Answer:
$2.27
Step-by-step explanation:
Huong's expense is the sum of the cost of the magazine and the cost of 7 candy bars. If c represents the cost of a candy bar, then Huong's expense was ...
$4.94 +7c = $20.83
7c = $15.89 . . . . . . . . subtract 4.94
c = $2.27 . . . . . . . . divide by 7
Each candy bar was $2.27.
The daily sleep duration among college students is normally distributed with a mean of 8.13 and standard deviation of 1.87. You want to use a sample size such that 95% of the averages fall within +/- 15 minutes (.25 of an hour) of the true mean of 8.13. Determine the smallest number of students you need to sample.
Using the z-distribution, as we have the standard deviation for the population, it is found that 215 students must be sampled.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The margin of error is of M = 0.25, with a population standard deviation of [tex]\sigma = 1.87[/tex], hence we solve for n to find the minimum sample size.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.25 = 1.96\frac{1.87}{\sqrt{n}}[/tex]
[tex]0.25\sqrt{n} = 1.96(1.87)[/tex]
[tex]\sqrt{n} = \frac{1.96(1.87)}{0.25}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96(1.87)}{0.25}\right)^2[/tex]
[tex]n = 214.9[/tex]
Rounding up, 215 students must be sampled.
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The average transaction at an automatic teller can be completed in six minutes and customers arrive at the average rate of one every ten minutes. On average, how many customers are there in the queue? a. 0.375 Customers b. 0.900 Customers c. 1.160 Customers d. 4.000 Customers
Answer:
Zero, based on the information provided.
Step-by-step explanation:
The output rate of the teller machine is (1 transaction/6 minutes). The input rate is (1 customer/10 minutes). This means that the machine completes a cycle faster than the customers arrive, on the average. I don't know how an average can be calculated without more information. If we assume customers arrive every 10 minutes, and no one screws up the machine, that there should be no waiting line. Is there more information about when the customers arrive? E.g., 50 arrive in the first hour the machine is open.
If the average transaction at an automatic teller can be completed in six minutes and customers arrive at the average rate of one every ten minutes. The average number of customers in the queue is: B. 0.900 customers.
What is the average number?M represent Markovian (memoryless) arrivals and service times
1 represents a single server.
Arrival rate (λ) is 1 customer every 10 minutes and the service rate (μ) is 1 customer every 6 minutes.
The formula to determine the average number of customers in the queue (Lq) is:
Lq = (λ^2) / (μ * (μ - λ))
Plugging in the values:
λ = 1/10
μ = 1/6
Lq = ((1/10)^2) / ((1/6) * ((1/6) - (1/10)))
Lq = (1/100) / ((1/6) * (10 - 6)/60))
Lq = (1/100) / ((1/6) * (4/60))
Lq = (1/100) / ((1/6) * (1/15))
Lq = (1/100) / (1/90)
Lq = (1/100) * (90/1)
Lq = 90/100
Lq = 0.9
Therefore, the correct option is B.
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Zoe planted a walnut tree. Every week, she measures the tree and records its
growth. On the first week, the tree was 27 1/2 inches tall. On the second week, it was
29 1/4 inches tall. On the third week, it was 31 1/3 inches tall. How much did the tree
grow from the first week until it was measured on the third week? Show your work.
The tree grew about 3.83 inches between the first and third week.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
On the first week, the tree was 27 1/2 inches (27.5) tall. On the second week, it was 29 1/4 inches (29.25) tall. On the third week, it was 31 1/3 inches (31.33) tall.
The length grown = 31.33 - 17.5 = 3.83 inches
The tree grew about 3.83 inches between the first and third week.
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Help picture below problem 4
Answer:
Step-by-step explanation:
Line segments: MN , NO , MO
Line segment has beginning and ending point
A culture started with 3000 becteria. after 8 hours it grew to 3300 becteria. Predict how many bacteria will be present after 12 hours. Round your answer to the nearest whole number. p=ae^kt
Answer: I think 5000
Step-by-step explanation:
I’m probably completely wrong lol sorry
A guest walks in and needs a room for the night. The rack rate for rooms is 15% higher than the average rate of $165 per night. What rate will the walk-in guest pay for the night?
The rate which the walk-in guest is how fast a guest needs a room
The rate which the walk-in guest pay for the night is $189.75
How to determine the rate?The given parameters are:
Average rate = $165 per night
The walk-in guest is 15% greater than the average rate.
