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2 years ago

Will these three sides form a right triangle 7yd,3yd,9yd ? yes or no?

Mathematics

1 answer:

Brut [27]2 years ago

3 0

Answer:

No, these three sides form a right triangle 7yd,3yd,9yd wont work

Step-by-step explanation:

a^2 + b^2 = c^2

lonest length is c (hypotenuse) : 9yd

(7)^2 + (3)^2 = (9)^2

49 + 9 = 81

58 = 81 NOT TRUE

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USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counse

pychu [463]

Answer:

a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

b) $E(X) = np = 4*0.75=3$

c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=4, p=1-0.25=0.75)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

4 0

3 years ago

The sphere is _____ cubic centimeters bigger than the cube. (Round to the nearest cubic centimeter.)

Misha Larkins [42]

ANSWER

The sphere is 10762 cubic centimeters bigger than the cube.

EXPLANATION

We want to find the difference in the volumes of the sphere and the cube.

To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.

The volume of a sphere is given as:

$V=\frac{4}{3}\pi r^3$

where r = radius

The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:

$\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot15^3 \\ V\approx14137\operatorname{cm}^3 \end{gathered}$

The volume of a cube is given as:

$V=s^3$

where s = length of the side

The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:

$\begin{gathered} V=15^3 \\ V=3375\operatorname{cm}^3 \end{gathered}$

Therefore, the difference in the volumes of the sphere and cube is:

$\begin{gathered} V_d=V_s-V_c \\ V_d=14137-3375 \\ V_d=10762\operatorname{cm}^3 \end{gathered}$

Therefore, the sphere is 10762 cubic centimeters bigger than the cube.

6 0

1 year ago

What is the area of the figure? <br> A. 66 <br> B. 84 <br> C. 60 <br> D. 72

Lerok [7]

Answer:

C.60

Step-by-step explanation:

4×12=48

18-12=6

6×2=12

48+12=60

3 0

3 years ago

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(d) Mrs. Ferguson has a conversation on the phone with her best friend Judy, who stayed at the same hotel last year. They compar

faltersainse [42]

Rooms are 3 dimentional
they have volume
area times height=volume

if dimentions are the same, that means that the legnth, width, height are same, so therefor they have same area (Judy is correct)

if area area same, then the height could be different, so Mrs. Ferguson is wrong

Judy is correct and Mrs. Ferguson is wrong

8 0

3 years ago

Carlene sells magazine subscriptions door-to-door. She receives $4 for each

lapo4ka [179]

The last option is correct

7 0

3 years ago

Read 2 more answers