Answer:
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
Step-by-step explanation:
[tex]4^1 = 4\\4^2 = 16\\4^3 = 64\\4^4 = 256 \\4^5 = 1024\\4^6 = 4096\\4^7 = 16384\\4^8 = 65536[/tex]
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
To prove this conjecture
[tex]4^1 = 4\\4^2 = 16[/tex] unit digit = 6
hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1 to 8 )
Simplify 6(x + 2)- x(x - 1)
The length of the rectangle is 3ft less than twice the width,and the area of the rectangle is 27ft^2,find the diameter
Answer:
The dimensions of rectangle are:
width = w = 4.5 ftlength = l = 6 ftStep-by-step explanation:
Let 'l' be the length and 'w' be the width of the rectangle
The length 'l' of the rectangle is 3ft less than twice the width 'w'.so
[tex]l=2w-3[/tex]
Also, the area of the rectangle is 27ft^2.
[tex]A=27\:ft^2[/tex]
As the area of the rectangle has the formula:
[tex]\:A\:=\:l\times w[/tex]
so
[tex]27=\:l\times w[/tex]
so the equation becomes
[tex]27=\left(2w-3\right)\times \:w[/tex]
[tex]27=2w^2-3w[/tex]
[tex]2w^2-3w-27=0[/tex]
[tex]\left(w+3\right)\left(2w-9\right)=0[/tex]
if [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]w+3=0\quad \mathrm{or}\quad \:2w-9=0[/tex]
[tex]w=-3,\:w=\frac{9}{2}[/tex]
as the width can not be negative, so
[tex]w=\frac{9}{2}=4.5[/tex] ft
As
[tex]l=2w-3[/tex]
[tex]l=2\left(4.5\right)-3[/tex]
[tex]l=9-3[/tex]
[tex]l=6[/tex]
So the dimensions of rectangle are:
width = w = 4.5 ftlength = l = 6 ftEvaluate the expression 9x for x= 2.
9x = when x = 2.
(Simplify your answer.)
A surgical procedure requires choosing among four alternative methodologies. The first can result in five possible outcomes, the second can result in two possible outcomes, and the remaining methodologies can each result in four possible outcomes. What is the total number of outcomes possible?
Answer:
15 possible outcomes
Step-by-step explanation:
Since each one of these methodologies are not related to one another and they do not need to be chosen in any order or consecutively then the possible outcomes would only need to be added all together to calculate the total possible outcomes. Since each outcome is independent. Therefore,
m1 = 5 outcomes
m2 = 2 outcomes
m3 = 4 outcomes
m4 = 4 outcomes
5 + 2 + 4 + 4 = 15
we can see that there are a total of 15 possible outcomes
Question 2 (1 point)
For problem 2 - 26, what is the slope of line C?
A
B
2-26.
D
+
E
8
10
2
a
m = 2
Ob
m = -2/3
c
m = 0
Answer:
Option e: 2/3 is the correct answer.
Step-by-step explanation:
The slope of a line is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Two-points on line are needed to calculate slope of a line. In the attached diagram, two points are highlighted which are located on line C.
The two points are:
(x1,y1) = (9,4)
(x2,y2) = (3,0)
Putting the values in the formula
[tex]m = \frac{0-4}{3-9}\\=\frac{-4}{-6}\\=\frac{2}{3}[/tex]
The slope of line C is: 2/3
Hence,
Option e: 2/3 is the correct answer.
Solve for h: h + 4.18 = 19.74
Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
ABC is scalene
Answer:
Perimeter = 32.3
Area = 95.24
Step-by-step explanation:
Given:
△ABC, m∠A=60°
m∠C=45°, AB = 9
To find:
Perimeter of △ABC
Area of △ABC
Solution:
Using angle sum property in a triangle:
m∠A + m∠B + m∠C = 180°
m∠B = 180° - 45° - 60° = 75°
As per Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
[tex]a[/tex] is the side opposite to [tex]\angle A[/tex]
[tex]b[/tex] is the side opposite to [tex]\angle B[/tex]
[tex]c[/tex] is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08[/tex]
[tex]\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22[/tex]
Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3
Area of a triangle is given as:
[tex]\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)[/tex]
[tex]\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}[/tex]
Cathy's food usually costs $212.90 a week. One week, it cost $198.98. How
much less money did she spend that week?