So, the rate of the walk-in guest is:
Walk-in = 165 * (1 + 15%)
Evaluate the product
Walk-in = $189.75
Hence, the rate which the walk-in guest pay for the night is $189.75
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Help with this question pls
Answer:
Exact: [tex]4\sqrt{55}[/tex] m
Approximate: 29.7 m
Step-by-step explanation:
[tex]a^2+b^2=c^2[/tex]
[tex]9^2+b^2=(31\sqrt{5} )^2[/tex]
[tex]81+b^2=31^2(5)[/tex]
[tex]b^2=961-81[/tex]
[tex]b=\sqrt{880} =4\sqrt{55}[/tex]
[tex]4\sqrt{55}[/tex] ≈ 29.7 m
Hope this helps!
Solve for X and Y 1. y = 2x
6x + 3y = 12
2. y = -4x + 2
y = 6x - 8
3. y = x - 4
-4x - 6y = -16
4. x = 3y + 1
2x + 4y = 12
Answer:
Step-by-step explanation:
1. If y =2x
solve for y in (6x +3y) = 12
6x + 3(2x) = 12, 6x + 6x =12
12x = 12 , x= 1
to find y , from y =2x
y = 2(1) , ( x = 1 and y = 2)
2. y = -4x + 2
y = 6x -8
y = (-4x + 2)(6x-8)
= -4x ( 6x -8) + 2(6x-8)
-24[tex]x^{2}[/tex] + 32x + 2(6x-8)
-24x2 + 44x - 16
3. y = x -4
-4x -6y = -16
-4x - 6(x - 4) = -16
-4x - 6x - 24 = -16
-10x - 24 = -16
-10x = -16 + 24, -10x = -8
x = 0.8 , to get y , we input x value into eqn(y = x-4)
y = 0.8 -4, y = -3.2
x = 0.8, y = -3.2.
4. x = 3y + 1
2x + 4y =12
2(3y + 1) + 4y = 12
6y + 2 + 4y = 12
10y + 2 = 12
10y = 12 -2
10y = 10
y = 1, to get x
x = 3y + 1
x = 3(1) + 1 , x = 4
( x = 4 and y = 1).
PLEASE HELP
The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
Part A: What do the x-intercepts and maximum value of the graph represent?What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent?
Part C: Describe the constraints of the domain.
Answer:
See below ↓
Step-by-step explanation:
Part A
The x-intercepts represents when the profit of the company is 0 dollars. It means they are making no profit when selling the pens at that pricePart B
y-value when x = 3 ⇒ 120y -value when x = 5 ⇒ 60rate of change = Δy/Δx = -60/2 = -30This rate represents the depreciating profit of the company when increasing the price of a pen from $3 to $5Part C
Domain of the graph is only true for positive values of yDomain ⇒ 0 ≤ x ≤ 6Answer:
Part A
The x-intercepts are when f(x) = 0.
Since x represents the price of pens, and f(x) represents the company's profit, the x-intercepts give the price of the pens when the profit is zero.
⇒ the profit is zero when the price of pens are $0 and $6
The maximum value of the graph (vertex) represents the cost of pens when the profit is at its highest. Therefore, the optimal amount to price the pens to get the maximum profit.
⇒ maximum profit of $120 occurs when the pens are priced at $3
Part B
[tex]\sf average \ rate \ of \ change=\dfrac{change \ in \ y}{change \ in \ x}[/tex]
From inspection of the graph, f(3) = 120 and f(5) ≈ 60
[tex]\sf \implies average \ rate \ of \ change=\dfrac{60-120}{5-3}=-30[/tex]
This means that as the price of the pens increases by $1 (between $3 and $5), the average profit decreases by approximately $30.
Part C
The domain is the set of input values (x-values). As the price of a pen cannot be less than zero, the domain will be x ≥ 0
Unless the company is happy to make a loss, the restricted domain should be 0 ≤ x ≤ 6
Given the points (-10, -3) and (4,8) find the slope.
Answer: [tex]\frac{11}{14}[/tex]
Step-by-step explanation:
1) Identify Format
(x1,y1) = (−10,−3)
(x2,y2) = (4,8)
2) Use the Slope Formula
m=y2−y1x2−x1
=8−−3/4−−10
=11/14
=11/14
Bonus: Graph
Answer provided by Education Point
Jessica sells 50.5 ounces of lemonade for a total of 20.20.
Find the unit price in dollars per ounce.
