Hillary works at a video store. she earns $8.50 per hour plus 12% commission on all the weekly sales she makes. If she works 24 hours in a week, which expression best describes her sales (x) if she earns at least $324 during that week
Answer: See explanation
Step-by-step explanation:
Let her sales be represented by x.
Based on the information given in the question, the equation to calculate her sales goes thus:
(8.50 × 24) + (12% × x) ≥ 324
204 + (0.12 × x) ≥ 324
204 + 0.12x ≥ 324
0.12x ≥ 324 - 204
0.12x ≥ 120
x ≥ 120/0.12
x ≥ 1000
Her sales is at least $1000
A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 42 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter xi* as xi.)
Answer:
the work done in pulling the bucket to the top of the well is 2125 ft-lb
Step-by-step explanation:
Given that;
Weight of the bucket is 3 lb
weight of water which can be filled in the bucket is 42 lb
Total weight of bucket and water = 3 + 42 = 45 lb
distance, the bucket filled with water is to be pulled 50 ft
now, let at any time t be the bucket at distance x ft from the bottom of the well
then, t = x/2 × S
where S is the rate at which water is leaking from the bucket
so at this time t, the amount pf water which leaked from the bucket is;
⇒ x ft / 2.5 ft/s × 0.25 lb/s
= 0.25 lb.s⁻¹ / 2.5 ft.s⁻¹ × x ft
= 0.1 lb/ft × x ft
= 0.1x lb
now, as x represent the distance that the bucket has been raised, we the force F applied to the bucket x to be;
F = ( 45 - 0.1x ) lb
so, the required worked by Riemann sum as;
[tex]\lim_{n \to \infty}[/tex]ⁿ∑_[tex]_{i=1}[/tex] ( 45 - 0.1x[tex]_i[/tex]* ) Δx
so, the work done, pulling the bucket up will be;
[tex]\lim_{n \to \infty}[/tex]ⁿ∑_[tex]_{i=1}[/tex] ( 45 - 0.1x[tex]_i[/tex]* ) Δx = [tex]\int\limits^{50}_0 {(45-0.1x)} \, dx[/tex]
= [ 45x - 0.1[tex]\frac{x^2}2}[/tex] ]⁵⁰₀
= 45 × 50 - 0.1/2 × (50)²
= 2250 - 125
= 2125 ft-lb
Therefore, the work done in pulling the bucket to the top of the well is 2125 ft-lb
Alexis is working for a GPS company. The GPS software has recently been updated with a new algorithm and Alexis needs to
check to see if it is calculating properly. Alexis places Charlotte area on a grid and finds Charlotte to be at (6,7) and Gastonia
is at (-1,4). What is the distance between them, if each unit is two miles?
Answer:
2root(58) == 15.23 miles
Step-by-step explanation:
Find distance between two points --> root( (x2 - x1)^2 + (y2 - y1)^2 ) = root (3^2 + 7^2) = root ( 58), as one unit is two miles then 2* root(58) = 15.23 miles.
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The total service time of a multistep manufacturing operation has a gamma distribution with mean 18 minutes and standard deviation 6 minutes.
(a) Determine the parameters alpha and lambda of the distribution. (solving these two parameters using the mean and the standard deviation)
(b) Assume that each step has the same exponential distribution for service time. What distribution for each step and how many steps produce this gamma distribution of total service time?
Answer:
The answer is "[tex]\bold{r=9, \lambda=\frac{1}{2}\ and \ \ \text{exponential, 9 steps}}[/tex]"
Step-by-step explanation:
In point a:
We are aware of the random gamma variable X:
[tex]\to \mathbb{E} =\frac{r}{\lambda}\\\\\to Std(X) =\frac{\sqrt{r}}{\lambda}\\\\[/tex]
It is given:
[tex]\to \mathbb{E} = 18 \\\\\to std(X)=6[/tex]
[tex]\to 18=\frac{r}{\lambda}\\\\ \to 6=\frac{\sqrt{r}}{\lambda}\\\\[/tex]
Substituting the value:
[tex]\to \frac{\sqrt{r}}{6}=\frac{r}{18}\\\\\to r=9\\\\\to \lambda=\frac{1}{2}\\\\[/tex]
In point b:
When building the Erlang/Gammas distribution, these could reasonably be assumed to become an exponential distribution only with \lambda = 1/2 parameter with one step but to be r = 9 for one step.
