We know that tan = opp / adj
arctan x = theta
Taking the tan of each side
x = tan theta = opp / adj
x/1 = tan theta
The hypotenuse :
We can find this using the pythagorean theorem
a^2 + b^2 = c^2
1^2 + x^2 = hyp ^2
The hypotenuse = sqrt( 1+x^2)
Now we can find the cos of the angle
cos theta = adj side/ hypotenuse
cos theta = 1/ sqrt(1+x^2)
Rationalizing the denominator
cos theta = sqrt(1+x^2)/ (1+x^2)
cos ( tan^-1 x) = sqrt(1+x^2)/ (1+x^2)
A Gardner has 1 1/4 cubic feet of soil available for filling pots. Each pot will need 2/5 cubic foot to be filled. What is the greatest number of pots that the gardener fill
The greatest number of pots that can be filled is 3.
In order to determine the greatest number of pots that can be filled, the quantity of soil available would be divided by the capacity of each pot.
Number of pots that can be filled = 1 1/4 ÷ 2/5
= 5/4 ÷ 2/5
= 5/4 x 5/2 = 25/8 = 3 1/8
Thus, the greatest number of pots that can be filled is 3.
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Math Homework: Unit 3 Assignment
What are the points of the image of the line in Q4 after the dilation?
Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)
How is this so ?To rotate a point 90 degrees clockwise about a given point,we can follow these steps -
Translate the coordinates of the given point so that the center of rotation is at the origin. In this case,we subtract the coordinates of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).
Perform the rotation by swapping the x and y coordinates and changing the sign of the new x coordinate. In this case,we swap the x and y coordinates of (-5, 3) to get (3, -5).
Translate the coordinates back to their original position by adding the coordinates of the center (0,1) to the result from step 2. In this case, we add (0,1) to (3, -5) to get (3, -4).
Therefore, the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).
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Jim can type 3850 words in 70 minutes.
David can type 3300 in 60 minutes.
Dan can type 2400 words in 40 minutes.
Who types at the fastest rate of words per minute?
Answer:
Dan, because he types 60 words per minute.
Step-by-step explanation:
Jim: 3850/70 = 55 words/minute
David: 3300/60 = 55 words/minute
Dan: 2400/40 = 60 words/minute
How to write any power of 1 without multiplying?
In indices, the way to write any power of 1 without multiplying is to just write the original number back.
How to compute the value?It should be noted that indices simply means the lose or exponent that is raised to a number or another variable.
For example 2⁴ simply means that 2 is raised to the power of 4.
It should be noted that in indices, the way to write any power of 1 without multiplying is to just write the original number back.
For example, 2¹ is still 2.
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write the sentence as an inequality. A number x is greater than 6 but less than 10.
Answer:
6>x<10
Step-by-step explanation:
also put a line under both > <
What meaning of the statement this?
Note that the notation "∪C = {x : x ∈ for some S ∈ C} = ∪ { S:S ∈ C}" represents a mathematical statement involving sets.
What is the explanation of this ?∪C : This represents the union (∪) of the sets in C.
{x : x ∈ for some S ∈ C}: This is the description or definition of the elements in the set formed by the union of sets in C.
It states that an element x belongs to the union of sets in C if and only if x belongs to at least one set S that is an element of the set C.
= ∪{ S:S ∈ C} : This means that the union (∪) of sets in C is equal to the union of all sets S that belong to the set C.
In summary, the statement is saying that the union of sets in C consists of all elements that belong to at least one set in C. It is the combined collection of elements from all sets in C.
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bought furniture 10,000. wht is credit wht is debit
Answer:
Answer
Furniture A/C DR
To Cash A/C
Answer:
what you owe
Step-by-step explanation:
Is urgent If a line passes through the points (2, 7) and (7,9), its slope is
necessary, use the slash (/) to indicate a fraction.
