Answer:
The least amount is $75.50
Step-by-step explanation:
Given
[tex]p \to profit[/tex]
[tex]x \to amount[/tex]
[tex]p = -0.5x^2 + 36x - 231[/tex]
Required
The smallest amount to make at least 363
We have:
[tex]p = -0.5x^2 + 36x - 231[/tex]
Rewrite as:
[tex]-0.5x^2 + 36x - 231=p[/tex]
Substitute 363 for p
[tex]-0.5x^2 + 36x - 231 = 363[/tex]
Collect like terms
[tex]-0.5x^2 + 36x - 231 + 363 = 0[/tex]
[tex]-0.5x^2 + 36x + 132 = 0[/tex]
Using quadratic formula, we have:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
[tex]a = -0.5; b= 36; c = 132[/tex]
So, we have:
[tex]x = \frac{-36 \± \sqrt{36^2 - 4*-0.5*132}}{2*-0.5}[/tex]
[tex]x = \frac{-36 \± \sqrt{1560}}{-1}[/tex]
[tex]x = \frac{-36 \± 39.50}{-1}[/tex]
Split
[tex]x = \frac{-36 + 39.50}{-1}; x = \frac{-36 - 39.50}{-1}[/tex]
[tex]x = \frac{3.50}{-1}; x = \frac{-75.50}{-1}[/tex]
[tex]x = 75.50[/tex] and [tex]x = -3.50[/tex]
The amount can't be negative.
So:
[tex]x = 75.50[/tex]
Hence, the least amount is $75.50
A manufacturing facility is responsible for producing two components that are produced at states 1 (poor), 2 (below average), 3 (average), 4 (good), and 5 (excellent). For the final product (con- sisting of both components) to be acceptable the sum of the two states needs to be at least equal to 6. At the moment, the manufacturing processes are random, and hence each component is equally likely to be at any of the 5 states. Answer the following questions.
Required:
a. What is the probability that a final product is acceptable? What is the probability that a final product is unacceptable?
b. What is the probability that a final product is acceptable given that the first component is produced at a state of 2?
c. What is the probability that the second component was produced at a state of 3 given that the final product is acceptable?
Answer:
a) i) P( final product is acceptable ) = 3/5
ii) P ( final product not acceptable ) = 2/5
B) P ( final product is acceptable | X =2 ) = 2/5
C) P ( Y = 3 | Final product is acceptable ) = 2/5
Step-by-step explanation:
Given data :
5 states : 1 (poor), 2 (below average), 3 (average), 4 (good), and 5 (excellent)
Number of components produced = 2
X ( component 1 ) ∴ P(X) = 1/5
Y ( component 2 ) ∴ P(Y) = 1/5
Aim : Sum of Final product needs to be ≥ 6
A) Probability of a final product been acceptable and also unacceptable
P( final product is acceptable ) ; P(X + Y ≥ 6 )
= 1/5 ∑ P( Y ≥ 6 - x )
= 1/5 ( P( Y ≥ 5 ) + P( Y ≥ 4 ) + P( Y ≥ 3 ) + P( Y ≥ 2 ) + P( Y ≥ 1 )
= 1/5 ( 1/5 + 2/5 + 3/5 +4/5 + 1 )
= 3/5
P ( final product not acceptable ) = 1 - 3/5 = 2/5
B) P ( final product is acceptable | X =2 )
∴ P ( Y ≥ 4 )
= 2/5
C) P ( Y = 3 | Final product is acceptable )
∴ P ( X ≥ 3 ) ≠ P( Y ≥ 3 ) ( because they are not independent )
= 1 - 3/5 = 2/5.
The pie chart above shows the percentage of land in Rhode Island split up among the different counties. If Rhode Island has a total of 1,045 square miles of land, how many
square miles does Kent County have?
