Answer:
1/3
Step-by-step explanation:
Hope This Helps!
Which values represent solutions to the equation?
Tangent (StartFraction 3 pi Over 4 EndFraction minus 2 x) = negative where x Is an element of [0, Pi]
The solution set for the given expression is {0, π/2, π}.
Which values of x are solutions for the given expression?Here we have the expression:
\(tan(\frac{3\pi}{4} -2x) = -1\)
First, we know that:
\(tan(\frac{3\pi}{4}) = -1\)
So, if x = 0, the equation is true, which means that x = 0 is a solution.
And the tangent function as a period of pi.
This means that:
tan(x) = tan(x - π) = tan(x - 2*π) etc.
Then if x = π/2 and x = π also are solutions, so we conclude that the solution set is:
{0, π/2, π}
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PLEASE HELP ME WITH PRE CAL!!
A drone is flying over a college campus. The drone spots the cafeteria on the west end of campus at a 27 ° angle of depression and the sports complex on the east end of campus at a 34° angle of depression. If the cafeteria and sports complex are separated by a straight road 2.3 mi long, how high is the drone?
Answer:
0.67 mi
Step-by-step explanation:
The diagram illustrating the question is shown in the attach photo.
In triangle DCA,
Opposite = H
Adjacent = b
Angel θ = 27°
Tan θ = Opp /Adj
Tan 27° = H/b
Cross multiply
H = b x Tan 27°... (1)
From triangle DSA,
The diagram illustrating the question is shown in attach photo.
In triangle DCA,
Opposite = H
Adjacent = 2.3 – b
Angel θ = 34°
Tan θ = Opp /Adj
Tan 34° = H/ 2.3 – b
Cross multiply
H = Tan 34° (2.3 – b) .. (2)
Equating equation (1) and (2)
b x Tan 27° = Tan 34° (2.3 – b)
0.5095b = 0.6745(2.3 – b)
0.5095b = 1.55135 – 0.6745b
Collect like terms
0.5095b + 0.6745b = 1.55135
1.184b = 1.55135
Divide both side by 1.184
b = 1.55135/1.184
b = 1.31 mi
Substitute the value of b into any of the equation to obtain the height (H). In this case we shall use equation 1.
H = b x Tan 27°
H = 1.31 x Tan 27°
H = 0.67 mi
Therefore, the height of the drone is 0.67 mi
The height of the drone is 0.67 mi
The calculation is as follows:In triangle DCA,
Opposite = H
Adjacent = b
Angel θ = 27°
Tan θ = \(Opp \div Adj\)
Tan 27° =\(H\div b\)
Now we have to do the cross multiply
\(H = b \times Tan 27^{\circ}... (1)\)
Now
From triangle DSA,
In triangle DCA,
Opposite = H
Adjacent = 2.3 – b
Angel θ = 34°
Tan θ = \(Opp \div Adj\)
Tan 34° = \(H\div 2.3 - b\)
Now we have to do the cross multiply
H = Tan 34° (2.3 – b) .. (2)
Now
Equating equation (1) and (2)
\(b \times Tan 27^{\circ} = Tan 34^{\circ} (2.3 - b)\)
0.5095b = 0.6745(2.3 – b)
0.5095b = 1.55135 – 0.6745b
Now
0.5095b + 0.6745b = 1.55135
1.184b = 1.55135
b = 1.31 mi
Now
\(H = b \times Tan 27^{\circ}\\\\H = 1.31 \times Tan 27^{\circ}\)
H = 0.67 mi
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The expected return on MSFT next year is 12% with a standard deviation of 20%. The expected return on AAPL next year is 24% with a standard deviation of 30%. If James makes equal investments in MSFT and AAPL, what is the expected return on his portfolio. 3. Siebling Manufacturing Company's common stock has a beta of .8. If the expected risk-free return is 2% and the market offers a premium of 8% over the risk-free rate, what is the expected return on Siebling's common stock
The expected return on James's portfolio is 18%.
The expected return on Siebling Manufacturing Company's common stock is 8.4%.
To calculate the expected return on James's portfolio, we need to take the weighted average of the expected returns of MSFT and AAPL based on their respective investments.
