Answer:
Step-by-step explanation:
k = 6
To find the value of k, rationalize the denominator of 2/√3, and compare it with 2k/3 to find k = √3.
To rationalize the denominator of the fraction 2/√3, we need to make the denominator a rational number. We can do this by multiplying both the numerator and the denominator by √3.
Multiply the numerator and the denominator by √3:[tex]\frac{2}{\sqrt3} * \frac{\sqrt3}{\sqrt3} = \frac{2\sqrt3}{3}[/tex]So, after rationalizing, the fraction becomes 2√3/3. According to the problem statement, this is equivalent to 2k/3.
Therefore, we can equate 2k to 2√3:
2k = 2√3
k = √3
So, the value of k is √3.
The complete question is
When the denominator of 2/√3 is rationalized ,it becomes 2k/3. Find k
Andre sometimes mows on the weekend to make extra money. Two weeks ago, he mowed a neighbor's lawn for 1/2 hour and earned $10. Last week, he mowed his uncles lawn for 3/2 hours and earned $30. This week, he mowed the lawn of a community center for 2 hours and earned $30. Which job paid better than others?
Answer:
Andre got better paid when he mowed for neighbor's and uncle's lawn which is $20/hr than Community center's lawn which is $15/hr.
Step-by-step explanation:
Given:
Andre mowed a neighbor's lawn for 1/2 hour and earned $10.
For 1/2 hour = $10
So for 1 hour = Money earned in 1 hour.
By using Unitary method we get;
Money earned in 1 hour = [tex]\frac{10}{\frac{1}{2}} = \frac{10\times2}{1} = \$20[/tex]
Hence Andre hourly rate to mowed neighbor's lawn is $20.
Also Given:
Andre mowed a Uncle's lawn for 3/2 hour and earned $30.
For 3/2 hour = $30
So for 1 hour = Money earned in 1 hour.
By using Unitary method we get;
Money earned in 1 hour = [tex]\frac{30}{\frac{3}{2}} = \frac{30\times2}{3} = \$20[/tex]
Hence Andre hourly rate to mowed Uncle's lawn is $20.
Also Given:
Andre mowed Community center's lawn for 2 hour and earned $30.
For 2 hour = $30
So for 1 hour = Money earned in 1 hour.
By using Unitary method we get;
Money earned in 1 hour = [tex]\frac{30}{2}=\$15[/tex]
Hence Andre hourly rate to mowed Community Center's lawn is $15.
Now Since we can see that when he mowed neighbor and uncle's lawn he was paid at rate of $20 and when he mowed Community Center's lawn he got paid at rate of $15.
Hence Andre got better paid when he mowed for neighbor's and uncle's lawn which is $20/hr than Community center's lawn which is $15/hr.
Which system of linear inequalities is represented by the graph?
y ≥ 2x + 1
y ≤ 2x – 2
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
So, the lines of this system are:
1) [tex]y= 2x + 1[/tex]
Where:
[tex]m=2\\b=1[/tex]
2) [tex]y=2x- 2[/tex]
Where:
[tex]m=2\\b=-2[/tex]
Notice that:
- Since both lines have the same slope, they are parallel.
- The symbol of the first inequality is [tex]\geq[/tex] . This indicates that the line is solid and the shaded region must be above the line.
- The symbol of the second inequality is [tex]\leq[/tex] . This indicates that the line is solid and the shaded region must be below the line.
Therefore, the second graph represents the system of linear inequalities.
Answer:
b
Step-by-step explanation:
Martina creates the graph of function g by applying a transformation to function f.
f(x) = 4x-2
g(x) = 4x+7
Which transformation did Martina apply?
A.a vertical shift of 9 units down
B.a vertical shift of 9 units up
C. a horizontal shift of 9 units left
D. a horizontal shift of 9 units right
Answer:
B.a vertical shift of 9 units up
Step-by-step explanation:
Given [tex]f(x) = 4x-2\\g(x) = 4x+7[/tex]
[tex]g (x) = f (x) + k[/tex]
It means shifting [tex]f (x)\ k[/tex] unit vertically.
Now, we will find the value of [tex]k[/tex] for the given function
[tex]g(x) = 4x+7\\\\add\ 2\ and\ subtract\ 2\\\\g(x) = 4x+7+2-2\\g(x) = 4x-2+9\\\\We\ have\ f(x)=4x-2\\\So,\ g(x)=f(x)+9[/tex]
[tex]k=9[/tex]
Hence, vertical shift of 9 units.
