Answer:
6/50
Step-by-step explanation:
There are 50 tiles
6 purple
18 pink
26 orange
P( purple) = purple/ total
= 6/50
Partition the circle into 4 equal sections. What unit fraction of the circle’s area does each section represent?
Answer:
1/4
Step-by-step explanation:
If the 4 sections have equal areas, then each section has 1/4 of the original circle's area.
in this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answer:
2.7 in²
Step-by-step explanation:
Area of ∆BAC : ∆Area of EDF = BC² : EF² (based on the area of similar triangles theorem)
Thus:
[tex] 6 in^2 : x in^2 = (3 in)^2 : (2 in)^2 [/tex]
[tex]\frac{6}{x} = \frac{3^2}{2^2}[/tex]
[tex]\frac{6}{x} = 2.25[/tex]
[tex]\frac{6}{x}*x = 2.25*x[/tex]
[tex]6 = 2.25x[/tex]
[tex]\frac{6}{2.25} = \frac{2.25x}{2.25}[/tex]
[tex]2.67 = x[/tex]
Area of ∆EDF = 2.7 in²
Two balls are drawn in succession out of a box containing 5 red and 4 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw. (A) Find the probability that at least 1 ball was red, given that the first ball was replaced before the second draw. StartFraction 24 Over 49 EndFraction (Simplify your answer. Type an integer or a fraction.) (B) Find the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw.
Answer:
The answer is below
Step-by-step explanation:
The box contains 5 red and 4 white balls.
A) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was (Upper A )Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81
P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81
The probability that at least 1 ball was red = 25/81 + 20/81 + 20/81 = 65/81
B) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was not Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)
P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72
The probability that at least 1 ball was red = 20/72 + 20/72 + 20/72 = 60/72
A television screen has a length to width ratio of 8 to 5 and a perimeter of 117 inches. What is the diagonal measure of the screen (to the nearest tenth of an inch)?
Answer:
[tex]D = 42.5\ inch[/tex]
Step-by-step explanation:
Given
[tex]L = Length[/tex] and [tex]W = Width[/tex]
[tex]L:W = 8: 5[/tex]
[tex]Perimeter = 117[/tex]
Required
Determine the Diagonal
First, the dimension of the screen has to be calculated;
Recall that; [tex]L:W = 8: 5[/tex]
Convert to division
[tex]\frac{L}{W} = \frac{8}{5}[/tex]
Multiply both sides by W
[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]
[tex]L = \frac{8W}{5}[/tex]
The perimeter of a rectangle:
[tex]Perimeter = 2(L+W)[/tex]
Substitute [tex]L = \frac{8W}{5}[/tex]
[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]
Take LCM
[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]
[tex]Perimeter = 2(\frac{13W}{5})[/tex]
Substitute 117 for Perimeter
[tex]117 = 2(\frac{13W}{5})[/tex]
[tex]117 = \frac{26W}{5}[/tex]
Multiply both sides by [tex]\frac{5}{26}[/tex]
[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]
[tex]\frac{5 * 117}{26} = W[/tex]
[tex]\frac{585}{26} = W[/tex]
[tex]22.5 = W[/tex]
[tex]W = 22.5[/tex]
Recall that
[tex]L = \frac{8W}{5}[/tex]
[tex]L = \frac{8 * 22.5}{5}[/tex]
[tex]L = \frac{180}{5}[/tex]
[tex]L = 36[/tex]
The diagonal of a rectangle is calculated using Pythagoras theorem as thus;
[tex]D = \sqrt{L^2 + W^2}[/tex]
Substitute values for L and W
[tex]D = \sqrt{36^2 + 22.5^2}[/tex]
[tex]D = \sqrt{1296 + 506.25}[/tex]
[tex]D = \sqrt{1802.25}[/tex]
[tex]D = \sqrt{1802.25}[/tex]
[tex]D = 42.4529150943[/tex]
[tex]D = 42.5\ inch[/tex] (Approximated)
The graph of y = −4x2 + 13x + 12 is shown below. What are the zeros of the function (as exact values), the y-intercept, and the maximum or minimum value of the function?
Answer:
zeros: -3/4, 4y-intercept: 12maximum: 22 9/16Step-by-step explanation:
The graph tells you the zeros of the function are x=-3/4 and x=4.
The y-intercept is the constant in the function: 12.
The maximum is 22.5625 at x = 1.625.
