80% of teenagers have access to some social media . If you do a random survey of 400 teenagers, what is the probability that between 300 and 340 of them will patronize it.
Answers
Answer:
P(300 < p^ < 340) = 0.9876 or 98.76%
Step-by-step explanation:
We are given;
Population proportion; p = 80% = 0.8
Sample proportion; p1^ = 300/400 = 0.75 and p2^ = 340/400 = 0.85
Sample size: n = 400
z-score formula for sample proportion is;
z = (p^ - p)/(√(p(1 - p)/n)
Thus;
z1 = (0.75 - 0.8)/(√(0.8(1 - 0.8)/400)
z1 = -0.05/0.02
z1 = -2.5
z2 = (0.85 - 0.8)/(√(0.8(1 - 0.8)/400)
z2 = 0.05/0.02
z2 = 2.5
From online calculator of probability between 2 z-scores, we have;
P(-2.5 < z > 2.5) ≈ 0.9876
Related Questions
cylindrical water container A is 1.2 meters high and diameter 4.6 meters. cylindrical container B is 8 meters in diameter and height 12 meters. what is the difference in the amount of water cylindrical A and cylindrical B will contain to the nearest hundredth?
Answers
Given:
Here two cylindrical containers are given with named A and B and the measures are 1.2 m height 4.6 m diameter and 12 meter height and 8 m in diameter respectively.
Required:
We need to find that what is the difference in the amount of water cylindrical A and cylindrical B will contain to the nearest hundredth.
Explanation:
Lets consider measures A as 1 and measures B as 2 means
measures of cylinder A is
\(\begin{gathered} r_1=\frac{4.6}{2}=2.3\text{ m} \\ h_1=1.2\text{ m} \\ \end{gathered}\)measure of cylinder A is
\(\begin{gathered} r_2=\frac{8}{2}=4\text{ m} \\ h_2=12\text{ m} \end{gathered}\)now find the volume of named A contained
\(V_A=\pi r_1^2h_1=3.14*2.3*2.3*1.2=19.94\text{ m}^3\)now for B
\(V_B=\pi r_2^2h_2=3.14*4*4*12=603.19\text{ m}^3\)now to find the difference
\(V_B-V_A=603.19-19.94=583.25\text{ m}^3\)Final answer:
Difference of both container is 583.25 cubic meter
make up two word problems on any multiplicatiob table of your choice. remember to give your answer in a sentence
Answers
2. At the shop, pencils are $2 each. Chloe wants to buy 12 pencils. How much does it cost altogether?
(Answer: $24)
A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked.
Suppose that x and y are related by the equation y = 53+2x.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change per day in the road's length?
miles
What was the road's length when the crew started working?
Answers
Answer: The equation y = 53+2x relates the variables x and y, where x represents the number of days the crew has worked and y represents the total length of the road.
The change per day in the road's length is given by the coefficient of x in the equation, which is 2. Thus, the change per day in the road's length is 2 miles.
The road's length when the crew started working is given by the constant term in the equation, which is 53. Thus, the road's length when the crew started working was 53 miles.
Step-by-step explanation:
If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to a. 38. b. 19. c. 18. d. 39.
Answers
Answer:
Null hypothesis: \(\mu_1= \mu_2\)
Alternative hypothesis:\(\mu_1 =\neq \mu_2\)
And for this case we assume that we have equal variances so that means:
\(\sigma =\sigma_1 =\sigma_2\)
For this case the degrees of freedom are given by:
\( df= n_1 +n_2 -2\)
And replacing we got:
\( df= 20+20 -2= 38\)
And the best answer would be:
a. 38
Step-by-step explanation:
For this problem we want to test the following:
Null hypothesis: \(\mu_1= \mu_2\)
Alternative hypothesis:\(\mu_1 =\neq \mu_2\)
And for this case we assume that we have equal variances so that means:
\(\sigma =\sigma_1 =\sigma_2\)
For this case the degrees of freedom are given by:
\( df= n_1 +n_2 -2\)
And replacing we got:
\( df= 20+20 -2= 38\)
And the best answer would be:
a. 38
Find the number that comes after 144five
Answers
Answer:
The number that comes after 144five is:
= 200five.