[tex] \huge{ \mathcal{ \underline{ Answer} \: \: ✓ }}[/tex]
Total land area of Rhode Island is :
[tex] \longmapsto\mathrm{1045 \: \: mi {}^{2} }[/tex]
And from the above pie chart, we can conclude that Kent County comprises 16% of total land area of Rhode Island, that is :
[tex]\longrightarrow \dfrac{16}{100} \times 1045[/tex]
[tex]\longrightarrow \dfrac{16720}{100} [/tex]
[tex]\longrightarrow167.2 \: \: mi {}^{2} [/tex]
Therefore, Total land area of Kent County :
[tex] \boxed{ \large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 167.2 \: \: \: mi {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
A market research team thinks that their new ad campaign is better than their old one. They used to be able to sell to 50% of those who saw their ads. To test their thought, they will run a hypothesis test. They take a random sample of 100 potential buyers and find that they convinced 60 of these people to buy their product. The test will be run at a 1% significance level.
a. The test statistic is 2 and we conclude that the new ad campaign is not signficantly better.
b. The test statistic is 2 and we conclude that the new ad campaign is signficantly better.
c. The test stat is 2.236 and we conclude that the new ad campaign is not significantly better.
d. The test stat is 2.236 and we conclude that the new ad campaign is significantly better.
e. The test stat is 2.5 and we are left with a test that is inconclusive.
Answer:
a. The test statistic is 2 and we conclude that the new ad campaign is not signficantly better.
Step-by-step explanation:
They used to be able to sell to 50% of those who saw their ads. Test if the new campaign is better.
At the null hypothesis, we test is it is the same, that is, the proportion is the same.
[tex]H_0: p = 0.5[/tex]
At the alternate hypothesis, we test if it is significantly better, that is, the proportion is above 50%.
[tex]H_1: p > 0.5[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.5 is tested at the null hypothesis:
This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5[/tex]
They take a random sample of 100 potential buyers and find that they convinced 60 of these people to buy their product.
This means that [tex]n = 100, X = \frac{60}{100} = 0.6[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.6 - 0.5}{\frac{0.5}{\sqrt{100}}}[/tex]
[tex]z = 2[/tex]
The test statistic is 2.
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.6, which is 1 subtracted the by p-value of z = 2.
Looking at the z-table, z = 2 has a p-value of 0.9772.
1 - 0.9772 = 0.0228.
The p-value of the test is 0.0228 > 0.01, which means that we cannot conclude that the new ad campaign is signficantly better, so the correct answer is given by option A.
The probability that a plant produces two or more seeds is 0.20. A sample of five plants is observed. What is the probability that at least three plants produce two or more seeds?
The probability that at least three plants produce two or more seeds is 0.793915.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
The probability that out of n trials, there be x successes is given by
Use binomial distribution, with p =0.20, n=5, x=3
[tex]P(X=x)=C(n,x)p^x (1-p)^{n-x}[/tex]
P(X> = 3)
[tex]=1-(P(X=0)+P(X=1)+P(X= 5 ))\\=1-(C(20,0)0.2^0 (0.8)^{20-0}+C(20,1)0.2^1 (0.8)^{20-1}+C(20,2)0.2^2 (0.8)^{20-2})[/tex]
=1-(0.0115292+0.057646+0.136909)
=1-0.206085
=0.793915
Hence, the probability that at least three plants produce two or more seeds is 0.793915.
Learn more about binomial distribution here:
brainly.com/question/13609688
#SPJ12
hiii please help
a- each person who takes a drink from the cooler drinks approximately ately 24 oz of water
b- the water cooler started off with 648 oz of drink in it
c- there are 24 people who take a drink from the cooler
d- each of the 24 who take a drinks from the cooler drinks 1oz
1. When three boys jumped on a weighing scale together, it read 200 kilograms One boy stepped off and it showed 142 kilograms One more jupmed off and it showed 72 kilograms What was each boys weight? (explain pls)
Answer:
58kg, 70kg and 72kg
Step-by-step explanation:
Starting weight was 200.
Boy 1- Changed from 200 to 142. 200kg - 142kg= 58 kg
Boy 2- Changed from 142 to 72. 142kg- 72kg = 70kg
Boy 3- Last one on the scale and it showed 72kg so his weight is 72kg
Answer:
58, 70, 72
Step-by-step explanation:
200-142=58
142-72=70
23
A university administered a survey to all incoming students regarding living arrangements for the upcoming school year. The results of the survey are displayed in the following two-way relative frequency table.
University Living Arrangements
On-Campus Off-Campus Total
Freshmen 0.44 0.28 0.72
Transfer Students 0.21 0.07 0.28
Total 0.65 0.35 1
What percentage of incoming freshmen plan to live on-campus?
A.
61.11%
B.
67.69%
C.
56%
D.
44%
The probability of incoming freshmen who plan to live on-campus in percentage will be 61.11%. Then the correct option is A.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
A university administered a survey to all incoming students regarding living arrangements for the upcoming school year.
