Answer:
a. The sum of the first 100 odd positive integers - Not a statement
b. Everybody needs somebody sometime - Atomic statement
c. The Broncos will win the Super Bowl or I'll eat my hat - Molecular statement (disjunction)
d. We can have donuts for dinner, but only if it rains - Molecular statement (conditional)
e. Every natural number greater than 1 is either prime or composite - Atomic statement
f. This sentence is false - Not a statement
Step-by-step explanation:
A statement in mathematics can be said to be any declarative statement that can either be true or false. While a sentence is considered to not be a statement if
Statements are divided into 2:
- Atomic statements: These are statements that cannot be split into mini statements.
- Molecular statements: These are the opposites of atomic statements. They are statements that cannot be spilt. This can further be divided into; conjunction, disjunction, conditional, bi-conditional and negation
Answer:

Step-by-step explanation:
First we need to find area of the triangle with a base of 4 cm and a height of 5cm, and then multiply that by the length of the prism of 15cm.
The area of the triangle is given by the formula:

where b is the base:
and h is the height: 
thus, in this case we have:

And now, the volume will be the area of the triangle multiplied by the length
of the prism:

Substituting the known values:

The volume in cubic centimeters is 150.
Answer:
d) The difference exists due to chance since the test statistic is small
Step-by-step explanation:
From the given information:
Population mean = 178 cm
the sample mean = 177.5 cm
the standard deviation = 2
the sample size = 25
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis:

Alternative hypothesis:

The t-test statistics is determined by using the formula:




Degree of freedom df = n- 1
Degree of freedom df = 25 - 1
Degree of freedom df = 24
At the level of significance ∝ = 0.05, the critical value = 2.064
Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance
Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small
Answer:
x = 16
Step-by-step explanation:
SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.
The angles opposite to equal sides are equal.
⇒ ∠STR = ∠R
∠STR = 4x - 28
Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair
∠STR + ∠STU = 180° {linear pair}
4x - 28 + 9x = 180
4x + 9x - 28 = 180 {Combine like terms}
13x- 28 = 180
Add 28 to both the sides
13x = 180 + 28
13x = 208
Divide both sides by 13
x = 208/13
