Answer:
Step-by-step explanation:
Assume that f(x) = 0 for x outside the interval [4,7]. We will use the following
[tex]E[X^k] = \int_{4}^{7}x^k f(x) dx[/tex]
[tex]Var(X) = E[X^2]- (E[X])^2[/tex]
Standard deviation = [tex] \sqrt[]{Var(X)}[/tex]
Mean = [tex]E[X][/tex]
Then,
[tex]E[X] = \int_{4}^{7}\frac{1}{3}dx = \frac{7^2-4^2}{2\cdot 3} = \frac{11}{2}[/tex]
[tex]E[X^2] = \int_{4}^{7}\frac{x^2}{3}dx = \frac{7^3-4^3}{3\cdot 3} = 31[/tex]
Then, [tex]Var(x) = 31-(\frac{11}{2})^2 = \frac{3}{4}[/tex]
Then the standard deviation is [tex]\frac{\sqrt[]{3}}{2}[/tex]
which of these shapes is congruent to given shape ?
Answer:
Step-by-step explanation:
shape D
Answer:
D.
Step-by-step explanation:
Well congruent means same size and same shape.
a) rectangle
This shape is a rectangle where as the given shape is a parallelogram.
This is not congruent to the given shape.
b) Parallelogram
This may be a parallelogram but it is too wide,
Hence, it is not congruent.
c) Rectangle
This is not a parallelogram,
Hence, this s not congruent
d) Parallelogram
This is a parallelogram with the same size just not in the same place but it is still congruent.
Thus, answer choices D. is the correct answer.
Find the value of the chi-square test statistic for the goodness-of-fit test. You wish to test the claim that a die is fair. You roll it 48 times with the following results. Number 1 2 3 4 5 6Frequency 5 10 12 9 4 8Observed frequency (O) 5,10,12,9,4,8Expected frequency (E) 8,8,8,8,8,8What is the value of the 2 test statistic?a. X2 = 3.538b. X2 = 4.182c. X2 = 5.75d. X2 = 7.667
Answer:
The value of Chi-square test statistic is χ² = 5.75.
Step-by-step explanation:
The Chi-square Goodness of fit test will be used to determine whether the die is fair or not.
The hypothesis can be defined as follows:
H₀: The die is fair.
Hₐ: The die is not fair.
The Chi-square test statistic is given by:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]
Consider the table attached below.
The value of Chi-square test statistic is χ² = 5.75.
If x + 4 = 12, what is the value of x?
Answer:
8
Step-by-step explanation:
To find the answer to these problems you can work backwards
12-4=8
Write your height in inches. Suppose it increases by 15%, what would your new height be? Now suppose your increased height decreases by 15% after the 15% increase; what is your new height?
Answer:
New height= 41.4 inches
Second new height= 36inches
Step-by-step explanation:
Height is assumed to be 36 inches
If it increases by 15%.
15%= 0.15
It's new height =( 36*0.15) +36
New height= 5.4+36
New height = 41.4 inches
This expression (36*0.15) is the expression of adding 15% to the height.
So if the 15% is taken away again , height= 41.4-(36*0.15)
Height= 41.4-5.4
Height= 36 inches
Find connection between Fibonacci numbers and the aspects of Engineering???????????????
if u answer i will mark u as brainliest
Answer:
Fibonacci numbers is a series of numbers in which each number is sum of two preceding numbers.
Step-by-step explanation:
It is a sequence in mathematics denoted F. Fibonacci numbers have important contribution to western mathematics. The first two Fibonacci numbers are 0 and 1, all the numbers are then sum of previous two numbers. Fibonacci sequence is widely used in engineering applications for data algorithms. Fibonacci sequence is basis for golden ratio which is used in architecture and design. It can be seen in petals of flower and snail's shell.
a study of the annual population of toads in a county park shows the population, S(t), can be represented by the function S(t) = 152(1.045)^t, where the t represents the number of years since the study started. based on the function, what is the growth rate?
Answer: 0.045 is the growth rate.
Step-by-step explanation:
A generic exponential growth function can be written as:
f(t) = A*(1 + r)^t
where A is the initial amount.
t is the unit of time.
r is the rate of growth.
For example if we have an increase of 10% per year, with an initial population of 100 we have that:
A = 100, r = 10%/100% = 0.10, t = number of years.
the equation will be:
f(t) = 100*(1 + 0.10)^t
Now, in this case the equation is:
S(t) = 152*(1.045)^t
We can write this as:
S(t) = 152*(1 + 0.045)^t
Then 152 is the initial amount and 0.045 is the growth rate.
