Answer:
R (t) = 60 - 60 cos (6t)
Step-by-step explanation:
Given that:
R(t) = acos (bt) + d
at t= 0
R(0) = 0
0 = acos (0) + d
a + d = 0 ----- (1)
After [tex]\dfrac{\pi}{12}[/tex] seconds it reaches a height of 60 cm from the ground.
i.e
[tex]R ( \dfrac{\pi}{12}) = 60[/tex]
[tex]60 = acos (\dfrac{b \pi}{12}) +d --- (2)[/tex]
Recall from the question that:
At t = 0, R(0) = 0 which is the minimum
as such it is only when a is negative can acos (bt ) + d can get to minimum at t= 0
Similarly; 60 × 2 = maximum
R'(t) = -ab sin (bt) =0
bt = k π
here;
k is the integer
making t the subject of the formula, we have:
[tex]t = \dfrac{k \pi}{b}[/tex]
replacing the derived equation of k into R(t) = acos (bt) + d
[tex]R (\dfrac{k \pi}{b}) = d+a cos (k \pi)[/tex] [tex]= \left \{ {{a+d \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.[/tex]
Since we known a < 0 (negative)
then d-a will be maximum
d-a = 60 × 2
d-a = 120 ----- (3)
Relating to equation (1) and (3)
a = -60 and d = 60
∴ R(t) = 60 - 60 cos (bt)
Similarly;
For [tex]R ( \dfrac{\pi}{12})[/tex]
[tex]R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60[/tex]
where ;
[tex]cos (\dfrac{\pi b}{12}) =0[/tex]
Then b = 6
∴
R (t) = 60 - 60 cos (6t)
I’m having a bit of trouble with this
Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why?
Pre-Employment Drug Screening Results
Positive test result Negative test result
Drug Use Is Indicated Drug Use Is Not Indicated
Subject Uses Drugs 38 12
Subject Is Not a drug user 19 29
Answer:
probability of a false positive test result = 0.010 The non-drug user will suffer from the result since it is positiveStep-by-step explanation:
The probability that the test result is a false positive
total number of cases studied (n) = 38 + 12 + 19 + 29 = 98
number of false positive cases ( x ) = 1
probability of false positive result = x / n = 1/98 = 0.010
The non-drug user will suffer from the result since it is positive
Use a power series to approximate the value of the integral with an error of less than 0.0001. (Round your answer to four decimal places.)
integral^1_0 sin(x)/x dx
integral^1_0 sin(x)/x dx approximately equal to summation^2_n=0 (-1)^n x^2n+1 (-1)^n (x-1)^n/(2n + 1)!
Answer:
The answer is "0.9461"
Step-by-step explanation:
Given:
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex]
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex] ≈[tex]\sum^2_{n=0}\frac{(-1)^n x^{2n+1} (-1)^n (x-1)^n}{(2n + 1)!}[/tex]
[tex]\therefore[/tex]
[tex]\to \sin x = \sum^{\infty}_{n=0} (-1)^n\frac{x^{(2n+1)}}{(2n + 1)!}[/tex]
[tex]\because \\\\ \to \frac{\sin x}{x} =\sum^{\infty}_{n=0} (-1)^n \frac{x^{2n+1-1}}{(2n+1)!}\\[/tex]
[tex]=\sum^{\infty}_{n=0} (-1)^n \frac{x^{2n}}{(2n+1)!}[/tex]
The value is in between 0 and 1 then:
[tex]\to \int^1_0 \frac{sin(x)}{x} = =\sum^{2}_{n=0} \frac{(-1)^n}{ (2n+1) (2n+1)!}[/tex]
The above-given series is an alternative series, and it will give an error, when the nth term is bounded by its absolute value, that can be described as follows:
[tex]\to \frac{1}{(2n+3) (2n+3)!}< 0.0001\\\\\to (2n+3) (2n+3)!> 0.0001\\\\\to n\geq 2 \\[/tex]
So,
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex] ≈[tex]1 - \frac{1}{3 \cdot 3!}+\frac{1}{5 \cdot 5!}\\\\[/tex]
[tex]\approx 1 - \frac{1}{3 \cdot 6}+\frac{1}{5 \cdot 120}\\\\\approx 1 - \frac{1}{18}+\frac{1}{600}\\\\\approx 1 - \frac{1}{18}+\frac{1}{600}\\\\\approx \frac{18-1}{18}+\frac{1}{600}\\\\\approx \frac{17}{18}+\frac{1}{600}\\\\\approx \frac{1700+3}{1800}\\\\ \approx \frac{1703}{1800}\\\\\approx 0.9461[/tex]
The given series is an alternative series and will give an error when the nth term is bounded by its absolute value, then the approximation summation is equal to 0.9461.