Let's assume James invests x% in MSFT and (100 - x)% in AAPL.
The expected return on James's portfolio can be calculated as:
Expected Return = (x * Expected Return of MSFT) + ((100 - x) * Expected Return of AAPL)
Substituting the given values:
Expected Return = (x * 12%) + ((100 - x) * 24%)
To find the value of x that makes James's investments equal, we set the weights equal:
x = 100 - x
Solving this equation gives us x = 50.
Now we can substitute this value back into the expected return equation:
Expected Return = (50% * 12%) + (50% * 24%)
Expected Return = 6% + 12%
Expected Return = 18%
Therefore, the expected return on James's portfolio is 18%.
To calculate the expected return on Siebling Manufacturing Company's common stock, we can use the Capital Asset Pricing Model (CAPM).
The CAPM formula is:
Expected Return = Risk-Free Rate + Beta * Market Premium
Risk-Free Rate = 2%
Market Premium = 8%
Beta = 0.8
Expected Return = 2% + 0.8 * 8%
Expected Return = 2% + 6.4%
Expected Return = 8.4%
Therefore, the expected return on Siebling Manufacturing Company's common stock is 8.4%.
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Write the Standard Form of the line with x-intercept of 3 and y-intercept of 4.
Answer:
Use a model to find the sum of two fractions with the same denominator
Add fractions with a common denominator without a model
Add fractions with a common denominator that contain a variable h
Step-by-step explanation:
h
what is the equation of the line that passes through the point(3,-6) and has a slope of 0
Answer:
y = 3 x − 3
Step-by-step explanation:
The equation for slope-intercept form is as follows:
To find c , substitute x = 3 , y= 6 and m = 3 into the equation,6=3 (3 ) + c c= 6 − 9 c = − 3 Since we found m = 3 and c= − 3 , we can form the equation, = 3 x− 3
:D
Answer:
y=-6
Step-by-step explanation:
I got it wrong and told me this was the answer! Im not good with math lol
Dell Eatery employs one worker whose job it is to load apple pies on outgoing company cars. Cars arrive at the loading gate at an average of 48 per day, or 6 per hour, according to a Poisson distribution. The worker loads them at a rate of 8 per hour, following approximately the exponential distribution in service times. a. Determine the operating characteristics of this loading gate problem. [6 Marks] b. What is the probability that there will be more than six cars either being loaded or waiting? [2 Marks] Formulae L= μ−λ
λ
W= μ−λ
1
L q
W q
rho
P 0
= μ(μ−λ)
λ 2
= μ(μ−λ)
λ
= μ
λ
=1− μ
λ
P n>k
=( μ
λ
) k+1
The required probability is 0.4408.
The operating characteristics of the loading gate problem are:
L = λ/ (μ - λ)
W = 1/ (μ - λ)
Lq = λ^2 / μ (μ - λ)
Wq = λ / μ (μ - λ)
ρ = λ / μ
P0 = 1 - λ / μ
Where, L represents the average number of cars either being loaded or waiting.
W represents the average time a car spends either being loaded or waiting.
Lq represents the average number of cars waiting.
Wq represents the average waiting time of a car.
ρ represents the utilization factor.
ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.
P0 represents the probability that the system is empty.
The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,
P (n > 6) = 1 - P (n ≤ 6)
Now, the probability of having less than or equal to six cars in the system at a given time,
P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]
Putting the values of λ and μ, we get,
P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]
P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592
Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408
Therefore, the required probability is 0.4408.
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Fill in the missing value with a whole number.
40 thousandths= hundredths?
Answer:
4
Step-by-step explanation:
The missing value with a whole number is 4.
What is the place value?Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
Given that, 40 thousandths= hundredths
Let the missing value with a whole number be x.
Now, 40 thousandths= x hundredths
40 thousandths
= 40 ×1/1000
= 0.04
So, 0.04= x ×1/100
0.04×100=x
x=4
So, 40 thousandths= 4 hundredths
Therefore, the missing value with a whole number is 4.