If necessary, round your answer to the nearest cent.
Answer:
2.5
Step-by-step explanation:
Answer: 2.5
Step-by-step explanation: do it yourself jk lol first you add then divide by 6.5
Which function is best represented by this graph? Brainliest
Answer:B
Step-by-step explanation:the slope is 1/4, and it crosses the y axis at -2.
- Kristen bought a container of spice for
her chili recipe. If a batch of the recipe
calls for 1 of the container of spice,
how many batches of chili can Kristen
make from that container?
Help!!!!!
Answer:
1 container per batch so 1 batch is 1 comtsiner
what number is between 1.3 and 1.45
Step-by-step explanation:
1.3+1.45/2
= 1.75/2
=0.875
Pls help im in a hurry
So im in 7th grade and im doing a practice test and you know my brain doesn't work so i need answers.
I have 10 mins to take it
Pls help
Answer:
x = -3.5
y = 1.5
so W = (-3.5, 1.5)
Step-by-step explanation:
Please answer this relatively quickly, I'm not in very much of a rush but would like to get this done.
Answer:
x=23
Step-by-step explanation:
2x-6/4 = 10
2x-6 = 10(4)
2x-6 = 40
2x = 40+6
2x = 46
x = 46/2
x = 23
Chris completes a word search in 3 minutes. Oliver takes
20 seconds longer. How long did Oliver take?
seconds
Answer: 200 seconds
Okay - so then Oliver would take 3 minutes and 20 seconds. There are 60 seconds in a minute so it would be 30 times 60 = 180 + 20 = 200
Help me please anybody. And I am in my school iPad
Answer:
(0,5)
Step-by-step explanation:
I'm really not sure but I'm pretty positive that this is the answer if not than my bad
MARK AS BRAINLIEST PLS HELP
Below is the table of values of a function. Write the output when the input is n.
input
1
2
8
n
output
5
6
12
?
The outputs are addition of 4 to their inputs therefore,if the input is n then the output will also be an addition of 4 hence n+4
a railroad crossing sign has a diameter of 30 inches. what is the area of the sign?
Answer:
706.5m^2
Step-by-step explanation:
The sign is a circle
Area of a circle is (pi)r^2
d = 30 in -> r = d/2 = 30/2 = 15
Area = 3.14 x (15)^2 = 706.5m^2
Answer:
about 706.5 or 706.86
Step-by-step explanation:
to find this answer we need to use the area formula of a circle which is A = πr ^2
we know the diameter is 30, and the radius is half the of diameter, so we take 30 and divide it by 2, which should give us 15 for the radius. ( 30/2 = 15, so r = 15)
depending on how your teacher wants u to answer this you can use π on a calculator or use 3.14
now just plug in your numbers to formula
A = 3.14 * 15^2 or A = π * 15^2
and should equal about 706.5 or 706.86 (depending on if you use 3.14 or π)
Elise is in a challenge with her gym class to run a total of 200 miles in one
school year. In the first month she ran 18 miles. If she wants to split the
remaining amount of miles over the
next seven months, how many miles will
she run each month?
Show your work.
3x²+5xy=–4
xy–2x=—3
[tex]solve simultinously[/tex]
[tex]xy - 2x = - 3[/tex]
[tex]xy = 2x - 3[/tex]
____________________________________________
[tex]3 {x}^{2} + 5xy + 4 = 0[/tex]
[tex]3 {x}^{2} + 5(2x - 3) + 4 = 0[/tex]
[tex]3 {x}^{2} + 10x - 15 + 4 = 0[/tex]
[tex]3 {x}^{2} + 10x - 11 = 0[/tex]
[tex]delta = {10}^{2} - 4(3)( - 11)[/tex]
[tex]delta = 100 + 132[/tex]
[tex]delta = 232[/tex]
Thus;
[tex]x = \frac{ - 10 + \sqrt{232} }{6} \: \: or \: \: x \frac{ - 10 - \sqrt{232} }{6} \\ [/tex]
[tex]x = \frac{ - 10 + 15.23}{6} \: \: or \: \: x = \frac{ - 10 - 15.23}{6} \\ [/tex]
[tex]x = \frac{5.23}{6} \: \: or \: \: x = \frac{ - 25.23}{6} \\ [/tex]
[tex]x = 0.8716 \: \: or \: \: x = - 4.205[/tex]
____________________________________________
If x = 0.8716 then :[tex]0.8716 \: y = 2(0.8716) - 3[/tex]
[tex]0.8716 \: y = 1.7432 - 3[/tex]
[tex]0.8716 y= - 1.2568[/tex]
[tex]y = \frac{ - 1.2568}{0.8716} \\ [/tex]
[tex]y = - 1.4419[/tex]
And if x = - 4.205 then :[tex] - 4.205 \: y = 2( - 4.205) - 3[/tex]
[tex] - 4.205 \: y = - 8.410 - 3[/tex]
[tex] - 4.205 \: y = - 11.410[/tex]
[tex]y = \frac{ - 11.410}{ - 4.205} \\ [/tex]
[tex]y = 2.7134[/tex]
And we're done
Have a great day ♡
a) the cost of. kg oranges is rs 350 how many kg of oranges can be bought for rs 665
b.). A car travel for 50 km.with the help of 5 litres of petrol how many litres of petrol is reauired to travel 120 km
A: 1.9 Kilograms of oranges for rs 665.
