Answer:
Step-by-step explanation:
Hello,
We will prove it by induction.
Step 1 - for n=2
2!=2*1=2
2^2=4
and 2 < 4 so this is true for n=2
Step2 - We assume that this is true for k and we have to prove it for k+1.
Induction hypothesis is [tex]k!<k^k[/tex]
[tex](k+1)!=(k+1)k![/tex]
We use the induction hypothesis and we we can write that
[tex](k+1)!=(k+1)k!<(k+1)k^k<=(k+1)(k+1)^k=(k+1)^{k+1}\\\\\text{As }k <= k+1[/tex]
so, we prove it for k+1
Step 3- conclusion
for n >= 2 we just proved that [tex]n!<n^n[/tex]
A study showed that for young women a breakfast containing approximately 27 g (grams) of protein, 58 g of carbohydrate, 21 g of fat, and 525 calories is a nutritious breakfast that prevents a hungry feeling before lunch. The following table shows the content of four breakfast foods. How much of each should be served to obtain the desired amounts of protein, carbohydrates, fat, and calories? Calories Fat Carbohydrates Protein 110 0 24 2 1 cup juice 120 8 4. 8 1 cup cereal 100 6 10 2 slice bread 85 0 13 10 cup milk c juice c cereal slice(s) of bread c milk
Answer:
1 C JUICE , 1 C MILK , 1.5 SLICE OF BREAD and 1.5 C CEREAL should each be served to obtain the desired amounts.
Step-by-step explanation:
Given that;
protein carbohydrate fat calories
1 cup juice 2 24 0 110
1 cup cereal 8 4 8 120
1 slice bread 2 10 6 100
1 cup milk 10 13 0 85
Now let number of cups of juice, cereal , bread milk be
j, c, b and m respectively
from the table and information from the given
protein
2j + 8c + 2b + 10m = 27 ------------------equ 1
carbohydrate
24j + 4c + 10b + 13m = 58 ---------------equ 2
fat
8c + 6b = 21 ----------------------------------equ 3
calories
110j + 120c + 100b + 85m = 525 ------- equ 4
Now
equ 1 × 12 - equ 11
⇒(24j + 96c + 24b + 120m = 324) - (24j + 4c + 10b + 13m = 58)
= 92j + 14b + 107m = 266 -----------------equ 5
also
equ 1 × 55 - equ 4
( 110j + 440c + 110b + 550m = 1485) - ( 110j + 120c + 100b + 85m = 525 )
320c + 10b + 465m = 960
divide through by 5
64c + 2b + 93m = 192 ----------------------- equ 6
then
equ(5)×93 - equ(6)×107
(8556j + 1302b + 9951m = 24738) - (6848j + 214b + 9951m = 20544)
1708j + 1088b = 4194
divide through by 2
854j + 544b = 2097 --------------------------- equ 7
Now
equ(3)×854 - equ(7)×8
(6832c + 5124b = 17934) - ( 6832c + 4352b = 16776)
772b = 1158
b = 1158 / 772
b = 1.5
now put (b=1.5) in equation 3
8c + 6(1.5) = 21
8c 9 = 21
8c = 21 - 9
8c = 12
c = 12/8
c = 1.5
now put (b=1.5) and (c=1.5) in equation 6
64(1.5) + 2(1.5) + 93m = 192
96 + 3 + 93m = 192
93m = 192 - 99
93m = 93
m = 93/93
m = 1
now put (b=1.5), (c=1.5) and (m=1) in equation 1
2j + 8(1.5) + 2(1.5) + 10(1) = 27
2j + 12 + 3 + 10 = 27
2j + 25 = 27
2j = 27 -25
2j = 2
j = 2/2
j = 1
Therefore 1 C JUICE , 1 C MILK , 1.5 SLICE OF BREAD and 1.5 C CEREAL should each be served to obtain the desired amounts.
Expand and simplify
8(n-1)-2(3n+5)
8(n-1)-2(3n+5)
8n-8-6n-10
8n-6n-8-10
2n-18
2(n-9)
co
..com
michael
What quantity of salt would you need to make 4 times as much as the original recipe?
