find the remainder when 1!+2!+3!...100! Is divided by 15
Answer: 33
======================================================
Explanation:
The exclamation mark means factorial.
Factorial's are operations in which we start with the given number, then count our way down to 1, multiplying along the way.
Examples:
7! = 7*6*5*4*3*2*14! = 4*3*2*1The original number must be a positive whole number (side note: other inputs are possible but we have to involve more complicated math which I'll ignore for this solution).
Let's expand out the first few terms. I'll leave them in factored form and not multiply out the values
1! = 1
2! = 2*1
3! = 3*2*1
4! = 4*3*2*1
5! = 5*4*3*2*1 ... note the 3 and 5 in bold
6! = 6*5*4*3*2*1
7! = 7*6*5*4*3*2*1
This keeps going until we reach 100!
As you can see in the factors above, we have 3 and 5 show up as soon as we reach 5! which means we'll have 3*5 = 15 as a factor of the following items: {5!, 6!, 7!, 8!, ..., 99!, 100!}
Each higher factorial just builds in the last factorial so to speak.
So what this means is that we can write this
15q = 5!+6!+7!+...+99!+100!
where q is some integer. We don't need to worry about what q is
--------------
Therefore,
1!+2!+3!+4!+5!+6!+7!+...+99!+100!
1!+2!+3!+4!+( 5!+6!+7!+...+99!+100! )
1!+2!+3!+4! + 15q
1+2+6+24 + 15q
33+15q
15q+33
--------------
Recall that if we divide integers x and y, then
x/y = q remainder r
x/y = q + r/y
x = yq+r
Where q and r are the quotient and remainder.
Since 1!+2!+3!...100! = 15q+33, we're in the form yq+r showing that r = 33 is the remainder.
Lee is a teacher at a local high school who wanted to assess whether or not dogs physically resemble their owners enough for people to be able to correctly match a dog to their owner better than if just guessing. Lee, who is also a dog owner, showed pictures of two dogs to her class of 16 students. One photo was of the teacher's dog (Yoda) and the other photo was of a dog the teacher had never met. The students were asked to guess which dog was actually the teacher's. If dogs do not physically resemble their owners, the students would get a correct match with probability 0.50. It turned out that 14 of the 16 students correctly picked out the teacher's dog. Does it appear that the population proportion of people who can correctly match a dog to their owner (out of two options) is better than just guessing? The hypotheses to be tested are H0: p = 0.50 versus Ha: p > 0.50, where the parameter p represents the population proportion of all people who can correctly match a dog to their owner (out of two options).
Answer:
Step-by-step explanation:
Given that:
The null hypothesis:
[tex]H_0: p = 0.50[/tex]
The alternative hypothesis:
[tex]H_a : p> 0.50[/tex]
Suppose the number of samples n from the population is 16
The observed value x of the test statistics for testing the hypothesis for this study is x = 14
However, if the null hypothesis is true, then the distribution of the test statistics follows a binomial distribution which is expressed as:
bin(n=16, p = 0.5) distribution
The p-value for this test statistics can be computed as:
p-value = P(X ≥ 14)
p-value = 1 - P (X ≤ 13)
p-value = [tex]1- \sum _{x=0^{x-1}} (n^C \ _x)p^x(q)^{(n-x)}[/tex]
p-value = [tex]1- \sum _{x=0^{x-1}} \dfrac{n!}{r!(n-r)! } p^x(q)^{(n-x)}[/tex]
p-value = 0.00209
I NEED HELP ASP!!!!! 3
Answer: what answer???
Step-by-step explanation: there's no equation
The distribution of IQ scores for students at a large university are known to be approximately normally distributed with σ = 15. One student claims that the mean IQ for all students at the university is 100. A. Assuming that the student’s claim is true (that µ = 100), what is the probability of obtaining a simple random sample of 20 students whose mean IQ score is greater than 108. B. Suppose that you actually did collect a simple random sample of 20 students and found their mean IQ score was greater than 108. Would this give you good evidence to suggest that the mean IQ for all students at the school is greater than 100? Explain.
