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Firlakuza [10]
3 years ago
11

What’s the measure of angle XYZ?

Mathematics
2 answers:
Murrr4er [49]3 years ago
5 0
In a circle, the measure of an inscribed angle is half the measure of the intercepted arc.

m∠XYZ = 68/2 = 34°
Dima020 [189]3 years ago
3 0

Answer:

Option B 34° is the answer.

Step-by-step explanation:

From the inscribed angle theorem, the measure of an inscribed angle is half of the intercepted arc.

Here intercepted arc is xz = 68° and inscibed angle is ∠xyz.

Therefore, by theorem,

∠xyz = \frac{1}{2}m(xz)

∠xyz = \frac{1}{2} (68)°

∠xyz = 34°

Option B 34° is the answer.

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ddd [48]

Answer:

34

Step-by-step explanation:

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3 years ago
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How many tons are in 40000 pounds
GarryVolchara [31]
If you're on about us tons then it = 20 
However if it's tonnes then it = 18.143695 
6 0
2 years ago
A company has 8 mechanics and 6 electricians. If an employee is selected at random, what is the probability that they are an ele
Andre45 [30]

Answer:

Probability = \frac{3}{7}

Step-by-step explanation:

Given

Electrician = 6

Mechanic = 8

Required

Determine the probability of selecting an electrician

First, we need the total number of employees;

Total = n(Electrician) + n(Mechanic)

Total = 6 + 8

Total = 14

Next, is to determine the required probability using the following formula;

Probability = \frac{n(Electrician)}{Total}

Probability = \frac{6}{14}

Divide numerator and denominator by 2

Probability = \frac{3}{7}

<em>Hence, the probability of selecting an electrician is 3/7</em>

4 0
3 years ago
celine mixes raisins and peanuts to make a snack. she uses 0.75 cup raisins for every 0.5 cup peanuts. write a proportion and us
PtichkaEL [24]

Answer:

6.375 cups of raisins

Step-by-step explanation:

The ratio of raisins to peanuts is 3:2. This is because 0.5 divided by 2 and then multiplied by 3 is equal to 0.75.

So to find the number of raisins we need to divide the number of peanuts by 2 and then multiply it by 3:

(4.25 ÷ 2) × 3 = 6.375

4 0
3 years ago
Read 2 more answers
Prove or disprove (from i=0 to n) sum([2i]^4) &lt;= (4n)^4. If true use induction, else give the smallest value of n that it doe
ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: \sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4

For n=1: \sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4

From this point we will assume that n\geq 2

As we can see, \sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4 and (4n)^4=256n^4. Then,

\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

Now, we will use the formula for the sum of the first 4th powers:

\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}

Therefore:

\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

and, because n \geq 0,

465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

Observe that, because n \geq 2 and is an integer,

n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5

In concusion, the statement is true if and only if n is a non negative integer such that n\leq 77

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute  (4n)^4- \sum^{n}_{i=0} (2i)^4 for 77 and 78 you will obtain:

(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064

(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992

7 0
3 years ago
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