Find the simple interest on $500 at 6% for one year

Determine the angle at the centre of a circle with radius 12.0 cm for an arc length of of 21.0 cm.

nata0808 [166]

Answer:

$\theta=\dfrac{7}{4}\ \text{radian}$

Step-by-step explanation:

We have,

Radius of the circle is 12 cm

Arc length, l = 21 cm

It is required to find the central angle of the circle. The formula for the length of an arc of a circle is :

$l=r\times \theta$

$\theta$ is central angle

$\theta=\dfrac{l}{r}\\\\\theta=\dfrac{21}{12}\\\\\theta=\dfrac{7}{4}\ \text{radian}$

So, the angle at the centre of the circle is $\dfrac{7}{4}\ \text{radian}$ .

7 0

2 years ago

A study of commuting times reports the travel times to work of a random sample of 1010 employed adults in Chicago. The mean is x

MrMuchimi

Answer:

standard error of the mean = 1.6960

Step-by-step explanation:

Given -

Mean $(\overline{X})$ = 53 minutes

Standard deviation ( s ) = 53.9 minutes

n = 1010

standard error of the mean =

$\sigma _{\overline{X}}$ = $\frac{s}{\sqrt{n}}$

= $\frac{53.9}{\sqrt{1010}}$

= 1.6960

3 0

3 years ago

Pink rose plants are on sale for $3 each and white ones for $5 each. A gardener decides to buy 13 in total, choosing more white

Anettt [7]

Answer:

8

Step-by-step explanation:

If the gardener bought more white than pink, that could mean he could have bought 12 white and one pink, 11 white and 2 pink, 10 white and 3 pink, 9 white and 4 pink, 8 white and 5 pink, or 7 white and 6 pink.

If you plug in the numbers, for example with 7 and 6, that would equal $53, which is not correct. Continue to do this with all of the answers.

With 8 white roses and 5 pink roses, this would equal $55 (40+15), which is the answer.

7 0

2 years ago

Can someone please help me with my maths question

DIA [1.3K]

Answer:

$a. \ \dfrac{625 \cdot m}{27 \cdot n^{11}}$

$b. \ \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}$

Step-by-step explanation:

The question relates with rules of indices

(a) The give expression is presented as follows;

$\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}$

By expanding the expression, we get;

$\dfrac{m^3 \times n^{-8} \times 5^4 \times m^4}{\left 3^3 \times m^6 \times n^3}$

Collecting like terms gives;

$\dfrac{m^{(3 + 4 - 6)} \times 5^4}{ 3^3 \times n^{3 + 8}} = \dfrac{625 \cdot m}{27 \cdot n^{11}}$

$\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}= \dfrac{625 \cdot m}{27 \cdot n^{11}}$

(b) The given expression is presented as follows;

$x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \div (x \cdot y^n)^4$

Therefore, we get;

$x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n}$

Collecting like terms gives;

$x^{3 \cdot m + 2 - 4} \times \left (y^{3 \cdot n - 3 -4 \cdot n}} \right ) = x^{3 \cdot m - 2} \times \left (y^{ - 3 -n}} \right ) = x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right )$