What is a power series?The finite series can be used as a polynomial with an infinite number of the term.
[tex]\int_{0}^{1} \dfrac{\sin x}{x} dx = \sum_{n=0}^{2} \dfrac{(-1)^{n}x^{2n+1}(-1)^{n}x^{n}}{(2n+1)!}[/tex]
Then we have
[tex]\Rightarrow \sin x = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n+1}}{(2n+1)!} \\\\\\\Rightarrow \dfrac{\sin x}{x} = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n+1-1}}{(2n+1)!}\\\\\\\Rightarrow \dfrac{\sin x}{x} = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n}}{(2n+1)!}[/tex]
Then the value is between 0 and 1, will be
[tex]\Rightarrow \int_0^1 \dfrac{\sin x}{x} = \sum_{n=0}^{2} \dfrac{(-1)^{n} }{(2n+1)(2n+1)!}[/tex]
The given series is an alternative series and will give an error when the nth term is bounded by its absolute value, then which can be described as
[tex]\Rightarrow \dfrac{1}{(2n+3)(2n+3)!} < 0.0001\\\\\\\Rightarrow (2n+3)(2n+3)! = > 0.0001\\\\\\\Rightarrow n > 2[/tex]
So,
[tex]\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{3\times 3!} + \dfrac{1}{5\times 5!}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{3\times 6} + \dfrac{1}{5\times 120}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{18} + \dfrac{1}{600}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 0.9461[/tex]
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Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges?
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
The 17 students on the math team want to raise $483.62 to buy practice books. They have already raised $218.25. If each student raises the same amount, how much money must each student raise?
Compute the critical value z Subscript alpha divided by 2 that corresponds to a 96% level of confidence.
Complete Question
Compute the critical value [tex]Z_{\frac{\alpha }{2} }[/tex] that corresponds to a 96% level of confidence.
Answer:
The value is [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.04}{2} }= 2.326[/tex]
Step-by-step explanation:
From the question we are told that
The confidence level [tex]C = 96\%[/tex]
Generally the level of significance is mathematically represented as
[tex]\alpha = (100 -96)\%[/tex]
[tex]\alpha = 0.04[/tex]
Now from the normal distribution table the critical value for [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.04}{2} }= 2.326[/tex]
Automobile repairs and maintenance cost
Jana Padgett $900 last year. She drove 15,900
miles. To the nearest cent, what was her cost
per mile?
Answer:
17.67
Step-by-step explanation:
You find the unit rate. So, 15,900 divided by 900 gives you 17.666666 (repeating). Then round to the nearest cent to get 17.67
Could you simplify this question? 4xy-6xy+5y-9x
The solution of expression is,
⇒ - 2xy + 5y - 9x
We have to given that,
An expression to solve,
⇒ 4xy - 6xy + 5y - 9x
Now, We can simplify the expression by combining like terms as,
⇒ 4xy - 6xy + 5y - 9x
⇒ - 2xy + 5y - 9x
Therefore, The solution of expression is,
⇒ - 2xy + 5y - 9x
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What is the equation of a vertical line passing through the point (-4, 7)?
There are 15 students in the preschool class. For every 7 kids there is 1 teacher. Which ratio shows the number of teachers to the number of students in the class?
15=2
7+7=14+1=15=2
sooooooooo just going to keep righting
The ratio of student to teacher is 1:7
What is a ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given: There are 15 students in a preschool class and for every 7 students there is 1 teacher. Clearly the ratio is 1:7
Hence, The ratio of student to teacher is 1:7
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3 folders cost $2.91 dollar sign . Which equation would help determine the cost of 2 folders? WRITE THE LETTER IN THE SPACE BELOW. see the file plz
Answer:
none of the above
Step-by-step explanation:
the equation is supposed to be 3=2.91, 2=x, I hope you get it.