Step-by-step explanation:
Adding 1 to 144 base 5 will result in:
144
+ 1
= 200
b) To obtain the next number that comes after 144five, add 1five to 144five. Since the numbers are in base 5, 1five added to 4five will result in 0 with 1 carried backward. When 1 is added to the next 4, the result will be 0 with 1 carried backward. 1 added to 1 = 2, all in base 5. Figures in base 5 cannot exceed 4. The usual numbers for a base 5 operation are 0, 1, 2, 3, and 4.
two students just finished ba 215. sam slacker did not complete any of the career smart goals assignments and reports. denise diligence, on the other hand, took the assignment to heart (didn't just jump through hoops) and scored 95% on all of them. assuming that each point earned will result in a $1500 increase in salary 20 years from now, how much higher will denise's salary be than slacker's? enter your answer to the nearest whole dollar. do not include the $ symbol. hint: you will need to first know how many total points all of the smart goals assignments and reports (career preparation and development section of the syllabus) are worth in order to make the calculations.
Answers
The difference in salary will be $71,250.
What is multiplication in mathematics?
Multiplication is a mathematical operation that is used to find the product of two or more numbers. It is usually represented by the symbol "x" or "*", and is often referred to as repeated addition.
Career Preparation and Development (Career SMART Goals) worth 50 points.
Denise Diligence scored 95/100 on all of the assignments and reports, so she earned a total of 47.5 points.
Since each point earned will result in a $1500 increase in salary 20 years from now, Denise's salary will be $1500 x 47.5 = $71,250 higher than Slacker's.
Sam Slacker did not complete any of the career smart goals assignments and reports, so he earned a total of 0 points.
Hence, the difference in salary will be $71,250.
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Identify the hypotenuse in ΔXYZ.
A. XZ
B. ZX
C. YZ
D. XY
Answers
Answer:
D
Step-by-step explanation:
in a right triangle the hypotenuse is the side opposite the right angle.
the right angle is at Z , then side opposite is XY
the hypotenuse is side XY
G varies inversely with the square
of H. When H is 4, G is 0.25.
Find the value of G when H is 0.3.
Answers
Answer:;4.4
Step-by-step explanation: Since it varies inversely we know G times H squared is equal to some constant, k. So we have G*H*H=k. We are told that when H=4, G=.25. Plugging this in, we have .25*4*4=k. This simplifies to 4=k. Our new equation is G*H*H=4. Now, we want to solve for G when H=.3. We plug it in. G*.3*.3=4 => G*.09=4. G=4/.09. This means G is approximately 44.4.
Answer:
G = 44.44
Step-by-step explanation:
Given the mathematical expression and data;
\( G = \frac {1}{H^{2}} \)
H = 4 and G = 0.25
First of all, we would determine the constant of proportionality, k.
\( G = \frac {k}{H^{2}} \)
Making k the subject of formula, we have;
k = GH²
Substituting the values, we have;
k = 0.25 * 4²
k = 0.25 * 16
k = 4
Next, we find the value of G when H = 0.3;
\( G = \frac {k}{H^{2}} \)
\( G = \frac {4}{0.3^{2}} \)
\( G = \frac {4}{0.09} \)
G = 44.44
what 2-7/8 divided by 3/4
Answers
The parabola X= √y-9 opens: right left down up?
Answers
The parabola x = √(y - 9) opens upwards.The given parabolic equation is x = √(y - 9). Let's identify the direction of opening of this parabola.The general form of the equation of a parabola is y = a(x - h)² + k.
Comparing this to the given equation, we can see that h = 0 and k = 9. The vertex is therefore (h, k) = (0, 9). Now, let's determine whether the parabola opens upwards or downwards.
If the coefficient of (x - h)² is positive, the parabola opens upwards, and if it's negative, the parabola opens downwards. In this case, since the coefficient of (x - h)² is 1, which is positive, the parabola opens upwards.
Therefore, the parabola x = √(y - 9) opens upwards.
