Use the permutation formula to solve a problem when n = 8 and r = 2.



A. 56
B. 672
C. 6,720
D. 40,320

As both angles are supplementary

[tex]\\ \Large\sf\longmapsto 3x+(2x+3y)=180°[/tex]

[tex]\\ \Large\sf\longmapsto 3x+2x+3y=180[/tex]

[tex]\\ \Large\sf\longmapsto 5x+3y=180[/tex]

[tex]\\ \Large\sf\longmapsto 3y=180-5x[/tex]

[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]

And

[tex]\\ \Large\sf\longmapsto 3x=90[/tex]

[tex]\\ \Large\sf\longmapsto x=\dfrac{90}{3}[/tex]

[tex]\\ \Large\sf\longmapsto x=30[/tex]

Now

[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]

[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5(30)}{3}[/tex]

[tex]\\ \Large\sf\longmapsto y=\dfrac{180-150}{3}[/tex]

[tex]\\ \Large\sf\longmapsto y=\dfrac{30}{3}[/tex]

[tex]\\ \Large\sf\longmapsto y=10[/tex]

Answer:

A. Fail to reject the claim that the average math SAT score is 498 when in fact it is not 498.

Step-by-step explanation:

Type II Error:

A type II error happens when there is a non-rejection of a false null hypothesis.

In this question:

The null hypothesis is H0​:μ=498.

Since there is a type II error, there was a failure to reject the claim that the average math SAT score is 498 when in fact it is not 498, and thus, the correct answer is given by option A.

Distance Formula: [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

Point 1: (9,0)

Point 2: (5,-8)

D = sqrt[ (5 - 9)^2 + (-8 - 0)^2 ]

D = sqrt[ (-4)^2 + (-8)^2 ]

D = sqrt[ 16 + 64]

D = sqrt(80)

Hope this helps!

Answer:

8m

Step-by-step explanation:

Answer:

x=57/2

Step-by-step explanation:

2x+3=60

<=> 2x=57

=> x=57/2

Answer: Choice A.)   88.2 < μ < 93.0

=============================================================

Explanation:

We have this given info:

Because n > 30 and because we know sigma, this allows us to use the Z distribution (aka standard normal distribution).

At 99% confidence, the z critical value is roughly z = 2.576; use a reference sheet, table, or calculator to determine this.

The lower bound of the confidence interval (L) is roughly

L = xbar - z*sigma/sqrt(n)

L = 90.6 - 2.576*8.9/sqrt(92)

L = 88.209757568781

L = 88.2

The upper bound (U) of this confidence interval is roughly

U = xbar + z*sigma/sqrt(n)

U = 90.6 + 2.576*8.9/sqrt(92)

U = 92.990242431219

U = 93.0

Therefore, the confidence interval in the format (L, U) is approximately (88.2, 93.0)

When converted to L < μ < U format, then we get approximately 88.2 < μ < 93.0 which shows that the final answer is choice A.

We're 99% confident that the population mean mu is somewhere between 88.2 and 93.0

Answer:

2×2×3×3

Step-by-step explanation:

Answer:

2×2×3×3

Step-by-step explanation:

36=3×12

12=3×4

4=2×2

=3×3×2×2

Hope this helps! <3

Answer:

[tex]C=27inch\ by\ 27inch[/tex]

Step-by-step explanation:

Squares [tex]h=4inch[/tex]

Volume [tex]v=1444in^3[/tex]

Generally the equation for Volume of box is mathematically given by

 [tex]V=l^2h[/tex]

 [tex]1444=l^2*4[/tex]

 [tex]l^2=361[/tex]

 [tex]l=19in[/tex]

Since

Length of cardboard is

 [tex]l_c=19+4+4[/tex]

 [tex]l_c=27in[/tex]

Therefore

Dimensions of the piece of cardboard is

[tex]C=27inch\ by\ 27inch[/tex]

Answer:

Following are the solution to the given points:

Step-by-step explanation:

