Mathematics College

Every year, a teacher surveys his students about the number of hours a week they watch television. In 2002, his students watched an average of 12 hours of television per week. In 2012, the number of hours spent watching television decreased to five per week. What is the percent decrease in the hours of television watched, rounded to the nearest tenth? 5.8% 4.2% 41.7% 58.3%

Answers

Answer 1

Answer:

58.3%

Step-by-step explanation:

Answer 2

The percent decreased in the hours of television watched is 58.3%.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. Also called per centum. one one-hundredth part; 1/100. percentage.

Given that, in 2002, the students watched an average of 12 hours of television per week. In 2012, the number of hours spent watching television decreased to 5 hours per week

We need to find the percent decrease in the hours of television watched,

Percent decreased = Difference in the initial and final quantity / initial quantity × 100

Percent decreased = 12-5 / 12 × 100 = 7/12 × 100

= 58.3%

Hence, the percent decreased in the hours of television watched is 58.3%

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Related Questions

What is the probability of selection for any man in a proportionate random sample, where a sample of 100 will be drawn from a population of 1,000 that is 50% male and 50% female?

Answers

Working Principle: Stratified Random Sampling

nx = (Nx/N)*n

where:
nx = sample size for stratum x
Nx = population size for stratum x
N = total population size
n = total sample size

Given:

Nx = 100
N = 1000
n = 0.5*(1000) = 500

Required: Probability of Man to be selected

Solution:

nx = (Nx/N)*n
nx = (100/1000)*500 = 50 men

ny = (Nx/N)*n
ny = (100/1000)*500 = 50 women

Probability of Man to be selected = nx/(nx + ny)*100 = 50/(50+50)*100 = 50%

ANSWER: 50%

In rectangle PQRS, PQ = 18, PS = 14, and PR = 22.8. Diagonals PR and QS intersect at point T. What is the length of TQ ?

Answers

rectangle PQRS, PQ = 18, PS = 14, and PR = 22.8
so
Diagonals PR = QS
if PR = 22.8 then QS = 22.8

TQ = QS/2 = 22.8 / 2 = 11.4

anser
TQ = 11.4

Answer:

TQ = 11.4

Step-by-step explanation:

Given : In rectangle PQRS, PQ = 18, PS = 14, and PR = 22.8. Diagonals PR and QS intersect at point T.

To find : What is the length of TQ .

Solution : We have given rectangle PQRS

Side PQ = 18.

Side PS = 14.

Diagonal PR = 22.8 .

Properties of rectangle : (1) Opposite sides of rectangle are equals.

(2) Diagonals of rectangle are equal .

(3) Diagonals of rectangle bisect each other.

Then by second property :

Diagonal PR= QS .

QS = 22.8

By the Third property TQ = [tex]\frac{1}{2} * QS[/tex].

TQ = [tex]\frac{1}{2} * 22.8 [/tex].

TQ = 11.4

Therefore, TQ = 11.4

When we toss a penny, experience shows that the probability (long term proportion) of a head is close to 1-in-2. suppose now that we toss the penny repeatedly until we get a head. what is the probability that the first head comes up in an odd number of tosses (one, three, five, and so on)?

Answers

2/3 or 0.66666

This is a sum of an infinite series problem. A sequence of 1 will happen with a probability of 0.5 A sequence of 3 will happen with a probability of 1/2^3, 1/8, = 0.125 In general we have an infinite series of 1/2^1 + 1/2^3 + 1/2^5 + ... + 1/2^(2n-1) where n >= 1 The sum of such a series with a constant ratio between sequential terms is S = s1/(1-r) where s1 = first term in the series r = ratio between terms. The value for s1 = 0.5 as shown above and the 2nd term is 0.125. So r = 0.125 / 0.5 = 0.25 And the sum of the infinite series is S = s1/(1-r) S = 0.5/(1 - 0.25) S = 0.5/0.75 S = 2/3 S = 0.666..66 So the probability of the first head coming up in an odd number of tosses is 2/3, or 66.6%

Final answer:

The probability that the first head comes up in an odd number of tosses can be determined using geometric probability.

Explanation:

When tossing a coin repeatedly until we get a head, the probability that the first head comes up in an odd number of tosses can be determined using geometric probability. Since the probability of getting a head in one toss is 0.5, the probability of getting a head in an odd number of tosses (one, three, five, etc.) can be calculated using the formula:

P(odd number of tosses) = P(tail) * P(tail) * P(tail) * ... * P(head)

The number of terms in the product is determined by the number of tosses required to get the first head. For example, if it takes 3 tosses to get the first head, the formula becomes:

P(odd number of tosses) = P(tail) * P(tail) * P(head)

Since the probability of getting a tail is 0.5 and the probability of getting a head is also 0.5, the formula simplifies to:

P(odd number of tosses) = 0.5 * 0.5 * 0.5 * ... * 0.5 = (0.5)^n

Where 'n' is the number of tosses required to get the first head.

What number should I multiply 1 1/4 by to get 7/12

Answers

Let's take our given information and transform it into numbers. We will let x equal the "mystery" number we need to find. Here is our equation:
[tex]1 \frac{1}{4} x= \frac{7}{12} [/tex]
Now, all we need to do is convert the mixed fraction into an improper fraction:
[tex] \frac{5}{4} x= \frac{7}{12}[/tex]
Now, just multiply the reciprocal of 5/4 with 7/12, giving us:
[tex] x=\frac{4}{5}* \frac{7}{12} [/tex]
Finally, just straight up multiply to get an answer of x = 28/60, which can be simplified down to x = 7/15. Therefore, the number you have to multiply 1 1/4 to get 7/12 is 7/15. Hope this helped!

1 and 1/4 is the same as 5/4 so essentially we are asking what do we multiple 5/4 by to get 7/12. Try to keep things as fractions initially to see if there is a fractional answer with whole numbers.

Let x represent the number:
x . 5/4 = 7/12
i.e. 5x/4 = 7/12
We want to get x on it's own so multiply both sides of equation by 4
5x = 4 . (7/12) = 28/12
now divide both sides by 5 to get x on its own
x = (28/12) / 5
This does not equate to a whole number fraction as 28 and 12 are not divisible by 5. So simply convert to decimal
x = 2.3333 / 5 = 0.46666

Find all values of x (if any) where the tangent line to the graph of the given equation is horizontal. HINT [The tangent line is horizontal when its slope is zero.] (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list.) y = −9x2 − 2x

Answers

By "y = −9x2 − 2x" I assume you meant y = −9x^2 − 2x (the "^" symbol represents exponentiation).

Let's find the first derivative of y with respect to x: dy/dx = -18x - 2. This is equivalent to the slope of the tangent line to the (parabolic) curve. Now let this derivative (slope) = 0 and solve for the critical value: -18x - 2 = 0, or
-18x = 2. Solving for x, x = -2/18, or x = -1/9.

When x = -1/9, y = -9(-1/9)^2 - 2(-1/9). This simplifies to y = -9/9 + 2/9, or
y = -7/9.

The only point at which the tangent to the curve is horiz. is (-1/9,-7/9).

The tangent line is the point that touches a graph at a point.

The value of x at the tangent line to the graph of [tex]\mathbf{y=-9x^2 - 2x}[/tex] is [tex]\mathbf{x = -\frac 19 }[/tex]

The function is given as:

[tex]\mathbf{y=-9x^2 - 2x}[/tex]

Differentiate both sides with respect to x

[tex]\mathbf{y' =-18x - 2}[/tex]

Set the above equation to 0, to calculate the value of x

[tex]\mathbf{-18x - 2 = 0}[/tex]

Collect like terms

[tex]\mathbf{-18x = 2 }[/tex]

Divide both sides by -18

[tex]\mathbf{x = -\frac 19 }[/tex]

Hence, the value of x when at tangent line to the graph of [tex]\mathbf{y=-9x^2 - 2x}[/tex] is [tex]\mathbf{x = -\frac 19 }[/tex]

Answers

First, you take 13,300 and divides it by 100, which will gives you 133, then take 2.74 and multiply it by 133, and the answer is B, which is 364,42

Answer:

The monthly payment is $364.42

B is correct

Step-by-step explanation:

The monthly payment on $13,300 financed at 7.9 percent for 4 years.

If the monthly payment per $100 is $2.74

Financed amount = $13,300

We are given monthly payment for $100 is $2.74

It means we pay $2.74 for $100.