The image of (-4,6) reflected along the y-axis is
a. (4, -6)
b. (-4,-6)
c. (4, 6)
d. (-4, 6)
Answer:
C(4,6)
Step-by-step explanation:
the x turns into its opposite when reflected across y same thing for y when reflected across x
Answer:
c. (4, 6)
Step-by-step explanation:
The rule of an reflection about the y-axis is: [tex]A(x,y)\rightarrow A'(-x,y)[/tex]
Apply the rule to point (-4, 6):
[tex]\frac{(-4,6)\rightarrow\boxed{(4,6)}}{(x,y)\rightarrow(-x,y)}[/tex]
Option C should be the correct answer.
Amira has 3/4 of a bag of cat food her cat eats 1/10 of a bag per week how many weeks will the food last
Find the odds in favor and the odds against a randomly selected person from Country X, age 25 and over, with the stated amount of education. four years (or more) of college
Answer:
25 : 63 and 63 : 25
Step-by-step explanation:
This is a complete question
The table shows the educational attainment of the population of Country X, ages 25 and over. Use the data in the table, expressed in millions, to solve the problem. of 10 questions ge 1: Ages 25 and Over, in Miltions 4 Years igh College 4 Years High School (Less than College School Only 4years) Cor Moce) Total Male 29 19 25 89 Female 11 28 23 Total 2 57 42 50 [176 Find the odds in favor and the odds against a randomty selected person from Country X.age 25 and over, with the stated amount of education. four years (or more) of college 21:67, 67:21 63:88, 88:63 25:63, 63:25 25:88, 88:25
According to the question, the relevant data provided in the question for the solution is as follows
Four years or more of college
Number of students = 50
Total = 176 students
Number of students does not belong = 126
So odds in favor is
= 50 : 126
= 25 : 63
And automatically out against the favor is 63 : 25
A ladder leans against a vertical at angle of 60° to the wall of the foot of the ladder is 5m away from the wall calculate the length of the ladder
Answer:
Your question indicates the ladder is at an angle of 60° to the wall, meaning the angle between the wall and the ladder is 60° and the angle between the ladder and the ground must be 30°. Not a very efficient way to set up a ladder.
5.7735 meters. The top of the ladder is 2.8868 meters off the ground.
Now, if you meant the ladder is 60° from the ground, that’s a different story.
Then, the ladder is 10 meters long and reaches 8.6603 meters from the ground.
A 30–60–90 right triangle is half of an equalateral triangle. Therefore the hypotenuse is double the length of the short leg, and by the Pythagorean theorum, we can determine that the other leg is the length of the short leg times the square root of 3.
All lengths in this answer are rounded to the nearest tenth of a millimeter.
Step-by-step explanation:
4. Solve the system of equations. (6 points) Part I: Explain the steps you would take to solve the system by eliminating the x-terms. (1 point) Part II: Explain the steps you would take to solve the system by eliminating the y-terms. (2 points) Part III: Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair. Show your work. (3 points)
Answer:
The system of equations you want to be solved is not given. I would however give an example with which the method of elimination will be shown, and can be used in solving problems of the nature.
Step-by-step explanation:
Consider the system of equations:
x + y = 7 ................................(1)
2x - y = 8 ..............................(2)
To eliminate x:
First multiply (1) by 2 to have
2x + 2y = 14 ...........................(3)
Next, subtract (2) from (3) to have
3y = 6
y = 6/3 = 2
To eliminate y:
Add (1) and (2) to have
3x = 15
x = 15/3 = 5
Therefore, (x, y) = (5, 2).
Pedro thinks that he has a special relationship with the number 6. In particular, Pedro thinks that he would roll a 6 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pp is the true proportion of the time Pedro will roll a 6.
Required:
a. State the null and alternative hypotheses for testing Pedro's claim.
b. Now suppose Pedro makes 42 rolls, and a 6 comes up 9 times out of the 42 rolls. Determine the P-value of the test: P-value.
c. Does this sample provide evidence at the 5% level that Pedro rolls a 6 more often than you'd expect?
