The money after 10 years is $ 13591.4091
Solution:
Given that,
If you have a bank account that is modeled by the following equation:
[tex]A = 5000e^{0.10t}[/tex]
To find: Money after 10 years
How much money would you have after 10 years
Substitute t = 10 in above given equation
[tex]A = 5000 \times e^{0.10 \times 10}\\\\A = 5000 \times e^{1}\\\\A = 5000 \times 2.71828\\\\A = 13591.4091[/tex]
Thus money after 10 years is $ 13591.4091
An open box is constructed from a square 10-inch piece of cardboard by cutting squares of length x inches out of each corner and folding the sides up. Express the volume of the box as a function of x, and state the domain.
Answer: V = 8x^3-80x^3 +200x
Domain 0<x<5
Step-by-step explanation:
Dimension of cardboard = 10 by 10
Let the length of box = 10-2x
Let the width of box = 10 - 2x
Let the height of box be =x
Volume = l×w×h
V = (10-2x)×(10-2x)×x
V= 100 - 40x +42 × x
V= 8x^3 -80x^2 +200x
The volume of the box as a function of x is 8x³ - 80x² + 200x
The formula to calculate volume will be:
= Length × Width × Height
The dimensions of the cardboard will be:
Length = 10 - 2x
Width = 10 - 2x
Height = x
Therefore, the volume will be:
= (10 - 2x) × (10 - 2x) × x
= 8x³ - 80x² + 200x
Therefore, the volume of the box as a function of x is 8x³ - 80x² + 200x.
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In your own words, describe how to find the rate of increase if the population of a town changes from 47,230 to 55,112 people. Then calculate the amount of change.
The population of the town increased by 7,882 people and the rate of increase is approximately 16.69%.
Finding the rate of increase in a town's population involves two steps: calculating the amount of change and expressing it as a percentage. Here's how:
1. Calculate the amount of change:
Imagine this change like climbing stairs. The initial population (47,230) is one step, and the final population (55,112) is another step higher. To find how many steps you climbed (the amount of change), simply subtract the starting step from the ending step:
Amount of change = Final population - Initial population
Amount of change = 55,112 people - 47,230 people
Amount of change = 7,882 people
2. Express the change as a rate of increase:
Now, imagine you want to tell someone how much faster you climbed compared to your starting position. To do that, you calculate the percentage increase, which is like expressing the number of steps climbed relative to your starting point (one step).
Rate of increase = (Amount of change / Initial population) * 100%
Rate of increase = (7,882 people / 47,230 people) * 100%
Rate of increase ≈ 16.69%
Therefore, the population of the town increased by 7,882 people and the rate of increase is approximately 16.69%. This means the population grew by roughly 16.69% compared to its original size.
The rate of transmission in a telegraph cable is observed to be proportional to x2ln(1/x) where x is the ratio of the radius of the core to the thickness of the insulation (0
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
[tex]f'(x) = k*((x^2)'*ln(1/x) + x^2*(ln(1/x)')) = k*(2x\,ln(1/x)+x^2*(\frac{1}{1/x}*(-\frac{1}{x^2})))\\= k * (2x \, ln(1/x)-x)[/tex]
We need to equalize f' to 0
k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp1/x = e^(1/2)x = 1/e^(1/2) = 1/√e ≅ 0.607Thus, the value of x that gives the maximum transmission is 1/√e.
The rate of transmission in a telegraph cable is given by the equation: rate of transmission = x^2 ln(1/x), where x is the ratio of the radius of the core to the thickness of the insulation.
Explanation:The rate of transmission in a telegraph cable is given by the equation: rate of transmission = x2 ln(1/x), where x is the ratio of the radius of the core to the thickness of the insulation.
This equation shows that the rate of transmission is directly proportional to the square of x and logarithmically inversely proportional to x.
For example, if x is 0.5, the rate of transmission is (0.5)2 ln(1/0.5) = 0.25 ln(2).
