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Answer:

the dimensions of the poster with the smallest area is 36cm by 54cm

Step-by-step explanation:

✓Let us represent the WIDTH of the printed material on the poster as "x"

✓Let us represent the HEIGHT of the printed material on the poster as "y"

✓ The given AREA is given as 864 cm2

Then we have

864 cm2= xy ...................eqn(1)

We can make "y" subject of the formula.

y= 864/x .......................eqn(2)

✓The total height the big poster which includes the 9cm margin that is at the bottom as well as the top is

(y+18)

✓The total width of the poster which includes the 6cm margin that is at the bottom as well as the top is

(x+12)

✓Then AREA OF THE TOTAL poster

A= (y+18)(x+12) ...................eqn(3)

Substitute eqn (2) into eqn(3)

A= ( 18+ 864/x)(x+12)

We can now simplify by opening the bracket, as

A=18x +1080 +10368/x

A= 18x +10368/x +1080

Let us find the first derivative of A which is A'

A'= 18-(10368/x²)

If we set A' =0

Then

0= 18- (10368/x²)

18= (10368/x²)

x²= 10368/18

x²= 576

x=√576

x=24

The second derivatives will be A"= 2(10368)/x³ and this will be positive for x> 0, and here A is concave up and x=24 is can be regarded as a minimum

The value of "y" when x=24 can now be be calculated using eqn(2)

y= 864/x

y= 864/24

y=36cm

✓The total width of the poster= (x+12)

= 24+12=36cm

✓The total height big the poster= (y+18)=36+18=54cm

the dimensions of the poster with the smallest area is 36cm by 54cm

Answer:

The total width of the paper [tex]=36 cm.[/tex]

The total height of the paper [tex]=54cm[/tex]

Step-by-step explanation:

Given information:

Top margin of the paper = 9 [tex]cm\\[/tex]

Bottom margin of the paper = 6 [tex]cm\\[/tex]

Area of the printed material = [tex]864[/tex] [tex]cm^2[/tex]

Let, the width of the printed material = [tex]x[/tex]

And the height of the printed material = [tex]y[/tex]

So, Area [tex]x \times y=864[/tex] [tex]cm^2[/tex]

After including margins;

Width of the paper [tex]= (x+12)[/tex]

Height of the paper [tex]= (y+18)[/tex]

Area [tex](A) = (y+18) (x+12)[/tex]

[tex]A=18x+(10368/x)+1080\\[/tex]

Take first derivative:

[tex]A'= 18- (10368/x^2)[/tex]

When [tex]A'=0[/tex]

Then,

[tex]18-(10368/x^2)=0\\x^2=576\\x=24[/tex]

Now ,when we take second derivative and check if it is positive or not ,

We find that it is grater than zero so the obtained value can be consider as minimum and can be proceed for further solution.

Hence ,

[tex]x \times y=864\\y=864/24\\y=36\\[/tex]

Now ,

The total width of the paper

[tex]= 24+12\\=36 cm.[/tex]

And , total height of the paper

[tex]=36+18\\=54 cm.[/tex]

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Answer:

Step-by-step explanation:

Given the expression [tex]3\left(q+\dfrac43\right) = 23[/tex], we are to find the value of q;

[tex]3\left(q+\dfrac43\right) = 23\\on\ expansion\\\\3q + 4/3(3) = 23\\\\3q+4 = 23\\\\subtract \ 4\ from \ both\ sides \ of \ the \ equation\\\\3q+4-4 = 23-4\\\\3q = 19\\\\Diviide \both\ sides \ by \ 3\\\\3q/3 = 19/3\\\\q = 19/3[/tex]

Hence the value of q is 19/3

Answer:

-2/3

Step-by-step explanation:

Don't worry about it, i got connections.

Answer:

  growth rate = 0.1733 per day, or 17.33% per day

Step-by-step explanation:

Since the doubling time is 4 days, the growth factor over a period of t days is ...

  2^(t/4)

Then the growth factor for 1 day is

  2^(1/4) ≈ 1.189207

The instantaneous growth rate is the natural log of this:

  ln(1.189207) ≈ 0.1733 . . . per day

Answer:

1.56 seconds

Step-by-step explanation:

When the ball hits the ground, h = 0.

0 = 20 − 5t − 5t²

Divide both sides by -5.