Please answer this correctly without making mistakes
Answer:
16 km
Step-by-step explanation:
Given:
Distance from Washington to Stamford = distance from Washington to Salem + distance from Salem to Stamford = 10.3 km + 11.9 km = 22.2 km
Distance from Washington to Oakdele = 6.2 km
Required: the difference between the distance from Washington to Stamford and from Washington to Oakdele
Solution:
Distance from Washington to Stamford = 22.2 km
Distance from Washington to Oakdele = 6.2 km
The difference = 22.2 km - 6.2 km = 16 km
Therefore, from Washington, it is 16 km farther to Stamford than to Oakdele.
Suppose that insurance companies did a survey. They randomly surveyed 410 drivers and found that 300 claimed they always buckle up.
We are interested in the population proportion of drivers who claim they always buckle up.
NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
(i) Enter an exact number as an integer, fraction, or decimal.
x =
(ii) Enter an exact number as an integer, fraction, or decimal.
n =
(iii) Round your answer to four decimal places.
p' =
Which distribution should you use for this problem? (Round your answer to four decimal places.)
P' _ ( , )
Answer:
x = 300
n = 410
p' = 0.7317
[tex]\mathbf{P' \sim Normal (\mu = 0.7317, \sigma = 0.02188)}[/tex]
Step-by-step explanation:
From the given information;
the objective is to answer the following:
(i) Enter an exact number as an integer, fraction, or decimal.
Mean x = 300
(ii) Enter an exact number as an integer, fraction, or decimal.
Sample size n = 410
(iii) Round your answer to four decimal places.
Sample proportion p' of the drivers who always claimed they buckle up is :
p' = x/n
p' = 300/410
p' = 0.7317
Which distribution should you use for this problem? (Round your answer to four decimal places.)
P' _ ( , )
The normal distribution is required to be used because we are interested in proportions and the sample size is large.
Let consider X to be the random variable that follows a normal distribution.
X represent the number of people that always claim they buckle up
∴
[tex]P' \sim Normal (\mu = p' , \sigma = \sqrt{\dfrac{p(1-p)}{n}})[/tex]
[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.7317(1-0.7317)}{410}})[/tex]
[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.7317(0.2683)}{410}})[/tex]
[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.19631511}{410}})[/tex]
[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{4.78817341*10^{-4}})[/tex]
[tex]\mathbf{P' \sim Normal (\mu = 0.7317, \sigma = 0.02188)}[/tex]
A simple random sample of 20 third-grade children from a certain school district is selected, and each is given a test to measure his/her reading ability. You are interested in calculating a 95% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. What is the margin of error associated with the confidence interval
Answer:
Margin of Error = ME =± 5.2592
Step-by-step explanation:
In the given question n= 20 < 30
Then according to the central limit theorem z test will be applied in which the standard error will be σ/√n.
Sample Mean = μ = 64
Standard Deviation= S= σ = 12
Confidence Interval = 95 %
α= 0.05
Critical Value for two tailed test for ∝= 0.05 = ±1.96
Margin of Error = ME = Standard Error *Critical Value
ME = 12/√20( ±1.96)=
ME = 2.6833*( ±1.96)= ± 5.2592
The standard error for this test is σ/√n
=12/√20
=2.6833
Emma words in a coffee shop where she is paid at the same hourly rate each day. She was paid $71.25 for working 7.5 hours on Monday. If she worked 6 hours on Tuesday, how much was she paid on Tuesday
Answer:
$57
Since $71.25 was paid for working 7.5 hours.
That means he was being paid $9.5 per hour.
Which is 71.25÷7.5.
And on tuesday that's 9.5×6 which is $57
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 259.2-cm and a standard deviation of 2.1-cm. For shipment, 17 steel rods are bundled together. Find the probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259-cm.
Answer:
The probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259 cm is 0.65173.
Step-by-step explanation:
We are given that a company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 259.2 cm and a standard deviation of 2.1 cm. For shipment, 17 steel rods are bundled together.
Let [tex]\bar X[/tex] = the average length of rods in a randomly selected bundle of steel rods
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean length of rods = 259.2 cm
[tex]\sigma[/tex] = standard deviaton = 2.1 cm
n = sample of steel rods = 17
Now, the probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259 cm is given by = P([tex]\bar X[/tex] > 259 cm)
P([tex]\bar X[/tex] > 259 cm) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{259-259.2}{\frac{2.1}{\sqrt{17} } }[/tex] ) = P(Z > -0.39) = P(Z < 0.39)
= 0.65173
The above probability is calculated by looking at the value of x = 0.39 in the z table which has an area of 0.65173.
