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3 years ago

Three and two thirds times a number equals two ninths

Mathematics

2 answers:

worty [1.4K]3 years ago

8 0

3 2/3 x # = 2/9
# = 2/9 \ 3 2/3
# = 2/33 or 0.067

zlopas [31]3 years ago

8 0

Answer:

The number is $\displaystyle\frac{2}{33}$ .

Step-by-step explanation:

Let x be the number.

We are given that:

Three and two thirds times a number

$3\displaystyle\frac{2}{3}\times x$

This is equal to two-ninths

Thus,

$3\displaystyle\frac{2}{3}\times x = \displaystyle\frac{2}{9}\\\\\displaystyle\frac{11}{3}\times x = \displaystyle\frac{2}{9}\\\\x = \displaystyle\frac{2\times 3}{9\times 11}\\\\x = \displaystyle\frac{2}{33}$

Hence, the number is $\displaystyle\frac{2}{33}$ .

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A new school banner is to be 4 1/2 feet wide by 7 1/4 feet long. what is the area? if a fabric for the banner costs $6 a square

lilavasa [31]

The area is 32 5/8 ft squared and It would cost$ 195.75

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3 years ago

Find Mx, My, and (x, y) for the lamina of uniform density rho bounded by the graphs of the equations. y = x2/3, y = 0, x = 1

erik [133]

Answer:

$\mathbf{(\overline x , \overline y ) = (\dfrac{5}{8}, \dfrac{5}{14})}$

Step-by-step explanation:

Given that:

$y = x^{2/3}$ at y = 0 , x = 1

Then:

Area = $\int^{1}_{0} x^{2/3} \ dx$

Area = $\begin {bmatrix} \dfrac{3}{5}x^{5/3} \end {bmatrix} ^1_0$

Area = $\dfrac{3}{5}$

Then:

$\overline x = \dfrac{1}{A} \int^b_a x (f(x) -g(x) ) \ dx$

$\overline x = \dfrac{5}{3} \int^1_0 x (x^{2/3} -0 ) \ dx$

$\overline x = \dfrac{5}{3} \int^1_0 x^{5/3} \ dx$

$\overline x = \dfrac{5}{3} \ [\dfrac{3}{8}x^{8/3}]^1_0$

$\overline x = \dfrac{5}{3} \times \dfrac{3}{8}$

$\overline x = \dfrac{5}{8}$

Similarly;

$\overline y = \dfrac{1}{A} \int^b_a \dfrac{1}{2} \begin{bmatrix} (f(x)^)2 - (g(x))^2 \end {bmatrix} \ dx$

$\overline y = \dfrac{5}{3} \int^1_0 \dfrac{1}{2} \begin{bmatrix} (f(x^{2/3})^2 -0 \end {bmatrix} \ dx$

$\overline y = \dfrac{5}{3} \int^1_0 \dfrac{1}{2} \begin{bmatrix} (x^{4/3} ) \end {bmatrix} \ dx$

$\overline y = \dfrac{5}{3} \begin{bmatrix} \dfrac{1}{2} (x^{7/3} ) \times \dfrac{3}{7} \end {bmatrix} ^1_0$

$\overline y = \dfrac{5}{3} \begin{bmatrix} \dfrac{3}{14} (x^{7/3} ) \end {bmatrix} ^1_0$

$\overline y = (\dfrac{5}{3} \times \dfrac{3}{14} )$

$\overline y = \dfrac{5}{14}$

Thus; $\mathbf{(\overline x , \overline y ) = (\dfrac{5}{8}, \dfrac{5}{14})}$

4 0

3 years ago

Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriage

hoa [83]

Answer:

(A) 0.377,

(B) 0.000,

(D) 0.047

Step-by-step explanation:

We assume that having a bone of intention means not liking one's Mother-in-Law

(A) P(all six dislike their Mother-in-Law) = (85%)^6 = (.85)^6 = 0.377

(B) P(none of the six dislike their Mother-in-Law) =

(100% - 85%)^6 =

0.15^6 =

0.000

P(exactly 4 dislike their Mother-in-Law) + P(exactly 5 dislike their Mother-in-Law) + P(exactly 6 dislike their Mother-in-Law) =

C(6,4) * (.85)^4 * (1-.85)^2 + C(6,5) * (.85)^5 * (.15)^1 + C(6,6) * (.85)^6 = (15) * (.85)^4 * (.15)^2 + (6) * (.85)^5 * .15 + (1) * (.85)^6 =

0.953

(D) P(no more than 3 dislike their Mother-in-Law) =

P(exactly 0 dislikes their Mother-in-Law) + P(exactly 1 dislikes her Mother) + P(exactly 2 dislike their Mother-in-Law) + P(exactly 3 dislike their Mother-in-Law) =

C(6,0) * (.85)^0 * (.15)^6 + C(6,1) * (.85)^1 * (.15)^5 + C(6,2) * (.85)^2 * (.15)^4 + C(6,3) * (.85)^3 * (.15)^3 =

(1)(1)(.15)^6 + (6)(.85)(.15)^5 + (15)(.85)^2 *(.15)^4 + (20)(.85)^3 * (.15)^3 =

0.047

3 0

3 years ago

Use the slope formula to find the slope. y2 -4 y1 2 x2 0 x1 2 m=ΔyΔx=y2−y1x2−x1 Usetheslopeformula m = Δ y Δ x = y 2 - y 1 x 2 -

jenyasd209 [6]

Answer:

The slope is, 3

Step-by-step explanation:

Formula for slope(m) is given by:

$m = \frac{\triangle y}{\triangle x}$