Answer:
the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
Step-by-step explanation:
From the given question.
Let p be the length of the of the printed material
Let q be the width of the of the printed material
Therefore pq = 2400 cm ²
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
To find the dimensions of the poster; we have:
the length of the poster to be p+30 and the width to be [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex]
The area of the printed material can now be: [tex]A = (p+30)(\dfrac{2400 }{p} + 20)[/tex]
=[tex]2400 +20 p +\dfrac{72000}{p}+600[/tex]
Let differentiate with respect to p; we have
[tex]\dfrac{dA}{dp}= 20 - \dfrac{72000}{p^3}[/tex]
Also;
[tex]\dfrac{d^2A}{dp^2}= \dfrac{144000}{p^3}[/tex]
For the smallest area [tex]\dfrac{dA}{dp }=0[/tex]
[tex]20 - \dfrac{72000}{p^2}=0[/tex]
[tex]p^2 = \dfrac{72000}{20}[/tex]
p² = 3600
p =√3600
p = 60
Since p = 60 ; replace p = 60 in the expression q = [tex]\dfrac{2400 \ cm^2}{p}[/tex] to solve for q;
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
q = [tex]\dfrac{2400 \ cm^2}{60}[/tex]
q = 40
Thus; the printed material has the length of 60 cm and the width of 40cm
the length of the poster = p+30 = 60 +30 = 90 cm
the width of the poster = [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex] = [tex]\dfrac{2400 \ cm^2}{60} + 20[/tex] = 40 + 20 = 60
Hence; the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
What is the solution to y + 8.5 = 17.2?
Answer:
y+8.5 = 17.2
y = 17.2-8.5
= 8.7
Answer:
y+8.5 = 17.2
y = 17.2-8.5
= 8.7
Step-by-step explanation:
yes the answer above me is correct
Please answer this correctly
Answer:
2 cups more was given to the flower with the most water because 5 cups - 3 cups = 2 cups.
Answer:
2 cups
Step-by-step explanation:
The most water was 5 cups and the least was 3 cups. So:
5-3=2 cups more
Para cubrir un tejado rectangular de 29,7 m de largo ,se gastaron 24 552 locetas de 25cm x19 cm las cuales pierden al colocarse la 1/5 parte de su extensión eficaz . ¿ Qué ancho tenía el tejado ?
Answer:
El tejado tenía un ancho de 31.4 m.
Step-by-step explanation:
Tenemos un techo rectangular, con un largo de 29.7 m y un ancho x, que debemos calcular.
Entonces, la superficie del tejado es:
[tex]S=29.7x\;\,\text{[m}^2\text{]}[/tex]
Las locetas tienen una superficie de 25x19 cm, de las cuales 1/5 se pierde en la colocación. La superficie eficaz que ocupa cada loceta una vez colocada es:
[tex]S_L=(25\cdot19)\cdot(1-1/5)=475\cdot(0.8)=380\;\text{cm}^2[/tex]
Entonces, si se utilizaron 24552 locetas para cubrir todo el techo, podemos expresar la superfice del techo como:
[tex]S=24552\;\text{locetas}\;\cdot380\dfrac{\text{cm2}}{\text{loceta}}\cdot \left(\dfrac{1\text{m}}{100\text{cm}}\right)^2=\dfrac{24552\cdot380}{10000}\;\text{m2}=932.976\;\text{m2}[/tex]
Podemos calcular x igualando este último resultado con la primer ecuación:
[tex]S=29.7x=932.976\\\\x=932.976/29.7=31.413\approx31.4[/tex]
Round $0.6683 to the nearest cent
Answer:
0.67
Step-by-step explanation:
0.668 is close to 0.67 than 0.66
Suppose a company's revenue function is given by R(q) = - q^3 + 220q^2 and its cost function is given by C(q) = 500 + 13q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively.
A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)
MP(q) =
B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)
Answer:
A) MP(q) = -3q² + 440q - 13
B) 146.64 units.
