Answer:
(a) 167
(b) 7
(c) 97
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
Then the formula to estimate the sample size is:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
(a)
For 99% confidence interval the critical value of z is:
z = 2.58.
The standard deviation is, 250.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{2.58\times 250}{50}]^{2}\\\\=(12.9)^{2}\\\\=166.41\\\\\approx 167[/tex]
The sample size that should be used is 167.
(b)
Now the standard deviation is, 50.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{2.58\times 50}{50}]^{2}\\\\=(2.58)^{2}\\\\=6.6564\\\\\approx 7[/tex]
The sample size that should be used is 7.
(c)
Now a 95% confidence level is used.
For 95% confidence interval the critical value of z is:
z = 1.96.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times 250}{50}]^{2}\\\\=(9.8)^{2}\\\\=96.04\\\\\approx 97[/tex]
The sample size that should be used is 97.
PLEASE HELP, I DON'T UNDERSTAND THIS! :(
Divide.
Answer:
first answer
(x+1)(x+2)/2
Step-by-step explanation:
flip the second term and multiply
(x²-4x-5)/(x-2) * (x²-4)/(2x-10)
(x-5)(x+1)/(x-2) * (x+2)(x-2)/2(x-5)
(x+1)(x+2)/2
one third divided by eight
Answer:
1/24
Step-by-step explanation:
1/3÷ 8
Copy dot flip
1/3 * 1/8
1/24
Answer:
1/24
Step-by-step explanation:
solve for n+4 + n/6=16
Answer:
n = 10.286 aprox.
Step-by-step explanation:
n+4 + n/6 = 16
n/6 = 16 - 4 - n
n = 6(12-n)
n = 6*12 + 6*-n
n = 72 - 6n
n + 6n = 72
7n = 72
n = 72/7
n = 10.286 aprox.
verify:
10.286 + 4 + (10.286/6) = 16
14.286 + 1.714 = 16
Divide. Give the quotient and remainder.
746+21
Answer:
well you put a plus sign, but im letting you know I did the division.
Step-by-step explanation:
The answer is 35 remainder 11.
Hope this helped
carol had 3/4 yard of ribbon .she wanted decorate two picture frames if she uses half the ribbon on each frame how many feet will she use for one frame
Answer:
1.125 feet
Step-by-step explanation:
1 yard = 3 feet
3/4 yard = 2.25 feet
2.25 feet / 2 = 1.125 feet per frame
i hope this helps!
-TheBusinessMan
Use the number line below, where RS=7y+2, ST=5y+7, and RT=14y−3. a. What is the value of y? b. Find RS, ST, and RT.
Answer:
j
Step-by-step explanation:
graph this function y+6=-3(x+5)
Answer:
Hey there!
It's easier to graph a function in slope intercept form:
y+6=-3(x+5)
y+6=-3x-15
y=-3x-21
So, the slope is -3, and the y intercept is -21.
I'll attach a graph of the function down below
Let me know if this helps :)
Two adjacent sides of a parallelogram are 6mm and 10mm respectively, and they form an angle measuring 60. Find the area of the parallelogram.
Answer:
51.96 mm² approximately
Step-by-step explanation:
the first thing you should know is that the area of a rectangle is base*height sin of (
the included angle i.e
Arectangle= bh sin90° since all angles of a rectangle are equal then the included angle is 90°
Arectangle= bh sin90° since sin90 is 1 we simply use the equation bh because multiplying bh by one is bh. bearing this in mind , the area of the parallelogram can be calculated as:
Aparallelogram= bh sin of sin of the included angle
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866Aparallelogram=51.96 mm² approximately
Find the value of x.
x = [?]
Answer:
25°
Step-by-step explanation:
[tex]55 \degree = \frac{1}{2} \bigg \{(100 \degree + 35 \degree) - x \bigg \} \\ 55 \degree \times 2 = 135 \degree - x \\ 110 \degree = 135 \degree - x \\ x = 135 \degree - 110 \degree \\ \huge \red{ \boxed{ x = 25 \degree}}[/tex]
Find the volume of the solid bounded by x = 0, y = z^2 , z = 0 z = 2-x-y
Answer:
volume = 4/3
Step-by-step explanation:
volume of the solid can be calculated using the given data :
x = 0,
y = z^2,
z = 0, z = 2-x-y
attached below is the detailed solution and a free hand sketch of the boundaries of the solid
What is 1000 words in 5 minutes rate as a unit rate.