Answer:
C. a horizontal shift of 9 units left
Step-by-step explanation:
Look at this helpful chart:
Vertical Translations
translation up k units: g(x) = f(x) + k, where k > 0
translation down k units: g(x) = f(x) – k, where k > 0
Horizontal Translations
translation left k units: g(x) = f(x + k), where k > 0
translation right k units: g(x) = f(x – k), where k > 0
The change happening in Martina's graph is therefore a horizontal translation to the left.
If 15 of the students are male and 18 of the students are female in a mathclass, what fractional part of the class is female?
Answer:
6/11
Step-by-step explanation:
Assuming all students are accounted for, the fraction that is female is ...
female/total = 18/(15+18) = 18/33 = 6/11
What is the average rate of change of the function on the interval from x = 0 to x = 5 f(x)=
1/2(3)x
What is the average rate of change of the function on the interval from x = 0 to x = 5 ; f(x)= 1\2 (3)^x
Answer:
Average rate of change of the function on the interval from x = 0 to x = 5 is 24.2
Solution:
Given function is:
[tex]f(x) = \frac{1}{2}(3^x)[/tex]
We have to find the average rate of change of function from x = 0 to x = 5
The formula for average rate of change can be expressed as follows:
[tex]{A\left( x \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}}[/tex]
So for rate of change of function from x = 0 to x = 5 is:
[tex]{A\left( x \right) = \frac{{f\left( 5 \right) - f\left( 0 \right)}}{{5 - 0}}}[/tex]
Let us find f(0) and f(5)
To find f(0), substitute x = 0 in f(x)
[tex]f(0) = \frac{1}{2}(3^0) = \frac{1}{2}[/tex]
To find f(5), substitute x = 5 in f(x)
[tex]f(5) = \frac{1}{2}(3^5) = \frac{1}{2}(243) = \frac{243}{2}[/tex]
Therefore,
[tex]A(x)=\frac{\frac{243}{2}-\frac{1}{2}}{5-0}=\frac{242}{\frac{2}{5}}=\frac{242}{2} \times \frac{1}{5}=24.2[/tex]
Therefore average rate of change of the function on the interval from x = 0 to x = 5 is 24.2
Special right triangles, find x and y
Answer:
The answer to your question is x = 17.32; y = 8.67
Step-by-step explanation:
Process
1.- Use trigonometric functions to find x and y
a) sin Ф = [tex]\frac{opposite side}{hypotenuse}[/tex]
Ф = 60°
opposite side = 15
hypotenuse = ?
[tex]hypotenuse = \frac{opposite side}{sin \alpha }[/tex]
[tex]hypotenuse = \frac{15}{sin 60}[/tex]
[tex]hypotenuse = \frac{15}{0.87}[/tex]
hypotenuse = 17.32
b) cosФ = [tex]\frac{y}{hypotenuse}[/tex]
[tex]y = hypotenuse x cos 60[/tex]
[tex]y = 17.32 x 0.5[/tex]
y = 8.67
Jenny drew a figure in art class.
Does it have rotational symmetry? If yes, what is the angle of rotation?
Answer:
60, yes.
Step-by-step explanation:
Yes, it has symmetry if you rotate it. Because it is a hexagon, the degree of rotation is 360 (circle of rotation) divided by 6 sides, because it takes that many degrees to rotate till the next side enters the position of the previous side. 360/6 is equal to 60.
Answer : Yes, it has rotational symmetry. The angle of rotation is, [tex]60^o[/tex]
Step-by-step explanation :
Rotational symmetry : It is a shape that has Rotational Symmetry when it still the same after the rotation.
The given figure is hexagon and it has rotational symmetry because it still the same after the rotation.
As there are 6 sides of hexagon geometry and the degree of rotation is, [tex]360^o[/tex].
So, the angle of rotation = [tex]\frac{360^o}{6}=60^o[/tex]
A running back was the MVP (most valuable player) in 0.14 of the first 50 Super Bowls. A. What percent of the MVPs were running backs? % were running backs. B. What fraction of the MVPs were not running backs? Were not running backs.
Answer:
A. 14%.
B. [tex]\frac{43}{50}[/tex]
Step-by-step explanation:
We have been given that a running back was the MVP (most valuable player) in 0.14 of the first 50 Super Bowls.
A. To find the percent, when the MVPs were running backs, we need to convert 0.14 into percent by multiplying by 100 as:
[tex]0.14\times 100=14\%[/tex]
Therefore, 14 percent of the MVPs were running backs.
