Answer:
18.85
Step-by-step explanation:
How many terms of the series of - 3+0+3+6+9+...are needed to give a sum of 105?
Answer:
10
Step-by-step explanation:
Remember that the formula for the sum of an arithmetic series is:
[tex]S=\frac{k}{2}(a+x_k)[/tex]
Where k is the number of terms, a is the initial term, and x_k is the last term of the series.
We essentially want to find k, the number of terms, given that the sum S is equal to 105. So, substitute 105 into our equation:
[tex]105=\frac{k}{2}(a+x_k)[/tex]
To do so, we need to final term x_k. We don't know what it is yet, but that doesn't matter. All we need to do is to write it in terms of k. First, remember that the standard form for the explicit formula of an arithmetic sequence is:
[tex]x_n=a+d(n-1)[/tex]
Where a is the first term, d is the common difference, and n is the nth term.
From our sequence, we can see that the first term is -3.
Also, we can determine that our common difference is +3, since each subsequent term is 3 more than the previous one. -3+3 is 0, 0+3 is 3, 3+3 is 6, and so on.
Therefore, our explicit formula is:
[tex]x_n=-3+3(n-1)[/tex]
Therefore, our final term, x_k, will be if we substitute k for n. So, we can acquire the equation:
[tex]x_k=-3+3(k-1)[/tex]
Now that we know what x_k is, we can substitute that into our original equation:
[tex]105=\frac{k}{2}(a+x_k)[/tex]
Substitute the equation into x_k. Also, let's substitute -3 (our first term) for a. So:
[tex]105=\frac{k}{2}(-3+(-3+3(k-1)))[/tex]
And now, all we have to do is to solve for k.
First, distribute the 3:
[tex]105=\frac{k}{2}(-3+(-3+3k-3))[/tex]
Add within the parentheses:
[tex]105=\frac{k}{2}(3k-9)[/tex]
Multiply both sides by 2. This removes the fraction on the right:
[tex]210=k(3k-9)[/tex]
Distribute. We will get a quadratic:
[tex]210=3k^2-9k[/tex]
So, let's solve for k. Let's divide everything by 3:
[tex]70=k^2-3k[/tex]
Subtract 70 from both sides:
[tex]0=k^2-3k-70[/tex]
Factor. We can use -10 and 7. So:
[tex]0=(k-10)(k+7)[/tex]
Zero Product Property:
[tex]k-10=0\text{ or } k+7=0[/tex]
Solve for k for each equation:
[tex]k=10\text{ or } k=-7[/tex]
-7 doesn't make sense (we can't have -7 terms). Remove that solution. So, we are left with:
[tex]k=10[/tex]
Therefore, the number of terms we have in our series for our sum to be 105 is 10.
And we're done!
sound travels 1129 feet per second air. how far can sound travel in 2 seconds when traveling through hair
Answer:
Sound travels 2258 feet in 2 seconds while travelling through air.
Step-by-step explanation:
What is this (x^2)^5 times (x^5)^2
Answer:
[tex]x^{20}[/tex]
Step-by-step explanation:
[tex](x^{2} )^{5}[/tex]·[tex](x^{5})^{2}[/tex]
[tex](x^{10} )[/tex] · [tex](x^{10})[/tex]
[tex]x^{20}[/tex]
5.4 inches of snow fell in 3.6 hours. How much snow fell per hour?
Answer:
1.5 per hour.
Step-by-step explanation:
By proportion that is 5.4 / 3.6
= 1.5 per hour.
simplify the following expression 2x cubed y cubed over 4y squared
3xcubed y to the fifth over 2
1-3. Find the center point, the radius and the diameter for the following equation: x² + y2 = 16
Answer:
Center: (0, 0)
Radius: 4
Step-by-step explanation:
Circle Standard Equation: (x - h)² + (y - k)² = r²
(h, k) is center
r is radius
We see that our h and our k are both 0.
∴ Our center is (0, 0), origin.
We see that our r² = 16
√r² = √16
∴ Our radius is equal to 4
Drag each expression to the correct location on the table. Not all expressions will be used.
Jennifer is buying a plane ticket to travel abroad. The price of the plane ticket is P dollars, and she has to pay the additional 8% airport
security tax
Match the expressions to their correct meaning for Jennifer.
Answer:
The price of the ticket before tax - P
The amount of tax Jennifer pays- 0.08P
Jennifer's total amount for the ticket- P + 0.08P
Step-by-step explanation:
The price of the plane ticket is P dollars, before airport security tax. Here P is an independent variable.
An airport security tax of 8% is applied to the price of a plane ticket. So, the amount of airport security tax that Jennifer pays is 8% of the cost of her plane ticket, or 0.08P.
