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3 years ago

An angle whose measure is -405° is in

Mathematics

1 answer:

lara [203]3 years ago

8 0

Answer:

Quadrant IV

Step-by-step explanation:

Given

$\theta = -405^\circ$

Required

The quadrant of the terminal side

To do this, we simply rotate the given angle in a clockwise direction.

A complete rotation is $-360^\circ$

So, we have:

$\theta = -405^\circ$

$\theta = -360^\circ -45^\circ$

Remove the complete rotation

$\theta = -45^\circ$

When $45^\circ$ is rotated in the clockwise direction, it stops at the 4th quadrant.

Hence, the terminal side falls in the quadrant IV

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Help, I’m stuck. Lol.

Darya [45]

Answer:

a. height = 12

b. area = 228

Step-by-step explanation:

a. To find the height, we can use the triangle formed by the side that measures 15, the side that measures 9. and the height. The hypotenuse of the triangle(the longest side opposite of the right angle), is 15. We can then use the Pythagorean Theorem, which states that $a^2+b^2=c^2$ , where c is the hypotenuse, and a and b are the two other sides. In this case, we need to find a leg of the triangle, not the hypotenuse. What do we do? We can first call the height a, and rearrange the Theorem into $c^2-b^2=a^2$ . $15^2=225, 9^2=81,$ and $225-81=\sqrt{144}$ =12. Therefore, the height of the parallelogram is $\boxed{12}$

b. To find the area of the parallelogram, we can use the area formula, which is Base*Height. The base is the flat side. We can find the base by adding 9+10=19, and $19\cdot12=\boxed{228}$

6 0

4 years ago

principal phillipi used a random sample of 20 students records to determine how far, in miles, students live from the school. Th

zzz [600]

To find the mean:

Take 3 4 5 3 4 5 6 5 4 3 2 3 4 5 6 4 8 4 3 2 and add them all together

=83

Now you divide 83 by the number of terms in the sample set, which is 20.

83/20 = 4.15

For rounding to the nearest tenth, look at the hundredths space, which is 5. Since it is 5 or higher, round the tenths up one.

final answer= 4.2

5 0

3 years ago

Read 2 more answers

The larger of two consecutive integers is 13 greater than four times the smaller. Find the integers

Mamont248 [21]

now, let's keep in mind that, the integers are consecutrive, therefore, if one is say 2, the other is either, 3 or 1, because 1,2,3 <--- notice, 1 is before 2 and 3 is after 2.

so say, our first integer is "a", then the next one can just be "a+1".

$\bf \begin{cases} a&=small\\ a+1&=\stackrel{consecutive}{large}\\ \end{cases}\qquad \begin{cases} \stackrel{\textit{4 times the small}}{4a}\\ \stackrel{\textit{13 greater than that}}{4a + 13} \end{cases}~\hfill \stackrel{\textit{large}}{a+1}=\stackrel{\stackrel{\textit{13 more than }}{\textit{4 times the small}}}{4a+13} \\\\[-0.35em] ~\dotfill$

$\bf a+1=4a+13\implies 1=3a+13\implies -12=3a\implies \cfrac{-12}{3}=a \\\\\\ \blacktriangleright -4=a \blacktriangleleft\qquad \qquad \stackrel{\textit{consecutive and large}~\hfill }{a+1\implies -4+1\implies \blacktriangleright -3 \blacktriangleleft}~\hfill \boxed{\stackrel{\textit{small}}{-4}~~,~~\stackrel{\textit{large}}{-3}}$

let's recall that, on the negative side in a number line, the closer to 0, the larger the number, therefore, -1,000,000 is a much smaller number than -1, because -1 is closer to 0, thus is larger.

7 0

3 years ago

1/3 (4 ∙ 3) + 23 I need help

ANTONII [103]

Answer:

But tell me the exact question it has on there

Step-by-step explanation:

8 0

3 years ago

According to Harper's Index, 40% of all federal inmates are serving time for drug dealing. A random sample of 20 federal inmates

loris [4]

Answer:

(a) P(X≥10) = 0.245

(b) P(X≤5) = 0.125

Step-by-step explanation:

We will use the binomial distribution to solve this problem. Let X be the number of federal inmates who are serving time for drug dealing. We will use the binomial probability formula:

P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

where n = total number of federal inmates

x = no. of federal inmates who serve time for drug dealing

p = probability that a federal inmate is serving time for drug dealing

q = probability that a federal inmate is not serving time for drug dealing

(a) P(X≥10) = 1 - P(X<10)

= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]

= 1 - [²⁰C₀(0.4)⁰(0.6)²⁰⁻⁰ + ²⁰C₁(0.4)¹(0.6)²⁰⁻¹ + ²⁰C₂(0.4)²(0.6)²⁰⁻² + ²⁰C₃(0.4)³(0.6)²⁰⁻³ + ²⁰C₄(0.4)⁴(0.6)²⁰⁻⁴ + ²⁰C₅(0.4)⁵(0.6)²⁰⁻⁵ + ²⁰C₆(0.4)⁶(0.6)²⁰⁻⁶ + ²⁰C₇(0.4)⁷(0.6)²⁰⁻⁷ + ²⁰C₈(0.4)⁸(0.6)²⁰⁻⁸ + ²⁰C₉(0.4)⁹(0.6)²⁰⁻⁹

= 1 - (0.000036 + 0.00048 + 0.00308 + 0.0123 + 0.0349 + 0.0746 + 0.1244 + 0.1658 + 0.1797 + 0.1597)

= 1 - 0.7549

P(X≥10) = 0.245

(b) P(X≤5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

since we have calculated these values in the previous part, we will simply plug them in here and then add them up.

P(X≤5) = 0.000036 + 0.00048 + 0.00308 + 0.0123 + 0.0349 + 0.0746

P(X≤5) = 0.125

(c) For a binomial distribution, the expected value can be calculated as:

μ = np

= (20)(0.4)

μ = 8

The expected number of inmates who are serving time for drug dealing is 8.

7 0

3 years ago