Answer:
The company's daily fixed cost=$8000
The marginal cost per cycle=Slope=$ 25
Step-by-step explanation:
We are given that
Factory produces bicycle in a day=[tex]x_1=[/tex]100
Total cost,[tex]y_1=[/tex]$10,500
Factory produces bicycles in a day,[tex]x_2[/tex]=120
Total cost=[tex]y_2=[/tex]$11,000
There are two points (100,10500) and (120,11000)
Slope =[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the formula
[tex]m=\frac{11000-10500}{120-100}=\frac{500}{20}=25[/tex]
Slope-intercept form
[tex]y=mx+c[/tex]
Where m=Slope of line
c=y-intercept
Substitute the values
[tex]10500=25(100)+c[/tex]
[tex]10500=2500+c[/tex]
[tex]c=10500-2500=8000[/tex]
y-intercept=8000
Substitute the values in the equation
[tex]y=25x+8000[/tex]
Therefore, company's daily fixed cost=$8000
The marginal cost per cycle=Slope=$ 25
Triangle MNO is an equilateral triangle with sides measuring 16 StartRoot 3 EndRoot units. Triangle M N O is an equilateral triangle with sides measuring 16 StartRoot 3 EndRoot units. A perpendicular bisector is drawn from point N to point R on side M O splitting side M O into 2 equal parts. What is the height of the triangle? 12 units 24 units 36 units 72 units
Answer:
The correct option is second one i.e 24 units.
Therefore the height of the triangle is
[tex]NR=24\ units[/tex]
Step-by-step explanation:
Given:
An equilateral triangle has all sides equal.
ΔMNO is an Equilateral Triangle with sides measuring,
[tex]NM = MO = ON =16\sqrt{3}[/tex]
NR is perpendicular bisector to MO such that
[tex]MR=RO=\dfrac{MO}{2}=\dfrac{16\sqrt{3}}{2}=8\sqrt{3}[/tex] .NR ⊥ Bisector.
To Find:
Height of the triangle = NR = ?
Solution :
Now we have a right angled triangle NRM at ∠R =90°,
So by applying Pythagoras theorem we get
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Substituting the values we get
[tex](MN)^{2} = (MR)^{2}+(NR)^{2}\\\\(16\sqrt{3})^{2}=(8\sqrt{3})^{2}+(NR)^{2}\\\\(NR)^{2}=768-192=576\\Square\ rooting\ we\ get\\NR=\sqrt{576}=24\ units[/tex]
Therefore the height of the triangle is
[tex]NR=24\ units[/tex]
Answer:
b 24
Step-by-step explanation:
The 5th grade is getting a special lunch to celebrate the end of first grading period.The cafeteria manager is planning to buy 0.3 pound of turkey for each student. If turkey is on sale for $0.79 per pound, what will it cost to give turkey to 100 students.
Final answer:
To calculate the cost, multiply the amount of turkey per student (0.3 pounds) by the number of students (100), then multiply the total pounds needed (30) by the cost per pound ($0.79), resulting in a total cost of $23.70 for turkey for 100 students.
Explanation:
The question asks us to calculate the cost of providing turkey to 100 students if each student requires 0.3 pounds of turkey, and turkey costs $0.79 per pound. To find the total amount of turkey needed, we multiply the amount each student gets by the total number of students: 0.3 pounds/student × 100 students. This calculation results in 30 pounds of turkey required for 100 students.
Next, to determine the total cost, we multiply the total pounds of turkey needed by the cost per pound: 30 pounds × $0.79/pound. This calculation gives us a total cost of $23.70 for the turkey.
Therefore, it will cost $23.70 to give turkey to 100 students.
If Alex and Brandon work together, they will clean the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself?
Answer:
I think it is 5 but don't take my word for it
Step-by-step explanation:
I think you minus 20 - 15 which equals to 5 so 20 - 15 = 5 hopefully i was a little helpful just try that if its not correct i'm so sorry i will practice my math and answer this question again thank you for being so understanding
Answer:
Correct answer: Alex can finish the same job in 60 hours
Step-by-step explanation:
The appropriate equation for this situation is:
1/20 + 1/x = 1/15 => (x + 20) / 20x = 1/15 => 15 · (x + 20) = 20x =>
15x + 300 = 20x => 5x = 300 => x = 300/5 = 60 hours
x = 60 hours
God is with you!!!