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hello loves!! I've been stuck on this question for like 2 hours lol! i need some help, ill give 100 points :)
Answer:
61.12 units²
Step-by-step explanation:
(½ × pi × r²) + (½ × b × h)
½ [(3.14 × 4²) + (8 ×9)]
½(122.24)
61.12 units²
Answer:
61.13 units squared
Step-by-step explanation:
This figure is composed of a semicircle and a triangle. Let's find these areas separately:
1) SEMICIRCLE:
The area of a semicircle is: [tex]A=\frac{\pi r^2}{2}[/tex] , where r is the radius (which is the distance from the center to a point on the circle). In this case, the radius of the circle is 4. So, we have:
[tex]A=\frac{\pi *4^2}{2} =\frac{16\pi }{2} =8\pi[/tex] ≈ 25.13 units squared
2) TRIANGLE:
The area of a triangle is: [tex]A=\frac{bh}{2}[/tex] , where b is the base and h is the height. Here, the base is 8 (b = 8) and the height is 9 (h = 9). So, we have:
[tex]A=\frac{8*9}{2} =\frac{72}{2} =36[/tex] units squared
Finally, we add these two areas together:
25.13 + 36 = 61.13 units squared.
Hope this helps!
Frank started out in his car travelling 45 mph. When Frank was 1 3 miles away, Daniel started out from the same point at 50 mph to catch up with Frank. How long will it take Daniel to catch up with Frank?
Final answer:
It will take Daniel approximately 0.26 hours, or 15.6 minutes, to catch up with Frank.
Explanation:
To find how long it will take Daniel to catch up with Frank, we can use the formula time = distance / speed. Since Frank started out first, we can calculate his distance using the formula distance = speed * time. Let's assume it takes Daniel t hours to catch up with Frank. The time it takes Frank to travel 13 miles is 13 miles / 45 mph = 0.289 hours. Therefore, when Daniel starts, Frank has already traveled a distance of 0.289 hours * 45 mph = 13 miles. To catch up with Frank, Daniel needs to travel the same distance in t hours at a speed of 50 mph. So, 13 miles = 50 mph * t hours. Dividing both sides by 50 mph gives us t = 13 miles / 50 mph = 0.26 hours. Therefore, it will take Daniel approximately 0.26 hours, or 15.6 minutes, to catch up with Frank.
Identify the zeros of the function f(x) =2x^2 − 2x + 13 using the Quadratic Formula. SHOW WORK PLEASE!! I NEED HELP!!
Answer:
[tex]x=\frac{1+5i} {2}[/tex] and [tex]x=\frac{1-5i} {2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]f(x)=2x^{2} -2x+13[/tex]
Equate the function to zero
[tex]2x^{2} -2x+13=0[/tex]
so
[tex]a=2\\b=-2\\c=13[/tex]
substitute in the formula
[tex]x=\frac{-(-2)\pm\sqrt{-2^{2}-4(2)(13)}} {2(2)}[/tex]
[tex]x=\frac{2\pm\sqrt{-100}} {4}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{2\pm10i} {4}[/tex]
Simplify
[tex]x=\frac{1\pm5i} {2}[/tex]
therefore
[tex]x=\frac{1+5i} {2}[/tex] and [tex]x=\frac{1-5i} {2}[/tex]
Most bees have a body temperature of 35 Celsius. When they sleep, it can drop by up to 2 Celsius. What's their range in body temperature written as an inequality
The range of the body temperature is [tex]2\leq x\leq 35[/tex]
Explanation:
Let x denote the body temperature of the bees.
The maximum body temperature of the bee is 35° Celsius.
When they sleep, the body temperature can drop by up to 2° Celsius.
Thus, the minimum body temperature of the bee is 2° Celsius.
Thus, the range of the body temperature is from 35° Celsius to 2° Celsius.
The range of body temperature is given by:
[tex]2\leq x\leq 35[/tex]
Thus, the range in body temperature of the bees is [tex]2\leq x\leq 35[/tex]
Two cars entered an interstate highway at the same time at different locations and traveled in the same direction. The initial distance between the cars was 30 miles. The first car was going 70 miles per hour and the second was going 60 miles per hour. How long will it take for the first car to catch the second one?
Answer: it will take 0.23 hours for the first car to catch the second one.
Step-by-step explanation:
Let t represent the time it will take for the first car to catch the second one.
The initial distance between the cars was 30 miles. This means that by the time both cars meet, they would have covered a total distance of 30 miles.
Distance = speed × time
The first car was going 70 miles per hour.