For point a:

[tex]fx|H(x) = 1;0< x<1\\\\fX|T(x) = 2x; 0\leq x \leq 1\\\\fx(x) = P(H \bigcap X = x) +P(T \bigcap X=x)\\\\[/tex]

[tex]=P(H)fX|H(x)+P(T)fX|T(x)\\\\= p(1) + (1-p)2x\\\\= p(1 -2x)+2x\\\\[/tex]

Using the PDF of the X value

[tex]fX(x) =2x +p(1 - 2x); \ 0\leq x\leq 1[/tex]

0 ; otherwise

For point b:

[tex]E(X)=\int^{1}_{0} \ x fX (x)\ dx=\int^{1}_{0} \ x(2x+p(1-2x))\ dx\\\\=\int^{1}_{0} \ (2x^2+(x-2x^2)p) dx\\\\[/tex]

[tex]= 2(\frac{x^3}{3}) + (\frac{x^2}{2}-2(\frac{x^3}{3}) \begin{vmatrix} x=1\\ x=0\end{vmatrix} \\\\[/tex]

[tex]= \frac{2}{3} + (\frac{1}{2} - \frac{2}{3})p\\\\= \frac{2}{3} -\frac{p}{6}\\\\= \frac{(4 - p)}{6}[/tex]

Answer:

A sample of 1699 would be required.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation is known to be $8.2.

This means that [tex]\sigma = 8.2[/tex]

How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.39?

This is n for which M = 0.39. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.39 = 1.96\frac{8.2}{\sqrt{n}}[/tex]

[tex]0.39\sqrt{n} = 1.96*8.2[/tex]

[tex]\sqrt{n} = \frac{1.96*8.2}{0.39}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*8.2}{0.39})^2[/tex]

[tex]n = 1698.3[/tex]

Rounding up:

A sample of 1699 would be required.

Answer:

✔ 0.4

✔ 0.4 centimeters less

✔ 9.2

1.16(5) + 3 = 8.8

9.2 - 8.8 = .4

ED2021

The residual is 0.4

'Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points.'

According to the given problem,

y = 3 + 1.16x

After 5 weeks, x = 5,

⇒ y = 3 + 1.16(5)

⇒ y = 3 + 5.8

⇒ y = 8.8

Now subtracting y from actual height of plant,

⇒ 9.2 - 8.8

=  0.4

Hence, we can conclude the residual to be 0.4.

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9514 1404 393

Answer:

  C.  3/5

Step-by-step explanation:

The distance from the origin to the given point is ...

  d = √(3² +(-4)²) = √(9+16) = 5

The cosine of the angle is the ratio of the x-coordinate to this value:

  cos(θ) = x/d

  cos(θ) = 3/5

Answer:

what is your Language I think it is Russian I don't understand Russian I only understand Nepali,English and Japanese

Answer:

The correct answer is - $1977.7913.

Step-by-step explanation:

Given:

Maturity value = 2000

time = 3 years

rate = 6% compounded quarterly

Solution:

If  A is the Maturity Value, P is the Principal Amount, r is the Rate of Return, n is the Frequency And t is the Time in Year then the Formula for Compound Interest would be -

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

Putting the given values in formula,

2000 = P*(1 + (0.06/4))^(3*4)

P = 2000/(1 + (0.06/4))^(3*4)

Thus,

P = $1977.7913

Answer:

y=0.5

Step-by-step explanation:

14y-6(y-3)=22

14y-6y+18=22

8y+18=22

8y=4

y=0.5

Then we check our work...

14(0.5)-6((0.5)-3)=22

7-6(-2.5)=22

7+15=22

7+15 does equal 22, so this solution is correct.

