Answer:
0.0004% probability that the student answers at least 9 questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he does not. All questions are answered independently. This means that we use the binomial distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this question, we have that:
[tex]n = 10, p = 0.2[/tex]
What is the probability that the student answers at least 9 questions correctly
[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} = 0.000004[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0 [/tex]
[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.000004 + 0 = 0.000004[/tex]
0.0004% probability that the student answers at least 9 questions correctly
A Pew Research study of 4726 randomly selected U.S. adults regarding scientific human enhancements, found that approximately 69% of the sample stated that they were worried about brain chip implants being used for improving cognitive abilities.
Required:
a. Show that the necessary conditions (Randomization Condition, 10% Condition, Sample Size Condition) are satisfied to construct a confidence interval. Briefly explain how each condition is satisfied.
b. Find the 90% confidence interval for the proportion of all U.S. adults that are worried about brain chip implants used for improving cognitive abilities.
(To show your work: Write down what values you are entering into the confidence interval calculator.)
c. Briefly describe the meaning of your interval from part (b).
Answer:
a)Randomization condition: Satisfied, as the subjects were randomly selected.
10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).
Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.
b) The 90% confidence interval for the population proportion is (0.68, 0.70).
Step-by-step explanation:
a) Evaluating the necessary conditions:
Randomization condition: Satisfied, as the subjects were randomly selected.
10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).
Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.
[tex]n(1-p)=4,726\cdot (1-0.69)=4,726\cdot 0.31=1,465>10[/tex]
b) We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.69.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.69*0.31}{4726}}\\\\\\ \sigma_p=\sqrt{0.000045}=0.007[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.007=0.01[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.69-0.01=0.68\\\\UL=p+z \cdot \sigma_p = 0.69+0.011=0.70[/tex]
The 90% confidence interval for the population proportion is (0.68, 0.70).
Explain why the sum of the angle measures in any
triangle is 180º.
Answer: I think In short, the interior angles are all the angles within the bounds of the triangle. ... If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring exterior angle, you always get 180—a straight line, A square has 4 90 degree angles so it adds to 360, think about how triangles having half the area of a square, just like how 180 is half of 360
hope this helped
Please answer this correctly
Answer:
5
Step-by-step explanation:
There are two ways you can solve this. First is to just count all the numbers in the list given that are within the range 15-19. This is an inclusive range meaning the numbers 15 and 19 are a part of it. The second method is to count how many numbers are in the list given and count all the numbers that have already been put on the table. There are 19 total numbers, and 14 have already been counted. If you subtract you are left with 5 numbers that are within the range. So the answer is 5.
Explanation:
One method is to count all of the values that are between 15 and 19. Those values are highlighted in the diagram below. There are 5 values marked.
An alternative method is to note there are 19 values total. The items in the given table add to 5+2+1+2+4 = 14, so there must be 19-14 = 5 items missing to completely fill out the table.
What is the value of Y ? I’ll give you a brainslist !!!
[tex]answer \\ = 5 \sqrt{3} \\ please \: see \: the \: attached \: picture \: for \: \: full \: solution \\ hope \: it \: helps[/tex]
Answer:
[tex]5 \sqrt{3} [/tex]
First answer is correct
Step-by-step explanation:
[tex] \frac{5}{x} = \cos(60) \\ \frac{5}{x} = \frac{1}{2} \\ x = 10 \\ \frac{y}{x} = \sin(60 ) \\ \frac{y}{10} = \frac{ \sqrt{3} }{2} \\ 2y = 10 \sqrt{3} \\ y = \frac{10 \sqrt{3} }{2} \\ y = 5 \sqrt{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢
580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of
GH¢2,358.60, how much was his total investment?
Answer:
GH¢. 18098.46
Step-by-step explanation:
Let the first investment giving 12% interest per annum be Bank A
Let the 2nd investment giving 10% per annum be bank B
Let the first amount invested be
GH¢. X and let the second amount invested be GH¢. X + 580
Thus; In bank A;
Principal amount in first = GH¢. x
rate = 12 %
time = 1 year
Formula for simple interest = PRT/100
Where P is principal, R is rate and T is time.
So, interest in his investment = 12X/100 = 0.12X
while in bank B;
principal amount = GH¢. X + 580
rate = 14%
time = 1 yr
So, interest in his investment = [(X + 580) × 14]/100
= 0.14(X + 580)
So, total accumulated interest is;
0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2
Now, we are given accumulated interest = GH¢. 2,358.60
Thus;
2358.60 = (0.26X + 81.2)
2358.6 - 81.2 = 0.26X
X = 2277.4/0.26
X = 8759.23
So,
first amount invested = GH¢. 8759.23
Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23
Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50 pounds each, and the small boxes weigh 35 pounds each. There are 115 boxes in all. If the truck is carrying a total of 5000 pounds in boxes, how many of each type of box is it carrying?