B. To find the fraction of the MVPs were not running backs, we will subtract 0.14 from 1 to find the MVPs, who were not running backs. Finally, we will convert the answer into fraction as:
[tex]1-0.14=0.86[/tex]
Now, we will multiply and divide 0.86 by 100 as:
[tex]0.86\times \frac{100}{100}=\frac{86}{100}[/tex]
Reduce the fraction by dividing numerator and denominator by 2:
[tex]\frac{43}{50}[/tex]
Therefore, [tex]\frac{43}{50}[/tex] of the MVPs were not running backs.
14% of the MVPs in the first 50 Super Bowls were running backs. Yet, 43 out of 50 MVPs (or 86%) were not running backs.
Explanation:The running back was the MVP in 0.14 of the first 50 Super Bowls according to the question. To find the percent of the MVPs that were running backs, we simply convert the 0.14 to percentage by multiplying it by 100. Hence, 14% of the MVPs were running backs.
For the fraction of the MVPs that were not running backs, we need to calculate the remaining part not covered by the running backs. Given as 1 (entirety) minus 0.14 gives 0.86. In fraction terms, this is same as 86/100 which simplifies to 43/50.
Learn more about Percentages and Fractions here:https://brainly.com/question/12715980
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In a business class there are 14 business majors and 7 non-business majors. 4 students are randomly selected to present a topic. What is the probability that at least 2 of the 4 students selected are business majors?
Answer: 52/57
Step-by-step explanation:please see attachment for explanation
Final answer:
The question involves calculating the probability of selecting at least 2 business majors from a group, using complementary probability and combinations. The probability that at least 2 of the 4 students selected are business majors is approximately [tex]\(0.1608\).[/tex]
Explanation:
To find the probability that at least 2 of the 4 students selected are business majors, we can calculate the probability of exactly 2, 3, and 4 students being business majors, and then sum these probabilities.
First, let's find the probability of selecting exactly 2 business majors and 2 non-business majors:
1. Probability of selecting 2 business majors: [tex]\( \frac{{14 \choose 2}}{{21 \choose 4}} \)[/tex]
2. Probability of selecting 2 non-business majors:[tex]\( \frac{{7 \choose 2}}{{21 \choose 4}} \)[/tex]
Then, we can find the probability of selecting exactly 3 business majors and 1 non-business major:
1. Probability of selecting 3 business majors: [tex]\( \frac{{14 \choose 3}}{{21 \choose 4}} \)[/tex]
2. Probability of selecting 1 non-business major: [tex]\( \frac{{7 \choose 1}}{{21 \choose 4}} \)[/tex]
Finally, we find the probability of selecting all 4 business majors:
1. Probability of selecting 4 business majors: [tex]\( \frac{{14 \choose 4}}{{21 \choose 4}} \)[/tex]
Now, we sum up these probabilities:
[tex]\[\text{Probability of at least 2 business majors} = \text{Probability of selecting exactly 2} + \text{Probability of selecting exactly 3} + \text{Probability of selecting all 4}\][/tex]
[tex]\[\text{Probability of at least 2 business majors} = \left( \frac{{14 \choose 2}}{{21 \choose 4}} \times \frac{{7 \choose 2}}{{21 \choose 4}} \right) + \left( \frac{{14 \choose 3}}{{21 \choose 4}} \times \frac{{7 \choose 1}}{{21 \choose 4}} \right) + \left( \frac{{14 \choose 4}}{{21 \choose 4}} \right)\][/tex]
[tex]\[= \left( \frac{{91}}{{5985}} \times \frac{{21}}{{5985}} \right) + \left( \frac{{364}}{{5985}} \times \frac{{7}}{{5985}} \right) + \left( \frac{{1001}}{{5985}} \right)\][/tex]
[tex]\[= \left( \frac{{1911}}{{5985^2}} \right) + \left( \frac{{2548}}{{5985^2}} \right) + \left( \frac{{1001}}{{5985}} \right)\][/tex]
[tex]\[= \frac{{1911 + 2548 + 1001}}{{5985^2}}\][/tex]
[tex]\[= \frac{{5460}}{{5985^2}}\][/tex]
[tex]\[\approx 0.1608\][/tex]
So, the probability that at least 2 of the 4 students selected are business majors is approximately [tex]\(0.1608\).[/tex]
Mike is riding his bike 8 mi./hr northwest, and Shelly is riding her bike 11 mi./hr southwest. Both are headed for the intersection of the two bike paths. At what rate are the bikes approaching each other when Mike is 0.2 mi. and Shelly is 0.5 mi. from the intersection?
