Answer:
CI 95 % = ( 28.92 ; 41.08 )
Step-by-step explanation:
Sample Information:
sample size n = 30
sample mean = 35 %
sample standard deviation s = 17
To construct a CI 95 %
significance level is α = 5 % α = 0.05 α/2 = 0.025
z critical for α/2 from z- table is : z (c) = 1.96
CI 95 % = ( x ± z(c) * s/√n )
CI 95 % = ( 35 ± 1.96 * 17/√30 )
CI 95 % = ( 35 ± 6.08 )
CI 95 % = ( 28.92 ; 41.08 )
A simple random sample of 27 filtered 100-mm cigarettes is obtained from a normally distributed population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.20 mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below. a. What are the null and alternative hypotheses?
Answer:
The null hypothesis is [tex]H_0: \sigma = 0.3[/tex]
The alternative hypothesis is [tex]H_1: \sigma \neq 0.3[/tex]
Step-by-step explanation:
Test if the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg.
At the null hypothesis, we test if the standard deviation is of 0.3, that is:
[tex]H_0: \sigma = 0.3[/tex]
At the alternative hypothesis, we test if the standard deviation is different of 0.3, that is:
[tex]H_1: \sigma \neq 0.3[/tex]
The cost of producing pens with the company logo printed on them consists of a onetime setup fee of $265.00 plus $0.95 for each pen produced. This cost can be calculated using the formula C=265.00+0.95p, where p represents the number of pens produced and C is the cost. Use the formula to calculate the cost of producing 2900 pens.
The initial population of the town was estimated to be 12,500 in 2005. The population has increased by about 5.4% per year since 2005.
Formulate the equation that gives the population, A(x) , of the town x years since 2005. If necessary, round your answer to the nearest thousandth.
A(x)=__(_)^x
Answer:
[tex]A(x) = 12500(1.054)^x[/tex]
Step-by-step explanation:
Exponential equation for population growth:
Considering a constant growth rate, the population, in x years after 2005, is given by:
[tex]A(x) = A(0)(1 + r)^x[/tex]
In which A(0) is the population in 2005 and r is the growth rate, as a decimal.
The initial population of the town was estimated to be 12,500 in 2005.
This means that [tex]A(0) = 12500[/tex]
The population has increased by about 5.4% per year since 2005.
This means that [tex]r = 0.054[/tex]
So
[tex]A(x) = A(0)(1 + r)^x[/tex]
[tex]A(x) = 12500(1 + 0.054)^x[/tex]
[tex]A(x) = 12500(1.054)^x[/tex]
Please show detailed work if possible-that will help me to better understand the questions
start with this expression:
f(x) = 2x2 − x − 10
1st- What are the x-intercepts of the graph of f(x)? Show work on how to get this
2nd- Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Show work on how to get this
Part C: What are the steps you would use to graph f(x)? show how you can use the answers obtained in Part A and Part B to draw a graph
Answer:
We are given the function:
[tex]f(x)=2x^2-x-10[/tex]
[tex]Here,\\a=2, b=-1,c=-10[/tex]
1. X-intercepts are the points at which the graph of a function intersects or cuts the x-axis. Since the x-intercept always lies on the x-axis, its ordinate or y-coordinate will always be 0. Since the function is quadratic, it will have at most 2 x-intercepts.
In order to find the x intercept, we basically solve for x at y=0:
[tex]f(x)=2x^2-x-10\\As\ y=0,\\0=2x^2-x-10\\2x^2-x-10=0\\ 2x^2-5x+4x-10=0\\x(2x-5)+2(2x-5)=0\\(x+2)(2x-5)=0\\Hence,\\Individually:\\x=-2,\ x=\frac{5}{2}[/tex]
Hence, the x-intercepts of the parabola of f(x) is (-2,0),(2.5,0)
2. The vertex of parabola is determined as maximum or minimum, solely on how it opens. This depends on the nature of the co-efficient of the x^2 term or 'a'. If a is positive the parabola opens upwards (minimum point) and downwards (maximum point) if negative. Hence, here as a=2, the parabola opens upwards and its vertex is minimum.
