Pedro thinks that he has a special relationship with the number 6. In particular, Pedro thinks that he would roll a 6 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pp is the true proportion of the time Pedro will roll a 6.

Required:
a. State the null and alternative hypotheses for testing Pedro's claim.
b. Now suppose Pedro makes 42 rolls, and a 6 comes up 9 times out of the 42 rolls. Determine the P-value of the test: P-value.
c. Does this sample provide evidence at the 5% level that Pedro rolls a 6 more often than you'd expect?

Answer:

C, D, E and F

Step-by-step explanation:

Given

4x+5y=18

6x−5y=20

Required

Determine which procedure will result in a single equation in one variable

To do this; we'll test each of the options

A. Subtract the first equation from the second equation.

[tex](6x - 5y=20) - (4x+5y=18)[/tex]

[tex]6x - 4x - 5y - 5y = 20 - 18[/tex]

[tex]2x - 10y = 2[/tex] --- This didn't produce the desired result

B.  Subtract the second equation from the first equation.

[tex](4x+5y=18) - (6x - 5y=20)[/tex]

[tex]4x - 6x + 5y + 5y =18 - 20[/tex]

[tex]-2x + 10y = -2[/tex] --- This didn't produce the desired result

C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.

First Equation

[tex]18 * (4x+5y=18)[/tex]

[tex]72x + 90y = 324[/tex]

Second Equation

[tex]18 * (6x - 5y=20)[/tex]

[tex]108x - 90y = 360[/tex]

Add Resulting Equations

[tex](72x + 90y = 324) + (108x - 90y = 360)[/tex]

[tex]72x + 108x + 90y - 90y = 324 + 360[/tex]

[tex]72x + 108x = 324 + 360[/tex]

[tex]180x = 684[/tex] --- This procedure is valid

D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.

First Equation

[tex]-6 * (4x+5y=18)[/tex]

[tex]-24x - 30y = -108[/tex]

Second Equation

[tex]4 * (6x - 5y=20)[/tex]

[tex]24x - 20y = 80[/tex]

Add Resulting Equations

[tex](-24x - 30y = -108) + (24x - 20y = 80)[/tex]

[tex]-24x + 24x - 30y -20y = -108+ 80[/tex]

[tex]-50y = -28[/tex]

[tex]50y = 28[/tex]  --- This procedure is valid

E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.

First Equation

[tex]3 * (4x+5y=18)[/tex]

[tex]12x + 15y = 54[/tex]

Second Equation

[tex]-2 * (6x - 5y=20)[/tex]

[tex]-12x + 10y = -40[/tex]

Add Resulting Equations

[tex](12x + 15y = 54) + (-12x + 10y = -40)[/tex]

[tex]12x - 12x + 15y - 10y =54 - 40[/tex]

[tex]5y = 14[/tex]  --- This procedure is valid

F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order

First Equation

[tex]3 * (4x+5y=18)[/tex]

[tex]12x + 15y = 54[/tex]

Second Equation

[tex]2 * (6x - 5y=20)[/tex]

[tex]12x - 10y = 40[/tex]

Subtract equation 1 from 2 or 2 from 1 will eliminate x;

Hence, the procedure is also valid;

Answer:

A. a line segment

Step-by-step explanation:

Answer:

The sample size is 50 and population proportion under null hypothesis is 25%  ( A )   meets the requirement

Step-by-step explanation:

when applying the central limit theorem on sample proportions in one sample proportion test .The conditions needed to be satisfied are np > 10, and   n( 1-p ) > 10

A)  sample size ( n ) = 50

population proportion = 25%

np = 50 * 0.25 = 12.5 which is > 10 ( 1st condition met )

n( 1 - p ) = 50( 1 - 0.25 ) = 37.5 which is > 10 ( second condition met )

B ) sample size (n) = 70

population proportion = 90%

np = 70*0.9 = 63 which is > 10 ( 1st condition met )

n(1-p) = 70 ( 1 - 0.9 ) = 7 which is < 10 ( second condition not met )

C) sample size ( n ) = 50

population proportion = 15% = 0.15

np = 50 * 0.15 = 7.5 which is < 10 ( 1st condition not met )

n ( 1 - p ) = 50 ( 1 - 0.15 ) = 50 * 0.85 = 42.5 which is > 10 ( second condition met )