Can you think of a situation where it would make the most sense to express your birth year in binary numbers?
Answer:
Yeah I've thought of it and have an example with the year 2000 as the birth year
So 2000 In binary= 11111010000
Step-by-step explanation:
Binary numbers consist of only 0 and 1
So to convert a number to binary we divide by 2
Let's assume a birth year of 2000
Now let's convert it to binary
2000/2= 1000 R 0
1000/2= 500 R 0
500/2= 250. R 0
250/2= 125. R 0
125/2 = 62. R 1
62/2= 31. R 0
31/2= 15. R 1
15/2 = 7. R. 1
7/2= 3. R 1
3/2 = 1. R 1
1/2 = 0. R 1
Where R signifies the remainder
So we'd pick the remainder from the bottom and that becomes our binary number
So 2000 In binary= 11111010000
Decide which of the two given prices is the better deal and explain why.
You can fill a 12 gallon tank of gas for $43.75 or buy gas for $3.30/gallon.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The better deal is to because the price to fill a 12 gallon tank of gas for $43.75 is $ ____ per gallon.
B. The better deal is to buy gas $3.30/gallon because the price to fill a 12-gallon tank of gas for $43.75 is $____per gallon.
Answer:
B; $3.30
Step-by-step explanation:
Since $43.75 is the cost of 12 gallon tanks, you want to multiply $3.30 by 12 to compare them when they each have the same amount of gallon tanks. This gets us to $39.60 which makes B the better deal.
However, the question asks for the unit price of one gallon tank, so you would want to put $3.30.
The better deal is to buy gas $3.30/gallon because the price to fill a 12-gallon tank of gas for $43.75 is $ 39.60 per gallon.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is given that You can fill a 12 gallon tank of gas for $43.75 or buy gas for $3.30/gallon.
Since $43.75 is the cost of 12 gallon tanks, we need to multiply $3.30 by 12 to compare them when they each have the same amount of gallon tanks.
$3.30 x 12 = 39.60
Thus, $39.60 which makes B the better deal.
However, the question asks for the unit price of one gallon tank, so we would want to put $3.30.
The better deal is to buy gas $3.30/gallon because the price to fill a 12-gallon tank of gas for $43.75 is $ 39.60 per gallon.
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EFGH is a rhombus. Rhombus E F G H is shown. Diagonals are drawn from point E to point G and from point F to point H. All sides are congruent. Given EG = 16 and FH = 12, what is the length of one side of the rhombus? 6 units 8 units 10 units 14 units
Answer:
10 units
Step-by-step explanation:
The diagnonals of a rhombus meet at right angle to their selves and bisect each other.
So one quarter will form a right angle triangle of base 6 and height 8.
Let The length of one side of the rhombus be x
X²= 8²+6²
X²= 64+36
X²= 100
X= √100
X= 10 units
Answer:
answer is C. 10 units. Just took the test
Step-by-step explanation:
given the sequence -2,-8/3,-10/3,-4,-14/3 find the recursive formula
Step-by-step explanation:
-2, -8/3, -10/3, -4, -14/3
Write as multiples of 1/3.
-6/3, -8/3, -10/3, -12/3, -14/3
This is an arithmetic sequence where the first term is -6/3 and the common difference is -2/3.
Therefore, the recursive formula is:
aᵢ₊₁ = aᵢ − 2/3, a₁ = -2
You decide to get a new job as a furniture salesman. Each day you work you get $180 plus an additional $27 for each couch , chair , table you sell. Write a linear equation for the pay p for x piece of furniture sold on a shift.
Answer:
180+27x=p
Step-by-step explanation:
A farmer harvests 15 cucumbers for every 45 carrots. Which of the following ratios represents the ratio of cucumbers to carrots, in simplest form? 4 3 please help
Answer:
1 : 3.
Step-by-step explanation:
15 : 45
Divide both numbers by 15 , we get:
1 : 3.
The perimeter of the rectangle is 56 cm. Find the value of x.
