John painted his most famous​ work, in his​ country, in 1930 on composition board with perimeter 101.14 in. If the rectangular painting is 5.43 in. taller than it is​ wide, find the dimensions of the painting.

Answer:

105 years

Step-by-step explanation:

Given the function :

Q(t) = 4e^(-0.00938t)

Q = Quantity in kilogram of an element in a storage unit after t years

how long will it be before the quantity is less than 1.5kg

Inputting Q = 1.5kg into the equation:

1.5 = 4e^(-0.00938t)

Divide both sides by 4

(1.5 / 4) = (4e^(-0.00938t) / 4)

0.375 = e^(-0.00938t)

Take the ln of both sides

In(0.375) = In(e^(-0.00938t))

−0.980829 = -0.00938t

Divide both sides by 0.00938

0.00938t / 0.00938 = 0.980829 /0.00938

t = 104.56599

When t = 104.56599 years , the quantity in kilogram of the element in storage will be exactly 1.5kg

Therefore, when t = 105 years, the quantity of element in storage will be less than 1.5kg

Answer:

∠ H ≈ 23°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus

∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )

Answer:

the number that is halfway between 250 and 300 is 275

Step-by-step explanation:

250+300= 550/2= 275

The number i,e halfway is 275.

[tex]= (250 + 300) \div 2\\\\= 550 \div 2[/tex]

= 275

Find out more information about the Number here : https://brainly.com/question/17429689?referrer=searchResults

Answer:

£39.20

Step-by-step explanation:

→ Identify which ratio goes to each person

2 : 1 : 5

2 = Paul

1 = Colin

5 = Brian

→ Divide the total tip by the total sum of the ratio's

£78.40 ÷ ( 2 + 1 + 5 ) ⇔ £78.40 ÷ 8 = £9.80

→ Now we know one part is equal to £9.80 we multiply this number by each of the associated ratio's

Paul = £9.80 × 2 ⇔ £19.60

Colin = £9.80 × 1 ⇔ £9.80

Brian = £9.80 × 5 ⇔ £49

→ Minus Brian's tip against Colin's tip

£49 - £9.80 = £39.20

Answer:

There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.

Step-by-step explanation:

Given:

There are 5 types of croissants:

plain croissants

cherry croissants

chocolate croissants

almond croissant

apple croissants

broccoli croissants

To find:

to choose 22 croissants with:

at least one plain croissant

at least two cherry croissants

at least three chocolate croissants

at least one almond croissant

at least two apple croissants

no more than three broccoli croissants

Solution:

First we select

At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants

So

1 + 2 + 3 + 1 + 2  = 9

Total croissants = 22  

So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.

n = 5

r = 13

C(n + r - 1, r)

= C(5 + 13 - 1, 13)

= C(17,13)

[tex]=\frac{17! }{13!(17-13)!}[/tex]

= 355687428096000 / 6227020800 ( 24 )

= 355687428096000 / 149448499200

= 2380

C(17,13) = 2380

C(n + r - 1, r)

= C(5 + 12 - 1, 12)

= C(16,12)

[tex]=\frac{16! }{12!(16-12)!}[/tex]

= 20922789888000 / 479001600 ( 24 )

= 20922789888000  / 11496038400

= 1820

C(16,12) = 1820

C(n + r - 1, r)

= C(5 + 11 - 1, 11)

= C(15,11)

[tex]=\frac{15! }{11!(15-11)!}[/tex]

= 1307674368000 / 39916800 (24)

= 1307674368000 / 958003200

= 1307674368000 / 958003200

= 1365

C(15,11) = 1365

C(n + r - 1, r)

= C(5 + 10 - 1, 10)

= C(14,10)

[tex]=\frac{14! }{10!(14-10)!}[/tex]

= 87178291200 / 3628800 ( 24 )

= 87178291200 / 87091200

= 1001

C(14,10) = 1001

Adding them:

2380 + 1820 + 1365 + 1001 = 6566 ways

Answer: C.  ±0.632.

Step-by-step explanation:

We have given,

Sample size : n= 10

Significance level : [tex]\alpha=0.05[/tex]

Test to check determine whether there is sufficient evidence to support a

claim of a linear correlation between two variables is a two tailed test.

Degree of freedom(df) = n- 2=8

Now , by the correlation coefficient(r) table ,

The critical r value corresponding to df = 8 and Significance level = 0.025  (0.05/2) is ±0.632.

