Answer:
Hope this helps ^^
Step-by-step explanation:
Part A: To determine the values where the pogo stick's spring will be equal to its non-compressed length, we set the function equal to zero:
f(θ) = 2cos(θ) + √3
To find the values of θ that satisfy this equation, we solve:
2cos(θ) + √3 = 0
Subtracting √3 from both sides:
2cos(θ) = -√3
Dividing by 2:
cos(θ) = -√3/2
Using the unit circle, we can find the angles where cosine is equal to -√3/2. These angles are π/6 and 11π/6.
Therefore, the values where the pogo stick's spring will be equal to its non-compressed length are θ = π/6 and 11π/6.
Part B: If the angle θ is doubled, that is, θ becomes 2θ, we substitute 2θ into the original function:
f(2θ) = 2cos(2θ) + √3
Using the double angle formula for cosine:
f(2θ) = 2(2cos²(θ) - 1) + √3
Expanding and simplifying:
f(2θ) = 4cos²(θ) - 2 + √3
Comparing this to the original function f(θ), we see that the new function has the same form but with different coefficients. The solutions for f(2θ) in the interval [0, 2π) will be the same as the solutions for f(θ), but they will occur at double the angles. In other words, if θ is a solution for f(θ), then 2θ will be a solution for f(2θ).
Part C: To find the times when the lengths of the springs from the original pogo stick and the toddler's pogo stick are equal, we set the two functions equal to each other:
f(θ) = g(θ)
2cos(θ) + √3 = 1 - sin²(θ) + √3
Rearranging the equation:
sin²(θ) + 2cos(θ) = 0
Using the Pythagorean identity sin²(θ) = 1 - cos²(θ), we substitute:
1 - cos²(θ) + 2cos(θ) = 0
Rearranging and simplifying:
cos²(θ) - 2cos(θ) + 1 = 0
Factoring:
(cos(θ) - 1)² = 0
Taking the square root:
cos(θ) - 1 = 0
cos(θ) = 1
This occurs when θ is a multiple of 2π.
Therefore, the lengths of the springs from the original pogo stick and the toddler's pogo stick are equal at θ = 2πn, where n is an integer.
A cylinder with a diameter 6 of mi and a height of 7 mi
With the values provided, we can find both the volume and surface area.
Volume:
Formula = pi x r^2 x h
---r is the radius, h is the height
Volume = pi x (3)^2 x 7
Volume = pi x 36 x 7
Volume = 252pi mi^3 = 791.68 mi^3
Surface Area:
Formula = 2 x pi x r x h + 2 x pi x r^2
---r is the radius, h is the height
Surface Area = 2 x pi x 3 x 7 + 2 x pi x (3)^2
Surface Area = 42pi + 18pi
Surface Area = 60pi mi^2 = 188.50 mi^2
Hope this helps!
Bank a charged 45 $ monthly fee with unlimited transaction. Bank b charged 20$ monthly fee plus 0.70for each transaction
Transactions are larger than others Bank B may be the cheaper option even if you make more than 35 transactions.
To compare the cost of using Bank A and Bank B need to consider the total cost based on the number of transactions.
Let's say you make x transactions in a month.
For Bank A the monthly cost is a fixed fee of $45 regardless of the number of transactions.
For Bank B the monthly cost is a fee of $20 plus $0.70 for each transaction.
So the total cost for Bank B is:
Total cost = $20 + $0.70x
The break-even point where the total cost of Bank A and Bank B are equal need to solve the following equation:
45 = 20 + 0.70x
Subtracting 20 from both sides, we get:
25 = 0.70x
Dividing both sides by 0.70, we get:
x = 35.71
If you make more than 35 transactions in a month Bank A is the cheaper option.
If you make fewer than 35 transactions Bank B is the cheaper option.
Analysis assumes that all transactions are of the same amount.
To compare the total cost of both banks based on the actual amounts of the transactions.
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Find the missing angles show your work
Answer: see below. the answers are bolded.
Step-by-step explanation:
1. Since x+55 forms a straight line, x+55 = 180. Solve that equation and you get x = 125. All interior angles in a triangle = 180. That means: 55+45+y = 180. Solve that equation and you get y = 80.
