Answer:
Maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm
Step-by-step explanation:
Surface area of box
[tex]4xy+x^2=120\\\Rightarrow y=\dfrac{120-x^2}{4x}[/tex]
Volume of box is
[tex]V=x^2y\\\Rightarrow V=x^2\times \dfrac{120-x^2}{4x}\\\Rightarrow V=\dfrac{120x-x^3}{4}\\\Rightarrow V=30x-\dfrac{1}{4}x^3[/tex]
Differentiating with respect to [tex]x[/tex]
[tex]\dfrac{dV}{dx}=30-\dfrac{3}{4}x^2[/tex]
Equating with zero
[tex]30-\dfrac{3}{4}x^2=0\\\Rightarrow x^2=\dfrac{30\times 4}{3}\\\Rightarrow x^2=40\\\Rightarrow x=6.32[/tex]
Double derivative of the volume
[tex]\dfrac{d^2V}{dx^2}=-\dfrac{6x}{4}=-\dfrac{6\times 6.32}{4}=-9.48<0[/tex]
So, the volume is maximum at [tex]x=6.32[/tex]
[tex]y=\dfrac{120-x^2}{4x}=\dfrac{120-40}{4\times \sqrt{40}}\\\Rightarrow y=3.16[/tex]
So, the maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm.
Simplify 42/56 please help
Answer:
3/4
Step-by-step explanation:
The GCF of 42 and 56 is 14. If you divide both the numerator and the denominator by 14 we get 3/4 = 0.75 or 75%
Answer: 3/4
Step-by-step explanation:
42 divided by 14 is 3
54 divided by 14 is 4
Diego scored nine points less than Andre in the basketball team Noah scored twice as many points as Diego if Noah scored 10 points how many ponts did Andre score
Answer:
1..........................
Answer:
Andre scored 14 points.
Step-by-step explanation:
set up expressions with the info given:
Diego's points: a –9
Andre's points: 2d. and
n = 2d
Noah's points = 10
Use the expressions to set up equations to solve.
To find a, Andre's points, we can work backwards.
Substitute the 10 from the last expression for n in the equation n=2d, and solve for d:
10 = 2d. Divide both sides by 2
5 = d
Substitute the value of d, Diego's points, to make an equation using the first expression:
5 = a –9 Add 9 to both sides.
5 + 9 = a a = 14
Andre scored 14 points
I will give brainiest.
Answer:
the third one is the answer
Consider the sample space given below.
A die is a cube with six sides on which each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space S are listed as follows, where in each case the die on the left is blue and the one on the right is gray.
S= {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66}
Write the following event as a set.
The event that the numbers showing face up are the same.
E = ....................?
Compute the probability of E.
Answer:
1 / 6
Step-by-step explanation:
Probability is a measure of the likelihood of an event to occur. The probability for an event to occur is between 0 and 1.
The Probability of an event occurring is the ratio of the number of event in the sample space to the total number of possible outcomes.
The number of possible outcomes [n(S)] from rolling a blue die and a gray die is 36.
n(S) = 36
Let E be an event that the numbers showing face up are the same.
E = {11, 22, 33, 44, 55, 66}, n(E) = 6
The probability of E = P(E) = number event / number of possible outcomes =
P(E) = n(E) / n(S) = 6 / 36 = 1 / 6
The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.
Required:
Construct a 92% Confidence Interval for the true proportion of girls in the ages 8-12 beginning ice-skating classes at the Ice Chalet.
Answer:
The answer is "(0.73,0.87)".
Step-by-step explanation:
Given:
number of girls[tex]= 64[/tex]
number of boys[tex]= 16[/tex]
Total number of children[tex]= 64+16= 80[/tex]
So,[tex]n=80[/tex]
Calculating the value of the proportion which is given by girls:
[tex]\hat{p}= \frac{\text{number of girls}}{\text{total number of childrens}}[/tex]
[tex]=\frac{64}{80}\\\\=\frac{8}{10}\\\\= 0.8[/tex]
Therefore the confidence interval is:
[tex]\to \hat{p}\pm z_{(1-\frac{\alpha }{2})}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to 0.8 \pm 1.75\sqrt{\frac{0.8(1-0.8)}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{\frac{0.8(0.2)}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{\frac{0.16}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{0.002}\\\\\to 0.8 \pm 1.75 (0.04)\\\\\to 0.8 \pm 0.07\\\\\to (0.73,0.87)[/tex]
[tex]\therefore \\\\\text{The lower confidence limit} = 0.73\\\\\text{The upper confidence limit} = 0.87\\[/tex]
A statistics student has a mean score of 92 in the first 3 tests. Suppose there are a total of 4 tests and all of them have equal weight. You can also assume that there is no extra credit in the last test. What is the best possible final average this student can get
Answer:
The best possible final average this student can get is 94.
