by-step explanation:
You can look at this solution as x being the number of batches of biscuits.
1x = 1 batch of biscuits
1x = 3 2/5 cups of flour, or 17/5 cups of flour
We need to make 2 1/2 batches, restated as 5/2 batches.
This can be restated as 5/2x.
To determine our answer, we multiply x by 5/2.
5/2*(1x) = 5/2*(17/5)
5/2x = 85/10
Simplify.
85/10 = 8 5/10 or 8 1/2 cups
8 1/2 cups of flour are needed to make 2 1/2 batches of biscuits.
Evaluate 3x^2-2x+8 when x=3
Step-by-step explanation:
f(x) = 3x² - 2x + 8 , x = 3
f(3) = 3.3² - 2.3 + 8
= 27 - 6 + 8
= 29
every year from 2002 to 2014 either joey chestnut of california or takeri kobayashi of japan won the contest. in the five of those years both men completed and the results od the rivalry are shown in the table below. ( after the tie in 2008 joey chestnut won in aan overtime) because the condition of the year natter this is a matched pairs situation witht he twi men going against each year. in a matched pair situation we ise the summary statistica of difference between paris of values
The sum of one and six times a number is -113. What is the number?
Answer: -19
Step-by-step explanation:
n=number
6n+1=-113
6n=-114
n=-19
Find the future value (in dollars) of an 18-month investment of $4,300 into a simple interest rate account that has an annual simple interest rate of 5.1%.
keeping in mind that a year has 12 months, thus 18 months is really 18/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4300\\ r=rate\to 5.1\%\to \frac{5.1}{100}\dotfill &0.051\\ t=years\to \frac{18}{12}\dotfill &\frac{3}{2} \end{cases} \\\\\\ A=4300[1+(0.051)(\frac{3}{2})] \implies A=4628.95[/tex]
An amusement park charges $70 for admission before 6 P.M.
and $25 for admission after 6 P.M. On Saturday, the park took in a total of $28,000.
a. Write an equation that represents the number of admissions that may have been
sold. Let x represent the admissions sold before 6 P.M., and let y represent the
admissions sold after 6 P.M.
b. Graph the equation.
c. Find the x- and y-intercepts of the graph. What does each intercept represent? Please help the due date is tomorrow
The x-intercept is 0.4 and the y-intercept is 1.2.
Given that, an amusement park charges $70 for admission before 6 P.M. and $25 for admission after 6 P.M. On Saturday, the park took in a total of $28,000.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let x represent the admissions sold before 6 P.M., and let y represent the admissions sold after 6 P.M.
According to the question, we get the equation as 70x+25y=28,000
The graph of the obtained equation is given below.
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
From the graph, the x-intercept is 0.4 and the y-intercept is 1.2.
Therefore, the x-intercept is 0.4 and the y-intercept is 1.2.
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Classify the relationship(s) between the two following sets: A = {Joe Hawley, Noah Spence, Clinton McDonald, DaVonte Lambert, Luke Stocker} B = {Andrew DePaola, Mike Lennon, Sealver Siliga, Freddie Martino}
Answer: both
Step-by-step explanation:
Which of the expressions are equivalent to the one below? Check all that
apply.
(6.1)-8
A. 6-(1-8)
B. (1-8) (6-8)
C. 8- (1.6)
D. (1.6)-8
Answer:
C. & D.
Step-by-step explanation:
I believe it is C & D because, They both are in the same order just switched around, combine like like terms on both sides of the equation then if they are identical then they're equivalent.
Can someone help me out please??
Answer:
1. 7/8
2. 1/2
Step-by-step explanation:
y2-y1 /x2-x1 = slope
1. points: (-4,-4) and (4,3)
M = (3+4)/(4+4)
M=7/8
2. points: (-5,-3) and (3,1)
M = (1+3)/(3+5)
M = 4/8 or 1/2
when Dallas committed to work one morning his average speed was 45 mph. On the return trip he average only 35 mph. Due to congestion on the highway if the total traveling time for the round-trip is 50 minutes 5/6 of an hour find the distance between Dallas‘s workplace and home
The required distance is 16.40 km.