D) sample size ( n ) = 200

population proportion = 4% = 0.04

np = 200 * 0.04 = 8 which is < 10 ( 1st condition not met )

n ( 1 - p ) = 200 ( 1 - 0.04 ) = 192 which is > 10 ( second condition met )

hence : The sample size of 50 with population proportion under null hypothesis of 25%  meets the requirement

Answer:

[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

Step-by-step explanation:

From the given question; the objective is to show that :

[tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x in the interval of convergence f(x)=cos x, a= π/2

Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if  [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]  

where;

[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-a)^{n+1}}[/tex]

is a remainder at x and c happens to be between x and a.

Given that:

a= π/2

Then; the above equation can be written as:

[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-\dfrac{\pi}{2})^{n+1}}[/tex]

so c now happens to be the points between π/2 and x

If we recall; we know that:

[tex]f^{(n+1)}(c) = \pm \ sin \ c \ or \ cos \ c[/tex] (as a result of the value of n)

However, it is true that for all cases that  [tex]|f ^{(n+1)} \ (c) | \leq 1[/tex]

Hence, the remainder terms is :

[tex]|R_n (x)| = | \dfrac{f^{(n+1)}(c)}{(n+1!)}(x-\dfrac{\pi}{2})^{n+1}| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

If [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]   for all x and x is fixed, Then

[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

Answer:

I thinksomething is wrong.

I'm getting another proving it's-tan thita.

I hope this is the one you are searching for..

Answer:

Perimeter=60.18cm

Area=215.495cm^2

Step-by-step explanation:

Given:

Length of book=18.34cm

Breadth=11.75cm

Solution:

Perimeter=2(l +b)

P=2(18.34+11.75)

P=2 x 30.09

P=60.18cm

Area=l x b

A=18.34 x 11.75

A=215.495 cm^2

Thank you!

Answer:

[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]

Step-by-step explanation:

The product means multiplication.

There are two positive consecutive integers.

Let the first positive consecutive integer be x.

Let the second positive consecutive integer be x+1.

[tex](x) \times (x+1) =306[/tex]

Solve for x.

Expand brackets.

[tex]x^2 +x =306[/tex]

Subtract 306 from both sides.

[tex]x^2 +x -306=306-306[/tex]

[tex]x^2 +x -306=0[/tex]

Factor left side of the equation.

[tex](x-17)(x+18)=0[/tex]

Set factors equal to 0.

[tex]x-17=0[/tex]

[tex]x=17[/tex]

[tex]x+18=0[/tex]

[tex]x=-18[/tex]

The value of x cannot be negative.

Substitute x=17 for the second consecutive positive integer.

[tex](17)+1[/tex]

[tex]18[/tex]

The two integers are 17 and 18.

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.

Hope it helped u if yes mark me BRAINLIEST

TYSM!

Answer:

The answer is

Step-by-step explanation:

To find the equation of the line we must first find the slope (m)

[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]

So the slope of the line using points

(-8,6) (-9,-9) is

[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]

So the equation of the line using point (-8,6) and slope 15 is

y - 6 = 15( x + 8)

y - 6 = 15x + 120

Writing the equation in the form

Ax+By=C

We have

15x - y = -120-6

The final answer is

Hope this helps you

Answer:

[tex](\frac{4}{3},-\frac{10}{3})[/tex]

Step-by-step explanation:

If the extreme ends of a line segment AC are A[tex](x_1,y_1)[/tex] and C[tex](x_2,y_2)[/tex].

If a point B(x, y) divides the segment in the ratio of m : n

Then the coordinates of the point B are,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

If the ends of AC are A(-2, 5) and C(2, -5) and a point B divides it in the ratio of m : n = 5 : 1

Therefore, coordinates of this point will be,

x = [tex]\frac{5\times (2)+1(-2)}{5+1}[/tex]

  = [tex]\frac{10-2}{5+1}[/tex]

  = [tex]\frac{8}{6}[/tex]

  = [tex]\frac{4}{3}[/tex]

y = [tex]\frac{5\times (-5)+1(5)}{5+1}[/tex]

  = [tex]\frac{-25+5}{6}[/tex]

  = [tex]-\frac{20}{6}[/tex]

  = [tex]-\frac{10}{3}[/tex]

Therefore, coordinates of the point B are [tex](\frac{4}{3},-\frac{10}{3})[/tex].