Answer:
$13.92
Step-by-step explanation:
$212.90-198.98
equivalent fraction of 6/126
Answer:
1/21
Step-by-step explanation:
Answer:
1/21
Step-by-step explanation:
6/126 = 1/21 because 6 divided by 6 equals 1 and 126 divided by 6 equals 21.
(c) What is the value of p if 4x² + 20x + p is a
perfect square
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]( {a + b})^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]
_________________________________
[tex]4 {x}^{2} + 20x + p = [/tex]
[tex]( {2x})^{2} + 2(2x)(5) + p = [/tex]
Thus ;
[tex]p = {5}^{2} [/tex]
So
[tex]p = 25[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer:
m= 1
Step-by-step explanation:
find to ordered pair on the graph and [tex]y^{1} - y^{2} \\ x^{1} - x^{2}[/tex]
Which lines from Natalie Merchant's song "Wonder" most likely inspired R. J. Palacio to give August's mother's great determination in the novel Wonder? O Doctors have come from distant cities just to see me O stand over my bed disbelieving what they're seeing with love, with patience and with faith she'll make her way I'm over your heads how I confound you and astound you
Answer:
C)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The guy above me is correct
Which of the following equations represent linear functions?
y=x2−3x
4x+y=5
y=|2x+1|
y=−5
Answer:
its y=-5x
Step-by-step explanation:
Why?
linear functions have only the slope, they dont include the y-intercept
I need help with this! 20 points pls dont take advantage.
the average adult drinks 1095 cups of coffee annually, About how many cups does the average adult drink per week? 1 year=52 weeks
15
91
21
3
Answer:
the answer is 21
Step-by-step explanation:
If they drink 1,095 cups per year, and there are 52 weeks in a year, you would divide 52 from 1,095(1,095/52) to get your answer which is 21.05769231. If you round it to the nearest whole number, than it is 21. I hope this helps have a great day.
what is the equation of aline that passes through the point (4,-8) and has a slope of -1/2?
Answer:
The equation of the line will be:
[tex]y=-\frac{1}{2}x-6[/tex]
Step-by-step explanation:
Given
slope = m = -1/2point (4, -8)Point slope form:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = -1/2 and the point (4,-8)
[tex]y-\left(-8\right)=\frac{-1}{2}\left(x-4\right)[/tex]
[tex]y+8=\frac{-1}{2}\left(x-4\right)[/tex]
subtract 8 from both sides
[tex]y+8-8=\frac{-1}{2}\left(x-4\right)-8[/tex]
[tex]y=-\frac{1}{2}x-6[/tex]
Therefore, the equation of the line will be:
[tex]y=-\frac{1}{2}x-6[/tex]
I don’t understand this at all pls help I will mark brainliest
Answer:
D
Step-by-step explanation:
-2/3 is -.666
-3/5 is -.60
1/2 is .5
and 5/8 is a little more than half since 4/8 is half. so -2/3, -3/5, 1/2, 5/8, or D
4n-(7-6n)
Helppp plz
7. Jenny is saving to buy a laptop worth $960. Her parents promise to match every $3 saved
by her with $5 of their own.
a. How much will Jenny contribute?
b. How much will Jenny's parents have to pay?