To find Jennifer's total amount for the plane ticket, add the price of the ticket before airport security tax and the amount of airport security tax Jennifer pays. So, the total amount of the plane ticket is P + 0.08P.
The table below shows the expressions matched to their meanings.
An expression is defined as a set of numbers, variables, and mathematical operations. Jennifer's total amount for the ticket is P+0.08P.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that Jennifer is buying a plane ticket to travel abroad. The price of the plane ticket is P dollars, and she has to pay the additional 8% airport security tax. Therefore, we can write the expressions as,
The price of the ticket before tax → P
The amount of tax Jennifer pays → 8% of P = 0.08p
Jennifer's total amount for the ticket → Price of ticket + Tax = P + 0.08P
Hence, Jennifer's total amount for the ticket is P+0.08P.
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which of the following pairs consists of equivalent fractions 9/24 and 21/56?
Answer:
3/8
Step-by-step explanation:
if u simplify you get half then add them the bigger dinominator is the bottom so only add the tops
Pleaseee. helpppl
Find the most important variable in the problem.
There are 13 fish in an aquarium. Seven of the fish are guppies. How many
non-guppies are in the aquarium?
A. the total number of fish
B. the number of guppies
c. the number of non-guppies
Answer:
C. the number of non-guppies
Step-by-step explanation:
The number of non-guppies is the only variable the other two options have defined values.
Answer:
C, The number of non- guppies is the most important variable.
Step-by-step explanation:
The answer is the unknown variable that you're trying to find and the entire problem is to help you find the unknown.
Find tan(13pi/4)-cos(pi/3)
Answer: [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})=\frac{1}{2}[/tex]
Step-by-step explanation:
To find [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})[/tex], we first need to understand the unit circle. Let's find the value of tan and cos before we subtract them.
[tex]tan(\frac{13\pi }{4} )[/tex] is the same as [tex]tan(\frac{5\pi }{4} )[/tex]. The point for [tex]\frac{5\pi }{4}[/tex] is (-0.5,-0.5). Tangent is [tex]\frac{sin}{cos}[/tex]. Since sin and cos are both -0.5, we can divide them.
[tex]\frac{-0.5}{-0.5} =1[/tex]
Now, we know that [tex]tan(\frac{13\pi }{4} )=1[/tex]. All we have to do is find [tex]cos(\frac{\pi }{3})[/tex].
[tex]cos(\frac{\pi }{3})=\frac{1}{2}[/tex]
Now that we know the values of both, we can directly subtract them.
1-0.5=0.5
Therefore, [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})=\frac{1}{2}[/tex].
Convert 50 grains to milligrams
Answer:
3239.95
Step-by-step explanation:
Y varies directly as x. If x=7 then y = 56. Find ybwhen x=3
When something varies directly as something else, their ratio of change always stays the same.
56 / 7 = 8
Therefore,
8 * 3 = 24
If x = 3 then y = 24
y < 2x - 5
Which of the following graphs represent the inequality?
Answer: C
Step-by-step explanation:
For this problem, we need to graph y=2x-5. We can eliminate A and D because the graph is not y=2x-5. The main difference between B and C is the shading and line. Since we see the inequality is less than, but NOT equal to, we know that the line will be dashed. The solid line tells us that the graph reaches the line, meaning it is equal to. Therefore, we can eliminate B. C is the correct answer. We also know that the shading would be under the dashed line because it is LESS THAN.
Which of the following is equal to 20x + 8y - 80?
A. 3x + y - 10
B. 5x+2y-20
c. 4(5x + 2y - 20)
D. 4(5x + 2y – 40)
E. 4(5x + 8y - 20)
Which expression can be used to solve
3/5•|• 7/10
Answer: D
Step-by-step explanation: if you write it out it will be the exact same thing as D so it will be d
MY NOTES
ASK YOU
A table of solutions for a linear equation is given below. From the table, determine the x-intercept and the y-intercept of the graph of the equation
x-intercept
(x, y) =(
y-intercept
(x, y) =
х
y
-6
0
(x, y)
(-6, 0)
(-3, 4)
(0,8)
-3
4
0
8
Let X1,..., Xn be a simple random sample from a distribution with density function Svorvo-1 O<331 fx (2:0) = otherwise where e > 0 is an unknown parameter.
(a) Find a MOM estimator for 0.
(b) If the observations are 1 1 1 2'3'2 Determine the point estimate with the estimator you find in part (a).
Answer:
The method of moment (MOM) estimator as: [tex]\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}[/tex]
[tex]\overline X = \dfrac{4}{9}[/tex]
[tex]\mathbf{\hat {\theta} =\dfrac{16}{25} }[/tex]
Step-by-step explanation:
From the question, the correct format for the probability density function is:
[tex]fx(x ; \theta) = \left \{ {{\sqrt{\theta x}^{\sqrt{\theta}-1}}\ \ 0 \leq x \leq 1 \atop {0} \ \ \ \ \ \ \ otherwise } \right.[/tex]
where θ > 0 is an unknown parameter.