Answer:

17 miles

Step-by-step explanation:

4+5+5+3=17

[tex] \Large{ \boxed{ \bf{ \color{blue}{Solution:}}}}[/tex]

By using the fact that,

When,

[tex] \large{ \sf{ {a}^{x} =b}}[/tex]

Then, With logarithm base a of a number b:

[tex] \large{ \sf{ log_{a}(b) = x}}[/tex]

☃️So, Let's solve ths question....

To FinD:

[tex] \large{ \sf{log_{2}(256) }}[/tex]

Let it be x,

[tex] \large{ \sf{ \longrightarrow{ log_{2}(256) = x}}}[/tex]

Proceeding further,

[tex] \large{ \sf{ \longrightarrow \: {2}^{x} = 256}}[/tex]

[tex] \large{ \sf{ \longrightarrow \: {2}^{x} = {2}^{8} }}[/tex]

Then, We have same base 2, So

[tex] \large{ \sf{ \longrightarrow \: x = 8}}[/tex]

Or,

➙ log₂(256) = log₁₀(256) / log₁₀(2)

➙ log₂(256) = 2.40823996531 / 0.301029995664

➙ log₂(256) = 8

☕️ Hence, solved !!

━━━━━━━━━━━━━━━━━━━━

Answer:

256

Step-by-step explanation:

log     256 can most easily be found by rewriting 256 as a power of 2:

      2

2^5 * 2^3 = 32*8 = 256, so 2^ (5 + 3) = 2^8.    

Then we have:

  log     256

2        2             = 256

Alternatively, write:

log (down)2 256 = log (down)2 2^8 = 2*8 = 256

Note that your "log (down)^2 and the function y = 2^x are inverse functions that effectively cancel one another.

Answer:

[tex]\boxed{x=15}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} =\frac{x}{20}[/tex]

[tex]\sf Cross \ multiply.[/tex]

[tex]4 \cdot x = 20 \cdot 3[/tex]

[tex]4x=60[/tex]

[tex]\sf Divide \ both \ sides \ by \ 4.[/tex]

[tex]\frac{4x}{4} =\frac{60}{4}[/tex]

[tex]x=15[/tex]

Answer:

3 years

Step-by-step explanation:

A = P(1 + r)^t

A = I + P

A = 14,000 + 4,634 = 18,634

18,634 = 14,000(1 + 0.1)^t

18,634/14,000 = 1.1^t

log (18,634/14,000) = log 1.1^t

log (18,634/14,000) = t * log 1.1

t = [log (18,634/14000)]/(log 1.1)

t = 3

Answer:

7(n + 4)

Step-by-step explanation:

Represent the number by n.  Then the verbal expression becomes

7(n + 4).

Answer:

2.952755906 ft

Step-by-step explanation:

We need to convert 90 cm to inches

90 cm * 1 inch / 2.54 cm =35.43307087 inches

Now convert inches to ft

12 inches = 1ft

35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft

Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16

Answer:

wrong position of tan 64

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

Answer:

Step-by-step explanation:

[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]

Answer:

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],

sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]

And now simplify the expression,

[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]

The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = [tex]\frac{1}{2}[/tex],

sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],

cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],

sin(- π / 6) = [tex]-\frac{1}{2}[/tex]

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒

[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]

The simplified expression will be the following,

[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]

The solution will be option a, as you can see.

Answer:

  find the difference of points on the graph

Step-by-step explanation:

The cumulative frequency graph (CDF) represents the integral of the probability distribution function (PDF). You find the probability that X is in some interval by subtracting the value of the CDF at the low end of the interval from the CDF value at the high end of the interval.

  p(a < x < b) = cdf(b) -cdf(a)

Step-by-step explanation:

f(x) = integral (-8x) dx = -4x^2 + C

f(1) = -3 = -4 + C

C = 1

f(x) = -4x^2 + 1

The particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is: f(x) = -4x² + 1.

Here, we have,

To find the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3,

we can integrate the equation and use the initial condition to determine the constant of integration.

First, integrate both sides of the equation with respect to x:

∫ f'(x) dx = ∫ -8x dx

Integrating, we get:

f(x) = -4x² + C

Now, we can use the initial condition f(1) = -3 to find the value of the constant C.

