Answer:
63.25 not an integer
Step-by-step explanation:
HCF(a,b)*LCM(a,b)=ab
11*368=64*x
x=11*368/64
x=63.25 not an integer, one of the given numbers must be incorrect
but you may use this method to find it yourself
g A psychic was tested for extrasensory perception (ESP). The psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, or square. Let p represent the probability that the psychic correctly identified the symbols on the cards in a random trial. How large a sample n would you need to estimate p with margin of error 0.01 and 95% confidence?
Answer:
Step-by-step explanation:
Hello!
The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.
Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.
p the probability that the psychic identified the symbol on the cards correctly
You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01
The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:
p' ± [tex]Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]
Where [tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex] is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:
Every time the psychic has to identify a card he can make two choices:
"Success" he identifies the card correctly
"Failure" he does not identify the card correctly
If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25
Let's say, for example, that the card has the star symbol.
The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25
And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75
So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.
The value of Z will be [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
Now using the formula you have to clear the sample size:
[tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]
[tex]\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }[/tex]
[tex](\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}[/tex]
[tex]n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')[/tex]
[tex]n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2[/tex]
[tex]n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203[/tex]
To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.
I hope this helps!
Answer:
The sample size should be 6157
Step-by-step explanation:
Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.
Let us assume that the guess p = 0.25 as the value of p.
α = 1 - C = 1 - 0.95 = 0.05
[tex]\frac{\alpha }{2} =\frac{0.05}{2}=0.025[/tex]
The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore [tex]Z_\frac{\alpha }{2}=Z_{0.025}=1.96[/tex]
To determine the sample size n, we use the formula:
[tex]Z_{0.025}*\sqrt{\frac{p(1-p)}{n} }\leq e\\Substituting:\\1.96*\sqrt{\frac{0.2(1-0.2)}{n} } \leq 0.01\\\sqrt{\frac{0.2(0.8)}{n} }\leq \frac{1}{196}\\\sqrt{0.16} *196 \leq \sqrt{n}\\78.4\leq \sqrt{n}\\ 6146.56\leq n\\n=6157[/tex]
Dora likes to explore. Recently, she explored southeast Australia where she found some very large trees known as Eucalyptus regnans or Mountain Ash. She wondered if they were taller, on average, than the coastal Douglas Firs of her native state of Oregon in the United States, which have an average height of 250 feet in old growth areas. Dora measured the heights of 15 Mountain Ash trees in southeast Australia and found an average height of these trees of 293 feet. Suppose s 25 feet. Assume the heights of the 15 trees in Dora's sample are representative of the heights of all Mountain Ash trees in southeast Australia. The t-statistic for this problem is 6.661. Based on this t-statistic, which of the following is true? Choose the correct answer below.
A. With a p-value of 0.999, there is sufficient evidence to accept the null hypothesis as true.
B. With a p-value less than 0.0001, there is not sufficient evidence to reject the null hypothesis and accept the alternative as true. y
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
D. With a p-value less than 0.0001, there is not sufficient evidence to accept the null hypothesis as true. 0 E. With a p-value of 0.999, there is not sufficient evidence to reject the null hypothesis and accept the alternative as true.
Answer:
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
Step-by-step explanation:
She performed an hypothesis test with the sample of size n=15 that she takes. The t-statistic has a value of 6.661.
The degrees of freedom for this sample size are:
[tex]df=n-1=15-1=14[/tex]
The P-value for a statistic t=6.661 and 14 degrees of freedom is:
[tex]\text{P-value}=P(t>6.661)=0.00001[/tex]
With these P-value we know that the effect is significant and the null hypothesis is rejected. There is enough evidence to support the claim that the mean height of Mountain Ash trees is greater than the coastal Douglas Firs.
3y-y please can you work it out
Isaac is a professional swimmer who trains, in part, by running. She would like to
estimate the average number of miles she runs in each week. For a random sample
of 20 weeks, the mean is
x
= 17.5 miles with standard deviation s = 3.8 miles. Find
a 99% confidence interval for the population mean number of weekly miles Isaac runs.
(a) 15.01 to 19.99 miles (b) 15.07 to 19.93 miles
(c) 15.34 to 19.66 miles (d) 15.31 to 19.69 miles
(e) 15.08 to 19.92 miles
Answer: (b) 15.07 to 19.93 miles
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 3.8
n = number of samples = 20
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 20 - 1 = 19
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.02/2 = 0.005
the area to the right of z0.005 is 0.025 and the area to the left of z0.025 is 1 - 0.005 = 0.995
Looking at the t distribution table,
z = 2.861
Margin of error = 2.861 × 3.8/√20
= 2.43
the lower limit of this confidence interval is
17.5 - 2.43 = 15.07 miles
the upper limit of this confidence interval is
17.5 + 2.43 = 19.93 miles
Translate the phrase into a variable expression. Use the letter d to name the variable. If necessary use the asterisk for multiplication and the slash for division. the product of 40 and distance to the finish line
Answer:
40*d
Step-by-step explanation:
The word product means multiplication, and here it is multiplying 40 and the distance(d).
