<span>1) We are given that PA = PB, so PA ≅ PB by the definition of the radius.
</span>When you draw a perpendicular to a segment AB, you take the compass, point it at A and draw an arc of size AB, then you do the same pointing the compass on B. Point P will be one of the intersections of those two arcs. Therefore PA and PB correspond to the radii of the arcs, which were taken both equal to AB, therefore they are congruent.
2) We know that angles PCA and PCB are right angles by the definition of perpendicular.
Perpendicularity is the relation between two lines that meet at a right angle. Since we know that PC is perpendicular to AB by construction, ∠PCA and ∠PCB are right angles.
3) PC ≅ PC by the reflexive property congruence.
The reflexive property congruence states that any shape is congruent to itself.
4) So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by CPCTC (corresponding parts of congruent triangles are congruent).
CPCTC states that if two triangles are congruent, then all of the corresponding sides and angles are congruent. Since ΔACP ≡ ΔBCP, then the corresponding sides AC and BC are congruent.
5) Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of the perpendicular bisector.
<span>The perpendicular bisector of a segment is a line that cuts the segment into two equal parts (bisector) and that forms with the segment a right angle (perpendicular). Any point on the perpendicular bisector has the same distance from the segment's extremities. PC has exactly the characteristics of a perpendicular bisector of AB. </span>
Complete Question
Riya is applying to her garden. She applies it at a rate of 25, 000 cm³ of mulch for every m² of garden space. At what rate is Riya applying mulch in m³/m²
Answer:
0.25m³/m²
Step-by-step explanation:
We are told the Riya sprays mulch at 250,000cm³ per m²
To find the rate at which Riya is spaying the mulch in m³/m² we would have to convert 250,00cm³/m² to m³/m²
1 cm³ = 1 × 10^-6m³
250,000 cm³ = x m³
Cross Multiply
1 cm³ × xm³ = 250,000cm³ × 1 × 10^-6 m³
X
x m³ = 250,000cm³ × 1 × 10^-6 m³/1 cm³
= 0.25m³
Therefore, the rate at which Riya is spraying the mulch = 0.25m³/m²
Answer:
Find the five number summary of the data:
Minimum = x
Quartile 1 = x
Quartile 2 (median) = x
Quartile 3 = x
Maximum = x
Then, make the plot based on that information. If you are provided with a list of data, you should be able to use a calculator to find out that information.
Answer:
Step-by-step explanation:
Hello!
In stratified sampling, the researcher separates the population into subgroups according to the criteria established for his experiment. These subgroups will be made up of homogeneous observation units in terms of the characteristics of interest. In this case, each of the people who make up the groups will have only one of the two possible opinions (support, do not support) but not both.
When this type of sampling is performed, it is the researcher who decides what sample size you want to take, depending on various economic factors, availability of materials, access to experimental units (for example, if they are endangered animals, that is, finite populations , you cannot take very large sample sizes)
You can perform a proportionate stratified sampling and take a proportion of people who answered "yes" and a proportion of people who answered "no."
In this type of sampling, when taking a given proportion of each population, it is easier to extrapolate the results obtained to the populations. Then, if for example you must take a sample of size n = 20 where both strata correspond to half, that is to say that the stratum corresponding to "yes" will be 10 people and the stratum corresponding to "no" will be ten people.
I hope this helps!
Answer:
400+4n ≥ 750; The club will need to raise an average of $87.50 or more per month.