Answer:
A
The probability of obtaining a simple random sample of 20 students whose mean IQ score is greater than 108 is
[tex]P(\= X > 108) = 0.0084242[/tex]
B
Comparing the p-value obtained with a low level of significance (say ∝= 0.01 ) we see that the p-value is less than ∝ which implies that the null hypothesis is rejected hence we can state that there is sufficient evidence to conclude that the mean IQ for all students at the school is greater than 100
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 15[/tex]
The population mean is [tex]\mu = 100[/tex]
The sample size n = 20
Generally the standard deviation of the sample mean (standard error ) is mathematically represented as
[tex]\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x} = \frac{15 }{\sqrt{20} }[/tex]
=> [tex]\sigma_{\= x} = 3.35[/tex]
Generally the probability of obtaining a simple random sample of 20 students whose mean IQ score is greater than 108 is mathematically represented as
[tex]P(\= X > 108) = P(\frac{\=X - \mu}{\sigma_{\= x} } > \frac{108 - 100}{3.35} )[/tex]
=> [tex]P(\= X > 108) = P(Z > \frac{108 - 100}{3.35} )[/tex]
=> [tex]P(\= X > 108) = P(Z > \frac{108 - 100}{3.35} )[/tex]
=> [tex]P(\= X > 108) = P(Z >2.39 )[/tex]
From the z-table
[tex]P(z > 2.39) = 0.0084242[/tex]
So
[tex]P(\= X > 108) = 0.0084242[/tex]
The null hypothesis is [tex]H_o : \mu = 100[/tex]
The alternative hypothesis is [tex]H_a : \mu > 100[/tex]
The sample mean is [tex]\= x = 108[/tex]
Generally the test statistics is = 2.39
Generally the p-value is equal to 0.0084242
Now comparing the p-value with a low level of significance (say ∝= 0.01 ) we see that the p-value is less than ∝ which implies that the null hypothesis is rejected and we can conclude that there is sufficient evidence to conclude that the mean IQ for all students at the school is greater than 100
Three kids are playing tennis at the same tennis courts. Mark plays every fourth day, David plays every seventh day, and Bryan plays every sixth day. All of them played at the tennis court today, Wednesday, July 18th. When will all three of them play again on the same day?
Answer:
They will play again together in 84 days, on October 10, only if it is the year 2029.
Step-by-step explanation:
I used the mode of the least common denominator. Hope this helps!
What is the base 10 representation of 11102?
Answer:
1.1102 * 10^4
Step-by-step explanation:
11102
= 1.1102 * 10^4
Answer:
14
Step-by-step explanation:
The base two number one one one zero is equal to one times eight, plus one times four, plus one times two, plus zero times one, which simplifies to fourteen.
The graph shows the cost for a crate of the flowers Molly is planting in her garden.
What is the cost of 4 crates of flowers?
Answer:
Little late but its 10
Step-by-step explanation:
Answer:
3 weeks Late my bad, but why let the question go to waste, the answer is 10
Let P be a point not on line k Let p be the image of P after a reflection about the line K and let A any point on line k. Determine whether each statement below is true for all points P true for some points P or not true for any points P
Answer: true false some true
Step-by-step explanation:
The johnsons just moved into their new home and are selecting furniture for the family room
Write a slop-intercept equation for a line that passes through (4,0) and (-5,6)
Answer: -2/3
Step-by-step explanation:
y2 - y1/ x2 - x1
6-0/-5-5
-6/9
-2/3
Answer:
y=-2/3x+10 1/3
Step-by-step explanation:
y=mx+b (m = slope)
(Equation) y2-y1/x2-x1
= 6-0/-5-4
= -6/9
= -2/3
y-y1 = m(x-x1)
y-6 = -2/3 +5
y-6 = 4 1/3
y = 10 1/3
In the early part of this century, the drug company, Merck, produced a powerful non- steroidal anti-inflammatory drug (NSAID) known as Vioxx. Vioxx was very effective in reducing pain due to arthritis and, unlike some NSAIDs, did not cause digestive system or liver problems. However, a couple of years after Vioxx was introduced to the market, some independent studies showed a possible connection between NSAIDs and increased risk of heart attack in the elderly. Since many arthritis sufferers (and many Vioxx users) are elderly, these studies were a cause of concern.
To test whether this was the case for Vioxx, Merck conducted a large-scale study in which 3025 randomly selected elderly Vioxx users were put on the drug while 2875 were given a placebo. The volunteers were monitored for 18 months. During this time, 334 of the Vioxx group members and 272 members of the placebo group suffered heart attacks.
Required:
a. Compute by hand a 90% confidence interval for the difference in heart attack risk between Vioxx users and non-Vioxx users (the placebo group.)
b. Interpret the interval. What action does it suggest should be taken regarding Vioxx?