10 cm
3x cm
Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges? F. H. G. J. CARDS, c 2 9 11 15 DOLLARS, d 9 40.5 50.5 67.5 CARDS, c 9 18 27 36 DOLLARS, d 2 4 6 8 CARDS, c 2 4 7 10 DOLLARS, d 9 18 31.5 45 CARDS, c 2 3 4 5 DOLLARS, d 9 10 11 12
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
Help ASAP! MATH!!! Important
Answer:
x=3
Step-by-step explanation:
BC= 5 ~ EC=25
And we can see that BC times 5 equals the EC value. This means that BA times 5 will equal ED.
So we can set 5 * (BC) = (ED)
5x=18-x
Then solve for x:
6x=18
x=3
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
So we are given that ΔABC and ΔDEC are similar.
In other words, AB and DE are similar. And CA and CD are also similar.
When the sides are similar, it means that their proportions are equal to the each other. Therefore:
[tex]\frac{AB}{DE}=\frac{CA}{CD}[/tex]
Substitute 30 for AB, 18 for DE, 2x-1 for CA and x+1 for CD. So:
[tex]\frac{30}{18}=\frac{2x-1}{x+1}[/tex]
Reduce the left by dividing both layers by 6. Thus:
[tex]\frac{5}{3}=\frac{2x-1}{x+1}[/tex]
Cross multiply:
[tex]3(2x-1)=5(x+1)[/tex]
Distribute:
[tex]6x-3=5x+5[/tex]
Add 3 to both sides:
[tex]6x=5x+8[/tex]
Subtract 5x from both sides:
[tex]x=8[/tex]
So, the value of x is 8.
And we're done :)
name all the values of x if
7|x|=63
(seven times the absolute value of x equals sixty-three)
Answer:
I think they are
|9|
|-9|
3n(5+3n-8-3n) what is the answer
Answer:
-9n
Step-by-step explanation:
3n(5 + 3n - 8 - 3n)
First we combine the like terms inside the parenthesis:
3n(-3)
Because 5 -8 = -3 and 3n - 3n = 0
Now we multiply:
-9n
because 3n × -3 = - 9n
So the answer is -9n
There are 45 children in a class. If
9 of them are absent, what
percentage of the class is absent?
Answer:
20%
Step-by-step explanation:
Total = 45
Absentees = 9
Percentage = (No. of absentees / total) × 100
= 9 / 45 × 100
= 0.2 × 100
= 20%
Answer:
20% of the children are absent
Step-by-step explanation:
Number of children absent = 9
Total children in the class = 45
Percent of absent children / total children is defined as the quotient 9/45 multiplied by 100. That is;
[tex]\frac{9}{45} \,*\,100 = 0.2 \,*\,100=20\,%[/tex]
SO the percentage is 20%
My square orchid garden abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs $2 per foot. Find the total cost of the fencing as a function of the length of a side x.
Answer:
The total cost of the fencing as a function of side is [tex]C = 8\cdot x[/tex].
Step-by-step explanation:
Dimensionally speaking, the total cost is equal to the product of length and cost per length. Given that orchid garden has a square form, there is only an input: Side ([tex]x[/tex]), measured in feet. Therefore, the total cost of fencing is represented by the following formula:
[tex]C = (c_{west} + c_{south} + c_{east})\cdot x[/tex]
Given that [tex]c_{west} = c_{east} = 2\,\frac{\$}{ft}[/tex] and [tex]c_{south} = \$\,4\,\frac{\$}{ft}[/tex], the total cost of the fencing as a function of side is:
[tex]C = 8\cdot x[/tex]
Jill says that
23
1
,
000
can be written as 0.23. Which explains whether or not Jill is correct?
Answer:
Jill is incorrect
Step-by-step explanation:
Given
[tex]\frac{23}{1000}= 0.23[/tex]
Required
Determine if Jill is correct or incorrect
Start by solving the expression on the left hand side:
[tex]\frac{23}{1000} = 0.023[/tex]
The result of [tex]\frac{23}{1000}[/tex] gives 0.023 and not 0.23 as Jill as said;
Hence;
Jill is incorrect and the expression is false;
Can anyone please help me solve this question? (If you can, of course)
Answer:
[tex]\frac{4}{9}[/tex]
Step-by-step explanation:
Create 2 equations with the repeating number after the decimal point, then subtract the equations to eliminate the repeating number.
let x = 0.4444.... → (1) ← multiply both sides by 10
10x = 4.4444.... → (2)
Subtract (1) from (2) eliminating the repeater
9x = 4 ( divide both sides by 9 )
x = [tex]\frac{4}{9}[/tex]
Thus 0.444444... = [tex]\frac{4}{9}[/tex]
To know which power of 10 to multiply by
The power of 10 is the value to ensure the repeating 4 is after the decimal point.
