14 ounces of olive oil for $3.59

Can you conclude from the figure that ABC is similar to DEF? Explain.

pishuonlain [190]

Answer:

Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.

Step-by-step explanation:

We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.

Triangle ABC:

Measure of angle A= 60°

Measure of angle C= 40°

Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°

Triangle DEF

Measure of angle E= 80°

Measure of angle F= 40°

Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°

The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.

The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.

Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.

8 0

3 years ago

Describe the sampling distribution of p(hat). Assume the size of the population is 30,000.

Naya [18.7K]

Answer:

a) $\mathbf{\mu_ \hat p = 0.6}$

b) $\mathbf{\sigma_p =0.01732}$

Step-by-step explanation:

Given that:

population mean $\mu$ = 30,000

sample size n = 800

population proportion p = 0.6

a)

The mean of the the sampling distribution is equal to the population proportion.

$\mu_ \hat p = p$

$\mathbf{\mu_ \hat p = 0.6}$

b)

The standard deviation of the sampling distribution can be estimated by using the formula:

$\sigma_p = \sqrt{\dfrac{p(1-p)}{n}}$

$\sigma_p = \sqrt{\dfrac{0.6(1-0.6)}{800}}$

$\sigma_p = \sqrt{\dfrac{0.6(0.4)}{800}}$

$\sigma_p = \sqrt{\dfrac{0.24}{800}}$

$\sigma_p = \sqrt{3 \times 10^{-4}}$

$\mathbf{\sigma_p =0.01732}$

7 0

3 years ago

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Archy [21]

(a) If the particle's position (measured with some unit) at time t is given by s(t), where

$s(t) = \dfrac{5t}{t^2+11}\,\mathrm{units}$

then the velocity at time t, v(t), is given by the derivative of s(t),

$v(t) = \dfrac{\mathrm ds}{\mathrm dt} = \dfrac{5(t^2+11)-5t(2t)}{(t^2+11)^2} = \boxed{\dfrac{-5t^2+55}{(t^2+11)^2}\,\dfrac{\rm units}{\rm s}}$

(b) The velocity after 3 seconds is

$v(3) = \dfrac{-5\cdot3^2+55}{(3^2+11)^2} = \dfrac{1}{40}\dfrac{\rm units}{\rm s} = \boxed{0.025\dfrac{\rm units}{\rm s}}$

(c) The particle is at rest when its velocity is zero:

$\dfrac{-5t^2+55}{(t^2+11)^2} = 0 \implies -5t^2+55 = 0 \implies t^2 = 11 \implies t=\pm\sqrt{11}\,\mathrm s \imples t \approx \boxed{3.317\,\mathrm s}$

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

$\dfrac{-5t^2+55}{(t^2+11)^2} > 0 \implies -5t^2+55>0 \implies -5t^2>-55 \implies t^2 < 11 \implies |t|$

In interval notation, this happens for t in the interval (0, √11) or approximately (0, 3.317) s.

(e) The total distance traveled is given by the definite integral,

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt$

By definition of absolute value, we have

$|v(t)| = \begin{cases}v(t) & \text{if }v(t)\ge0 \\ -v(t) & \text{if }v(t)$

In part (d), we've shown that v(t) > 0 when -√11 < t < √11, so we split up the integral at t = √11 as

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt = \int_0^{\sqrt{11}}v(t)\,\mathrm dt - \int_{\sqrt{11}}^8 v(t)\,\mathrm dt$

and by the fundamental theorem of calculus, since we know v(t) is the derivative of s(t), this reduces to

$s(\sqrt{11})-s(0) - s(8) + s(\sqrt{11)) = 2s(\sqrt{11})-s(0)-s(8) = \dfrac5{\sqrt{11}}-0 - \dfrac8{15} \approx 0.974\,\mathrm{units}$

7 0

3 years ago

Langston has $45$ greeting cards. He gives $18$ of the cards to his friends. What percent of his greeting cards does he give to

dalvyx [7]

Answer:

45-18=27 Greeting cards

Step-by-step explanation:

3 0

3 years ago

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You are making a snack that includes 5/6 pound of almonds and 7/9 pound of cashews. Which is greater, the weigh of the almonds o

devlian [24]

To compare the answers, you need to have the same denominator.

We know that, 18 is a common denominator between 6 and 9.

(5/6)*3/3 => 15/18 (ALMONDS)
(7/9)*2/2 => 14/18 (CASHEWS)

As seen, the weight of almonds is 1/18 bigger than the cashews.

Hope I helped :)

3 0

3 years ago

Read 2 more answers