Answer: GLOBAL WARMING FOESNT EXIST
Step-by-step explanation: STOP RIDING BIKES MORE CARS
A ladder is leaning against a garage. If the ladder is 25ft long. How high up the garage will it reach if it is placed 4ft from the bottom of the garage
Answer:
[tex]24.68\ ft[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
Let
x ----> ladder height in ft
Applying the Pythagorean Theorem
[tex]25^2=4^2+x^2[/tex]
solve for x
[tex]625=16+x^2[/tex]
[tex]x^2=625-16[/tex]
[tex]x^2=609[/tex]
[tex]x=\sqrt{609}\ ft[/tex]
[tex]x=24.68\ ft[/tex]
The ladder reaches up 24.7 ft on the garage wall.
The ladder reaches up 24 ft on the garage wall.
To find the height the ladder reaches, we can use the Pythagorean theorem, where the ladder is the hypotenuse:
Height² + Base² = Hypotenuse²
Height² + 4² = 25²
Height² + 16 = 625
Height² = 609
Height = √609
Height =24.67 ≈ 24.7 ft
Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 30 minutes without delay (say, on the hour and on the half hour). What is the expected value of your waiting time? Explain how you got your answer.
Answer:
E(x) = 15 minutes
Step-by-step explanation:
The random variable X (waiting time) has a uniform distribution between the interval [0,30], because it is just as likely that you arrive in any time and then your waiting time is minimum 0 minutes and maximum 30 minutes
The expected value of a random variable uniform is:
E(x) = [tex]\frac{a+b}{2}[/tex]
Where a and b are the interval's extremes
Thus
E(x) = [tex]\frac{0+30}{2}[/tex]
E(x) = 15 minutes
PLEASE HELP ME AND SIMPLIFY THE POLYNOMIAL 24 POINTS
Answer: it would be A
Wilma and Betty - Two neighbors, Wilma and Betty, each have a swimming pool. Both Wilma's and Betty's pools hold 10500 gallons of water. If Wilma's garden hose fills at a rate of 700 gallons per hour while Betty's garden hose fills at a rate of 400 gallons per hour, how much longer does it take Betty to fill her pool than Wilma? It takes Betty hours and minutes longer to fill her pool than Wilma.
Answer:
11 hours 15 mins
Step-by-step explanation:
Wilma & Betty both have a pool that holds 10500 gallons of water each.
Wilma's garden hose fills at the rate of 700 gallons per hour.
Betty's garden hose fills at a rate of 400 gallons per hour.
Volume = Rate * time
Time = Volume /rate
The time it will take for Wilma's pool to be filled = 10500/700
= 15 hours
The time it will take for Betty's pool to be filled = 10500/400
= 26.25hours
= 26 hours 15 minutes
it will take Betty (26.25 - 15) to fill her pool than Wilma.
= 11.25hours
= 11 hours 15 mins
Need help please answer what you can thank you
8)Find a ratio that compares the relative sizes of the quantities. (Use the same units of measurement for both quantities. Write the ratio as a fraction in simplest form.)
27 feet to 54 yards
9)Find the unit price (in dollars per ounce).
A 17-ounce box of cereal for $5.27
$ ? per ounce
12)A car uses 10 gallons of gasoline for a trip of 300 miles. How many gallons would be used on a trip of 240 miles?
? gal
13)Find a ratio that compares the relative sizes of the quantities. (Use the same units of measurement for both quantities. Write the ratio as a fraction in simplest form.)
1 quart to 1 gallon
14)Find a ratio that compares the relative sizes of the quantities. (Use the same units of measurement for both quantities. Write the ratio as a fraction in simplest form.)
3000 pounds to 4 tons
19)Find a ratio that compares the relative sizes of the quantities. (Use the same units of measurement for both quantities. Write the ratio as a fraction in simplest form.)
9 weeks to 7 days
Answer:
The answers to all the questions are given below.
Step-by-step explanation:
8)The ratio of the numbers 27 feet and 54 yard
1 foot = 0.3333 yard
27 feet = 9 yard
Required ratio = [tex]\frac{9}{54}[/tex] = 0.167
9)A 17 ounce bag costs $5.27.
Hence cost of 1 ounce bag = [tex]\frac{5.27}{17}[/tex] = $0.31
12)For trip of 240 miles ,it uses 8 gallons.
