A family has a monthly budget of $2,400. How much money is spent on each category? 44% is spent on housing. 23% is spent on food. 6% is spent on clothing. 17% is spent on transportation. The rest is put into savings.

The problem is solved by using calculus to find the maximum of the area function for a rectangle. The dimensions that yield maximum area with 24 yards of fencing are a length of 6 yards and a width of 12 yards, resulting in an area of 72 square yards.

The problem involves maximizing the area of a rectangle with a fixed perimeter. Let's define the length of the rectangle as x and the width as y. Since you have 24 yards of fencing and you need to enclose three sides of the rectangle, the perimeter equation becomes 2x + y = 24, which can be rearranged as y = 24 - 2x.

The area of the rectangle can be represented by the equation A = xy, and substituting the y value from our perimeter equation, we get A = x(24 - 2x). To maximize this area, we take the derivative of A with respect to x and set it equal to zero, yielding the equation 24 - 4x = 0, or x = 6. Substituting x = 6 back into the y equation gives y = 12.

Therefore, the dimensions that maximize the area of the deck are a length of 6 yards and a width of 12 yards. Substituting these values back into the area equation gives a maximum area of 72 square yards.

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Answer:

2

Step-by-step explanation:

Terms are products separated by +'s and −'s.  Here, there are 2 terms:

2 tan(1/t) / (1/t)

sec²(1/t)

Answer:

18 fastballs

Step-by-step explanation:

Let x represent each throw

fastball : curve ball = 3:2

For fastball we have 3x while for curve ball we have 2x

If Rick makes a relief appearance of 30 pitches with the same ratio,

3x + 2x = 30

5x = 30

x = 30/5

x = 6

fastball, 3x= 3*6

= 18

curveball = 2x = 2*6

= 12

Rick will throw 18 fast balls

Answer:

running distance =   78,18 m

swimmingdistance  =  92m

Step-by-step explanation:

Ann has to run a distance 100 - x    and swim  √ (50)² + x²

at speed of 5 m/sec   and 2 m/sec

As distance  = v*t       t  = d/v

Then running she will spend time doing d = ( 100-x)/5    

and   √[(50)² + x² ] / 2   swimming

Therefore total time of biathlon

t(x)  =  ( 100 - x )/5    +  √[(50)² + x² ] / 2

Taking derivatives both sides of the equation we get

t´(x)  =  - 1/5  + [1/2 ( 2x)*2] / 4√[(50)² + x²]

t´(x)  =  - 1/5  + 2x / 4√[(50)² + x²]      t´(x)  =  - 1/5  + x/2√(50)² + x²

t´(x)  = 0           - 1/5  + x/2√(50)² + x²  = 0

  - 2√[(50)²+  x²]   +  5x     =  0

  - 2√(50)²+  x² ) =  -5x

       √(50)²+  x²   = 5/2 *x

squared

        (50)²  +  x²   = 25/4 x²

             2500 - 21/4 x²  =  0

                           x²  =  2500*4/21

 x  =  21,8 m

Therefore she has to run  100 - 21,82  = 78,18 m

And swim    √(50)² + (78,18)²   =  92m

The question pertains to Physics and involves calculating the optimal path in a swim-and-run biathlon to minimize total time, which would typically involve physics and calculus. However, the scenario is incomplete and lacks necessary information for a precise solution.

The subject of this question is Physics, as it involves concepts of speed, velocity, and optimization of travel paths in a biathlon, which includes both swimming and running. To answer the question on the optimal path Ann should take in the swim-and-run biathlon, we would use principles of physics and calculus to find the path that minimizes the total time. The calculation would involve deriving the functional relationship between swimming and running speeds, and the distances covered in each stage, then determining the point at which Ann should exit the water to reach the end point in the shortest total time. However, since the problem in the question is incomplete and requires additional information, such as the current of the river or whether Ann swims at a constant speed relative to the water, we cannot solve it without making assumptions that may be incorrect.

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Answer: Berma is 5 years old

Rinna is 38 years old

Erwin is 37 years old

Step-by-step explanation:

Let x represent Berma's age

Let y represent Rinna's age

Let z represent Erwin's age

Since the sum of their ages is 80,

x + y + z = 80 - - - - - - -1

Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that

y +2 = [ (z+2) + 2(x+2) ] - 13

y +2 = z + 2 + 2x + 4 - 13

2x - y + z = 13 + 2 - 4 -2

2x - y + z = 9 - - - - - - -2

Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that

15(x - 3) = (y - 3) - 5

15x - 45 = y - 3 - 5

15x - y = - 8 + 45

15x - y = 37 - - - - - - - -3

From equation 3, y = 15x - 37

Substituting y = 15x - 37 into equation 1 and equation 2, it becomes

x + 15x - 37 + z = 80

16x + z = 80 + 37 = 117 - - - - - - 4

2x - 15x + 37 + z = 9

-13x + 2 = -28 - - - - - - - - -5

subtracting equation 5 from equation 4,

29x = 145

x = 145/29 = 5

y = 15x - 37

y = 15×5 -37

y = 38

Substituting x= 5 and y = 38 into equation 1, it becomes

5 + 38 + z = 80

z = 80 - 43

z = 37

Answer:

Step-by-step explanation:

The triangle is a right angle triangle. This is because one of its angles is 90 degrees.

Let us determine x

Taking 47 degrees as the reference angle,

x = adjacent side

11 = hypotenuse

Applying trigonometric ratio,

Cos # = adjacent side / hypotenuse

# = 47 degrees

Cos 47 = x/11

x = 11cos47

x = 11 × 0.6820

x = 7.502

Let us determine y

Taking 47 degrees as the reference angle,

y = opposite side

11 = hypotenuse

Applying trigonometric ratio,

Sin # = opposite side / hypotenuse

# = 47 degrees

Sin 47 = y/11

x = 11Sin47

x = 11 × 0.7314

x = 8.0454

Answer:

0.00597

Step-by-step explanation:

Given,

Total number of cards = 52,

In which flush cards = 20,

Also, the number of spade flush cards = 5,

Since,

[tex]\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}[/tex]

Thus, the probability of a hand containing a spade flush, if each player has 5 cards

[tex]=\frac{\text{Ways of selecting a spade flush card}}{\text{Total ways of selecting five cards}}[/tex]

[tex]=\frac{^{20}C_5}{^{52}C_5}[/tex]

[tex]=\frac{\frac{20!}{5!15!}}{\frac{52!}{5!47!}}[/tex]

[tex]=\frac{15504}{2598960}[/tex]

= 0.00597  

Answer:

2x^2 = 28 - x

-28+x -28+x

2x^2 + x - 28 = 0

ac=-56

m+p=-7,8

(2x-7)(2x+8)=0

2x-7+7=0+7

2x/2=7/2

x=3.5

2x+8-8=0-8

2x/2=-8/2

x= -4

Step-by-step explanation:

x=-4 or 3.5

Final answer:

The quadratic equation 2x² = 28 - x is solved by rearranging it to 2x² + x - 28 = 0, factoring by grouping, and finding the solutions x = 4 and x = -3.5. The solutions are verified by substituting them back into the original equation.

Explanation:

To solve the equation by factoring, we first need to rearrange the equation to set it to zero. The original equation given is 2x² = 28 - x. Moving all terms to one side gives us 2x² + x - 28 = 0. We can solve this quadratic equation by factoring:

First, look for two numbers that multiply to give ac (in this case, 2 * -28 = -56) and add to give b (in this case, 1).

These two numbers are 7 and -8 since 7 * -8 = -56 and 7 + (-8) = -1.

Rewrite the middle term using these two numbers: 2x² + 7x - 8x - 28 = 0.

Factor by grouping: (2x² + 7x) - (8x + 28) = 0.

Factor out the common terms: x(2x + 7) - 4(2x + 7) = 0.

Factor out the common binomial: (x - 4)(2x + 7) = 0.

Solving each factor separately gives us: x = 4 and x = -7/2 or -3.5.

The solutions we find are x = 4 and x = -3.5. To check if these solutions are correct, we can substitute them back into the original equation and verify if they satisfy the equation, thereby confirming they are correct.

Answer:

7

Step-by-step explanation:

Answer:

its 14 signs

Step-by-step explanation:

Answer: z=1.9065

Step-by-step explanation:

As per given , we have

[tex]H_0: p=0.10\\\\ H_a: p<0.10[/tex]

Sample size : n= 150

No. of potatoes sampled are found to have major defects = 8

The sample proportion of potatoes sampled are found to have major defects :

[tex]\hat{p}=\dfrac{8}{150}=0.0533[/tex]

The test statistic for population proportion is given by :-

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\ [/tex] , where p=population proportion.

n= sample size.

[tex]\hat{p}[/tex] = sample proportion.

[tex]z=\dfrac{0.0533-0.10}{\sqrt{\dfrac{0.10\times0.90}{150}}}\\\\=\dfrac{-0.0467}{0.02449}\\\\=-1.90651951647\approx1.9065[/tex]

Hence, the value of the large-sample z test statistic is z=1.9065 .

Answer:

√56/8

Step-by-step explanation:

Let the number be x

f(x) = 8x + 7(1/x)

f(x) = 8x + 7/x

Differentiate f(x) with respect to x

f'(x) = 8x - 7/x = 0

8 - 7/x^2 = 0

(8x^2 - 7)/2 = 0

8x^2 - 7 = 0

8x^2 = 7

x^2 = 7/8

x = √7/8

x = √7 /√8

x = (√7/√8)(√8/√8)

x = (√7*√8) / √8*√8)

x = √56/8

Answer:

Remainder = 64

Step-by-step explanation:

Given equation,

[tex]x^4+3x^3-6x^2-12x-8[/tex]

Remainder theorem says a polynomial can be reset in terms of its divisor (a) by evaluating the polynomial at x=a

Plug x=3,

[tex]=3^4+3(3)^3-6(3)^2-12(3)-8\\=81+81-54-36-8\\=162-54-36-8\\=64[/tex]

Thus the remainder is 64 at x=3 ,using polynomial remainder theorem.

Answer:

[tex]P(A\ or\ B)=\frac{7}{9}[/tex]

Step-by-step explanation:

We need to use the formula to calculate the probability of (A or B) where  

A=Probability a student likes pepperoni

B=Probability a student likes olive

A and B =Probability a student likes both toppings in a pizza

A or B =Probability a student likes pepperoni or olive (and maybe both), a non-exclusive or

The formula is

[tex]P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)[/tex]

Since 6 students like pepperoni out of 9:

[tex]P(A) = \frac{6}{9}[/tex]

Since 4 students like olive out of 9:

[tex]P(B) = \frac{4}{9}[/tex]

Since 3 students like both toppings out of 9

[tex]P(A\ and\ B) = \frac{3}{9}[/tex]

Then we have

[tex]P(A\ or\ B)=\frac{6}{9}+\frac{4}{9}-\frac{3}{9}[/tex]

[tex]P(A\ or\ B)=\frac{7}{9}[/tex]

Answer:

  9.6 units

Step-by-step explanation:

The area of the parallelogram is the product of the base length and distance between parallel sides, either way you figure it.

  16 × 6 = area = 10 × h

  96 = 10h

  h = 96/10 = 9.6 . . . . units

Answer:

first, second, and fourth are correct

Step-by-step explanation:

2(-4) + 0 = -8; this is correct because -8 + 0 = -8

(-4) - 0 = -4; this is correct because -4 - 0 = -4

We know that they are both true, so the fourth choice is true as well.

Statements first, second, and fourth are true about the ordered pair (−4, 0) and the system of equations, 2x+y=−8 and x−y=−4.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

2x+y=−8

x−y=−4

The correct statements for the ordered pair (−4, 0) are,

Because it makes the first equation true, the ordered pair (4, 0) is a solution to the first equation.

⇒2(-4) + 0 = -8

⇒-8 + 0 = -8

Because it makes the second equation true, the ordered pair (4, 0) is a solution to the second equation.

⇒(-4) - 0 = -4

⇒-4 - 0 = -4

The ordered pair (4, 0) makes both equations true, making it a solution to the problem.

Thus, statements first, second, and fourth are true about the ordered pair (−4, 0) and the system of equations, 2x+y=−8 and x−y=−4.

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Answer:

option A and C, (-0.7, 0.5) and (0.7, 0.5)

Step-by-step explanation:

The two equations are equal means, the points at which the  two graphs meet.

In that case the x and y coordinates satisfy both the graphs.

let the coordinates at the intersection point be (a,b).

Inserting in first equation,

[tex]b = -a^{2} + 1[/tex]

Inserting in second equation,

[tex]b = a^{2}[/tex]

Inserting value of b from second to first equation, we get

[tex]b = -b + 1[/tex]

[tex]b = \frac{1}{2} = 0.5[/tex]

Now inserting the value of b second equation, we get

[tex]\frac{1}{2} = x^{2}[/tex]

[tex]x = \sqrt{\frac{1}{2} } = +\frac{1}{1.414} or -\frac{1}{1.414}  = +0.7  or  -0.7[/tex]

Thus points are, (-0.7, 0.5) and (0.7, 0.5)

Answer:0.472

Step-by-step explanation:

Given

there are 36 slots with 0 and 00 as two slots which are neither odd nor even

i.e. there are 34 remaining slots numbered 1 to 34

there are 17 odd terms and 17 even terms

thus Probability of getting a odd number is [tex]=\frac{17}{36}=0.472[/tex]

Answer:

P(odd#'s) = number of odd numbers/total number of outcomes = 18/38 = 9/19

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total cost of producing a cylindrical can with radius r and height h will be ...

  cost = (lateral area)×(side cost) +(end area)×(end cost) +(seam length)×(seam cost)

__

The lateral area (LA) is ...

  LA = 2πrh

Since the volume of the can is fixed, we can write the height in terms of the radius using the volume formula.

  V = πr²h

  h = V/(πr²)

Then the lateral area is ...

  LA = 2πr(V/(πr²)) = 2V/r = 2·500/r = 1000/r

__

The end area (EA) is twice the area of a circle of radius r:

  EA = 2×(πr²) = 2πr²

__

The seam length (SL) is twice the circumference of the end:

  SL = 2×(2πr) = 4πr

__

So, the total cost in cents of producing the can, in terms of its radius, is ...

  cost = (1000/r)(0.01) +(2πr²)(.012) +(4πr)(0.015)

We can find the minimum by setting the derivative to zero.

  d(cost)/dr = -10/r² +0.048πr +.06π = 0

Multiplying by r² gives the cubic ...

  0.048πr³ +0.06πr² -10 = 0

  r³ +1.25r² -(625/(3π)) = 0 . . . . . . divide by .048π

This can be solved graphically, or using a spreadsheet to find the value of r to be about 3.671 cm. The corresponding value of h is ...

  h = 500/(π·3.671²) ≈ 11.810 . . . cm

The minimum-cost can will have a radius of about 3.671 cm and a height of about 11.810 cm.

_____

A graphing calculator can find the minimum of the cost function without having to take derivatives and solve a cubic.

Answer:

It is rotated by 72 degrees.

Step-by-step explanation:

        when u connect all the corners of it to the middle of the polygon, they       will meet at a point i.e, CENTER.

Because,

[tex]\frac{360}{60} = 6[/tex]

[tex]12*6 = 72[/tex]

( For every minute, it will be rotated by 6 degrees.

so, for 12 minutes it should be rotated by 12 times 6 ( 12*6) = 72 degrees)

Answer:

b(x)=24(1/2)x

Step-by-step explanation:

The situation can be modeled by the exponential function will be y = 24 (0.5)ˣ.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

There are 24 ball groups contending in a competition. After each round around 50% of the groups is dispensed with.

Then the value of the b will be 1/2 and the value of the variable 'a' will be 24. Then the exponential equation is given as,

y = 24 (1/2)ˣ

y = 24 (0.5)ˣ

The situation can be modeled by the exponential function will be y = 24 (0.5)ˣ.

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Answer:

  90 feet

Step-by-step explanation:

The perimeter is the sum of the side lengths of the enclosure. The length is given as 80 ft, but only one side that long counts as part of the 260 ft of fence. So, we have ...

  260 ft = 2×W + L = 2×W + 80 ft . . . . . length of fence for 3 sides

  180 ft = 2×W . . . . . . subtract 80

  90 ft = W . . . . . . . . . divide by 2

The width of the enclosure is 90 feet.

Final answer:

To find the width of the farmer's rectangular enclosure, we subtract the length of the barn (80 ft) from the total amount of fencing available (260 ft) to get the length available for the other three sides. Dividing this by two (because there are two widths), we find that the width of the enclosure will be 90 feet.

Explanation:

The question asks about creating a rectangular enclosure using a fixed length of fencing and a barn as one of the sides. With 260 feet of fencing available and the barn covering one side of 80 feet, the farmer must use the remaining fencing for the other three sides of the rectangle.

To find the width of the rectangular enclosure, we need to subtract the length of the barn side from the total amount of fencing available, and then divide by two (because there are two widths in a rectangle), as follows:

260 ft - 80 ft = 180 ft for both widths, so each width will be

180 ft / 2 = 90 ft.

Therefore, the width of the rectangular enclosure will be 90 feet.

Answer:

D) (0.443, 0.497)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval for a proportion is given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For the 99% confidence interval the value of [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2=0.005[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.

[tex]z_{\alpha/2}=2.58[/tex]

And replacing into the confidence interval formula we got:

[tex]0.47 - 2.58 \sqrt{\frac{0.47(1-0.47)}{2294}}=0.443[/tex]

[tex]0.47 + 2.58 \sqrt{\frac{0.47(1-0.47)}{2294}}=0.497[/tex]

And the 99% confidence interval would be given (0.443;0.497).

We are confident that about 44.3% to 49.7% of registered voters approved of the job Barack Obama was doing as president.

Answer:

  128

Step-by-step explanation:

There are a couple of ways to go at this. One is to use a proportion:

  (10 servings)/(1.25 cups) = (x servings)/(16 cups)

  160/1.25 = x = 128 . . . . . . . multiply by 16 and simplify

1 gallon of milk will make 128 servings.

__

Another way to go at this is to figure out how much milk is used in one serving. It is ...

  1.25 cups/(10 servings) = 0.125 cups/serving = 1/8 cup/serving

Now, you can work with several different conversion factors:

  1 cup = 8 oz

  1 gal = 128 oz

  1 gal = 16 cups

Obviously 1/8 cup is 1 oz. Since there are 128 oz in a gallon, the gallon will make 128 servings.

__

Or, you can divide 16 cups by (1/8 cup/serving) to find the number of servings:

  (16 cups/gal)/(1/8 cup/serving) = 16·8 servings/gal = 128 servings/gal

Answer:

128

Step-by-step explanation:

I can do math yay

Answer:

0.05x

This is equivalent to 5% of the total amount of sales.

Step-by-step explanation:

Previous Weekly pay function for Owen; f (x) = 0.15x +325-------------------- (1)

Current   Weekly pay function for Owen; g(x) = 0.20x +325--------------------(2)

Change in Owen's Salary plan is equation (2) minus equation (1)

g(x) - f(x) = (0.20x+325)-(0.15x+325)

              =  0.05x

The new change in Owen's salary is 5% of the total amount of sales

Answer:

C. Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly.

just passed on edge-nuity

Step-by-step explanation:

Kylie's explanation is incorrect. The simplified expression for (negative 4x + 9) squared is 16x squared - 72x + 81.

Kylie's explanation is incorrect.

The statement that (negative 4x + 9) squared results in a difference of squares is incorrect.

To simplify (negative 4x + 9) squared, we need to multiply the expression by itself. Using the formula (a + b) squared = a squared + 2ab + b squared, we can expand (negative 4x + 9) squared as follows:

(negative 4x + 9) squared = (negative 4x) squared + 2(negative 4x)(9) + (9) squared
= 16x squared - 72x + 81

So, the correct simplification of (negative 4x + 9) squared is 16x squared - 72x + 81, not 16x squared + 81.

Answer:

180000

Step-by-step explanation:

Answer:

Step-by-step explanation:

Whole Circle

The formula for the area of a circle is ...

  A = πr² . . . . . where r is the radius and π is the value given

The radius of the circle is half the diameter, so is 0.4 m. Putting the numbers into the formula, we get ...

  A = (314)(0.4 m)² = 0.5024 m²

Rounding to the nearest tenth, the area is ...

  0.5 m²

__

Area of Sector CTM

As above, the area of the circle is ...

  A = πr² = (3.14)(3 in)² = 28.26 in²

A whole circle has a central angle of 360°. The sector of interest has a central angle of 125°, so its area is the fraction 125/360 of the area of the whole circle.

  sector area = (125/360)(28.26 in²) = 9.8125 in²

Rounding to the nearest tenth, the sector area is ...

  9.8 in²

Answer:

10.54 pounds is right answer

Step-by-step explanation:

bananas 2.26  pounds

Grapes  1.5 pounds

water melon 6.78 pounds

total weight = 10.54 pounds

Answer:

10.54 pounds

Step-by-step explanation:

Answer:

Step-by-step explanation:

It can be helpful to draw a diagram. In the attached diagram, point H represents the harbor, point B represents the position of the boat, and point N represents a point directly north of the harbor and west of the boat.

The bearing N56E means the direction of travel is along a path that is 56° clockwise (toward the east) from north.

__

The mnemonic SOH CAH TOA reminds you of the relationships between the sides of a right triangle. Here, we are given the length of the hypotenuse, and we want to know the lengths of the sides opposite and adjacent to the angle. One of the useful relations is ...

  Sin = Opposite/Hypotenuse

In our diagram, this would be ...

  sin(56°) = BN/BH

We want to find length BN, so we can multiply by BH to get ...

  BN = BH·sin(56°) = 150·0.829038 = 124.4 . . . . miles (east)

__

For the adjacent side, we use the relation ...

  Cos = Adjacent/Hypotenuse

  cos(56°) = HN/HB

  HN = HB·cos(56°) = 150·0.559193 = 83.9 . . . . miles (north)

The boat has traveled 124.4 miles north and 83.9 miles east of the harbor entrance.

Answer:

The ratio is 2 to 3.

Step-by-step explanation:

The jar is comprised of only red and green jelly beans. We are given the number of total beans and the number of red beans. We calculate the number of green beans by doing 800-320 = 480.

The problem is asking for the ratio of red to green jelly beans, which is 320 to 480, or 320/480. Simplified, this is 2/3.

The ratio of red to green jellybeans will be 1/3.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -

A : B ∷ C : D

AND

A x D = B x C

Product of extremes equal to product of means

We have a jar that contains 800 red and green jelly beans. Of those, 320 are red and the rest are green.

Number of red beans = 320

Number of green jelly beans = 800 - 320 = 480

Ratio of red to green jellybeans = 320/480 = 1/3

Therefore, the ratio of red to green jellybeans will be 1/3.

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