Answer:
Step-by-step explanation:
a) The sample space, n(S) = 6^6 = 46656
Let the number fair dice toss that show 6 = n(A)
Hence, the probability of getting, P(A) = n(A)/n(S)
b) Sample space, n(S) = 6^42
n(A) = 6^9
∴ P(A) = n(A)/n(S) = 6^9/6^42 = 1/(6^33) = 2.09 X 10^(-26)
c) No
If x = -1 then how much is 2x - 1
a) 1
b) -3
c) -2
hurry please need to turn in 10 min
Answer: -3
Step-by-step explanation: 2x = -2 then you subtract 1 from that which is the same as adding negative one so -2 - 1 or -2 + -1 = -3
Find x . Round to the nearest tenth of a degree.
Answer:
36.9°
Step-by-step explanation:
Sin x = 9/15 = 3/5
x = sin^-1 3/5
x= 36.87
x= 36.9° to nearest tenth
The formula for the distance traveled over time t and at an average speed v. v times t. If Amit ran for 40 minutes at a speed of about 5 kilometers per hour. What calculation will give us the estimated distance Amit ran in kilometers? Can you help me figure out the answer?
Answer:
Thus, Amit ran 3.33 KM
calculation needed:
conversion of time (40 minutes to hour)
multiplying velocity and time (which we got in hours)
Step-by-step explanation:
Given
to calculate the distance: . v times t
that is multiply v with t
where v is average velocity
t is the time
__________________________________
Given
v = 5 km/hour
time = 40 minutes
since speed is in Km per hour and also we have to find distance in km
lets convert time which in 40 minutes to hour
we know
60 minutes = 1 hour
1 minute = 1/60 hour
40 minutes = 40/60 hour = 2/3 hour
distance = v times t
distance = 5*2/3 = 10/3 = 3 1/3 km = 3.33 km
Thus, Amit ran 3.33 KM
calculation needed:
conversion of time (40 minutes to hour)
multiplying velocity and time (which we got in hours)
Answer:
5 • 40/50
Is the correct answer
If 2y = 6 - 3x, find y when x = 0
Answer:
2y= 6-3x when x=0
2y= 6-3(0)
2y= 6-0
2y= 6
y= 6/2
y= 3
#i'm indonesian
#hope it helps.
Answer:
[tex] \boxed{y = 3}[/tex]
Step-by-step explanation:
Given, x = 0
[tex] \mathsf{2y = 6 - 3x}[/tex]
plug the value of x
⇒[tex] \mathsf{2y = 6 - 3 \times 0}[/tex]
Multiply the numbers
⇒[tex] \mathsf{2y = 6 - 0}[/tex]
Calculate the difference
⇒[tex] \mathsf{2y = 6}[/tex]
Divide both sides of the equation by 2
⇒[tex] \mathsf{ \frac{2y}{2} = \frac{6}{2} }[/tex]
Calculate
⇒[tex] \mathsf{y = 3}[/tex]
Hope I helped!
Best regards!
can someone simplify 4x-3y please!!
Answer:
I think you should change it to 4x + 3y
Step-by-step explanation:
hope this helps
There are 25,400,000 nanometers in an inch. What is this number written in scientific notation?
Answer:
254 x 10^5
Step-by-step explanation:
Hope this helps :)
If anything is misunderstood plz comment and I will change to the answer which you give me thank you very much :)
Answer:
2.54 x 10^5
hope this answer helps u ._.
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year. 1 year 5 years 2 years 16 years
Answer:
6 years
Step-by-step explanation:
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
Answer:
5 years
Step-by-step explanation:444
At α = 0.001, is the overall model significant?Group of answer choicesNo, F* < FcThe test is inconclusive because 0.001 < p < 0.10Yes, F* < Fc, and p < 0.05.Yes, F* > Fc, and p < 0.001.Yes, F* > Fc, and p > 0.05.
Answer:
No, F* < Fc
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis .
Solve for x: 3(x + 1)= -2(x - 1) + 6.
Answer:
x=1
Step-by-step explanation:
3(x + 1)= -2(x - 1) + 6.
Distribute
3x+3 = -2x+2+6
Combine like terms
3x+3 = -2x+8
Add 2x to each side
3x+3+2x = 8
5x+3 = 8
Subtract 3 from each side
5x =5
Divide by 5
x =1
Listed below are the commissions earned ($000) last year by a sample of 15 sales representatives at Furniture Patch Inc.
$4.0 $6.0 $7.4 $10.6 $12.5 $13.6 $15.4 $15.8 $16.8
$17.4 $19.1 $22.3 $37.1 $43.2 $81.4
a. Determine the mean, median, and the standard deviation. (Round your answers to 2 decimal places.)