0 = t² + t − 4

Solve with quadratic formula.

t = [ -1 ± √(1² − 4(1)(-4)) ] / 2(1)

t = (-1 ± √17) / 2

The time must be positive, so:

t = (-1 + √17) / 2

t ≈ 1.56

Answer:

Step-by-step explanation:

Assume that f(x) = 0 for x outside the interval [4,7]. We will use the following

[tex]E[X^k] = \int_{4}^{7}x^k f(x) dx[/tex]

[tex]Var(X) = E[X^2]- (E[X])^2[/tex]

Standard deviation = [tex] \sqrt[]{Var(X)}[/tex]

Mean = [tex]E[X][/tex]

Then,

[tex]E[X] = \int_{4}^{7}\frac{1}{3}dx = \frac{7^2-4^2}{2\cdot 3} = \frac{11}{2}[/tex]

[tex]E[X^2] = \int_{4}^{7}\frac{x^2}{3}dx = \frac{7^3-4^3}{3\cdot 3} = 31[/tex]

Then, [tex]Var(x) = 31-(\frac{11}{2})^2 = \frac{3}{4}[/tex]

Then the standard deviation is [tex]\frac{\sqrt[]{3}}{2}[/tex]

Answer:

f( x ) = - x² - x + 42

Step-by-step explanation:

The polynomial function will have to include the zeroes with opposing signs, considering that when you isolate the value x say, you will take that value to the opposite side, changing the signs,

f(x) = (x + 7)(x - 6)

Now as you can see, x extends to negative infinity, such that,

f(x) = - (x + 7)(x - 6) - that negative makes no difference whatsoever on the zeroes of the function. All we want to do now is to expand this, and we receive out simplified solution.

Goal : [tex]expand\:-\:\left(x\:+\:7\right)\left(x\:-\:6\right)[/tex],

[tex]- xx+x\left(-6\right)+7x+7\left(-6\right)[/tex] = [tex]- xx-6x+7x-7\cdot \:6[/tex] = [tex]-\left(x^2+x-42\right)[/tex],

Expanded Solution : [tex]-x^2-x+42[/tex],

Polynomial Function : f( x ) = [tex]-x^2-x+42[/tex]

Answer:

-7/5

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -3 -4)/(8-3)

   = -7/5

Answer:

-7/5

Step-by-step explanation:

Hey there!

To find the slope of a line with 2 given points we'll use the following formula,

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

-3 - 4 = -7

8 - 3 = 5

-7/5

Hope this helps :)

Answer:

Step-by-step explanation:

You did not provide the table, so I used a spreadsheet. Most have functions for finding the area under a standard normal curve.

Answer:

An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.

The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.

------

length = 91 - 2*10 = 71 ft.

-------------------------------

The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.

---------

2800 <= area <= 3200

2800 <= (length)(width) <= 3200

2800 <= 71w <= 3200

39.44 <= width <= 45.07

hope it helpsss

Step-by-step explanation:

Answer: An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.

The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.

------

length = 91 - 2*10 = 71 ft.

-------------------------------

The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.

---------

2800 <= area <= 3200

2800 <= (length)(width) <= 3200

2800 <= 71w <= 3200

39.44 <= width <= 45.07

Answer:

The answer is 4 + √15 .

Step-by-step explanation:

You have to get rid of surds in the denorminator by multiplying it with the opposite sign :

[tex] \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } [/tex]

[tex] = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } [/tex]

[tex] = \frac{ {( \sqrt{5} + \sqrt{3} ) }^{2} }{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) } [/tex]

[tex] = \frac{ {( \sqrt{5} )}^{2} + 2( \sqrt{5} )( \sqrt{3}) + {( \sqrt{3}) }^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3} )}^{2} } [/tex]

[tex] = \frac{5 + 2 \sqrt{15} + 3 }{5 - 3} [/tex]

[tex] = \frac{8 + 2 \sqrt{15} }{2} [/tex]

[tex] = 4 + \sqrt{15} [/tex]

Answer:

The GCF is the largest expression that is factor of all expressions

Answer:

The GCF of two expressions is the greatest expression that is a factor of both the expressions.

Step-by-step explanation:

For example 7x² and 14x.

7x² = 1, 7, x, x

14x = 2, 7, x

The greatest common factor of the two expressions is 7x.

Answer:

28

Step-by-step explanation:

Let x be the missing segment

We will use the proportionality property to find x

24/16 = 42/x

Simplify 24/16

24/16= (4×6)/(4×4)= 4/6 = 3/2

So 3/2 = 42/x

3x = 42×2

3x = 84

x = 84/3

x= 28

Answer:

21 purple marbles

Step-by-step explanation:

my explanation is i looked at it like a ratio so ¾= x/28

then i took 28 ÷ 4 which equals 7, then i took 7 and multiplied it by 3 which gave me 21, so the answer is 21 purple marbles

Work Shown:

Replace every x with 4. Use the order of operations PEMDAS to simplify

f(x) = x + 21

f(4) = 4 + 21

f(4) = 25

The input 4 leads to the output 25.

Answer:

The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625

Step-by-step explanation:

Given that:

60% of the batteries are from manufacturer 1

90% of these batteries last for over 40 hours

Let the number of the battery duration be n = 0.90

Therefore n' = 1 - 0.90 = 0.10

Let p = manufacturer 1  and q = manufacturer 2

q = 1 - p

q = 1 = 0.6

q = 0.4

Thus ; 40% of the batteries are from manufacturer 2

However;

Only 75% of the batteries from manufacturer 2 last for over 40 hours.

Let number of battery duration be m = 0.75

Therefore ; m' = 1 - 0.75 = 0.25

A battery in a critical tool fails at 32 hours.

Thus; the that the battery in a critical tool fails at 32 hours was from manufacturer 2 is:

[tex]= \dfrac{q \times m' }{ p \times n' + q \times m' }[/tex]

[tex]= \dfrac{0.4 \times0.25 }{ (0.6 \times 0.1) + (0.4 \times 0.25 ) }[/tex]

[tex]=\dfrac{0.1}{0.06+ 0.1}[/tex]

[tex]=\dfrac{0.1}{0.16}[/tex]

= 0.625

The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625

The probability that the battery was from manufacturer 2 is 62.5%.

Since the Ambell Company uses batteries from two different manufacturers, and historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours, while only 75% of the batteries from manufacturer 2 last for over 40 hours, if a battery in a critical tool fails at 32 hours, to determine what is the probability it was from manufacturer 2 the following calculation must be performed:

Therefore, the probability that the battery was from manufacturer 2 is 62.5%.

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Answer:

The painting is [tex]t = 10911.1 \ years \ old[/tex]

Step-by-step explanation:

From the question we are told that

    The amount of carbon present after t year is

           [tex]y(t) = y_o * e ^{-0.00012t}[/tex]    {Note ; This is the function }

Here  [tex]y(t)[/tex] is the amount of carbon-14 after time t

        [tex]y_o[/tex] the original amount of carbon-14

Now given that the paint as at now contain 27% of the original carbon-14

  Then it mean that

            [tex]y(t) = 0.27 y_o[/tex]

So the equation is represented as

       [tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]

=>    [tex]0.27 = * e ^{-0.00012t}[/tex]

=>    [tex]ln(0.27) = -0.00012t[/tex]

=>  [tex]- 1.30933 = -0.00012t[/tex]

=>  [tex]t = \frac{-1.30933}{-0.00012}[/tex]

=>   [tex]t = 10911.1 \ years[/tex]

You reject the Null Hypothesis when you have a small P-Value. Here is an example! Also we never accept the null hypothesis, think of it like this if we bring someone to court you wouldn't say their innocent of a crime, you only know that if they do not get convicted of the crime they are not guilty in the eyes of the law. Same thing applies here, since there could be several answers that satisfy our assumptions made, we can not be certain that 1 of those assumptions is the REAL answer it's just AN answer.

Step-by-step explanation:

kindly find attached detailed information of the remaining information as requested for your reference

1. The lower class limit is the left number in the age column

   i.e in the 25-34 the lower class limit is 25          

2. The upper class limit is the right number in the age column

   i.e in the 25-34 the lower class limit is 34

3. The class width is the difference  between the class boundaries of a single class

 class width = 34.5-24.5= 10

4. The number of individuals is= 29+34+16+3+5+1+2= 90    

Answer:

The meadian decreases by 1.5 when the outlier is removed.

Step-by-step explanation:

Well first we need to find the median of the following data set,

(75, 63, 58, 59, 63, 62, 56, 59)

So we order the set from least to greatest,

56, 58, 59, 59, 62, 63, 63, 75

Then we cross all the side numbers,

Which gets us 59 and 62.

59 + 62 = 121.

121 / 2 = 60.5

So 65 is the median before the outlier is removed.

Now when we remove the outlier which is 75.

Then we order it again,

56, 58, 59, 59, 62, 63, 63

Which gets us 59 as the median.

Thus,

the median height decreases by 1.5 units when the outlier is removed.

Hope this helps :)

Answer:

  1.9 units

Step-by-step explanation:

Since we have ...

  MN : NP = 9 : 1

then ...

  NP : MN+NP = 1 : (9+1) = 1 : 10

If MP is 2 units, then NP is 1/10 × 2 units = 0.2 units. Point K will be half that distance from N or P, so will be 0.1 unit from P.

So, the distance from M to K, the midpoint of NP is ...

  2 units - 0.1 units = 1.9 units

Answer:

1.9

Step-by-step explanation:

Answer:

Design thinking skills

Step-by-step explanation:

The design thinking skills is observable in individuals who can effectively use Intuition to create prototypes of abstract objects.

Jessie thus shows that she possess design thinking skills by been able to imagine abstract concepts at the same and she applies advanced mathematical formulas which in turn provides solutions to problems.