What is the 6th value in the sequence with the explicit formula an=−2n−14?
Answer:
-26
Step-by-step explanation:
a(6)=-2(6)-14
a(6)=-12-14
a(6)=-26
Hope this helped!
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-Shadyk
The 6th value in the sequence = an=−2n−14 = -4.3
Take n = 6
⇒ a6 = -2·6 -14 = -12-14 = -26
∴ a= [tex]\frac{-26}{6}[/tex] = -4.3
Explicit formulaThe explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geomrietc, or harmonic sequence.
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Last spring Janessa made 30 to one cup serving of lemonade for a lemonade stand this year she will make two times the amount I live in a that she made last year how many gallons of lemonade will Janessa make this year
Answer:
3.75 gallons
Step-by-step explanation:
Bryce, a previous winner of the contest, made a trip of 360 miles in a 6.5 hours. At this same average rate of speed, how long will it take Bryce to travel an additional 300 miles so that he can judge the contest?
Answer:
5.42 hours
Step-by-step explanation:
Let x represent time taken to complete 300 miles.
We have been given that Bryce a previous winner of the contest, made a trip of 360 miles in a 6.5 hours.
We will use proportions to solve our given problem since rates are same for both distances.
[tex]\frac{\text{Distance covered}}{\text{Time taken}}=\frac{360\text{ Miles}}{6.5\text{ Hours}}[/tex]
Upon substituting our given values in above proportion, we will get:
[tex]\frac{300\text{ Miles}}{x}=\frac{360\text{ Miles}}{6.5\text{ Hours}}[/tex]
Cross multiply:
[tex]x\cdot 360\text{ Miles}=300\text{ Miles}\times6.5\text{ Hours}}[/tex]
[tex]x=\frac{300\text{ Miles}\times6.5\text{ Hours}}{ 360\text{ Miles}}[/tex]
[tex]x=\frac{300\times6.5\text{ Hours}}{360}[/tex]
[tex]x=5.41666\text{ Hours}\approx 5.42\text{ Hours}[/tex]
Therefore, it will take approximately 5.42 hours to travel additional 300 miles.
You are designing a wall Mural that will be composed of squares of different sizes. One of the requirements of your design is that the side length of each square itself is a perfect square. If you represent the side length of the square as x to the power of 2 write an expression for the area of the mural square.
Answer:
1. Area of a square = (x^2)^2 = x^4
(each side is x^2, area of a square = side^2
so (x^2)(x^2) = x^4 )
2. when x = 5
area = 5^4 = 625
3. when x = 10
area = 10^4 = 10000
Step-by-step explanation:
Hope its right!
Final answer:
The area of a square mural where the side length is a perfect square, represented as x², can be expressed as A = x⁴, which simplifies the concept of multiplying the side length by itself twice.
Explanation:
The area of a mural square, where the side length is a perfect square represented as x to the power of 2 (x²), is calculated by squaring the side length. Therefore, if x itself is a perfect square, the area A of the square mural is given by A = x² * x², which simplifies to A = x⁴. Since the side length is a perfect square, x could be expressed as y² where y is an integer, resulting in the area being y⁴, where y⁴ represents the side length squared twice.
Which 2 statements are correct regarding reconciling a bank account in QuickBooks Online? (Select all that apply) You can only undo a bank reconciliation via a link in the Accountant Toolbox To successfully reconcile and run a reconciliation report you need to enter the Statement Ending Date and Ending Balance from the relevant bank statement Reconciliations must only be run at period end to estimate tax owed To see the Reconciliation report, select View report after you've successfully reconciled the account
Answer:
The correct statements are:
To successfully reconcile and run a reconciliation report you need to enter the Statement Ending Date and Ending Balance from the relevant bank statement
To see the Reconciliation report, select View report after you've successfully reconciled the account.
