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2 years ago

Angles P and Q are complementary.

Mathematics

1 answer:

GenaCL600 [577]2 years ago

5 0

Answer:

Explained below.

Step-by-step explanation:

Complementary angles are angles that sum up to 90°.

Here,

Angle P = 2x
Angle Q = 7x

Then,

Angle P + Angle Q = 90°

2x + 7x = 90°

9x = 90°

x = 90/9

x = 10°

Therefore,

Measurement of Angle P = 2x = 2*10 = 20°
Measurement of Angle Q = 7x = 7*10 = 70°

$\rule{150pt}{2pt}$

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Trigonometry questions

Evgen [1.6K]

Answer:

what is the question and give the question first

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3 years ago

Which properties justify the steps taken to solve the system?

Nutka1998 [239]

Answer:

X=-1

Y=1

Step-by-step explanation:

6x-12y

-18

) 6x + 4y

-2

Subtract the two equations

6x - 12y - (6x + 4y) = -18 - (-2)

Determine the sign

6x- 12y - 6x- 4y

=-18 + 2

Simplify

-12y

- Ay

=-18 + 2

Solve the equation

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6 0

1 year ago

Find the greatest number that divides451, 328 and 673 leaving 1, 4 and 1,respectively as remainders.

Vesna [10]

You're looking for the largest number x such that

x ≡ 1 (mod 451)

x ≡ 4 (mod 328)

x ≡ 1 (mod 673)

Recall that

x ≡ a (mod m)

x ≡ b (mod n)

is solvable only when a ≡ b (mod gcd(m, n)). But this is not the case here; with m = 451 and n = 328, we have gcd(m, n) = 41, and clearly

1 ≡ 4 (mod 41)

is not true.

So there is no such number.

4 0

2 years ago

If a+ar=b+r, the value of a in terms of b and r can be expressed as

nikdorinn [45]

A + ar = b + r
a(1 + r) = b + r
a = (b + r) / (1 + r)

Its c

4 0

3 years ago

A researcher wishes to estimate the average blood alcohol concentration (BAC) for drivers involved in fatal accidents who are f

Mnenie [13.5K]

Answer:

A 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .

Step-by-step explanation:

We are given that a researcher randomly selects records from 60 such drivers in 2009 and determines the sample mean BAC to be 0.16 g/dL with a standard deviation of 0.080 g/dL.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean BAC = 0.16 g/dL

s = sample standard deviation = 0.080 g/dL

n = sample of drivers = 60

$\mu$ = population mean BAC in fatal crashes

Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, a 90% confidence interval for the population mean, $\mu$ is;

P(-1.672 < $t_5_9$ < 1.672) = 0.90 {As the critical value of t at 59 degrees of

freedom are -1.672 & 1.672 with P = 5%} P(-1.672 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.672) = 0.90

P( $-1.672 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.672 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.672 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.672 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.672 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.672 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $0.16-1.672 \times {\frac{0.08}{\sqrt{60} } }$ , $0.16+1.672 \times {\frac{0.08}{\sqrt{60} } }$ ]

= [0.143, 0.177]

Therefore, a 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC is [0.143, 0.177] .

7 0

3 years ago