Distance covered by the first car after t hours is
70 × t = 70t
The second was going 60 miles per hour. Distance covered by the second car after t hours is
60 × t = 60t
Since the total distance covered is 30 miles, then
70t + 60t = 30
130t = 30
t = 30/130 = 0.23 hours
I have some geometric sequence questions, will give 5 points for every answer and will give Brainliest!
1. List the first four terms of a geometric sequence with t5 = 24 and t6 = 3
2. List the first four terms of a geometric sequence with t1 = 4 and tn = -3tn-1
3. Find the three geometric means between 1/2 and 8
Thank you so much!!
Answer:
Step-by-step explanation:
1) since the sixth term is 3 and the fifth term 24, the common ratio would be 3/24 = 1/8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
If t6 = 3,r = 1/8, then
3 = a × 1/8^(6 - 1) = a × (1/8)^5
a = 3/(0.125)^5 = 98304
The first term is 98304.
Second term is 98304 × 1/8 = 12288
Third term is 12288 × 1/8 = 1536
Third term is 1536 × 1/8 = 192
2) t1 = 4
t2 = - 3t(2- 1) = - 3t1 = - 3 × 4 = - 12
t3 = - 3t(3- 1) = - 3t2 = - 3 × - 12 = 36
t4 = - 3t(4- 1) = - 3t3 = - 3 × 36 = - 108
3) let the numbers be t2,t3 and t4
The sequence becomes
1/2, t2,t3, t4,8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
8 = 1/2 × r^(5 - 1)
8 = 1/2 × r^4
16 = r^4
2^4 = r^4
r = 2
t2 = 1/2 × 2 = 1
t3 = 1 × 2 = 2
t4 = 2 × 2 = 4
please help with a, b, and c. thank you!:)
Answer:
The answer to your question is below
Step-by-step explanation:
a) The intervals in which the graph is decreasing are the right section of the first parabola, the left section of the second parabola and also the right section of the third parabola.
(9, 11) U (14.5, 17) U (21, 27)
b) There are only two intervals in which the graph is increasing
(1, 9) U (17, 21)
c) During the time the graph is increasing, Andre is getting away from his origin.
Which is the graph of f (x) = 4 (1/2) Superscript x?
Answer:
Option (2) is correct graph.
Step-by-step explanation:
Given:
The function to graph is given as:
[tex]f(x)=4(\frac{1}{2})^x[/tex]
Now, the above function is an exponential function of the form [tex]f(x)=ka^x[/tex]
Where, 'k' and 'a' are constants.
The range of an exponential function is always greater than 0.
The domain is all real numbers.
Now, for graphing it, we need to find some points on it and its end behaviour.
Now, for x = 0, the function value is given as:
[tex]f(0)=4(\frac{1}{2})^0=4[/tex]
So, (0, 4) is a point on the graph.
Now, for x = 1, the function value is given as:
[tex]f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2[/tex]
So, (1, 2) is another point on the graph.
Now, for x = 2, the function value is given as:
[tex]f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1[/tex]
So, (2, 1) is another point on the graph.
Now, as 'x' tends to ∞, the function value tends to:
[tex]f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0[/tex]
So, as
[tex]x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty[/tex]
Now, from among all the options, only option (2) fulfills all the conditions given above.
So, option (2) is correct graph.
Answer:
option 2
Step-by-step explanation:
The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?A. 21/55
B. 28/55
C. 34/55
D. 5/8
E. 139/220
Answer: B. [tex]\dfrac{28}{55}[/tex] .
Step-by-step explanation:
Given : Number of blue disks =4
Number of green disks = 8
Total disks = 12
Total number of combinations of drawing any 3 disks from 12 = [tex]^{12}C_3[/tex]
Number of combinations of drawing 1 blue and 2 green disks = [tex]^{4}C_1\times^{8}C_2[/tex]
Now , the probability that 1 of the disks selected is blue, and 2 of the disks selected are green will be :
[tex]\dfrac{^{4}C_1\times^{8}C_2}{^{12}C_3}\\\\=\dfrac{4\times\dfrac{8!}{2!6!}}{\dfrac{12!}{3!9!}}\\\\=\dfrac{4\times28}{220}\\\\=\dfrac{28}{55}[/tex]
Hence, the correct answer is B. [tex]\dfrac{28}{55}[/tex] .