This problem can be solved if we know the concept of speed, time and distance.
We know the speed=[tex]\frac{distance}{time}[/tex]
To solve the problem let us assume that the total distance between the workplace and home is x km.
Given that his speed while going from home to work is 45 mph and while returning is 35 mph.
Time for the complete journey is [tex]\frac{5}{6}hr[/tex].
Now according to question;
[tex]\frac{x}{45}+\frac{x}{35}=\frac{5}{6}[/tex]
⇒[tex]\frac{7x+9x}{315}=\frac{5}{6}[/tex]
⇒[tex]16x=\frac{5*315}{6}[/tex]
⇒ [tex]x=\frac{5*315}{6*16}[/tex]
∴ [tex]x=16.40\ km[/tex]
So, the required distance is 16.40 km.
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Write the equation of the line in fully simplified slope-intercept form
Answer:
y = 3x - 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (1, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{1-3}[/tex] = [tex]\frac{-6}{-2}[/tex] = 3
the line crosses the y- axis at (0, - 7 ) ⇒ c = - 7
y = 3x - 7 ← equation of line
A quadratic function has A) straight lines that do both increase, decrease or stay constant on the same graph. B) curved lines that only increase or decrease. C) curved lines that do both increase and decrease on the same graph. D) straight lines that only increase or decrease. E) straight lines that do both increase and decrease on the same graph
The reading on a mercury manometer at 25 C ( open to the atmosphere at one end ) is 56.38 cm the local acceleration of gravity is 9.832m.s^-2 atmospheric pressure is 101.78kpa what is the absolute pressure in kpa being measured? The density of mercury at 25 C is 13.534 g.cm^-3
If the reading on a mercury manometer at 25 C is 56.38 cm the local acceleration of gravity is 9.832m.s^-2 atmospheric pressure is 101.78kpa The absolute pressure in kpa being measured is: 176.803kPa.
Absolute pressureUsing this formula
Pabs=Pg+Patm
Where:
Pabs= Absolute pressure.
Patm=Atmospheric pressure
ρm=Density of mercury
g=Acceleration of gravity
h=Reading on a mercury manometer
Let plug in the formula
Pabs=101.78×10³Pa+( 13.534×10³kg/m×9.832 m/s²×0.5638 m.
Pabs=101.78×10³Pa+75.023×10³kg/m.s²
Pabs=101.78×10³Pa+75.023×10³Pa
Pabs=176.803×10³Pa
Pabs=176.803kPa
Therefore If the reading on a mercury manometer at 25 C is 56.38 cm the local acceleration of gravity is 9.832m.s^-2 atmospheric pressure is 101.78kpa The absolute pressure in kpa being measured is: 176.803kPa.
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Please help me redo this vin diagram. I will give a Brainly and extra pouts.
Answer:
see attached
Step-by-step explanation:
You want a Venn diagram that represents the flavor preferences of 135 students.
Venn DiagramThe diagram you show is a good start. It usually works best to start by filling in the center spot, where all three circles overlap. You have correctly identified the number liking all three flavors as 15.
Working outward, the next step is to fill in the numbers for those who like two flavors. These numbers already include the number who like all three. This means ...
caramel + vanilla (only) = (caramel + vanilla) (28) - (caramel +vanilla +chocolate (15)
caramel + vanilla (only) = 28 -15 = 13
Similar computations are done for the other "likes 2 only" spots on the diagram:
chocolate + caramel (only) = 31 -15 = 16
chocolate + vanilla (only) = 22 -15 = 7
In like fashion, the numbers for one flavor only need to subtract out the numbers already inside the circle for that flavor.
chocolate (only) = 63 -16 -15 -7 = 25
Finally, the number of students having no preference is found by subtracting the numbers inside the parts of the circles from the total number of students:
no preference = 135 -111 = 24
The attachment shows the completed diagram.
