When a fair dice is thrown, what is the probability of getting a number greater than 4? (Reduce to simplest form)

Answer: you can buy 6apples for$1

Step-by-step explanation: you divide 36 by 6 and get 6 so it’s 6apples.

Answer:

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Step-by-step explanation:

To solve this question, we need to use the binomial and the normal probability distributions.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability the president will have an IQ of at least 107.5

IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that [tex]\mu = 100, \sigma = 15[/tex]

This probability is 1 subtracted by the p-value of Z when X = 107.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{107.5 - 100}{15}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 probability that the president will have an IQ of at least 107.5.

Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{130 - 100}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 0.0451[/tex]

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?

0.3085 probability that the president will have an IQ of at least 107.5.

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Independent events, so we multiply the probabilities.

0.3082*0.0451 = 0.0139

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

The value of x is 7.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The two triangles PQR and P'Q'R' are similar triangles

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Firstly let us find the P'Q' by using pythagoras theorem

R'Q'²=PR'²+P'Q'²

12²=10²+P'Q'²

144-100=P'Q'²

44=P'Q'²

P'Q'=6.6

The value of PR is x

The value of x is 7. as R it is a midpoint of P'Q'R'

Hence the value of x is 7

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ2

Answer:

Step-by-step explanation:

Answer:

total of the data points = 1200

Step-by-step explanation:

The 'average' of a data set is the total of the data points divided by the number of data points.

Here:

total of the data points

---------------------------------- = 48

                 25

Multiplying both sides of this equation by 25 yields:

total of the data points = 1200

Answer:

3/36 or 8.333

Step-by-step explanation:

the way you get it is write all the possibilities and that how you get 3/36

Answer:

Step-by-step explanation:

A = P(1+r/n)^ nt

A = 2000(1+.04/2)^(5*2)

A = [tex]2000(1.02)^{10}[/tex] = $2437.99

Answer:

5000

Step-by-step explanation:

but this depends upon how much room each person needs

Answer:

[tex]m {}^{2} - 100 = - 99[/tex]

Step-by-step explanation:

Set up the binomial.

[tex](m - 10)[/tex]

[tex](m + 10)[/tex]

Multiply the binomial.

[tex](m - 10)(m + 10) = - 99[/tex]

Apply difference of squares rule

[tex](p + q)(p - q) = p {}^{2} - q {}^{2} [/tex]

[tex]m {}^{2} - 100 = - 99[/tex]

Answer: m^2-100=-99

Step-by-step explanation:

Set up the binomial.

(m-10)

(m+10)

Multiply the binomial.

(m-10)(m+10)=-99

Apply difference of squares rule

(p+q)(p-q) = p2-q2

Answer: m^2-100=-99

Answer:C=10

Step-by-step explanation:

Follow along with the picture below

The formula for this type of problem is a^2+b^2=c^2

We know that 6=a and 8=b so we fill in the formula and square them

we then add the two values we got which get us to 100=c^2

we want to get rid of that square with we square root bothe sides and get c and the square root of 100 is 10.

So C=10

Answer:

Step-by-step explanation:

y is the remote exterior angle. The remote exterior angle has the strange property that it is equal to the two remote interior angle. The two remote interior angles are the two, neither of which is the supplement of the exterior angle

So y = x/2 + x/2 which are marked as being opposite equal angles.

1/2 x + 1/2 x = x

y by substitution is = x /2 + x/2

y = x

Answer:

Root         Multiplicity

 -4                    2

 -1                     2

  2                     1

   5                    3

---------------------------

y = a(x + 4)²(x + 1)²(x - 2)(x - 5)³

find "a" using point (0, 20000)

20000 = a(0 + 4)²(0 + 1)² (0 - 2)(0 - 5)³

20000 = a(16)(1)(-2)(-125)

20000 = a (4000)

a = 20000/4000

a = 5

y = 5(x + 4)²(x + 1)²(x - 2)(x - 5)³

Answer:

The student is comparing the different heart rates due to the temperature. The independent variable is the Temperature and the dependent variable is the beats of the heart from the larva.

Answer:

54.3°

Step-by-step explanation:

sinθ=opposite/hypotenuse

sinθ=26/32

sinθ=0.8125

θ=54.3°

Answer:

-2

Step-by-step explanation:

range is y values

Answer:

-2

Step-by-step explanation:

That's the minimum range, which is basically the lowest point on the y-axis that the line touches

Answer:

Surface area add together all 6 sides = 24+36+108=168m^2

Volume L x W x D = 2 x 6 x 9 = 108 m ^3

Step-by-step explanation:

2 x 6 = 12

12 x 2 = 24 base and top

2 x 9 = 18

2 x 18 = 36 identical pair sides

6 x 9 = 54

2 x 54 = 108 identical pair sides

Surface area add together all 6 sides = 24+36+108=168m^2

Volume L x W x D = 2 x 6 x 9 = 108 m ^3

Answer:

[tex]P(A_1\ n\ A_2) = 0.40[/tex]

Step-by-step explanation:

Let:

[tex]A_1 \to[/tex] An Individual likes vehicle 1

[tex]A_2 \to[/tex] An Individual like vehicle 2

[tex]P(A_1) = 0.55[/tex]

[tex]P(A_2) = 0.65[/tex]

[tex]P (A_1\ u\ A_2 ) = 0.80[/tex]

Required

[tex]P(A_1\ n\ A_2)[/tex] --- probability that both vehicles are liked by the individual.