2. 110+x forms a straight line. 110+x = 180. Solve that equation and you get x = 70. Now that you have x, and you know that the interior angles of a triangle add up to 180, set up an equation. 70 + 65 + y = 180. Solve, and
y = 45
Hope I helped :)
Favorite Pastimes Number Hobby Reading 25 Sports 40 Crafts 20 Cooking 15 20 Other . Explain how to find the probability that a person's favorite pastime is cooking. Then find the probability.
The probability that a person's favorite pastime is cooking is 0.125 (or 12.5%).
Understanding ProbabilityTo find the probability that a person's favorite pastime is cooking, we need to divide the number of people whose favorite pastime is cooking by the total number of people.
Given the following pastimes,
Reading = 25
Sports = 40
Crafts = 20
Cooking = 15
Others = 20
Since 15 people listed cooking as their favorite pastime. To find the total number of people, we can add up the number of people who listed each pastime:
Total = Reading + Sports + Crafts + Cooking + Others
Total = 25 + 40 + 20 + 15 + 20 = 120
Therefore, the probability that a person's favorite pastime is cooking is:
P(cooking) = Cooking / Total
= 15 / 120
= 0.125 or 12.5%
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HELPPPPPP WILL GIVE BRAINLESS
The coordinates of point A' are (4,1) in the given rectangle.
According to the shown figure, the coordinate of the given rectangle can be written as:
The coordinates of vertice A are (4, 3)
As we know that the x-coordinate of the reflected point will be the same as the x-coordinate of the original point.
Therefore, the x-coordinate of point A' will be:
x-coordinate of A' = 4
Here, the y-coordinate of point A is 3, which is 1 unit above the line y = 2. So, the reflection of point A across the line y = 2 will be 1 unit below the line y = 2.
So, the y-coordinate of point A' will be:
y-coordinate of A' = 2 - 1 = 1
Therefore, the coordinates of point A' are (4,1).
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Pleaseeee helppp in class ASAP!!!
Answer: 678
Step-by-step explanation: ii
Please help me out. I need help and don’t understand.
Part A: The table that displays a complete list of possible outcomes would be = Table B, that is option B.
Part B: The probability that the chosen events will take place = 0.3.
How to calculate the probability of the given event?To calculate the probability of the given event the formula that should be used is given below. That is;
Probability = possible outcome/sample space
The total number of blues balls = 1
The total number of red balls = 2
The total number of yellow balls = 2
The total number of balls = 5, while total number of colour = 3
For part A: the possible sample outcomes = (H,B), (HR), (HY), (TB), (TR), (TY).
For part B:
Using the formula the possible outcome = 2
Sample space = 7
Probability = 2/7 = 0.3
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how much would you pay a draper for 13 yards of a material which is sold at #1000 per yard
The cost of 13 yards of material sold at #1000 per yard would be:
13 x #1000 = #13,000
POLICEE HELPPPPP. POLICE HELPPPP. IM GIVING OUT 5O POINTS BRO IM DESPERATE I NEED HELPPPPPP. HELP HELP HELP HELP HELPPPPP.
Answer:
[tex]g(x) = f(x) - 4[/tex]
Step-by-step explanation:
We have been given a graph for f(x) and a table for g(x) and we have to find the transformation to map f(x) to g(x)
Let's find the function values for f(x) and g(x) at specific (easily distinguishable) x values for both
x f(x) from graph g(x) from table
0 4 0
1 3 -1
2 4 0
The function values for f(x) for x = -1 and x = 3 are a bit difficult to read since they do not cross at a grid intersection
From the above table we see that for a specific x, g(x) value is 4 less than the f(x) value
Therefore the transformation is
g(x) = f(x) - 4
Therefore g(x) is shifted downward by 4 points
I have plotted both f(x) and g(x) using the transformation; You can see the points fit
[tex]-------------------------------[/tex]
Ignore this part if you wish
The equation for f(x) is
f(x) = (x - 1)² + 3 in vertex form
or
f(x) = x² − 2x + 4 in polynomial form
g(x) will then be
x² - 2x + 4 - 4 = x² -2x
In a class of students, the following data table summarizes how many students have a
brother or a sister. What is the probability that a student has a brother given that they
have a sister?
Answer:
The answer is zero.
Step-by-step explanation:
Based on the model, the company hired approximately workers in 2019.The r2 value for this model is 0,56, indicating that this functions good model of the data
Answer:
Step-by-step explanation:
so how to help you but you do a good job
Use the laws of exponents to write an equivalent expression.