Answer:
40x5
Step-by-step explanation:
if you’re good with probability in math 30 please help and answer the question below!!
A six-sided number cube has faces with the numbers 1 through 6 marked on it. What is the probability that a number less than 3 will occur on one toss of the number cube?
a) 1/6
b) 1/2
c) 1/3
d) 2/3
Answer: b) 1/3
Step-by-step explanation:
The numbers LESS THAN 3: 1, 2
[tex]\dfrac{\text{Quantity of numbers less than 3}}{Total\ number}\quad =\dfrac{2}{6}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]
Express 1.8meter in seconds given answer in scientific notation
Answer:
Dear user,
Answer to your query is provided below
Scientific notation = 1.8x10^0
Step-by-step explanation:
This is usually expressed simply as 1.8 (Recall that 10^0 = 1.)
1.8×10^0
Please answer this correctly
Answer:
20-39 => 2
40-59 => 1
60-79 => 1
80-99 => 6
100-119 => 5
Answer: 2, 1, 1, 6, 5
Step-by-step explanation:
20-39
2 | 3
3 | 9
40-59
5 | 0
60-79
7 | 5
80-99
8 | 1 2 4
9 | 3 9 9
100-119
10 | 1 1 5 6
11 | 1
Are the two terms on each tile like terms? Sort the tiles into the appropriate categories.
-7y^2and y^2
-4p and p^2
0.5kt and -10kt
6 and 9
5x and 5
3ad and 2bd
Answer:
LIKE TERMS: 6 and 9, 0.5kt and -10kt, and -7y2 and y2. UNLIKE TERMS: 3ad and 2bd, 5x and 5, and the last one is -4p and p2
Step-by-step explanation:
Answer: like terms: 6&9 , 0.5kt&-10kt , -7y^2&y^2
unlike terms 3ad&2bd, 5x&5, -4p&p^2
Step-by-step explanation:
passed
The following is a Markov (migration) matrix for three locations
[1/5 1/5 2/5
2/5 2/5 1/5
2/5 2/5 2/5]
(a) Initially, there are 130 individuals in location 1, 300 in location 2, and 70 in location 3. How many are in each location after two time periods?
(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?
Answer:
(a) [tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
(b) After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
Step-by-step explanation:
The Markov Matrix can be interpret as :
[tex]M = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]
From (a) ; we see that the initial population are as follows: 130 individuals in location 1, 300 in location 2, and 70 in location 3.
Le P represent the Population; So ; [tex]P = \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]
The objective is to find How many are in each location after two time periods;
So, after two time period ; we have the population [tex]P_2 = [M]^2 [P][/tex]
where;
[tex][M]^ 2 = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right] \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]
[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc} 1+2+4 & 1+2+4 &1+2+4 \\ \\ 2+2+4&2+2+4&2+2+4\\ \\ 2+4+4&2+4+4& 2+4+4 \end{array}\right][/tex]
[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right][/tex]
Now; Over to after two time period ; when the population [tex]P_2 = [M]^2 [P][/tex]
[tex]P_2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right] \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]
[tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?
After a long time; that is referring to an infinite time (n)
So; [tex]P_n = [M]^n [P][/tex]
where ;
[tex][M]^n \ can \ be \ [M]^2 , [M]^3 , [M]^4 .... \infty[/tex]
; if we determine the respective values of [tex][M]^2 , [M]^3 , [M]^4 .... \infty[/tex] we will always result to the value for [tex][M]^n[/tex]; Now if [tex][M]^n[/tex] is said to be a positive integer; then :
After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
You are a medical assistant in a pediatrician’s office and one of your responsibilities is evaluating the growth of newborns and infants. Your first patient, a baby girl named Ivy Smith, was 21.5 inches long at 3 months old. At 8 months, you measure her at 24 inches long. For your medical records, all measurements must be given both in inches and in centimeters: 1 inch = 2.54 cm
I need to come up with an equation for this.
Which of the following is the perimeter of a triangle with side lengths of 18 cm, 26 cm, and 32 cm?
Answer:
76 cm
Step-by-step explanation:
To find the perimeter, add up all of the side lengths.