EXPLANATION:
The steps to reconciling a bank account using QuickBooks Online include:
1. Click on the Gear button, then on “Tools” and then “Reconcile.”
2. Click on the drop-down menu under “Accounts” and select the account you want to reconcile.
3. Enter the “Ending balance” and “Ending date” based on your bank statement information.
4. Match transactions to your bank statement and check them off one by one.
5. Apply filters so transactions are easier to find.
6. Keep going until the “Difference” field is zero and you see the Success! page.
7. Select "View Report" from the Report period drop-down arrow to view your reconciliation report.
The two options that are correct regarding bank account reconciliation QuickBooks online are:
Quickbooks is an Accounting Application that aids in the collection, processing, analyses, and reporting of Accounting and Financial Information for organizations.
It is a tool that is very useful for business owners.
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a hexagonal aquarium is 15.5 on each side of its base and 28.5cm high. whats the area
Answer:
17807cm2
Step-by-step explanation:
Surface area of a hexagonal prism is =( (3√3)/2) a^2 h
= 2.598 * 15.5^2 *28.5
= 2.598* 240.5* 28.5
=17807.34cm2
19 in2 17 in2 12 in2 22 in2
Answer:22in2
Step-by-step explanation:
A triangle has sides with lengths a,b,and c.The longest side is b.Write An Equation or inequality that shows the relationships of the lengths of the three sides
the equations are:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ a^2 = c^2 - b^2 \][/tex]
[tex]\[ b^2 = c^2 - a^2 \][/tex]
In a right triangle, according to the Pythagorean theorem, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. So, we have:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
This equation represents the relationship among the side lengths of a right triangle.
Therefore, the equations are:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ a^2 = c^2 - b^2 \][/tex]
[tex]\[ b^2 = c^2 - a^2 \][/tex]
This completes the three relations among a, b, andc.
The complete Question is given below:
A right triangle has side lengths of a,b , and c units. The longest side has a length of c units. Complete each equation show three relations among a,b , and c .
Type the answers in the boxes below.
c^(2)= _____
a^(2)= _____
b^(2)= _____
Rebecca is three years younger than twice Anthony's age. Write an expression that represents the relationship of Rebecca's age in terms of Anthony's age.
Answer:
X=2y-3
Step-by-step explanation:
Let Rebecca's age be x
Let Anthony's age be y
Twice Anthony =2y
Rebecca's age (x) to be 3 years younger than twice Anthony's =2y-3
So, it's x=2y-3
Suppose the average price for new cars in 2012 has a mean of $30,100 and a standard deviation of $5,600. Based on this information, what interval of prices would we expect at least 89% of new car prices to fall within?
Answer:
($13,300,$46,900)
Step-by-step explanation:
We are given the following in he question:
Mean, μ = $30,100
Standard Deviation, σ = $5,600
Chebyshev's Theorem:
According to theorem atleast [tex]1 - \dfrac{1}{k^2}[/tex] percent of data lies within 2 standard deviations of mean.For k = 3,[tex]1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%[/tex]
Thus, 89% of data lies within three standard deviation of mean.
[tex]\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900[/tex]
Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)
Three fair dice are rolled, one red, one green and one blue. What is the probability that the upturned faces of the three dice are all of different numbers?
Answer: [tex]\dfrac{5}{9}[/tex]
Step-by-step explanation:
When we throw a die , Total outcomes =6
When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]
Given : Three fair dice are rolled, one red, one green and one blue.
Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed
By Permutations , the number of favorable outcomes = [tex]^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120[/tex]
The probability that the upturned faces of the three dice are all of different numbers = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{120}{216}=\dfrac{5}{9}[/tex]
The probability that the upturned faces of the three dice are all of different numbers is [tex]\dfrac{5}{9}[/tex] .
The level of a lake in inches is falling linearly . The lake level is 452 inches on Jan 1 and then 378 inches on Jan 21. Find a function to represent the lake level
Answer:
[tex]y=-\frac{74}{21}x+452[/tex]
Step-by-step explanation:
Given:
The level of a lake is falling linearly.