(a) The MOM estimator can be calculated as follows:
[tex]E(X) = \int ^1_0x. \sqrt{\theta} \ x^{\sqrt{\theta}-1} \ dx[/tex]
[tex]E(X) = \int ^1_0 \sqrt{\theta} \ x^{\sqrt{\theta}} \ dx[/tex]
[tex]E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 } ( x ^{\sqrt{\theta}+1})^1_0[/tex]
[tex]E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }[/tex]
suppose E(X) = [tex]\overline X[/tex]
Then;
[tex]\overline X = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }[/tex]
[tex]\dfrac{1}{\overline X} = \dfrac{\sqrt{\theta} +1 }{\sqrt{\theta}}[/tex]
[tex]\dfrac{1}{\overline X} =1 + \dfrac{1}{\sqrt{\theta}}[/tex]
making [tex]\dfrac{1}{\sqrt{\theta}}[/tex] the subject of the formula, we have:
[tex]\dfrac{1}{\sqrt{\theta}} =\dfrac{1}{\overline X} - 1[/tex]
[tex]\dfrac{1}{\sqrt{\theta}} =\dfrac{1-\overline X}{\overline X}[/tex]
[tex]\sqrt{\theta} =\dfrac{\overline X}{1-\overline X}[/tex]
squaring both sides, we have:
The method of moment (MOM) estimator as: [tex]\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}[/tex]
b) If the observations are [tex]\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{2}[/tex]
Then,
[tex]\overline X = \dfrac{\dfrac{1}{2}+ \dfrac{1}{3}+\dfrac{1}{2}}{3}[/tex]
[tex]\overline X = \dfrac{\dfrac{3+2+3}{6}}{3}[/tex]
[tex]\overline X = \dfrac{\dfrac{8}{6}}{3}[/tex]
[tex]\overline X = \dfrac{8}{6} \times \dfrac{1}{3}[/tex]
[tex]\overline X = \dfrac{8}{18}[/tex]
[tex]\overline X = \dfrac{4}{9}[/tex]
Finally, the point estimate of the estimator [tex]\theta[/tex] is
[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{1-\dfrac{4}{9}} \end {pmatrix}^2}[/tex]
[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}} \end {pmatrix}^2}[/tex]
[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{4}{5} \end {pmatrix}^2}[/tex]
[tex]\mathbf{\hat {\theta} =\dfrac{16}{25} }[/tex]
If 25% of a number is 30, then what is 40% of the same number?
Divide 30 by 25% to find the full amount:
30/0.25 = 120
Now multiply the full amount by 40%:
120 x 0.40 = 30
Eliana has $2600 to invest for 6 months. If she needs the money to earn $104 in that time, at what rate of simple interest must Eliana invest?
What equation would I use to solve this?
Answer:
8%
Step-by-step explanation:
I=Pr
104=2600*r/2
r/2=104/2600
r=(104/2600)(2)
r=0.08=8%
Eliana must invest at a rate of 0.33% of simple interest to earn $104.
Given,
Eliana has $2600 to invest for 6 months.
If she needs the money to earn $104 in that time.
We need to find at what rate of simple interest must Eliana invest.
What is the formula for simple interest?It is given as:
SI = PRT / 100
P = principal amount
R = rate
T = time in years.
Find the rate of interest.
We have,
Simple interest = PRT / 100
SI = $104
T = 6 months
Convert it into years.
12 months = 1 year
6 months = 6/12 years
T = 1/2 years
$104 = ($2600 x R x 1/2) / 100
104 = (2600 x R x 1/2) / 100
100 x 104 = 2600 x R x 12
R = (100 x 104 ) / (2600 x 12)
R = 104 / 312
R = 0.33 %
Thus the rate of simple interest is 0.33%
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Find f '(a). f(x) = 1 − 2x
-3(-5)+7y=5(-5)+2y solve for y
Answer:
-2
Step-by-step explanation:
-15+7y=-25+2y
7y-2y=-25+15
5y= -10
5y/5= -10/5
y= -2
Answer:
y= -17/5 or -3.4
Step-by-step explanation:
-8+7y= -25+2y
5y= -17
y= -17/5 or -3.4
Colin Davis machine company maintains a general ledger
Step-by-step explanation:
yf.bfz
vcg ,kgu nkkgfgvvxvh
Order the following rational numbers from greatest to smallest.
- 7
0.40
4.1
-3/4
A coin was tossed 60 times and the coin landed on Heads 35 times. What proportion of the time did the coin land on Heads?