Assume that the weight of two year old babies have distribution that is approximately normal with a mean of 29 pounds and a standard deviation of 3 pounds. what weight of two year old baby corresponds to 10th percentile?
Answer:
25.15 ponds is the weight of two year old baby corresponds to 10th percentile.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 29 pounds
Standard Deviation, σ = 3 pounds
We are given that the distribution of weight of two year old babies is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.10
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 29}{3})=0.10[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < -1.282) = 0.10[/tex]
[tex]\displaystyle\dfrac{x - 29}{3} = -1.282\\x = 25.154 \approx 25.15[/tex]
Thus, 25.15 ponds is the weight of two year old baby corresponds to 10th percentile.
In 1995, Orlando, Florida was about 175,000. At that same time , the population was growing at a rate of about 2000 per years, write an equation in slope - intercept form to find orlando's population for any year
Answer:
Y=2000x+175,000
Step-by-step explanation:
y=mx+b so your M will be your 2000 and your x is gonna be years, and your b is gonna be 175,000
4 Erin and Devon are playing a game. Erin has 42 points. If Devon had 14 more points, he'd have double the points Erin has. How many points does Devon have?
Final answer:
The question is a mathematical problem where we find that Devon has 70 points after setting up and solving an algebraic equation based on the conditions given.
Explanation:
The student's question revolves around a Mathematical problem concerning the points scored by two players, Erin and Devon, in a game. Erin has 42 points, and the question provides a condition that if Devon had 14 more points, he would have double the points Erin has. This scenario can be translated into an algebraic equation to solve for the number of points Devon currently has.
Let's denote the current number of points Devon has as D. According to the problem, if Devon had 14 more points, his total would be D + 14. We are also told that this hypothetical total would be double the points Erin has, which is 42. Therefore, we can write the equation as:
D + 14 = 2 × 42
By solving this equation, we can find out how many points Devon has:
D + 14 = 84 (since 2 × 42 equals 84)D = 84 - 14D = 70Devon currently has 70 points.
Erin has 42 points. Devon has 70 points. If he had 14 more, he'd have double Erin's points.
let's break it down step by step:
Given:
- Erin has 42 points.
- If Devon had 14 more points, he'd have double the points Erin has.
Let's denote Devon's points as [tex]\( D \).[/tex]
According to the given information, if Devon had 14 more points, he'd have double the points Erin has. So, mathematically, we can represent Devon's points as [tex]\( 2 \times 42 \)[/tex] when we add those 14 points.
So, we can write the equation:
[tex]\[ D + 14 = 2 \times 42 \][/tex]
Now, let's solve for [tex]\( D \):[/tex]
[tex]\[ D + 14 = 84 \][/tex]
Subtract 14 from both sides of the equation:
[tex]\[ D = 84 - 14 \]\[ D = 70 \][/tex]
So, Devon currently has 70 points.
The math club has $1256 to send on food for a party. Beef = $11, chicken = $9 and vegetarian = $7. * Vegetarian dishes are purchased. Write an inequality
Answer:
[tex]11b+9c+7v\leq 1256[/tex]
Step-by-step explanation:
Let 'b' plates of beef, 'c' plates of chicken, and 'v' plates of vegetarian dishes are purchased for the party.
Given:
Cost of 1 plate of beef dish = $11
Cost of 1 plate of chicken dish = $9
Cost of 1 plate of vegetarian dish = $7
Total money available to spend = $1256
So, as per question:
Total money spent on purchasing the dishes must be less than or equal to the total money available by the Math club.
Total cost of all the dishes is equal to the sum of the costs of 'b' plates of beef, 'c' plates of chicken, and 'v' plates of vegetarian dishes.
Therefore, total cost of all the dishes is given as:
Total cost = [tex]11b+9c+7v[/tex]
Now, the inequality for the given situation is:
Total cost on dishes ≤ Total money available to spend
⇒ [tex]11b+9c+7v\leq 1256[/tex]
Hence, the inequality is [tex]11b+9c+7v\leq 1256[/tex]
Identify the zeros of the function f(x) =2x^2 − 2x + 13 using the Quadratic Formula. SHOW WORK PLEASE!! I NEED HELP!!
Answer:
The zeros of the given function are not real. The zeros of the function is at :
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=2x^2-2x+13[/tex]
To find the zeros of the function using quadratic formula.