13)1 quart = 0.25 gallons
Hence the ratio would be [tex]\frac{1}{4}[/tex]
14)1 pound = 0.0005 tonnes.
Hence the ratio would be [tex]\frac{1}{2000}[/tex]
19)1 week = 7 days
So the ratio would be [tex]\frac{1}{9}[/tex]
These are the required ratios
Solve for x.
Round only your final answer to the nearest tenth.
9.1
11.2
8.2
18
Answer:
11.2
Step-by-step explanation:
tan( angle ) = opposite / adjacent
You have a deck that has an area of 160 sq. Ft. You and your family have decided to increase the area of your deck to 180 sq. Ft. What is the percent of increase to the area of the deck? Round your answer to the nearest tenth if necessary. Show your work.
Answer:The percent of increase of the area of the deck is 12.5%
Step-by-step explanation:
The initial area of the deck is 160 square feet. You and your family have decided to increase the area of your deck to 180. The amount by which the area of the deck was increased is is 180 - 160 = 20 square feet.
The percent of increase of the area of the deck would be
Increase / initial area × 100.
20/160 × 100 = 12.5℅
A recent survey showed that 102 adults out of a sample of 400 do not like cold weather. However, 115 of those studied said that they had interest in taking skiing lessons. Based on this sample, if an adult is chosen at random, what is the probability that he or she has no desire to take skiing lessons? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that a randomly chosen adult from the survey has no desire to take skiing lessons is 57/80, or as a decimal, 0.7125.
Out of a sample of 400 adults, 115 expressed an interest in taking skiing lessons. Therefore, to find the number of adults who have no interest in skiing lessons, we subtract the number interested (115) from the total number surveyed (400).
The calculation is as follows: 400 - 115 = 285 adults who have no interest in taking skiing lessons. The probability that a randomly selected adult has no desire to take skiing lessons is the number of adults with no interest divided by the total number surveyed. This gives us:
Probability = (Number of adults with no desire to take skiing lessons) / (Total number of adults surveyed)Probability = 285 / 400
To simplify this fraction, we find that both numbers are divisible by 5:Probability = 57 / 80
If we want to express this as a decimal rounded to the nearest millionth, we perform the division:
Probability = 0.7125
This result is already rounded to the fourth decimal place, which is more precise than rounding to the nearest millionth.
How would you define the following ad placed by a broker in NY, "Two-family home, $190,000, Call 212-123-4567"?
Answer:
The ad is about the price of a house which is sufficient for two families to live in it along with the contact details to purchase this house.
According to the ad, the total cost of the home is $190,000. It is sufficient for two families. It may be double story as well. To purchase this house, one can call at the given number which is 212-123-4567. This can be the original number or the format by the editor to show original number. Actual area of the house is not mentioned in the ad.
If y=sin(x-sinx), what is the smallest positive value of x for which the tangent line is parallel to the x-axis
(a) 1.677
(b) 2.310
(c) 3.142
(d) 3.973
(e) 6.283
Answer:
Option b ) 2.310
Step-by-step explanation:
Given that the function is
[tex]y = sin (x-sinx)[/tex]
For finding when the tangent is parallel to x axis, we must find the least positive value of x for which y' i.e. derivative =0
Differentiate y with respect to x using chain rule.
[tex]y' = cos(x-sinx) * (1-cosx)[/tex]
Equate this to 0
Either one factor should be zero.
[tex]cos(x-sinx)=0\\x-sinx =\frac{\pi}{2} \\[/tex]
x=2.31 satisfies this
For the other root,
[tex]1-cos x =0\\cos x =1\\x =0\\[/tex]
Since positive least value is asked we can say
x =2.310
Option b
Unless otherwise posted, what is the speed limit for cars in a residential area?
Answer:
In general if speed limit is not posted it will be 25 mph in residential area
Step-by-step explanation:
When speed limit is not posted then it is 25 mph in residential area or school zones
But its also depend on the density of population in that area is density is very low then speed limit can go up to 35 mph and if density of population is high then speed limit will be restricted up to 25 mph
So in general if speed limit is not posted it will be 25 mph in residential area
The Thomas family and the Clark family each used their sprinklers last summer. The water output rate for the Thomas family's sprinkler was 35L per hour. The water output rate for the Clark family's sprinkler was 15L per hour. The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 1100L. How long was each sprinkler used?
