In a survey, 9 out of 15 people named math as their favorite class. Express the rate as a decimal.

!!!! I need help with numbers 1 and 9 please !!!!!

Nataly_w [17]

(1)

given $\frac{j}{6}$ = $\frac{9}{10}$ ( cross- multiply )

10j = 54 ( divide both sides by 10 )

j = $\frac{54}{10}$ = $\frac{27}{5}$ ← in simplest form

(9)

let h be the hours worked daily , then

3h = 20 $\frac{2}{3}$ = $\frac{62}{3}$ ( divide both sides by 3 )

h = $\frac{62}{3}$ ÷ 3

= $\frac{62}{3}$ × $\frac{1}{3}$ = $\frac{62}{9}$ = 6 $\frac{8}{9}$

She worked 6 $\frac{8}{9}$ hours each day

5 0

3 years ago

Koji has 5,502 in savings this is 30 less than 6 times the amount in his checking, how much money?

omeli [17]

Answer:

$922

Step-by-step explanation:

5 0

4 years ago

Em quantos meses um capital de R$4.000,00 aplicado a uma taxa de juros simples de 29,3% ao ano, renderá de juros o valor de R$58

Akimi4 [234]

Responda:

6 meses

10 meses

Explicação passo a passo:

Dado que:

Principal = 4000

Juros = 586

Taxa (r) = 29,3% ao ano = 0,293

Juros simples = principal * taxa * tempo

586 = 4000 * 0,293 * t

586 = 1172t

t = 586/1172

t = 0,5 anos

Tempo = (0,5 * 12) = 6 meses

B.)

principal = $ 90909,09

Montante final = 100.000

Taxa (r) = 12% = 0,12

Usando a fórmula:

Quantidade final = p (1 + rt)

Taxa = r; t = tempo

100000 = 90909,09 (1 + 0,12t)

100000 = 90909,09 + 10909,0908t

100000 - 90909,09 = 10909,0908t

9090,91 = 10909,0908t

t = 9090,91 / 10909,0908

t = 0,8333334

Número de meses:

0,8333334 * 12

= 10 meses

4 0

3 years ago

Which Lines Are Parallel if M<4 = m<5? Justify Your Answer.

vazorg [7]

Y is parallel to S because angle 4 and angle 5 are alternate interior angles.
Hope that helps.

6 0

3 years ago

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

4 years ago