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Nana76 [90]
3 years ago
15

The digits 1, 2, 3, 4, 5, 6, and 7 are randomly arranged to form a? three-digit number. ? (digits are not? repeated.) find the p

robability that the number is even and greater than 700.
Mathematics
1 answer:
lubasha [3.4K]3 years ago
4 0
Nice twist of similar questions.
There are 7*6*5=210 possible 3-digit numbers formed by digits 1-7 without repetition.
For numbers greater than 700, the first digit must be 7.
Of the 30, the last digit must be a 2,4, or 6 to be an even number, that leaves 3 possibilities for the last digit.
The middle digit can be any number of the remaining 5 digits.
So the number of qualifying candidates would be
1*5*3=15 (1 for the first digit, 5 choices for the second, and 3 choices for the last digit).
Probability of randomly choosing a qualifying candidate (>700 & even) is therefore 15/210=1/14
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A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax 2 about the y-
Setler79 [48]

Answer:

a = \frac{1}{2}. Surface Area = \frac{4}{3}ft^{2}. and area of the Dish = \frac{4}{3}ft^{2}+pi4^{2} = \frac{4}{3}ft^{2}+50.27=51.6ft^{2}

Step-by-step explanation:

(1) Constant. y(x) = ax^{2} that is the curve that we need to rotate around the y axis to get the parabola with diameter of 8 feet and 2 meter depth that statement is translated in mathematics as x = -4 to 4 and y = 0 to 2.

y max = 2, x max = 4 setting up a equation with a unknown gives

2=a4 and  a = \frac{1}{2}.

so we have now.

y(x) = \frac{1}{2}x^{2} (Done with solving for a Constant).

(2) Surface Area.

Setting Up surface integral.

(i) range in x = 0 to 4.

(ii) range in y = 0 to 2.

integral is.

Integral(0-2)[{integral[(0-4)\frac{1}{32}x^{2}]}]dy

Evaluating this integral gives. \frac{4}{3}ft^{2}.

and area is surface area + area of the circle with 8ft diameter.

= \frac{4}{3}ft^{2}+pi4^{2} = \frac{4}{3}ft^{2}+50.27=51.6ft^{2}...

Note the Difference between area and aurface area.!

6 0
3 years ago
The base of a triangle is nine centimeters longer than the perpendicular height. If the area of the triangle is 180 square centi
Rom4ik [11]

Answer:

<em>The base is 24 cm long.</em>

Step-by-step explanation:

<u>Equations</u>

Let's call

b= base of the triangle

h=height of the triangle

The base is 9 cm longer than the height, thus:

b = h + 9

The area of the triangle is:

\displaystyle A=\frac{bh}{2}

\displaystyle A=\frac{(h+9)h}{2}

And its value is 180:

\displaystyle \frac{(h+9)h}{2}=180

Multiplying by 2:

(h+9)h=360

Operating:

h^2+9h-360=0

Factoring:

(h-15)(h+24)=0

The only valid positive solution is:

h = 15 cm

And b = h + 9 = 24

b = 24 cm

The base is 24 cm long.

7 0
3 years ago
Online school is not the move:( HELP PLEASE (40 points!!) (bottom right one says ✔️2 = 1.414213
klasskru [66]

Answer:

What do you want me to help you on

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6 0
3 years ago
What is 9/7 times -9/5?
pochemuha

Answer:

- 2 11/35

Step-by-step explanation:

Step 1:

9/7 × - 9/5     Equation

Step 2:

- 81/35      Multiply

Answer:

- 2 11/35       Convert

Hope This Helps :)

8 0
2 years ago
Hey! i just need you to tell me how you got your answer! thank you!
Yakvenalex [24]

5 + 27 ÷ 3 / 6 + 1 - Remember PEMDAS, so start by dividing 27 by 3.

5 + 9 / 6 + 1 - Next, add

14 / 7 Lastly, Divide.

2

5 0
3 years ago
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