Each week, Mrs.Mack buys exactly 3 5/8 pounds of cheese for her mac-and-cheese recipe. She chooses from these kinds of cheese. Mrs.Mack buys as many packages as she needs— up to three packages of any kind. What packages of cheese (and how many of each kind) does Mrs.Mack buy? 7/8pounds of american cheese. 0.5 pounds of cheddar cheese. 0.2 pounds of swiss cheese. HELP PLEASE
9514 1404 393
Answer:
3 packages of American (7/8 lb)2 packages of cheddar (1/2 lb)Step-by-step explanation:
The amount of cheese Mrs Mack needs is an odd number of eighths of a pound. So, she must buy an odd number of the 7/8 pound packages.
If she were to buy any 1/5 pound packages, she would have to buy a multiple of 5 of them so as to have an integral number of eighths. The only suitable multiple is 0.
If Mrs Mack buys 1 of the 7/8 pound packages, she cannot make up the difference with half-pound packages. She must buy 3 of the 7/8 pound packages, for a total of 2 5/8 pounds of American cheese. The remaining pound can be bought as 2 of the 1/2 pound packages.
To buy 3 5/8 pounds, Mrs Mack must purchase ...
3 packages of American cheese (7/8 lb each)
2 packages of Cheddar cheese (1/2 lb each)
The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. The probability that the average pregnancy length for nine randomly chosen women exceeds 268 days is about a) 0.35 b) 0.40 c) 0.65 d) 0.27
Answer:
The probability is [tex]P( \= X > 268 ) =0.35376[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 266[/tex]
The standard deviation is [tex]\sigma = 16[/tex]
Generally the standard error of mean is mathematically represented as
[tex]\sigma_{\= x} = \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x} = \frac{16}{\sqrt{9} }[/tex]
=> [tex]\sigma_{\= x} = 5.33[/tex]
Generally the probability that the average pregnancy length for nine randomly chosen women exceeds 268 days is mathematically represented as
[tex]P( \= X > 268 ) = P (\frac{ \= x - \mu }{ \sigma_{\= x}} > \frac{268 - 266}{5.33 } )[/tex]
[tex]\frac{\= X -\mu}{\sigma_{\= x} } = Z (The \ standardized \ value\ of \ \= X )[/tex]
[tex]P( \= X > 268 ) = P (Z > 0.3752 )[/tex]
From the z table the area under the normal curve to the right corresponding to 0.3752 is
P (Z > 0.3752) = 0.35376
So
[tex]P( \= X > 268 ) =0.35376[/tex]
20+20 omg.please help :(
Answer:
40
Step-by-step explanation:
Solve five and three sixths minus two and one third.
(GIVING EXTRA POINTS ON THIS ONE! IM ALSO GIVING BRAINLIEST!) (Btw three and two ninths is incorrect :) )
A) Two and three eighteenths
B) two and two ninths
C) three and two ninths
D) three and three eighteenths
(Here is an image if needed) :
Answer:
3 3/18
Step-by-step explanation:
I did this on paper, but im typing on computer, sorry I cant send a photo
Answer:
D is the answer 3 3/18 i am sure it is correct
What is the value of X in this Diagram
I will give a brainlist for the correct answer
Answer: 31°
Step-by-step explanation:
180° - 149° = 31°
Mrs. Chin paid a 20 percent tip on the bill for lunch.
Percents
Total
20%
20%
20%
20%
20%
100%
$2.75
$2.75
$2.75
$2.75
$2.75
If the tip amount was $2.75, what was the bill for lunch before the tip was added to it?
$5.50
$13.75
$16.50
$55.00
Answer:
The bill before the tip was $13.75 if you add a 20% tip of $2.75 the total bill including the tip would be $16.50
The bill before the tip is $13.75
Answer:
Answer is B hope it helps
Step-by-step explanation:
The table shows the weekly profits of a fruit
vendor. What is the mean profit for these weeks?
Week
1
2
3
4
Profit -$125 -$86
$54
- $35
The mean profit is $
Answer:
-48
Step-by-step explanation:=-48
The mean profit of the fruits will be $75.