If
find x and y please explain really well
Answer:
x=10,y=120
Step-by-step explanation:
3x-30=60 CDA
3x=30
x=10
again,
y+60=180 straight line
y = 120
1 22.8 ÷ 0. 92 =
2 34.08 ÷ 0.24 =
3 28.9 ÷ 0.85 =
4 7. 15 ÷ 0.05 =
5 210.21 ÷ 0.91 =
Please answer it
Answer:
1. 24.7826087
2. 142
3. 34
4. 143
5. 231
if the answer wants number 1. rounded in tenths, put 24.8
if they want it rounded in hundreths, put 24.78
hope this helps
1) 24.78
2) 142
3) 34
4) 143
5) 231
hope u liked this answer
#keep learningPart 2: Consider this word problem: "Professor has several tarantulas and frogs. She counts 104 legs and 80 eyes in the room (not including her own). How many of each creature does she have?" Answer the question in a paragraph form. Answer the following: • What bits of information are not explicitly stated in the problem that would help us figure out the answer? Do you need to look anything up orpull some information from the back of your head?• Which mathematical concept(s) that we've gone over so far would be helpful for solving this problem?• Now, solve the problem and explain your solution. (It's OK if your answer isn't completely right. We're here to learn!)
Okay, here we have this:
Considering the provided information we are going to calculate how many of each creature does she have, so we obtain the following:
• What bits of information are not explicitly stated in the problem that would help us figure out the answer? Do you need to look anything up or
pull some information from the back of your head?:
The missing information of the exercise is the amount of legs and eyes of each type of animal
• Which mathematical concept(s) that we've gone over so far would be helpful for solving this problem?:
The mathematical concept that we apply to solve this exercise will be the systems of equations of two equations by two incognites.
• Now, solve the problem and explain your solution. (It's OK if your answer isn't completely right. We're here to learn!):
According to the given information we obtain the following systems of equations:
8x+4y=104 (Equation of the legs)
8x+2y=80 (Eye equation)
"X" corresponds to the number of tarantulas and "y" to the number of frogs.
Solving:
We will clear x in the second equation:
8x+2y=80
8x=80-2y
x=(80-2y)/8
x=10-2y/8
Replacing in the first equation:
8x+4y=104
8(10-2y/8)+4y=104
80-2y+4y=104
80+2y=104
2y=24
y=24/2
y=12
Using this value of y in the equation of x:
x=10-2y/8
x=10-2(12)/8
x=10-24/8
x=10-3
x=7
Finally we obtain that she has 7 tarantulas and 12 frogs.
Solve the equation 34 - (x + 8) = 6x-2
Answer:
x = 4
Step-by-step explanation:
To solve the equation, we would have to solve for the variable x.
34 - (x + 8) = 6x - 2
Remove the parentheses.
34 - x - 8 = 6x - 2
Add 2 to both sides and combine like terms.
28 - x = 6x
Add x to both sides.
28 = 7x
Swap sides.
7x = 28
Divide both sides by 7.
x = 4
So the solution to the equation would be x = 4
I hope you find my answer and explanation to be helpful. Happy studying. :)
The money used in poland is called the zlotych. the exchange rate is 3 zlotych for would $1. find how many zlotych you would receive if you exchanged $3
find the whole number
Answer:
You would receive 9$
Step-by-step explanation:
if you multiply 3 by 3, then you will get 9
evaluate the numerical value of the final momentum of the t-shirt using the results from parts a and b.
The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is the sum of the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied.
The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is calculated by summing the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied. Momentum is a vector quantity which is equal to the product of the mass and velocity of an object. In this case, the t-shirt has a mass of 4 kg and a velocity of 4 m/s. The force of 15 N applied to the t-shirt for 3 seconds causes the t-shirt to accelerate, increasing its velocity from 4 m/s to 8 m/s. This increase in velocity results in an increase in the momentum of the t-shirt from 2 kg⋅m/s to 17.5 kg⋅m/s. Thus, by calculating the change in momentum due to the applied force, we can determine the final momentum of the t-shirt.