Barbecue sauce
INGREDIENTS:
4 cups ketchup
2 teaspoons vinegar
teaspoon salt
teaspoon pepper
1 cup honey
1 tablespoon garlic
Write your answer as a fraction or as a whole or mixed number
teaspoons
Submit
2:47
o
300e
Lenovo
Answer: go to quizlet it has the answer i got that question aced
Step-by-step explanation:
mark brainly btw
Answer:
1/2
Step-by-step explanation:
— 7x(—8) help me plz
Answer: 56x
Step-by-step explanation: Multiply -8 by -7. Be sure to add your x at the end. VERY important.
I hope this helps you out! ♥
Answer:
[tex]56x[/tex]
Step-by-step explanation:
[tex]-7x(-8)[/tex]
The one and only thing you have to do in this question is to simplify.
[tex]-7x)(-8)[/tex]
This equals
[tex]56x[/tex]
Now you got your answer!
Hope this helps!
Please look at the picture and answer. Thanks! :)
29/16= 1.8125
as decimal
I need help on this..... please
Answer:
[tex]q(x)=2x-5,x\neq-2[/tex]
Step-by-step explanation:
So we have:
[tex]a(x)=2x^2-x-10\\b(x)=x+2[/tex]
And we want to find the quotient q(x). Thus:
[tex]q(x)=\frac{a(x)}{b(x)}[/tex]
Substitute:
[tex]q(x)=\frac{2x^2-x-10}{x+2}[/tex]
Factor the numerator:
[tex]2x^2-x-10\\=2x^2+4x-5x-10\\=2x(x+2)-5(x+2)\\=(2x-5)(x+2)[/tex]
Substitute:
[tex]q(x)=\frac{(2x-5)(x+2)}{x+2}[/tex]
The (x+2)s cancel out. Therefore:
[tex]q(x)=2x-5[/tex]
However, we must restrict x such that it cannot equal -2.
In the original equation, if it did, our answer would be undefined. Thus, our final answer is:
[tex]q(x)=2x-5,x\neq-2[/tex]
And we are done :)
Edit: Typo
Convert 43/7 into a proper fractions show work?
Step-by-step explanation:
Hey, there!!
[tex] = \frac{43}{7} [/tex]
Divide 43 by 7.
you will get quotient as 6 and remainder is 1.
so,
The proper fraction is:
[tex] = 6 \frac{1}{7} [/tex]
Hope it helps...
First must do the division:
43 : 7 = 6 with 1 of rest
so 43 = 6 * 7 + 1
with the denominator:
[tex]\frac{43}{7} = \frac{6*7+1 }{7}[/tex]
[tex]\frac{43}{7} = \frac{6*7 }{7}+\frac{1}{7}[/tex]
semplify:
[tex]\frac{43}{7} = 6+\frac{1 }{7}[/tex]
Encrypt the word TO using an alphabetic Caesar shift cipher with shift 10 (mapping A to K). Use only capital letters in your answer.
Answer:
DY
Step-by-step explanation:
TO ENCRYPT TO USING CAESAR ALPHABETIC SHIFT CIPHER OF 10. THIS MEANS WE'RE EXPECTED TO LOOP EVERY ALPHABET BY 10, SKIPPING EVERYONE TILL WE GET TO THE TENTH.
TO ENCRYPT T, WE HAVE
T = U - V - W - X - Y - Z - A - B - C - D
THEREFORE, T WILL BE ENCRYPTED AS D
TO ENCRYPT O, WE HAVE
O = P - Q - R - S - T - U - V - W - X - Y
HENCE, O WILL BE ENCRYPTED AS Y.
THIS MEANS THAT OUR QUESTION, TO, WILL BE ENCRYPTED AS DY
The line graph shows the time spent by people visiting the
Department of Motor Vehicles to renew their driver's license during
their birth month. To the nearest minute, what is the average waiting
time for all the months shown on the graph?
A)
18 minutes
B)
29 minutes
C)
37 minutes
D)
41 minutes
Answer:
Option (B)
Step-by-step explanation:
Average waiting time in the month of October = 20 minutes
Average waiting time in the month of November = 30 minutes
Average waiting time in the month of December = 60 minutes
Average waiting time in the month of January = 40 minutes
Average waiting time in the month of February = 10 minutes
Average waiting time in the month of March = 10 minutes
Average waiting time in the month of April = 30 minutes
Average waiting time in the month of May = 40 minutes
Average waiting time in the month of June = 20 minutes
Total waiting period from October to June = 20 + 30 + 60 + 40 + 10 + 10 + 30 + 40 + 20 = 260
Average waiting period = [tex]\frac{260}{9}[/tex]
= 28.89
≈ 29 minutes
Option (B) is the answer.
