Step-by-step explanation:
sec(90-A) . Sin A = cot (90-A) . tan(90-A)
cosec X sinA = tanA X cotA
1/sinA X sinA = tanA X 1/tanA
1=1
Hence proved
L.H.S=sec(90-A)·sinA
=cosecA·sinA ;[sec(90-A)= cosecA]
=1/sinA·sinA ;[cosecA=1/sinA]
=1
R.H.S=cot(90-A)·tan(90-A)
=tanA·cotA ;[cot(90-A)=tanA, tan(90-A)=cotA]
=tanA·1/tanA ;[cotA=1/tanA]
=1
thus, L.H.S=R.H.S
[Proved]
Penguin can swim 68 miles in four hours.
A rate is defined as the ratio which is used to compare two different types of quantities that have different units.
Unit rate defines the ratio of the amount of one quantity with respect to the single unit of the other quantity. Or in other words, the denominator of unit rate will be always 1.
Here we have the unit rate as 17 miles per hour.
Here unit rate is defined in terms of distance covered per time which is actually the speed of penguin.
We have to the distance covered by the penguin in 4 hours.
Rate = Distance / Time
⇒ Distance = Rate × Time
= 17 × 4
= 68 miles
Hence, penguin can swim 68 miles in 4 hours if the rate of swimming is 17 miles per hour.
To learn more about Rate, click:
#SPJ2
Answer:
20%
Step-by-step explanation:
1/5 = 0.20 → multiply by 100 = 20%
Answer:
20 percent
Step-by-step explanation:
All percentages have a denominator of 100, and 100 divided by 5 is 20.
B. We can't determine from the given information.
C. Exactly one
D. None
(a) The length of time it takes to fill up your gas tank - Continuous
(b) The number of students applying to graduate schools - Continuous
(c) The number of voters who vote Democratic - Discrete
(d) The number of customers waiting at the grocery store-Discrete
Continuous data can have an infinite range of values while Discrete data can take some certain values only.
Let us consider the given examples
a) The length of time it takes to fill up your gas tank.
In this case, the time duration can be of a wide range. Time taken while filling up a gas tank can take many values. So it is an example of continuous data.
b) The number of students applying to graduate schools.
In this case, the number of students applying to graduate schools can be of a wide range. it can be n number of values. So it is an example of continuous data.
c)The number of voters who vote Democratic.
The number of voters who vote can be of a certain value. Hence, this is an example of discrete data.
d)The number of customers waiting in line at the grocery store.
The number of customers waiting in line at the grocery store can be of a certain value. Hence, this is an example of discrete data.
Therefore, we can say that
(a) The length of time it takes to fill up your gas tank - Continuous
(b) The number of students applying to graduate schools - Continuous
(c) The number of voters who vote Democratic - Discrete
(d) The number of customers waiting at the grocery store-Discrete
To get more about continuous and discrete data refer to the link,
Answer:
(a) The length of time it takes to fill up your gas tank - CONTINUOUS
(b) The number of students applying to graduate schools - CONTINUOUS
(c) The number of voters who vote Democratic - DISCRETE
(d) The number of customers waiting in line at the grocery store - DISCRETE
Step-by-step explanation:
To determine either the set of data are discrete or continuous, let consider their characteristics.
CONTINUOUS
continuous data is quantitative data, It can be measured, it has an infinite values within selected range.
DISCRETE
Discrete data is counted, it can only take certain values.
Answer:
True
Step-by-step explanation:
We assume that is true for the nth case and prove it for the n+1 case
and show that it is true for the case when n=1