Answer:
The answer to your question is 26
Step-by-step explanation:
Median is the middle number of a list order from lowest to highest.
Process
1.- Order the numbers from lowest to highest
4 9 17 22 24 28 51 76 83 98
2.- Look for the middle number, if the total number of items is pair, take the 2 middle number and divide by two.
Middle numbers = 24 and 28
Median = (24 ´+ 28) / 2
Median = 52/2
Median = 26
Answer:
Step-by-step explanation:
First the numbers are arranged in ascending order from the least to the biggest number:
4 9 17 22 24 28 51 76 83 98
The numbers on the 5th and 6th position are in the middle
5th= 24
6th = 28
Since they are two numbers, we add them and divide by 2
= (24 + 28) / 2
= 52 / 2
= 26
9) Order the fractions from least to greatest. 2 4 , 4 5 , 7 10 , 2 3 A) 2 4 , 7 10 , 2 3 , 4 5 B) 7 10 , 2 4 , 2 3 , 4 5 C) 2 4 , 2 3 , 7 10 , 4 5 D) 2 4 , 7 10 , 4 5 , 2 3
Answer:
C) [tex]\frac{2}{4}, \frac{2}{3}, \frac{7}{10}, \frac{4}{5}[/tex]
Step-by-step explanation:
Given fractions:
[tex]\frac{2}{4}, \frac{4}{5}, \frac{7}{10},\frac{2}{3}[/tex]
To arrange the fractions from least to greatest.
Solution:
In order to arrange the fractions from least to greatest, we need to make the denominators common by taking LCD.
LCD of 4,5,10,3 can be found using their multiples.
4= 4,8,12,16,20,24,28,32,36,40,.........60
5= 5,10,15,20,25,30,.........60
10= 10,20,30,40,50,60
3= 3,6,9..........................60
So, 60 is the LCD.
Making the denominators common by multiplying same numbers to numerator and denominator.
[tex]\frac{2}{4}=\frac{2\times 15}{4\times 15}=\frac{30}{60}[/tex]
[tex]\frac{4}{5}=\frac{4\times12}{5\times 12}=\frac{48}{60}[/tex]
[tex]\frac{7}{10}=\frac{7\times 6}{10\times 6}=\frac{42}{60}[/tex]
[tex]\frac{2}{3}=\frac{2\times 20}{3\times 20}=\frac{40}{60}[/tex]
Comparing the numerators we can arrange the fractions.
[tex]\frac{2}{4}, \frac{2}{3}, \frac{7}{10}, \frac{4}{5}[/tex]
The length of a rectangle is 1 7/9 in., and its width is 3/4 of its length. Find the area of this rectangle.
Answer:
The answer to your question is Area = 1024/243 or 4 52/243
Step-by-step explanation:
Data
length = 1 7/9
width = 3/4 of its length
Area = ?
Formula
Area of a rectangle = length x width
Process
1.- Convert the mixed fraction to improper fraction
1 7/9 = (9 + 7) / 9 = 16/9
2.- Get the width
16/9 / 3/4 = (16 x 4) / (9 x 3)
= 64 / 27
3.- Get the area
Area = (16/9)(64/27)
= 1024/243
= 4 52/243
Answer:
2.37 square inches
Step-by-step explanation:
l = 16/9 = 1.78
b = 16/9 *3/4 = 1.33
Area = l * b
Area = 1.78 * 1.33
Area = 2.37 square inches
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠X.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠X = °
Answer:
45°
Step-by-step explanation:
From the figure;
Triangle WVX is a right-angled triangle
WV= 2
WX = 1
We are required to determine, m∠X
We need to determine the appropriate trigonometric ratio to use;
Therefore, since WV is the opposite and WX is the adjacent to m∠x, then the appropriate trigonometric ratio is tangent.
That is;
Tan m∠X = WV/WX
= 2/1
tan m∠X = 1
Thus,
angle m∠X = tan⁻¹ 1
= 45°
Thus, m∠X = 45°
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
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
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).
Learn more about Rate of transmission here:https://brainly.com/question/3311292
#SPJ11
A ship's mast is sighted just over the horizon at 4 nautical miles. How far is this in kilometers? There are 1.609 kilometers in a mile and there are 6,076 feet in a nautical mile.
Answer:
This is 7.408 kilometres far.
Step-by-step explanation:
Given:
A ship's mast is sighted just over the horizon at 4 nautical miles.