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The length of each side of an equilateral triangle having an area of square root of 243sq.cm is
Answers
Answer:
\(\textrm{Each side = 23.6893 cm}\\\\\\\textrm{Rounded to 2 decimal places = 23.69 cm}\\\\\textrm{Rounded to 1 decimal place = 23.7 cm}\)
You can choose the level of precision as desired from the above
Step-by-step explanation:
The area of an equilateral triangle of side a
is
\(A = \dfrac{(a^2 \sqrt{3})}{4}\)
We are given A = 243
Plugging in values we get
\(243 = \dfrac{a^2\sqrt{3}}{4}\)
Switch sides so \(a^2\) term is on the left
\(\dfrac{a^2\sqrt{3}}{4} = 243\)
Multiply by 4 both sides to get rid of the denominator:
\(\dfrac{a^2\sqrt{3}}{4} \times 4 = 243 \times 4\\\\a^2\sqrt{3} = 972\\\\\)
Divide by \(\sqrt{3}\) both sides:
\(a^2 = \dfrac{972}{\sqrt{3}}\\\\a^2 = 561.18446\\\\a = \pm \sqrt{561.18446}\\\\\)
Taking only positive square root:
\(a = \sqrt{561.18446}\\\\a = 23.6893\\\\\)
Can the following quadrilateral be proven to be a parallelogram based on the given information? Explain.
(picture shown below)
A.) No. It cannot be proven because at least two of the adjacent angles are not congruent to each other
B.) Yes. It can be proven because both pairs of opposite sides are congruent.
C.) No. It cannot be proven because it does not have an angle that is supplementary to both of its consecutive angles.
D.) Yes. It can be proven because both pairs of opposite angles are congruent.
Answers
Answer:
Step-by-step explanation:
The answer is, no!
Step-by-step explanation:
The reason to that answer is that some other shapes are also, having the same properties as shown. An example for that property would also mean a rectangle and not always a parallelogram.
So, here is the given information on what we need to classify a shape as a parallelogram:-
1) Parallel Sides
2)Opposite Sides are equal.
3) Adjacent sides are not equal.
4) Opposite angles are equal.
5)Adjacent angles are not equal.
Based on this, we can classify a shape as a parallelogram.
Hope, this answer helps!
A container with an open top is to have 10 m3 capacity and be
made of thin sheet metal. Calculate the dimensions of the box if it
is to use the minimum possible amount of metal.
Answers
The dimensions of the box if it is to use the minimum possible amount of metal are,
⇒ 2.714 m, 2.714 m, 1.358 m
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A container with an open top is to have 10 m³ capacity.
Now,
Let the dimensions are x, y and z.
Since, Volume of box = 10 m³
Hence, We get;
⇒ xyz = 10
⇒ z = 10/xy
Since, A container is open in top.
Hence, The surface area = 2xz + 2yz + xy
Substitute z = 10/xy;
⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy
= 20/y + 20/x + xy
For minimum metal;
⇒ d (S.A)/ dx = 0
⇒ - 20/x² + y = 0
⇒ y = 20/x² ..(i)
And, d (S.A) / dy = 0
⇒ - 20/y² + x = 0
⇒ x = 20/y² ..(ii)
Divide equation (i) and ((ii);
⇒ x = y
Hence, We get;
⇒ xyz = 10
⇒ x³ = 10
⇒ x = 2.714
And, y = 2.714
So, The value of z is,
⇒ z = 10/xy
⇒ z = 10 / 2.714×2.714
⇒ z = 1.358 m
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Prob-1A random sample of 21 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.12 mm and sample standard deviation is S = 0.14 mm. Construct a 95% two-sided confidence interval for the mean glass thickness.
Answers
For the typical glass thickness of 3.12 mm, the 95% two-sided confidence interval will be (3.067,3.173).
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.
Here,
mean x=3.12 mm
Standard deviation s=0.14 mm
number of sample n=21
two-sided confidence interval,
=x±tₐ÷₂(s/√n)
a=1-0.95
a=0.05
t₀.₀₅,₂₀=1.725
=3.12±1.725*(0.14/√21)
=3.12±1.725*(0.14/4.58)
=3.12±1.725*0.0306
=3.12±0.053
=(3.067,3.173)
The 95% two-sided confidence interval for the mean glass thickness of 3.12 mm will be (3.067,3.173).