Type your numeric answer and submit
Answer:
35:60 times
Step-by-step explanation:
The proportion of time in which the coin land on Heads is 0.58
What is proportion?A proportion is an equation in which two ratios are set equal to each other.
Now it is given that,
Number of times coins tossed = 60
Number of times coin landed on Heads = 35
Therefore, the proportion of time in which the coin land on Heads is given as,
Proportion of time the coin land on Heads = Number of times coin landed on Heads/Number of times coins tossed
⇒ Proportion of time the coin land on Heads = 35/60
⇒ Proportion of time the coin land on Heads = 7/12 = 0.58
Thus, the proportion of time in which the coin land on Heads is 0.58
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Can anyone help with this question
Which number is not in the solution set of X - 6 > 10?
A) 14
B) 17
C) 20
D) 23
Answer:
A) 14
Step-by-step explanation:
x - 6 > 10
Add 6 to both sides.
x > 16
The solution is all numbers greater than 16.
In the choices, only 14 is less than 16.
Answer: A) 14
Answer:
a
Step-by-step explanation:
x-6 [tex]>[/tex] 10
14-6 [tex]>[/tex]10
8 is less than 10
Find the particular solution to ty''-(1+t)y'+y=t^2e^t.
Complete Question
Find a particular solution to [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]
[tex]y_1 = 1 + t , \ y_2 = e^t[/tex]
Answer:
The solution is [tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]
Step-by-step explanation:
Now the given equation is [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]
dividing through by t
We have
[tex]y'' - \frac{1 + t }{t}y' + \frac{1}{t} y = te^t \\\\ let's\ call\ it \ g(t)[/tex]
Now for the given initial value we can generate our Wronskian as follows
[tex]W(y_1 ,y_2) = | \left y_1} \atop {y_1'}} \right. \left y_2} \atop {y_2'}} \right | = | \left {(1 + t)} \atop {1}} \right. \left e^t} \atop {e^t}} \right | = (1 + t )e^t - e^t = te^t[/tex]
Now applying method of variation of parameters to obtain the particular solution
So here we assume that
[tex]y_p = v_1 y_1 + v_2 y_2[/tex]
So
[tex]v_1 = - \int\limits {\frac{y_2 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{e^t te^t}{te^t} } = - \int\limits { e^t} } = -e^t[/tex]
And
[tex]v_2 = - \int\limits {\frac{y_1 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{(1 + t) te^t}{te^t} } = - \int\limits (1 + t) = t + \frac{t^2}{2}[/tex]
So
[tex]y_p = -e^t * e^t + t + \frac{t^2}{2} * 1 + t[/tex]
[tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]
William and his puppy Rover are out for a morning jog at a comfortable pace of 10 minutes per mile. If they keep up this pace for 2 hours, how many miles will they jog?
Answer:
12 miles
Step-by-step explanation:
60 min in 1 hr and 10 min = 1 mile..... so 6, 10 min intervals..... and so 6 time 2 is 12
In Exercises 37– 40, BD ⃗ bisects ∠ABC. Find m∠ABD,
m∠CBD, and m∠ABC.
Answer:
37, ABD = CBD = 44 degrees, and ABC = 88 degrees
38. ABD = CBD = 24 degrees, and ABC = 48 degrees
39. ABD = CBD = 65 degrees, and ABC = 130 degrees
40. ABD = CBD =67 degrees, and ABC = 134 degrees
Step-by-step explanation:
Recall that when a segment bisects an angle, the angle is divided in equal parts then we have:
37.
6 x + 14 = 3 x + 29
3 x = 19 - 14 = 15
x = 15/3
x = 5
then ABD = 6 (5) + 14 = 30 + 14 = 44 degrees
CBD must equal ABD , so CBD = 44 degrees
And the total angle ABC = 88 degrees
38.
3 x + 6 = 7 x - 18
24 = 4 x
x = 24/4 = 6
Then ABD = 3 (6) + 6 = 24 degrees. Also CBD = 24 degrees and ABC = 48 degrees
39.
- 4 x + 33 = 2 x + 81
- 6 x = 81 - 33
-6 x = 48
x = - 48/6
x = -8
Then ABD = -4 (-8) + 33 = 32 + 33 = 65 degrees
The also CBD = 65 degrees, and ABC = 130 degrees
40.
8 x + 35 = 11 x + 23
35 - 23 = 11 x - 8 x
12 = 3 x
x = 12/3
x = 4 degrees
Therefore:
ABD = 8 (4) + 35 = 32 + 35 = 67 degrees.
Then also CBD = 67 degrees, and ABC = 134 degrees
If each group has the greatest possible number of club members,
how many groups of sixth graders and how many groups of seventh
graders will there be? Use numbers and words to explain your answer.
9 = a - 8
Help me please