Solution:
Applying quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
For the given function:
[tex]a=2, b=-2\ and\ c=13[/tex]
Thus, we have:
[tex]x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(13)}}{2(2)}[/tex]
[tex]x=\frac{2\pm\sqrt{4-104}}{4}[/tex]
[tex]x=\frac{2\pm\sqrt{-100}}{4}[/tex]
[tex]x=\frac{2\pm\sqrt{100}i}{4}[/tex]
[tex]x=\frac{2\pm10i}{4}[/tex]
[tex]x=\frac{2+10i}{4}[/tex] and [tex]x=\frac{2-10i}{4}[/tex]
[tex]x=\frac{2}{4}+\frac{10i}{4}[/tex] and [tex]x=\frac{2}{4}-\frac{10i}{4}[/tex]
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
Thus, the zeros of the given function are not real. The zeros of the function is at :
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
A broker/dealer bought ABC stock at 8 for its inventory position. A month later when the inter-dealer market for ABC was 10.50 -- 11.25, the broker/dealer sold the stock to a customer. The basis for the dealer's markup will be:[A] 8.00[B] 8.75[C] 10.50[D] 11.25
Answer:
[D] 11.25
Step-by-step explanation:
Broker/dealers must trade with customers based on the current bid and ask.
10.50 Bid for customers selling
11.25 Ask for customers buying
Help asap, thank you! :) 2 questions, multiplying monomials.
Answer:
Correct answer choices are [tex]27x^{2}[/tex] and [tex]657 cm^{2}[/tex]
Step-by-step explanation:
We are able to arrive at these answers through basic equation used to calculate area of an triangle and monomial laws
Home Away, a nongovernmental not-for-profit organization, provides food and shelter to victims of natural disasters. Home Away received a $15,000 gift with the stipulation that the funds be used to buy beds. In which net asset class should Home Away report the contribution?
Answer:
Home away should record the contribution to a Net assets with donor restriction
Step-by-step explanation
A Net asset with donor restriction is the part of net assets of a not- for - profit making organisation that is subject to donor-imposed restrictions.
The stipulation that the fund of $15,000 should be used to buy beds automatically makes it to be classified as a Net assets with donor restriction item.
At a college, the cost of tuition increased by 10%. Let b represent the former cost of tuition. Use the expression b+0.10b for the new cost of tuition.
Question is Incomplete,Complete question is given below;
At a college, the cost of tuition increased by 10%. Let b be the former cost of tuition. Use the expression b + 0.10b for the new cost of tuition.
a) Write an equivalent expression by combining like terms.
b) What does your equivalent expression tell you about how to find the new cost of tuition?
Answer:
a. The equivalent expression is [tex]1.1b[/tex].
b. The new cost of tuition is 1.1 times the former cost of tuition.
Step-by-step explanation:
Given:
Former cost of tuition = [tex]b[/tex]
the cost of tuition increased by 10%.
New cost of tuition = [tex]b+0.10b[/tex]
Solving for part a.
we need to find the equivalent expression by combining the like terms we get;
Now Combining the like terms we get;
new cost of tuition = [tex]b(1+0.1) = 1.1b[/tex]
Hence The equivalent expression is [tex]1.1b[/tex].
Solving for part b.
we need to to say about equivalent expression about how to find the new cost of tuition.
Solution:
new cost of tuition = [tex]1.1b[/tex]
So we can say that.
The new cost of tuition is 1.1 times the former cost of tuition.
60 POINTS AND RAINLIEST!
Koji is installing a rectangular window in an office building. The window is 823 feet wide and 534 feet high.
The formula for the area of a rectangle is A=bh.
What is the area of the window?
Enter your answer as a mixed number in simplest form in the box.
$$
Area of the window [tex]=49\frac{5}{6}\ \text{ft}^2[/tex]
Solution:
Width of the window = [tex]8\frac{2}{3}[/tex] feet
Height of the window = [tex]5\frac{3}{4}[/tex] feet
To find the area of the window:
The window is in rectangular shape.
Formula for the area of the rectangle = base × height
Substitute the given values in the formula.
Area of the window = [tex]8\frac{2}{3}\times 5\frac{3}{4}[/tex]
Convert mixed fraction into improper fraction.
[tex]$=\frac{26}{3}\times \frac{23}{4}[/tex]
Multiply the numerators and denominators separately.
