Chapter 1 Test
What is the simplified form of the expression 3 + 8x - 2y - x + 1 + 4y? Enter your answers in the boxes.
X +
ly+
Answer:
7x+4+2y is your answer
Calculus hw, need help asap with steps.
Answers are in bold
S1 = 1
S2 = 0.5
S3 = 0.6667
S4 = 0.625
S5 = 0.6333
=========================================================
Explanation:
Let [tex]f(n) = \frac{(-1)^{n+1}}{n!}[/tex]
The summation given to us represents the following
[tex]\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\[/tex]
There are infinitely many terms to be added.
-------------------
The partial sums only care about adding a finite amount of terms.
The partial sum [tex]S_1[/tex] is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say [tex]S_1 = f(1) = 1[/tex]
I'm skipping the steps to compute f(1) since you already have done so.
-------------------
The second partial sum is when things get a bit more interesting.
We add the first two terms.
[tex]S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\[/tex]
The scratch work for computing f(2) is shown in the diagram below.
-------------------
We do the same type of steps for the third partial sum.
[tex]S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\[/tex]
The scratch work for computing f(3) is shown in the diagram below.
-------------------
Now add the first four terms to get the fourth partial sum.
[tex]S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\[/tex]
As before, the scratch work for f(4) is shown below.
I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.
This means something like [tex]S_3 = S_2 + f(3)[/tex] and [tex]S_4 = S_3 + f(4)[/tex]
In general, [tex]S_{n+1} = S_{n} + f(n+1)[/tex] so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.
-------------------
Let's use that recursive trick to find [tex]S_5[/tex]
[tex]S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333[/tex]
The scratch work for f(5) is shown below.
How many different outcomes are possible when three coins are flipped at the same time?
Answer:
8
Step-by-step explanation:
Now consider an experiment of tossing three coins simultaneously. The possible outcomes will be HHH, TTT, HTT, THT, TTH, THH, HTH, HHT. So the total number of outcomes is 23 = 8.
Answer:
8
Step-by-step explanation:
The value of A is .
The value of B is .
Answer:a=10 b=35
Step-by-step explanation:
1*8=8 1.25*8=10
1*28=28 1.25*28=35
Natalie randomly answered the last three
true-or-false questions on her math quiz.
What is the probability that she got at least
two correct?
The probability that Natalie got at least two correct on the last three
true-or-false questions is 1/4.
What is the probability that Natalie got at least two correct?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The sample space is 2. The question is either correct or wrong.
The probability that Natalie got at least two correct = 1/2 x 1/2 = 1/4
To learn more about probability, please check: https://brainly.com/question/795909
Help!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
53
Step-by-step explanation:
[tex] \frac{sin(56)}{78.6} = \frac{sin(90)}{ab} \\ \\ absin(56) = sin(90) \times 78.6 \\ \\ ab = \frac{sin(90) \times 78.6}{sin(56)} \\ ab = 94.8 \\ \\ {x}^{2} + {78.6}^{2} = {94.8}^{2} \\ {x}^{2} = {94.8}^{2} - {78.6}^{2} \\ {x}^{2} = 8987.04 - 6177.96 \\ {x}^{2} = 2809.08 \\ x = \sqrt{2809.08} \\ x = 53[/tex]
Help help ASAP math math
Answer:
-1/1
Step-by-step explanation:
=64/-8
over
36-30+2
= -8
over
8
= -1
over
1
Answer:
[tex] \rightarrow - 1[/tex]
Step-by-step explanation:
[tex] \rightarrow \frac{ {4}^{3} }{ \frac{ - 12 + {2}^{2} }{(2 \times 3) {}^{2} + ( - 5 \times 2 \times 3) + 2 }} \\ [/tex]
[tex] \rightarrow \frac{ {4}^{3} }{ \frac{ - 12 + {2}^{2} }{ {6}^{2} + ( - 30) + 2 }} \\ [/tex]
[tex] \rightarrow \frac{ 64 }{ \frac{ - 12 + 4 }{ 36 + ( - 30) + 2 }} \\ [/tex]
[tex] \rightarrow \frac{ 64 }{ \frac{ - 8 }{ 8 }} \\ [/tex]
[tex] \rightarrow - \: \frac{ 64 }{ \frac{ 8 }{ 8 }} \\ [/tex]
[tex] \rightarrow - \frac{ 8 }{ 8 } \\[/tex]
[tex] \rightarrow \: - 1[/tex]
I need help with this question
Answer:
301 feet
Step-by-step explanation:
plug in the known values
[tex]85=\sqrt{24d}[/tex]
square both sides to cancel the square root
[tex]7225=24d[/tex]
divide both sides by 24 to get d on its own
[tex]d=301.041[/tex] feet
to the nearest foot is 301 feet
What is the value of log625^5
Answer:
13.979
Step-by-step explanation:
log 625^5 = 5 log 625 = 5*2.79588=
Answer:
Exact Form:
1/4
Decimal Form:
0.25
Step-by-step explanation:
Use the compound interest formulas A = P1+
and A = Pert to solve.
