Answer:
(a) The probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams is 0.4091.
(b) The probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams is 0.6808.
Step-by-step explanation:
We are given that the average weight of their "Smart Cow" brain is 485 grams instead of the regular 458 grams.
Assume that the standard deviation of Smart Cow brain weights is the same as the entire population's standard deviation = 64 g.
Let X = weight of the brain of a randomly selected Smart Cow
So, X ~ Normal([tex]\mu=485, \sigma^{2} = 64^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 485 grams
[tex]\sigma[/tex] = standard deviation = 64 grams
(a) The probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams is given by = P(X [tex]\geq[/tex] 500 grams)
P(X [tex]\geq[/tex] 500 g) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{500-485}{64}[/tex] ) = P(Z [tex]\geq[/tex] 0.23) = 1 - P(Z < 0.23)
= 1 - 0.59095 = 0.4091
The above probability is calculated by looking at the value of x = 0.23 in the z table which has an area of 0.59095.
(b) Let [tex]\bar X[/tex] = sample mean weight of the brain of a randomly selected Smart Cow
The z-score probability distribution for the sample meanis given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 485 grams
[tex]\sigma[/tex] = standard deviation = 64 grams
n = sample of cows = 36
Now, the probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 480 grams)
P([tex]\bar X[/tex] [tex]\geq[/tex] 480 g) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{480-485}{\frac{64}{\sqrt{36} } }[/tex] ) = P(Z [tex]\geq[/tex] -0.47) = P(Z < 0.47)
= 0.6808
The above probability is calculated by looking at the value of x = 0.47 in the z table which has an area of 0.6808.
The width of a rectangle is 6 less than the length. Let L represent the length of the rectangle. Write an expression for the width of the rectangle.
Answer:
W+6 = Y.
Or
Y -6 = W
Step-by-step explanation:
Let's call the length of the rectangle L.
And let W represent the width of the rectangle.
Let's write an expression to determine the width of the rectangle relative to the length of the rectangle.
From the question, the width W is 6 less than the length L of the rectangle.
It means the length is greater than the width with 6 units.
The expression is
W+6 = Y.
Or
Y -6 = W
The correlation matrix obtained for the variables bp (y) (blood pressure), age (x1) (age), smk (x2) (smoke) and WET(X3) (Weight), is given by:
BP AGE SMK WET
BP 1 0.64 0.72 0.48
AGE 1 0.32 0.78
SMK 1 0.40
WET 1
Based on this matrix please calculate the partial correlation.
a. 0.53
b. 0.48
c. 0.62
d. 0.32
Answer:
c) 0.62
Step-by-step explanation:
In this case, we are required to find the partial correlation, [tex] r_Y_X_1_|_X_2[/tex].
To find the partial correlation, use the formula:
[tex] r_Y_X_1_|_X_2 = \frac{r_Y_X_1 - r_Y_X_2 * r_X_1_X_2}{\sqrt{1 - r_X_1_X_2}^2 - \sqrt{1 - r_Y_X_2}^2} [/tex]
[tex] r_Y_X_1_|_X_2 = \frac{0.64 - 0.72 * 0.32}{\sqrt{1 - 0.32}^2 - \sqrt{1 - 0.72}^2} [/tex]
[tex] = \frac{0.410}{0.657}[/tex]
[tex] r_Y_X_1_|_X_2 = 0.62 [/tex]
The partial correlation is 0.62.
Option C
URGENT!! Solve the triangle for all missing sides and angles. Part 2: Use the law of sines to find the length of side a. Part 3: Use any method to find the length of side c.