Answer:
Step-by-step explanation:
First, "boxes of two sizes" means we can assign variables:
Let x = number of large boxes
y = number of small boxes
"There are 115 boxes in all" means x + y = 115 [eq1]
Now, the pounds for each kind of box is:
(pounds per box)*(number of boxes)
So,
pounds for large boxes + pounds for small boxes = 4125 pounds
"the truck is carrying a total of 4125 pounds in boxes"
(50)*(x) + (25)*(y) = 4125 [eq2]
It is important to find two equations so we can solve for two variables.
Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2. Let's solve for x:
x = 115 - y [from eq1]
50(115-y) + 25y = 4125 [from eq2]
5750 - 50y + 25y = 4125 [distribute]
5750 - 25y = 4125
-25y = -1625
y = 65 [divide both sides by (-25)]
There are 65 small boxes.
Put that value into either equation (now, which is easier?) to solve for x:
x = 115 - y
x = 115 - 65
x = 50
There are 50 large boxes.
Check (very important):
Is 50+65 = 115 ? [eq1]
115 = 115 ?yes
Is 50(50) + 25(65) = 4125 ?
2500 + 1625 = 4125 ?
4125 = 4125 ? ye
Sonya has two red marbles and three yellow marbles. She chooses three marbles at random. What is the probability that she has at least one marble of each color?
Answer:
90% probability that she has at least one marble of each color
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the probability that she has at least one marble of each color?
Desired outcomes:
Two red(from a set of 2) and one yellow(from a set of 3)
Or
One red(from a set of 2) and two yellows(from a set of 3).
So
[tex]D = C_{2,2}*C_{3,1} + C_{2,1}*C_{3,2} = \frac{2!}{2!(2-2)!}*\frac{3!}{1!(3-1)!} + \frac{2!}{1!(2-1)!}*\frac{3!}{2!(3-2)!} = 3 + 6 = 9[/tex]
Total outcomes:
Three marbles, from a set of 3 + 2 = 5. So
[tex]T = C_{5,3} = \frac{5!}{3!(5-3)!} = 10[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{9}{10} = 0.9[/tex]
90% probability that she has at least one marble of each color
WILL GIVE BRAINLIEST HELP ASAP
Answer:
x = -3
Step-by-step explanation:
1.8 - 3.7x = -4.2x +.3
Add 4.2x to each side
1.8 - 3.7x +4.2x= -4.2x+4.2x +.3
1.8 +.5x = .3
Subtract 1.8 from each side
1.8 +.5x -1.8 = .3 -1.8
.5x = -1.5
Divide each side by .5
.5x/.5 = -1.5/.5
x = -3
Answer:
x=-3
Step-by-step explanation:
In order to solve this equation, we have to isolate x. Perform the opposite of what is being done to the equation. Remember to perform everything to both sides.
1.8-3.7x= -4.2x +0.3
3.7x is being subtracted from 1.8 (-3.7x). The inverse operation of subtraction is addition. Add 3.7x to both sides.
1.8-3.7x+3.7x= -4.2x+3.7x+0.3
1.8= -4.2x+3.7x+0.3
1.8= -0.5x+0.3
0.3 is being added to -0.5x. The opposite of addition is subtraction. Subtract 0.3 from both sides.
1.8-0.3= -0.5x+0.3-0.3
1.8-0.3 = -0.5x
1.5=-0.5x
-0.5 and x are being multiplied (-0.5*x= -0.5x). The opposite of multiplication is division. Divide both sides by -0.5.
1.5/-0.5=-0.5x/-0.5
1.5/-0.5=x
-3=x
Solve sin2x=-1/2 on the interval 0≤ angle≤360°
Answer:
x=135
Step-by-step explanation:
We know that sin(270) = -1/2
So 2x = 270
x = 135
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
-1, 1
13, 15
Step-by-step explanation:
x and x+2 are the integers
x*(x+2)= 7(x+x+2) -1x²+2x= 14x+14-1x² - 12x -13= 0Roots of the quadratic equation are: -1 and 13.
So the integers pairs are: -1, 1 and 13, 15
A and b are similar shapes. B is an enlargement of a with scale factor 1.5 Work out the value of x, h and w
Answer:
x = 54°
h = 7.5cm
w= 6cm
Step-by-step explanation:
Find attached the diagrams as found at Maths made easy.
Similar shapes have same shapes but different sizes.
When two shapes are similar, the ratios of the lengths of their corresponding sides are equal.
B is an enlargement of A with scale factor 1.5. That is, each of the sides of B = 1.5 of each side of A
To determine the value of x, h and w, let's look at the relationship of A and B.
h = 1.5 × 5cm
h = 7.5cm
9cm = 1.5 × w
w = 9cm/1.5
w= 6cm
Since the angles do not change when a shape is enlarged, the value of x = 54°
x = 54°
True or False? A prism must have a triangular or rectangular base.