Sin (angle) = opposite leg / hypotenuse

Sin(62) = 18/x

The answer is the third choice.

Answer:

Option (B)

Step-by-step explanation:

To determine the length of arc of a circle we use the formula,

Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Where θ = measure of the central angle subtended by the arc

r = radius of the circle

For the circle given in the picture attached,

Length of arc NM = [tex]\frac{30}{360}(2\pi)(2)[/tex]

                             = [tex]\frac{4\pi }{12}[/tex]

                             = [tex]\frac{\pi }{3}[/tex]

Therefore, length of [tex]\widehat{NM}=\frac{\pi }{3}[/tex]

Option (B) will be the answer.

Answer: C

Step-by-step explanation:

4#/12 = #

Problem 10

Explanation: You'll use the equation cos(28) = d/65 to solve for d to get d = 65*cos(28) = 57.39159 approximately. We use the cosine ratio because it ties together the adjacent and hypotenuse.

=====================================

Problem 11

Explanation: This time we use the sine rule. We have the height as the opposite side (which is unknown, call it x) and the hypotenuse is the ladders length (11). So we have sin(72) = x/11 which solves to x = 11*sin(72) = 10.46162

=====================================

Problem 12

Explanation: Now we use the tangent rule to connect the opposite and adjacent sides.

tan(37) = 12.1/x

x*tan(37) = 12.1

x = 12.1/tan(37)

x = 16.05724 approximately

The lines of the inequalities are parallel, and the system of inequalities do not have any solution.

The system of inequalities are  given as:

The inequality y ≥ 2x + 1 has the following characteristics:

The inequality y ≤ 2x – 2 has the following characteristics:

See attachment for the graphs of the system of inequalities

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Hi

Below the formulas to convert Celsius into Fahrenheit.

9/5 C +32 = degree in fahrenheit.

Where C is the degree in celsius. So have a try and find the answer.

Answer:

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius

From the question V = 1436 cm³

[tex]1436 = \frac{4}{3} \pi {r}^{3} [/tex]

Multiply through by 3

We have

[tex]4308 = 4\pi {r}^{3} [/tex]

Divide both sides by 4π

[tex] {r}^{3} = \frac{4308}{4\pi} [/tex]

[tex] {r}^{ 3} = \frac{1077}{\pi} [/tex]

Find the cube root of both sides

[tex]r = \sqrt[3]{ \frac{1077}{\pi} } [/tex]

r = 6.99

We have the final answer as

Hope this helps

Complete Question

In a small private​ school, 5 students are randomly selected from 13 available students. What is the probability that they are the five youngest​ students?

Answer:

The  probability is [tex]P(x) = 0.00078[/tex]

Step-by-step explanation:

From the question we are told that

    The number of student randomly selected is  r =  5

   The  number of available students is  n  =  13

Generally the number of ways that 5 students can be selected from 13 available students is mathematically represented as

      [tex]n(k)=\left n} \atop {}} \right.C_r = \frac{n ! }{(n-r ) ! r!}[/tex]

substituting values    

      [tex]\left n} \atop {}} \right.C_r = \frac{13 ! }{(13-5 ) ! 5!}[/tex]

    [tex]\left n} \atop {}} \right.C_r = \frac{13 * 12 * 11 * 10 * 9 *8! }{8 ! * 5 * 4 * 3 * 2 *1}[/tex]

     [tex]\left n} \atop {}} \right.C_r = 1287[/tex]

The  number of method by which  5 youngest  students are selected is n(x) =  1

   So  

          Then the probability of  selecting the five youngest students is mathematically represented as

        [tex]P(x) = \frac{n(x)}{n(k)}[/tex]

substituting values

        [tex]P(x) = \frac{1}{1287}[/tex]

        [tex]P(x) = 0.00078[/tex]

Answer:

its 14/C

Step-by-step explanation:

i got i right on edg U^U

Answer:

16

Step-by-step explanation:

i did edge test yea dont  be imma fake :***    

Answer:

(b) 32

Step-by-step explanation:

From the information given :

sample mean of Philadelphia μ₁ = $1240

Sample size of Philadelphia n₁ = 15

Sample Standard deviation σ₁ = $270

sample mean of Paris μ₂ = $1,060

Sample size of Paris  n₂ = 19

Sample Standard deviation of Paris  σ₂ = $240

If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris;

the degrees of freedom for this hypothesis test can be calculated as;

degree of freedom df = n - 1

degree of freedom for both hypothesis test = (n₁ - 1 + n₂ -1)

degree of freedom for both hypothesis test  = (n₁ + n₂ - 2)

degree of freedom for both hypothesis test  = ( 15 + 19 - 2)

degree of freedom for both hypothesis test are   32