[tex]$=\frac{598}{12}[/tex]
Divide the numerator and denominator by the common factor 2.
[tex]$=\frac{598\div2}{12\div2}[/tex]
[tex]$=\frac{299}{6}[/tex]
Now convert improper fraction into mixed fraction.
[tex]$=49\frac{5}{6}\ \text{ft}^2[/tex]
Area of the window [tex]=49\frac{5}{6}\ \text{ft}^2[/tex].
Answer:
49 5/6 will be your answer
Step-by-step explanation:
(6-2i)^2 which is the coefficient of i ?
A.−24
B.−12
C.16
D.24
Option A: -24 is the coefficient of i
Explanation:
The expression is [tex](6-2 i)^{2}[/tex]
To determine the coefficient of i, first we shall find the square of the binomial for the expression [tex](6-2 i)^{2}[/tex]
The formula to find the square of the binomial for this expression is given by
[tex](a-b)^{2}=a^{2}-2 a b+b^{2}[/tex]
where [tex]a=6[/tex] and [tex]b=2i[/tex]
Substituting this value and expanding, we get,
[tex](6-2 i)^{2}=6^{2} -2(6)(2i)+(2i)^{2}[/tex]
Simplifying the terms, we have,
[tex](6-2 i)^{2}=36-24i-4[/tex]
Thus, from the above expression the coefficient of i is determined as -24.
Hence, Option A is the correct answer.
Suppose a fair coin is tossed nine times. Replace the resulting sequence of H’s and 74 Chapter 2 Probability T’s with a binary sequence of 1’s and 0’s (1 for H, 0 for T). For how many sequences of tosses will the decimal corresponding to the observed set of heads and tails exceed 256?
Answer:
255 sequence
Step-by-step explanation:
Since
Head replaced by 1
Tail replaced by 0
For each toss, there are two possible outcomes: heads 1, or tails 0.
For 9 toss the possible outcome sequence range from
000000000 to 111111111
000000000 in binary = 0 in decimal
111111111 in binary = 511 in decimal
Since we are asked to find decimal corresponding to the observed set of heads and tails that exceed 256?
That is sequence that exceed 256 (100000000)
Which is 257 (100000001) to n
So the outcome sequence will range from 257 to the last possible outcome sequence for 9 tosses which is 511
Therefore between 257 to 511.
Number of outcome sequence is 255
Chau will run at most 28 miles this week. So far, he has run 18 miles. What are the possible numbers of additional miles he will run? Use t for the number of additional miles he will run. Write your answer as an inequality solved for t.
Answer:
Step-by-step explanation:
18 + x ≤ 28
x ≤ 28 - 18
x ≤ 10
1 ≤ x ≤ 10
The possible number of additional miles Chau can run ranges from 0 to 10 miles, which is expressed by the inequality t ≤ 10, where t represents the additional miles.
To find the possible number of additional miles Chau will run, we use the inequality that represents the situation:
Chau has run 18 miles and will run at most 28 miles in total. Thus, we have:
18 miles + t additional miles ≤ 28 miles
By isolating t, we subtract 18 from both sides of the inequality:
t ≤ 28 miles - 18 miles
t ≤ 10 miles
This inequality means that Chau can run at most 10 additional miles this week.
Therefore, the possible numbers of additional miles t that Chau can run range from 0 to 10 miles.
Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) HINT [See Example 4.] (Round your answers to five decimal places.) f(x) = 3 x ; a = 7
Step-by-step explanation:
average rate of change of function is given by :
[tex]f= (f(a+h)-f(a))/h[/tex]
where
[tex]f(x)=3x[/tex]
and a= 7
so inserting values is formula for h=1
[tex]f=(f(7+1)-f(7))/1[/tex]
[tex]f= f(8)-f(7)= 3(8)-3(7)=24-21=3[/tex]
now for h= 0.1
[tex]f=(f(7+0.1)-f(7))/0.1=(f(7.1)-f(7))/0.1=(3(7.1)-3(7))/0.1[/tex]
[tex]f=3[/tex]
similarly average rate of change of given function is same for all given step sizes.
Final answer:
The question involved calculating the average rate of change of the function f(x) = 3x over various intervals, showing that the rate of change is constant and equals 3 for all given values of h.