Answer: No
Step-by-step explanation:
Simple! No. There can be hexagonal, octagonal, and other types of prisms that do not have a triangular/rectangular base.
Hope that helped,
-sirswagger21
Please answer this correctly
Answer:
1.2 km
Step-by-step explanation:
The first thing that we should go over is the formula for the area of a trapezoid.
Recall that it is [tex]A= \frac{b_1 +b_2}{2} *h[/tex]
From this image, we have the following information
[tex]b_1=2.5\\\\b_2=1.5\\\\A=2.4[/tex]
Now, we can plug this information into our formula and then solve for h.
[tex]2.4=\frac{2.5+1.5}{2} *h\\\\2.4=\frac{4}{2} *h\\\\2.4=2h\\\\h=1.2[/tex]
Another method that can be employed is to use the pythagorean theorem.
A trapezoid can be be broken into a rectangle and two triangles.
If we look at the difference in the sizes of the bases, the bottom base is 1 km larger. This means that the base of each triangle would be 0.5 km long.
As we have two side lengths of the triangle, we can now use the Pythagorean theorem to find the third side, which is h.
[tex](1.3)^2=h^2+(0.5)^2\\\\h^2=1.69-0.25\\\\h=\sqrt{1.44} \\\\h=1.2[/tex]
Answer:
h=1.2 km
Step-by-step explanation:
This is the formula of a Trapezium
A=[tex]\frac{h(a+b)}{2}[/tex]
[tex]2.4=\frac{(2.5+1.5)h}{2}\\ 2.4=\frac{4h}{2}\\ 2.4*2=4h\\4.8=4h\\h=1.2[/tex]
NEED GEOMETRY HELP ASAP
Answer:
HJ > KP
Step-by-step explanation:
Form the figure attached,
Two triangles PKL and JGH have been given with HG ≅ KL and PL ≅ GJ
m∠HGJ = 90°
m∠KLP = 85°
Since m∠HGJ > m∠PLK
Therefore, measure of opposite sides of these angles have the same relation.
HJ > KP
What is the missing side length?
Answer:
8 yds
Step-by-step explanation:
The sides have to have the same length
14 yd = 6yd + ?
Subtract 6 from each side
14-6 = 8
8 yds
Determine whether the given value of the variable is a solution of the inequality.
Answer:
Yes, [tex]\frac{3}{4}[/tex] is a solution of the inequality.
Step-by-step explanation:
Solution of an inequality is given by the values of the variable t ≥ [tex]\frac{2}{3}[/tex]
Or t ≥ 0.67
If a solution of this inequality is t = [tex]\frac{3}{4}[/tex]
Or t = 0.75
Since, on a number line 0.75 > 0.67
Therefore, [tex]\frac{3}{4}[/tex] will be a solution of the inequality.
The circular area covered by a cell phone tower can be represented by the expression 225π miles2. What is the approximate length of the diameter of this circular area
Answer:
The length of the diameter of this circular area is of 30 miles.
Step-by-step explanation:
The area of a circular region can be represented by the following equation:
[tex]A = \pi r^{2}[/tex]
In which r is the radius. The diameter is twice the radius.
In this question:
[tex]A = 225\pi[/tex]
So
[tex]A = \pi r^{2}[/tex]
[tex]225\pi = \pi r^{2}[/tex]
[tex]r^{2} = 225[/tex]
[tex]r = \pm \sqrt{225}[/tex]
The radius is a positive measure, so
[tex]r = 15[/tex]
Area in squared miles, so the radius in miles.
What is the approximate length of the diameter of this circular area
D = 2r = 2*15 = 30 miles
The length of the diameter of this circular area is of 30 miles.
If the point (7,6) lies on the graph of y = (x - 5)2 + k, where k is some constant, which other point must also
lie on the same graph?
Answer:
k = -4 (0, -14) also lies on the graph
Step-by-step explanation:
6 = (7 - 2)2 + k
6 = 10 + k
-4 = k
y = (0 - 5)2 - 4, y = -14
55c + 13 < 75c + 39
Solve for c
Answer:
c>-13/10
Step-by-step explanation:
55c+13<75c+39
55c+13-75c<39
-20c+13<39
-20c<39-13
-20c<26
c>26/-20
c>-13/10
7. Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first
three terms is 26.
Answer:
Step-by-step explanation:
Let the first term is n, then the second term must be an where a is a common ratio, and the third term is a^2 n
so, n + an = 24
n + an + a^2 n = 26
solve for a, then solve for n
What’s the correct answer for this?
Answer:
The capital B refers to the base of the area
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The capital B means the area of the base
The table represents a linear equation.
Which equation correctly uses point (-2, -6) to write the
equation of this line in point-slope form?