Which of the hypothesis tests listed below is a left-tailed test? Select all correct answers. Select all that apply: H0:μ=18, Ha:μ<18 H0:μ=19.3, Ha:μ>19.3 H0:μ=8, Ha:μ≠8 H0:μ=11.3, Ha:μ<11.3 H0:μ=3.7, Ha:μ<3.7
Answer:
H0:μ=18, Ha:μ<18
H0:μ=11.3, Ha:μ<11.3
H0:μ=3.7, Ha:μ<3.7
Step-by-step explanation:
A left tailed test is a type of test usually taken from the alternative hypothesis that includes only one of either the less than or greater than options and not both.
A left tailed test corresponds with the less than option and in this case study, the left tailed test are:
H0:μ=18, Ha:μ<18
H0:μ=11.3, Ha:μ<11.3
H0:μ=3.7, Ha:μ<3.7
The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown. Step 1: –c = ax2 + bx Which best explains or justifies Step 1?
Answer:
Subtract c from each side, using the subtraction property of equality
Step-by-step explanation:
0 = ax^2 + bx + c
Subtract c from each side, using the subtraction property of equality
-c = ax^2 + bx + c-c
-c = ax^2 + bx
Answer:
subtract c from each side, so the answer would be D
Solve of the following equations for x: 2x = 4.
Answer:
[tex]\boxed{ x = 2}[/tex]
Step-by-step explanation:
=> [tex]2x = 4[/tex]
Dividing both sides by 2
=> [tex]\frac{2x}{2} = \frac{4}{2}[/tex]
=> x = 2
2x=4
x=4/2=2
.............
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far (in miles) is it from Jeremy's home to school?
Answer:
9 miles
Step-by-step explanation:
Let's say that the speed that Jeremy's father drives Jeremy through traffic is x. When there is no traffic, Jeremy's father drives 18 miles per hour faster than his speed in traffic, x. This would make the speed that Jeremy's father drives Jeremy to school without traffic, 18 / 60 + x. This is as it is 18 miles per hour faster, not 18 miles per minute faster.
Now recall the formula Speed = Distance / Time, or S = D / T. We want the distance here ( How far (in miles) from Jeremy's home to school ) so let's isolate D here in this formula,
S = D / T ⇒ D = S [tex]*[/tex] T - and as you know, the distance from Jeremy's home to school is the same, with or without traffic. So, we can consider case 1 : Jeremy's " distance traveled " in traffic, and case 2 : Jeremy's " distance traveled " without traffic, and make them equal to one another.
20 [tex]*[/tex] x = 12 [tex]*[/tex] ( 18 / 60 + x ),
20x = 3.6 + 12x,
8x = 3.6,
x = 0.45 - Now the distance is 20 [tex]*[/tex] x, and hence 20 [tex]*[/tex] 0.45 = 9 miles
Pat is taking an economics course. Pat's exam strategy is to rely on luck for the next exam. The exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it. If a grade on the exam is 60% or more, Pat will pass the exam. Find the probability that Pat will pass the exam.
Answer:
The probability that Pat will pass the exam is 0.02775.
Step-by-step explanation:
We are given that exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it.
If a grade on the exam is 60% or more, Pat will pass the exam.
Let X = grade on the exam by Pat
The above situation can be represented through binomial distribution such that X ~ Binom(n = 100, p = 0.50).
Here the probability of success is 50% because there is a true-false question and there is a 50-50 chance of both being the correct answer.
Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).
So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]100 \times 0.50[/tex] = 50
and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{100 \times 0.50 \times (1-0.50)}[/tex]
= 5
So, X ~ Normal([tex]\mu=50, \sigma^{2} = 5^{2}[/tex])
Now, the probability that Pat will pass the exam is given by = P(X [tex]\geq[/tex] 60)
P(X [tex]\geq[/tex] 60) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{60-50}{5}[/tex] ) = P(Z [tex]\geq[/tex] 2) = 1 - P(Z < 2)
= 1 - 0.97725 = 0.02275
Hence, the probability that Pat will pass the exam is 0.02775.
