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3 years ago

Factor the expression x^2-16x+63

Mathematics

1 answer:

Airida [17]3 years ago

7 0

The factors should add to the b value and multiply to the c value.

Final answer: (x-9)(x-7)

Check:
-9*-7=63
-9-7=-16

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In DEF DE=17 m angle =32 Find DF nearest tenth

Andrej [43]

Since we are asked to find DF, and we are given an angle and the side opposite to it, we can use the sine function to find DF.
let x be the length of side DF.

sin(32)= 17/x
x= 17 / sin(32)
x= 32.08

approximately 32.1

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3 years ago

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The complement of an angle is 25°. What is the measure of the angle?

lisabon 2012 [21]

Complement of an alngle means what you need to add to it to make 90 degrees

comlement of angle x is y such that x+y=90

so if complement of angle x is 25, that means the angle x is found by
x+25=90
minus 25 both sides
x=65 degrees

the angle measures 65 degree

8 0

3 years ago

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The age of the children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.8 years old. A fir

Kazeer [188]

Answer:

(1) (c) 5.30 years.

(2) (b) 0.289.

(3) (b) 0.80.

(4) (d) 0.50.

(5) (a) 5.25 years.

Step-by-step explanation:

Let X = age of the children in kindergarten on the first day of school.

The random variable X follows a continuous Uniform distribution with parameters a = 4.8 years and b = 5.8 years.

The probability density function function of X is:

$f_{X}(x)=\left \{ {{\frac{1}{b-a}} ;\ a$

(1)

The expected value of a Uniform random variable is:

$E(X)=\frac{1}{2}(a+b)$

Compute the mean of X as follows:

$E(X)=\frac{1}{2}(a+b)=\frac{1}{2}\times (4.8+5.8)=5.3$

Thus, the mean of the distribution is (c) 5.30 years.

(2)

The standard deviation of a Uniform random variable is:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}=\sqrt{\frac{1}{12}\times (5.8-4.8)^{2}}=0.289$

Thus, the standard deviation of the distribution is (b) 0.289.

(3)

Compute the probability that a randomly selected child is older than 5 years old as follows:

$P(X>5)=\int\limits^{5.8}_{5} {\frac{1}{5.8-4.8}}\, dx\\$

$=\int\limits^{5.8}_{5} {1}\, dx\\=[x]^{5.8}_{5}\\=(5.8-5)\\=0.8$

Thus, the probability that a randomly selected child is older than 5 years old is (b) 0.80.

(4)

Compute the probability that a randomly selected child is between 5.2 years and 5.7 years old as follows:

$P(5.2$

$=\int\limits^{5.7}_{5.2} {1}\, dx\\=[x]^{5.7}_{5.2}\\=(5.7-5.2)\\=0.5$

Thus, the probability that a randomly selected child is between 5.2 years and 5.7 years old is (d) 0.50.

(5)

It is provided that a randomly selected child is at the 45th percentile.

This implies that:

P (X < x) = 0.45

Compute the value of x as follows:

$P (X < x) = 0.45$

$\int\limits^{x}_{4.8} {\frac{1}{5.8-4.8}}\, dx=0.45$

$\int\limits^{x}_{4.8} {1}\, dx=0.45$

$[x]^{x}_{4.8}=0.45$

$x-4.8=0.45\\$

$x=0.45+4.8\\x=5.25$

Thus, the age of the child at the 45th percentile is (a) 5.25 years.

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3 years ago

Which of the following statements must be true about this diagram? Check all that apply.

Vinvika [58]

Answer:

The statements must be true are A , D , E

Step-by-step explanation:

* Lets explain the figure

- There is a triangle

- Its interior angles are x° , y° , z°

- The angle of measure w° is an exterior angle of the triangle at the

vertex whose measure is z°

- There a fact in the triangle is the measure of the exterior angle of a

triangle at one of its vertices is equal to the sum of the measures

of the two opposite interior angles to this vertex

∵ w° the measure of the exterior angle of the vertex whose measure

is z°

∵ x° , y° are the measures of the opposite interior angles of the angle

whose measure is z°

∴ w° = x° + y°

∴ w° > x°

∴ w° > y°

* Lets find the statements must be true

# w > x ⇒ A

# x + y = w ⇒ D

# w > y ⇒ E

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4 years ago

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the length of a rectangular pool is three times its width. The perimeter of the rectangular pool is 168 feet. find the length an

igor_vitrenko [27]

Step-by-step explanation:

breadth = 21 m

length = 63 m

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3 years ago

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