Explanation:
The question asks to calculate the average rate of change of the function f(x) = 3x over the intervals [a, a + h] for values of h = 1, 0.1, 0.01, 0.001, and 0.0001, where a = 7.
The average rate of change is calculated using the formula [tex]\frac{f(a+h) - f(a)}{h}[/tex]
For each value of h, we substitute a and h into the function and use the formula to find the average rate of change.
For h = 1, the average rate of change is 3.
For h = 0.1, the average rate of change is also 3.
For h = 0.01, the average rate of change remains 3.
For h = 0.001, the average rate is again 3.
Similarly, for h = 0.0001, the average rate of change is 3.
Using technology for values of h smaller than 0.1 is recommended due to the precision required in calculations. However, for this particular function, the rate of change is constant across these intervals, simplifying the process.
Zeke is racing his little brother niko they are running a total of 30 yards and zeke gives Niko a 12 yard head start zeke runs 2 yards every second but Niko only runs 1 yard every 2 seconds if x represents the number of seconds they have been racing and y represents the distance from the start line then
Answer:
Zeke will catch up with Niko at 16 yards from the start line, y = 16 yards.
Zeke will catch up Niko after 8 seconds, x = 8 seconds.
Step-by-step explanation:
i) distance to be run = 30 yards
ii) Niko has a head start of 12 yards.
iii) speed of Zeke = 2 yards / second
iv) speed of Niko = 1 yard every 2 seconds = 0.5 yard / second
v) x represents the number of seconds they have been racing.
vi) y represents the distance from the start line.
vii) the time at which Zeke catches up with Niko will be given by
[tex]x = \frac{y - 12}{0.5} = \frac{y}{2}[/tex]
Therefore 2y - 24 = 0.5y [tex]\Rightarrow[/tex] 1.5 y = 24 [tex]\therefore[/tex] y = 24 / 1.5 = 16 yards
Therefore x = 16 /2 = 8 seconds
The equations that represent Niko's and Zeke's distance from the start line are [tex]y = 12 + \frac 12 x[/tex] and [tex]y = 2 x[/tex], respectively.
The given parameters are:
[tex]Total = 30[/tex] --- the total distance
Niko is 12 yards ahead, and runs at 1 yard per 2 seconds. So, Niko's equation is
[tex]N i k o = 12 + \frac 12 x[/tex]
Zeke runs 2 yards per seconds. So, Zeke's equation is
[tex]Zeke = 2 x[/tex]
Hence, Niko's and Zeke's distance from the start line are [tex]y = 12 + \frac 12 x[/tex] and [tex]y = 2 x[/tex], respectively.
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Two different suppliers, A and B, provide a manufacturer with the same part. All supplies of this part are kept in a large bin. in the past, 5% of the parts supplied by A and 9% of the parts supplied by B have been defective. A supplies four times as many parts as B. Suppose you reach into the bin and select a part, and find it is nondetective. What is the probability that it was supplied by A
Answer:
The probability of selecting a non-defective part provided by supplier A is 0.807.
Step-by-step explanation:
Let A = a part is supplied by supplier A, B = a part is supplied by supplier B and D = a part is defective.
Given:
P (D|A) = 0.05, P(D|B) = 0.09
A supplies four times as many parts as B, i.e. n (A) = 4 and n (B) = 1.
Then the probability of event A and B is:
[tex]P(A)=\frac{n(A)}{n(A)+N(B)}= \frac{4}{4+1}=0.80\\P(B)\frac{n(B)}{n(A)+N(B)}= \frac{1}{4+1}=0.20[/tex]
Compute the probability of selecting a defective product:
[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)\\=(0.05\times0.80)+(0.09\times0.20)\\=0.058[/tex]
The probability of selecting a non-defective part provided by supplier A is:
[tex]P(A|D')=\frac{P(D'|A)P(A)}{P(D')} = \frac{(1-P(D|A))P(A)}{1-P(D)}\\=\frac{(1-0.05)\times0.80}{(1-0.058)}\\ =0.80679\\\approx0.807[/tex]
Thus, the probability of selecting a non-defective part provided by supplier A is 0.807.
The required probability of selecting a non-defective part provided by supplier A is 0.807.
Let,
A part is supplied by supplier A,
B part is supplied by supplier B,
And D = a part is defective.