A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager decides to mix 10 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?
There should be __ pounds of cashews in the mixture.
(Type an integer or a decimal.)
Answer:
7.5 pounds
Step-by-step explanation:
The computation is shown below:
let us assume x be the pounds of cashews,
and the total pounds will be x + 10
Now the equation is
10($1.5) + x(5.00) = (10 + x)(3.00)
15 + 5x = 30 + 3x
2x = 15
x = 7.5 pounds
need help with this right now
Answer:
i believe number 4 is the answer
10 PONITS
Can someone help me
Answer:
1st step
Step-by-step explanation:
7/10 is greater than 1/2
Answer:
Step 1
Step-by-step explanation:
please. help me
thank you
Answer:
-30,10
Step-by-step explanation:
How to get 60 to -30 : 60 divided by -30 is -2
How to get -20 to 10: -20 divided by 10 is -2
find each measurement indicated. Round your answers to the nearest tenth. Please show work. Part 1
9514 1404 393
Answer:
33.0 m26.1 mi28.0 mi33.0 miStep-by-step explanation:
In each of these Law of Sines problems, you are given side a and angles B and C and asked for side c (problems 1, 3, 4) or side b (problem 2). The solution is basically the same for each:
Find the missing angle. Find the side from ...
c = a·sin(C)/sin(A)
__
1. angle A = 180°-89°-58° = 33°
c = (18 m)sin(89°)/sin(33°) ≈ 33.0 m
__
2. angle C = 180°-13°-17° = 150°
b = (58 mi)sin(13°)/sin(150°) ≈ 26.1 mi
__
3. angle A = 180°-61°-89° = 30°
c = (16 mi)sin(61°)/sin(30°) = 28.0 mi
__
4. angle A = 180°-39°-127° = 14°
c = (10 mi)sin(127°)/sin(14°) ≈ 33.0 mi
Question 2 of 10
What is the slope-intercept equation of the line below?
O A. y = -2x-3
O B. y = -2x + 3
O C. y = 2x-3
O D. y = 2x + 3
Answer:
y=2x-3
Step-by-step explanation:
First we find the y-intercept of this graph whic in this case is -3. Then we plot two pints on the graph and caculate the rise over run which is 2/1=2. Finally, we get the equation- y=2x-3.
If 26 feet 10 inches is cut from a wire that is 44 feet 8 inches long what is the length of wire that is left ?
Answer:
17 feet 10 inches
Step-by-step explanation:
26 feet 10 inches is cut from a wire that is 44 feet 8 inches
Therefore the length of wire that is left can be calculated as follows
44 feet 8 inches - 26 feet 10 inches
= 17 feet 10 inches
1 pipe can drain a swimming pool in 4 hours. A second pipe can drain the pool in 6 hours. How long will it take to drain the pool if both pipes are used?
3 hours
2 2/5 hours
10 hours
2 hours
Answer:
[tex]2 \dfrac25[/tex]
Step-by-step explanation:
The first pipe drains 1/4 of the pool every hour, and the second pipe drains 1/6 of the pool every hour. Combined, they drain [tex]\dfrac14 + \dfrac16 = \dfrac{5}{12}[/tex] of the pool per hour. Therefore, it will take 12/5 hours, or 2 2/5 hours.
(brainliest pls ty)
Both pipe are together then they take 6 hour to fill the pool.
In 1 hour they fill the pool is 110 hours
What is the explanation?In 1 hour pipe A can fill the pool = x/1
In 1 hour pipe B can fill the pool= y/1
so
4 hours=x/4
6 hours=y/6
If both pipe are together then they take 6 hour to fill the pool.