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Add. *
A rancher uses a water bowl for her dog that holds 8,500 milliliters and a water trough for her
horse that holds 2.7 X 10 milliliters. How many milliliters of water will the rancher use to
completely fill both the bowl and the trough?
A 1.12 x 105 mL
B 2.785 X 10 mL
C 5.8 x 10 ml
D 1.12 x 10 ml
What’s the answer I need help asap? Help me
Parameter 1 corresponds to the cosine function because it has a period of 2, an amplitude of 1, and contains the point (1).
Parameter 2 corresponds to the sine function because it has a period of 2π/2=π, an amplitude of 1, and contains the point (2,-1).
How did we arrive at these assertions?Parameter 1 corresponds to the cosine function because it has a period of 2, an amplitude of 1, and contains the point (1). The equation for a cosine function is:
f(x) = A*cos (Bx) + C
where A is the amplitude, B (2π/period) is the frequency , and C (the average value of the function) is the midline.
A= 1, B = π, and C = 0.
Hence, equation for this function is f(x) = cos (πx)
This function has a period of 2, an amplitude of 1, and contains the point (1).
Parameter 2 corresponds to the sine function because it has a period of 2π/2=π, an amplitude of 1, and contains the point (2,-1).
g(x) = A* sin (Bx) + C (sine function)
where A is the amplitude, B (2π/period) is the frequency , and C (the average value of the function) is the midline
A= 1, B = 2π/2 = π, and C = -1.
g(x) = sin (πx) - 1
This function has a period of 2, an amplitude of 1, and contains the point (2, -1).
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Simplify each expression. a²b-31²2 a²b² a=0,b=0
Answer:
0Step-by-step explanation:
Simplify each expression.
a²b-31²2 a²b²
a=0,b=0
0^2 - 31^2 * 0^2 * 0^2=
-31^2*0=
961 * 0 =
0
Answer:
\(\sf a^2b-31^22 a^2b^2\) When, \(\sf a=0, b=0\)
We'll substitute a with 0 and b with 0.
\(\sf \left(0\right)^2\left(0\right)-31^22\left(0\right)^2\left(0\right)^2\)
Calculate the exponents.
\(\sf 0 \times\left(0\right)-31^2\times\:2\left(0\right)^2\left(0\right)^2\)
\(\sf 0\times\left(0\right)-961\times\:2\left(0\right)^2\left(0\right)^2\)
\(\sf 0\times\left(0\right)-961\times\:2\times \:0\times \left(0\right)^2\)
\(\sf 0\times\left(0\right)-961\times\:2\times\:0\times\:0\)
\(\sf 0-961\times\:2\times\:0\times\:0\)
\(\sf 0-0\)
\(\sf 0\)
____________________________
A group of 12 students is deciding whether to go to the science center or the zoo. Science center tickets are 3 for $36.75 and zoo tickets are 4 for $51.
How much will a group of 12 students save by choosing the science center?
Enter your answer in the box.
Answer:
The money saved is $153-$147= $6
Step-by-step explanation:
Science center tickets are 3 for $36.75
so 12 tickets costs =4*36.75=$147
and zoo tickets are 4 for $51
so 12 tickets costs =3* 51=$153
The money saved is $153-$147= $6
when can we conceptually isolate the strength of the evidence from the prior probability of the theory? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a only in cases when we observe the relevant evidence and then form hypotheses to explain them b only in cases when we can form hypotheses prior to testing them with evidence c whether we make observations first or form our hypotheses first d we can never reliably do this because of the problem of ad hoc modification
We can conceptually isolate the strength of the evidence from the prior probability of the theory when we make observations first or form our hypotheses first. Correct option is C.
The concept of isolating the strength of evidence from the prior probability of the theory is known as Bayesian inference, which involves updating our prior beliefs about a theory or hypothesis based on the observed evidence.
This process can be done whenever we have some initial prior belief about the theory or hypothesis and then collect new evidence to test it.
In Bayesian inference, the strength of evidence is measured by the likelihood of the observed data given the theory or hypothesis, and the prior probability is the initial belief or probability assigned to the theory or hypothesis before the evidence is considered.
