Answer:
a) -1.25
b) 0.2112
c) -1.96
Step-by-step explanation:
Data provided in the question:
Sample size, n = 400
H0 : p = 20
= 175
Now,
a) The test statistic is given as:
Z = 
on substituting the respective values, we get
Z = 
= -1.25
b) The p-value = 2 × P(Z <-1.25)
Now from the standard normal table
P(Z <-1.25) = 10.56% = 0.1056
Thus,
p-value = 2 × 1056 = 0.2112
c) for a = 0.05,
the critical value is
i.e 
Now from standard normal table
= -1.96
Answer:
The correct answer is;
ΔANT ≅ ΔFLE by the SIde-Side-Side (SSS) rule of congruency
Step-by-step explanation:
The given information are;
Segment TN is congruent ts segment EL
Segment TA is congruent ts segment EF
Segment AN is congruent ts segment FL
Therefore, triangle ΔANT is congruent to ΔFLE by the Side-Side-Side (SSS) rule of congruency
One of the rule used to serve as proof that two or more triangles are congruent, is the Side-Side-Side (SSS) rule of congruency. The Side-Side-Side rule of congruency states that if the dimensions of the three sides of one triangle are equal to the dimensions of the three sides of another triangle, the two triangles are congruent.
Therefore, the correct option is ΔANT ≅ ΔFLE by the Side-Side-Side (SSS) rule of congruency
Find the area of both first. The sidewalk is 12 * 12 = 144 ft^2, and grass is 10 * 10 = 100 ft^2. Subtract the area of the grass from the sidewalk, 144-100 = 44 ft^2.
An equation to solve for the time when the high school will have exactly 100 students is (1-.06)^x = (250/100).
That simplifies to 94^x = .4.
We can then take the log of both sides to isolate the x variable from the exponent. Here's with natural log.
x*ln(.94)=ln(.4)
x = ln(.4)/ln(.94)
Solving this gives x ~= 14.80. So in about 15 years, the high school will have 100 students.
Answer:
Therefore the measure of RS is 12 unit.
Step-by-step explanation:
Given:
In ΔNPQ,
R is a midpoint of NP and
S is a midpoint of PQ.
RS = 47 - 5x, and NQ = 5x - 11
To Find:
RS = ?
Solution:
Mid Point Theorem:
The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is equal to one half of the third side.
Here ,R is a midpoint of NP and
S is a midpoint of PQ.
∴ 
Substituting the values we get

Now Substituting ' x ' in RS we get

Therefore the measure of RS is 12 unit.