Answer:
200 words per minute
Step-by-step explanation:
1000:5
1000/5 reduced will give you your unit rate.
200 words/minute
If 1000 words were read in 5 minutes, each minute would be 1000 divided by 5 which is 200.
Mark this question Select the following statement that describes non-overlapping events.
A. Jon needs to roll an even number to win. When it's his turn, he rolls a two.
B. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
C. Receiving the King of Hearts fulfills Jon's need of getting both a face card and a heart.
D. To win, Jon needs a red card. He receives a Queen of Diamonds.
Answer:
B. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
Step-by-step explanation:
non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa. From the example, Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent. So if Jon got a face card, he would not have eight of clubs
Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
Given,
Statements .
Here,
Non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa.
For instance,
Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent.
So if Jon got a face card, he would not have eight of clubs .
Thus option B is correct statement .
Know more about mutually exclusive events,
https://brainly.com/question/28565577
#SPJ6
Determine the value of x
Answer:
3x+4=72-x (congruent triangle side are equal)
3x+x=72-4
4x=68
X=68/4
therefore,X=17 ans
Answer:
x = 17
Step-by-step explanation:
[tex]\because\triangle IJK \cong \triangle PQR.....(given)\\\therefore \angle I \cong \angle P....(cact)\\\therefore m\angle I = m\angle P\\\therefore 3x+4 = 72-x\\\therefore 3x+x = 72-4\\\therefore 4x = 68\\\therefore x = \frac{68}{4}\\\therefore x = 17[/tex]
An instructor of a biology class believes the average final exam score for his biology class was more than 75. Suppose a sample of 25 was taken and the sample mean he observed was 78.48 and a standard deviation of 5 points. What is the value of the test statistic?Report your answer to 2 decimal places.
Answer:
The value for the test statistics = 3.48
Step-by-step explanation:
Given that:
population mean [tex]\mu[/tex] = 75
sample size n = 25
sample mean [tex]\overline x[/tex]= 78.48
standard deviation = 5
The value for the test statistics can be computed by using the formula:
[tex]z = \dfrac{\overline x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{78.48- 75}{\dfrac{5}{\sqrt{25}}}[/tex]
[tex]z = \dfrac{3.48}{\dfrac{5}{5}}[/tex]
z = 3.48
The value for the test statistics = 3.48
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
x3 sin(x) dx, n = 8
1) The Trapezoidal Rule
2) The Midpoint Rule
3) Simpson's Rule
Answer:
-1392.09-1744.43-1636.41Step-by-step explanation:
using the given integral
calculate: Δx = (12-0) / 8 = 3/2
Xo = 0, f(x) = [tex]x^3sin(x)[/tex]
X1 = 3/2 , X2 = 3, X3 = 9/2, X4 = 6, X5 = 15/2, X6 = 9, X7 = 21/2, X8 = 12
Inputting the given values into the Trapezoid rule, midpoint rule and Simpson's rule to approximate the given integral with the specified value of n = 8
A spherical bowl of radius r cm is a quarter full when 6 liters of water is poured into it.calculate correct to three significant figures, the diameter of the bowl.
Answer:
The bowl's diameter is 35.8 cm
Step-by-step explanation:
Recall that 1 liter = 1000 cubic cm ad have in mind that in order to get a diameter in cm, we would need to write the volume of the bowl in cubic cm.
if 6 liters is 1/4 of the bowl, then 4 times 6 liters must fill the bowl. That is: the volume of the sphere is 24 liters.