Answer:
B = 55°
a ≈ 143
c ≈ 212
Step-by-step explanation:
From the triangle above we are given a triangle with two known angles and a known side. The sum of angles in a triangle is 180°. Since we are given two angles, the last angle can be gotten when you subtract the two known angles from 180°. Therefore,
angle B = 180° - 42° - 83°
angle B = 55°
To find side a we can use law of sine
a/sin A = b/sin B
a/sin 42° = 175/sin 55°
a/0.66913060635 = 175/0.81915204428
cross multiply
0.81915204428 a = 117.097856113
divide both sides by 0.81915204428
a = 117.097856113 /0.81915204428
a = 142.950087143
a ≈ 143
To find side c
b/sin B = c/sin C
175/sin 55 = c/sin 83°
cross multiply
c sin 55° = 175 sin 83°
divide both sides by sin 55°
c = (175 × 0.99254615164)/0.81915204428
c = 173.695576537 / 0.81915204428
c = 212.043146019
c ≈ 212
Arrange in ascending order. 8/13, 2/9,28/29
Step-by-step explanation:
he operation of sorting fractions in ascending order: 18/46, 28/41, 29/38, 29/44, 32/30 ... terms equivalents: 18/46=(2×3^2)/(2×23)=((2×3^2)÷2)/((2×23)÷2)=9/23; 28/41 already reduced to ... by the largest exponents: LCM (9, 28, 29)=2^2×3^2× 7×29=7308 Calculate LCM, the least ... /10 </13 </19
how do you mathematically write 6 inches and 4 1/2 inches
I’m not exactly sure what this means.
But you can use “ to abbreviate the labels.
So it would be 6” and 4.5”
Answer:
Step-by-step explanation:
There is some ambiguity in this question. I think you want 4.5 + 6 = 10.5 inches.
What is the greatest common factor of 48 and 32?
Answer:
GCF - 16
Step-by-step explanation:
48 - 1, 2, 3, 4, 6, 8, 12, 16
32 - 1, 2, 4, 8, 16
Hope this helps! :)
Answer:
16
Step-by-step explanation:
48=3*16
32=2*16
Beginning three months from now, you want to be able to withdraw $2,300 each quarter from your back account to cover college expenses over the next four years. If the account pays .45 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years?
Answer:
$36,450.46
Step-by-step explanation:
The amortization formula can be used to figure this. For quarterly payment A, the principal invested must be P for interest rate r and compounding n times per year for t years.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
2300 = P(0.0045/4)/(1 -(1 +0.0045/4)^(-4·4))
2300 = P·0.06309934
P = 2300/0.06309934 = 36450.46
You need $36,450.46 in your account today so that you can withdraw $2300 quarterly for 4 years.
can someone help me asap pls?
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Trigonometry.
so here, we gonna use the cosine ratios.
so here, we also use the Pythagoras Theorem.
[tex] {h}^{2} + {k}^{2} = {r}^{2} [/tex]
so we here, we get
h= 1 ,
[tex]h = 1 \: r = 2 \: k = \sqrt{3} \: \\ \alpha = 60 \: \beta = 30[/tex]
Find the values of x and y in these equations. (x + yi) + (4 + 6i) = 7 − 2i (equation A) (x + yi) − (-8 + 11i) = 5 + 9i (equation B)
Answer:
Step-by-step explanation:
(x+yi)+4+6i=7-2i
x+yi=7-2i-4-6i
x+yi=3-8i
equating real and imaginary parts
x=3,y=-8
B.
x+yi=5+9i+(-8+11i)
x+yi=5+9i-8-11i
x+yi=-3-2i
equating real ,and imaginary parts
x=-3
y=-2
The value of x and y for equation A is
[tex]x=3, y=-8[/tex]
The value of x and y for equation B is
[tex]x=-3 , y=20[/tex]
Given :
[tex](x + yi) + (4 + 6i) = 7 - 2i[/tex]
find the value of x and y in the given equation
Lets open the parenthesis and combine like terms
Equate the real and imaginary part to solve for x and y
[tex]\left(x+4\right)+\left(y+6\right)i=7-2i\\x+4=7\\x=3\\\\y+6=-2\\y=-2-6\\y=-8[/tex]
The value of x=3 and y=-8
Now we do the same with second equation
[tex](x + yi) - (-8 + 11i) = 5 + 9i\\\\x+8+yi-11i=5+9i\\\left(x+8\right)+\left(y-11\right)i=5+9i\\x+8=5\\x=-3\\\\y-11=9\\y=9+11\\y=20[/tex]
The value of x and y is x=-3 and y=20
Learn more : brainly.com/question/18552411
g The p-value of a test is the probability of obtaining a result as or more extreme as the one obtained in the sample, assuming the null hypothesis is false
Answer:
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
Step-by-step explanation:
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
We reject the null hypothesis if the p-value of a statistic is lower than the level of significance α.