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a researcher has conducted a survey using a simple random sample of 500 gold club members to create a confidence interval to estimate the proportion of golf club members favoring a 1% annual increase in dues to remodel the clubhouse assume that the sample proportion does not change the researcher now decides to survey a random sample of 125 people instead of 500 golf club members which of the following statments best describes how the confidence interval is affected by this change
a. The width of new interval is aobut t same width as the original interval
b. the width of the new interval is about twice the width of the original interval
c. the width of the new interval is about one hald the width of the original interval
d. the width of the new interval is about on fourth the width of the original interval
e. the width of the new interval is about 4 times the width of the original interval
Answer: B.
Procedure we follow in calculating confidence level for proportion.
i. standard error = sqrt ( (p*q) /n) )
ii. margin of error = z a/2 * (stanadard error)
where,
za/2 = z-table value
level of significance, alpha
from standard normal table, two tailed z alpha/2
iii. ci = [ p ± margin of error ]
with above, we see that sample size n is inversely proportional to the confidence level
i.e increasing the sample size narrow the confidence interval
& decreasing the sample size widen the confidence interval.
CI ~ sqrt(1/n)
size is cut down to 4 times, i.e 500/125 = 4 times decreased
CI ~ sqrt(1/(n/4))
CI ~ sqrt(4/(n)
CI ~ 2 * sqrt(1/(n)
from above, we conclude that it is twice the previous
Substitute 3 for x in new equation. Do you get a ture statement explain
URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS
Shawn has some nickels in a jar he put 174 nickels in the jar now he there are 435 nickels in the jar how many nickels were in the jar at the start?
Shawn has some nickels in a jar
Let x be the number of nickels in the jar
he put 174 nickels in the jar
Number of nickel added = 174
there are 435 nickels in the jar
Total number of nickel in jar = 435
So, Total number of nickel in jar = intial number of nickel in jar + number of nickels added
435 = x + 174
x = 435 - 174
x = 261
There are 261 nickels in the jar.
Answer: 261
Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'. What are the coordinates of X'Y'Z'?
Answer:
59
Step-by-step explanation:
6 plus 4 equals 8 plus 9
Someone help me please and thank you
Answer: 2a < 2b
Step-by-step explanation:
We are given a statement:
a < b and b < c, then 2a ____ 2b
We can use simple numbers that make the statement true.
Where,
a = 2
b = 3
c = 4
Now lets plug it in.
2 < 3 and 3 < 4, then 2(2) ____ 2(3)
and lets simplify:
2 < 3 and 3 < 4, then 4 ____ 6
We can see that 4 is less than 6,
so as a is less than b, 2a is less than 2b.
The only thing changing is the coefficient being multiplied by the variables a and b.
A certain virus infects one in every 150 people. A test used to detect the virus in a person is positive 70% of the time when the person has the virus and 15% of the time when the person does not have the virus. (This 15% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive."(a) Using Bayes' Theorem, when a person tests positive, determine the probability that the person is infected.(b) Using Bayes' Theorem, when a person tests negative, determine the probability that the person is not infected. Here is the formula that we are given for this particular problem:P(A|B)= P(A) x P(B|A) divided byP(A) x P(B|A) + P(A') x P(B|A')
A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 11 students, he found the average time was 4.52 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.1 level of significance. Assume normality. (can you please show how to do this without a calculator or excel i just dont want answer but want to know how to do it).
a) What are the appropriate null and alternative hypotheses?