[tex]Vertex=(\frac{-b}{2a},\frac{-D}{4a})\\Hence,\\D=b^2-4ac\\Substituting\ a=2,b=-1,c=-10:\\D=(-1)^2-4*2*-10=1+80=81\\Hence,\\Vertex\ of\ f(x)=(\frac{-(-1)}{2*2},\frac{-81}{4*2})=(\frac{1}{4},\frac{-81}{8})[/tex]
3. [Please refer to the attachment]
From the graph, we observe that the parabola cuts the x-axis at (-2,0),(2.5,0). Also, its clear that the axis of symmetry passes through [tex](\frac{1}{4},\frac{-81}{8})[/tex], which is its minimum point.
Answer:
A chord of a circle is 9cm long if it's distance from the centre of the circle is 5cm calculate the radius of the circle
Corresponding sides of what triangles are proportional
Answer:
In a pair of similar triangles, the corresponding sides are proportional.
Step-by-step explanation:
Corresponding sides touch the same two angle pairs. When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number.
If a $6 per unit tax is introduced in this market, then the new equilibrium quantity will be
Answer:
soory i dont know just report me if you angry
II. Round to the nearest hundred.
11. 582
12. 1,234
13. 640
14. 770
15. 1,104 can you please tell what the answer?
Answer:
582-600
1,234-1,200
640-600
770-800
1,104-1,100
What is the x intercept of the graph that is shown below? Please help me
Answer:
(-2,0)
Step-by-step explanation:
The x intercept is the value when it crosses the x axis ( the y value is zero)
x = -2 and y =0
(-2,0)
Simplify 4^-4.
please help I have 10 minutes
Answer:
1/256
Step-by-step explanation:
[tex]4^{-4}[/tex]
[tex](1/4)^{4}[/tex]
=> 1/256
Find the missing side lengths leave your answer as a racials simplest form
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
1. How can a matrix be used to solve a system of equations? Demonstrate by solving the following system. Show your work. In other words, use a problem of system of equations problem as an example.
Answer:
Step-by-step explanation:
Assuming the system is solvable in the first place, create an augmented matrix of coefficients from the equations. Then put the matrix into reduced row echelon form.
Example is attached.
"Demonstrate by solving the following system."
You need to provide the system of equations.
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 10 (newly deceased) adults, the mean failure strain (%) was 24.0, and the standard deviation was 3.2.
Required:
a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
PLEASE HELP AND BE RIGHT PLEASE AND THANK YOU
Answer:
4 units
Step-by-step explanation:
A'B' = 2 × AB
8 = 2×AB
AB = 8/2 = 4
Answer:
16 units
Step-by-step explanation:
The triangle will get bigger because it has a scale factor that is greater than 1.
k=scale factor
k<1=reduction
k>1=enlargement
A sample of 13 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 1.96,1.81,1.97,1.83,1.87,1.84,1.85,1.94,1.96,1.81,1.86,1.95,1.89
===============================================
Explanation:
Add up the values to get
1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54
Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.
So the mean is approximately 1.8876923
---------------------
Now make a spreadsheet as shown below
We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.
After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.
That sum is approximately 0.04403076924
Next, we divide that over n-1 = 13-1 = 12
0.04403076924 /12 = 0.00366923077
That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.
sqrt(0.00366923077) = 0.06057417576822
This rounds to 0.061 which is the final answer.
whats the scale factor of this one please?????
Answer:
0.5
Step-by-step explanation:
E to E'
(0, 3) to (0, 1.5) each term of E' is ½ of the corresponding term of E
N to N'
(-1, 1) to (-0.5, 0.5) each term of N' is ½ of the corresponding term of N
U to U'
(2, -2) to (1, -1) each term of U' is ½ of the corresponding term of U
V to V'
(1, -3) to (0.5, -1.5) each term of V' is ½ of the corresponding term of V
A meat packaging plant uses a machine that packages chicken livers in six pound portions. A sample of 91 packages of chicken livers has a standard deviation of 0.47. Construct the 98% confidence interval to estimate the standard deviation of the weights of the packages prepared by the machine. Round your answers to two decimal places.