By combining these two sources of information, we can calculate a posterior probability or updated probability of the theory or hypothesis given the observed evidence.
Therefore, the answer is c) whether we make observations first or form our hypotheses first. The order in which we collect the evidence or form hypotheses does not affect our ability to conceptually isolate the strength of the evidence from the prior probability of the theory, as long as we use Bayesian inference to update our beliefs.
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In the given figure ABCD, prove that
angleBCD= angleBAD+ angle ABC+angle ADC.
[Hint: Join A and C then extended AC to the point E]
We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:
Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.
Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.
Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).
Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.
Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).
Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.
Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.
Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.
Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.
Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
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Given: Quadrilateral \(\displaystyle\sf ABCD\)
To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)
Proof:
1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).
2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).
3. In triangle \(\displaystyle\sf ACD\):
- \(\displaystyle\sf \angle ACD = \angle BAD + \angle ADC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).4. In triangle \(\displaystyle\sf BCE\):
- \(\displaystyle\sf \angle BCE = \angle BAD + \angle ABC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):
- \(\displaystyle\sf \angle BCE = \angle BCD\).6. Combining the equations from steps 3 and 4:
- \(\displaystyle\sf \angle BCD = \angle ACD = \angle BAD + \angle ADC\). - \(\displaystyle\sf \angle BCD = \angle BCE = \angle BAD + \angle ABC + \angle ADC\).Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
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What is the graph of this compound inequality?
Answer:
The second one
Step-by-step explanation:
The first graphic would be correct if the connector was "AND" instead of "OR"
"AND" --> Both conditions must ALWAYS be fulfilled
"OR" ---> It's only necessary that one of the conditions is fulfilled
The price of a sandwich is $5.50 more than the price of a smoothie, which is d dollars. What does theexpression d +55 representiThe expression represents the select)
Given :
The price of a sandwich is $5.50 more than the price of a smoothie, which is d dollars
so, the expression :
d + 5.5 represents : The price of of a sandwich
a pool with dimensions of 10 ft radius and 4 ft height fill with water at a rate of 20 gallons a minutes. about how many hours will it take to fill the pool if 1 cubic foot of water is about 7.5 gallons?
It will take approximately 7.85 hours to fill the pool.
To determine the time needed to fill the pool, first calculate the volume of the pool, then convert the volume to gallons, and finally, divide by the fill rate.
The pool is a cylinder with a radius of 10 ft and a height of 4 ft. The volume of a cylinder is given by the formula V = πr²h.
V = π(10 ft)²(4 ft) = 400π cubic feet ≈ 1256.64 cubic feet
Next, convert the volume to gallons using the given conversion factor:
1256.64 cubic feet * 7.5 gallons/cubic foot ≈ 9424.8 gallons
Now, divide the total gallons by the fill rate of 20 gallons/minute to find the time in minutes:
9424.8 gallons ÷ 20 gallons/minute ≈ 471.24 minutes
Finally, convert the time to hours:
471.24 minutes ÷ 60 minutes/hour ≈ 7.85 hours
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Find m∠CDE I already found x
Answer:
72 degrees.
2 parallel lines cut by a transversal result in alternate interior angles.
Find the length of the hypotenuse in each right triangle.
(Do 2 of each)
Answer:
2.
a. 14 cm
b. 17 cm
c. 6 cm
d. 8 cm
3.
a. 22 cm
b. 36 cm
c. 16 cm
d. 15 cm
4.
a. 10 cm
b. 40 cm
c. 28 cm
Step-by-step explanation:
The Pythagorean Theorem states the sum of two sides length equals the length of the hypotenuse of the triangle.
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Can someone pls help me?
A fair 6-sided die is rolled 300 times. What is a reasonable prediction for the number of times the event of landing on an odd number will occur?
A. 150
B. 50
C. 175
D. 100
Answer:
A. 150
Step-by-step explanation:
Calculate the probability of landing on an odd number: 1/2.
Multiply the probability by the number of trials: (1/2) * 300.
Simplify the expression: 150.
Therefore, a reasonable prediction is that the event of landing on an odd number will occur 150 times out of the 300 rolls of the fair 6-sided die.