Using the laws of exponents, the equivalent expression would be 1 / 64.
How to find the equivalent expression?To find the equivalent expression of ( 4 / 7 ) ⁻ ³ . 7 ⁻³, we can use the law of exponents.
Using this law, we get:
( 4 / 7 ) ⁻ ³ = ( 1 / ( 4 / 7 )) ³
( 1 / ( 4 / 7 )) ³ = ( 7 / 4 ) ³
( 7 / 4) ³ x 7 ⁻³
( 7 / 4) ³ x ( 1 /7 ³ )
(( 7 ³ ) /( 4 ³ ) ) x ( 1/ 7 ³ )
( ( 7 ³ ) / ( 4 ³ ) ) x ( 1 / 7 ³ ) = 1 / (4 ³ )
1 / (4 ³ ) = 1 / 64
In conclusion, the equivalent expression is 1 / 64.
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Solve the following equation. 25 + 2 � = 3 ( 4 � + 3 ) 25+2x=3(4x+3)
The solution to the equation is x = 1.6.
Let's start by distributing the 3 on the right side of the equation:
25 + 2x = 12x + 9
Next, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side. To do this, we'll subtract 2x from both sides:
25 = 10x + 9
Then, we'll subtract 9 from both sides:
16 = 10x
Finally, we'll divide both sides by 10:
x = 1.6
So the solution to the equation is x = 1.6.
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a
50⁰
Solve for a.
17
64°
a=
[?]
Round your final answer
to the nearest tenth
Using the law of sines, the value of a in the given triangle, to the nearest tenth, is calculated as: 19.9.
How to Solve for a Using the Law of Sines?The law of sines that we would apply is given as:
sin A/a = sin B/b = sin C/c.
Given the following:
a = ?
A = 64 degrees
b = 17
B = 50 degrees
Plug in the values into the equation, sin A/a = sin B/b:
sin 64/a = sin 50/17
Cross multiply:
a * sin 50 = sin 64 * 17
Divide both sides by sin 50
a * sin 50 / sin 50 = sin 64 * 17 / sin 50
a ≈ 19.9 [nearest tenth]
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The value of a to the nearest tenth is 20.0
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Using sine rule to solve for a;
The side opposite to angle 64 is a and the side opposite to angle 50 is 17
a/sinA = b/sinB
a/sin64 = 17/sin50
asin50 = 17sin64
0.766a = 17 × 0.899
0.766a = 15.283
a= 15.283/0.766
a = 20.0( nearest tenth)
Therefore the value of a is 20.0
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[45 - (25 +8)] X 18 I NEED THE ANSER
Answer:
216.
Step-by-step explanation:
To solve this expression, you can first simplify the expression inside the parentheses:
45 - (25 + 8) = 45 - 33 = 12
Then you can substitute this simplified expression back into the original equation and multiply by 18:
(12) X 18 = 216
11. Which inequality does the graph represent?
-54-3 -2 -1 0 1 2 3
Ox2-2
Ox ≥-3
Ox>-2
Ox>-3
Please help
The inequality that represents the graph is:
x≥ -3
The inequality that represents the graph is:
x < 2
We have,
11.
From the number line,
The dot is in -3 and it extends infinitely to the right.
So,
The inequality that represents the graph is:
x≥ -3
And,
From the number line,
The open dot is in 2 and it extends infinitely to the left.
So,
The inequality that represents the graph is:
x < 2
Thus,
The inequality that represents the graph is:
x≥ -3
The inequality that represents the graph is:
x < 2
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need to find the population variance and standard deviation of the values 15 43 2 19 26 14 and 16
Answer:11.7
Step-by-step explanation:
σ =√137.63265306122
σ= 11.731694381513
What is 1/3-2/11+9/33?
Answer:
14/33
Step-by-step explanation:
1/3
= 1/3 x 11/11
= (1 x 11)/(3 x 11)
= 11/33
2/11
= 2/11 x 3/3
= (2 x 3)/(11 x 3)
= 6/33
1/3 - 2/11 + 9/33
= 11/33 - 6/33 + 9/33
= (11 - 6 + 9)/33
= (5 + 9)/33
= 14/33
convert 500 cm to m?
Hello!
m dm cm mm
5 , 0 0
500cm = 5m
Which word phrase can you use to represent the algebraic expression ÷ 8 ?
This phrase can be used in a variety of contexts, from simple arithmetic problems to more complex Algebraic equations and expressions.
