Five sixths of Forty two

BaLLatris [955]

The answer to the triangle problem is C

4 0

3 years ago

Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a multiple-cho

nadezda [96]

Answer:

The correct answer is 4294967296 possible ways to complete such a test.

Step-by-step explanation:

Step 1

The first step is to define the fundamental principle of counting. The fundamental principle of counting states that if a process can be carried out in n steps, where there are $n_1$ ways to complete the first step, $n_2$ ways to complete the second step, $n_3$ , and $n_k$ ways to complete the $k^{th}$ step, this process can be carried out in $n_1\times n_2\times n_3\times ...\times n_k$ ways.

Step 2

We use the fundamental principle of counting with $n=4$ for a total of $k=16$ steps. This test can be carried out in $4^{16}=4294967296$ ways. This comes from multiplying 4 by itself 16 times.

3 0

3 years ago

In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of <img src="https://tex.z-dn.net/?f=%20%5Cangle" id="TexFormula1

svetlana [45]

Answer:

See Below.

Step-by-step explanation:

Statements: Reasons:

$1)\, XY=XZ$ Given

$2) \text{ $ m\angle Y= m\angle Z$}$ Isosceles Triangle Theorem

$\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}$ Angle Addition

$\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}$ Given

$5) \text{ $m\angle XYQ=m\angle QYZ$}$ Definition of Bisector

$\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}$ Substitution

$7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}$ Angle Addition

$8)\text{ $ZP$ bisects $\angle XZY$}$ Given

$\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }$ Definition of Bisector

$\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}$ Substitution

$11)\text{ } 2m\angle QYZ=2m\angle PZY$ Substitution

$12)\text{ }m\angle QYZ=m\angle PZY$ Division Property of Equality

$13)\text{ } YZ=YZ$ Reflexive Property

$14)\text{ } \Delta YZP\cong\Delta ZYQ$ Angle-Side-Angle Congruence*

$15)\text{ } YQ=ZP$ CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

5 0

3 years ago

Read 2 more answers

In a 45-45-90 right triangle, what is the ratio of the length of one leg to the

balandron [24]

A 1:12 is the answer for this question

5 0

3 years ago

joe has a piggy bank with $8.90 split upon nickels, dimes, and quarters. The piggy bank contains 76 coins in all. The number of

kozerog [31]

Answer:

There are 38 dimes, 22 nickels and 16 quarters.

Step-by-step explanation:

Let n, d and q represent the # of nickels, dimes and quarters respectively.

Then n + d + q = 76

The value of a nickel is $0.05; that of a dime is $0.10, and that of a quarter is $0.25.

Thus, the value of n nickels is $0.05n (and so on).

The total value of the coins is $0.05n + $0.10d + $0.25q = $8.90.

d = n + q allows us to eliminate d.

First, n + d + q = 76 becomes n + (n + q) + q = 76, and second:

$0.05n + $0.10(n + q) + $0.25q = $8.90. Here we have succeeded in eliminating d from two different equations, and now we have these two different equations in two unknowns (n and q), which is solvable.

Simplifying both equations, we get:

2n + 2q = 76 and

5n + 10n + 10q + 25q = 890, or 15n + 35q = 890

Let's use the substitution method of solving linear equations:

Rewrite 2n + 2q = 76 as n + q = 38, or n = 38 - q. Substituting this result into the second equation, we get:

15(38 - q) + 35 q = 890, or

570 - 15q + 35q = 890, or

570 + 20 q = 890. Then 20q = 890 - 570 = 320, and q = 320/20 = 16.

There are 16 quarters. Thus, the number of nickels is n = 38 - 16 = 22.

Finally, since n + d + q = 76, 22 + d + 16 = 76, or:

22 + d = 60, or d = 60 - 22 = 38.

There are 38 dimes, 22 nickels and 16 quarters.

4 0

3 years ago