Conduct the hypothesis test and provide the test statistic and the critical​ value, and state the conclusion. A person drilled a hole in a die and filled it with a lead​ weight, then proceeded to roll it times. Here are the observed frequencies for the outcomes of​ 1, 2,​ 3, 4,​ 5, and​ 6, respectively: ​, ​, ​, ​, ​, . Use a significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair​ die?

Answer:

Ok, we have a total of 26 letters, and we want to select 5 of them.

Of the 26 letters, 21 are consonants and 5 are vowels.

Suppose that we want to have the consonant in the first selection, so the probability of picking a consonant is equal to the quotient between the number of consonants and the total number of letters.

p = 21/26

now a letter has been selected, so in the set, we have 25 letters left.

In the next 4 selections, we must select vowels.

In the second selection the probability is:

p = 5/25

in the third, the prob is:

p = 4/24 (we already selected one vowel before, so now we only have 4 vowels)

The fourth selection:

p = 3/23

and the last selection:

p = 2/22

The total probability is equal to the product of all the individual proabilities, so we have:

P = (2/22)*(3/23)*(4/24)*(5/25)*(21/26)

Now, remember that we said that the consonant must be in the first place, but it can be in any of the five places, so if we add the permutations of the consonant letter we have:

P = 5*(2/22)*(3/23)*(4/24)*(5/25)*(21/26) =  0.0018

Answer:

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]

Step-by-step explanation:

Hey there!

Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.

Look at the image below ↓

By looking at the image we can conclude that the equation for the perpendicular line is,

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].

Hope this helps :)

Answer:

[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]

Step-by-step explanation:

Part 1: Finding the new slope of the line

Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.

Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].

Part 2: Using point-slope formula and solving in slope-intercept form

Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].

Then, use the point-slope equation to get b, or the y-intercept of the equation.

[tex](y-y_{1})=m(x-x_{1})[/tex]

[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]

Answer:

d ≈ 8.3

Step-by-step explanation:

This is kind of like the pythagorean theorem, but with one extra value.  Thus, [tex]d^2=l^2+w^2+h^2[/tex].

Plug in the values to get:

[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]

Thus d ≈ 8.3

Answer:

Max area is 16

Step-by-step explanation:

If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.

So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.

The maximal area of a right triangle is 90.496

Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given:

let the perpendicular be 'x'

and base be 'y'

Using Pythagoras theorem

x² + y² = 8²

x² + y² = 64

y²= 64- x²

y = √64-x²

Now, Area of triangle

= 1/2* base* height

=xy/2

=x *√64-x²*1/2

On differentiating both side

A' = 64-2x²/√64-x²*1/2

Setting derivative function equal to zero,

64= 2x²

32=x²

x=5.656

So, Area of triangle = x *√64-x²*1/2

= 90.496

Learn more about differentiation here:

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Answer:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Answer:

1 - Correct

2 - incorrect

3- incorrect

4 - incorrect

5 - Correct

Step-by-step explanation:

Notice that

3x  + 5 + 4x -1  =    3x + 4x + 5 -1 = 7x  + 4

therefore the two expressions are equivalent for ANY number, specially x = 4 and x = 6 therefore

1 - Correct

Since that is true for all numbers  

2 - incorrect

3- incorrect

4 - incorrect

The expressions are equivalent for all numbers therefore

5 - Correct

Answer: 36

Step-by-step explanation:

Simply do 24/(2/3) to get 36 2/3 ounce slices.

Hope it helps <3

Answer:

y = 1.44

Step-by-step explanation:

What are you aiming to do here?  Please share all instructions with each problem.

If you want to solve 4.5/y = 12.5/4 for y:  Multiply both sides by 4y:

18 = 12.5y.  Then y = 1.44

Answer:

42 gallons 45% antifreeze

28 gallons 95% antifreeze

Step-by-step explanation:

If x is volume of 45% antifreeze, and y is volume of 95% antifreeze, then the total volume is:

x + y = 70

And the total amount of antifreeze is:

0.45 x + 0.95 y = 0.65 (70)

Solving by substitution:

0.45 x + 0.95 (70 − x) = 0.65 (70)

0.45 x + 66.5 − 0.95 x = 45.5

21 = 0.5 x

x = 42

y = 28

Answer:

a

   [tex]P(X = 10 ) = 0.0096[/tex]

b

   [tex]P(X = 10 ) = 0.0085[/tex]

c

 Option A is correct

Step-by-step explanation:

From the question we are told that

     The sample size is   n =  15

     The  probability of success is  [tex]p = 0.35[/tex]

     The number of success we are considering is  r = 10  

Now the probability of failure is mathematically evaluated as

        [tex]q = 1- p[/tex]

substituting value

       [tex]q = 1- 0.35[/tex]

       [tex]q = 0.65[/tex]

Now using  the binomial distribution  to find the probability of exactly 10 successes we have that

    [tex]P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}[/tex]

substituting values

    [tex]P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}[/tex]