Mean $
Median $
Standard deviation $
b. Determine the coefficient of skewness using Pearson
Answer:
Mean= $21.5067
Median = $15.8
Standard deviation= $19.02
Coefficient of skewness= $0.8991
Step-by-step explanation:
Mean =( $4.0 +$6.0 +$7.4+ $10.6 +$12.5+ $13.6+ $15.4+ $15.8 +$16.8
+$17.4+ $19.1 +$22.3+ $37.1 +$43.2 +$81.4)/15
Mean =$ 322.6/15
Mean= $21.5067
Median= middle number
Median = $15.8
Variance=( ($4.0-.$21.5)²+( $6.0. -.$21.5)²+( $7.4 -.$21.5)²+( $10.6 -.$21.5)²+( $12.5 -.$21.5)²+( $13.6. -.$21.5)²+ ($15.4 -.$21.5)²+( $15.8 -.$21.5)²+ ( $16.8 -.$21.5)²+ ($17.4-.$21.5)² +($19.1 -.$21.5)²+ ($22.3 -.$21.5)²+ ($37.1 -.$21.5)²+ ($43.2-.$21.5)²+( $81.4-.$21.5)²)/15
Variance=$ 5424.79/15
Variance=$ 361.65
Standard deviation= √ variance
Standard deviation= √361.65
Standard deviation= $19.02
Coefficient of skewness
=3( mean-median)/standard deviation
= 3(21.5-15.8)/19.02
= 3(5.7)/19.02
= 17.1/19.02
Coefficient of skewness= 0.8991
A sample of bacteria is decaying according to a half-life model. If the sample begins with 700 bacteria, and after 10 minutes there are 140 bacteria, after how many minutes will there be 40 bacteria remaining? Round your answer to the nearest whole number.
Answer:
18 minutes
Step-by-step explanation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is the time,
and T is the half life.
A = 140 when t = 10. Solve for the half life:
140 = 700 (½)^(10 / T)
0.2 = ½^(10 / T)
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31
When A = 40, t is:
40 = 700 (½)^(t / 4.31)
0.057 = ½^(t / 4.31)
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8
Rounded to the nearest whole number, it takes 18 minutes.
The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes.
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
The half-life decay formula is given as,
N(t) = N₀ [tex](1/2)^{(t / T)}[/tex]
Where T is half-life while t is the time taken.
N₀ is the initial amount,
As per the given,
N(t) = 140 when t = 10.
140 = 700 [tex](1/2)^{(t / T)}[/tex]
Take log both sides,
log 0.2 = (10 / T) log 0.5
10 / T = 2.32
T = 4.31 minutes
Put N(t) = 40
40 = 700[tex](1/2)^{(t / 4.31)}[/tex]
Take log both sides,
log 0.057 = (t / 4.31) log 0.5
t / 4.31 = 4.13
t = 17.8 ≈ 18 minutes
Hence "The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes".
For more about exponential function,
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The probability distribution of number of televisions per household in a small town is given below.
x 0 1 2 3
P(x) 0.05 0.15 0.25 0.55
a. Find the probability of randomly selecting a household that has one or two televisions.
b. Find probability of randomly selecting a household that has one or two televisions
Answer: 0.20
Step-by-step explanation:
The given probability distribution of number of televisions per household in a small town:
x 0 1 2 3
P(x) 0.05 0.15 0.25 0.55
To find : The probability of randomly selecting a household that has one or two televisions ( in both parts a. and b.).
The computations for this would be :
P( 1 or 2) = P(1)+P(2)
= 0.05+0.15
= 0.20
Hence, the required probability= 0.20
Answer:
Step-by-step explanation:
Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (Enter your answer using interval notation.)
Answer:
(-∞,-3) and (3,∞)
Step-by-step explanation:
f(x) = x³ − 27x + 3
1. Find the critical points
(a) Calculate the first derivative of the function.
f'(x) = 3x² -27
(b) Factor the first derivative
f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)
(c) Find the zeros
3(x + 3) (x - 3) = 0
x + 3 = 0 x - 3 = 0
x = -3 x = 3
The critical points are at x = -3 and x = 3.
2. Find the local extrema
(a) x = -3
f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57
(b) x = 3
f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51
The local extrema are at (-3,57) and (3,-51).