On Jan 1, the level is 452 inches
On Jan 21, the level is 378 inches.
Now, a linear function can be represented in the form:
[tex]y=mx+b[/tex]
Where, 'm' is the rate of change and 'b' is initial level
[tex]x\to number\ of\ days\ passed\ since\ Jan\ 1[/tex]
[tex]y\to Lake\ level[/tex]
So, let Jan 1 corresponds to the initial level and thus b = 452 in
Now, the rate of change is given as the ratio of the change in level of lake to the number of days passed.
So, from Jan 1 to Jan 21, the days passed is 21.
Change in level = Level on Jan 21 - Level on Jan 1
Change in level = 378 in - 452 in = -74 in
Now, rate of change is given as:
[tex]m=\frac{-74}{21}[/tex]
Hence, the function to represent the lake level is [tex]y=-\frac{74}{21}x+452[/tex]
Where, 'x' is the number of days passed since Jan 1.
Final answer:
The lake level can be represented by a linear function L(t) = -3.7t + 452, where L(t) is the lake level in inches and t is the time in days from January 1st.
Explanation:
To find a function representing the lake level as it drops linearly over time, we need to determine the linear equation that corresponds to the change in the lake level.
We are given that the lake level is 452 inches on January 1st and 378 inches on January 21st.
First, we will define the variables where L(t) is the lake level in inches and t is the time in days with t=0 corresponding to January 1st.
We are given two points on the linear function: (0, 452) and (20, 378), since January 21st is 20 days after January 1st.
Next, we calculate the slope of the line using the formula:
slope = (change in lake level) / (change in time) = (378 - 452) / (20 - 0) = -74 / 20 = -3.7 inches per day.
Now, we can use the slope and a point to write the equation of the lake level as a function of time in the slope-intercept form:
L(t) = mt + b
where m is the slope and b is the y-intercept. Plugging in the slope and the point (0, 452):
L(t) = -3.7t + 452
This equation represents the function of the lake level over time.
The unit price on a 100-pound container of a swimming pool chlorine is $.06 per pound less than the unit price on a 75-pound container. If the 100-pound container costs $55.50 more than the 75-pound container, find the cost of each.
Answer:
100 lb: $24075 lb: $184.50Step-by-step explanation:
Let u represent the unit price of the 100 lb container. Then u+.06 is the unit price of the 75 lb container.
The difference in prices is ...
100u - 75(u+.06) = 55.50
25u -4.50 = 55.50
25u = 60
u = 60/25 = 2.40
The cost of the 100 lb container is 100u = 240. The cost of the 75 lb container is $55.50 less: 240 -55.50 = 184.50.
The 100 lb container costs $240. The 75 lb container costs $184.50.
The current global human population is about 6.1 billion and is growing at an annual rate of 1.35 percent. If world population were to grow at this rate for the next year, approximately how many people would be added?
Answer:
Step-by-step explanation:
The current global population is growing at an annual rate of 1.35 percent. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 6.1 × 10^9
r = 1.35% = 1.35/100 = 0.0135
t = 1
Therefore
A = 6.1 × 10^9(1 + 0.0135)^1
A = 6.1 × 10^9(1.0135)^1
A = 6182350000
The number of people that would be added is
6182350000 - 6100000000
= 82350000
If the world population were to keep growing at 1.35%, we number of people who would be added next year is 82,350,000 people.
The population of the world is growing at 1.35%. This means that next year, the number of people added will be 1.35% of the current population.
The current population is 6.1 billion so the number of people who will be added is:
= Population x Incremental rate
= 6,100,000,000 x 1.35%
= 82,350,000 people
In conclusion, 82,350,000 people will be added.
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Find m∠H.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠H = °
Answer:
Step-by-step explanation:
Triangle GHI is a right angle triangle.
From the given right angle triangle,
HI represents the hypotenuse of the right angle triangle.
With m∠H as the reference angle,
GH represents the adjacent side of the right angle triangle.
GI represents the opposite side of the right angle triangle.