If the are together then in 1 hour they fill the pool.
x/1 + y/1 = 6/1+4/1= −−−−(1)
=10 hours
Example:A swimming pool may be filled using two pipes in 12 hours. Only half of the pool can be filled if the larger pipe is utilized for 4 hours and the smaller pipe for 9 hours.
10,000 divided by 240 minutes, or 4 hours, yields approximately 41.6. With the drain blocked, your pool would therefore fill at a rate of about 41 gallons per minute.
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Slope Intercept Form
y=mx+b
How can I explore it? It's for a presentation, please help
Answer:
I don't understand the question.
Step-by-step explanation:
I don't know how to explore the slope intercept line equation.
However, 'b' is the y axis intercept (the point where is crosses the y axis and 'm' is the slope of the line. The 'm' and the 'b' can be positive or negative numbers.
A positive 'm' is a line that goes 'up' (the y value increases from the left to right) and a negative 'm' is a line that goes 'down' (the y value decreases from left to right).
Answer:
vjfkkfjjkuuoooo99999
24, 3, 29, 24, 8, 38, 62
Find the range of the data set
Answer:
Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 62−3=59 62 - 3 = 59 .
Step-by-step explanation:
Answer:
The answer is 59
Step-by-step explanation:
See the photo to answer, worth 25 pts
Answer:
ITS C plz mark me brainliest
Step-by-step explanation:
patrick walks at 6/8 kilometer per 8 hour. how far will he in 5 hours?
Answer:
In 5 hours, he will go 3 ¾ kilometers far.
Step-by-step explanation:
When data is collected, the most common calculations computed are the Measures of Central Tendency, mean, median and mode. It is important to know how to compute these values and it is also extremely important to know what these values mean in context of the data set. Use the internet to find a data set. Key terms to search: Free Public Data Sets and Medical Data Sets. Introduce your Data Set and Cite the Source. Why was this data interesting to you? Calculate measures of central tendency (Mean, Median & Mode) and measures of variation (Range and Standard Deviation) for your data. Write a sentence for each calculation explaining what that value means in context of your data.
Answer:
Following are the responses to these questions:
Step-by-step explanation:
In point a:
Please find the graph file in the attachment.
In point b:
This information is interesting for us, because we inform us about an important disease outbreak in such days and how the pandemic impacts major global communities like London as well as how the pattern in the recorded cases is increasing and decreasing.
In point c:
The data are sorted: 551, 1683, 3194, 4053, 4079, 5842, 5868
Mean[tex]= \frac{(551+1683+....+586)}{7} =3610[/tex]
Median proves middle value or class so if ascending data is arranged = 4th term = 4053
A mode is of max [tex]= 3_{median} -2_{mean} = 4939[/tex]
Range It is also the difference between max and min values which indicates the overall distribution range [tex]= 5868 -551=5317[/tex]
The standard deviation[tex]= 1841.60[/tex]
Find the radius or diameter of the circle with the given dimentions.
r = 21 ft
Answer Choices:
a. 50 ft
b. 42 ft
c. 131.9 ft
d. 10.5 ft
Answer:
b. 42
Step-by-step explanation:
Your trying to find the diameter since radius is r
diameter is always double of radius
A manufacturer of a new nicotine nasal spray claims that their product has a 30% success rate for smoking cessation. In a clinical study involving 150 smokers, 93 of them quit smoking. Test the hypothesis that the success rate claimed by the manufacturer is valid at the 5% level of significance.
answer:
we reject null and conclude that this manufacturers claim is false
Step-by-step explanation:
p = 30% = 0.30
p^ = 93/150 = 0.62
we state the hypothesis
H0: p = 0.30
h1: p not equal to 0.30
we find the z test stattistics
[tex]z=\frac{p^--p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
[tex]z=\frac{0.62-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }[/tex]
[tex]z=\frac{0.32}{\sqrt{\frac{0.30*0.70}{150} } }[/tex]
[tex]z=\frac{0.32}{0.03741}[/tex]
z = 8.5538
at alpha = 0.05
z-critical = Z₀.₀₅/₂ = Z₀.₀₂₅
= 1.96
we compare z critical with the test statistic
z statistic > z critical so we have to reject H₀ and conclude that the manufacturers claim is not valid at 0.05 level of significance.