Answer:
x = 15 hours
y = 25 hours
Step-by-step explanation:
Lets call "x" number of working hours of Clark family sprinklers
and " y " number of working hours of Thomas family sprinklers
Then they both worked in such way that
x + y = 40 (1)
On the other hand the total water output 1100 lts were supplied according to:
35 lts/h * y (hours) + 15 lts/h * x (hours) = 1100 lts
Then
35*y + 15*x = 1100 (2)
Equations 1 and 2 become a system of two equations with two uknown variables x and y
We solve that system
y = 40 - x and 35* ( 40 - x ) + 15* x = 1100
1400 - 35x + 15x = 1100 ⇒ - 20x = -300
x = 15 hours
And
y = 40 - 15 = 25 hours
The high temperature in Fairbanks, Alaska was 15.7 degrees. That night it fell 38.4 degrees. The next morning, it rose 12.2 degrees. What was the temperature in the morning? Answer with just the number, no units. *
Answer:
The temperature in the morning was [tex]-10.5^o[/tex]
Step-by-step explanation:
we know that
1) The high temperature in Fairbanks, Alaska was 15.7 degrees
That night it fell 38.4 degrees
so
The temperature at night was
[tex]15.7^o-38.4^o=-22.7^o[/tex]
2) The next morning, it rose 12.2 degrees.
so
The temperature in the morning was
[tex]-22.7^o+12.2=-10.5^o[/tex]
There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?I. dbIII. c/3
Answer:
C) I and III only
Step-by-step explanation:
Let full pool is denoted by O
Days Hose x takes to fill pool O = a
Pool filled in one day x = O/a
Days Hose y takes to fill pool O = b
Pool filled in one day y = O/b
Days Hose z takes to fill pool O = c
Pool filled in one day z = O/c
It is given that
a>b>c
[tex]a>b>c>d\\\implies x<y<z<(x+y+z)\\[/tex]
Days if if x+y+z fill the pool together = d
1 day if x+y+z fill the pool together [tex]=O(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=\frac{O}{d}---(1)[/tex]
I) d < c
d are days when hose x, y, z are used together where as c are days when only z is used so number of days when three hoses are used together must be less than c when only z hose is used. So d < c
III) [tex]\frac{c}{3}<d<\frac{a}{3}[/tex]
Using (1)
[tex]\frac{bc+ac+ab}{abc}=\frac{1}{d}\\\\d=\frac{abc}{ab+bc+ca}\\\\As\quad(a>b>c)\\(ab+bc+ca)<3ab\\\\d=\frac{abc}{ab+bc+ca}>\frac{abc}{3ab}\\\\d>\frac{c}{3}[/tex]
Similarly
[tex]\frac{bc+ac+ab}{abc}=\frac{1}{d}\\\\d=\frac{abc}{ab+bc+ca}\\\\As\quad a>b>c\\(ab+bc+ca)>3bc\\\\d=\frac{abc}{ab+bc+ca}<\frac{abc}{3bc}\\\\d<\frac{a}{3}[/tex]
So,
[tex]\frac{c}{3}<d<\frac{a}{3}[/tex]
The Atlanta Braves marketing staff knows it has 20,000 seats in the stadium priced at $20 per ticket, 13,000 priced at $30 per ticket, and 17,000 priced at $50 per ticket. Jim says that the marketing materials should say that average ticket price is $30, Jill says it should be $33, and Fred says it should be $35.20. Who is most correct?
Answer:
Jill is most correct and it should be $33
Step-by-step explanation:
Total number of seats = x =20000+13000+17000
x =50000
Total cost of seats as per the price;
a = 20*20000
a =400,000
b = 30*13000
b =390,000
c = 50*17000
c =850,000
Average = (a + b + c) /x
Average = (400,000+390,000+850,000)/50,000
Average cost = 1,640,000/50,000
Average cost = $32.8
Sandy is a jeweler. She has 2 grams of gold. Each erring she makes contains 3/16 grams of gold. How many errings could she make from a gold bar of 1,000 grams of gold. Show your work
Sandy would be able to make 5,333 earrings with a gold bar of 1,000 grams.
Given that;
Sandy has 2 grams of gold, and each earring requires 3/16 grams of gold.
Now for the number of earrings she can make, divide the total amount of gold she has by the amount of gold needed for each earring.