Step-by-step explanation:
The average score is given by the sum of the scores of all tests divided by the number of tests.
In this question:
First three tests: Mean score of 92, so total score of 92*3 = 276
Best possible score, with 4 tests:
In the first three, the total is 276. The best possible score is with a grade of 100 in the fourth test. The score will be:
[tex]M = \frac{276+100}{4} = \frac{376}{4} = 94[/tex]
The best possible final average this student can get is 94.
An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then list them in order of preference. Suppose the same cola has actually been put into all three glasses. What is the probability that C is ranked first and D is ranked last?
Answer and explanation:
Probability = number of favorable outcomes/ total number of outcomes
Since all glasses labelled C, D, and P are all same Cola
Probability that C is ranked first = 1/3
Probability that D is ranked last = 1/3
Given f(x)= 5x®, what is the domain? O 5
Answer:
all real numbers (D)
the range is y>= 0 (option B)
Step-by-step explanation:
the question isn't really clear, but assuming that it's f(x)=5x^6, the domain (or at least edge says the domain) is all real numbers. Next is y is greater than or equal to 0
hope this helps and you have a very nice day !! :)
help i don’t know how to do this
Answer: E and F
Step-by-step explanation:
really long story, but those two are the correct answers. hope this helps! :)
What is the volume of the rectangular prism shown?
Answer:
18 3/64
Step-by-step explanation:
i did test trust me
A man borrowed $3500 from a bank for 6 months. The bank collected 7-1/2% simple interest on the date of maturity. How much did the man pay for use of the money and what was the amount he repaid the bank on the due date of the note
Answer:
$3762.50
Step-by-step explanation:
From the problem, we can see our initial loan is 3500. On the return date, the interest of the loan is collected 7.5%. To find out how much the man paid for the loan, we need to find out how much he paid in interest, which is the percentage of the interest converted to a decimal x the initial loan. We get $262.5, and then we need to pay back the interest plus the initial loan we borrowed from the bank, so we need to add those together to get:
$3762.50
Can someone help? Will give brainliest!! Ty
how many months are in y years and m months?
Answer:
Step-by-step explanation:
There are 12 months in one year, so there would be 12*y in y years.
Answer:
there 12 months in one 1 year
Step-by-step explanation:
5. That cool CD you have been waiting to purchase has finally gone on sale over at Wal-Mart for 25% off the original price. You borrow your room-mates employee discount card and head on over to your local Wal-Mart. It turns out the employee discount entitles you to an additional 15% off the sale price of the CD. If the original price was $32.99, what was the total final price you paid for your cool new CD including the 7.5% sales tax
Answer: $22.61
Step-by-step explanation: A 25% discount means that instead of paying the full value, you will pay 25% less. So the total price you will pay for a CD of $32.99:
P₁ = 32.99 * (1 - 0.25)
P₁ = 32.99 * (0.75)
P₁ = 24.7425
However, you still have a discount of 15% over the price, so:
P₂ = 24.7425 * (1 - 0.15)
P₂ = 24.7425 * (0.85)
P₂ = 21.03
The sales tax is a value incorporated over the price after all the discounts:
P = 21.03 * (1 + 0.075)
P = 21.03 * (1.075)
P = 22.61
The total final price for the CD is $22.61.
In the first quadrant you start at (6, 10) and move 6 units right and 4 units down what point will you end up with
Answer:
(12,6)
Step-by-step explanation:
If you move 6 units right, you get to (12,10). Moving 4 units down takes you to (12,6).
What language your figure the thunder rose
Answer: ok buddy
Step-by-step explanation:
Answer:
?
Step-by-step explanation:
Match each sum or difference with the correct simplified expression.
(x - 5) - (x - 1)
2x - 4
(x - 5) + (x + 1)
2x - 6
(x - 5) - (x + 1)
4.
(x - 5) + (x - 1)
-6
Answer:
[tex](x-5)-(x-1)=-4[/tex]
[tex]=2x-4[/tex]
[tex](x-5)+(x+1)=-6[/tex]
[tex](x-5)+(x-1)=2x-6[/tex]
Step-by-step explanation:
In each of the expressions we first need to open the brackets and change the sign according to the sign preceding the bracket. After that we perform simple arithmetic to find the result.
