Answer:97/125
Step-by-step explanation:
“As illustrated in the Venn diagram,
We let
U=[The total number of people at the sport center]
This implies that,
n(U)=125
G=[Those who use the gym]
This implies that,
n(G)=59
P=[Those who use the pool]
This implies that,
n(P)=70
T=[Those who use the track]
This implies that,
n(T)=55
a=[Those who use the gym only]
This implies that,
n(a)=59-(6+11+19)=59-36=23
b=[Those who use the pool only]
This implies that,
n(b)=70-(6+19+24)=70-49=21
c=[Those who use the track only]
This implies that,
n(c)=55-(6+24+11)=55-31=14
Also, number of people who use gym and track=11+23+19+6+14+24=97”
<span>First, the formula would be like this dP / dt= KP.
Secondly, since dP is given which is 6.9. Substitute it from the equation.
P(0) = 6.9 x 10^6
integral 1 divided by pdp which will look like this,
integral 1/ PdP = integral kdt
the answer would be .0019 or
k=.0019</span>
Answer:
C
Step-by-step explanation:
Since this is an indererminate form, use L'Hopital
d(sint)/dt = cos(t)
d[ln(2e^t) - 1] = (2e^t)/[2e^t - 1]
As t --> 0,
cos(0) = 1
(2e^t)/[2e^t - 1] = 2
1/2 is the limit
Answer:
So Philip made 5 bracelets and 4 necklaces.
Step-by-step explanation:
Let x = number of bracelets and y = number of necklaces.
Since we have a total of 9 bracelets and necklaces,
x + y = 9 (1)
Also, we have 8 inches of cord for each bracelet and 20 inches of cord for each necklace, then the total length for the bracelet is 8x and that for the necklace is 20y.
So, the total length for both is 8x + 20y. Since the total length of cord used is 120 inches,
8x + 20y = 120 (2)
Simplifying it we have
2x + 5y = 30 (3).
Writing equations (1) and (3) in matrix form, we have
![\left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}9\\30\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C2%265%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D9%5C%5C30%5Cend%7Barray%7D%5Cright%5D)
Using Cramer's rule to solve for x and y,
![x = det \left[\begin{array}{ccc}9&1\\30&5\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\](https://tex.z-dn.net/?f=x%20%3D%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D9%261%5C%5C30%265%5Cend%7Barray%7D%5Cright%5D%20%2Fdet%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C2%265%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
x = (9 × 5 - 30 × 1) ÷ (1 × 5 - 1 × 2)
x = (45 - 30) ÷ (5 - 2)
x = 15 ÷ 3
x = 5
![y = det \left[\begin{array}{ccc}1&9\\2&30\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\](https://tex.z-dn.net/?f=y%20%3D%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%269%5C%5C2%2630%5Cend%7Barray%7D%5Cright%5D%20%2Fdet%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C2%265%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
y = (30 × 1 - 9 × 2) ÷ (1 × 5 - 1 × 2)
y = (30 - 18) ÷ (5 - 2)
y = 12 ÷ 3
y = 4
So Philip made 5 bracelets and 4 necklaces.
BD = AC Given. BD cuts AC in half. That's what bisectors do.
BD = BD Reflexive property of a line (it is always equal to itself).
<ADB = <ADC = 90o
DB is perpendicular to AC Given.
<ADB + <ADC = 180o The two are supplementary.
Each angle = 90o Perpendicular means that one line meets another at 90o
2x = 180
x = 90o
Since each of the enclosed angles = 90, two have two triangles congruent by SAS <<<< Answer