Suppose that you have $11,000 to invest. Which investment yields the greater return over 9 years: 7.5% compounded
continuously or 7.6% compounded semiannually?
Answer:
7.5% compounded continuously yields the greatest return after 9 years
Step-by-step explanation:
Compounded interest = P(1+r/n)^(nt), where P is the principle, r is the rate of interest, n is the number of times compounded annually, and t is the time of the investment.
7.6% compounded semiannually:
I = 11000(1+0.076/2)^(2*9) --> 11000(1.038)^18 ~ $21525.09
7.5% compounded continuously:
Since it is compounded continuously, we use the mathematical constant e.
I = 11000e = $29901.01
5.Find the area of the parallelogram. *
10 m
16 m
8 m
16 m
10 m
Answer:
128 because formula is bh
Step-by-step explanation:
help plsssssssssssssssssssssssssssssssssssss
Answer:
84
Step-by-step explanation:
The number 1 is a common factor of _________.
A) all odd numbers
B) all even numbers
C) all whole numbers
Step-by-step explanation:
The number 1 is a common factor of C) all whole numbers
Answer:
C
Step-by-step explanation:
6 / 1 = 6. 5 / 1 = 5. every whole number is divisble by 1, even prime numbers.
If 4–(x – 4) = 1 over 16 what is the value of x?
Answer:
4x+4=16
4x= 16–4
4x= 12
x= 12/4
x= 3
Alternatively,
4x+4=16
Taking 4 common,
4 (x+1) = 16
x+1 = 16/4
x+1 = 4
x = 4–1
x = 3
Step-by-step explanation:
The value of x is 68.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Parts of an Equation
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.
Given equation:
4/(x - 4) = 1 /16
Now, solving for x
4/(x - 4) = 1 /16
64 = x - 4
x= 68
Hence, the value of x is 68.
Learn more about equation here:
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Judi Salem opened a law office on July 1, 2022. On July 31, the balances in the accounts were as follows: Cash $5,000, Accounts Receivable $1,500, Supplies $500, Equipment $6,000, Accounts Payable $4,200, and Owner’s Capital $8,800. During August, the following transactions occurred.
1. Collected $1,200 of accounts receivable.
2. Paid $2,800 cash on accounts payable.
3. Recognized revenues of $7,500 of which $3,000 is collected in cash and the balance is due in September.
4. Purchased additional equipment for $2,000, paying $400 in cash and the balance on account.
5. Paid salaries $2,500, rent for August $900, and advertising expenses $400.
6. Withdrew $700 in cash for personal use.
7. Received $2,000 from Standard Federal Bank—money borrowed on a note payable.
8. Incurred utility expenses for month on account $270.
Step-by-step explanation:
what is that called into the comet or ok
9 ft
58.5 ft
33 ft
16.5 ft
Question 7 of 11
Two angles in a triangle have measures of 13' and 65.
What is the measure of the third angle?
A 52
B. 102
C. 78
D. 143
SUBMIT
The diameter of a circle is 8 miles. What is the angle measure of an arc 3 miles long?
Answer:
[tex]\sf \theta=\dfrac34 \ radians=42.97 \textdegree \ (nearest \ hundredth)[/tex]
Step-by-step explanation:
Formulae
[tex]\sf radius (r)=\dfrac12 d[/tex]
(where d is the diameter of a circle)
[tex]\sf arc \ length =r\theta[/tex]
(where r is the radius and [tex]\theta[/tex] is measured in radians)
Calculation
Given:
[tex]\sf radius (r)=\dfrac12 \cdot 8=4 \ mi[/tex]arc length = 3 miSubstituting these values into the formula for arc length:
[tex]\implies \sf 3 =4\theta[/tex]
[tex]\implies \sf \theta=\dfrac34 \ radians[/tex]
To convert radians to degrees use
[tex]\sf 1 \ rad \cdot \dfrac{180\texrdegree}{\pi}[/tex]
[tex]\implies \sf \dfrac34 \cdot \dfrac{180\texrdegree}{\pi}=42.97183463...\textdegree[/tex]
Now
[tex]\\ \rm\rightarrowtail \theta=\dfrac{l}{r}[/tex]
[tex]\\ \rm\rightarrowtail l=r\theta[/tex]
[tex]\\ \rm\rightarrowtail 3=4\theta[/tex]
[tex]\\ \rm\rightarrowtail \theta=\dfrac{3}{4}^c[/tex]
Write the Equation of the conic.