B: 12 liters of petrol will make a car travel 120 km.
(3/5)^2 + 4 x 3 - 2
Please help :)
Answer:
[tex]10 \frac{9}{25} [/tex]
Step-by-step explanation:
[tex] \bigg( \frac{3}{5} \bigg)^{2} + 4 \times 3 - 2 \\ \\ = \frac{9}{25} + 12 - 2 \\ \\ = \frac{9}{25} + 10 \\ \\ = \frac{9 + 10 \times 25}{25} \\ \\ = \frac{9 + 250}{25} \\ \\ = \frac{259}{25} \\ \\ = 10 \frac{9}{25} [/tex]
Find LCD in number 16 and multiply all numerators by it to clear the fractions
The LCD of the given terms of expression will be x² - 4 since others can divide it.
How to find the LCDThe least common denominator is the smallest number or expression of all the common multiples of the denominators when 2 or more fractions or expressions are given.
Given the terms of the expressions
(x+2)(x-2) and (x^2 - 4)
Expand (x^2 - 4) using the difference of two square:
x² - 4 = x² - 2²
x² - 4 = (x+2)(x-2)
Based on the expansion, we can conclude that the LCD of the given terms of expression will be x² - 4
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There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?
Answer:
85 dogs have signed up to compete
Step-by-step explanation:
its 85 small dogs because 49+36=85
Help picture below problem 13
Answer:
the measure of 3 is 80 because its l is parlell to r so 80 will be vertical with 3
Step-by-step explanation:
How much of a radioactive kind of promethium will be left after 20 days if you start with
9,056 grams and the half-life is 5 days?
in 20 days 4 half life will be completed
so n = 4
formula :-
[tex] \frac{ A\degree}{ {2}^{n} } = \frac{9056}{ {2}^{4} } = \frac{9056}{16} = 566grams[/tex]
The radioactive kind of promethium will have 566 grams left after 20 days.
What is half-life?Half-life is the time required for a quantity to reduce to half of its initial value.
Given, A radioactive kind of promethium with 9,056 grams and a half-life is 5 days.
∴ In the next 5 days, it'll have (9056/2) = 4528 grams.
Next 5 days it'll have (4528/2) = 2269 grams.
As it has a half-life in 5 days and 20 is multiple (4×5).
After 20 days the radioactive material will have (9056/2⁴) grams.
= 566 grams left.
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If you could help me out I would appirecate it. The question is 4 (3x + x)
12x. And when ever you see the x you put 6
no. correct answer: 16(x)
using BODMAS rule:
4(3x+x)4(4x)16xAnswer:
no they are not, explanation down.
Step-by-step explanation:
4(3x + x)
4(3×6 + 6)
4(18 + 6)
4(24)
96
12x
12×6
72
hope dis helps!!!!!
solve the equation: 4 x 2 + 8 = - 7
X=
Answer:
Hope the picture will help
[tex]\frac{16}{7}[/tex]Answer:
X = -16/7
Step-by-step explanation:
Multiply the numbers
4 x 2 + 8 = -7x
8 + 8 = -7x
Add the numbers
8 + 8 = -7x
16= -7x
Divide both sides by the same factor
16= -7x
16 divided bu -7x and -7x divided by -7x
Simplify
-16 divided by 7 not negative 7 and -7 divided by -7
Cancel terms that are in both the numerator and denominator
cancel out -7 divided by -7 and you get -16/7 left
so, therefore x= -16/7