This is calculated as:

[tex]P(A_1\ n\ A_2) = P(A_1) + P(A_2) - P(A_1\ u\ A_2)[/tex]

So, we have:

[tex]P(A_1\ n\ A_2) = 0.55 + 0.65 - 0.80[/tex]

[tex]P(A_1\ n\ A_2) = 0.40[/tex]

Answer:

a) 95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

b) Margin of error  = 0.0270.

Step-by-step explanation:

a)

[tex]\hat{p}[/tex] = point estimate of p [tex]= 268/1020 =0.2627[/tex]

[tex]\hat{q}= 1 - 0.2627 = 0.7373[/tex]

[tex]SE = \sqrt{\hat{p}\hat{q}/n}\\\\=\sqrt{0.2627\times 0.7373/1020}=0.0138\\\alpha = 0.05[/tex]

From Table, critical values of [tex]Z= \pm1.96[/tex] ,

Lower limit

                  [tex]= \hat{p} - Z SE\\ = 0.2627 - (1.96 X 0.0138) \\ = 0.2627 - 0.0276 \\ = 0.236[/tex]

upper limit = 0.2627 + 0.0276

                 = 0.2903

Correct option:

95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

b) Margin of error =Z SE

                              = 1.96 X 0.0141

                              = 0.0270.

Answer:

1/3

Step-by-step explanation:

Hope this is useful even though there isn't any working

Answer:

Step-by-step explanation:

For independent events,

P(AB)=P(A)orP(B)

= P(A)uP(B)

=P(A)×P(B)

= 0.55×0.72

P(AB)=0.396

Answer:

Project A :

NPV : $703,888.64

IRR : 44.882%

Project B:

NPV : $5,241.26

IRR : 49.662%

Project B is more profitable

Step-by-step explanation:

The NPV gives the difference between the present value of cash inflow and cash outflow over a certain period of time.

The Internal rate of return is the discount rate which makes the NPV of an investment 0. It is used to estimate the potential return on an investment. Investments with higher IRR are said to be better than those with lower IRR value.

Using the net present value, (NPV) Calculator, the NPV for project A is : $703,888.64

The IRR of project A is : 44.882%

The NPV for Project B is : $5,241.26

The Internal rate of return (IRR) : 49.662%

From the Internal rate of return value obtained, we can conclude that, project B is more profitable as it has a higher IRR than project A.

Answer:

3179cm^3

Step-by-step explanation:

[tex]volum = height × width × length \\ = 17cm \times 17cm \times 11cm \\ = {3179cm}^{3} [/tex]

Answer:

p-value = 0.0145

Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )

we reject null hypothesis.

Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year

Step-by-step explanation:

Given the data in the question;

Hypothesis;

Null hypothesis             : H₀ : Car accidents are equally distributed throughout the year

Alternative hypothesis : Hₐ : Car accidents are NOT equally distributed throughout the year

significance level ∝ = 0.05

x ;

Spring = 27

Summer = 39

Fall = 31

Winter = 53

Test Statistics;

Chi Square = ∑[ (O – E)²/E ]

                         O               E                   (O – E)²/E

Spring               27            37.4                2.94

Summer            39            37.4                0.06

Fall                    31             37.4                1.1267

Winter               53            37.4                6.4067

Total                 150           150                 10.5334

so; z = ∑[ (O – E)²/E ] = 10.5334

{from table}

p-value = 0.0145

Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )

we reject null hypothesis.

Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year

In this exercise we have to use probability knowledge to calculate the distribution during the year, so we find that:

There is sufficient evidence to conclude that car accidents are not equally distributed throughout the year.

Given the data in the question;

Now the values ​​given in the statement can be exemplified below as:

In this way, we can assemble a table of values ​​with the statistical data previously informed and using the formula given below:

[tex]Z=\sum[\frac{(O-E)^2}{E}][/tex]

[tex]Z = 10.5334[/tex]

So:

[tex]\ \ \ \ \ \ \ \ \ \ \ O \ \ \ \ \ E \ \ \ \ (O - E)^2/E\\Spring \ \ 27 \ \ 37.4 \ \ \ \ 2.94\\Summer \ 39 \ 37.4 \ \ \ \ 0.06\\Fall \ \ \ \ \ \ 31 \ 37.4 \ \ \ \ 1.1267\\Winter \ \ \ 53 \ 37.4 \ \ \ 6.4067\\Total \ 150 150 \ 10.5334[/tex]

Hence, Since pvalue ( 0.0145 ) is less than significance level ( 0.05 ), so we reject null hypothesis.

See more about probability at brainly.com/question/795909

Answer:

Step-by-step explanation:

( x - 1 )2 + ( y + 3 )2 = 90

Answer:

D (The square root property should have been applied to both complete sides of the equation instead of to select variables)

Step-by-step explanation:

On edge 2021