12. A circle with endpoints of a diameter at(1, -3) and (1,3).
Need help please thanks
Answer:
(x² -1) + y² = 9
Step-by-step explanation:
diameter=6 so radius means 6/2=3 (thus,radius²=3²=9)
centre (1 and midpoint of diameter is at y=0, so 1,0)
The polynomial below is a perfect square trinomial of the form A^2 - 2AB + B^2
9x^2 - 18x + 36
A. True
B. False
Answer:
False
Step-by-step explanation:
[tex]9x^2-18x+36\\\\=(3x)^2- 3x \cdot 6+6^2\\\\\text{It is not in the form of}~ A^2-2AB+B^2[/tex]
Is quadrilateral ABCD angle is equals to 60 degrees Angle B is equals to 80 degrees and angle C is equals to 120° find angle d
Pls help me what’s the answer
Answer:
the answer is D...... ..........
Answer:
226,080 cm3
Step-by-step explanation:
According to the Knot, 22% of couples meet online. Assume the sampling distribution of p follows a normal distribution and answer the following questions.
a. Suppose a random sample of 150 couples is asked, "Did you meet online>" Describe the sampling distribution of p, the proportion of couples that met online.
b. What is the probability that in a random sample of 150 couples more than 25% met online?
c. What is the probability that in a random sample of 150 couples between 15% and 20% met online?
Using the normal distribution and the central limit theorem, we have that:
a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.
b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.
c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
22% of couples meet online, hence p = 0.22.A sample of 150 couples is taken, hence n = 150.Item a:
The mean and the standard error are given by:
[tex]\mu = p = 0.22[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.22(0.78)}{150}} = 0.0338[/tex]
The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.
Item b:
The probability is one subtracted by the p-value of Z when X = 0.25, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.25 - 0.22}{0.0338}[/tex]
Z = 0.89
Z = 0.89 has a p-value of 0.8133.
1 - 0.8133 = 0.1867.
There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.
Item c:
The probability is the p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15, hence:
X = 0.2:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.2 - 0.22}{0.0338}[/tex]
Z = -0.59
Z = -0.59 has a p-value of 0.2776.
X = 0.15:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.15 - 0.22}{0.0338}[/tex]
Z = -2.07
Z = -2.07 has a p-value of 0.0192.
0.2776 - 0.0192 = 0.2584.
There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
If you want to be 99% confident of estimating the population mean to within a sampling error of 14 and the standard deviation is assumed to be 14, what sample size
is required?
The sample size required is
(Round up to the nearest integer.)
In
Help me solve this
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Clear all
Check answer
Answer:
16641
Step-by-step explanation:
Thank you!
Express √12+√27 in the form n√3, where n is an integer.
Answer:
5sqroot3
Step-by-step explanation:
see image.
An integer is just a whole positive or negative (positive in this case) number that's not a fraction or decimal or mixed number. In the answer that is the 5.
To simplify a radical, look for a factor that is a perfect square. Radicals and multiplying are very friendly to each other and you can separate the "radicand" (the inside number) into factors inside the radical also into separate radicals to simplify. See image
Find the missing numerator that will make the rational expressions equivalent.
82x+7=?6(2x+7)
The missing numerator that will make the rational expressions equivalent is (82x + 7) / (12x + 42)
What is an equation?
An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the missing numerator, hence:
82x + 7 = y * 6(2x+7)
82x + 7 = y * (12x + 42)
y = (82x + 7) / (12x + 42)
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If f(x)=3x−1 and f(a)=−43, what is the value of a ??
Answer:
a = -14
Step-by-step explanation:
f(a) = -43
3a - 1 = -43
3a = -43 + 1
3a = -42
a = -42/3
a = -14
what is 5(m-2) equil to
Answer:
5m - 10
Step-by-step explanation:
Use distributive property;
5(m - 2)
(5 x m) (5 x -2)
5m - 10
Find the solution(s) to the system
y = x2-4
y = -2x – 5
Answer:
=(-1,-5)
Step-by-step explanation:
y=X1=4
y=-2x-5-2
the present ages of a father and his son are 40 years and 8 years respectively how many years ago the product of their ages was 105
Answer:
5 years ago
Step-by-step explanation:
5 years ago, they were 35 years old and 3 years old. 35*3=105.