24 liters in cubic cm is: 24000 cubic cm
now, we need to use the formula for the volume of a sphere of radius R:
[tex]Vol=\frac{4}{3} \pi\,R^3\\24000=\frac{4}{3} \pi\,R^3\\R^3=\frac{24000\,(3)}{4\,\pi} \\R=\sqrt[3]{\frac{24000\,(3)}{4\,\pi} } \\R\approx 17.894\,\,cm[/tex]
therefore, the diameter of the bowl is twice this radius value:
[tex]Diameter\approx 17.894\,* 2=35.788\,\,cm[/tex]
this value rounded to 3 significant figures is: 35.8 cm
find the first principle f(x)=1/x
Answer:
see explanation
Step-by-step explanation:
Assuming you require the derivative of f(x) from first principles, then
f' (x) = [tex]lim_{h>0}[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{1}{(x+h)}-\frac{1}{x} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-(x+h)}{x(x+h)} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-x-h}{x(x+h)} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{-h}{hx(x+h)}[/tex] ← cancel h on numerator/ denominator
= - [tex]\frac{1}{x^2}[/tex]
What is the equation in point slope form of the line passing through (0,2) and (1,5)
Start by finding the slope of the line.
m = y2 - y1 / x2 - x1
m = 5 - 2/1 - 0 ⇒ 3/1 ⇒ 3.
So the slope of the line is 3.
This can be used with either one of our two points
to write the equation of the line in point-slope form.
So let's go with the point (0, 2).
Point-slope form is written y - y1 = m(x - x1).
Since we are using the point (0, 2), y - y1 would be y - 2.
"m" would be 3 and x1 would be 0.
So we have y - 2 = 3(x - 0).
amanda has 5 pairs of knee high socks and 5 pairs of crew socks in her drawer.If she picks a pair at random, what is the probability that it is a pair of knee high socks.
Answer:
50%
Step-by-step explanation:
There are a total of 5 + 5 = 10 socks
Knee high socks = 5
=> 5/10 = the probability of getting knee high socks
=> 1/2
=> 50%
Answer:
1/2
Step-by-step explanation:
5 pairs of knee high socks and 5 pairs of crew socks= 10 pairs of socks
P ( knee high) = number of knee high/ total
= 5/10 = 1/2
Simplify the expression below.
Answer:
c or b
Step-by-step explanation:
100POINTS!!!!!!!!!!!!!!! Use the table to answer the questions. The values in the table form a(n) ______ sequence. The term values are shown in the ______ row, and the term numbers are shown in the ______ row. This sequence is associated with a(n) ______ function. The domain of the function is the set of time values: __________.
Answer:
arithmeticbottomtoplinear≥ 0Step-by-step explanation:
We observe that the values in the top row are sequential, and that the values in the bottom row have a common difference of 32. That means the sequence is an arithmetic sequence.
__
The values in the table form an arithmetic sequence. The term values are shown in the bottom row, and the term numbers are shown in the top row. This sequence is associated with a linear function. The domain of the function is the set of time values: greater than or equal to zero.
__
Comment on the function
This function seems to be the linear function ...
distance = 32×time - 16
It seems a little odd that the distance associated with time zero is negative. We usually think of distance as a positive value, whereas displacement can be a signed value.
As a rule, time is measured as positive from some reference point (the start of motion, for example). Here, we have no reason to believe that the function is intended to be defined for negative time values.
Answer:
arithmetic
bottom
top
linear
≥ 0
Step-by-step explanation:
iven h (t) = t squared + t + 12 andk (t) = StartRoot t minus 1 EndRoot, evaluate (k compose h) (10)
Answer:
11Step-by-step explanation:
Given h(t) = t²+t+ 12 and k(t) = √t-1, we are to find k(k.h)(10)
k{h(t)} = k{ t²+t+ 12}
Since k(t)= √t-1, we will replace the variable t in the function with t²+t+ 12
k(h(t)) = √{(t²+t+ 12)-1}
k(h(t)) = √t²+t+12-1
k(h(t)) = √t²+t+11
Substituting t = 10 into the resulting function;
k(h(10)) = √(10)²+(10)+11
k(h(10)) = √100+10+11
k(h(10)) = √121
k(h(10))= 11
hence the value of (k compose h) (10) is 11
Planes A and B intersect. Vertical plane B intersections horizontal plane A at line k. Line k contains points Y and Z. Line m intersects line n at point W. Which describes the intersection of line m and line n? point W point X point Y point Z
Answer:
It's point W!!!