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If A has the coordinate -10 and C has the coordinate 14 and B is the midpoint of a AC, then what is the coordinates of D which is the midpoint of BC?
Answers
Answer:
8
Step-by-step explanation:
The midpoint of AC is ...
B = (A +C)/2 = (-10 +14)/2 = 2
The midpoint of BC is ...
D = (B +C)/2 = (2 +14)/2 = 8
The midpoint of BC is 8.
Please awnser asap I will brainlist
Answers
Answer:
V = 180 (vans)
S = 90 (small trucks)
L = 40 (large trucks)
Step-by-step explanation:
Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.
Write the equations:
V + S + L = 310 (total number of vehicles)
V = 2S (twice as many vans as small trucks)
35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)
Substitute equation 2) into equation 1):
2S + S + L = 310
3S + L = 310
Simplify equation 3) by substituting V = 2S:
70,000S + 70,000S + 60,000L = 15,000,000
140,000S + 60,000L = 15,000,000
Set up a system of equations:
3S + L = 310
140,000S + 60,000L = 15,000,000
Eliminate L by multiplying equation 1) by 60,000:
60,000(3S + L) = 60,000(310)
180,000S + 60,000L = 18,600,000
Subtract equation 2) from the new equation:
(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000
40,000S = 3,600,000
Solve for S:
S = 90
Substitute the value of S into equation 1) to solve for L:
3(90) + L = 310
270 + L = 310
L = 40
Substitute the values of S and L into equation 2) to solve for V:
V = 2S
V = 2(90)
V = 180
The final answer is:
V = 180 (vans)
S = 90 (small trucks)
L = 40 (large trucks)
Answer:
180 Vans 90 Small trucks and 40 Large trucks
Step-by-step explanation:
both clocks ring toget (b) Two bells hanged at a school were adjusted at 10:00 am in such a way th one of them rings at the interval of every 45 minutes and another at every minutes. At what time will both bells ring together ?
Answers
The Least common multiple (LCM) The time at which both bells will ring together is 10:45 am, and the Subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.
The time at which both bells will ring together, we need to find the least common multiple (LCM) of the intervals at which each bell rings.
The first bell rings every 45 minutes, and the second bell rings every minute. We want to find the point at which both intervals align, meaning they both divide evenly into the same amount of time.
To find the LCM, we can list the multiples of each interval until we find a common multiple.
Multiples of 45 minutes: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
Multiples of 1 minute: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
From the lists above, we can observe that the least common multiple occurs when both intervals coincide at the same time, which is 45 minutes.
Thus, the two bells will ring together every 45 minutes.
If we consider the initial adjustment time of 10:00 am, the first time both bells will ring together is at 10:45 am. After that, they will continue to ring together every 45 minutes throughout the day.
Therefore, the time at which both bells will ring together is 10:45 am, and the subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.
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Jonathan will run a 614-mile relay with 4 other team members, where each team member runs an equal distance. How many miles will Jonathan run?
Answers
Answer: Jonathan will rum \(1\dfrac14\text{ mile}\) .
Step-by-step explanation:
Given: Total distance to run =\(6\dfrac14\) miles \(=\dfrac{25}{4}\) miles
Total members = 1+4 = 5
if each member runs equal distance.
Then, each member will run = \(\dfrac{\text{Total distance}}{\text{Total members}}\)
\(=\dfrac{\dfrac{25}{4}}{5}\\\\ \lim_{n \to \infty} a_n =\dfrac{25}{4\times5}\\\\=\dfrac{5}{4}\\\\ = 1\dfrac14 \text{miles}\)
Hence, Jonathan will rum \(1\dfrac14\text{ mile}\) .
1. Luis wants to buy Jordans for 75.23. He saves 10.27 per month. Write an equation to solve how many months he'll need to save. Use x for the variable and do not have any spaces.
2. Jovie earns $8.25 for the hours that she is at work. This week she earned $288.75. Write an equation to solve how many hours she worked. Use x for the variable and do not have any spaces. Pls help :(
Answers
Answer:
Chicken nugget
Step-by-step explanation:
Average movie prices in the United States are, in general, lower than in other countries. It would cost $81.23 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $77.17. How much does an average movie ticket cost in each of these countries?