18 cm + 26 cm + 32 cm = 76 cm
I hope this helps :))
Rewrite the expression in the form z^n
[tex] \sqrt[5]{z {}^{4}z {{}^{ \frac{ - 3}{2} } } } [/tex]
Answer:
[tex]z^{0.5}[/tex]
Step-by-step explanation:
So first simplify inside:
[tex]z^4z^{-1.5}=z^{2.5}[/tex]
Now divide that by 5:
[tex]z^{0.5}[/tex]
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico. x = 5.22 5.69 6.25 6.75 7.25 y 17 12 33 37 62What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? a. 95.7% b. 0.7% c. 8.4% d. 91.6% e. 4.3%
Answer:
(B) 0.7%
Step-by-step explanation:
X = Land Elevation (in ,000 feet)
Y = Unidentified Artifacts (in %)
The hypothetical theory says that:
The higher the elevation, the higher the percentage of unidentified artifacts in the location.
To find the percentage of variation in Y that can be explained by variations in X, we find the slope of the graph of X on Y.
Transforming X to thousand feets, we have 5220, 5690, 6250, 6750, 7250. This is in the attachment, plotted against 17, 12, 33, 37 and 62 respectively.
Further calculations, along with the graph, are in the attachment below. The answer therein is (B) 0.7%
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it. Square root of the quantity x + 6 end quantity - 4 = x.
Answer:
x = 2 is the solution of the given equation
Step-by-step explanation:
Step(i):-
Given equation
[tex]\sqrt{x+6-4} = x[/tex]
squaring on both sides , we get
[tex](\sqrt{x+2})^{2} = x^{2}[/tex]
⇒ x + 2 = x²
⇒x² - x -2 =0
Step(ii):-
Given x² - x -2 =0
⇒ x² - 2x + x - 2 =0
⇒ x ( x-2) + 1(x - 2) =0
⇒ (x + 1) ( x-2) =0
⇒ x = -1 and x =2
x = 2 is the solution of the given equation
Verification:-
[tex]\sqrt{x+6-4} = x[/tex]
Put x= 2
[tex]\sqrt{2+6-4} = 2[/tex]
[tex]\sqrt{4} = 2[/tex]
2 = 2
What is the area of the circle?
Answer:
A =50.24 in ^2
Step-by-step explanation:
The diameter is 8 inches
The radius is 1/2 diameter
r = d/2 = 8/2 = 4
The area of the circle is given by
A = pi r^2
A = 3.14 (4)^2
A =50.24 in ^2
Answer:
C. 50.24 in²
Step-by-step explanation:
d= 8 in
r= 8/2= 4 in
Area= πr²= 3.14×4²= 50.24 in²
To solve VX +VX-5 = 5 for x, begin with which of these steps?
Answer:
x = 5/v
Step-by-step explanation:
Solve for x:
2 v x - 5 = 5
Add 5 to both sides:
2 v x = 10
Divide both sides by 2 v:
Answer: x = 5/v
Answer:
I'd say start with "Add 5 to both sides"
Step-by-step explanation:
VX +VX-5 = 5
Add 5 to both sides
2VX=10
Divide both sides by 2
VX=5
Divide both sides by V
X=[tex]\frac{5}{V}[/tex]
Does this graph represent a function? Why or why not?
A
B
C
D
Answer:
B
Step-by-step explanation:
As said in B, use the vertical line test. For any vertical line, does it hit the graph in two points? No. Therefore, the answer is B.
This particular function is f(x)=x^2.
Hope that helped,
-sirswagger21
Answer:
Yes is passes the vertical line test
Step-by-step explanation:
This parabola is a function. it has a one to one correspondence and passes the vertical line test
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions. CHECK ALL THAT APPLY.
Answer:
B, E
Step-by-step explanation:
A line has a negative slope when it decreases going left to right.
As the absolute value of the slope gets larger (-2 to -3 would be 2 to 3), the graph gets steeper (-3 is steeper than -2).
Answer:
B & E
Step-by-step explanation:
URGENT!! EASY IM DUMB MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
18. Using the diagram below as reference, write a paragraph proof to prove that the symmetric property of congruence exists for any two angles. (IMAGE BELOW)
Given: ∠A is congruent to ∠B
Prove: ∠B is congruent to ∠A
Plan: Show that ∠A and ∠B have the same measure, thus ∠B and ∠A have the same measure under symmetry for equality. Conclude with ∠B being congruent to ∠A.
Answer:
Below.
Step-by-step explanation:
18. Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.
The web publisher www.exploreiceland.is (Links to an external site.)Links to an external site. provides information on traveling to Iceland. Access to the website is free but revenues are generated by selling ads that are posted on the website. In the following month, the website has committed to displaying ads to 650,000 viewers, i.e., 650,000 impressions. Based on data from previous months the traffic to the website is estimated to be normally distributed with a mean of 850,000 viewers and a standard deviation of 150,000.