Answer:
a
[tex]0.0028 < p_1 - p_2 < 0.0288[/tex]
b
The interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack and the non-Vioxx users (the placebo group ) who suffered from heart attack lie within the interval
The use of Vioxx drug should be stopped
Step-by-step explanation:
From the question we are told that
The sample size for Vioxx users is [tex]n_1 = 3025[/tex]
The second sample size for placebo is [tex]n_2 = 2875[/tex]
The number of Vioxx users that suffered heart attack is [tex]k = 334[/tex]
The number of non-Vioxx users that suffered heart attack is [tex]g = 272[/tex]
Generally the sample proportion for Vioxx users is mathematically represented as
[tex]\r p_1 = \frac{k}{n_1}[/tex]
=> [tex]\r p_1 = \frac{334}{3025}[/tex]
=> [tex]\r p_1 = 0.11041 [/tex]
Generally the sample proportion for placebo users is mathematically represented as
[tex]\r p_2 = \frac{g}{n_2}[/tex]
=> [tex]\r p_2 = \frac{272}{2875}[/tex]
=> [tex]\r p_2 = 0.09461 [/tex]
Generally the confidence level is 90% , then the level of significance is [tex]\alpha = (100-90)\%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }[/tex]
=> [tex]SE = \sqrt{\frac{0.11041 (1- 0.11041)}{3025} + \frac{0.09461 (1-0.09461)}{2875} }[/tex]
=> [tex]SE = 0.0079[/tex]
Generally the margin of error is mathematically represented as
[tex] E= Z_{\frac{\alpha }{2} } * SE[/tex]
=> [tex] E= 1.645 * 0.0079[/tex]
=> [tex] E= 0.013[/tex]
Generally the 90% confidence interval is mathematically represented as
[tex]0.11041 - 0.09461- 0.013 < p_1 - p_2 < 0.11041 - 0.09461+ 0.013 [/tex]
=> [tex]0.0028 < p_1 - p_2 < 0.0288[/tex]
The interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack and the non-Vioxx users (the placebo group ) lie within the interval
Looking at the interval we see that proportion of Vioxx users who suffered is more compared to non-Vioxx users (the placebo group )[i.e the both limit of the interval is positive ] hence the use of Vioxx drug should be stopped
can someone make this for me with a compass but just different colors please
Answer:
so basically you want a drawing identical to that just with different colours?
Solve for x
a)41
b)17
c)19
d)18
Answer:
18
Step-by-step explanation:
3x+1=55
(alternate angle theorem)
3x=55-1
3x=54
x=54/3
x=18
Answer:
d
Step-by-step explanation:
3x + 1 and 55 are alternate angles and congruent, thus
3x + 1 = 55 ( subtract 1 from both sides )
3x = 54 ( divide both sides by 3 )
x = 18 → d
Rick has a magnet shaped like a right rectangular prism which is 8 cm long, 4 cm wide, and 2 cm high. What is the volume in cubic cm?
Answer:
the answer is 64 because you need to multiply all of them together to get the cubic volume. first you multiply 8 x 4 and that leaves you with 32. 32 x 2 is 64 and there are no numbers left to that means 64 is the cubic volume.
Jen and Nikki are making bracelets to sell at the local market. They determined that each bracelet would have eight beads and two charms. Create 5 ordered pairs (charms, beads) that could be used to graph this relationship
Answer:
Step-by-step explanation:
Ordered Pair1: (8,2)
2:(8*2,2*2)=(16,4)
3:(8*3,2*3)=(24,6)
4: (8*4,2*4)=(32,8)
5: (8*5,2*5)=(40,10)
Englis
Which sets of values belong to the domain and range of a relation?
output values
Domain
Range
values for the independent variable
input values
values for the dependent variable
Answer:
See below
Step-by-step explanation:
Domain ⇔ Input values ⇔ Values for the independent variableRange ⇔ Output values ⇔ Values for the dependent variableWhat is the height of the stairs
Answer:
12 in
Step-by-step explanation:
15^2 = 9^2 + h^2
225-81 =h^2
h^2 = 144
h = 12 inches
Find the midpoint M of the line segment joining the points P= (-7,-8) and Q = (3,2)
Answer:
(-2, -3)
Step-by-step explanation:
To solve this problem, we use the midpoint formula.
M = [tex]\frac{x1 + x2}{2} , \frac{y1+ y2}{2}[/tex]
Plug your coordinates in:
M = [tex]\frac{-7 + 3}{2} , \frac{-8 + 2}{2}[/tex]
Simplify:
M = [tex]\frac{-4}{2} , \frac{-6}{2}[/tex]
M = (-2,-3)
Write this equation in slope intercept form. -x + y = -10
Answer:
y=x-10
Step-by-step explanation:
Refer to the table on the previous slide to help answer
the questions.
What is the proportional relationship represented by the
table
Answer:
It has a steady line the entire way
Step-by-step explanation:
What is the difference in the range of temperatures recorded last year and the range of temperatures recorded two years ago ? In degrees
What was the modal temperature last year ?
What was the median temperature 2 years ago ?
explain how crime contributes to social injustices
The difference between the range will be 5.
What is the range?When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.
Given that last year, the highest value of temperature is 29 and the lowest is 6. After two years the maximum temperature is 25 and the lowest is 7.
The range difference will be calculated as,
Range = ( 29 - 6 ) - ( 25 - 7 )
Range = ( 23 - 18 )
Range = 5
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Susan runs 2 1/2 miles in 0.25 of an hour.what is the unit rate in miles per hour?
Exploring the Columbian Exchange
What do we know about the discovery of the New
World? List as many facts as you can
Answer:
Christopher Columbus introduced horses, sugar plants, and disease to the New World, while facilitating the introduction of New World commodities like sugar, tobacco, chocolate, and potatoes to the Old World. The process by which commodities, people, and diseases crossed the Atlantic is known as the Columbian Exchange.
(-9)^-2 * (-9)^0 ÷ (-9)^1
Answer:
Your answer is: 1/80 or -1/729
Simplify the expression.
↓
Step-by-step explanation:
Hope this helped : )
What is the measurement of ABC?
D. 1180
A. 28°
ОО
E. 208°
B. 62°
O c. 90°
Answer:
118°
Step-by-step explanation:
Line b is a perpendicular bisector so 90°+28°=118°
What is 20x - 4x + x?
Answer:
17x
Step-by-step explanation:
Combine terms with like variables. Like terms are terms with the same amount of variables as well as the same variable. Combine their coefficients:
20x - 4x = 16x
16x + (1)x = 17x
17x is your answer.
~
Answer:
17x
Step-by-step explanation:
20x-4x = 16x
16x + x = 17x
17x
Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this problem, think of Sandy’s wake as a line. m∠1 = (2x + 10)° and m∠2 = (4y − 30)°. Find x and y
Angle 2 is the same as the given angle of 70 degrees so we can solve for y:
4y-30 = 70
Add 30 to both sides:
4y = 100
Divide both sides by 4:
Y = 25
Angle 1 and angle two are supplementary angles and when added together need to equal 180:
We know angle 2 = 70, so angle 1 must equal 180-70 = 110
2x + 10 = 110
Subtract 10 from both sides:
2x = 100
Divide both sides by 2:
X = 50
The answer is:
X = 50, y = 25
If you look at the figure, the angle marked red is equal to 70° because vertical angles are equal. So, that also means that the opposite angle 2 is also 70°. So, the first equation is:
70 = 5x + y
Next, the green angle as marked is equal to
Green angle = 180 - 70 = 110
Being vertical angles, angle 1 is then equal to 110°. So,the second equation is
110 = 5x + 3y
Subtract the two equations:
5x + y = 70
- 5x + 3y = 110
________________
-3y = -40
y = -40/-3 = 13.33°
Substituting y to either one of the equations,
5x + 13.33 = 70
Solving for x,
x = 11.33°
Question 19 (5 points)
1199
100"
12
88
15
116"
18
Determine the value of x.
OA) 59°
B) 63°
OC) 90°
OD 117°
Answer:
The value of x is 63° ⇒ B
Step-by-step explanation:
The rule for finding the sum of the interior angles of a polygon with n sides is S = (n - 2) × 180°
In the given figure
There is a polygon with 5 sides
∵ n = 5
∴ S = (5 - 2) × 180°
∴ S = 3 × 180°
∴ S = 540°
→ We have the measure of 4 angles of them
∵ The sum of the 4 given angles = 119° + 100° + 88° + 116°
∴ The sum of the 4 given angles = 423°
→ To find the 5th angle subtract 423° from 540°
∵ The measure of the fifth angle = 540° - 423°
∴ The measure of the fifth angle = 117°
→ x and 117° are linear pair angles, then their sum is 180°
∵ x + 117° = 180° ⇒ linear pair angles
→ Subtract 117 from both sides to find x
∴ x + 117 - 117 = 180 - 117
∴ x = 63°
A chord in a circle is 16cm long and its perpendicular distance from the centre is 6cm. what is the radius of the circle
Answer:
10 cm
Step-by-step explanation:
the perpendicular from centre bisect the chord in equal halves. hence you can use pythagoras therom as
r^2 = 6^2 + 8^2
Lily uses the function f(x)+ 23,000(1.021) X( power) to model the future annual population growth of the city where she lives, Which of the following respresents Lily's estimate population in 8 years
a 3,395
b 23,483
c 27,160
d 187,864
Answer: The answer is B, 23,483
Step-by-step explanation:
If you multiply 23,000 times 1.021 you get 23,483. Your welcome
The Lily's estimate population in 8 years is 187864.
It is required to find the population in 8 years.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
The function f(x)= 23,000(1.021) X( power) to model the future annual population growth of the city.
According to given question we have,
To put x= 8 years
Lily's estimate population in 8 years are
f(x)= 23,000*(1.021) *8
f(x)= 187864
Therefore, the Lily's estimate population in 8 years is 187864.
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