Answers
Answer:
Let the cost in Japan be m and that of Switzerland be n
n=13.35
Step-by-step explanation:
Find the future value of an investment if $650 is deposited at the beginning of each month for 4 years and the interest rate is 2.2% compounded monthly.
$28,600.00
$35,252.54
$32,615.54
$22,425.51
Answers
The future value of the investment is equals to $\(32,582.78\).
What is future value of the monthly investment?The number of monthly payments over 4 years is:
= 4 years x 12 months/year
= 48 months.
We will use future value of an annuity formulae to solve which is FV = PMT x [(1 + r)^n - 1] / r
Plugging in the values, we get:
FV = 650 * [(1 + 0.022/12)^48 - 1] / (0.022/12)
FV = 650 * (0.09190014604/0.00183333333)
FV = 650 * 50.1273524766
FV = 32582.7791098
FV = $32,582.78.
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I need help asap!!!!!!!!!!!!! I will give brainiest!! Just give me the inequality plz
Answers
The answer is D.
Step-by-step explanation:
Answer: 11 weeks
Step-by-step explanation:
First we need to check what variables we have.
Beginning Balance = $1000
Goal = $350
Withdrawal = $55 per week
Now let's declare a variable as the number of weeks.
Let x = number of weeks
1000 - 55x = 350
-55x = 350-1000
-55x = -650
Then we divide both sides by -55 to find the value of x.
x = 11.81 or 11 since we're looking for how many weeks in total
Now let's see if we still have 350 if we have a total of 11 as the value of x.
1000 - 55(11) = 350
1000 - 605 = 350
395 = 350
We can see that Kendall will have $395 compared to the $350 goal.
So Kendall can withdraw $55 a week for 11 weeks to still be within her goal of having $350 in her savings account.
Solve using tangent and cosine
Answers
The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.
What are the sides of the triangle labelled x?The figures in the image are right triangles.
A)
angle D = 17 degree
Adjacent to angle D = 14 mm
Opposite to angle D = x
To solve for the missing side length x, we use the trigonometric ratio.
Note that: tangent = opposite / adjacent
Hence:
tan( 17 ) = x/14
x = tan( 17 ) × 14
x = 4.3mm
B)
angle Z = 82 degree
Adjacent to angle Z = 43.1 m
Hypotenuse = x
Using trigonometric ratio,
cosine = adjacent / hypotenuse
cos( 82 ) = 43.1 / x
x = 43.1 / cos( 82 )
x = 309.7 m
Therefore, the measure of x is 309.7 meters.
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Brennan knew his parents had set up their will some years ago. Neither he nor his sister, Maureen, had ever discussed the will with their parents. When both parents passed away, they met with the family lawyer about the will. What they found was that the money their parents had been giving them over the last few years was a gift and part of their estate planning. The gifts reduced the size of the estate to ensure the value of the estate upon their passing would be under the tax-free limit.
Their parents had not really talked with Brennan or Maureen about how the “gift” money they had been receiving would affect their final inheritance. As they listened to
the estate lawyer give them details of their inheritance, they were shocked to learn there was less than what they had thought.
1. Discuss your thoughts on how Brennan’s and Maureen’s parents handled the informationin the will prior to their passing. Should the parents have explained more clearly about the “gift” money and how it affected their inheritance?
2. What responsibility did Brennan and Maureen have to discuss the will with their parents?
3. What experience do you have with a family member’s will? How would you approach
the topic of writing a will with a family member?
Answers
1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.
2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.
3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.
1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.
2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.
3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.
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To which of the following expressions could you apply the associative property?
A.9-5-2
B.5+3-2
C.8÷4÷1
D.7+3+1
Answers
The associative property states that the order in which three or more numbers are added or multiplied does not affect the result of the operation. You can apply the associative property to the expressions A. 9-5-2, B. 5+3-2, and D. 7+3+1.
In expression A, 9-5-2, you can rearrange the numbers as follows: 9-5-2 = (9-5)-2 = 4-2 = 2.