I need help. Will give brainliest
Answer:
4/15
i have my ways
The probability mass function of X is f(x)= 1/6, x 1.2...,6 then find out the value
of mean and standard deviation.
For the given probability mass function of X, the mean is 3.5 and the standard deviation is 1.708.
A discrete random variable X's probability mass function (PMF) is a function over its sample space that estimates the likelihood that X will have a given value. f(x)=P[X=x]. The total of all potential values for a random variable X, weighted by their relative probabilities, is known as the mean (or expected value E[X]) of that variable. Mean(μ) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6).Mean(μ) = (1+2+3+4+5+6)/6Mean(μ) = 21/6Mean(μ) = 3.5The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. It is denoted by 'σ'. A random variable's variance (or Var[X]) is a measurement of the range of potential values. It is, by definition, the squared expectation of the distance between X and μ. It is denoted by 'σ²'. σ² = E[X²]−μ²σ² = [1²(1/6) + 2²(1/6) + 3²(1/6) + 4²(1/6) + 5²(1/6) + 6²(1/6)] - (3.5)²σ² = [(1² + 2²+ 3² + 4²+ 5²+ 6²)/6] - (3.5)²σ² = [(1 + 4 + 9 + 16 + 25 + 36)/6] - (3.5)²σ² = (91/6) - (3.5)²σ² = 15.167-12.25σ² = 2.917σ = √2.917Standard deviation (σ) = 1.708To learn more about variance, visit :
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35) A family is planning an annual picnic in Arizona. Rain is forecast for 45 days of the year, but when
rain is forecast, the prediction is correct only 90% of the time. What is the probability that it will rain on
the day of the picnic? Note that it is not a leap year.
Answer:
81/730
Step-by-step explanation:
The chance of picking a day forecasted to have no rain is 45/365.
There is a 90% chance it actually rains on this day, so the probability is
[tex](45/365)(0.9)=81/730[/tex]
How long would it take for a ball dropped from the top of a 121-foot building to hit the ground? Round your answer to two decimal places.
I don't need to know the actual answer, I'm just not sure what to plug in where into this formula: h=-½gt^2 +v0t+h0
The time that it will take the ball to hit the ground in 4 seconds.
How to solve equation of motion?To solve this problem you need the function;
h(t) = -16t² + v₀t + h₀
where;
t = time
v₀ is the initial velocity, which in our case is 0
h₀ is initial height, which in our case is 121 ft
h(t) = 0 since we want to know when the ball will hit the ground.
Thus;
0 = -16t² + 121
And we can solve for t;
If we rearrange the terms we see that this is a difference of 2 squares
0 = 121 - 16t²
0 = (11 - 4t)(11 + 4t)
Setting each factor = 0 gives;
11 - 4t = 0 11 + 4t = 0
t = 11/4 or t = -11/44
The second solution is discarded as time cannot be negative.
Thus, the ball will hit the ground in 4 seconds.
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may anyone please help me with math
Answer:
In decimal
[tex] - 2.8[/tex]
As fraction
[tex] \frac{ - 14}{5} [/tex]
And as mixed fraction
[tex] - 2 \frac{4}{5} [/tex]
Step-by-step explanation:
Greetings !
Given expression
[tex]f(x) = \frac{x - 8}{x + 11} [/tex]
Thus, plug in -6 in the variable x and solve
[tex]f( - 6) = \frac{ - 6 - 8}{ - 6 + 11} [/tex]
solve -6-8 = -14
solve -6+11 = 5
[tex] = \frac{ - 14}{5} [/tex]
Apply fraction rule
[tex] \frac{ - a}{b} = - \frac{a}{b} [/tex]
Thus
[tex] = - \frac{14}{5} [/tex]
Convert iimproper fraction to mixed fraction .