Lower endpoint______ Upper endpoint__
Answer:
it simple as look
Step-by-step explanation:
He y I a m r a v I t ha n k S
Wowowowowowowowowk
Drag the tiles to the correct boxes to complete the pairs.
Given that x= 3 + 81 and y= 7 - 1 match the equivalent expressions.
-15 + 19
58 + 106
-&
411
-29 - 531
I. 2y
-
y
–50 ty
23 - 3y
9514 1404 393
Answer:
58 +106i-29 -53i-8 -41i-15 +19iStep-by-step explanation:
For the purpose of selecting the appropriate tile, it is only necessary to figure the real part of the sum or product.
We notice that the second product (-xy) is -1/2 times the first product (2xy). This can let you find the answers on that basis alone. The only tiles with a (-1) : (2) relationship are (-29 -53i) : (58 +106i).
__
The sum -5x +y has a real part of -5(3) +7 = -8.
The sum 2x -3y has a real part of 2(3) -3(7) = 6 -21 = -15.
Hence the sequence of answers needed on the right side is as shown above.
_____
Additional comment
You know that arithmetic operations with complex numbers (multiplication and addition) are identical to those operations performed on any polynomials. That is, "i" can be treated as a variable. The simplification comes at the end, where any instances of i² can be replaced by -1.
xy = (3 +8i)(7 -i) = 3·7 -3·i +8·7·i -8·i·i = 21 +53i -8i²
= (21 +8) +53i . . . . replaced i² with -1, so -8i² = +8
= 29 +53i
f (x) = sqrt(x)+ 2, g(x)=x^2+ 1
find f(g(x))
and g(f(x))
Answer:
[tex]f(x) = \sqrt{x} + 2 \\ \\ g(x) = {x}^{2} + 1 \\ \\ f{g(x)} = \sqrt{ {x}^{2} + 1 } + 2 \\ \\ g{f(x)} = {( \sqrt{x} + 2 )}^{2} + 1[/tex]
Write the coefficient of x².
A coefficient is a numerical value that is multiplied with a variable.
Coefficient of x² is -3When Asia was young, her father marked her height on the door frame every month. He noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches, and multiplying the result by one-third.
Create an equation linking her predicted height, h, with her age in months, m.
[tex]The \: text \: tells \: us \: that \: we \: can \\ predict \: her \: height \: by \: taking \\ her \: age \: in \: months, \: adding \: 75, \\ and \: multiplying \: by \: \frac{1}{3} . \: So \: our \\ equation \: is [/tex]
[tex]h = (m + 75). \frac{1}{3} [/tex]
(or)
[tex]h = \frac{1}{3} (m + 75)[/tex]
b) Determine her predicted height on her second birthday
To predict Asia’s height on her second birthday, we substitute m=24
into our equation (because 2 years is 24 months) and solve for h.
[tex]h = \frac{1}{3} (24 + 75)[/tex]
[tex]h = \frac{1}{3} (99)[/tex]
[tex]h = 33[/tex]
Asia’s height on her second birthday was predicted to be 33 inches.
What is the quotient of the synthetic division problem below, written in
polynomial form?
5)2 1 -55
O A. -2x+11
O B. -2x+9
O C. 2x+11
O D. 2x+9
Answer:
C. 2x+11
Step-by-step explanation:
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
Answer:
628 mi^3
Step-by-step explanation:
the volume of a cylinder is given by:
V = base area x height
thus,
V = (3.14)(5)^2(8)
V = (3.14)(25)(8)
V = 628 mi^3
the volume of the cylinder is 628 cubic miles
The volume of the cylinder is 628 cubic miles.
We have a cylinder of radius 5 mi and height 8 mi.