х
-4
-2
6
10
y
-11
-6
14
24
y-6 = {(x - 2)
• y-6 = (x - 2)
y +6 = } (x + 2)
y+6= {(x + 2)
Answer:
see below
Step-by-step explanation:
Considering the last two table entries, we can find the slope of the line to be ...
Δy/Δx = (24 -14)/(10 -6) = 10/4 = 5/2
The point-slope form of the equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
For (h, k) = (-2, -6) and m = 5/2, this is ...
y -(-6) = 5/2(x -(-2))
y +6 = 5/2(x +2) . . . . . matches the last choice
Answer:
d is the right choice
Step-by-step explanation:
Hypothesis Test for Two Populations including:t-Test for μ1-μ1t-Test for μdF-Test forWe are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the followingStore A Store BnA=21 nB=16SA=28.284 SB=20Which of the following is critical values of F at 95% confidence?A. a and dB. 2.57C. 0.3891D. 0.3623E. 2.76
Answer:
The critical values of F at 95% confidence are 0.359 and 2.788.
Step-by-step explanation:
We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:
Store A Store B
nA = 21 nB = 16
SA = 28.284 SB = 20
And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.
AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.
The test statistics for F-test is = [tex]\frac{S_A^{2} }{S_B^{2} } \times \frac{\sigma_B^{2} }{\sigma_A^{2} }[/tex] ~ [tex]F__n_A_-_1,_ n_B_-_1[/tex]
where, [tex]S_A[/tex] and [tex]S_B[/tex] are sample standard deviations.
Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;
2.788 for right-part and 0.359 for the left-part.
Someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi. We think the actual amount is lower than that and want to run the test at an alpha level of 5%. What would our sample size need to be if we want to reject the null hypothesis if the sample mean is at or below 1,997.2956?
Answer:
The sample size must be greater than 37 if we want to reject the null hypothesis.
Step-by-step explanation:
We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.
Also, we are given a level of significance of 5%.
Let [tex]\mu[/tex] = mean breaking strength of their climbing rope
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2,000 psi {means that the mean breaking strength of their climbing rope is 2,000 psi}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 2,000 psi {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}
Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = ample mean strength = 1,997.2956 psi
[tex]\sigma[/tex] = population standard devaition = 10 psi
n = sample size
Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.
So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.
SO, T.S. < -1.645 {then reject null hypothesis}
[tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645[/tex]
[tex]\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645[/tex]
[tex](\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645[/tex]
[tex]-0.27044 \times \sqrt{n}< -1.645[/tex]
[tex]\sqrt{n}> \frac{-1.645}{-0.27044}[/tex]
[tex]\sqrt{n}>6.083[/tex]
n > 36.99 ≈ 37.
SO, the sample size must be greater than 37 if we want to reject the null hypothesis.
Simplify -2(-5) - 7 + 1(-3)
Answer:
Step-by-step explanation:
BRUH YOU STUPID
Answer:
0
[tex] \\ solution \\ - 2( -5) - 7 + 1( - 3) \\ = 10 - 7 + ( - 3) \\ = 10 - 7 - 3 \\ = 3 - 3 \\ = 0 \\ hop \: it \: helps...[/tex]
During the late 1980s and the early 1990s the Pepsi Challenge was in full swing. During the challenge, participants were asked to taste cola from both Coke and Pepsi. Once they had tasted both drinks, the participants were asked to report which was better tasting. The results indicated that participants found Pepsi products to be better tasting. What is the dependent variable in this study? coruse hero psyc 255
Answer:
Taste
Step-by-step explanation:
In the challenge, participants were asked to taste cola from both Coke and Pepsi. They were to give a report on which of the two drinks tasted better.
The taste reported by the participants is dependent on the type of cola taken (either Coke or Pepsi).
Therefore, the taste is the dependent variable while the types of cola are the independent variables.
Each roll of tape is 30.5 feet long. A box contains 454 rolls of tape. How many yards are there in total
Answer:
Answer: 4615.66667
Steps: 1 foot=0.33333
total feets=30.5×454=13847
13847 feets=46.1566667 yards
What is the graph of 3x+5y=15
Answer: y= -15 - 3x/5 is the answer.
Step-by-step explanation:
Answer:
The second graph
Step-by-step explanation:
A magazine asks its readers to complete a survey on their favorite music and tv celebrities. Classify this sample
Answer:
All the elements in the sample share a common characteristic. All of them read the magazine, so we may have a biased sample. And we also have the bias of the fact that only the volunteers will respond to this survey, so this is a biased sample.
This type of sample is usually called convenience sampling, where the elements in the sample are the most readily available (and what is most readily available for a magazine than its own readers?)
Then the type of sample is a convenience sample and a biased sample.
Write the number that is ten thousand more than
1,853,604,297:
Answer:
The answer would be 1,853,614,297