[tex](x-5)-(x-1)=x-5-x+1[/tex]
[tex]=-4[/tex]
[tex](x-5)+(x+1)=x-5+x+1[/tex]
[tex]=2x-4[/tex]
[tex](x-5)-(x+1)=x-5-x-1[/tex]
[tex]=-6[/tex]
[tex](x-5)+(x-1)=x-5+x-1[/tex]
[tex]=2x-6[/tex]
The answers are
[tex](x-5)-(x-1)=-4[/tex]
[tex](x-5)+(x+1)=2x-4[/tex]
[tex](x-5)+(x+1)=-6[/tex]
[tex](x-5)+(x-1)=2x-6[/tex]
Answer:
Step-by-step explanation:
I got it right on edge 2022!
A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are randomly selected as they come off the production line, what is the probability that both are defective (assuming that they are independent)
Answer:
0.0025 = 0.25% probability that both are defective
Step-by-step explanation:
For each item, there are only two possible outcomes. Either they are defective, or they are not. Items are independent of each other. So we use the binomial probability distribution 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.
5 percent of these are defective.
This means that [tex]p = 0.05[/tex]
If two items are randomly selected as they come off the production line, what is the probability that both are defective
This is P(X = 2) when n = 2. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.05)^{2}.(0.95)^{0} = 0.0025[/tex]
0.0025 = 0.25% probability that both are defective
The sum of the squares of two numbers is 26. The difference of the two
numbers is 4. Find the two numbers.
Answer:
i dont know the answer but good luck
Step-by-step explanation:
1) All cars are blue. (2) All pigs have wings. Therefore, (3) All buses have three wheels. Question 2 options: Passes the true premises test and passes the proper form test. Passes the true premises test and fails the proper form test. Fails the true premises test and passes the proper form test. Fails the true premises test and fails the proper form test. None of the above.
Answer:
Fails the true premises test and fails the proper form test
Explanation:
A valid argument must pass the true premises test and the proper form test.
True premises test checks to see if what the premises is saying is true about the world, example- pigs do not have wings and so the argument fails the true premises test. Proper form test assumes the premises is true and then checks to see if a valid conclusion was drawn based on the premises(even though it might fail the true premises test and may not be true about the world)
Which pair
angles must be supplementary?
21
5
3 4
4 and 1
Step-by-step explanation:
Supplementary means the angle is 180 degrees so 4 is the only complete obvious 180 degree angle and 1 just cause i know it can't be 5.
Answer:
C. 4 and 5
I hope I was able to help.
Please provide with an explanation to get brainiest
If there are 52 successful outcomes in a sample with a size of 80, what is the
sample proportion?
A. 0.36
B. 0.72
C. 0.52
D. 0.65
Answer:
D. 0.65
Step-by-step explanation:
Do 52/80 to get the answer which is D.
Please tell me weather it’s true or fade for each one please!
Answer:
False, true, true, false, false
Step-by-step explanation:
Sam earned $154 washing 7 cars. He earned the same amount for washing each car
Select all the equations that show reasonable estimates for the amount Sam eamed washing each car
A $140 = 7 = $20
B. $190 = 9 = $10
C. $160 = 8=320
D. $150 = 5= $10
E $150 = 3= $50
Answer:
the answer is A cause you divide 7 by 140 and the answer is 22 so 20 is the closest
(4,9) (2,6) (0,3) y intercept please
Hi there!
Hope this helps!
I really need help with this so plz give a good answer
Y-21<85 help me pls
I don’t get this stuff lol
Answer:
it is y<106
Step-by-step explanation:
remember to add 85 and 21 together :)
There are 600 members of a sports club.
The ratio of men to women is 2:3
1/4 of the men are under 30 years old
20% of the women are under 30 years old
HOW MANY MEMBERS ARE OVER 30?
9514 1404 393
Answer:
468
Step-by-step explanation:
Men:
(3/4)(2/5)(600) = (6/20)(600) = 6(30) = 180 men over 30
Women:
(4/5)(3/5)(600) = (12/25)(600) = 48(6) = 288 women over 30
The total number of members over 30 is ...
180 +288 = 468 . . . members over 30
The graph shows the price of
different lengths of two types of
rope.
If you buy $1.00 of each kind of
rope, which one will be longer?
Answer:
Nylon
Nylon has a longer x-input for its' y-output, so it is longer.