And we fail to eject the null hypothesis if the p-value of a statistic is greater than the level of significance α.
A lower p-value indicates that the result is statistically significant.
And a higher p-value indicates that the result is not statistically significant.
What is this expression in simplified form?
3^3 x 6^6
Answer:
i think its 1259712.
Step-by-step explanation:
when we find3^3 and 6^6 we get, 27×46656
and by multiplying them we get, 1259712...
is answer
Answer:
1,259,712
Step-by-step explanation:
Follow the order of operations, evaluating exponents first:
3^3 × 6^6 = 27 × 46,656 = 1,259,712
_____
When in doubt, the Google calculator can be relied upon to follow the order of operations. (Use an asterisk (*) for multiplication.)
You wish to accumulate $14,580 in 6 years. Payments are made at the end of every six-month period into an account earning 7.2% compounded semi-annually. Find the required payment amount to accomplish your goal.
What is coefficient of the term of degree of degree 5 in the polynomial below 3x^6+5-x^2+4x^5-9 which one is the right answer A. 3 B. 4 C. 6 D. 5
Answer:
B. 4
Step-by-step explanation:
We are looking for the coefficient of the term x⁵. When we see it in the polynomial as 4x⁵, our coefficient and answer would then be 4.
Please help! Need Geometry help!!!!!
Answer:
938 feet
Step-by-step explanation:
b/c every angle of a rectangle is 90° u can u Pythagorean theroem to solve the question
a*a+ b*b=c*c
900*900+264*264=c*c
c=√879,696
c=938feet
Answer:
938 feet
Step-by-step explanation:
Well to solve this we need to use the Pythagorean Theorem,
[tex]a^2 + b^2 = c^2[/tex].
So we have a and b which are 900 and 264,
and we need to find c or the walking distance.
So we plug in 900 and 264 for a and b.
[tex](900)^2 + (264)^2 = c^2[/tex]
So, 900*900 = 810,000
264 * 264 = 69696
810000 + 69696 = 879696
So now we have,
879696 = c^2
To get the c by itself we do,
[tex]\sqrt{879696} = \sqrt{c}[/tex]
= c = 937.921105424
c = 938 rounded to the nearest foot
Thus,
the solution is 938.
Hope this helps :)
Box A contains 5green and 7 red balls. Box B contains 3green, 3 red and 6 yellow balls. A box is sleeted at random and a ball is drawn at random from it. What is the probability that the drawn ball is green?
Answer:
5/48Step-by-step explanation:
Given
the sample space for box A
green balls = 5
red balls= 7
sample size= 5+7= 12
the sample space for box B
green balls = 3
red balls= 3
yellow balls= 6
sample size= 3+3+6= 12
The probability of drawing a green ball from box A= 5/12
The probability of drawing a green ball from box B= 3/12= 1/4
Therefore the probability of picking a green ball from either of the boxes at random is =[tex]=\frac{5}{12} *\frac{1}{4}[/tex][tex]=\frac{5}{48}[/tex]
the twelve inch square tiles are shipped in boxes of sixteen pieces per box. each of the boxes weighs twenty four pounds. approximately how many ounces does each tile weigh?
Answer:
1.411764706
Step-by-step explanation:
24/17=1.411764706
solve for n n/5+0.6=2
Answer:
N=7
Step-by-step explanation:
It is correct on Khan
During a 5 5 -day period, a florist served a different number of customers at a flower shop each day. The mean number of daily customers served during this period was 17 17 . In the following month, during another 5 5 -day period, the florist served 16 16 customers per day for four of the days, but served 25 25 customers on the fifth day. What is the difference between the mean number of customers the florist served during each of the two five-day periods?