In expression B, 5+3-2, you can rearrange the numbers as follows: 5+3-2 = (5+3)-2 = 8-2 = 6.
In expression D, 7+3+1, you can rearrange the numbers as follows: 7+3+1 = (7+3)+1 = 10+1 = 11.
You cannot apply the associative property to expression C, 8÷4÷1, as this is a division expression, and the associative property does not apply to division.
Overall, the associative property allows you to rearrange the order of addition or multiplication of three or more numbers without affecting the result of the operation.
The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A mathematical principle that states the product of a multiplication issue is unaffected by the way the elements are organized.
The associative property for addition and multiplication is valid but not for division.
The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.
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In the diagram below, FC = 10.9,
DE = 17.5, and DF = 13.1. Find the
length of EB. Round your answer to the
nearest tenth if necessary.
D
F
E
C
B
Answers
The length of EB is approximately 14.6 units when rounded to the nearest tenth.
To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.
Using the similarity ratio, we can set up the proportion:
DF / CF = DE / EB
Plugging in the given values, we have:
13.1 / 10.9 = 17.5 / EB
To find EB, we can cross-multiply and solve for EB:
13.1 * EB = 10.9 * 17.5
EB = (10.9 * 17.5) / 13.1
EB ≈ 14.6
Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.
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i need helpppppppp ??ASAP
Answers
Answer:
60.32
Step-by-step explanation:
Given R=1/4 Q^2 solve for Q
Answers
9514 1404 393
Answer:
Q = ±2√R
Step-by-step explanation:
Take the square root:
±√R = 1/2Q
Multiply by 2:
Q = ±2√R
A Web music store offers two versions of a popular song. The size of the standard version is 2.5 megabytes (MB). The size of the high-quality version is 4.8 MB. Yesterday, there were 1060 downloads of the song, for a total download size of 3593 MB. How many downloads of the standard version were there?
Answers
We are given the details for downloads of songs of two size categories.
The first is a standard size which is 2.5MB. The second one is a high quality version which is 4.8MB.
Note that we do not know how many of each was downloaded (at least not yet). however, we do know that the total download for both category sizes was a total of 1060 songs. In other words
Standard size plus High quality size = 1,060.
We shall now assign variables to both categories;
Let standard size be letter a
Let High quality size be letter b.
For a total download size of 3593 MB in all, we can determine that;
\(2.5a+4.8b=3593\)We can now set up a system of equations which are as follows;
\(\begin{gathered} a+b=1060---(1) \\ 2.5a+4.8b=3593---(2) \end{gathered}\)Note that in equation (1), what we've done is add up standard size and high quality size and that means a total of 1060 songs (regardless of its size/category).
We can now solve the following by means of the substitution method;
\(\begin{gathered} a+b=1060 \\ \text{Make a the subject of the equation;} \\ a=1060-b \end{gathered}\)Now we substitute for the value of a into equation (2);
\(\begin{gathered} 2.5a+4.8b=3593 \\ 2.5(1060-b)+4.8b=3593 \\ 2650-2.5b+4.8b=3593 \\ 2650+2.3b=3593 \end{gathered}\)Next we subtract 2650 from both sides;
\(2.3b=943\)Next we divide both sides by 2.3;
\(\begin{gathered} \frac{2.3b}{2.3}=\frac{943}{2.3} \\ b=410 \end{gathered}\)This means there were 410 downloads of the 4.8MB size.
We can now substitute the value of b into equation (1);
\(\begin{gathered} a+b=1060 \\ a+410=1060 \\ \end{gathered}\)Subtract 410 from both sides;
\(a=650\)ANSWER:
There was 650 downloads of the standard version
how to solve this?
given
\( \frac{4}{25} = 0.16\)
what is
\( \frac{21}{25} \)
as a decimal
![how to solve this?given[tex] \frac{4}{25} = 0.16[/tex]what is [tex] \frac{21}{25} [/tex]as a decimal](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Ke59HD2tE5mtvwNXN2eZNnOKE8DVy4ep.jpeg)
Answers
Answer:
= 0.375
Step-by-step explanation:
then 3/8 to it decimal fraction
\( \frac{3}{8} \\ = 0.375\)