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vodka [1.7K]
3 years ago
15

If m∠4 = 35, find m∠2. Explain.

Mathematics
1 answer:
Bad White [126]3 years ago
4 0

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

Triangle CAB is a right triangle.

Therefore, m∠1 = 90°

Similarly, m∠ACD = 90°

m∠ACD = m∠ACB + m∠BCD = 90°

             = m∠3 + m∠4 = 90°

Since m∠4 = 35°,

m∠3 + 35° = 90°

m∠3 = 90° - 35°

        = 55°

In the triangle ABC,

m∠ACB + m∠CBA + m∠BAC = 180° [Property of a triangle]

m∠3 + m∠2 + m∠1 = 180°

55° + m∠2 + 90° = 180°

m∠2 + 145° = 180°

m∠2 = 180° - 145°

        = 35°

Since, AB║CD and BC is a transverse,

Therefore, m∠2 = m∠4 = 35° [Alternate interior angles]

Option (1) is the correct option.

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Bess [88]

Answer:

344

Step-by-step explanation:

Um..... sorta confusing, but I think you are only allowed to increase by 10 each time, so then you need to add 20 to make 344, where the units digit and tens digit are the same

4 0
2 years ago
An unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6
SIZIF [17.4K]

Answer:

Probability of rolling at least 4 sixes is 0.01696.

Step-by-step explanation:

We are given that an unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6  times.

The above situation can be represented through binomial distribution;

P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......

where, n = number trials (samples) taken = 6 trials

            r = number of success = at least 4

           p = probability of success which in our question is probability of

                 rolling a “six", i.e; p = 0.20

<u><em>Let X = Number of sixes on a die</em></u>

So, X ~ Binom(n = 6, p = 0.20)

Now, Probability of rolling at least 4 sixes is given by = P(X \geq 4)

P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6)

=  \binom{6}{4} \times 0.20^{4} \times (1-0.20)^{6-4}+\binom{6}{5} \times 0.20^{5} \times (1-0.20)^{6-5}+\binom{6}{6} \times 0.20^{6} \times (1-0.20)^{6-6}

=  15 \times 0.20^{4} \times 0.80^{2}+6 \times 0.20^{5} \times 0.80^{1}+1 \times 0.20^{6} \times 0.80^{0}

=  0.0154 + 0.00154 + 0.000064

=  0.01696

<em />

Therefore, probability of rolling at least 4 sixes is 0.01696.

8 0
3 years ago
What is the slope of y=45x
Lapatulllka [165]

Answer:

45/1

Step-by-step explanation:

45x is the rate at which the line goes up

8 0
2 years ago
Ebony's gross income is $46 660 with allowable tax deductions of $4120. a What is Ebony's taxable income? b Calculate the amount
jasenka [17]

Answer:

(a) Ebony's taxable income = $42,540

(b) Amount of tax due = $5190.3

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Step-by-step explanation:

Ebony's gross income = $46,660 (given)

Allowable tax deductions = $4,120 (given)

(a) Taxable Income = Gross income - Tax deductions

Ebony's taxable income = $46,660 - $4,120

Ebony's taxable income = $42,540

(b) Amount of tax due = 22% of Taxable Income,

Refer to the USA Tax Brackets for 2019 (See Attached image)

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Amount of tax due = $970 + $3573 + $647.3

Amount of tax due = $5190.3

(c) Ebony pays $95 per week in tax. In four weeks (a month), she'd pay

$95 * 4 = $380

Amount of tax owed = Amount of tax due - Amount of tax paid

Amount of tax owed = $5190.3 - $380 = $4810.3

3 0
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Two $5 bills, Two $1 bills, Two Quarters, Two Nickles

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5 0
3 years ago
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