HELP ME PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEE WILL GIVE BRAINLIST
Answer:
[tex]24m^{3}[/tex]
Step-by-step explanation:
V = [tex]a^{2} \frac{h}{3}[/tex]
a = 3
h = 8
If we put this on out formula, it would look:
V = [tex]3^{2} \frac{8}{3}[/tex]
V = 9[tex]\frac{8}{3}[/tex]
[tex]\frac{8}{3}[/tex] = 2.67
V = 9 x 2.67
V = 24.03
Round to the nearest whole number:
24.03 = 24
Answer:
A) 24 m 3
Step-by-step explanation:
Fill in the blank so that the ordered pair is a solution of y = 6x +7: 4,25)
a) 13
b) 1
c) 18
d) 3
Answer:
it is either A OR B
Step-by-step explanation:
Please Help Me!!! (15 points)
Answer:
Step-by-step explanation:
y = 5x + 1
Table for input-output values is,
x 0 1 2 3
y 1 6 11 16
Now we can plot these points to get the graph.
y = x + 2
Table for the Input-output values,
x 0 1 2 3
y 2 3 4 5
We can get the graph as attached.
the river falls vertically compared to how far it flows horizontally. Find the
slope of the river shown to the right. (Hint: The slope of a river is positive.)
46 ft
252 ft
Answer:
23 / 126
Step-by-step explanation:
46/252 = 23/126
How many license plate numbers consisting of three letters followed by
two numbers are possible when repetition is not allowed?
mr sigmon has 24 students in his classroom 1/4 of them are girls
Answer:
6 of his class are girls
Step-by-step explanation:
24/4=6
Four friends share of a gallon of lemonade equally. What fraction of the gallon of lemonade does each friend get?
Answer:
if theres four friends and they share the whole gallon equally then each friend would get a quart of lemonade
Step-by-step explanation:
Answer:1/4 of the lemonade
Step-by-step explanation: Each person gets 1/4 of the lemonade
Please send help. I really need this asap
Answer:
Part a) The area of the figure is [tex]\frac{9}{2} (4+\pi ) cm^{2}[/tex]
Part b) The perimeter of the figure is [tex]3(2+2\sqrt{2} +\pi )cm[/tex]
Use the Distributive Property to correctly rewrite or simplify the expression:
21k+13k+9k
Answer:
21k+9k+13, and simplified into 43k.
Step-by-step explanation:
The distributive property means that you can put addends or factors in any order to get the same result(9+1=10, 1+9=10)
21k+13k+9k can be re-written into 21k+9k+13, and simplified into 43k.
Answer:
43k
Step-by-step explanation:
In ΔMNO, the measure of ∠O=90°, the measure of ∠N=38°, and OM = 87 feet. Find the length of NO to the nearest tenth of a foot.
Answer:
111.4
Step-by-step explanation:
trust
Which is equivalent to the complex number i^32?
Answer:
where i^2 = -1 (minus one)
So, i^2 = -1
i^4 = (i^2)^2 = (-1)^2 = -1 X-1 = 1
like ;
i^32 = (i^2)^16 = (-1)^16 = -1 X -1 X-1 X -1 X-1 X -1 X-1 X -1 X-1 X -1 X-1 X -1 X-1 X -1 X-1 X -1 X
= 1
Step-by-step explanation:
The equivalent to the complex number i³² is 1.
What is a complex number?A complex number is a component of a number system that includes the imaginary unit, represented by the letter i as an extension of the real numbers.
Given:
i³²
As we know that i² = -1
The i³² can be written as,
(i²)¹⁶
Put the value of i² = -1
(-1)¹⁶
As the power is an even number, so the result will be a positive number,
i³² = (-1)¹⁶ = 1
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