Given: angle 1 and angle 2 form a linear pair; angle 1 and angle 3 are supplementary
Prove: angle 2 is congruent to angle 3
Answer:
Step-by-step explanation:
1.) angle 1 and angle to form a linear pair (given)
2.) angle 1 and 2 are supplementary (supplement theorem)
3.) measure of angle 1 + measure of angle 2 = 180 degrees (def. of supplementary angles)
4.) angle 1 and 3 are supplementary (given)
5.)measure of angle 1 + measure of angle 3 = 180 degrees (def. of supplementary angles)
6.) measure of angle 1+ measure of angle 2 = measure of angle one + measure of angle 3 (congruent supplements theorem)
7.) measure of angle 2 = measure of angle 3 (subtraction property of equality)
8.) angle 2 is congruent to angle 3 (definition of congruence)
Jason had to replace the floor of a triangular portion of his dining room. The portion had a height that was twice as high as the base. If the total area of the portion he needed to replace was 16 square feet (16ft2),how long in feet was the base of the portion he needed to replace?
Answer:
4 feet
Step-by-step explanation:
We know the the area of a triangle can be represented as [tex]\frac{bh}{2}[/tex].
Since the height is twice the base, we can substitute the value [tex]2b[/tex] in as [tex]h[/tex] in the expression, making it [tex]\frac{b\cdot2b}{2}[/tex]. If the area is 16, we can make the equation
[tex]\frac{b\cdot2b}{2} = 16[/tex]
Now to solve for b.
[tex]\frac{2b^2}{2} = 16\\\frac{2b^2}{2}\cdot2 = 16\cdot2\\\\2b^2 = 32\\\\2b^2\div2 = 32\div2\\\\b^2 = 16\\\\b=4[/tex]
Hope this helped!
The area of a rectangle is the product of its length and width. Both length and width are whole numbers. A rectangular poster has an area of 204 square inches. The width of the poster is greater than 10 inches and is prime. What is the width of the poster?
Answer:
The width of the poster will be 17 inches
Step-by-step explanation:
The area = 204 square inches
Note:
- both length and width are whole numbers
- The width of the poster is greater than 11 inches
- The width is a prime
The prime numbers greater than 11 are
13, 17, 19, 23, 29, ...,
all these numbers divide 204 with a remainder except for 17
Therefore, the width will be 17 inches, and the length will be 12
since 17 divides 204 into 12 places
Simplify as much as possible.
2w?V32wu? + u V 18w5
?
Answer:
[tex]11 {w}^{2}u \sqrt{2w}[/tex]
Step-by-step explanation:
I'm never sure how far to go on these questions but I think what I'e done looks pretty nice. Essentially I simplified each radical, factored out each variable, combined the radicals after more simplification, and then picked the answer you were most likely looking for. I gave some alternatives in my work that are "simple" too, but the answer above is most likely I'd say.
Work is in the attachment, comment with any questions.
7w+6-3w
Please help
I don’t understand how to do this
Answer:
4w + 6
Step-by-step explanation:
Group like terms
7w - 3w + 6 = 4w + 6
Hope this Helps :)
You estimate that the driving distance from Raleigh, NC to Charlotte, NC is around 180 miles. When you looked it up on the internet, you found that the actual distance is only 167.5 miles. What was the relative (percent) error of your estimate? In other words, how far off were you from the actual value?
Answer:
7.5%
Step-by-step explanation:
Approximate distance = 180 miles
Actual distance = 167.5 miles
Percent error = { (approximate value - actual value) / actual value } × 100
= { (180 - 167.5) / 167.5 } × 100
= (12.5 / 167.5) × 100
= 0.075 × 100
= 7.5%
What is the vertex of g(x) = 8x2 – 48x + 65? (–3, –7) (3, –7) (24, –7) (–24, –7)
B. (3, -7)
When the equation is graphed, the vertex is at the point (3,-7). I hope this helps!!!