3, Identify the local extrema as maxima or minima
Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)
f'(-4) = 3x² -27 = 3(4)² - 27 = 21
f'(0) = 3(0)² -27 = -27
f'(4) = 3(4)² - 27 = 51
The function is increasing on the intervals (-∞,-3) and (3,∞).
The graph below shows the critical points of your function.
The length of each side of a cubical wooden block is 16 inches. What is the volume of
the block
Hey there! I'm happy to help!
To find the volume of a cube, you simply take whatever the side length is and multiply it by itself 3 times, which is also known as cubing the number!
16×16×16=4096
You can also write it as 16³=4096
This is because the length is 16, the width is 16, and the height is 16, so you multiply them all together!
I hope that this helps! Have a wonderful day!
A planet rotates on an axis through its poles and 1 revolution takes 1 day 1 day is 24 hours. The distance from the axis to a location the planet 30 degrees north latitude is about 3387.5 miles. Therefore, a location on the planet at 30 degrees north latitude is spinning on a circle of radius 3387.5 miles.
Compute the linear speed on the surface of the planet at 30 degrees north latitude.
Answer:
The velocity is [tex]v = 886.96 \ m/s[/tex]
Step-by-step explanation:
From the question we are told that
The period of each revolution is [tex]T = 1\ day = 24 \ hours[/tex]
The angle is [tex]\theta = 30^o[/tex]
The radius is [tex]r = 3387.5 \ miles[/tex]
Generally the linear speed is mathematically represented as
[tex]v = w * r[/tex]
Where [tex]w[/tex] is the angular speed which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 *3.142 }{24}[/tex]
[tex]w = 0.2618 \ rad/s[/tex]
Thus
[tex]v = 0.261833 * 3387.5[/tex]
[tex]v = 886.96 \ m/s[/tex]
There are three commercial tax-preparation offices in City A. The local Better Business Bureau has been receiving some complaints that one of the offices does not understand tax law well enough to provide expert advice. The Better Business Bureau has decided to invest several hundred dollars in grant money to test the claim. It has selected four people at random and has asked that they allow each of the offices to prepare their taxes using the same information. The following data show the tax bills ($1,000s) as figured by each office. The following data show the tax bills as figured by each office. The data are also located in the CD-ROM file Tax-test.Return Office 1 Office 2 Office 31 4376.20 5100.10 4988.032 5678.45 6234.23 5489.233 2341.78 2242.60 2121.904 9875.33 10300.30 9845.605 7650.20 8002.90 7590.886 1324.80 1450.90 1356.89Required:Use the ANOVA procedure on your calculator for completely randomized designs to determine whether there is a significant difference in the mean taxes due on tax returns?
Answer:
I have not answer
plz follow me....
A carpenter is making doors that are 20582058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 1010 doors is made, and it is found that they have a mean of 20462046 millimeters with a standard deviation of 1515. Is there evidence at the 0.050.05 level that the doors are too short and unusable
Answer:
Z= 0.253
Z∝/2 = ± 1.96
Step-by-step explanation:
Formulate the null and alternative hypotheses as
H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test
Here ∝= 0.005
For alpha by 2 for a two tailed test Z∝/2 = ± 1.96
Standard deviation = s= 15
n= 10
The test statistic used here is
Z = x- x`/ s/√n
Z= 2058- 2046 / 15 / √10
Z= 0.253
Since the calculated value of Z= 0.253 falls in the critical region we reject the null hypothesis.
There is evidence at the 0.05 level that the doors are too short and unusable.
Find X using the Angle Sum Theorem
Answer:
x = 20°
Step-by-step explanation:
So when I learned it we called it the exterior angle theorem not the angle sum theorem but here goes.
Since exterior angle = 110 Degrees,
--> The Inner 2 angles's sum = 110 Degrees
so, 70 + 2x = 110
=> 2x = 40
x = 20
x = 20°
Hope this helps!
Write 11 numbers in a row so that the sum of any 3 consecutive numbers is negative, while the sum of all the numbers is positive. Is it possible?
Explanation:
Let the 11 numbers be {a1, a2, ..., a11} such that a1 is the smallest and a11 is the largest. So, a1 < a2 < ... < a11. Furthermore, these numbers are consecutive.
If we add consecutive numbers to get a negative result, then each of the numbers must be negative. So every value in the set {a1, a2, ..., a11} is a negative value which makes it impossible to have a1+a2+...a11 be a positive sum.