Consider a triangle ABC like the one below. Suppose that B=36°, C= 62°, and b= 40. (The figure is not drawn to scale.) Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
Answer:
A=82°
a= 67.4
c = 60.1
Step-by-step explanation:
For A
A+B+C =180°
A= 180-(B+C)
A= 180-(36+62)
A= 189-(98)
A= 82°
For a
a/sinA= b/sinB
a/sin82= 40/sin36
a= (40*sin82)/sin36
a=( 40*0.9903)/0.5878
a=67.39
Approximately = 67.4
For c
c/sinC= b/sinB
c= (sinC*b)/sinB
c= (sin62*40)/sin36
c =(0.8829*40)/0.5878
c = 60.08
Approximately = 60.1
Assume that y varies directly with
x, then solve.
If y=6 when x=2/3 find x when y=12.
Х=? (It’s a fraction)
Answer:
x = 4/3
Step-by-step explanation:
Direct variation:
y = kx
We use the given x-y point to find k.
6 = k * 2/3
k = 6 * 3/2
k = 9
The equation is
y = 9x
For y = 12,
12 = 9x
x = 12/9
x = 4/3
4.0.3x= 2.1 Equals what
Answer:
x= 1.75
Step-by-step explanation:
Answer:
1.75 = x?
Step-by-step explanation:
verify sin4x - sin2x = cos4x-cos2x
Answer:
sin⁴x - sin²x = cos⁴x - cos²x
Solve the right hand side of the equation
That's
sin⁴x - sin²x
From trigonometric identities
sin²x = 1 - cos²xSo we have
sin⁴x - ( 1 - cos²x)
sin⁴x - 1 + cos²x
sin⁴x = ( sin²x)(sin²x)
That is
( sin²x)(sin²x)
So we have
( 1 - cos²x)(1 - cos²x) - 1 + cos²x
Expand
1 - cos²x - cos²x + cos⁴x - 1 + cos²x
1 - 2cos²x + cos⁴x - 1 + cos²x
Group like terms
That's
cos⁴x - 2cos²x + cos²x + 1 - 1
Simplify
We have the final answer as
cos⁴x - cos²xSo we have
cos⁴x - cos²x = cos⁴x - cos²xSince the right hand side is equal to the left hand side the identity is true
Hope this helps you
Find the total area of the prism.
Answer:
[tex]\boxed{\mathrm{864 \: in^2}}[/tex]
Step-by-step explanation:
The shape is a cube.
Apply formula for total surface area of cube.
[tex]SA=6a^2[/tex]
[tex]SA=\mathrm{total \: surface \: area}\\ a =\mathrm{side \: length}[/tex]
[tex]SA=6(12)^2[/tex]
[tex]SA=6(144)[/tex]
[tex]SA=864[/tex]
Answer:
[tex]\boxed{Area = 144 inches^2}[/tex]
Step-by-step explanation:
Area of a cube = Volume/Length
Where Length = 12 inches, Volume = 1728
Area = 1728/12
Area = 144 inches^2
Which table represents the inverse of the function defined above?
Hello!
Answer:
Table B.
Step-by-step explanation:
An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:
We can use points on the table:
[tex]f(x)[/tex] = (7, 21)
The inverse of this function would 7 as its y value, and 21 as its x value:
[tex]f^{-1} (x)[/tex] = (21, 7)
The only table shown that correctly shows this relationship is table B.
Solving exponential functions
Answer:
approximately 30Step-by-step explanation:
[tex]f(x) = 4 {e}^{x} [/tex]
[tex]f(2) = 4 {e}^{2} [/tex]
[tex]f(2) = 4 \times 7.389[/tex]
[tex]f(2) = 29.6[/tex]
( Approximately 30)
Hope this helps..
Good luck on your assignment..
Answer:
approximately 30
Step-by-step explanation:
[tex]f(x)=4e^x[/tex]
Put x as 2 and evaluate.
[tex]f(2)=4e^2[/tex]
[tex]f(2)=4(2.718282)^2[/tex]
[tex]f(2)= 29.556224 \approx 30[/tex]
find 10th term of a geometric sequence whose first two terms are 2 and -8. Please answer!!
Answer:
The 10th term is -524,288
Step-by-step explanation:
The general format of a geometric sequence is:
[tex]a_{n} = r*a_{n-1}[/tex]
In which r is the common ratio and [tex]a_{n+1}[/tex] is the previous term.
We can also use the following equation:
[tex]a_{n} = a_{1}*r^{n-1}[/tex]
In which [tex]a_{1}[/tex] is the first term.