Step-by-step explanation:
The profit function is given by the revenue minus the cost function:
[tex]P(q) = R(q) - C(q)\\P(q) = -q^3+220q^2-500-13q[/tex]
A) The Marginal profit function is the derivate of the profit function as a function of the quantity sold:
[tex]P(q) = -q^3+220q^2-500-13q\\MP(q) = \frac{dP(q)}{dq} \\MP(q)=-3q^2+440q-13[/tex]
B) The value of "q" for which the marginal profit function is zero is the number of items (in hundreds) that maximizes profit:
[tex]MP(q)=0=-3q^2+440q-13\\q=\frac{-440\pm \sqrt{440^2-(4*(-3)*(-13))} }{-6}\\q'=146.64\\q'' = - 0.03[/tex]
Therefore, the only reasonable answer is that 146.64 hundred units must be sold in order to maximize profit.
If 6 newborn babies are randomly selected, how many different gender sequences are possible?
Answer:
720
Step-by-step explanation:
6!
6x5x4x3x2x1=720
A bag contains some number of marbles. It is known that 20 of them are red. When 15 marbles are drawn, without replacement, we get 6 red. Assuming E(X)=6 red, what is the total number of marbles in the bag?
Answer:
The total number of marbles in the bag is 50.
Step-by-step explanation:
Here, we have n trials, without replacement. So the hypergeometric distribution is used.
The mean of the hypergeometric distribution is:
[tex]E(X) = \frac{n*k}{N}[/tex]
In which n is the number of items in the sample, k is the number of items in the population that are classified a success and N is the size of the population.
15 marbles are drawn:
This means that [tex]n = 15[/tex]
A bag contains some number of marbles. It is known that 20 of them are red.
This means that [tex]k = 20[/tex], since a success is drawing a red marble.
Assuming E(X)=6 red, what is the total number of marbles in the bag?
We have to find N when [tex]E(X) = 6[/tex]
So
[tex]E(X) = \frac{n*k}{N}[/tex]
[tex]6 = \frac{15*20}{N}[/tex]
[tex]6N = 300[/tex]
[tex]N = \frac{300}{6}[/tex]
[tex]N = 50[/tex]
The total number of marbles in the bag is 50.
Can anybody please help me with this one??
Answer:
[tex]the \: answer \: is \: d.(x + 4) {}^{2} = 8(y + 4)[/tex]
Use the formula v = u + at to find the velocity when the initial velocity is 3 m/s the acceleration is 1.5 m/s the time is 7 s
[tex]answer \\ 13.5 \: m/s \\ given \\ initial \: velocity(u) = \: 3 \: m/s \\ acceleration(a) = 1.5 \: m/s ^2\\ time(t) = 7 \: second \\ now \\ v = u + at \\ or \: v = 3 + 1.5 \times 7 \\ \: or \: v = 3 + 10.5 \\ v = 13.5 \: m/s \\ hope \: it \: helps[/tex]
While filing your income tax, you report annual contributions of $100 to a public radio station, $300 to PBS (television station), $150 to a woman’s shelter, and $450 to other charitable organizations.
Find your monthly expense.
Hey there! I'm happy to help!
Let's add up all of these contributions.
100+300+150+450=1000
However, this is annual. We want monthly. So, we simply divide by 12.
1000/12≈83.33
Therefore, the monthly expense is $83.33
I hope that this helps! Have a wonderful day!
Bernard bought 8gal of paint. Convert the volume to liters. Round to the nearest tenth
Answer:
In one gallon of paint there are about 3.8 liters so 8 gallons is about 30.3 liters.
You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h = 130 and a square base with side s = 870
To impress your Egyptian subjects, find the volume of the pyramid.
Answer:
32799000 cubic units
Step-by-step Explanation:
Height if the Pyramid=130 Units
Side Length of square base=870 Units
Volume of a Pyramid=[tex]\frac{1}{3}[/tex]* Base Area*Height
Since the base is a square,
Area of a Square of side length s[tex]=s^2[/tex]
Therefore:
Volume[tex]=\frac{1}{3}*870^2*130[/tex]
=32799000 cubic units
The volume of your pyramid is 32799000 cubic units.
Answer:
V = 3.28x10⁷
Step-by-step explanation:
The volume of a pyramid is given by:
[tex] V = \frac{1}{3}bh [/tex]
Where:
b: is the base of the pyramid
h: is the height of the pyramid = 130
The base of the square base of the pyramid is given by:
[tex] b = s^{2} [/tex]
Where:
s: is the side of the square base = 870
Thus, the base of the square base of the pyramid is:
[tex] b = s^{2} = (870)^{2} = 7.56 \cdot 10^{5} [/tex]
Now, the volume of a pyramid is:
[tex] V = \frac{1}{3}bh = \frac{1}{3}(7.56 \cdot 10^{5})*130 = 3.28 \cdot 10^{7} [/tex]
Therefore, the volume of the pyramid is 3.28x10⁷.
I hope it helps you!
A factory received a shipment of 10 generators, and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.
Answer:
A) 0.026
B) 0.130
Step-by-step explanation:
Complete Question
A factory received a shipment of 10 generators and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.
(A) If a sample of 4 generators is selected, find the probability that all in the sample are defective.
(B) If a sample of 4 generators is selected, find the probability that none in the sample is defective.
Solution
A) This is a binomial distribution problem
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of generators to be picked = 4
x = Number of successes required = number of defective generators required = 4
p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40
q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60
P(X = 4) = ⁴C₄ (0.40)⁴ (0.6)⁴⁻⁴ = 0.0256 = 0.026 to 3 d.p.
B) n = total number of sample spaces = number of generators to be picked = 4
x = Number of successes required = number of defective generators required = 0
p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40
q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60
P(X = 0) = ⁴C₀ (0.40)⁰ (0.6)⁴⁻⁰ = 0.1296 = 0.130 to 3 d.p.
Hope this Helps!!!
.
A students received a score of 50 on his history test. The test had a mean of 69 and a standard deviation of 10. Find the z score and assess whether his score is considered unusual.
1.90; unusual
–1.90; not unusual
–1.90; unusual
1.90; not unusual
Answer:
c) The Z-score = - 1.90 unusual
Step-by-step explanation:
Explanation:-
Let 'X' be the random variable in normal distribution
Given student received a score X = 50
Mean of the Population x⁻ = 69
standard deviation of the Population 'σ' = 10
now
[tex]Z = \frac{x^{-}-mean }{S.D}[/tex]
[tex]Z = \frac{x^{-}-mean }{S.D} = \frac{50 -69}{10} = - 1.90[/tex]
The Z-score = - 1.90
Conclusion:-
The Z-score = - 1.90 unusual
Answer: The Z-score = - 1.90 unusual
Step-by-step explanation:
(5m+100) (2m+10) what’s the value of m
Answer:
m=-30
Step-by-step explanation:
5m+100=2m+10
We want to get the variable on one side of the equation. First we subtract 100 from both sides.
5m=2m-90
Subtract 2m from both sides.
3m=-90
Divide both sides by 3.
m=-30
What value of c makes x2 + 6x + c a perfect square trinomial?
Answer:
9
Step-by-step explanation:
x^2 + 6x + c
Take the coefficient of x
6
Divide by 2
6/2 = 3
Square it
3^2 = 9
That is the value of c required
Answer:
C. 9
Step-by-step explanation:
c = 9
x² + 6x + 9
= (x+3)(x+3)
= (x + 3)²
it is a perfect square trinomial when c is equal to 9
Chris has been hired to assess a new version of a college entrance exam. He randomly assigns 100 high school juniors to take the new exam and 100 high school juniors to take the old exam. So that the participants were unaware of the two versions, the new exam was administered in the school gym while the old exam was administered in the school auditorium. The students taking the exam in the gym complained about the smell, the temperature and the uncomfortable seats. The students taking the exam in the auditorium made no complaints. Chris calculated a statistically significant difference between the two versions of the exam (t(198)= 3.1, p< 0.005) and concluded that the new exam was not a valid substitute for the old exam. There is a problem with validity. Which validity is weak in this example?
a. external validity
b. construct validity
c. statistical validity
d. internal validity
Answer:
Internal validity
Step-by-step explanation:
The internal validity here is weak
Internal validity describes the extent to which an evidence weighs the cause and effect claim. In this study, the internal validity that brought about failure in the new exam is mainly due to the environment where the exam was written and not the new exam itself.