Now, to find the distance in kilometers.
As, given ship's mast is sighted just over the horizon at 4 nautical miles.
So, by using conversion factor we get the nautical mile into kilometers:
1 nautical mile = 1.852 kilometer.
Thus, 4 nautical miles
= [tex]4\times 1.852[/tex]
= [tex]7.408\ kilometers.[/tex]
Therefore, this is 7.408 kilometres far.
Answer:
7.4
Step-by-step explanation:
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.
Kairi spent $40.18 on CDs. Each CD cost the same amount. The sale tax was$2.33. Kairi also used a coupon for $1.00 off his purchase. How much did each CD cost?
Therefore the cost of each CD is =$2.30
Step-by-step explanation:
Given , Kairi spent $40 .18 no CDs. The sale tax was $2.33.Kairi also used a coupon for $1.00 0ff his purchase.
Total cost price of The CDs is = $(40+2.33-1.00)
=$41.33
Therefore the cost of each CD is =$(41.33÷18)
=$2.30
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]
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]
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:
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
If ABC ~ DEF and the scale factor from ABC to DEF is 1/5, what are the lengths of DE , EF and DF , respectively?
Answer:
option a (2,2,5)
Step-by-step explanation:
First we have to notice that it tells us that the scale is 1/5.
This means that the measures of the new triangle will be 5 times smaller than those of the other triangle.
Now we just have to take the measurements of the sides of the triangle and multiply them by 1/5 or divide them by 5
AB = 10 DE = 10/5 = 2
BC = 10 EF = 10/5 = 2
AC = 25 DF = 25/5 = 5
DE = 2
EF = 2
DF = 5
(2, 2, 5)
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]
Sheila has a plan to save $45 a month for 18 months so that she has $810 to remodel her bathroom. After 13 months Sheila has saved $510. If the most Sheila can possibly save is $70 per month, which of the following statements is truea. Sheila will meet her goal and does not need to adjust her plan. b. Sheila must save 50permonthtoachievehergoal.c.Sheilamustsave60 per month to achieve her goal. d. Sheila will not be able to achieve her goal.
Answer:
The answer is C.
Step-by-step explanation:
810 (goal) - 510 (amount saved so far) = 300 (Balance left to achieve goal) divided by 5( months remaining to achieve goal) = $60 a month
The statement is Sheila needs to save $60 per month to achieve her goal, the option is C.
We are given that;
Monthly saving= $45
Bathroom remodel amount= $810
Now,
To find the answer, we need to calculate how much more Sheila needs to save and how many months she has left.
We can subtract the amount she has saved from the amount she needs to save:
810 - 510 = 300
So, Sheila needs to save $300 more. We can also subtract the number of months she has saved from the number of months in her plan:
18 - 13 = 5
So, Sheila has 5 months left. To find the monthly amount she needs to save, we can divide the remaining amount by the remaining months:
300 / 5 = 60
Therefore, by algebra the answer will be $60 per month.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ6
Can someone help me with this Exponential Growth and Decay word problem? I have been able to get the rest of them done but this one stumps me...
Answer:
A) 61.68
Step-by-step explanation:
This is an exponential decay of 0.875. The way to know that is to get that is[tex]\frac{right}{left} \\[/tex] (Pick a random number and divide by the number to the left of it) From there, there is a 12 hour difference from 7 am to 7pm! Divide 306.25/0.875 and divide it by 0.875 by the answer of that each time 12 times. The exact answer is 61.68402914
Answer: option A is the correct answer.
Step-by-step explanation:
Looking at the table, the amount of medicine in her system is decreasing constantly with time. This constant amount by which this amount of medicine is decreasing is the decay constant.
Decay constant = 350/400 = 306.25/ 350 = 0.875
Let y represent the amount of medicine in her system after t hours.
Let a represent the initial amount of medicine in her system.
Let b represent the decay constant.
Let t represent the number of hours. Therefore, the function representing the exponential decay would be
y = 400b^t
When she wakes up at 7.00 am, the time from 5.00 pm would be 14 hours. Therefore
y = 400 × 0.875^14
y = 61.7 mg
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.
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.
Read related link on:
https://brainly.com/question/14108283
A rectangular swimming pool measures 30 meters by 50 meters. Tope swims back and forth the complete length of the pool parallel to the long side of the pool. She swims at a constant speed of 50 meters per minute. Meanwhile, her sister Tomi walks clockwise along the edges of the pool at a constant positive speed in such a way that they meet every time Tope reaches her starting point at the shorter side of the pool. What is Tomi's slowest possible walking speed, in meters per minute?