The common ratio of a geometric sequence is the division of the term [tex]a_{n+1}[/tex] by the term [tex]a_{n}[/tex]
In this question:
[tex]a_{1} = 2, a_{2} = -8, r = \frac{-8}{2} = -4[/tex]
10th term:
[tex]a_{10} = 2*(-4)^{10-1} = -524288[/tex]
The 10th term is -524,288
The tee for the sixth hole on a golf course is 400 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard. Answer any time! :D
Answer:
181.8 yd
Step-by-step explanation:
The law of cosines is good for this. It tells you for triangle sides 'a' and 'b' and included angle C, the length of 'c' is given by ...
c^2 = a^2 +b^2 -2ab·cos(C)
For the given geometry, this is ...
c^2 = 400^2 +240^2 -2(400)(240)cos(16°) ≈ 33,037.75
c ≈ √33037.75 ≈ 181.8 . . . yards
Marsha's ball is about 181.8 yards from the hole.
Answer:
181.8 yds
Step-by-step explanation:
I got it correct on founders edtell
Perform the indicated operation and write the result in standard form: (-3+2i)(-3-7i)
A. -5+27i
B. 23+15i
C. -5+15i
D. 23-15i
E-5-27I
Answer:
23+15i
Step-by-step explanation:
(-3+2i) (-3-7i)
multiply -3 w (-3+2i) and multiply -7i w (-3+2i)
9-6i+21i-14i^2
combine like terms
9+15i-14i^2
i squared is equal to -1 so
9+15i-(14x-1)
9+14+15i
23+15i
hope this helps :)
A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 556 randomly selected Americans surveyed, 421 were in favor of the initiative. Round answers to 4 decimal places where possible.
Required:
a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between ______ and______ .
b. If many groups of 593 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About ________percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about _______? percent will not contain the true population proportion.
Answer:
(A) With 99% confidence, the proportion that favours the Green initiative is between 418.895 and 423.105 (no approximation; answers were gotten exactly in 3 decimal places).
(B) If many groups of 593 (greater than the initial sample size of 556) randomly selected Americans were surveyed then a different confidence interval would be used or produced from each group.
About 90% of these confidence intervals will contain the true population proportion of Americans who favour the Green initiative and about 10% will not contain the true population proportion.
Step-by-step explanation:
(A) 99% of 421 = 416.79
421 - 416.79 = 4.21
4.21 ÷ 2 = 2.105
(421-2.105), (421+2.105)
The lower and upper limits are:
[418.895 , 423.105]
(B) A wider confidence interval such as 90% will be better suited in a case of multiple samples like this.
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
DAC
A
Statements
Reasons
00
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Triangle DAC is congruent to triangle BCA by SAS congruence theorem.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, AD = BC and AD || BC.
AD = BC (Given)
AD || BC (Given)
AC = AC (Reflexive property)
∠DAC=∠BCA (Interior alternate angles)
By SAS congruence theorem, ΔDAC≅ΔBCA
By CPCT, AB=CD
Therefore, triangle DAC is congruent to triangle BCA by SAS congruence theorem.
To learn more about the congruent theorem visit:
https://brainly.com/question/24033497.
#SPJ5
ASAP!!! NEED HELP!!!! Max is stacking logs at his campground for firewood. After his first load of logs, he has 8 logs on the stack. After his seventh load of logs, he has 62 logs on the stack. Use sequence notation to represent the arithmetic function. ANSWER CHOICES: A. an = 8 + 6(n − 1) B. an = 62 + 6(n − 1) C. an = 8 + 9(n − 1) D. an = 62 + 9(n − 1)
Answer: Choice C. an = 8 + 9(n-1)
===========================================
Work Shown:
a1 = 8 is the first term
a7 = 62 is the seventh term
an = a1+d(n-1) = nth term of arithmetic sequence
a7 = a1+d(7-1) ... plug in n = 7; solve for d
62 = 8+d(6)
62 = 6d+8
6d+8 = 62
6d = 62-8
6d = 54
d = 54/6
d = 9 is the common difference
an = a1 + d(n-1)
an = 8 + 9(n-1) is the nth term of this arithmetic sequence
Answer:
Choice C. an = 8 + 9(n-1)
Step-by-step explanation:
I just took the test
what is 20% of 50naira?
Answer:
10
Step-by-step explanation:
To find 20% of 50 you need to times 20 with 50 and divide by 100.
20×50÷100
=10