The results of the survey are displayed in the following two-way relative frequency table.
On-Campus Off-Campus Total
Freshmen 0.44 0.28 0.72
Transfer Students 0.21 0.07 0.28
Total 0.65 0.35 1
Then the probability of incoming freshmen who plan to live on-campus in percentage will be
P = (0.44 / 0.72) x 100
P = 0.6111 x 100
P = 61.11%
The probability of incoming freshmen who plan to live on-campus in percentage will be 61.11%.
Then the correct option is A.
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ5
What is the slope of a line that runs through (-2,4) and (3,7)
Answer: m=0.6
Step-by-step explanation:
Use the m= y2-y1/x2-x1 formula to calculate slope.
7-4=3
Divided by
3-(-2)=5
3/5= 3/5 or 0.6
Answer:
slope = 3/5
Step-by-step explanation:
slope = rise/run
---------------------------
y rises from 4 to 7 = 3
x runs from -2 to 3 = 5
slope = 3/5
What the correct answer
Its ‘B’
100% sure
Plz mark me brainliest
Which raises can be represented by algebraic expression 2x + 1 check all that apply
Answer:
two times a number plus 1
Step-by-step explanation:
What is the result when the number 79 is decreased by 17%?
Answer:
65.57 should be the correct answer!
Step-by-step explanation:
Here is the whole work I did, hope this helps!
100 - 17 = 83
79 x 0.83 = 65.57
Answer:
65.57
Step-by-step explanation:
Method 1:
[tex]\frac{y}{79} :\frac{17}{100}[/tex]
y · 100 = 17 · 79
100y = 1343
100y ÷ 100 = 1343 ÷ 100
y = 13.43
79 - 13.43
65.57
Method 2:
100% - 17% = 83%
[tex]\frac{y}{79} :\frac{83}{100}[/tex]
y · 100 = 83 · 79
100y = 6557
100y ÷ 100 = 6557 ÷ 100
y = 65.57
65 ppl are at a movie and if 40% of them purchase sodas, how many ppl is this that have a soda?
Answer:
26
Step-by-step explanation:
Joey wants to read 2,000 pages by the end of the summer. He has already read 1,250 pages. The rest of his reading will be spread over 5 weeks, and Joey wants to read the same number of pages each week. How many pages will he need to read each week?
Answer:
150 pages
Step-by-step explanation:
want to read 2,000 pages
already read 1,250 pages
Number of pages left to read
= 2000-1250
= 750
Rest of the reading spread over 5 weeks
wants to read same number of pages each week
Number of pages that need to be read each week over 5 weeks
= Number of pages left to read / total number of weeks
=750 / 5
= 150
He will need to read 150 pages a week.
Order the following units of a capacity families to greatest gallon paint cup quart
Answer:
7 yards
Step-by-step explanation:
1.6(5x-10)-(12x+15) I WILL AWORD BRILLNESTTTT
Answer:
-4x-31
Step-by-step explanation:
1.6(5x-10)-(12x+15)
8x-16-12x-15
-4x-31
The simplified expression is -4x - 31.
We know,
In mathematics, an expression refers to a combination of numbers, variables, operations, and mathematical symbols that represents a mathematical statement or computation. It can involve arithmetic operations (addition, subtraction, multiplication, division).
We have Equation,
1.6(5x - 10) - (12x + 15)
Now simplifying the equation
1.6(5x - 10) - (12x + 15)
= 8x - 16 - 12x - 15
= -4x - 31
Thus, the simplified expression is -4x - 31.
Learn more about Equation here:
https://brainly.com/question/29538993
#SPJ1
Given f(x) = 3x2 + x and g(x) = 2x. What is Limit of g (f (x)) as x approaches negative 4?
44
88
104
188
Answer: 88
Step-by-step explanation:
got it right 2022 edge
Can someone please help me with this fast?
Answer:
65*
Step-by-step explanation:
12x-7+16x+19=180
28x=168
x=6
12(6)-7=65
What is the degree of the polynomial below?
7x^5+6x^3+ 4x + 2
A. 0
B. 3
C. 1
D. 5
Reason: It's the largest exponent
When a polynomial is written in standard form like this, the term with the largest exponent is written first, then the next largest and so on. So in cases like this, we simply need to look at the left-most term; however, this may not always be the case as your teacher could easily mix up the terms to make sure you're paying attention.
This is considered a quintic polynomial due to the degree of 5.