To determine m∠H, we would apply
the Sine trigonometric ratio.
Sine θ = opposite side/hypotenuse. Therefore,
Sin H = 9/10 = 0.9
m∠H = Sin^-1(0.9)
m∠H = 64.2° to the nearest tenth.
Leah had 50 stickers. Leah gave 1/2 of the stickers to her sister. Of the amount left, she gave 2/5 to her friend.How many does Leah have left for herself?
Answer: Leah has 15 stickers left for herself.
Step-by-step explanation:
Total number of stickers that Leah had initially is 50. Leah gave 1/2 of the stickers to her sister. This means that the number of stickers that Leah gave to her sister is
1/2 × 50 = 25 stickers
Of the amount left, she gave 2/5 to her friend. This means that the number of stickers that Leah gave to her friend is
2/5 × 25 = 10 stickers
Therefore, the number of stickers that Leah have left for herself is
50 - (25 + 15)
= 50 - 35
= 15
After giving away some of her stickers to her sister and friend, Leah has 15 stickers left for herself.
Explanation:Leah initially had 50 stickers. She gave half of them to her sister, which left her with 50/2 = 25 stickers. Then, she gave away 2/5 of these remaining stickers to her friend.
To calculate how many she gave her friend, we multiply 25 * 2/5 = 10 stickers.
To find out how many Leah has left for herself, we subtract this from the number she had after giving stickers to her sister: 25 - 10 = 15 stickers.
So, Leah has 15 stickers left for herself.
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7. In which reaction is mass converted to energy by the process of fission?
suppose the model boat were traveling at a rate of 4 feet per second. How long would it take the model boat to get from the edge of the pond to the center
Answer:
[tex]25\ seconds[/tex]
Step-by-step explanation:
Hi,
Time, speed and distance are related by a very simple formula:
[tex]Distance = Time \times Speed[/tex]
Which can easily be used here to solve the question.
To find the time, we require:
Speed:
This is given in the question as 4 ft/ sec.
Distance:
On a circle, the distance from the end of the circle to the centre is referred to as "Radius". We shall assume the radius here is [tex]r[/tex].
To calculate the radius, we can use the formula of the circumference: [tex]C = 2 \pi r[/tex]
Were are given that C = 628 feet.
Using the formula: [tex]r = \frac{628}{2 \pi} = 100\ feet[/tex]
The distance the boat needs to travel is 100 feet.
Time:
To calculate time, we alter the provided formula to: [tex]Time = \frac{Distance}{Speed}[/tex]
Substituting the values in this: [tex]Time = \frac{r}{4}[/tex]
[tex]Time = \frac{100}{4} = 25\ seconds[/tex]
The boat requires 25 seconds to travel from the edge of the pond to centre.
Let us first concentrate on the central value. take f0 = n and 0 = . find the central value of fx, in n
Answer:
Fx=N177.007
Step-by-step explanation:
Let us first concentrate on the central value. Take F0 = 325 and theta 0 = 57 degrees. Find the central value of Fx, in N
can be pu as thus from an online resource
To resolve forces into the horizontal component , we have
Fx=fCosФ
Fx=325Cos57
Fx=N177.007
Take Note that a force is that which tends to change a body's state of rest or uniform motion in a straight line.
A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?
In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon. How much cinnamon does the spice mix contain per pound? A. 5/8 B. 9/10 C. 1 1/9 D. 1 3/5
Answer:
option C
Step-by-step explanation:
In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon
The ration of spice mix over Cinnamon is
[tex]\frac{\frac{3}{4} }{\frac{5}{6} } =\frac{3}{4} \cdot \frac{6}{5} =\frac{9}{10}[/tex]
Let x be the spice mix per pound
make a proportion
[tex]\frac{9}{10} =\frac{1}{x}[/tex]
cross multiply
[tex]9x=10\\x=\frac{10}{9}\\x= 1 \frac{1}{9}[/tex]
option C is the answer
Estimate the solution to the graph shown below.
