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Debora [2.8K]
3 years ago
10

The art club had an election to select a president. 39 members voted in the election and 13 did not vote. What percentage of the

members voted?
Write your answer using a percent sign (%).
Mathematics
1 answer:
expeople1 [14]3 years ago
6 0

Answer:

92.85%

Step-by-step explanation:

Add 39+13=42

Divide 39 by 42

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Julie had $20.00 in her pocket. She spent $7.40. About what percent of her money does she still have?
posledela

63%


First, we have to take 20.00 - 7.40 which gets us 12.60.


Then, we use the formula where we put the 12.60 on top of a fraction bar, and the 20.00 on bottom.

We do 12.60 x 100 which makes 1260.


Lastly, we divide that by the 20.00 which gets us 63.


So, Julie has 63% of her money left.


I hope this helped!!!

4 0
11 months ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false
asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1) be the characteristic polynomial of B.

a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)

b) Remember that p(\lambda)=\det(B-\lambda I). 0 is a root of p, so we have that p(0)=\det(B-0 I)=\det B=0.

c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.

d) det(B)=0 by part c) so B is not invertible.

e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.      

8 0
3 years ago
M(-5, 2) and N(5, 2) are the endpoints of the segment MN on the coordinate plane. What is the length of MN¯¯¯¯¯¯ ?
stira [4]
Use the distance formula

\sqrt{(2-2)^2+(5--5)^2}=\sqrt{100}=10
5 0
3 years ago
Read 2 more answers
Mr. Jones feeds his big cat 1/3 of a can of cat food and he feeds his small cat half
sasho [114]

Answer:

1/2

Step-by-step explanation:

1/3 + 1/6 = 1/2

5 0
3 years ago
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