[tex] \frac{14}{5} = 2 \: \: remainder \: \: 4[/tex]
[tex]convert \: to \: mixed \: number \\ quotient \frac{remainder}{divisor} [/tex]
whereas
[tex] \frac{14}{5} = 2 \frac{4}{5} [/tex]
[tex] = - 2 \frac{4}{5} [/tex]
Hope it helps !!!
ABCD is an area in the shape of rhombus in which
120°. Find the measure of
If u answer will mark brainlyest and will give 40 points
Answer:
The measure of <CDO and <DCo are 60° and 30°.
Step-by-step explanation:
∠CDO = 1/2 ∠CDA
= 1/2 (120)° = 60°
∠ADC + ∠DCB = 180°
120° + ∠DCB = 180°
⇒ ∠DCB = 180° – 120° = 60°
∠DCO = 1/2 ∠DCB
= 1/2 (60°) = 30°
I hope this helps, have a good day! :D
An automobile purchased for $28,000 is worth $2500 after 5 years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year?
The value 3 years after it was purchased is
Answer:
$3285.47
Step-by-step explanation:
We know the value decreased by a factor of 2500/28000 after 5 years.
This means the value decreased by a factor of (2500/28000)⅕ per year.
Therefore, after 3 years, the value is
[tex]28000(2500/28000)^{3/5} \approx 3285.47[/tex]
Compare 71.815 and 701.815
Answer:
71.815<701.815
Step-by-step explanation:
A doctor has found that, over the years, 95% of the babies he has delivered weighed x pounds, where |x-8.1 | ≤1.3. What range of weights corresponds to
this inequality?
This range defines that the babies delivered weigh between 6.9 and 9.5 pounds.
Part 1.
Given inequality is | x − 8.1 | ≤ 1.3
Simplifying this inequality as
x - 8.2 ≤ 1.3 or x - 8.2 ≥ -1.3
Solving x - 8.2 ≤ 1.3 we get, x ≤ 9.5
And
Solving x - 8.2 ≥ -1.3 we have, x ≥ 6.9
Now combining the ranges we get,
6.9 ≤ x ≤ 9.5
Part 2.
This range defines that the babies delivered weigh between 6.9 and 9.5 pounds.
Hence, This range indicates that the babies' weights fall within the range of 6.9 to 9.5 pounds.
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A business has a budget of $720 to spend on their marketing campaign. Each month, x, the business spends $40 on different advertisements. The amount of money remaining in the budget
for marketing can be modeled by the function Mx)=-40x+720. Based on the graph of the linear function M(x) and the context of the problem, what is the domain?
O [10, 18]
O [10, 720]
0 [10, 8]
O [R]
A reasonable domain for this function is [0, 18)
Domain of a functionThe domain of a function is a value of the independent variable of the function for which it exists.
Given the equation below:
M(x)= -40x+720
Since the function represents the The amount of money remaining in the budget for marketing then the function f(x) must be greater than zero;
−40x + 720 > 0
-40x> -720
x < 720/40
x < 18
This shows that a reasonable domain for this function is [0, 18)
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Round 1803.2684 to the nearest thousand
Answer: 2000
Step-by-step explanation:
1803.2684=
1803.2684=2000
4 divided by 527 step by step
What is the area of a triangle ABC with AB=AC=5cm and BC=6cm?
Answer: 12 cm^2
Step-by-step explanation:
BC ==> Base of triangle
Divide the triangle in two parts:
BC/2=BC'
6/2=BC'
BC'=3
Distance formula: a^2+b^2=c^2
c^2-a^2=b^2
5^2-3^2=b^2
25-9=b^2
b^2=16
b=4 ==> height of triangle
Area of triangle=A. b=base. h=height
A=1/2 * b * h=
A=1/2 * 6 * 4
A=1/2 * 24
A=12 cm^2
Solve for g.
G+1/ 2=2
Answe
G=1.5
Step-by-step explanation: