Four integers have a mean of 14, a median of 14, a mode of 14 and a range of 4.
Find the four integer.

A rectangular container with a square base, an open top, and a volume of 4,000 cm³. The minimum surface for the container is 1,200 cm².

The result is obtained by using the derivative.

These are the specified parameters:

Volume container is 4,000 cm³.

Let side of square base = a, and height of the container = h, so:

Volume = a × a × h

4,000 = a² h

       h = [tex]\displaystyle \frac{4000}{a^2}[/tex]     ... (1)

Surface area with a square base, an open top is area of a square + 4 times the vertical side.

Surface area (A) = a² + 4ah

Substitute the value of h = [tex]\displaystyle \frac{4000}{a^2}[/tex] into surface area.

A = a² + 4ah

A = a² + 4a ([tex]\displaystyle \frac{4000}{a^2}[/tex])

A = a² + [tex]\displaystyle \frac{16000}{a}[/tex]

So that the surface area is minimal, when the derivative and equate to 0.

A = a² + 16000 a⁻¹

A' = 0

2 a²⁻¹ + (-1) 16000 a⁻¹⁻¹

2a - 16000 a⁻²  = 0

2a - [tex]\displaystyle \frac{16000}{a^2}[/tex] = 0

2a = [tex]\displaystyle \frac{16000}{a^2}[/tex]

2a³ = 16000

 a³ = [tex]\displaystyle \frac{16000}{2}[/tex]

 a³ = 8000

 a = ∛8000

 a = 20

Surface area with a square base, an open top.

Substitute the value of a = 20

A = a² + [tex]\displaystyle \frac{16000}{a}[/tex]

A = 20² + [tex]\displaystyle \frac{16000}{20}[/tex]

A = 400 + 800

A = 1200

The minimum surface for the container is 1,200 cm².

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For the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.

As given in the question,

For the given rectangular playpen,

Perimeter of rectangular playpen is equal to 150 feet .

Area of the rectangular playpen is equal to at least 1,000 squared feet .

Area = length × width

Let x be the length of the rectangular playpen .

Then its width is equal to 1000 / x.

Substitute the value of length and width in perimeter we get,

Perimeter of rectangular playpen = 2 ( length + width )

⇒ 150 = 2 [ x + (1,000/x)]

⇒ 150 / 2 = ( x² + 1,000 ) / x

⇒ x² + 1000 = 75x

⇒ x² -75x + 1,000 =0

Simplify quadratic equation using discriminant we get,

x = [ -( -75) ± √(-75)² - 4(1) (1,000) ] / 2(1)

⇒ x = (  75 ± √5625 - 4000) /2

⇒ x = (75 ± 40.31) / 2

⇒ x = 57.66 or 17.35

Therefore, for the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.

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Answer:

The amount of cholesterol in 11 ounces of lobster is 220 mg

Step-by-step explanation:

The amount of cholesterol in 11 ounces of lobster can be calculated as follows

The first step is to convert all units of measure from ounce to mg

1 gram = 0.0352 ounce

Divide both sides by 0.0352 to get the value of 1 ounce

[tex]\frac{1}{0.0352}[/tex] gram = [tex]\frac{0.0352}{0.0352}[/tex] ounce

28.35 gram = 1 ounce

Since 1 gram equals 1000 milligrams, then multiply the left side by 1000 and change the unit of measure to milligram

28.35 [tex]\times[/tex] 1000 mg = 1 ounce

28350 mg = 1 ounce

Convert 3.6 ounces to milligrams

3.6 ounces = 3.6 [tex]\times[/tex] 28350 mg

3.6 ounces = 102060 mg

Convert 11 ounces to milligrams

11 ounces = 11 [tex]\times[/tex] 28350 mg

11 ounces = 311850 mg

Since there are 72 mg of cholesterol in a 3.6 ounces serving of lobster, then the ratio equation to follow is

[tex]\frac{72}{102060}=\frac{x}{311850}[/tex]

Where x is the amount of cholesterol in 11 ounces of lobster

Multiply both sides by 311850 to isolate x

[tex]\frac{72}{102060}\times 311850=\frac{x}{311850}\times 311850[/tex]

[tex]\frac{22453200}{102060} =x[/tex]