[tex]\text {Number of earrings} = \dfrac{\text {Total gold} }{\text {Gold per earring} }[/tex]
[tex]\text {Number of earrings} = \dfrac{\text {2} }{\text {3/16} }[/tex]
To divide by a fraction, multiply by its reciprocal:
[tex]\text {Number of earrings} = \text {2} \times \dfrac{16}{3}[/tex]
Now, let's simplify the calculation:
[tex]\text {Number of earrings} = \dfrac{32}{3}[/tex]
Therefore, Sandy can make 10 earrings with 2 grams of gold, leaving 2 grams remaining.
When she had a gold bar of 1,000 grams, use the same approach to find out how many earrings she can make:
[tex]\text {Number of earrings} = \dfrac{\text {1000} }{\text {3/16} }[/tex]
[tex]\text {Number of earrings} = 5333[/tex]
So, Sandy would be able to make 5,333 earrings with a gold bar of 1,000 grams.
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Sandy could make about 5,333 earrings from 1,000 grams of gold by dividing 1,000 grams by the weight of gold in each earring (3/16 grams), which equates to multiplying 1,000 by the reciprocal of 3/16
Explanation:To solve this, we need to figure out how many times 3/16 grams goes into 1,000 grams. To do this, we divide 1,000 by 3/16.
However, when dividing by a fraction, it's often easier to multiply by its reciprocal (flip the fraction) instead. So we'll turn 1,000 into 1,000/1, and multiply by 16/3 (the reciprocal of 3/16).
First convert 1,000 into fraction form: 1,000 = 1,000/1Write the problem as a multiplication problem: 1,000/1 x 16/3Multiply the numerators (top numbers) together: 1,000 x 16 = 16,000Multiply the denominators (bottom numbers) together: 1 x 3 = 3So, 1,000/1 x 16/3 = 16,000/3Finally, take this result and divide the numerator by the denominator: 16,000 ÷ 3 ≈ 5333.3Therefore, Sandy could make about 5,333 earrings from 1,000 grams of gold.
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HELP ASAP PLEASE!!!!
The image shows the rational equation from part A with an incorrect solution process that a student performed. Explain the error the student made, and give the correct solution.
Only problem is with the simplifying.
We all know that 5/5 = 1, it is natural to assume (x+a)/(x+a) is also 1, but in some cases where x+a=0, it is undefined. In this equation, where they simplify (x-2) and (x-6), you must say that x is not 2 nor 6 or, you just delete 0/0 which is undefined.
Therefore the only solution would be x=-1
The error that the student made in the rational equation simplification is that; She made 6 and -1 to be a solution but 6 is not a solution but only x = -1 because 6 makes the function undefined
Simplifying Rational EquationsFrom the simplification of the rational equation, the solution the person got is; x = 6 or -1
Now, when we put 6 for x in the rational equation, it is discovered that the denominator becomes zero for two of the expressions.
Now, when the denominator of a fraction is zero, that fraction is said to be undefined.
Whereas when x = -1, we don't get an undefined function. Thus, the mistake the student made is that 6 is not a solution but only x = -1
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Abby's car gets approximately 24 miles per gallon she is planning a 1200 mile trip about how many gallons of gas should she plan to buy at an average price of $4.20 per gallon how much should she expect to spend for gas
Answer:
Step-by-step explanation:
Abby's car gets approximately 24 miles per gallon. This means that for every 24 mile that her car covers, it uses 1 gallon of gas. She is planning a 1200 mile trip. This means that the number of gallons of gas that she would need would be 1200/24 = 50 gallons.
One average price of 1 gallon of gas is $4.20. The total amount that she would spend in buying 50 gallons of gas would be
50 × 4.2 = $210
Abby needs 50 gallons of gas for her 1200-mile trip. At $4.20 per gallon, the total cost will be $210. This calculation helps Abby budget for her fuel expenses.
Abby needs to calculate the amount of fuel and the cost for a 1200-mile trip with her car that gets approximately 24 miles per gallon. Here's how to find out:
First, determine the number of gallons of gas needed:To find the number of gallons Abby needs, divide the total trip distance by her car's miles per gallon (MPG):
1200 miles / 24 MPG = 50 gallons
Next, calculate the cost of the gas:Multiply the number of gallons by the cost per gallon:
50 gallons x $4.20 per gallon = $210
Abby should plan to buy 50 gallons of gas for her 1200-mile trip, costing about $210 at $4.20 per gallon.
Watching TV: In 2012, the General Social Survey asked a sample of 1326 people how much time they spent watching TV each day. The mean number of hours was 3.02 with a standard deviation of 2.64. A sociologist claims that people watch a mean of 3 hours of TV per day. Do the data provide sufficient evidence to conclude that the mean hours of TV watched per day differs from the claim? Use the =α0.05 level of significance and the P-value method with the TI-84 Plus calculator.