Answer:
0.8
Step-by-step explanation:
Mean for the first 5 day period = 17
Mean for the second 5 day period = 17.8
Difference 17.8 - 17 = 0.8
The difference between the mean number of customers the florist served during each of the two five-day periods is of 0.8.
-------------------------------
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
-------------------------------
First period:
5 days, mean of 17.
-------------------------------
Second period:
First four days, mean of 16, thus total of [tex]4 \times 16 = 64[/tex]Fifth day, 25 customers.Thus, 64 + 25 = 89 customers in 5 days, and the mean is:
[tex]M = \frac{89}{5} = 17.8[/tex]
-------------------------------
Difference:
17.8 - 17 = 0.8
The difference between the mean number of customers the florist served during each of the two five-day periods is of 0.8.
A similar question is given at https://brainly.com/question/10235056
PLEASE HELP ASAP!!! A toy store has 10 stores all about the same size in a city the graph shows sales for one of the stores last month. Which statement is best supported by the information in the graph?
Answer:
The first one
Step-by-step explanation:
Took the test
Answer: 1/10 of the store's total sales last month were in appliances (lower right corner)
Step-by-step explanation:
Let's go through the four possible answers
In the upper left corner it says "Total mobile phone sales is likely 27,000" which is a paraphrase of what is given. The chart gives 9000 as the phone sales for that one particular store. If all stores are identical in performance, then we have 4*9000 = 36000 in total mobile phone sales. Of course, it's impossible to know for sure how the other stores did. So we can eliminate this as one of the answers.
In the upper right corner, it says "13% of the stores sales was in car electronics" (also paraphrased). We have 13 thousand in car electronics out of 17+13+6+9+15 = 60 thousand total. Divide the two values: 13/60 = 0.2167 = 21.67% approximately. So we can eliminate this as an answer.
In the lower left corner, it says "the total sales is likely greater than $300,000" but we don't know for sure because again we don't have the other charts for the three other stores. Assuming the four stores perform the same, then we'd have 4*60 = 240 thousand as the total and not 300 thousand. It's safe to say we can eliminate this as an answer.
In the lower right corner, it says "1/10 of the stores sales were appliances". This statement is true. Why? Because 6 thousand is the sales figure for appliances out of 60 thousand total. Divide the values: 6/60 = 1/10. So this is why the lower right corner is the answer.
whats 1/2 + 2/4 - 5/8?
Answer:
3/8
Step-by-step explanation:
Step 1: Find common denominators
1/2 = 4/8
2/4 = 4/8
Step 2: Evaluate
4/8 + 4/8 - 5/8
8/8 - 5/8
3/8
Alternatively, you can just plug this into a calc to evaluate and get your answer.
Answer:
3/8
Step-by-step explanation:
Look at the denominator:
2, 4, 8. The LCM (Lowest Common Multiple) is 8.
So this equation becomes
4/8+4/8-5/8=3/8
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion
Answer:
A sample of 385 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample:
We need a sample of n.
n is found when M = 0.05.
We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]
[tex]n = 384.16[/tex]
Rounding up
A sample of 385 is needed.
You just purchased two coins at a price of $1,030 each. Because one of the coins is more collectible, you believe that its value will increase at a rate of 7.7 percent per year, while you believe the second coin will only increase at 7.1 percent per year. If you are correct, how much more will the first coin be worth in 20 years
Answer:4541(Rounded) 4541.99779(Unrounded)
Step-by-step explanation:
A= P(1 + r)^T
A= answer
P=principle(amount of money)
r=Rate(percent / 100)
T=Time(Annually)
1030(1 + .077)^20
Brainliest would be appericiated!
I flip a fair coin 17 times. Answer the following questions:
a. What is the probability of getting 9 heads?
b. What is the probability of getting 2 heads?
c.. What is the probability of getting 1 tail?
d. What is the probability of getting 14 or more heads?
e. What is the probability of getting 17 tails?