The vertex of the quadratic expression g(x) = 8x² - 48x + 65 is (3, -7).
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
The vertex of a quadratic function f(x) = ax² + b x + c is,
(-b/2a, f(-b/2a)).
Here the function is,
g(x) = 8x² - 48x + 65
b = -48 and a = 8.
Vertex = (-(-48) / 16, g(-(-48) / 16))
= (3, g(3))
g(3) = 8(3)² - 48(3) + 65 = 0
g(3) = -7
Hence the correct option is B.
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In 1990 the average family income was about $ 39 , 000 , and in 2010 it was about $ 70 , 768 . Let x = 0 represent 1990, x = 1 represent 1991, and so on. Find values for a and b so that f ( x ) = a x + b models the data A= _____. B=______. What was the average family income in 2005?
Answer:
[tex]f(x) = 1588.4x + 39000[/tex]
[tex]f(15) = 62826[/tex]
Step-by-step explanation:
Given
In 1990; Income= $39000
In 2010; Income= $70768
Solving (a): An equation in form of f(x) = ax + b
First, we need to determine the slope, a
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Taking y as income and x as year index.
When x = 0; y = 39000
When x = 20; y = 70768
Substitute these values in the above formula
[tex]a = \frac{70768 - 39000}{20 - 0}[/tex]
[tex]a = \frac{31768}{20}[/tex]
[tex]a = 1588.4[/tex]
Next, is to determine the formula using:
[tex]y - y_1 = a(x - x_1)[/tex]
Considering :When x = 0; y = 39000, we have
[tex]y - 39000 = 1588.4(x - 0)[/tex]
[tex]y - 39000 = 1588.4x[/tex]
Make y the subject of formula
[tex]y = 1588.4x + 39000[/tex]
Express y as a function of x
[tex]f(x) = 1588.4x + 39000[/tex]
Solving (b): Income in 2005
In 2005, x = 15
So:
[tex]f(x) = 1588.4x + 39000[/tex] becomes
[tex]f(15) = 1588.4 * 15 + 39000[/tex]
[tex]f(15) = 62826[/tex]
A standard number cube is rolled . What is the probability of getting a factor of 4?A standard number cube is rolled . What is the probability of getting a factor of 4?
Answer:
1 out is six
Step-by-step explanation:
there are six numbers on a dice cube to get four that is a one out of six.
Answer:
3/6, 1/2 or 50%
Step-by-step explanation:
The answer would be 3/6
because there are 3 factors of 4 and there are 6 total sides so the answer would be 3/6 or 1/2 or 50%
Find the coordinate vector [Bold x ]Subscript Upper B of x relative to the given basis B
Answer:
coordinate value is [-3,4].
Reltive is mio pie x 78.9 :)
hoped this helped :)
Round the value 44.981 to three significant figure
Answer:
45.0
Step-by-step explanation:
44.981 = 45.0 (to 3 s.f.)
*important point to note: the 0 must be included as the question asked for 3 significant figures. In this case, 0 is significant.
I hope this helps :)
Rounding 44.981 to three significant figures gives us 44.9.
To round the value 44.981 to three significant figures, we start counting from the leftmost non-zero digit.
The three significant figures in this case are "44.9".
The digit immediately after the third significant figure is 8.
Since 8 is greater than or equal to 5, we round up the last significant figure, which is 9.
Therefore, rounding 44.981 to three significant figures gives us 44.9.
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Felix needs to determine whether x + 3 is a factor of f(x)=−2x4−8x3−2x−63. How can Felix use the factor theorem to determine whether x + 3 is a factor of f(x)? Drag a value, expression, or phrase into each box to correctly complete the statements. Felix evaluates{ } Response area and determines its value to be{ } Response area. Felix concludes that x + 3{ } Response area a factor of f(x)=−2x4−8x3−2x−63.
Answer:
1st Slot: f(-3)
2nd Slot: -3
3rd Slot: is not
Step-by-step explanation:
Using the Remainder Theorem, we plug in the root of x + 3 (which is x = -3) and see the remainder.
If the remainder = 0, it is a factor
If the remainder ≠ 0, it is NOT a factor
f(-3) = -2(-3)⁴ - 8(-3)³ - 2(-3) - 63
f(-3) = -3
So, x + 3 is NOT a factor.