Find the missing measure for a right circular cone given the following information.
Find h if r = 5 and V = 100 pi.
4
12
30
Answer:
[tex]Volume = \frac{1}{3} \pi r^2 h \\\\r= 5\\Volume = 100\pi\\\\Find \ h.\\\\h = 3\frac{V}{\pi r^2} = 3 \times \frac{100 \pi}{\pi \times 5^2} = 3\times \frac{100}{25} = 3 \times 4 = 12[/tex]
Given a box of 8 color crayons (Red, Blue, Green, Orange, Yellow, Brown, Black, Purple). If I remove a single crayon randomly, and without putting it back in the box, I remove a second crayon randomly, what is the probability that I will remove the Red and the Green crayon from the box
Answer: 1/56
Step-by-step explanation:
Since the box has 8 different colors, the probability of picking any color of crayon will be 1/8.
This question relates to a probability without replacement, therefore, the probability of picking the red crayon first will be 1/8. After then, there'll be 7 crayons left and the probability of picking the green crayon next will be 1/7.
Therefore, the probability that I will remove the Red and the Green crayon from the box will be:
= 1/8 × 1/7
= 1/56
Consider the following functions which map Rn to Rn.
(a) T multiplies the jth component of~x by a nonzero number b.
(b) T replaces the ith component of~x with b times the jth component added to the ith component.
(c) T switches the ith and jth components.
Show these functions are linear transformations and describe their matrices A such that T (~x).
Answer: c
Step-by-step explanation:
A certain town has 25,000 families. The average number of children per family is 2.6, with an SD of 0.80. The distribution is not normal, however, since 20% of the families have no children at all. (a) If one draws a simple random sample of five families from the 25,000, what is the chance that exactly two of the five sample families will have no children
Answer:
0.2048 = 20.48% probability that exactly two of the five sample families will have no children.
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they have no children, or they do have children. The probability of a family not having children is independent of any other family. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
20% of the families have no children at all.
This means that [tex]p = 0.2[/tex]
Five families:
This means that [tex]n = 5[/tex]
What is the chance that exactly two of the five sample families will have no children?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.2)^{2}.(0.8)^{3} = 0.2048[/tex]
0.2048 = 20.48% probability that exactly two of the five sample families will have no children.
What is the equation of the graph
-2
y = 1x + 1
O y = 1x-2
y = 2x - 2
O y = 2x + 1
9514 1404 393
Answer:
the correct choice is marked
Step-by-step explanation:
The line has a rise of 2 for a run of 1, so a slope of 2. The line crosses the y-axis at y=-2, so the y-intercept is -2. The slope-intercept equation for the line is ...
y = mx + b . . . . . . for slope m and y-intercept b
y = 2x -2
Answer:
the answer is c y=2x-2
Step-by-step explanation:
:)
Solve the problem. An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. Assuming that each of the numbers between 1 and 10 is equally likely to be chosen, find P(E).
A) .5
B) .8
C) .1
D) .2
Answer:
A.
Step-by-step explanation:
1. the required probablilty is: P=(number_of_even_numbers)/(number_of_all_the_numbers);
2. according the condition the number of all the numbers is 10; the number of even numbers is 5 (they are: 2; 4; 6; 8; 10), then
3. P=5/10=0.5 (option 'A').
Enter the coordinates of the vertex of the graph of y = 2(x + 5)2 − 4.
Vertex: (
,
)
9514 1404 393
Answer:
(-5, -4)
Step-by-step explanation:
Compare the given equation to vertex form:
y = a(x -h)² +k
You see that a=2, h=-5, k=-4.
The vertex is (h, k) = (-5, -4).
What is one effect of World Bank loans to developing countries?
Answer:
Improved climate for foreign investment
Step-by-step explanation:
I just took the test gs
Which of the following is equal to 2?
6 + 4 = (2 + 1) * 3
(6 + 4 + 2) - 13
6 + (4 + 2) + 1 x 3
(6 + 4) - 2 - 1 x 3
Answer:
no equation is equal to 2 all are greater than 2
Help.. please.. I have no idea how to do this..
56+ ? +11=94
Help me
Answer:
? = 27
Step-by-step explanation:
56 + ? + 11 = 94
? + 67 = 94
? = 27
Does anyone understand this?
Answer: understand what
Step-by-step explanation:
Answer:
where qurstion
Step-by-step explanation:
??????????????