Step-by-step explanation:
Have a great day :)
The expression 0.09x+(x−30) models the final price of a bicycle with an instant rebate in a state that charges a sales tax. The tax is on the original price. Which expression represents the amount of tax that is paid on the bicycle?
A. x−30
B. 0.09x
C. 1.09x
D. 0.09x−30
Answer:
B. 0.09x
Step-by-step explanation:
x is the initial price.
0.09x is the 9% sales tax.
-30 is the instant rebate.
Can someone help explain how i would solve this using the pascals triangle? Like how to convert it into (x + 4)^3 = ax^b+cx^d+ex^f+g
Pascal's triangle is a way of organizing the coefficients in the binomial expansion, [tex](a+b)^n[/tex]:
n = 0 => 1
n = 1 => 1 1
n = 2 => 1 2 1
n = 3 => 1 3 3 1
n = 4 => 1 4 6 4 1
and so on, where each row starts and ends with a 1, and the numbers in the middle are obtained by adding together the two numbers directly above and to the left. These coefficients are then mulitplied by descending powers of a and descending powers of b (or vice versa, because the pattern is symmetric), starting with 0 and going up to n.
In this case, we have
[tex](x+4)^3=1\cdot x^3\cdot4^0+3\cdot x^2\cdot4^1+3\cdot x^1\cdot4^2+1\cdot x^0\cdot4^3[/tex]
Notice how the powers of x and 4 always sum to n = 3.
Simplifying, we get
[tex](x+4)^3=x^3+12x^2+48x+64[/tex]
so that
a = 1
b = 3
c = 12
d = 2
e = 48
f = 1
g = 64
Select all the correct answers.
Which expressions are equivalent to the given expression.
y^-8y^3x^0x^-2
Answer:
[tex]x^{-2}y^{-5}[/tex]
Step-by-step explanation:
The options are not given; however, the question can still be solved
Given
[tex]y^{-8}y^3x^0x^-2[/tex]
Required
Simplify
Start by rewriting the expression
[tex]y^{-8} * y^3 * x^0 * x^{-2}[/tex]
Apply the following laws of indices: [tex]a^x * a^y = a^{x+y}[/tex]
This gives:
[tex]y^{-8+3} * x^{0-2}[/tex]
Evaluate the exponents
[tex]y^{-5} * x^{-2}[/tex]
[tex]x^{-2}y^{-5}[/tex]
Hence, [tex]x^{-2}y^{-5}[/tex] is equivalent to [tex]y^{-8}y^3x^0x^-2[/tex]
Answer:
The answer is- (Drumroll)
Step-by-step explanation:
The answers are [tex]x^-2y^-5[/tex], and [tex]1/x^2y^5[/tex]
Points P, Q, and R are shown on the number line. What is the distance between point P and point R?
Answer:
5
Step-by-step explanation:
2.75-(-2.25)=
2.75+2.25=
5
solve the equation 44-x/5 = x/6 - - - -- - -- - - -- - --- - - -- - - -- -
Answer:
120
Step-by-step explanation:
44 - x/5 = x/6 ⇒ add x/5 to both sidesx/6 + x/5 = 44 ⇒ add up fractions by bringing to common denominator11x/30 = 44x = 44*30/11 ⇒ multiply both sides by 30/11x = 4*30x = 120 ⇒ answerA company has 3 mechanics in 8 electricians if an employee is selected at random what is the probability that they are an electrician
Answer:
8/11
Step-by-step explanation:
3 mechanics and 8 electricians = 11 employees total
if one selected at random the possibility of the employee to be an electrician is 8/11
Manolo has a toy in the shape of a triangle pyramid If x=6" y=8" and z=10", what is the volume of the toy
Answer:480
Step-by-step explanation:
To find volume u need to multiply height * width * length