Simplify the left side of the equation

220 = x

Since the value of x is 220, then the amount of cholesterol in  11 ounces of lobster is 220 mg

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[tex]\frac{5}{2}x+\frac{1}{4} +\frac{3}{4} x=\frac{1}{8} \\\\\frac{5}{2}(8)x+\frac{1}{4} (8)+\frac{3}{4}(8) x=\frac{1}{8}(8)\\20x+2+6x=1\\20x+6x=1-2\\26x=-1\\\frac{26x}{26} =\frac{-1}{26} \\x=-\frac{1}{26}[/tex]

Answer:

Where the angle bisectors cross

Where the perpendicular bisectors cross

Part a:  The side of the square is found as 6 cm.

Part b: The side length of the square is found as 10 cm.

For the given dimensions for the question,

Part a: Area of square is same as area of rectangle.

Rectangle area = Length x breath

Rectangle area =  18 x 2

Rectangle area =  32 sq. cm

Now,

Area of square = Rectangle area

Area of square = side²

36 =  side²

side = √36

side = 6 cm.

Thus, the side of the square is found as 6 cm.

Part b: Side length of square.

Rectangle perimeter =  square perimeter

Rectangle perimeter =  2(length + width)

Rectangle perimeter =  2(18 + 2)

Rectangle perimeter =  40

square perimeter = 4 side

40 = 4 side

side = 40/4 = 10 cm.

Thus, the side length of the square is found as 10 cm.

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aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters

this is an arithmetic sequence whose n th term ( explicit formula) is

aₙ = a + (n - 1 )d

where d is the common difference and  a the first term

The given sequence is 12,10,8,6

twelve comma ten comma eight comma six

d=10-12=-2

a=12

Apply in explicit formula

aₙ = 12+ (n - 1 )(-2)

aₙ = 12-2n +2

aₙ = 14- 2n

Hence aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6

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The slope is 6.25, it means that her day pay increases by $6.25 for each computer sold

A general linear equation in the point-slope form is written as:

y = a*x + b

Where y and x are the two variables, a is the slope, and b is the y-intercept.

In this case, the linear equation is:

P(x) = 6.25*x + 75

We know that P(x) represents her pay, and x represents the amount of computers she sold.

Here we can see that the slope is 6.25, it means says how much her pay increases per computer sold.

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Answer:

the amount of birdseed leftover is 32

Step-by-step explanation:

Answer:

-4/-5

Step-by-step explanation:

Gotchu bro

Answer:

4/5 or 0.8

Step-by-step explanation:

may i have the brainiest crown pls

If there are four consecutive odd integers such that five times the second number minus twice the fourth number is the third number subtracted by 252 then the four consecutive integers are -2, -3, -4, -5 (or) -2, -1, 0, 1.

What are consecutive integers?

Whole numbers that follow each other without gaps are known as consecutive integers.

For example, the numbers 15, 16, and 17 are all consecutive integers.

If 'n' is an integer, then the following consecutive integers begin at n, n+1, n+2, n+3, and so on.

Let x be the 1st of the four consecutive integers.

the other three consecutive integers could be

(x + 1) , (x + 2), and (x + 3).

By using the given conditions, we get

From the question,

(x + 1) = (5 * (x + 2)) - (x + 3)

Expand, and subtract like terms:

x + 1 = 5x + 10 - x - 3.

Simplifying the above expression, we get

x + 1 = 4x + 7.

3x = -6.

x = -2.

Hence, the four consecutive integers are -2, -3, -4, -5 (or) -2, -1, 0, 1.

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one example of terminating decimal and one repeating decimal between -1/2and -1/3

terminating decimal = -2/5

repeating decimal = -3/11

A decimal with an end digit is referred to as a terminating decimal. It is a decimal with a limited number of digits.

examples of terminating decimal are

When a number's digits are periodic and its indefinitely repeated portion is not zero, the representation of that number as a decimal is said to be repeating or recurring.

Examples of a repeating decimal are

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Answer:

156

Step-by-step explanation:

36*3=108

8*-6=-48

108-(-48)=156

The solution of the expression 36(3) - 8(-6) will be 156.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 36(3) - 8(-6). the expression will be solved as below,

E = 36(3) - 8(-6)

E = 108 - ( -48 )

E = 108 + 48

E = 156

Hence, the solution will be 156.