So this validity is weak in claiming that the new exam is not a good substitute for the old exam.
Putting them in the same good environment might help the researchers to draw a better conclusion.
ملی
A man left one-fifth of his property to his
Son , one third to his daughter
and remaining
to his wife. If his wife got 35ooo RS what was the
worth of his total property?
Answer:
Rs 75,000
Step-by-step explanation:
Let the total value of property be x
If one-fifth of that is given to son
property with son = 1/5 of total value of property = 1/5 of x = x/5
If one-third of that is given to daughter
property with daughter = 1/3 of total value of property = 1/3 of x = x/3
remaining property after giving the portions to son and daughter
= total value of property - property with son -property with daughter
= x - x/5 - x/3
taking LCM of 5 and 3 (15)
= (15x - 3x - 5x)/15
= 7x/15
Given that remaining property was given to wife
property with wife = 7x/15
it is given that wife got 35000 Rs
thus,
7x/15 = 35,000
7x = 35,000*15 = 525,000
x = 525,000/7 = 75,000
Thus, total worth of property =Rs 75,000 Answer
Answer:
Rs 75,000
Step-by-step explanation:
Let the total value of property be x
If one-fifth of that is given to son
property with son = 1/5 of total value of property = 1/5 of x = x/5
If one-third of that is given to daughter
property with daughter = 1/3 of total value of property = 1/3 of x = x/3
remaining property after giving the portions to son and daughter
= total value of property - property with son -property with daughter
= x - x/5 - x/3
taking LCM of 5 and 3 (15)
= (15x - 3x - 5x)/15
= 7x/15
Given that remaining property was given to wife
property with wife = 7x/15
it is given that wife got 35000 Rs
thus,
7x/15 = 35,000
7x = 35,000*15 = 525,000
x = 525,000/7 = 75,000
Thus, total worth of property =Rs 75,000 Answer
please help !!!
Find the probability that x = -10
Answer:
20%
Step-by-step explanation:
Use the table provided... it says -10 is .2 which is the same as 20%
Answer:
0.20
Step-by-step explanation:
requires decimal not percentage
Find the measure of angle x in the figure below: A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 56 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 51 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 72 degrees. The interior angle on the left is labeled as x.
Answer:
[tex]x=35^\circ[/tex]
Step-by-step explanation:
From the diagram which I have drawn and attached below:
[tex]56^\circ+y+51^\circ=180^\circ$ (Sum of Angles on a Straight Line)\\y=180^\circ-(56^\circ+51^\circ)\\y=73^\circ[/tex]
Next, in the triangle, the sum of the three interior angles:
[tex]y+x+72^\circ=180^\circ\\$Since y=73^\circ\\73^\circ+x+72^\circ=180^\circ\\x=180^\circ-(73^\circ+72^\circ)\\x=35^\circ[/tex]
The value of angle x is 35 degrees.
Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?
Which set of three angles could represent the interior angles of a triangle? A 26 degrees, 51 degrees, 103 degrees B 29 degrees, 54 degrees, 107 degrees C 35 degrees, 35 degrees, 20 degrees D 10 degrees, 90 degrees, 90 degrees
Answer:
it is option A
Step-by-step explanation:
What is the value of the discriminant for the quadratic equation?
6x^2 - 2x + 5 = 0
Answer: -116 is value of discriminant
Tony rode his bicycle 3 7/10 miles to school. What is this distance written as a decimal?
Answer:
the distance written as a decimal is 3.7
37/10 = 3,7
Achievements :)
Determine whether the sampling method is independent or dependent. A stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks. He randomly selects 13 energy stocks and computes the rate of return for the past year.
Answer:
The sampling method is independent.
Step-by-step explanation:
Samples are said to be dependent when the data chosen in one sample has an effect on the data to be chosen in the other sample, while samples are said to be independent if the data chosen in one sample has no effect on the data to be chosen on the other sample.
Here, the stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks, so, he randomly selects 13 energy stocks. Since the energy stocks he chose were randomly selected, it means the data he selected from the energy stock will not dictate the type of data to be selected from the financial stock. Thus, the sampling method is said to be independent.
A farmer planted corn in two different fields. He planted 500 seeds of regular corn in Field A and 500 seeds of experimental corn in Field B. At
harvest time, more ears of corn had grown in Field A than in Field B. The farmer concluded that more corn grew in Field A because of the type
of corn planted.
Choose two other possible variables that could have caused more corn to grow in Field A.
Answer:
1. More pollination process in the regular corn planted in field A than that of field B.
2. Low pest and insect attack on corn planted in field A compared to that of B.
Step-by-step explanation:
1. Pollination is the process in which a plant becomes fertilized, so as to produced seeds. The process requires some agent which could be; air, human, wind etc.
Therefore more pollination of the corn planted in field A than those in B would lead to more yield (ears of corn harvested) than that of B.
2. Pests and insects are agents which could reduce the yield of the corn after harvest. Comparing the two fields A and B, if the corn planted in field A were not affected by pests or insects, while those planted in B were affected, then more ears of corn would be harvested in field A.
Answer:
a,c, And gg gamer
Step-by-step explanation:
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 38 hours and the median is 34.2 hours. Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours. Step 2 of 5 : Approximately how many families are in the sample? Round your answer to the nearest integer.
Answer:
There are approximately 171 families in the sample.
Step-by-step explanation:
Percentile meaning:
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours.
This means that 24 is 14% of the total number of families.
Approximately how many families are in the sample?
Using a rule of three.
24 - 0.14
x - 1
0.14x = 24
x = 24/0.14
x = 171.4
Rounding to the nearest integer
There are approximately 171 families in the sample.
I will mark you as BRANLIEST and I will give you 55 points if you answer correctly.
~Solve each system of equations using elimination. SHOW YOUR WORK
1) -4x+3y=-5
4x-5y=3
2) 2x+3y=36
10x-6y=12
Answer:
1. x = 2 y = 1
2. x = 17 y = 29/3
Step-by-step explanation:
1. Use elimination
-4x+3y=-5
4x-5y=3
x's cancel, so add them
-2y = -2
y = 1
substitute
4x -5(1) = 3
4x - 5 = 3
4x = 8
x = 2
2. Use elimination
2x+3y=36
10x-6y=12
Multiply top equasion by 5
10x+30y = 360
10x-6y = 12
x's cancel so subract
36y = 348
y = 29/3
Substitute
2x+3(2/3)=36
2x+2 = 36
2x = 34
x = 17
If log a = x and log b = y, then log (ab2) equals
1
1.
2 (x +y)
1
2.
x + 2 y
x + 2y
3
4.
2x + 2y
Su
uid Toolhar
Answer:
The answer for log(ab²) is x + 2y.
Step-by-step explanation:
You have to apply Logarithm Law,
[tex] log(a) + log(b) \: ⇒ \: log(a \times b) [/tex]
[tex] log( {a}^{n} ) \: ⇒ \: n log(a) [/tex]
In this question, you have to seperate it out :
[tex] log(a {b}^{2} ) = log(a) + log( {b}^{2} ) [/tex]
[tex] log( {b}^{2} ) = 2 log(b) [/tex]
[tex]let \: log(a) = x[/tex]
[tex]let log(b) = y[/tex]
[tex] log(a {b}^{2} ) = log(a) + 2 log(b) [/tex]
[tex] log(a {b}^{2} ) = x + 2y[/tex]
Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication a at what time will you need to stop the infusion
Answer:
6 PM
Step-by-step explanation:
125 mg --- 300 mL
500 mg --- x mL
x = 500*300/125 = 1200 mL solution contains 500 mg
rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
You need to stop infusion at 6 PM
It is found that You need to stop infusion at 6 PM.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication.
125 mg = 300 mL
500 mg = x mL
x = 500*300/125
x = 1200 mL
Here solution contains 500 mg
The rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
Therefore, You need to stop infusion at 6 PM.
Learn more about the unitary method;
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