How many impressions should the web publisher have taken on, to be able to guarantee a 95% service level?
Answer:
1096750 impressions
Step-by-step explanation:
Given that :
Mean = 850,000
Standard deviation = 150,000
If we assume that X should be the numbers of impressions created;
Then ;
[tex]X \approx N (\mu , \sigma^2)[/tex]
Now ; representing x as the value for the number of impression needed ; Then ;
[tex]P(X>x) = 0.95[/tex]
[tex]P(\dfrac{X- \mu}{\sigma} > \dfrac{x -850000}{150000}) = 0.95[/tex]
[tex]P(Z> \dfrac{ x -850000}{150000}) = 0.95[/tex]
From normal tables:
[tex]P(Z >1.645) = 0.95[/tex]
[tex]\dfrac{x - 850000}{150000} =1.645[/tex]
(x- 850000) = 1.645(150000)
x - 850000 = 246750
x = 246750 + 850000
x = 1096750 impressions
Set F1 = 5N at 0 degrees, F2= 5N at 90 degrees, F3 = 5N at 270 degrees and run the simulation. Using trigonometry, what net force of F4 in the negative x-direction is necessary to produce an angle of 15 degrees between F2 and F3 and the y-axis? Set F4 to that value and run the simulation. Does the angle formed approximate 15 degrees?
Answer: find the solution in the explanation
Step-by-step explanation:
Let's use resolution of forces by resolving into x - component and y- component.
X - component.
Sum of forces = F1 - F3 - F4cos 15
Sum of forces = 0
5 - 5 - 0.97F4 = 0
- 0.97 F4 = 0
F4 = 0
Y - component
Sum of forces = F2 + F4 sin 15
Sum of forces = 0
5 + 0.26F4 = 0
0.26 F4 = -5
F4 = -5/0.26
F4 = -19.23 N
Simulating F4 back into the equation
Sum of forces = F1 - F3 - F4cos 15
- F4cos Ø = 0
- (-19.23) cos Ø = 0
Cos Ø = 0
Ø = 1
Does the angle formed approximate 15 degrees ? NO
What is the formula to find the area of parallelogram
Step-by-step explanation:
area of parallelogram= height * length of base
In a sample of real estate ads, 62% of homes for sale have garages, 19% have swimming pools, and 15% have both features. What is the probability that a home for sale has a pool, a garage or both? State your answer as a decimal, not as a percent.
Answer:
66%
Step-by-step explanation:
15% of homes have both features.
The percentage of homes that have a pool and no garage is:
Pool only = 19% - 15% = 4%
The percentage of homes that have a garage and no pool is:
Garage only = 62% - 15% = 47%
Therefore, the percentage of homes that have a pool, a garage or both is:
[tex]P = 4\%+47\%+15\%\\P=66\%[/tex]
Please answer this correctly
Answer:
A=450
Step-by-step explanation:
A=a+b
2h=12+33
2·20=450
Answer:
Area=450
Step-by-step explanation:
[tex]a+b/2h[/tex]
Please answer this correctly
Answer:
3 3/5 hours.
Step-by-step explanation:
There are 3 students who logged 1 1/5 so:
[tex]1\frac{1}{5} +1\frac{1}{5} +1\frac{1}{5} =3\frac{3}{5}[/tex]
3 3/5 hours have been logged total by those who logged 1 1/5 hours.
Jamie needs the following items from the hardware store a drill bit that cost 4.99 nails that caused 0.46 and sandpaper that cost 0.89 how much money was spent if the sales tax rate is 6%
Answer: $5.96
Step-by-step explanation:
4.99 + 0.46 + 0.89 is what she paid, not with tax. That equals 6.34.
Applying 6% means we calculate 6% of 6.34 and then subtract it from 6.34. (Or, we can also calculate 100-6%=94% of 6.34). Either way, the answer is 5.9596, or rounded, 5.96.
Hope that helped,
-sirswagger21
If a line crosses the y-axis at (0,1) and has a slope of 4/5 what is the equation of the line
Answer:
y = 4/5x + 1
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
y = 4/5x + 1
Answer:4y-5x=5
Step-by-step explanation:
What is the value of m squared minus 2 m n + n squared for m = negative 2 and n = 4?
-4-2×-2×64
-4+4×64
-4+256
=252
Answer: (36)
hope this helps you have a wonderful day
Step-by-step explanation:
A spinner has 10 equally sized sections, 8 of which are gray and 2 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue ? Write your answer as a fraction in simplest form.
Answer:
4/25
Step-by-step explanation:
The probability the first spin lands on gray is 8/10 = 4/5.
The probability the second spin lands on blue is 2/10 = 1/5.
The probability of both events is 4/5 × 1/5 = 4/25.