The algebraic expression ÷ 8 can be written in a variety of ways depending on the context and the specific operation being performed. However, in general, the phrase "divided by 8" or "the quotient of x and 8" can be used to represent this expression.
For example, if we have an algebraic expression such as 24 ÷ 8, we can write it as
24 divided by 8
the quotient of 24 and 8
24/8
In each case, the idea is the same: we are dividing 24 into 8 equal parts, or finding how many groups of 8 are contained in 24.
In the context of an algebraic equation or expression, the phrase "divided by 8" is often used to indicate that the variable or expression preceding it is being divided by 8. For example:
3x ÷ 8
(2y + 5) ÷ 8
In these cases, we are dividing the value of 3x or the sum of 2y and 5 by 8. The quotient of these expressions will depend on the specific values of x and y."divided by 8" is a commonly used phrase to represent the algebraic expression ÷ 8. This phrase can be used in a variety of contexts, from simple arithmetic problems to more complex algebraic equations and expressions.
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Combine like terms to simplify the expression:
Enter any coefficients as simplified proper or improper fractions or integers.
2|5k-3/5+1/10k
The simplified expression of 2|5k - 3/5 + 1/10k| is |51/5k - 6/5|
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
2|5k-3/5+1/10k
Express properly
So, we have
2|5k - 3/5 + 1/10k|
Collect the like terms in the expression
So, we have the following representation
2|5k - 3/5 + 1/10k| = 2|5k + 1/10k - 3/5|
Evaluate the like terms
This gives
2|5k - 3/5 + 1/10k| = 2|51/10k - 3/5|
Expand the brackets
2|5k - 3/5 + 1/10k| = |51/5k - 6/5|
Hence, the simplified expression of 2|5k - 3/5 + 1/10k| is |51/5k - 6/5|
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(c) What is the sum of the squares of the differences between each data value and the mean? mean = 33 Use the table to organize your work. x 15 15-33=-18 (15-33)^2=324 27 27-33=-6 (27-33)^=36 28 28-33=-5 (28-33)^=25 34 34-33=1 (34-33)^2=1 42 42-33=9 (42-33)^2=81 52 52-33=19 (52-33)^2=361 Sum:828 (d) What is the standard deviation of the data set? Use the sum from Part (c) and show your work.
The standard deviation of the data set is 11.75.
To calculate the standard deviation of the data set, we first need to find the variance, which is the average of the sum of squares of the differences between each data value and the mean. We already calculated the sum of squares of the differences in Part (c), which is 828.
The formula for variance is:
variance = sum of squares of differences / number of data values
Since we have six data values, the variance is:
variance = 828 / 6
variance = 138
Now we can calculate the standard deviation, which is the square root of the variance:
standard deviation = sqrt(variance)
standard deviation = sqrt(138)
standard deviation = 11.75 (rounded to two decimal places)
Therefore, the standard deviation of the data set is 11.75.
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PLEASEEEEEEEE HELP WHAT IS THE APOTHEM..
The # are the blue ones. Please help me
Answer:
it is 20.00 hope this answer helps.
Help Quickly! Use the table. Estimate the total deer population for year 8.
A. about 1,815 deer
B. about 2,467 deer
C. about 1,934 deer
D. about 2,081 deer
The total deer population for year 8 will be D. about 2081 deer.
How to determine the estimate of the deer populationTo calculate the total deer population, we use the mark-recapture formula where: N = M * C/R
M = Total number of deer population captured and marked
C = Total number of deer population that had or did not have a mark
R = Total deer population recaptured and marked
So, for the given problem, the figures are as follows:
M = 1608
C = 110
R = 85
N = 1608 * 85 = 176,880/85 = 2080.94
So, the estimated deer population is about 2081 deer.
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Help pls! ( Don’t mind this text)
The above is a long division problem, where 40 is the divisor and 10 is the dividend. the answer is 00.250 or 0.250. Long division is also called synthetic division.
How did we arrive at this?
00. 250___________________
40 | 10.000
- 0
1 0
- 0
1 0 0
- 80
2 0 0
- 2 0 0
0 0
- 0
0
Note that the answer is given in three decimal places that is 0.250
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From previous experience, the owner of an apple orchard knows that the mean weight of gala apples is 140 grams. This year there has been more precipitation than usual and the owner believes the weights of the apples will be heavier than usual. The owner takes a random sample of 30 apples and records their weights.