Answer:
We fail to reject H₀ as there is insufficient evidence at 0.5% level of significance to conclude that the mean hours of TV watched per day differs from the claim.
Step-by-step explanation:
This is a two-tailed test.
We first need to calculate the test statistic. The test statistic is calculated as follows:
Z_calc = X - μ₀ / (s /√n)
where
X is the mean number of hoursμ₀ is the mean that the sociologist claims is trues is the standard deviationn is the sample sizeTherefore,
Z_calc = (3.02 - 3) / (2.64 /√(1326))
= 0.2759
Now we have to calculate the z-value. The z-value is calculated as follows:
z_α/2 = z_(0.05/2) = z_0.025
Using the p-value method:
P = 1 - α/2
= 1 - 0.025
= 0.975
Thus, using the positive z-table, you will find that the z-value is
1.96.
Therefore, we reject H₀ if | Z_calc | > z_(α/2)
Thus, since
| Z_calc | < 1.96, we fail to reject H₀ as there is insufficient evidence at 0.5% level of significance to conclude that the mean hours of TV watched per day differs from the claim.
Using a statistical hypothesis test, we do not find sufficient evidence to conclude that the mean number of hours per day people spend watching TV in 2012 differs from the sociologist's claim of 3 hours.
Explanation:The question pertains to evaluating a claim about population mean using a sample mean. Given the data, we can perform hypothesis testing. The null hypothesis (H0) is that the mean number of hours spent watching TV is 3, and the alternative hypothesis (H1) is that the mean is not 3. The sample mean is 3.02, standard deviation is 2.64, and the sample size is 1326.
Firstly, we need to calculate the standard error: SE = standard deviation/sample size square root = 2.64/ sqrt(1326) = 0.072. Then, we calculate the test statistic (Z): Z = (sample mean - population mean)/SE = (3.02-3)/0.072 = 0.278. Given α=0.05, the Z value for a two-tailed test is +/- 1.96.
The computed Z value of 0.278 falls within the acceptance region (-1.96 < Z < 1.96), so we do not reject the null hypothesis. Therefore, the data do not provide sufficient evidence to conclude that the mean hours of TV watched per day differs from the sociologist's claim.
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Find the four vertices of the cube, starting with (1, 1, 1), that form a regular tetrahedron. Confirm your answer by finding the length of an edge and explaining why all edges have the same length.
Answer:
the vertices (1,1,1), (1,0,0), (0,1,0) and (0,0,1) form a tetrahedron. The length of each side is √2
Step-by-step explanation:
The cube has 8 vertices: (0,0,0), (1,1,0), (0,1,0), (1,0,0), (0,0,1), (0,1,1), (1,0,1), (1,1,0) and (1,1,1). The first four of them are the vertices of the bottom square and the last four are the vertices of the upper square of the cube.
We will take two non-consecutive vertices from each square. For the upper one we take (1,1,1) as the problem suggests, and (0,0,1), which is not consecutive from (1,1,1) and its distance is √2. The non consecutive vertices from the bottom square respect to the vertex (1,1,1) are (0,0,0), (0,1,0) and (1,0,0).
We take (0,1,0) and (1,0,0) because (0,0,0) is consecutive from (0,0,1) hence its distance from it is not √2, but 1.
Note that we take (1,1,1), (0,0,1), (0,1,0) and (1,0,0). If we take any two vertices and compare them toguether we will notice that both of those vertices differ in two places and are equal in the other. In the places where they differ one has the value 1 and the other 0, so the distance between those vertices is √(1²+1²) = √2.
Thus, the vertices (1,1,1), (1,0,0), (0,1,0) and (0,0,1) form a tetrahedron.
Final answer:
Explaining how to find the vertices of a cube forming a regular tetrahedron and confirming why all cube edges have the same length.
Explanation:
To find the four vertices of a cube that form a regular tetrahedron starting with (1, 1, 1), we can consider the cube's diagonals. The vertices of the regular tetrahedron can be located at the center of each face of the cube, which are at coordinates (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2).
The length of an edge of a cube is the distance between two adjacent vertices. To calculate the edge length, we can use the distance formula. Since all edges of a cube connect two adjacent vertices, they have the same length due to the cube's symmetry.
Therefore, all edges of the cube have the same length because each connects two adjacent vertices with equal coordinates.