Given:
P ([tex]\frac{D}{A}[/tex]) =5% = 0.05,
P([tex]\frac{D}{B}[/tex]) = 9% = 0.09
A supplies four times as many parts as B, .
Then, n (A) = 4 and n (B) = 1.
The probability of event A and B is:
Probability of event P(A) = [tex]\frac{n (A)}{n (A) + n(B)}[/tex] = [tex]\frac{4}{4+1}[/tex]
P(A) = [tex]\frac{4}{5}[/tex]
And Probability of Event P(B) = [tex]\frac{n (B )}{n (A) + n(B)} = \frac{1}{4+1}[/tex]
P(B) = [tex]\frac{1}{5}[/tex]
Then , the probability of selecting a defective product:
P(D) = [tex]P(\frac{D}{A}) P(A) + P(\frac{D}{B}) P(B)[/tex]
P(D) = 0.50×0.80 + 0.09×0.20
P(D) = 0.058
The probability of selecting a non-defective part provided by supplier A is
[tex]P(\frac{A}{D'} )= \frac{P(D'(A)) . P(A)}{P(D')} \\\\[/tex]
= [tex]\frac{1- P(D(A)). P(A)}{1-P(A)} \\\\\frac{(1-0.05) . 0.80}{1- 0.05} \\\\[/tex]
= 0.807
Hence, the probability of selecting a non-defective part provided by supplier A is 0.807.
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Please help : ) - square roots how do i do this?
Step-by-step explanation:
a) √ 8/10
= to get the bench mark we have to look for perfect square that are closer to the numbers 8 and 10
= for 8, it is 9 ; for 10 it is also 9
Therefore, √ 8/10 is about√ 9/9
= 3/3 = 1
b) √17/5
= to get the bench mark we have to look for perfect square that are closer to the numbers 17 and 5
= for 17, it is 16; for 5 it is 4
Therefore, √ 17/5 is about √ 16/4
= 4/2= 2
c) √7/13
= to get the bench mark we have to look for perfect square that are closer to the numbers 7 and 13
= for 7, it is 9; for 13 it is 16
Therefore, √ 7/13 is about √ 9/16
= 3/4
d) √29/6
= to get the bench mark we have to look for perfect square that are closer to the numbers 29 and 6
= for 29, it is 25; for 6 it is 4
Therefore, √ 29/6 is about √ 25/4
= 5/4
Riverside elementary school is holding a schoolwide election to choose a color. 5/8 of the votes were for blue. 5/9 of the remaining votes were for green and the remaining 48 votes were for red.How many votes were for blue
Answer:
There were 180 votes for blue.
Step-by-step explanation:
Given:
Riverside elementary school is holding a schoolwide election to choose a color. 5/8 of the votes were for blue. 5/9 of the remaining votes were for green and the remaining 48 votes were for red.
Now, to find the votes for blue.
Let the total votes be [tex]x.[/tex]
The votes for blue:
[tex]\frac{5}{8} \ of\ x[/tex]
[tex]=\frac{5}{8} \times x[/tex]
[tex]=\frac{5x}{8}[/tex]
Remaining votes are:
[tex]x-\frac{5x}{8} \\\\=\frac{8x-5x}{8} \\\\=\frac{3x}{8}[/tex]
The votes for green:
[tex]\frac{5}{9} \ of\ \frac{3x}{8} \\\\=\frac{5}{9} \times \frac{3x}{8} \\\\=\frac{15x}{72}[/tex]
The remaining votes for red = 48.
Now, the total votes are:
[tex]\frac{5x}{8} +\frac{15x}{72} +48=x\\\\\frac{45x+15x+3456}{72}=x\\\\\frac{60x+3456}{72}=x[/tex]
Multiplying both sides by 72 we get:
[tex]60x+3456=72x[/tex]
Subtracting both sides by 60[tex]x[/tex] we get:
[tex]3456=12x[/tex]
Dividing both sides by 12 we get:
[tex]288=x\\\\x=288.[/tex]
Thus, the total votes = 288.
Now, to get the votes for blue:
[tex]\frac{5}{8} \ of\ 288\\\\=\frac{5}{8}\times 288\\\\=0.625\times 288\\\\=180.[/tex]
Therefore, there were 180 votes for blue.