32. CAMPING Michael is planning to ride a horse to a campsite. The sum of
Michael's weight and the combined weight of his camping supplies must
be at most 20% of the weight of the horse. Michael weighs 177 pounds,
and the horse weighs 1000 pounds. What are the possible weights of the
camping supplies?
Answer:
At most the camping supplies can weigh 23 pounds
Step-by-step explanation:
solve the linear equation 4x-(2x-1)=x+5+x-6
The linear equation doesn't have a solution.
How to compute the value?The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6
This will be solved thus:
4x - 2x + 1 = x+5+x-6
4x - 2x + 1 = 2x - 1.
2x + 1 = 2x - 1
Collect like terms
2x - 2x = -1 - 1
0 = -2
This illustrates that the equation doesn't have a solution.
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Compute the value of the discriminant and give the number of real solutions of the quadratic equation.-4x²+2x–5=0
ANSWER
\(\begin{gathered} \text{Discriminant}=-76 \\ No\text{ real solutions} \end{gathered}\)EXPLANATION
We want to find the discrimininant of the equation:
\(-4x^2+2x-5=0\)The general form of a quadratic equaion is given as:
\(ax^2+bx+c=0\)The discriminant is given as:
\(b^2-4ac\)Therefore, we need to find that.
From the given equation:
\(\begin{gathered} a=-4 \\ b=2 \\ c=-5 \end{gathered}\)Therefore, we have that the discriminant is:
\(\begin{gathered} 2^2-4(-4)(-5) \\ 4-(4\cdot20) \\ 4-80 \\ -76 \end{gathered}\)That is the discriminant.
Since the discriminant is less than 0, then there are no real solutions of the equation.
the manager of a supermarket tracked the amount of time needed for customers to be served by the cashier. after checking with his statistics professor, he concluded that the checkout times are exponentially distributed with a mean of 5 minutes. what propotion of customers require more than 10 minutes to check out? proportion
Approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.
Exponential Checkout Time ProportionTo find the proportion of customers who take more than 10 minutes to check out, we need to calculate the cumulative distribution function (CDF) of an exponential distribution at 10 minutes and subtract it from 1. The CDF for an exponential distribution with mean (lambda) 5 minutes is given by:
CDF = 1 - e^(- λ * x)
Plugging in λ = 0.2 (1/mean) and x = 10, we get:
CDF = 1 - e^(-0.2 * 10) = 1 - e^(-2) = 1 - 0.135 = 0.865
So, approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.
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Factor the trinomial and show your work!!
2x^2 + 22x + 60
Answer: 2(x+6)(x+5)
Step-by-step explanation:
1. 2(x²+11x+30)
2. 2(x²+6x+5x+30)
3. 2(x(x+6) + 5(x+6))
4. 2(x+6)(x+5)
how do you graph data?
The unit rate of change of y with respect to x is the amount y changes for a change of one unit in x. Is the unit rate of change of y with respect to x greater in the equation y =0.32 or in the graph below?
answers:
a. the equation
b. the graph
c. the unit rates are the sam
Note that the unit rate of change of the equation is 0.32, and the one of the graph is 1, so the correct option is B.
Which one has a greater unit rate of change?We define the unit rate of change as the slope or constant of proportionality.
y = 0.32 * x
The unit rate of change is 0.32
In the graph we can see that for each unit moved in horizontally, the line moves one unit vertically, then the unit rate of change is just 1.
y = x
Then we can conclude that the graph has the greater unit rate of change.
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In the figure, RV, WS, and QT intersect at point P.
What is the value of x? Show your work.
Answer:
x = 12
Step-by-step explanation:
67+42+6x-1=180
108+6x=180
6x=72
x=12
Combine like terms to write the expression in standard form (−r +s) + (s − r)
First we clear brackets
-r+s+s-r
Second we collect like terms
-r-r+s+s
then we add it
-2r +2s
if we read the question it says standard form so we out the G.C.F of the
expression
2(-r+s)
What is the solution to -4-2x + 6 = -24?
x = 0 or x = -6
O x = 0 or x = 6
O no solution
Answer:
x=13
Step-by-step explanation: