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3 years ago

According to the lecture, a valedictory speech should last approximately ________ minutes.

Mathematics

1 answer:

fiasKO [112]3 years ago

6 0

<span>According to the lecture, a valedictory speech should last approximately 15 minutes. </span>

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Increase 80 by 12.5%

Luden [163]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The ratio x:y is 3: 1 Which of the following statements is correct? A x is 3/4 of y B y is 1/3 of x C x is 1/3 of y D y is 1/4 o

krok68 [10]

Answer: i say B is correct

5 0

3 years ago

Johnny invested $20,000.A portion returned 5% and another portion returned 8%. The total interest earned on the investment was $

damaskus [11]

Answer:

Amount invested that yielded interest of 5% is $15000 and amount invested that yielded interest of 8% is $5000

Step-by-step explanation:

Johnny invested $20,000

We are told that it consisted of 2 portions because one returned an interest of 5% and the other one 8%

Now, Let x be the amount invested that earned 5% and y be the amount invested that earned 8%

Thus:

x + y = 20000 - - - (eq 1)

The total interest earned on the investment was $1150

Thus;

5%x + 8%y = 1150

This can be rewritten as;

0.05x + 0.08y = 1150 - - -(eq 2)

From eq 1, let's make x the subject.

x = 20000 - y

Putting 20000 - y for x in eq 2 gives;

0.05(20000 - y) + 0.08y = 1150

1000 - 0.05y + 0.08y = 1150

Rearranging, we have;

0.03y = 1150 - 1000

0.03y = 150

y = 150/0.03

y = 5000

Thus,

x = 20000 - 5000

x = 15000

Thus,

Amount invested that yielded 5% is $15000 and amount invested that yielded 8% is $5000

3 0

3 years ago

Is it possible for a right triangle with a leg that is 12 inches long and a hypotenuse that is 37 inches long to be congruent to

Llana [10]

9514 1404 393

Answer:

x = 35

Step-by-step explanation:

It appears the only missing piece of the explanation is ...

x² = 1225 ⇒ x = 35

7 0

3 years ago

A plane flying horizontally at an altitude of 1 mi and a speed of 470 mi/h passes directly over a radar station. Find the rate a

kiruha [24]

Answer:

407 mi/h

Step-by-step explanation:

Given:

Speed of plane (s) = 470 mi/h

Height of plane above radar station (h) = 1 mi

Let the distance of plane from station be 'D' at any time 't' and let 'x' be the horizontal distance traveled in time 't' by the plane.

Consider a right angled triangle representing the above scenario.

We can see that, the height 'h' remains fixed as the plane is flying horizontally.

Speed of the plane is nothing but the rate of change of horizontal distance of plane. So, $s=\frac{dx}{dt}=470\ mi/h$

Now, applying Pythagoras theorem to the triangle, we have:

$D^2=h^2+x^2\\\\D^2=1+x^2$

Differentiating with respect to time 't', we get:

$2D\frac{dD}{dt}=0+2x\frac{dx}{dt}\\\\\frac{dD}{dt}=\frac{x}{D}(s)$

Now, when the plane is 2 miles away from radar station, then D = 2 mi

Also, the horizontal distance traveled can be calculated using the value of 'D' in equation (1). This gives,

$2^2=1+x^2\\\\x^2=4-1\\\\x=\sqrt3=1.732\ mi$

Now, plug in all the given values and solve for $\frac{dD}{dt}$ . This gives,

$\frac{dD}{dt}=\frac{1.732\times 470}{2}=407.02\approx 407\ mi/h$

Therefore, the distance from the plane to the station is increasing at a rate of 407 mi/h.

6 0

4 years ago