A) H0: μ = 5 versus Ha: μ < 5
B) H0: μ = 5 versus Ha: μ ≠ 5
C) H0: x = 5 versus Ha: x ≠ 5
D) H0: μ = 5 versus Ha: μ > 5
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
A) Fail to reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
B) Reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
C) Reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
D) Fail to reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
Answer:
A) Null Hypothesis;H0: μ = 5
Alternative Hypothesis;Ha: μ ≠ 5
B) test statistic = -2.1226
C) p-value = 0.0598
D) Option A is correct
Step-by-step explanation:
We are given;
x = 4.52 minutes
s = 0.75 minutes
μ = 5 minutes
n = 11
degree of freedom = n - 1 = 11 - 1 = 10
A) The hypotheses are;
Null Hypothesis;H0: μ = 5
Alternative Hypothesis;Ha: μ ≠ 5
B) t-statistic = (x - μ)/(s/√n)
(4.52 - 5)/(0.75/√11) = -2.1226
C) From the t-score calculator results attached, the p-value is approximately 0.0598.
D) The P-value of 0.0598 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant. So option A is correct.
Given that 8 tan = 3 cos
a) Show that the above equation can be rewritten in the form 3 sin2 + 8 sin − 3 = 0
b) Hence solve, for 0 ≤ ≤ 90, the equation 8 tan 2 = 3 cos 2, giving your answers to 2 decimal places.
The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.
a) We are given the equation 8 tan θ = 3 cos θ.
Dividing both sides of the equation by cos θ, we have:
8 tan θ / cos θ = 3
Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:
8 (sin θ / cos θ) / cos θ = 3
Simplifying further, we get:
8 sin θ / cos^2 θ = 3
Now, multiplying both sides of the equation by cos^2 θ, we have:
8 sin θ = 3 cos^2 θ
Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:
8 sin θ = 3(1 - sin^2 θ)
Expanding the equation, we get:
8 sin θ = 3 - 3 sin^2 θ
Rearranging the terms, we have:
3 sin^2 θ + 8 sin θ - 3 = 0
Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.
b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.
To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.
In this case, the equation factors as:
(3 sin θ - 1)(sin θ + 3) = 0
Setting each factor equal to zero, we have two equations:
3 sin θ - 1 = 0 or sin θ + 3 = 0
For the first equation, solving for sin θ, we get:
3 sin θ = 1
sin θ = 1/3
Taking the inverse sine (sin^-1) of both sides, we find:
θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)
For the second equation, solving for sin θ, we have:
sin θ = -3
Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).
Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.
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A battery company produces 12,000 batteries per day. Each day they randomly select 50 to test. If they find that 1 is dead, how many dead batteries would they expect to find among the entire 12,000
Could someone help me solve this please:)
Using the binomial distribution, it is found that they would expect to find 240 dead batteries among the entire 12,000.
For each battery, there are only two possible outcomes, either it was dead or it was not. The probability of a battery being dead is independent of any other battery, hence the binomial distribution is used to solve this question.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
In this problem, we have that:
One in 50 batteries are dead, hence p = 1/50 = 0.02.There is a total of 12,000 batteries, hence n = 12000.Then:
E(X) = np = 12000(0.2) = 240
They would expect to find 240 dead batteries among the entire 12,000.
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What values of x
and y
satisfy the system of equations {8x+9y=−36 x+7y=1}
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475),
enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.
To solve the given system of equations:
Equation 1: 8x + 9y = -36
Equation 2: x + 7y = 1
We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:
From Equation 2, we can solve for x:
x = 1 - 7y
Substituting this value of x into Equation 1:
8(1 - 7y) + 9y = -36
8 - 56y + 9y = -36
-47y = -44
y = 44/47
Substituting the value of y back into Equation 2 to find x:
x + 7(44/47) = 1
x + 308/47 = 1
x = 1 - 308/47
x = (47 - 308)/47
x = -261/47
Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).
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y=-0.024x^2+0.0791x+4.873
The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol
The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.
The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.
The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.
The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.
The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.
To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.
Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.
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Can someone please help
Answer:
48
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180°.
We know one angle measures 42°.
Another angle is a right angle, so it measures 90°.
Only the angle labeled x is unknown.
42 + 90 + x = 180
132 + x = 180
x = 48
Answer: 48
The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Find the product.
902 x 27
A. 18,054
B. 20,354
C. 25,254
D. 24,354