Answer:
A) 0.1855
B) 0.0010376
C) 0.0001297
D) 0.006363
E) 0.000007629
Step-by-step explanation:
In calculation of a probability, we normally take the ratio of the number of ways to meet a certain condition (i.e. the numerator) divided by the number of ways to pick from a pool (i.e. the denominator).
So what are the number of ways the flip of a coin 17 times can come out?
A coin has a head and tail, so each toss will have two possible results. If we toss once, we have 2 possible results. If we toss, twice we have 2² = 4 possible results.
If we toss thrice, we have 2³ = 8 possible results, etc.
Thus, for 17 tosses, we will have 2^(17) = 131072 possible results.
A) To achieve the probability of getting 9 heads, we will use combination formula;
C(n, k) = n! / (k!(n - k)!)
In this case, n = 17 and k = 9
So,
P(9 heads) = 17! / (9!(17 - 9)!) = 24310
Thus,
P(9 heads in 17 tosses of a fair coin) = 24310/131072 = 0.1855
B) Similar to A above;
P(2 heads) = 17! / (2!(17 - 2)!) = 136
Thus,
P(2 heads in 17 tosses of a fair coin) = 136/131072 = 0.0010376
C) Similar to A above;
P(1 tail) = 17! / (1!(17 - 1)!) = 17
Thus,
P(1 tail in 17 tosses of a fair coin) = 17/131072 = 0.0001297
D) probability of getting 14 or more heads?
Since, there are 17 tosses, this will be;
P(14 or more heads in 17 tosses) = P(14 heads in 17 tosses) + P(15 heads in 17 tosses) + P(16 heads in 17 tosses) + P(17 heads in 17 tosses)
P(14 heads) = 17! / (14!(17 - 14)!) = 680
P(15 heads) = 17! / (15!(17 - 15)!) = 136
P(16 heads) = 17! / (16!(17 - 16)!) = 17
P(17 heads) = 17! / (1!(17 - 17)!) = 1
Thus;
P(14 heads in 17 tosses) = 680/131072 = 0.005188
P(15 heads in 17 tosses) = 136/131072 = 0.0010376
P(16 heads in 17 tosses) = 17/131072 = 0.0001297
P(1 head in 17 tosses) = 1/131072 = 0.00000763
P(14 or more heads in 17 tosses) = 0.005188 + 0.0010376 + 0.0001297 + 0.00000763 = 0.006363
E) Similar to A above;
P(17 tails) = 17! / (17!(17 - 17)!) = 1
Thus,
P(17 tails in 17 tosses of a fair coin) = 1/131072 = 0.000007629
Which equation, when solved, gives 8 for the value of x?
A: 5/2x+7/2x=3/4x+14
B: 5/4x-9=3/2x-12
C: 5/4x-2=3/2x-4
D: 5/2x-7=3/4x+14
Answer:
Step-by-step explanation:
C. 5x/4-2=3x/2-4
5x/4 -2=6x/4-4
+4 +4
5x/4+2=6x/4
-5x/4
2=x/4
*4
x=8
Answer:
your answer is C
Step-by-step explanation:
The shape on the left is transformed to the shape on the right. Figure A B C D is rotated to form figure A prime B prime C prime D prime. Which of the following statements describes the transformation? A B C D right-arrow A prime B prime C prime D prime A prime B prime C prime D prime right-arrow A B C D A B C D right-arrow D prime A prime C prime B prime D prime B prime C prime A prime right-arrow C A D B
Answer:
A
Step-by-step explanation:
I did the test and it is the only one that makes sense
Answer:
a
Step-by-step explanation:
Suppose a random variable X is best described by a uniform probability distribution with range 1 to 5. Find the value of that makes the following probability statements true.