5,-3)
(4,-3)
(-3,4)
Solve the following linear system any way you like.
x+ y= 4
x - y= 2
(2, 0)
(2, 4)
No solution
(0, 6)
(0, 4)
(-6,0)
Answer:
The answer to your question is 1.- (-3, 4) 2.- (3, 1) None of the choices
Step-by-step explanation:
1.- The solution of a system of equation by the graph method is the point in which the lines cross. In this graph we observe that this point is approximately
(-3, 4).
2.-
Equation 1 x + y = 4
Equation 2 x - y = 2
Solve by the combination method
x + y = 4
x - y = 2
2x 0 = 6
2x = 6
Solve for x
x = 6/2
x = 3
Substitute x in equation 1 to find y
3 + y = 4
Solve for y
y = 4 - 3
y = 1
Solution (3, 1)
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠D.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠D = °
Answer:
27° (as an integer)
Step-by-step explanation:
From the figure given;
Triangle BCD is a right triangle;We are given the two shorter sides;DC = 8 units
BC = 4 units
We are required to determine m∠D
We need to use the appropriate trigonometric ratio;
In this case, DC is adjacent and BC is opposite to m∠D
Therefore, the appropriate trigonometric ratio is tangent;
That is;
Tan m∠D = BC ÷ DC
= 4 ÷ 8
= 0.5
Thus;
m∠D = Tan^-1 (0.5)
= 26.57
= 27 (as an integer)
Thus, m∠D is 27°
Mona and Shakira play on a basketball team. In one game, Shakira scored twice as many points as Mona. Together they scored 24 points in that game. How many points did each girl score?
Answer:
Mona = 8, Shakira = 16
Step-by-step explanation:
S = 2m....m = S/2
2S + S = 24
3S = 24
S = 24/3
S = 8
Mona = 8
Shakira = 16
The headline "Drugs shown in 98 percent of movies" accompanied a news story that described a "government study" claiming that drug use, drinking, or smoking was depicted in 98% of the top movie rentals. Discuss whether the headline accurately represents the story.
Answer:
Discussed below.
Step-by-step explanation:
The headline states that 98% of all movies show imagery of drugs. There are a few assumptions that the wording can insinuate:
By stating "drugs shown" it is not specified what kind of drugs are shown nor whether the consumption of these drugs is also shown (showing drug can allude to the consumption of drugs).Drugs can have different meanings in different contexts, some are not harmful such as pharmaceutical drugs. Without any specification, one assumes the worst. 98% of movies refers to 98% of all movies produced thus one can assume that 98% of the total output of movie production show imagery of drug use, which is highly unlikely.However, the story refers to a more specific statistic: that not 98% of all movies but 98% of the top movie rentals depicted drug use, drinking or smoking.
The key differences:
the story is more specific as to what the statistic is referring to (not the total movie output but the top rented movies)the story specifically mentions the use of drugs is shown the story also mentions other types of harmful substances such as smoking and drinkingThus, the headline misrepresents the content of the story which may lead one to make broader and misplaced conclusion about imagery of drugs in movies.
The headline accurately reflects the information provided in the news story, but the accuracy is dependent on the credibility and methodology of the government study.
Explanation:The headline "Drugs shown in 98 percent of movies" accompanied a news story about a "government study" claiming that drug use, drinking, or smoking was depicted in 98% of the top movie rentals.
First, it's important to note that the headline accurately reflects the information provided in the news story. However, the accuracy of the headline is dependent on the credibility and methodology of the government study being referenced.
Without additional information about the study, such as the sample size, selection criteria, and methodology, it is difficult to fully assess the accuracy of the headline. It's always important to critically evaluate the sources of information and consider multiple perspectives in order to draw accurate conclusions.
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How many positive integers $n$ with $n\le 500$ have square roots that can be expressed in the form $a\sqrt{b}$ where $a$ and $b$ are integers with $a\ge 10$?
Answer:
23
Step-by-step explanation:
We take a methodical approach by considering the different possible values of b when asqrtb is the simplest form of sqrtn.
