Answer:
Volume left = 404.32 cubic inches
Step-by-step explanation:
volume of a cylinder = 
h
volume of ice cream in the cylindrical tub =
x
x 9
=
x 25 x 9
= 707.1429
Volume of ice cream in the cylindrical tub is 707.14 cubic inches.
The ice cream scoop has a spherical volume, so that;
volume of a sphere = 


r = 
=
inches
volume of the scoop =
x
x 
=
x
x 
= 8.1845
volume of the scoop is 8.19 cubic inches.
If he scoops 37 scoops,
volume of the 37 scoops = 37 x 8.1845
= 302.8265
volume of 37 scoops is 302.83 cubic inches.
Volume of ice cream left in the tub = 707.1429 - 302.8265
= 404.3164
Volume of ice cream left in the tub is 404.32 cubic inches.
Answer:
x = 10°
Step-by-step explanation:
a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"
Therefore, in cyclic quadrilateral ABDE,
m∠ABD + m∠AED = 180°
110° + m∠AED = 180°
m∠AED = 180° - 110°
= 70°
b). AD = ED [Given]
m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]
m∠EAD = m∠AED = 70°
By triangle sum theorem in ΔABD,
m∠BAD + m∠ABD + m∠ADB = 180°
m∠BAD + 110° + 40° = 180°
m∠BAD = 180 - 150
= 30°
m∠AEB = m∠AED + m∠DAB [By angles addition postulate]
m∠AEB = 70° + 30°
= 100°
By triangle sum theorem in the large triangle,
x° + m∠AEB + m∠EAB = 180°
x° + 100° + 70° = 180°
x = 180 - 170
x = 10°
Hello There!
The first statement is incorrect as congruent angles have the same measure but it doesn't have to 45°. It can be any value.
The second one is also incorrect. Congruent angles have the same measure but don't always total to 180° (which is what supplementary means). It would only be true if they are congruent right angles.
The third one is also incorrect as they don't always total to 90° either (Which is what complementary means).
The fourth one is correct, this is because congruent angles are simply angles with the same measure.
In short, you're answer is 4. Congruent angles always have the same measure.
Hope This Helps You!
Good Luck :)
The correct option will be : 14 years
<u><em>Explanation</em></u>
Current account balance of Susan is $1,336.60 and her initial deposit was $820
So, the amount of interest earned
dollar
Formula for Simple Interest is:
, where
is the amount of interest,
is the initial amount,
is the rate of interest in decimal and
is the time duration in years.
Here,
% 
Now according to the above formula, we will get...

So, Susan has held the account for 14 years.
Given the formula for future value annuity:
FV of annuity=P[(1+r)^n-1]/r
where:
P=principle
r=rate
n=time
the time taken to repay the loan will be:
1500=90[(1+0.06)^n-1]/0.06
90=90[(1+0.06)^n-1]
1=(1+0.06)^n-1
1+1=(1+0.06)^n
2=1.06^n
introduce natural log
ln2=nln1.06
n=ln2/ln1.06
n=11.8957=12 years
the answer is 12 years.