Here it was [tex]10^{1}[/tex] as we required 0.4444.. → 4.444...
A family visits a car show to research information on vehicles they might consider purchasing. Brochures for each vehicle provide helpful information for the vehicle. Which of the following is an example of a discrete quantitative variable that might be included in the brochure? A. number of seats B. type of transmission C. presence of a sunroof D. fuel efficiency (in mpg)
Answer:
Option A:
Number of seats
Step-by-step explanation:
A discrete quantitative variable is a variable that can be enumerated. This means that they are in units in which numbers can be assigned to and can be counted.
The number of seats present in the car can be counted. This feature can also be evaluated based on its numeral value, rather than its quality. In a simple form, the buyers feel that the more the number of seats present in the car, the more people it can carry. Hence, the family would love to buy a car with a good number of seats in it.
The other features in the options are rather continuous, qualitative, or boolean. Some of them are continuous because they cannot be counted e.g fuel efficiency. The others such as the presence of a sunroof can be seen as a boolean variable. (it can either be true or false)
Type of the transmission is a qualitative variable
Answer: fuel efficiency
Step-by-step explanation:
took the exam review on edg
If M is the midpoint of XY, find the coordinates of X if M(-3, -1) and Y(-8, 6) A. (2.5, -5.5) B. (-5.5, 2.5) C. (0, 0) D. (2, -8)
Answer:
(2, -8)
Step-by-step explanation:
(x, y)=(-3, -1)
(x1+x2)/2=-3,
(y2+y2)/2=-1,
-------------------
(x1+x2)/2=-3
(y1+y2)/2=-1
---------------------
x1-8=-6
x1=2
----------
y1+6=-2
y1=-8
(2, -8)
how many times does 3/4 go into 4.5
Answer:
6 times
Step-by-step explanation:
Turn that fraction into a decimal. 3/4=0.75
Divide!
4.5/0.75=6
A number 4.5 is 6 times of number 3/4.
We have to given that,
To find how many times does 3/4 go into 4.5.
Let us assume that,
x times does 3/4 go into 4.5.
Hence, It can be written as,
⇒ x × 3/4 = 4.5
Solve for x,
⇒ 3x /4 = 4.5
⇒ 3x = 4.5 × 4
⇒ 3x = 18
Divide by 3;
⇒ x = 18/3
⇒ x = 6
Therefore, 4.5 is 6 times of number 3/4.
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Karen Sullivan delivers newspapers for the Tribune Dispatch. She
receives 18.2 cents per paper, 6 days a week (for the daily paper),
and 70 cents for the Sunday paper. She delivers 124 daily papers each
day and 151 Sunday papers each week. What is her total pay?
The correct answer is $241.1 each week and $964.4 each month
Explanation:
To calculate the amount Karen should receive, it is required to calculate the money she earned from Monday to Saturday and then the money she earned on Sunday as the amount paid per paper is different on Sunday.
Monday to Sunday:
Karen delivers 124 papers each day from Monday to Sunday. This means she delivers a total of 744 papers (124 papers each day x 6 days = 744 papers). Now, let's find the money she earned from Monday to Sunday:
744 papers x 18.2 cents = 13540 cents or 135.4 dollars (each dollar is equivalent to 100 cents, which means if you divide the cents into 100 you get the equivalent in dollars)
This means the total Karen earned from Monday to Saturday is $135.4
Sunday:
Karen delivers 151 Sunday papers and with each of these she earns 70 cents
151 papers x 70 cents = 10570 cents or 105.7 dollars
Total per week:
$135.4 + $105.7 = $241.1 each week, which is equivalent to $964.4 a month ($241.1 x 4 weeks = $964.4 )