Hence, the correct option is C.  ±0.632.

A(t) = 100t^2 + 500t + 625

3,025 square pixels

Answer:

A(t) equals 100t²+ 500t + 625.

The area of the square image after 3 seconds is 3,025 square pixels.

Answer:

This year:

dads: 36 years

Alex: 6 years

Step-by-step explanation:

a = d/6

a+4 = (d+4)/4

a = Alex´s actual age  

d = actual age of the dad

d/6 + 4 = (d+4)/4

4{(d/6) + 4} = d+4

4*d/6 + 4*4 = d+4

4d/6 + 16 = d + 4

4d/6 = d + 4 - 16

4d = (d-12)*6

4d  = 6*d +6*-12

4d = 6d - 72

4d - 6d = -72

-2d = -72

d = -72/-2

d = 36

a = d/6

a = 36/6

a = 6

probe:

a+4 = (d+4)/4

6 + 4 = (36+4)/4

10 = 40/4

Hey there! I'm happy to help!

When graphing a system of equations, the solution is the point where the two lines meet. We see that they intersect at (-2,4).

Therefore, the solution to the system of equations is (-2,4).

Have a wonderful day! :D

Answer:

A

Step-by-step explanation:

edge 2020 Dec 9

Answer:

x = -1

Step-by-step explanation:

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

Distribute

2x -2+3 = x -3x-3

Combine like terms

2x +1 = -2x-3

Add 2x to each side

2x+1 +2x = -2x-3+2x

4x+1 = -3

Subtract 1 from each side

4x+1-1 = -3-1

4x= -4

Divide by 4

4x/4 = -4/4

x = -1

[tex] \Large{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]

Let one of those even numbers be x, Then other even number would be x + 2.

According to question,

⇛ Their reciprocal add upto 3/4

So, we can write it as,

⇛ 1/x + 1/x + 2 = 3/4

⇛ x + 2 + x / x(x + 2) = 3/4

⇛ 2x + 2 / x² + 2x = 3/4

Cross multiplying,

⇛ 3(x² + 2x) = 4(2x + 2)

⇛ 3x² + 6x = 8x + 8

⇛ 3x² - 2x - 8 = 0

⇛ 3x² - 6x + 4x - 8 = 0

⇛ 3x(x - 2) + 4(x - 2) = 0

⇛ (3x + 4)(x - 2) = 0

Then, x = -4/3 or 2

☃️ It can't be -4/3 because it is fraction and negative number. So, x = 2

Then, x + 2 = 4

✤ So, The even numbers are 2 and 4.

━━━━━━━━━━━━━━━━━━━━

Answer:

+20° to -25° = 45° C/F temperature change

Step-by-step explanation:

Answer: b. False

Step-by-step explanation:

Hence, the given statement is absolutely false.

Answer:

[tex]volume = 0.32 m^3[/tex]

Step-by-step explanation:

The object shown above consists of 5 cubes having side lengths of ⅖m each.

Volume of a cube = [tex] a^3 [/tex]

Where, a = side length = ⅖ m

Volume of the object = [tex]5* (\frac{2}{5})^3[/tex]

[tex]volume = 5*\frac{8}{125} = 5*0.064 = 0.32 m^3[/tex]

Answer:

C. [tex] y = 3\sqrt{7} [/tex]

Step-by-step explanation:

Based on the right triangle altitude theorem, the altitude, y, in the diagram above, equals the geometric mean of 9 and 7.

This implies => [tex] y = \sqrt{9*7} [/tex]

Thus, solve for y.

[tex] y = \sqrt{9} * \sqrt{7} [/tex]

[tex] y = 3\sqrt{7} [/tex]

The answer is C. [tex] y = 3\sqrt{7} [/tex]

The shape is missing, so i have attached it.

Answer:

2.6

Step-by-step explanation:

From the image attached, the diameter of the inner semi - circle is 0.5 yards while the length of each side of the pillow is 0.2 yards.

Thus, for us to find the length of the seam which is along the edges of the pillow, we will calculate the perimeter of the outer semicircle, then add the perimeter of the inner semicircle and also add the sides too.

Now, due to the fact that the length of the sides of the pillow are 0.2 yards each, the diameter of the outer circle would be;

0.5 + 0.2 + 0.2 = 0.9 yards. So, the perimeter of the outer semicircle is,

P0 = πd/2 = π × 0.9/2 =0.45π yds

The perimeter of the inner semicircle would be given as;

PI = πd/2 = π × 0.5/2 =0.25π yds.

Thus, we can calculate the total perimeter of the pillow as;

PT = P0 + PI + 0.2 + 0.2

PT = 0.45π + 0.25π + 0.2 + 0.2

PT ≈ 2.6 yards

Alex will need 2.6 yds

Answer:

0.5

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

6x + 3 = 2x + 19  ------ subtract 3 both sides

6x + 3 - 3 = 2x + 19 - 3   simplify

6x = 2x + 16         ------ subtract 2x both sides

6x - 2x = 2x + 16 - 2x      simplify

4x = 16

x = 16 / 4

x = 4

Answer: x = 4

Step-by-step explanation: If the variable appears on both sides of the equation, we put the variables together on one side of the equation and the numbers together on the other side of the equation.

So let's put our variables on the left side by first subtracting

2x from both sides of the equation to get 4x + 3 = 19.

Next, we subtract 3 from both sides to get 4x = 16.

Finally, we divide both sides by 4 to get x = 4.

Answer:

The  test statistic is  [tex]t = 3.744[/tex]

Step-by-step explanation:

From the question we are told that

  The population mean is  [tex]\mu = 140[/tex]

  The  The  level of significance is  [tex]\alpha = 0.05[/tex]

  The  sample size is  n =  18

   The  null hypothesis is  [tex]H_o : \mu = 140[/tex]

    The  alternative hypothesis is  [tex]H_a : \mu > 140[/tex]

    The sample mean is  [tex]\= x = 155[/tex]

     The  standard deviation is  [tex]\sigma = 17[/tex]

Generally the test statistics is mathematically represented as

       [tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]

substituting values

      [tex]t = \frac{ 155 - 140 }{ \frac{ 17 }{ \sqrt{18} } }[/tex]

      [tex]t = 3.744[/tex]

Answer:

1.691

Step-by-step explanation:

Standard error of the mean is expressed as SEM = S/√n

S is the population standard deviation

n is the sample size (number of observation)

Given S = 27 and n = 255

SEM = 27/√255

SEM = 27/15.97

SEM = 1.691

Hence the standard error of the mean is 1.691

Answer:

(C) 408 miles

Step-by-step explanation:

Looking at this table, we can see that the beginning point is (0,0) so this is a linear slope, meaning we won’t have to add anything.

This means that for every time we rise in x, y will rise by the same amount.

When x is 1, y is 68 - so the constant of proportionality here is 68.

So, to find how much 6 hours would be we just multiply.

[tex]6\cdot68=408[/tex]

Hope this helped!

Answer:

342 m

Step-by-step explanation:

SIn(20) * 1000 = RS

342 = RS

This question is solved using proportions.

Doing this, we get that he should take 3 packs.

How many calories he burns in the hike?

In 45 minutes, he burns 345 calories. How many calories in 6*60 = 360 minutes?

45 minutes - 345 calories

360 minutes - x calories

Applying cross multiplication:

[tex]45x = 345*360[/tex]

[tex]x = \frac{345*360}{45}[/tex]

[tex]x = 2760[/tex]

He burns 2760 calories in the hike.

How many calories he wants to replace?

Roughly 1/3, so he have to find one third of 2760, that is:

[tex]\frac{2760}{3} = 920[/tex]

How many packs?

One pack recovers 310 calories, how many packs for 920 calories?

1 pack - 310 calories

x packs - 920 calories

Applying cross multiplication:

[tex]310x = 920[/tex]

[tex]x = \frac{920}{310}[/tex]

[tex]x = 2.97[/tex]

Rounding up, he should take 3 packs.

A similar question is found at https://brainly.com/question/14426926

Answer:

6×6 tile

Step-by-step explanation:

First let's calculate the total area Hakim should fill.

Let A be that area.

The area is a rectangle so its area is the product of the length and the width.

● A = 180*150

● A = 27000 mm^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

The tiles Hakim has are all squares with different sides(4,6,8).

Let calculate the area of each tile.

Let A' , A" and A"' be the areas respectively of the 4,6 and 8 squares.

Since all tiles are squares, the area is the side times itself.

■■■■■■■■■■■■■■■■■■■■■■■■■■

● A' = 4^2 = 16 mm^2

● A" = 6^2 = 36 mm^2

● A"' = 8^2 = 64 mm^2

Divide the total area by each area and see wich one will give you a whole number.

●A÷A' = 27000÷16 = 1687.5

This isn't a whole number

● A÷A" = 27000÷36 = 750

This is a whole number, so it is the right tile.

● A+A"' = 27000÷64 = 421.875

This isn't the right tile.

Hakil should use the 6×6 tile

Hakim should use a tile of 6×6 side.

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Given that, Hakim is making a mosaic from square tiles. The area he needs to fill measures 150 mm by 180 mm. The tiles have side lengths of 4, 6 or 8 mm and are too small to cut.

To know that which tile fits best, we will divide the area of mosaic to the area of the tile, and see if we get a whole number if not a whole number then it should be cut, but we are restricted to do so, therefore we will look for the whole number,

Area of the mosaic = 150×180 = 27000 mm²

Area of the tile with side 4 mm = 4² = 16 mm²

Number of tile = 27000/16 = 1687.5 tiles. (not a whole number)

Area of the tile with side 6 mm = 6² = 36 mm

Number of tile = 27000/36 = 750 tile. (a whole number)

Hence, Hakim should use a tile of 6×6 side.

For more references on area, click;

https://brainly.com/question/27683633

#SPJ2

Answer:

x=16.1

Step-by-step explanation:

open the brackets

-4.5= -0.5x-3.55

Take 3.55 to the other side.

-4.5-3.55 = -8.05

5/10x= -805/100

0.5x= - 8.05 = 16.1

Answer:

[tex]-x^3-x^2+x-9[/tex]

Step-by-step explanation:

Distribute -1

Combine Like Terms

[tex](x^2+2x-4)-(x^3+2x^2+x+5)\\= x^2+2x-4+-x^3-2x-x-5\\= -x^3-x^2+x-9[/tex]

Answer:

[tex]x^{3} -3x^{2} +x-9[/tex]

Step-by-step explanation:

-x^2+2x-4-(-x^3+2x^2+x+5)

Combine like terms

x^3-3x^2+x-9

Step-by-step explanation:

I(S) = aS / (S + c)

As S approaches infinity, S becomes much larger than c.  So S + c is approximately equal to just S.

lim(S→∞) I(S)

= lim(S→∞) aS / (S + c)

= lim(S→∞) aS / S

= lim(S→∞) a

= a

As S approaches infinity, I(S) approaches a.

Answer:

x = 58

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

90  = 32+x

Subtract 32 from each side

90-32 = x

58 =x

Answer:

B

Step-by-step explanation:

-(-a)/b = a/b

Option A is not equal to a/b

But Option B is, after cancelling out the negative sign

Answer:

[tex]\large \boxed{ \mathrm{B.} \ - \frac{a}{-b} }[/tex]

Step-by-step explanation:

[tex]\displaystyle -\frac{-a}{b} =-(- \frac{a}{b} ) = \frac{a}{b}[/tex]

The first option is not equivalent to a/b.

[tex]\displaystyle \frac{a}{-b}\neq \frac{a}{b}[/tex]

The second option is equivalent to a/b.

[tex]\displaystyle -\frac{a}{-b} =\frac{-a}{-b} = \frac{a}{b}[/tex]

Answer:

y>-2x+3

Dashed

Solid

Above

(1, 5)

Step-by-step explanation:

Edge2020

The slope-intercept form of the first inequality is (y > - 2x + 3), the first inequality has dash boundary lines because the sign of the inequality is ">", and the second inequality has solid boundary lines because the sign of the inequality is [tex]\geq[/tex].

Given :

The slope-intercept form of a line is given by:

y = mx + c

So, the slope-intercept form of the first inequality is:

y > - 2x + 3

The first inequality has dash boundary lines because the sign of the inequality is ">".

The second inequality has solid boundary lines because the sign of the inequality is [tex]\geq[/tex].

For more information, refer to the link given below:

https://brainly.com/question/19491153

Answer:

Step-by-step explanation:

To find this probability, we shall be using the z-score route

Mathematically ;

z-score = (x -mean)/SD

From the question, x = 1.99, mean = 0 and SD = 1

So z = (1.99-0)/1 = 1.99

So the probability we want to calculate is;

P(z<1.99)

This value can be obtained from the standard normal distribution table.

P(z < 1.99) = 0.9767

The sketch of the region is as shown as in the attachment.