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Answer:

Explanation:

Selling price:$75

Profit made:25%

Cost price:100/100-25

100/75

1.3333

Situations a and c can represent a proportional relationship. Options a and c are correct.

It is defined as the relationship between two quantities as one quantity increases the other quantity also increases and vice versa.

The following situations are found to represent proportionality using the concept of proportionality:

A) The total amount a babysitter makes who earns $10 an hour for babysitting r hours.

C) The total amount Andrew saves when he saves $24 a week for w weeks.

Thus, situations a and c can represent a proportional relationship. Options a and c are correct.

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Answer:

26

Step-by-step explanation:

Supplemental means that the two angles together equal 180

124 + 2x + 4 = 180  Combine like terms

128 + 2x = 180  Subtract 128 from both sides of the equation

2x = 52  Divide both sides by 2

x = 26

Answer:

n = 8

Step-by-step explanation:

to solve this equation you must first isolate the variable

that is n

so first

add 2n to both sides to get rid of n on one of the sides

-4n + 2n + 14 = -2 - 2n + 2n

-2n + 14 = -2

now subtract 14 to both sides to isolate n

-2n + 14 - 14 = -2 - 14

-2n = -16

now divide everything by -2 to isolate n completely

(-2n)/(-2) = (-16)/(-2)

n = 8

that is your answer

Answer:

[tex]\boxed{\sf n=8}[/tex]

Step-by-step explanation:

[tex]\sf -4n+14=-2-2n[/tex]

Subtract 14 from both sides:-

[tex]\sf -4n+14-14=-2-2n-14[/tex]

Simplify:-

[tex]\sf -4n=-2n-16[/tex]

Add 2n to both sides:-

[tex]\sf -4n+2n=-2n-16+2n[/tex]

Simplify:-

[tex]\sf -2n=-16[/tex]

Divide both sides by -2:-

[tex]\sf \cfrac{-2n}{-2}=\cfrac{-16}{-2}[/tex]

Simplify:-

[tex]\sf n=8[/tex]

____________________

Hope this helps!

Have a great day!

Answer:

- 5/2 (z + 2)

Step-by-step explanation:

Distribute

- 7/2 z - 2 + z - 3

Subtract the numbers

- 7/2 z - 5 + z

Combine like terms

- 5/2 z - 5

Common factor

- 5/2 (z + 2)

Answer: y=9/7

Step-by-step explanation:

Percentage discount is 11.36%

Given in question,

Marked price = MP = $2200

Selling price = SP = $1950

Discount = D

               = MP - SP

               = 2200 - 1950

               = 250

Discount % = (D/MP)*100

                   = (250/2200)*100

                   = 250/22

                   = 11.36

Hence, discount percent is 11.36%.

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Answer:1/9 or decimal form it’s ≅ 0.111111

The 95% Confidence Interval for the mean number of defects per screen for all screens produced by this manufacturer is (1.447646, 2.352354)

Given Data:

3, 5, 0, 3, 5, 2, 5, 1, 0, 0, 0, 4, 2, 1, 0, 5, 1, 0, 1, 1, 0, 2, 0, 2, 1, 0, 2, 4, 4, 3, 2,

2, 3, 2, 1, 2, 1, 1, 4, 1, 1, 6, 0, 3, 1, 0, 2, 2, 1, 3

We calculate sample mean and standard deviation from given data.

Sample Mean, a = 2 (2) _ 95

-50

= 1.9

Sample Variance, $2 _ _(2 -x)2 _130.5

= 2.663265

n - 1

49

Sample std dev, s = V82 = v2.663265 ~ 1.631951

95% CI for u using Normal dist

Sample Mean = T = 1.9

Since sample size is large, sample standard deviation can be taken as an approx-

Limation of population standard deviation.

Population Standard deviation = o ~ 1.631951

Sample Size = n = 50

Significance level = 0 = 1- Confidence = 1 - 0.95 = 0.05

The Critical Value = za/2 = 20.025 = 1.96 (From z table)

Critical Values , 1za/2 = 41.96

Margin of Error = E = za/2 X -= 1.96 x 1.631951

0.452354

V50

Margin of Error, E = 0.

Limits of 95% confidence interval are given by:

Lower limit = I - E = 1.9 -0.452354 ~ 1.447646 ~ 1.448

Upper limit = I + E = 1.9 + 0.452354 ~ 2.352354 ~ 2.352

95% confidence interval is: T + E = 1.9 4 0.452354

= (1.447646, 2.352354)

95% CI using normal dist: (1.448 ) < < (2.352)

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Number 1

Step-by-step explanation:

Number 1 it is a good answer

Form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.

As given in the question,

Probability distribution established by baker :

    x :       1               2                3              4

P(x) :       0.10        0.30         0.40          0.20

As it is give that number of batches made by baker to sell muffins .

For selling 1 batch x = 1.

For selling 2 batch x = 2.

For selling 3batch x = 3.

For selling 4 batch x = 4

Probability of selling exactly one batch by baker is given by when x =1

Probability of x  = 1 is given by :

P( x = 1 )  = 0.10

Therefore, form the given probability distribution, the probability of selling exactly one batch by baker is equal to 0.10.

The complete question is :

A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.10 2 0.30 3 0.40 4 0.20 What is the probability the baker will sell exactly one batch.

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It is nonlinear because linear functions, which correspond to option D on the provided graph, grow or shrink at the same rate.

On the coordinate plane, a straight line can be represented by a linear function. In the coordinate plane, for instance, the linear function denoted by the equation y = 3x - 2 is a straight line. The graph of a linear function is a straight line. The form of a linear function is depicted below. a + bx = y = f (x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

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Choices made by consumer leads to financial irresponsibility are as follow:

As given in the question,

Choices made by consumer leads to financial irresponsibility are as follow:

When a person is spending money just on emotional feeling and buying large gifts for children which is beyond the budget. Due to this habits a person may have to take debt.

When a person is not saving enough money for the time of emergency, it can be a medical emergency then it is financial  irresponsible behavior.

When you are not making any budget and spending money ,it might possible at the end of the month or some time you have to face financial crises.

Don't compare yourself with anyone, this might lead you to take loan or debts which lead your life in facing financial trouble.

Therefore, choices made by consumer leads to financial irresponsibility are as follow:

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Annual nominal rate compounded monthly has the account earned is 0.84% .

In the question ,

it is given that ,

An employee opened a credit union account ,

amount deposited each month (PMT) = $90

number of period (n) = 2 years = 24 months

Future value after 2 years (FV) = $2177.48

let the rate of interest  compounded monthly has the account earned be "r"

we know that the future value formula is

Future Value = PMT× [tex](\frac{(1+\frac{r}{12})^{n} -1 }{\frac{r}{12} } )[/tex]

Substituting the value of n = 24 , PMT = 90 and FV = 2177.48 in the Future Value Formula ,

we get ,

2177.48 = 90 × [tex](\frac{(1+\frac{r}{12})^{24} -1 }{\frac{r}{12} } )[/tex]

[tex](\frac{(1+\frac{r}{12})^{24} -1 }{\frac{r}{12} } )[/tex] = 2177.48/90

( 1 + r/12 )²⁴ -1 = (r/12) × 24.194

Solving further , we get

r = 0.0084

that means rate is = 0.84%

Therefore , Annual nominal rate compounded monthly has the account earned is 0.84% .

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Answer:

13

Step-by-step explanation:

This is a special right triangle with side lengths 5-12-13 respectively.

If we can't remember the lengths we can use the following formula to calculate the lentgh of hypotenuse:

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

the sum of square measure of both legs is equal to the square measure of hypotenuse

[tex] {5}^{2} + {12}^{2} = {c}^{2} [/tex]

25 + 144 = c^2

169 = c^2 find the root of both sides

13 = c, hypotenuse.

The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12).

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given translation rule,

(x,y) → (x+8,y+7)

The next translation is (x,y) → (x-5,y+5)

The resultant translation will be,

(x,y) → (x+8,y+7) to (x+8-5,y+7+5)

⇒ (x+3,y+12)

Hence "The new coordinate after the given composite translation (x,y) → (x-5,y+5) will be (x+3,y+12)".

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Answer:yesno

Step-by-step explanation:

yes