Now we find how many number of $100 in $13,300

Number of $100 in $13,300 [tex]=\dfrac{13300}{100} = 133[/tex]

133 number of hundred in $13,300

For each $100 monthly payment = $2.74

For 133 payment = 133 x 2.74

Monthly Payment for $13,300 finance = $364.42

Hence, The monthly payment is $364.42

Find the length and width of a rectangle when the width is 4ft. Shorter than the length. The perimeter of the rectangle is greater than 72ft.

Answers

length- 38 ft
width= 34

There are 365,493 blue pens in a warehouse and 549384 black pens how many pens are there in all

Answers

365,493 + 549,384 = 914,877

To find the answer you add the numbers together to find the sum.
365,493+549,384

Your answer would be 366,042.384

I hope this helps!

f+0.2=−3 what does f equal

Answers

f + 0.2 =-3

f = -3 -0.2

f = -3.2

I believe the answer is -2.8 because if you add -3+0.2 you will get -2.8. Hope I helped!

George has $49 which he decides to spend on x and y. commodity x costs $5 per unit and commodity y costs $11 per unit. he has the utility function u(x, y) = 3x 2 + 6y 2 and he can purchase fractional units of x and y. george will choose

Answers

We are given the equations:

5 x + 11 y = 49 --> eqtn 1

u = 3 x^2 + 6 y^2 --> eqtn 2

Rewrite eqtn 1 explicit to y:

11 y = 49 – 5 x

y = (49 – 5x) / 11 --> eqtn 3

Substitute eqtn 3 to eqtn 2:

u = 3 x^2 + 6 [(49 – 5x) / 11]^2

u = 3 x^2 + 6 [(2401 – 490 x + 25 x^2) / 121]

u = 3 x^2 + 14406/121 – 2940x/121 + 150x^2/121

u = 4.24 x^2 – 24.3 x + 119.06

Derive then set du/dx = 0 to get the maxima:

du/dx = 8.48 x – 24.3 = 0

solving for x:

8.48 x = 24.3

x = 2.87

so y is:

y = (49 – 5x) / 11 = (49 – 5*2.87) / 11

y = 3.15

Answer:

George will choose some of each commodity but more y than x.

Charlie has 5 times as many stamps as Ryan. They have 1,608 stamps in all. How many more stamps does CHarlie have than Ryan?

Answers

Charlie-5x Charlie has 268*5=1340
Ryan-x 1340+268=1608

5x+x=1608 1340-268=1072
6x=1608
x=268 Charlie has 1072 more stamps then Ryan

Ryan has 268 stamps

The cost CC (in dollars) of making nn watches is represented by C=15n+85C=15n+85. How many watches are made when the cost is $385?

Answers

[tex]\bf \stackrel{cost}{C}=15\stackrel{watches}{n}+85\qquad \boxed{C=385}\qquad \stackrel{cost}{385}=15n+85 \\\\\\ 380=15n\implies \cfrac{380}{15}=n\implies \cfrac{76}{3}=n\implies 25\frac{1}{3}=n[/tex]

so, 25 whole watches and hmmmm just the wristband of another maybe.

Which equation can be used to find the answer? A playground with four sides has a perimeter of 52 ft. Three of the sides have lengths of 9 ft, 16 ft, and 19 ft. What is the length of the fourth side? A. s – 9 + 16 + 19 = 52 s =26 26 ft B. s + 9 + 16 + 19 = 52 s = 8 8 ft C. s – 52 = 9 + 16 – 19 s = 58 58 ft D. s – 9 – 16 – 19 = 52 s = 96 96 ft

Answers

What we know:
Perimeter=52 ft
Perimeter=s1+s2+s3+s4
s1=9ft
s2=16ft
s3=19ft
s4=s

What we need to find: equation for given information and solution to s4=s

Perimeter=s1+s2+s3+s4
52=9+16+19+s

52=9+16+19+s
52=44+s like terms added
52-44=44-44+s additive inverse
8=s

Solution: B. s + 9 + 16 + 19 = 52 s = 8 8 ft

Option B)s + 9 + 16 + 19 = 52. Solving this gives the fourth side as 8 ft.

To find the length of the fourth side, you need to know the equation that correctly represents the given information. The perimeter of the playground is the sum of all four sides. Therefore, the correct equation to find the fourth side (s) is:

B. s + 9 + 16 + 19 = 52

9 + 16 + 19 = 44.

s + 44 = 52.

s = 52 - 44.

s = 8.

Therefore, the length of the fourth side is 8 ft.

So, the correct option is B. s + 9 + 16 + 19 = 52.

A rectangular garden must have an area of 64 square feet. find the minimum perimeter of the garden.

Answers

A rectangular garden must have an area of 64 square feet then the minimum perimeter of the garden is 32 feet and this can be determined by using the formula of the perimeter of a rectangle.

Given :

A rectangular garden must have an area of 64 square feet.

The area of a rectangle is given by:

[tex]\rm A =l\times w[/tex]

where 'l' is the length of the rectangle and 'w' is the width of the rectangle.

Given that area of the rectangular garden is 64 square feet that is:

64 = lw

[tex]\rm w = \dfrac{64}{l}[/tex] ---- (1)

Now the perimeter of a rectangle is given by:

P = 2(l + w)

Put the value of w in the above equation.

[tex]\rm P = 2 (l + \dfrac{64}{l})[/tex] ---- (2)

For minimum perimeter differentiate the above equation with respect to the length of the garden.

[tex]\rm P' = 2 - \dfrac{128}{l^2}[/tex]

Now, equate the above equation to zero.

[tex]\rm 0 = 2-\dfrac{128}{l^2}[/tex]

[tex]l^2 = 64[/tex]

[tex]l = 8[/tex]

Now put the value of l in equation (2).

[tex]\rm P = 2(8 + \dfrac{64}{8})[/tex]

P = 32 feet.

A rectangular garden must have an area of 64 square feet then the minimum perimeter of the garden is 32 feet.

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Cameron can display his 12 models cars

Answers

I don’t understand your question.

Given point M(0,6),N (5,3), Rc (-7,-5) nd S(-2,-2) determine if MN is congruent to Rs

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) M&({{ 0}}\quad ,&{{ 6}})\quad % (c,d) N&({{ 5}}\quad ,&{{ 3}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ MN=\sqrt{(5-0)^2+(3-6)^2}\implies MN=\sqrt{5^2+(-3)^2} \\\\\\ MN=\sqrt{25+9}\implies \boxed{MN=\sqrt{34}}\\\\ [/tex]

[tex]\bf -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) R&({{-7}}\quad ,&{{ -5}})\quad % (c,d) S&({{ -2}}\quad ,&{{ -2}}) \end{array}\quad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ RS=\sqrt{[-2-(-7)]^2+[-2-(-5)]^2} \\\\\\ RS=\sqrt{(-2+7)^2+(-2+5)^2}\implies RS=\sqrt{5^2+3^2} \\\\\\ RS=\sqrt{25+9}\implies \boxed{RS=\sqrt{34}}[/tex]

well, are they?

What is the probability that Eric rolls an even number or draws an ace from a standard deck of cards?

Answers

Evidently the quesiton is incomplete.

It is logic that the actions are roll a die and draw a card.

The two events are indepent, so the combined probability is the sum of the individual probabiliites.

Probability = number of positive events / number of possible events

Probability of rolling an even number = number of faces with even numbers / total number of numbers.

Probability of rolling an even number = 3 / 6 = 1/2

Probability of drawing an ace = number of aces in the deck of cards / number of cards

Probability of drawing an ace = 4 / 52 = 1 / 13

Combined probability = 1/2 + 1/13 = (13 + 2) / 26 = 15 / 26

Answer: option D. 15 / 26

Johns collection contains US, Indian and British stamos. If the stamps ratios of US to Indian stamps is 5 to 2, and the ratio of Indian stamps to British stamps is 5 to 1, what is the ratio of US to British stamps

Answers

Final answer:

The ratio of US to British stamps is 25 to 2.

Explanation:

To find the ratio of US to British stamps, we need to consider the ratios provided in the question. The ratio of US to Indian stamps is 5 to 2, and the ratio of Indian stamps to British stamps is 5 to 1. We can combine these ratios by multiplying the two ratios together. 5/2 multiplied by 5/1 is equal to 25/2. Therefore, the ratio of US to British stamps is 25 to 2.

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Two planes which are 3540 miles apart fly toward each other. Their speeds differ by 35 mph. If they pass each other in 4 hours, what is the speed of each?

Answers

3540 miles divided by 4 hours is 885, divided by 2 planes is 442.5 mph if their speeds differ by 35 miles per hour, split the difference: 17.5 + 442.5=460 mph for plane A, 442.5-17.5= 425 for plane B. So one is flying at 460 mph and the other at 425 mph

Final answer:

The speed of the slower plane is 425 mph, and the speed of the faster plane is 460 mph, determined by using the concept of relative speed and algebra to solve the given equation.

Explanation:

To solve the problem of two planes flying towards each other, we need to use the concept of relative speed. We know that the two planes are 3540 miles apart and that they pass each other after 4 hours. The speeds of the planes differ by 35 mph. The relative speed of the two planes combined is the distance divided by the time, so we calculate it as follows:

Relative Speed = Total Distance / Time = 3540 miles / 4 hours = 885 mph

So, if we denote the speed of the slower plane as S mph, the speed of the faster plane will be S + 35 mph. Since their combined speed is the relative speed, we can set up the following equation:

S + (S + 35) = 885

From this equation, we need to find the value of S which represents the speed of the slower plane. We can then add 35 to S to find the speed of the faster plane. Here's how it's done step by step:

Combine like terms: 2S + 35 = 885Subtract 35 from both sides: 2S = 850Divide by 2 to solve for S: S = 425 mphAdd 35 to S to find the speed of the faster plane: 425 + 35 = 460 mph

Therefore, the speed of the slower plane is 425 mph and the speed of the faster plane is 460 mph.

A Petri dish contains 100 bacteria cells. The number of cells increases 5% every minute. How long will it take for the number of cells in the dish to reach 2000? Use logarithms to solve.

Answers

Using logarithm, the following equation will apply:
Y = P * [1 + z]^x
Where Y = 2000
P = 100
z = 5% = 0.05
x is the quantity we are calculating for
The equation becomes
2000 = 100 * [1+ 0.05]^x
Dividing both side by 100, we have
20 = 10 * [ 1 + 0.05]^x
Taking the log of both sides, we have
Log 20 = Log [1 + 0.05]^x
log 20 = x * log 1.05
x = log 20/ log 1.05 = 61.40
Thus, it will takes 61.40 minutes for the number of cells in the petri dish to reach 2000.

If seven integers are selected from the first 12 negative integers, how many pairs of these integers will have a sum of −13?

Answers

Answer:

At least 1, possibly as many as 3.

Step-by-step explanation:

There are 6 pairs of integers among those from -1 to -12 that will sum to -13. If you choose 7 integers, you may only choose one pair, or you may choose as many as three pairs.

One to three pairs will sum to -13.

If an article costs a store $7.45 and if it sells the article for $9.95, what percentage (to the nearest tenth) markup is it using?

Answers

subtract to find the difference:

9.95 - 7.45 = 2.50

divide 2.50 by cost price to get mark up percentage

2.50 / 7.45= 0.3355

= 33.6 percent to the nearest tenth

Answer:

Markup Percentage is 33.56 %

Step-by-step explanation:

Given: Cost of an article = $ 7.45

Selling price of the article = $ 9.95.

To find: Markup percentage or profit percentage

Clearly Selling price is greater we have profit in this case.

Profit amount = 9.95 - 7.45 = $ 2.50

Profit percentage = [tex]\frac{2.50}{7.45}\times100=33.5570469799=33.56[/tex] %

Therefore, Markup Percentage is 33.56 %

What is the value of r, the part of the job that Marina can complete in 1 hour? 0.1 0.4 0.5 0.6

Answers

so, Katherine can do 0.1 of the job per hour. (if she needs 10 hours for the job, each hour she can do the whole divided by the time, so 1/10, which is 0.1)

if in two hours she and Marina can be done, then Marina will do 1(the whole job)-2/10 (twice as much as she can do in an hour)=0.8 of the job. So if Marina does 0.8 of the job in two hours, each hour she will do half of it: 0.4 - and this is the correct answer

Suppose you deposit $5,000 in a savings account that earns 3% annual interest. If you make no other withdrawals or deposits, how many years will it take the account balance to reach at least $6,000? A. 10 years. B. 6 years. C. 7 years. D. 4 years

Answers

Which point on the x-axis lies on the line that passes through point P and is perpendicular to line MN?

(0, 1)
(0, 4)
(1, 0)
(4, 0)

Answers

the answer is C. (1,0)

1. Points M and N have coordinates (-4,0) and (4,2), respectively.

Then vector [tex]\overrightarrow{MN}=(4-(-4),2-0)=(8,2)[/tex] is perpendicular to the neede line.