Answer:
Tomi's slowest possible walking speed is 80 meters per minute
Step-by-step explanation:
Tope swims at a speed of 50 meters per minute
Distance back and forth the long side of the pool is 50+50 meters = 100 meters
Time required to complete one round (back and forth) is 100 / 50 = 2 minutes
Perimeter of the pool is 50+50+30+30 = 160 meters
To walk around the perimeter and meet Tope at the starting point, Tomi has to walk 160 meters in 2 minutes
Tomi’s speed = 160 meters / 2 minutes or 160 / 2 = 80 meters per minute
Tomi's slowest possible speed should be 80 meters per minute
Beth gets on the elevator at the sixth floor. She rides up three floors to meet Doris. They ride down seven floors to meet Julio. How many floors have is Beth from where she started
Answer:
4
Step-by-step explanation:
Firstly, she gets on the elevator at the 6th floor. This means she was originally at the 6th floor.
She then stopped in the next three floors. This means she got off at floor 9 where we had Doris.
From Doris, she has to take 7 floors down to meet Julio. This means she went back to floor 2.
Now since her starting position was 6 and she is presently at the 2nd floor, this means she is four floors away from her starting position on the sixth floor.
(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.
Evaluate the given expression. 5 P 2
Answer:
20
Step-by-step explanation:
nPr = n!/(n-r)!
5P2 = 5!/(5-2)!
= 5!/3!
= 5×4×3!/3!
= 5×4
= 20
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.
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
A company collected data for the number of text messages sent and received using a text-message application since October 2011. The table shows the number of text messages sent and received in billions over time. The data can be modeled by a quadratic function. Which function best models the data?
A. n(t) = -0.002t^2 + 0.55t + 5.02
B. n(t) = 0.072t^2 - 0.15t + 2.73
C. n(t) = -0.002t^2 + 5.02
D. n(t) = 0.072t^2 + 2.73
Answer:
B. n(t) = 0.072t^2 - 0.15t + 2.73
Step-by-step explanation:
Plot data as pair of coordinates where t =x and n(t)=y
Use a graph tool to plot the coordinate points and join the points with a smooth curve
From the answers, test for the function that fits the points as plotted on the tool.
In this case, the function that fits the plot of the data is ;
n(t) = 0.072t^2 - 0.15t + 2.73
See attached;
The function that best used to model this situation is n(t) = 0.072t² - 0.299t + 2.57
Quadratic functionQuadratic function is in the form:
y = ax² + bx + cwhere a, b, c are constants.
Let n(t) represent the number of text at time t months.
It is given by:
n(t) = at² + bt + c
At point (5, 3):
3 = a(5)² + 5b + c25a + 5b + c = 3 (1)At point (20, 27):
27 = a(20)² + 20b + c400a + 20b + c = 27 (2)At point (40, 112):
112 = a(40)² + 40b + c1600a + 40b + c = 112 (3)a = 0.072, b = -0.29, c = 2.57
n(t) = 0.072t² - 0.299t + 2.57
The function that best used to model this situation is h(t) = -4.9t² + 295 + 2
Find out more on quadratic at: https://brainly.com/question/24216590
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.
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.
Read more linear equations at:
https://brainly.com/question/14323743
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]
Jenny uses a roller to paint a wall. The roller has a radius of 1.75 inches and a height of 10 inches. In two rolls, what is the area of the wall that she will paint. Use 3.14 for pi
In two rolls, 219.8 square inches of wall she will paint
Solution:
Given that,
Jenny uses a roller to paint a wall
The roller has a radius of 1.75 inches and a height of 10 inches
We have to find the area of the wall that she will paint in two rolls
Find the lateral surface area of cylinder
[tex]A_L = 2 \pi r h[/tex]
Where, "r" is the radius and "h" is the height
From given,
r = 1.75 inches
h = 10 inches
Substituting the values we get,
[tex]A_L = 2 \times 3.14 \times 1.75 \times 10\\\\A_L = 6.28 \times 1.75 \times 10\\\\A_L = 109.9[/tex]
Thus lateral surafce area is 109.9 square inches
For two rolls,
Area = 2 x 109.9 = 219.8
Thus in two rolls, 219.8 square inches of wall she will paint