Substituting x = 1 and f(x) = -3 into the equation, we have:

-3 = -4(1)² + C

-3 = -4 + C

C = -3 + 4

C = 1

Therefore, the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is:

f(x) = -4x² + 1

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Answer:

117 cm³

Step-by-step explanation:

To find the volume of a rectangular prism, we can simply multiply the length, width and height so the answer is 13 * 3 * 3 = 117 cm³.

Answer:

117 cubic centimeters

Step-by-step explanation:

Assuming that the stick of butter is a perfect rectangular prism, we can calculate the volume by simply multiplying the length, width, and the height as modeled by the volume equation:

V = LWH

For this, the L = 13cm, W = 3cm, and H = 3cm

So our volume in cubic centimeters will be:

V = LWH

V = (13cm) * (3cm) * (3cm)

V = (13cm) * (9cm^2)

V = 117 cm^3

So the volume of the stick of butter is 117 cubic centimeters.

Cheers.

Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

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Answer:

C. H0 : p = 0.8 H 1 : p ≠ 0.8

The test is:_____.

c. two-tailed

The test statistic is:______p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]

The p-value is:_____. 0.09887

Based on this we:_____.

B. Reject the null hypothesis.

Step-by-step explanation:

We formulate null and alternative hypotheses as  proportion of people who own cats is significantly different than 80%.

H0 : p = 0.8 H 1 : p ≠ 0.8

The alternative hypothesis H1 is that the 80% of the  proportion is different and null hypothesis is , it is same.

For a two tailed test for significance level = 0.2 we have critical value  ± 1.28.

We have alpha equal to 0.2  for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28

The test statistic is

p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]

Where p = 0.8 , q = 1-p= 1-0.8= 0.2

n= 200

Putting the values

0.8 ± 1.28 [tex]\sqrt{\frac{0.8*0.2}{200} }[/tex]

0.8 ± 0.03620

0.8362, 0.7638

As the calculated value of z lies within the critical region  we reject the null hypothesis.

Answer:

D. (-7, 3)

Step-by-step explanation:

The equation given is in point-slope form.

Point-slope form is:

y-y1=m(x-x1)

This is where:

y1 is the y-coordinate of a point it goes through

m is the slope of the line

x1 is the x-coordinate of a point that it goes through

That said, in the given equation:

y1=3

m=4

x1=-7

Note that a point is (x-coordinate, y-coordinate)

Therefore, (-7, 3) is the point that lies on the line.

Answer:

500,000

Step-by-step explanation:

(2.1 * 10^8)/(4.2 * 10^2) =

= 2.1/4.2 * 10^8/10^2

= 0.5 * 10^6

= 500,000

The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10².

The number system is a way to represent or express numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given exponents 2.1 × 10⁸

Let's assume 2.1 × 10⁸ is x times 4.2 × 10².

2.1 × 10⁸ = x (4.2 × 10²)

x = 2.1 × 10⁸/4.2 × 10²

x = 500000

Hence "The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10²".

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Answer:

1+5.3=6.3

Step-by-step explanation:

not sure what your asking for with the 2

explain what your looking for with the 2 and maybe we can help you further

(I have to do it the way I did it because the 2 in the question is confusing)

Answer:

For expression 1 + 5.32: 6.32

For expression 1 + 5.3 × 2: 11.6

Step-by-step explanation:

If the expression is 1 + 5.32:

If the expression is 1 + 5.3 × 2:

Answer:

Option 1: The terms in Pattern B is 4 times the corresponding terms of Pattern A

Step-by-step explanation:

Answer:

Pattern B has more then pattern A so option 2

Step-by-step explanation:

Answer: 1.609344 kilometers.

Step-by-step explanation:

A mile is an English Unit that is used to measure the length of a linear surface.

Even though the kilometre has replaced it to a large extent as the standard measure of length, it is still the main unit of measurement for distances in the United States, the United Kingdom, Liberia and UK and US oversees territories.

Miles are longer than kilometres as a kilometer is equivalent to only 0.621371 miles.

1 mile is therefore;

= 1/0.621371

= 1.609344 kilometers.

Answer:

wat do u want me to do

Step-by-step explanation: