You can get the tens digit of any number n by computing the quotient
(n (mod 100)) / 10
and ignoring the remainder.
Taking the given sum (mod 100) gives
7! + 8! + … + 2006! ≡ 7! + 8! + 9! (mod 100)
since the last 1997 terms (i.e. 10! up to 2006!) in the sum are multiples of 100. That is,
• every term beyond 100! is obviously a multiple of 100
• every term beyond 25! contains a factor of both 4 and 25
• every term beyond 10! contains two factors each of both 2 and 5 (i.e. every factorial term contains 4, 5, and 10)
The remaining sum is easy to compute by hand:
7! + 8! + 9! = 7! (1 + 8 + 8 × 9) = 5040 × 81 = 408,240
so the tens digit is 4.
if f(×) = [tex] \frac{1}{ \sqrt{x - 1} } [/tex]
then find [tex] \frac{f(x) - f(2)}{x - 2} [/tex]
9514 1404 393
Answer:
(1 -x +√(x -1))/(x² -3x +2)
Step-by-step explanation:
Fill in the given function definition and simplify.
[tex]\dfrac{f(x)-f(2)}{x-2}=\dfrac{\dfrac{1}{\sqrt{x-1}}-\dfrac{1}{\sqrt{2-1}}}{x-2}=\dfrac{1-\sqrt{x-1}}{(x-2)\sqrt{x-1}}\\\\=\dfrac{\sqrt{x-1}-x+1}{(x-2)(x-1)}=\boxed{\dfrac{\sqrt{x-1}-x+1}{x^2-3x+2}}[/tex]
the cost price of an articles was 4000 find the marked price of the article so that there will be profit of 20%after allowing a discount of 20%
Answer:
The marked price of the article was $ 6000.
Step-by-step explanation:
Since the cost price of an article was $ 4000, to find the marked price of the article so that there will be profit of 20% after allowing a discount of 20%, the following calculation must be performed:
4000 x X x 0.8 = 4000 x 1.2
4000 x X x 0.8 = 4800
4000 x X = 4800 / 0.8
4000 x X = 6000
X = 6000/4000
X = 1.5
4000 x 1.5 = 6000
Therefore, the marked price of the article was $ 6000.
Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sample of pharmacy assistants.
Class Frequency
8.26 20
10.01-11.75 38
11.76 36
13.51-15.25 25
15.26-17.00 27
Sample Variance: ___________
Sample Standard Deviation: _________
Answer:
(a) The sample variance is 16.51
(a) The sample standard deviation is 4.06
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}[/tex]
Solving (a); The sample variance.
First, calculate the class midpoints.
This is the mean of the intervals.
i.e.
[tex]x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13[/tex]
[tex]x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88[/tex]
[tex]x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63[/tex]
[tex]x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38[/tex]
[tex]x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13[/tex]
So, the table becomes:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}[/tex]
Next, calculate the mean
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}[/tex]
[tex]\bar x = \frac{1845.73}{146}[/tex]
[tex]\bar x = 12.64[/tex]
Next, the sample variance is:
[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]
So, we have:
[tex]\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}[/tex]
[tex]\sigma^2 = \frac{2393.6875}{145}[/tex]
[tex]\sigma^2 = 16.51[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\sigma^2}[/tex]
[tex]\sigma = \sqrt{16.51}[/tex]
[tex]\sigma = 4.06[/tex]
The perimeter of a rectangle is 12cm the area is 5cm square what is the length of the sides
Answer:
???
Step-by-step explanation:
Express the following repeating decimal as a fraction in simplest form.
Answer:
[tex]0.\overline{369} = \frac{41}{111}[/tex]
Step-by-step explanation:
x = 0.369369369...
10x = 3.69369369...
100x = 36.9369369...
1000x = 369.369369...
1000x - x = 369
999x = 369
[tex]x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}[/tex]
If 137 is subtracted from three times of square of a natural number the result is 55. Find the number
Answer:
8
Step-by-step explanation:
Let the unknown number be x.
Therefore, we can write the question as a mathematical statement and this will be:
3x^2 - 137 = 55. (Note: ^2 = to the power of 2 or "squared"
(In the question, we can break it up as being three times of a square of a natural number = (3x^2) and 137 is subtracted from = (- 137) and the result is 55 = (= 55). Therefore, this gives 3x^2 - 137 = 55
Then, we add 137 first to get rid of the (-137)
Therefore:
3x^2 = 192
Then, we divide 3 from both sides to get rid of the (3) in (3x^2).
Therefore,
x^2 = 64.
So, we square root 64. This gives
x = 8.
Therefore, the answer is 8.
A table is made using the following two patterns.
Pattern 3: Starting number: 5, Rule: add 1
Pattern y: Starting number: 10, Rule: add 2
Complete the table for the given patterns.
Answer:
x = 6, y = 12
x = 7 y = 14
Step-by-step explanation:
im pretty sure that right, hope this helps!
Help please i will mark brainlist !!!!
Answer:
You need to add the numbers up
0.4 +0.2+0.1=0.7
1-0.7=0.3
Ans=0.3
A florist shop represents its first month’s sales with the equation y = 168 x + 8, where x represents the number of days that the shop is open and y represents the sales in dollars. The owner of the shop would like to calculate the number of days it took to reach $3,200 in sales. Which would be used to solve the problem?
Substitute 3,200 for x.
Add 8 and 3,200.
Divide 3,192 by 168.
Isolate y in the equation.
Answer:
Divide 3,192 by 168.
Step-by-step explanation:
Given
[tex]y = 168x + 8[/tex]
[tex]y = 3200[/tex]
Required
Step to required to get x when [tex]y = 3200[/tex]
The first step is to substitute [tex]3200[/tex] for [tex]y[/tex]
[tex]3200 = 168 * x + 8[/tex]
Subtract both sides by 8
[tex]3192 = 168 * x[/tex]
Divide both sides 168 ---- [this answers the question]
[tex]19 = x[/tex]
[tex]x = 19[/tex]
Answer:
Divide 3,192 by 168.
Step-by-step explanation:
Divide 3,192 by 168.
Step-by-step explanation:
Given
Required
Step to required to get x when
The first step is to substitute for
Subtract both sides by 8
Divide both sides 168 ---- [this answers the question]
9.
Write the equation of a line through points (5, 5) and (1, 0) in point-slope form.
9514 1404 393
Answer:
y = 5/4(x -1)
Step-by-step explanation:
The slope formula can be used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (0 -5)/(1 -5) = -5/-4 = 5/4
The point-slope form is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Using the point (1, 0), we can write the equation as ...
y = 5/4(x -1)
How many inches are in 1.8 yards?
Answer:
64.8 inches is the correct answer.
Step-by-step explanation:
64.8in
Factor each trinomial completely.
A. 2x^2 + 17x + 21
B. 3x^2 - 17x + 10
Answer:
A) (2x+3)(x+7) B) (3x-2)(x-5)
Step-by-step explanation:
A) 2x^2+17x+21=(2x+3)(x+7)
B) 3x^2-17x+10=(3x-2)(x-5)
A group of people were asked if they had run a red light in the last year. 315 responded "yes", and 190 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Answer:
0.624
Step-by-step explanation:
Number who have run a red light = 315
Number who haven't run a red light = 190
From the data :
The total number of people sampled = total possible outcome = (315 + 190) = 505
Selecting a person at random, probability that the selected person has run a red light :
P = required outcome / Total possible outcomes
Required outcome = Number who have run a red light = 315
P(having run a red light) = 315 / 505 = 0.624
Find the value of y for a given value of x, if y varies directly with x. If y = 0.15 when x = 1.5, what is y when x = 6.3? a. –0.63 b. 0.63 c. 63 d. –63 Please select the best answer from the choices provided A B C D
Answer:
b
Step-by-step explanation:
I believe its b, because1.5 is 10 times 0.15
and 6.3 is 10 times 0.63
247 1372 as a number
Answer:
Do you mean in words?
Step-by-step explanation:
then it is
Two million,four hundred and seventy one thousand,three hundred and seventy two.
prove that 1 + sin a + cos 2A upon 1 + Sin A minus Cos 2A = 2 cot a prudent
Answer:
LHS×0=RHS×0
0=0
hence,proved
HELP!!!!
Car Survey In a survey of 3,200 people who owned a certain type of car, 2,080 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
___% of the people surveyed were satisfied with the car.
Answer:
65%
Step-by-step explanation:
2080/3200times100%
Find X in the triangle. Round answer to the nearest TENTH of a degree (GIVING BRAINLEST TO BEST ANSWER :D )
Answer:
x = 59,53445508
Tan(x) = 34/20
Step-by-step explanation:
Answer:
30÷20 degree x=n
Step-by-step explanation:
Mark me as brainliest
Verify that a÷(b+c)=(a÷b)+(a ÷c), a=10 , b=5 , 6=2
Answer:
a÷(b+c)≠(a÷b)+(a ÷c)
Step-by-step explanation:
To verify that a÷(b+c)=(a÷b)+(a ÷c)
Using the values ;
a=10 , b=5 , 6=2
plugging the values into a÷(b+c) should give the same result as (a÷b)+(a ÷c) ;
That is, right hand side = left hand side
a÷(b+c) = 10 ÷ (5+ 2)
a÷(b+c) = 10 / 7
Also;
(a÷b)+(a ÷c) = (10/5) + (10/2) = 2 + 5 = 7
Given the result, it can be seen that ;
RHS ≠ LHS
10/7 ≠ 7
If f(x) = 6x + 2 and g(x) = 4x - 5, find f(x) - g(x).
A. 2x - 7
B. 2x + 7
C. 10x - 3
D. 10x + 7
Answer: D
Step-by-step explanation:
set the functions to subtract
What is the equation of the following line? Be sure to scroll down first to see
(-1/2, 3) (0,0)
A. y = 1/2 X
B. y = -1/2 X
C. y = 3 X
D. y= 2X
E. y= 6
F. y= -6

a p e x :(
Answer: (f)
Step-by-step explanation:
Given
Line that passes through [tex](-\frac{1}{2},3)[/tex] and [tex](0,0)[/tex]
Using two point form, equation of a line is given by
[tex]\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Insert the values
[tex]\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x[/tex]
Thus, option (f) is correct
Given that yx is a diameter of V, find mZVX if mYVZ=(15r -1)", mWVX =(8x- 2).mUVW =(7x +15).
and mYVU = 3x + 5).
A 32
B 45°
C 70
D. 134
find the 11th term of the series
8,14,20,26.......
Answer:
a11 = 8+(11-1)6
a11 = 8+54
a11=68
hopefully this is correct
Step-by-step explanation:
what is a 36% markup to $150 dallors
Answer:
Markup amount: $54
New price with markup: $204
Step-by-step explanation:
36% markup to $150
We can find the amount of markup by finding 36% of 150.
36% of $150
Write 36% as a decimal and multiply it by the price
0.36(150) = $54
The amount of markup (36%) is equal to $54
When this is added to the original price, the new price is $150 + $54 = $204
Let me know if you have any questions!
is the function given by G(x) - 1/x-6 continuous over the interval (1, ∞)? Why or why not?
a. No, the function is not continuous at x=
b. Yes, the function is continuous over (1,∞) because lim x>a G(x)= G(a) for all a in (1,∞).
Answer:
No, the function is not continuous at x=
Which function is a translation of the parent absolute value function?
f(x) = 2x1
f(x) = |x+6| f(x)=|x| f(x)=-4|x|
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Step-by-step explanation; did it on the website euphoria
The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the transformation of the function be a translation , where
The parent function is f ( x ) = | x |
And , the translated function is f ( x ) = | x + 6 |
So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
And , the function is translated 6 units to the left
Hence , the translated function is f ( x ) = | x + 6 |
To learn more about transformation of function click ;
https://brainly.com/question/26896273
#SPJ7
can someone answer pleaseeee
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
Miranda's financial aid stipulates that her tuition not exceed $1500. If her college charges a $55 registration fee for the term plus $275 per course, what is the greatest number of courses for which Miranda can register? Miranda can register for at most how many courses?
Answer:
5
Step-by-step explanation:
275x5= 1375
1375+55=1430
Which of the following is most likely the next step in the series?
B
Answer:
C
Step-by-step explanation:
The pattern seems to go as follows:
1. Top left portion is in blue
2. Top left portion is in blue as well as the rest of the upper half filled with red.
3. Another portion of blue is added directly underneath the red.
This leads me to believe that the colors are alternating from blue to red to blue to finally, red. This makes your answer C. Please let me know if you still need help!
Payment types vary at the grocery store. Here are the proportions of the leading three payment methods: Payment Method Cash Credit Cards Debit Cards Proportion 0.11 0.43 0.21 If a transaction is selected at random, the probability that the customer did not pay with a Debit Card is .
Answer:
0.79
Step-by-step explanation:
Given the probability distribution :
Payment Methd: Cash Credit Cards Debit Cards Proportion : ____0.11 ____ 0.43 _____0.21
The probability that a customer did not pay with debit card can be obtained as :
If customer did not pay with debit card, then he would have paid with any of the other payment methods
This Can best be obtained using the complement method
P(not debit card) = 1 - P(debit card)
P(debit card) = 0.21
P(not debit card) = 1 - 0.21
P(not debit card) = 0.79