We have to find the volume of the figure and round it to nearest tenth.
What is the volume of cylinder?The volume of cylinder is given by the formula -
Volume [tex]=\pi r^{2} h[/tex]
We can use the above formula to calculate the volume of cylinder. In our case -
r = 5 mi
h = 8 mi
Substituting the values in the formula -
Volume [tex]=\pi\times5^{2}\times 8\\\\[/tex] = 628 cubic miles.
Hence, the volume of the cylinder is 628 cubic miles.
To solve more questions on finding the volume of cylinder, visit the link below -
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Will give brainliest
A tablet at a local electronics store is in high demand and will only be available to customers for a limited time. The store initially has 4 cases of the tablet on hand. The store manager receives new supplies of the tablet each week. At the beginning of week 1, the store manager receives an additional order from the distributor of 5 cases of tablets. At the beginning of week 6, the manager receives another order of 10 cases. Which of the following equations best models the scenario for how many cases of the tablet the store can expect to receive each week?
a. y=4
b. y=x+4
c. y=-6x
Aubrey's dinner cost $85. She tips the waitstaff 30%, for excellent service.
How much does Aubrey tip the waitstaff?
Describe the following sequence using an algebraic expression as a rule 0; 2,4; 6
Answer:
Step-by-step explanation:
I assume the sequence is 0, 2, 4, 6
nth term = 2(n-1)
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting 2 queens and 2 kings.
The probability is ___.
(Round to six decimal places as needed.)
Answer:
1.083
Step-by-step explanation:
Exact form: 13/12
Decimal form: 1.083 (put a line above the 3)
Mixed number form: 1 1/12
Which of the following statements accurately describes the period of a trigonometric function?
Answer:
b
Step-by-step explanation:
b is correct.
The perimeter of a rectangle is 202 the length is 26 more than 4 times the width find the dimensions
Answer:
Width = xLength = 26 + 4xPerimeter
[tex]202 = x + x + 26 + 4x + 26 + 4x\\202-26-26=10x\\150=10x\\x=15[/tex]
Therefore, the dimensions are
Width = x = 15Length = 26 + 4x = 26 + 4(15) = 86can someone explain step by step what to do next? I am trying to find the vertex, focus, and directrix of this parabola.
y=2x^2
y=2x^2 im using this equation (x-h)^2=4p(y-k)
y/2=x^2
this is my problem I dont know where to put y/2 in the equation I am using
Answer:
Hey hi how are you can you be my friend please..Step-by-step explanation:
And can you give me a fever can you please just marks me as brainliests please..Answer:
Step-by-step explanation:
Parabola: y=2x²
Let say (a,b) the focus and y=k the directrix.
[tex]formula\ to\ use:\ \boxed{y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} }\\\\\left \{\begin {array}{ccc}a&=&0\\2&=&\dfrac{1}{2(b-k)} \\\dfrac{b+k}{2} &=&0\\\end {array} \right.\\\\\\\left \{\begin {array}{ccc}a&=&0\\b-k&=&\dfrac{1}{4} \\b+k &=&0\\\end {array} \right.\\\\\\\left \{\begin {array}{ccc}a&=&0\\b&=&\dfrac{1}{8} \\k &=&\dfrac{-1}{8} \\\end {array} \right.\\\\\\focus=(0,\dfrac{1}{8} )\\\\directrix:\ y=\dfrac{-1}{8}[/tex]
Choose the system of inequalities that best matches the graph below. A. B. C. D.
The system of inequalities that is graphed is:
y ≤ - (2/3)*x
y < x - 3
So the correct option is B.
Which system of inequalities is the graphed one?First, we can see that for both of the inequalities the shaded part is below the lines.
You also can see that the solid line (correspondent to the symbol ≤) is the one with a negative slope, and the dashed line (correspondent with the line <) is the one with a positive slope.
Only with that, we conclude that the correct option is B.
y ≤ - (2/3)*x
y < x - 3
If you want to learn more about inequalities:
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