Answer:
Jennifer should expect a number less than 3 23 times
Step-by-step explanation:
The probability of rolling a number less than 3 on a number cube is 2/6. .
The probability of rolling a number less than 3 on a number cube is 2/6
= 1/3
Jennifer rolls a number cube 69 times
Expectations= probability*total outcome
Expectations= 1/3 * 69
Expectations= 69/3
Expectations= 23 times
Answer:
$1317.14
Step-by-step explanation:
compounded continuously formula is A=Pe^rt
given that you want to have $1500 in 2 years while the rate is 6.5%, you have A, r, and t of the formula and you are just looking for the P.
plugging everything in...
1500=P (e)^2x0.065
P=1500/1.139
P=1317.14
Answer:
Cells are the basic building blocks of all living things. The human body is composed of trillions of cells. They provide structure for the body, take in nutrients from food, convert those nutrients into energy, and carry out specialized functions.
Step-by-step explanation:
I hope that helps you out.
Answer:
7.1 miles
Step-by-step explanation:
Consider right triangle HospitalSchoolSupermarket. In this triangle:
- HospitalSchool = 14.7 mi;
- HospitalSupermaket = 11.76 mi;
- School Supermarket = 8.82 mi.
The shortest road from the main entrance of the supermarket to the highway that connects the school and hospital will be the height drawn from the point Supermarket to the hypotenuse HospitalSchool.
Let the length of this road be x mi and the distance from School to point A be y mi. Use twice the Pythagorean theorem for right triangles Supermarket SchoolA and SupermarketHospitalA:
![\left\{\begin{array}{l}x^2+y^2=8.82^2\\ \\x^2+(14.7-y)^2=11.76^2\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%5E2%2By%5E2%3D8.82%5E2%5C%5C%20%5C%5Cx%5E2%2B%2814.7-y%29%5E2%3D11.76%5E2%5Cend%7Barray%7D%5Cright.)
Subtract from the second equation the first one:
![x^2+(14.7-y)^2-x^2-y^2=11.76^2-8.82^2\\ \\14.7^2-2\cdot 14.7y+y^2-y^2=11.76^2-8.82^2\\ \\-29.4y=11.76^2-8.82^2-14.7^2\\ \\29.4y=155.5848\\ \\y\approx5.24\ mi](https://tex.z-dn.net/?f=x%5E2%2B%2814.7-y%29%5E2-x%5E2-y%5E2%3D11.76%5E2-8.82%5E2%5C%5C%20%5C%5C14.7%5E2-2%5Ccdot%2014.7y%2By%5E2-y%5E2%3D11.76%5E2-8.82%5E2%5C%5C%20%5C%5C-29.4y%3D11.76%5E2-8.82%5E2-14.7%5E2%5C%5C%20%5C%5C29.4y%3D155.5848%5C%5C%20%5C%5Cy%5Capprox5.24%5C%20mi)
Thus,
![x^2=8.82^2-5.24^2=50.3348\\ \\x\approx 7.1\ mi.](https://tex.z-dn.net/?f=x%5E2%3D8.82%5E2-5.24%5E2%3D50.3348%5C%5C%20%5C%5Cx%5Capprox%207.1%5C%20mi.)
Answer:
yeah it is
y is directly proportional to x
proportionality constant is 9