Answer:

0 senior tickets were sold

5 more adult tickets were sold than chil tickets

Step-by-step explanation:

You need to see the frequency of each bar

Answer by Gauthmath

9.03 divided by 899.8 is closest to a.0.01

Answer: a) 0.01

Step-by-step explanation:

Step-by-step explanation:

Let

[tex]m_p[/tex] = mass of the painter

[tex]m_s[/tex] = mass of the scaffold

[tex]m_e[/tex] = mass of the equipment

[tex]T[/tex] = tension in the cables

In order for this scaffold to remain in equilibrium, the net force and torque on it must be zero. The net force acting on the scaffold can be written as

[tex]3T = (m_p + m_s + m_e)g\:\:\:\:\:\:\:(1)[/tex]

Set this aside and let's look at the net torque on the scaffold. Assume the counterclockwise direction to be the positive direction for the rotation. The pivot point is chosen so that one of the unknown quantities is eliminated. Let's choose our pivot point to be the location of [tex]m_e[/tex]. The net torque on the scaffold is then

[tex]T(1.4\:\text{m}) + m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m}) - 2T(5.2\:\text{m}) = 0[/tex]

Solving for T,

[tex]9T = m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})[/tex]

or

[tex]T = \frac{1}{9}[m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})][/tex]

[tex]\:\:\:\:= 423.3\:\text{N}[/tex]

To solve for the the mass of the equipment [tex]m_e[/tex], use the value for T into Eqn(1):

[tex]m_e = \dfrac{3T - (m_p + m_s)g}{g} = 14.6\:\text{kg}[/tex]

Answer:

The 100 trees closest to a ranger station are assessed for damage.

Step-by-step explanation:

Convenience samples are samples taken from only around the focal point.

Option B is correct, The 100 trees closest to a ranger station are assessed for damage.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

A convenience sample is a non-random method of sampling that involves selecting subjects that are easy to access or readily available.

Of the methods listed, the convenience sample is the one where the trees are selected based on their proximity to a ranger station:

The 100 trees closest to a ranger station are assessed for damage.

This method is a convenience sample because it does not involve random selection of trees.

Instead, the trees are chosen based on their proximity to a specific location.

This can introduce bias into the sample, as trees near the ranger station may not be representative of the overall health of white pine trees in the state park.

Hence, Option B is correct, The 100 trees closest to a ranger station are assessed for damage.

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Answer:

12

Step-by-step explanation:

Given the data :

X : 10,8,18,17,7

The mean value of scores obtained can be obtained thus :

Mean = ΣX / n

n = sample size = 5

Mean = ΣX / n = (10+8+18+17+7) / 5

Mean = 60 / 5 = 12

Step-by-step explanation:

Fraction =

[tex] \frac{10}{100} = \frac{1}{10} [/tex]

Ratio is 1 : 10

Answer:

A.x<-8

Step-by-step explanation:

=1/2x<−4

=2*(1/2x)< (2)*(-4)

= x<-8

Answer:

We know that the angle which lineer and divided by |AB| equal to 130°

Step-by-step explanation:

if 130° look at the 2x+260 we can say that 2x+260=260° so X equal to Zero (0)

Answer:

I could be wrong but I calculated 2 years 8 months and 15 days.

2 years

8 months

15 days

Answer:

-8 and 3

Step-by-step explanation:

The slope of the line will be - 8, the equation is y=-8x+3

Answer:

y=3x+1

Step-by-step explanation:

Determine slope with two coordinates and use it in the formula

Answer:

972pi in ^3

Step-by-step explanation:

We need to find the volume of the sphere

V = 4/3 pi r^3

The diameter is 18

r = d/2 = 18/2 = 9

V = 4/3 pi ( 9)^3

V = 972pi in ^3

Answer:

-2

Step-by-step explanation:

5 + (-7)

Since the 7 is larger than 5, the 7 will overpower the 5 in a way. So, all you do is subtract 7 and 5.

7 - 5 = 2

But the 7 has a negative with it (since it's larger), so you add the negative to the 2.

7 - 5 = -2

The answer will be -2.

Answer:

98

Step-by-step explanation:

2, 10, 18, 26, 34, 42, 50... 98

Hope this helps. Have a great day!