Case 1: b=1. We can't forget the perfect squares! If n=100, for example, then sqrt100 can be written as 10sqrt1. So, we must include the perfect squares from 10^2=100 up through 22^2 = 484. (All greater squares are greater than 500.) There are 13 such squares.
Case 2: b=2. If b=2, then we have asqrtb = asqrt2 = sqrta^2 x sqrt2 = sqrt2a^2. We still must have a {>_} 10, but now we need 2a^2 to be no greater than 500. This means that a^2 must be no greater than 250, so a can be 10, 11, 12, 13, 14, or 15. There are 6 such values.
Case 3: b=3. We then have asqrtb = asqrt3 = sqrt3a^2. Since 3a^2 {<_} 500, we know that a^2 is less than 167. We still need a {>_} 10, so there are only 3 values of a in this case: 10, 11, 12.
We skip b=4 because then asqrtb would not be in simplest form.
Case 4: b=5. We then have asqrtb = sqrt5a^2, and a=10 is the only possible value for this case.
For any greater value of b, the resulting value of n is greater than 500 when a {>_} 10. So, there are no more possible numbers asqrtb that satisfy the problem. Since each of the 13+6+3+1 = 23 possibilities listed above represent different simplified forms, they give us 23 different possible values of n that satisfy the problem.
There are infinitely many positive integers less than 500 that have square roots in the form of a√b, where a and b are integers with a≥10.
The number of such positive integers n is infinite, as there is no finite value for the count.
Here,
We are looking for positive integers n that are less than 500.
The square roots of these integers can be expressed in the form a√b.
And [tex]a\ge 10[/tex]
To find the number of positive integers less than 500 that have square roots in the form of a√b,
Analyze the possible values of a and b separately:
For a,
We know that it must be an integer greater than or equal to 1. So,
We have a total of a = 10, 11, 12 ..., and so on. (since a ≥ 10)
As for b,
it can be any perfect square less than or equal to 500.
Let's list a few examples:
b = 1, since 1√1 = 1
b = 4, since 1√4 = 2
b = 9, since 1√9 = 3
b = 16, since 1√16 = 4
...
b = 484, since 1√484 = 22
Now, we can count the number of possibilities for a and b.
We have an infinite number of possibilities for a, but b has a finite number of perfect squares less than or equal to 500.
There are 22 perfect squares within this range.
Therefore, the total number of positive integers n, with n < 500, that have square roots in the form of a√b is 22 x infinity = infinity.
Since there are infinitely many possible values for n,
Hence,
We can conclude that there is no finite value for the number of positive integers n that satisfies this condition.
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A group of 86 people consist of men women and children. There are twice as many women then there are men. There are 6 more children than there are women. How many men women and children in group
Answer: 16 men
32 women
38 children
Step-by-step explanation:
Let x represent the number of men in the group.
Let y represent the number if women in the group.
Let z represent the number of children in the group.
A group of 86 people consist of men women and children. This means that
x + y + z = 86 - - - - - - - - - - - - 1
There are twice as many women than there are men. It means that
x = y/2
There are 6 more children than there are women. This means that
z = y + 6
Substituting x = y/2 and z = y + 6 into equation 1, it becomes
y/2 + y + y + 6 = 86
multiplying through by 2, it becomes
y + 2y + 2y + 12 = 172
5y = 172 - 12 = 160
y = 160/5 = 32
x = y/2 = 32/2
x = 16
z = y + 6 = 32 + 6
z = 38
There are 16 men, 32 women, and 38 children in the group.
Explanation:Let the number of men be M, the number of women be W, and the number of children be C.
From the given information, we have the following equations:
W = 2M (Twice as many women as men)
C = W + 6 (6 more children than women)
The total number of people is given as 86:
M + W + C = 86
Substituting the values of W and C in terms of M into the third equation, we have:
M + 2M + (2M + 6) = 86
5M + 6 = 86
5M = 80
M = 16
Substituting the value of M in the first equation, we have:
W = 2(16) = 32
Finally, substituting the value of W in the second equation, we have:
C = 32 + 6 = 38
Therefore, there are 16 men, 32 women, and 38 children in the group.
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