a) P(X <-a)= 0.95
b) P(X
c) P(X
d) P(X ->a)= 0.89
e) P(X >a)= 0.31
Answer:
a) 4.8
b) 2.96
c) 4.4
d) 1.44
e) 3.76
Step-by-step explanation:
What we will do is solve point by point, knowing the following:
Fx (x) = P (X <= x) = (x - 1) / 4
a) P (X <-a) = 0.95
Fx (a) = 0.95
(a -1) / 4 = 0.95
a = 1 + 0.95 * 4
a = 4.8
b) P (X <a) = 0.49
Fx (a) = 0.49
(a -1) / 4 = 0.49
a = 1 + 0.49 * 4
a = 2.96
c) P (X <a) = 0.85
Fx (a) = 0.85
(a -1) / 4 = 0.55
a = 1 + 0.85 * 4
a = 4.4
d) P (X> a) = 0.89
P (X <a) = 1 - 0.89 = 0.11
Fx (a) = 0.11
(a -1) / 4 = 0.11
a = 1 + 0.11 * 4
a = 1.44
e) P (X> a) = 0.31
P (X <a) = 1 - 0.31 = 0.69
Fx (a) = 0.69
(a -1) / 4 = 0.69
a = 1 + 0.69 * 4
a = 3.76
Write your answer using only positive exponents
Answer:
Step-by-step explanation:
Hello
[tex](-4b^5c^{-6})^3\\\\=(-1)^34^3b^{15}v^{-18}\\=-64b^{15}c^{-18}\\\\=\dfrac{-64b^{15}}{c^{18}}\\[/tex]
hope this helps
The simplified form of the given exponential expression is -64b¹⁵/c¹⁸.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given exponential expression is (-4b⁵c⁻⁶)³.
Here, the given expression can be written as -4³(b⁵)³(c⁻⁶)³
= -64b¹⁵c⁻¹⁸
= -64b¹⁵/c¹⁸
Therefore, the simplified form of the given exponential expression is -64b¹⁵/c¹⁸.
To learn more about an exponents visit:
https://brainly.com/question/15993626.
#SPJ2
if there are about 3.346x10^26 molecules of water in a liter of water and the ocean is about 1.26x10^21 liters in volume, how many water molecules are there in the ocean?
Answer: 4.21596 x 10⁴⁷
Step-by-step explanation:
(3.346 x 10²⁶) (1.26 x 10²¹)
= (3.346 x 1.26) x 10²⁶⁺²¹
= 4.21596 x 10⁴⁷
I NEED HELP ASAP,THANKS! :)
Roland’s Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 1 economy seats must be sold and at least 6 deluxe seats must be sold. The maximum number of passengers allowed on each boat is 30 Roland’s Boat Tours makes $40 profit for each economy seat sold and $35 profit for each deluxe seat sold. What is the maximum profit from one tour? Show work.
Answer:
$1170
Step-by-step explanation:
Let x and y represent the numbers of economy and deluxe seats sold. The constraints are ...
x ≥ 1y ≥ 6x +y ≤ 30And the objective function we want to maximize is ...
p = 40x +35y
__
I find it convenient to graph the equations and locate the objective function line as far from the origin as possible. The graph is shown, along with the solution.
Here, it's even simpler than that. The profit per seat is the greatest for economy seats, so Roland's should sell as many of those as they can. The only limit is that 6 seats must be deluxe. The remaining 30-6=24 can be economy. So, the profit will be maximized for ...
24 economy seats and 6 deluxe seats
The corresponding profit will be ...
24(40) +6(35) = 1170
The maximum profit from one tour is $1170.
help with this I don't know how to solve
Answer:
86.53
Step-by-step explanation:
Area of Triangle Formula: A = 1/2bh
Pythagorean Theorem: a² + b² = c²
Step 1: Draw altitude and label numbers
If we draw a line down the middle, we can see that we get a perpendicular bisector and that we get 2 right triangles with a hypotenuse of 29 and a leg of 3. We need to find h using Pythagorean Theorem in order to use area formula:
3² + b² = 29²
b² = 29² - 3²
b = √832 = h
Step 2: Plug in known variables into area formula:
A = 1/2(√832)(6)
A = 3√832
A = 86.5332