What is the appropriate inference procedure?
one-sample t-test for Mu
one-sample z-test for p
one-sample t-test for Mu Subscript difference
two-sample t-test for Mu Subscript c Baseline minus Mu Subscript p
The appropriate inference procedure is the t test for μdiff.
We know that,
The mean is a basic mathematical average of two or more values.
There are several methods for computing the mean for a given collection of numbers, including the arithmetic mean approach, which utilizes the sum of the numbers in the series, and the geometric mean method, which is the average of a set of products.
The t test is used to compare the means of two groups.
We also know that,
Inferential statistics is a field of statistics that employs a variety of analytical procedures to draw conclusions about population data from sample data. Aside from inferential statistics, descriptive statistics are a subset of statistics. Inferential statistics aid in drawing inferences about the population, whereas descriptive statistics summarize the data set's features.
It is a very important tool that can be used in inferential statistics.
Since it shows whether the means of two groups are significantly different, we can say that, the appropriate inference procedure is the t test for μdiff.
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PLEASE HELP! I WILL GIVE BRAINLIEST!! A worker at an animal shelter recorded data about the adoption of cats in the table shown below.
Based on the table, which of these statements are true? Choose all that are correct.
a
Of all the cats adopted, 34.9% are between 6 months and 1 year old
b
Of the cats 1 year or older, about 58% took more than 1 month to be adopted.
c
Of all the cats adopted, about 66% were adopted in a month or less.
d
Of the cats that took more than a month to adopt, 12.5% were younger than 6 months
e
Of the cats who took 1 to 7 days to be adopted, 25% were between 6 months and 1 year old.
You win $12,000 in the lottery. You decide
to deposit the money in a savings account
until you graduate from college in 7 years.
Your bank can give you an interest rate of
7.5% compounded continuously. How
much will you have in your account after
7 years?
Please give me a hand
After 7 years, you will have approximately $[tex]24,156.36[/tex] in your savings account.
To calculate the final amount in your savings account after 7 years with continuous compounding, we can use the formula for compound interest with continuous compounding:
[tex]\[ A = P \times e^{rt} \][/tex]
Where:
- A is the final amount in the account
- P is the initial principal (the amount you deposit)
- e is Euler's number (approximately 2.71828)
- r is the interest rate (expressed as a decimal)
- t is the time period in years
In this case, you have won $12,000 in the lottery, so P = $12,000. The interest rate is [tex]7.5\%[/tex], which is equivalent to [tex]0.0.75[/tex] in decimal form. The time period is [tex]7[/tex] years.
Plugging these values into the formula, we get:
[tex]\[ A = 12000 \times e^{0.075 \times 7} \][/tex]
Calculating the exponential term:
[tex]\[ e^{0.075 \times 7} \approx 2.013 \][/tex]
Substituting this back into the equation:
[tex]\[ A = 12000 \times 2.013 \]\[ A \approx 24156.36 \][/tex]
So, after 7 years, you will have approximately $[tex]24,156.36[/tex] in your savings account.
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Nippon is taking a quiz that consists of 4 true-false questions. If he guesses on each question, what's the probability that Nippon will get 100% on the quiz? 1/2 1/4 1/16 1/8
The probability that Nippon will get 100% on the quiz by random guessing is 1/16.
To calculate the probability of Nippon getting a 100% on the quiz by guessing on all 4 true-false questions, you need to consider the probability of guessing correctly on each individual question.
The probability of guessing correctly on a single true-false question is 1/2, as there are two possible answers (true or false).
Since there are 4 questions, you need to find the probability of guessing correctly on all 4 questions.
To do this, you multiply the probabilities of guessing correctly on each individual question: [tex](1/2) \times (1/2) \times (1/2) \times (1/2).[/tex]
When you multiply these probabilities, we get (1/16), which is the probability of Nippon getting 100% on the quiz by guessing on all 4 true-false questions.
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Mr. Lucci put together 5 bags of pens. He put 19 black pens and 12 red pens in each bag.
Which expression shows the total number of pens Mr. Lucci put into bags?
A. (5x 19) + 12
B. 5x (1912)
C. 5+ (19 x 12)
D. (5+19) x 12
Answer:
5 (19 + 12)
Step-by-step explanation:
You add up the red and black pens and multiply by 5, which indicates the 5 bags