2. Write the equation of line that passes through the point P(2,-4) and is perpendicular to vector [tex]\overrightarrow{MN}=(8,2):[/tex]

[tex]8(x-2)+2(y+4)=0,\\8x-16+2y+8=0,\\8x+2y-8=0,\\4x+y-4=0.[/tex]

3. Find the point on x-axis, that lies on the perpendicular line.

When y=0, then 4x-4=0, x=1 and point (1,0) lies on perpendicular line.

Answer: correct choice is C.

A cylindrical shaped vase has the radius of 3cm and a height of 18cm. how much water is needed to fill the vase 3/4 of the way?

Answers

Answer:

Step-by-step explanation:

To fill the entire vase:

pi(3)^2(18)= 508.9 cubic centimeters

To fill vase 3/4 of the way:

3/4= .75

So then you take what it takes to fill the vase (508.9) and multiply that by .75 which equals 381.70 cubic centimeters.

3/4 of the volume of water needed to fill the vase is 162π cm^3.

To find how much water is needed to fill the vase 3/4 of the way, we first need to calculate the volume of the vase and then determine 3/4 of that volume.

The formula to calculate the volume of a cylinder is:

[tex]Volume = \pi * radius^2 * height[/tex]

Given:

Radius (r) = 3 cm

Height (h) = 18 cm

Volume of the entire vase:

[tex]Volume = \pi * (3 cm)^2 * 18 cm\\Volume = \pi* 9 cm^2 * 18 cm\\Volume = 162\pi cm^3[/tex]

Now, to find 3/4 of the volume, multiply the total volume by 3/4:

[tex]3/4 * 162\pi cm^3 = 3 * 54\pi cm^3 = 162\pi cm^3[/tex]

So, 3/4 of the volume of water needed to fill the vase is 162π cm^3.

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10+6 has the same sum as 7+

Answers

10+6=16
7+9=16
Therefore, the mystery number is 9.

A student correctly answers 15 of the first 20 questions on an examination.

Answers

I imagine you're being asked to predict the success rate in answering questions AFTER the 20th has been answered. 15/20 represents a success rate of 0.75. It's reasonable to use 0.75 as the probability of success on the 21st question and beyond.

The sum of two positive numbers is 12. what two numbers will maximize the product g

Answers

Given two numbers x and y such that:

x + y = 12 ... (1)

two numbers will maximize the product g

from equation (1)

y = 12 - x

Using this value of y, we represent xy as

xy = f(x)= x(12 - x)

f(x) = 12x - x^2

Differentiating the above function:

f'(x) = 12 - 2x

Maximum value of f(x) occurs at point for which f'(x) = 0.

Equating f'(x) to 0 we get:

12 - 2x = 0

2x = 12

> x = 12/2 = 6

Substituting this value of x in equation (2):

y = 12 - 6 = 6

Therefore, value of xy is maximum when:

x = 6 and y = 6

The maximum value of xy = 6*6 = 36

The two numbers that sum up to 12 and maximize the product are 6 and 6.

Let's denote the two numbers by x and y. We know that x + y = 12, and we want to maximize the product P = xy.

First, express y in terms of x,

y = 12 - x

P = x(12 - x)
= 12x - x²

To find the maximum value of P, we can take the derivative of P with respect to x and set it to zero,

dP/dx = 12 - 2x

Set dP/dx to 0: 12 - 2x = 0

x = 6

Since x + y = 12, if x = 6, then y = 12 - 6 = 6.

The two numbers are 6 and 6.
This combination will maximize the product, which is 6 * 6 = 36.

In conclusion, the two numbers that add up to 12 and maximize their product are both 6.

50% of all the cakes jenny baked were party cakes, 1/5 were fruit cakes and the remainder were sponge cakes. What percentage of cakes were sponge cakes?

Answers

So basically you want to find the total percentage of cakes that weren't sponge cakes first.

You already have the 50% of party cakes. For the 1/5 percent of fruit cakes, you can multiply it by 20/20, to get 20/100, and then just take the 20 to get 20% that were fruit cakes.

Now you can just add the percentages together.

50% + 20% = 70%

So now you know 70% weren't sponge cakes, out of 100%.

So here you can just subtract 70% from 100% to figure out the remaining part of 100%, which must be sponge cakes.

100% - 70% = 30%

So 30% of the cakes were sponge cakes.

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