What is mean?Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is just like an average it is calculated by taking the ratio of the sum of all the numbers to the total count of the numbers.
Given that the weekly profit of the fruits is $125, $86, $54, and $35. The mean will be calculated as:-
Mean = ( 125 + 86 + 54 + 35 ) / 4
Mean = 300 / 4
Mean = $75
Therefore, the mean profit of the fruits will be $75.
To know more about mean follow
https://brainly.com/question/968894
#SPJ5
Pls answer professionally or with the right answer I’m beg you
Answer:
Step-by-step explanation:
Hello friend!!!
here's ur answer
1) <y = 180 - 74 = 106° ( linear pair )
<x = <y ( alternate angles )
therefore, <x = <y = 106°
2) <x = 68° ( corresponding angles )
<y = 180 - 68 = 112° ( linear pair )
<z = 112° ( vertically opposite angles )
Hope this helps
plz mark as brainliest!!!!!
A statement of an employee's biweekly earnings is given below.
Earnings
Deductions
Week Ended
Regular
FED. SOC. MED STATE
WITH. WITH. CARE. WITH.
NET PAY
8/18
$_____
$72.00 $35.05 $15.54 $14.40
$793.01
What is the employee's gross pay?
A.
$900.50
B.
$1000
C.
$930
D.
$975.10
Answer:
kjj ,mStep-by-step explanation:
Please help this one is also due tomorrow
The correct answer is 0.73737373 or answer C. An irrational number is a number that cannot be expressed as a fraction for any integers and. . Irrational numbers have decimal expansions that neither terminate nor become periodic
BRAINLIEST FOR CORRECT ANSWER!
At a sale, dresses were sold for $24 each. This price was 12% of a dress's original price. How much did a dress originally cost?
Answer:
$200
Step-by-step explanation:
To find the original price, divide the price by 0.12:
24/0.12
= 200
So, the dress originally cost $200
Answer:
$200.
Step-by-step explanation:
To find the original price, divide the discounted price by 0.12.
$24 ÷ 0.12% = $200
The dress originally cost $200.
Determine the check digit for the UPCs that have these initial 11 digits. a) 73232184434 b) 63623991346 c) 04587320720 d) 93764323341
Answer:
The check digits
a) x₁₂ ≡ 5( mod 10 )
b) x₁₂ ≡ 2( mod 10 )
c) x₁₂ ≡ 0( mod 10 )
d) x₁₂ ≡ 3( mod 10 )
Step-by-step explanation:
Given the data in the question;
We know that the formula for determining the UPCs check is;
3x₁ + x₂ + 3x₃ + x₄ + 3x₅ + x₆ + 3x₇ + x₈ + 3x₉ + x₁₀ + 3x₁₁ + x₁₂ ≡ 0( mod 10 )
now we will substitute the given values to determine the value of the last bit
a)
73232184434
we substitute into the formula
3×7 + 3 + 3×2 + 3 + 3×2 + 1 + 3×8 + 4 + 3×4 + 3 + 3×4 + x₁₂ ≡ 0( mod 10 )
x₁₂ ≡ 5( mod 10 )
b)
63623991346
we substitute into the formula
3×6 + 3 + 3×6 + 2 + 3×3 + 9 + 3×9 + 1 + 3×3 + 4 + 3×6 + x₁₂ ≡ 0( mod 10 )
x₁₂ ≡ 2( mod 10 )
c)
04587320720
we substitute into the formula
3×0 + 4 + 3×5 + 8 + 3×7 + 3 + 3×2 + 0 + 3×7 + 2 + 3×0 + x₁₂ ≡ 0( mod 10 )
x₁₂ ≡ 0( mod 10 )
d)
93764323341
we substitute into the formula
3×9 + 3 + 3×7 + 6 + 3×4 + 3 + 3×2 + 3 + 3×3 + 4 + 3×1 + x₁₂ ≡ 0( mod 10 )
x₁₂ ≡ 3( mod 10 )