We then have our 3 answers.
Give another name for line r
Answer:
line AC
Step-by-step explanation:
because those are two points along line r
it can't be line AB because that would make it a line segment
Answer:
Line ac
Step-by-step explanation:
1
Molly bought a recliner on sale for
off. The original price was $1, 299.99. How much did she save?
3
What did Molly pay for the recliner?
Answer:
1/3 is 33.33%
1299.99 x 33.33 =433.286
1299.99 - 433.286= 866.704
Step-by-step explanation:
$866.704 is what she paid
Discount was $433.286
Whats the midpoint of (4,8) and (10, -3)
Answer: (7, 2.5)
Step-by-step explanation:
Midpoint formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]
(x1, y1)= (4, 8)
(x2, y2)= (10, -3)
------------------------------------------------------
[tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]
=[tex](\frac{4+10}{2}, \frac{8-3}{2} )[/tex]
=[tex](\frac{14}{2}, \frac{5}{2} )[/tex]
=[tex](7, 2.5)[/tex]
Hope this helps!! :)
Please let me know if you have any question
Suppose you plan on driving 600 miles in Canada how many kilometers is that
Answer:
9656.064 rounded its 9656
Step-by-step explanation:
multiply the length value by 1.609344
6000*1.609344
Question 8 Find the unit vector in the direction of (2,-3). Write your answer in component form. Do not approximate any numbers in your answer.
Answer:
The unit vector in component form is [tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex] or [tex]\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j[/tex].
Step-by-step explanation:
Let be [tex]\vec u = (2,-3)[/tex], its unit vector is determined by following expression:
[tex]\hat {u} = \frac{\vec u}{\|\vec u \|}[/tex]
Where [tex]\|\vec u \|[/tex] is the norm of [tex]\vec u[/tex], which is found by Pythagorean Theorem:
[tex]\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}[/tex]
[tex]\|\vec u\| = \sqrt{13}[/tex]
Then, the unit vector is:
[tex]\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)[/tex]
[tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex]
The unit vector in component form is [tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex] or [tex]\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j[/tex].
Which value of x makes this equation true?
-8(x+5) = -3x - 7+ x-3
A.
1 =
-
NIP
B.
I = -5
C.
=
1
D.
= 12
Answer:
x=-5
Step-by-step explanation:
opening the bracket on the LHS, we have
-8x-40= -3x+x-7-3
-8x-40= -2x-10
collecting like terms
-8x+2x= -10+40
-6x= 30
divide both sides by -6
x= -5
x = 3 - 3y
x + 3y = -6
please explain too
Answer:
(x ; y) ∈ ∅
Step-by-step explanation:
x = 3 - 3y
x + 3y = - 6
replace x
(3 - 3y) + 3y = - 6
3 - 3y + 3y = - 6
3 = - 6
(x ; y) ∈ ∅
Step-by-step explanation:
we have given the value of x is 3 - 3y
[tex]\blue\star[/tex]x+3y = -6. (eq 1)
put the value of x in equation 1 we get
[tex]\blue\star[/tex] x + 3y = -6
[tex]\blue\star[/tex] 3-3y+3y.= -6
[tex]\blue\star[/tex] 3 = -6
Hope it helps.
Mike bought 1/3 of a pound of cashews and 1/5 of a pound of
peanuts. How much money did he spend?
peanuts
$5.00
cashews
$12.00
pecans
$7.00
Answer:
5.00 +12.00=17.00
Step-by-step explanation:
specify whether the money is in pounds like $12 for a pound of cashews I can't tell what you need
select the value(s) of x. Check all of the boxes that apply. -11 1 9 21
Answer:
x = 5 +/- 4 ([tex]\sqrt{16}[/tex])
so the answer is 1 and 9
Step-by-step explanatio:
The values of x can be 1 or 9.
The correct option is (B) and (C).
What is equation?A statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of a mathematics has been driven by attempts to find answers to those questions in a systematic way.
For example
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.
Given:
x= 5 ± √16
Now, taking the root of 16 which is +4 and -4.
So, x= 5 ± 4
We have two values ,
x= 5+4 or x= 5-4
x=9 or 1
Hence, the solution to x= 5 ± √16 is B. 1 and C. 9.
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