Where  [tex][\left 15 } \atop {10}} \right. ][/tex] mean 15 combination 10  which is evaluated with a calculator to obtain  

       [tex][\left 15 } \atop {10}} \right. ] = 3003[/tex]

So

      [tex]P(X = 10 ) = 3003 * 0.35 ^{10}* 0.65^{15- 10}[/tex]

       [tex]P(X = 10 ) = 0.0096[/tex]

Now using  the normal distribution to approximate the probability of exactly 10 successes, we have that

  [tex]P(X = r ) = P( r < X < r )[/tex]

Applying continuity correction

          [tex]P(X = r ) = P( r -0.5 < X < r +0.5)[/tex]

substituting values

        [tex]P(X = 10) = P( 10-0.5 < X < 10+0.5)[/tex]

       [tex]P(X = 10 ) = P( 9.5 < X < 10.5)[/tex]

Standardizing  

         [tex]P(X = r ) = P( \frac{9.5 - \mu }{\sigma } < \frac{X - \mu }{\sigma } < \frac{10.5 - \mu}{\sigma } )[/tex]

The  where  [tex]\mu[/tex] is the mean which is mathematically represented as

        [tex]\mu = n * p[/tex]

substituting values

        [tex]\mu = 15 * 0.35[/tex]

         [tex]\mu = 5.25[/tex]

The standard deviation is evaluated as      

     [tex]\sigma = \sqrt{n * p * q }[/tex]

substituting values

    [tex]\sigma = \sqrt{15 * 0.35 * 0.65 }[/tex]

    [tex]\sigma = 1.8473[/tex]

Thus  

     [tex]P(X = 10 ) = P( \frac{9.5 - 5.25 }{1.8473 } < \frac{X - 5.25 }{1.8473 } < \frac{10.5 - 5.25}{1.8473 } )[/tex]

     [tex]P(X = 10 ) = P( 2.30 < Z < 2.842 )[/tex]

     [tex]P(X = 10 ) = P(Z < 2.842 ) - P(Z < 2.30 )[/tex]

From the normal distribution table we obtain the [tex]P(Z < 2.841)[/tex] as

      [tex]P(Z < 2.841) = 0.99775[/tex]

And  the  [tex]P(Z < 2.30)[/tex]

     [tex]P(Z < 2.30) = 0.98928[/tex]

There value can also be obtained from a probability of z calculator at (Calculator dot net website)

So  

    [tex]P(X = 10) = 0.99775 - 0.98928[/tex]

     [tex]P(X = 10 ) = 0.0085[/tex]

Looking at the calculated values for question a and b  we see that the values are fairly different.

Answer:

[tex]\boxed{\mathrm{Option \ 4}}[/tex]

Step-by-step explanation:

Given that

[tex]y-4 = x[/tex]

Adding 4 to both sides

[tex]y-4+4 = x+4\\[/tex]

[tex]y = x+4[/tex]

Answer:

3906250

Step-by-step explanation:

We can notice that the ratio is 5. 10/2 = 5

Each term gets multiplied by 5 to get the next term.

250 × 5 = 1250 (5th term)

1250 × 5 = 6250 (6th term)

6250 × 5 = 31250 (7th term)

31250 × 5 = 156250 (8th term)

156250 × 5 = 781250 (9th term)

781250 × 5 = 3906250 (10th term)

The 10th term of the geometric sequence is 3906250.

Answer: 1 30/39

Step-by-step explanation:

Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.

Hope it helps <3

Answer:

3 pounds

51 ounces

Step-by-step explanation:

Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

Answer: x= 7

Step-by-step explanation:

-2x= -14    Divide both sides by -2

x= 7  

check

-2(7) = -14

-14 = -14

Answer:

x = 7

Step-by-step explanation:

-2x = -14

Divide each side by -2

-2x/-2 = -14/-2

x = 7

Hey there! :)

Answer:

m = 4.

Step-by-step explanation:

We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)

Where 'm' is the slope and 'b' is the y-intercept. Therefore:

y = -5 + 4x becomes y = 4x - 5

The 'm' value is equivalent to 4, so the slope of the equation is 4.

Answer:

4

Step-by-step explanation:

because of y= mx + b where m is the slope

m= 4 in the equation

━━━━━━━☆☆━━━━━━━

▹ Answer

Slope = -3

Y-intercept = 8

▹ Step-by-Step Explanation

y = mx + b

mx represents the slope.

b represents the y intercept.

therefore,

y = -3x + 8

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

[tex]\boxed{\mathrm{Slope:}-3 \: \: \: \:\: \mathrm{Y \: intercept:}8}[/tex]

Step-by-step explanation:

The general form of slope-intercept:

[tex]y=mx+b[/tex]

[tex]m:slope\\b:y \: intercept[/tex]

[tex]y=-3x+8[/tex]

[tex]m=-3\\b=8[/tex]

The slope is -3.

The y-intercept is (0, 8) or 8.

Answer:

1) Amplitude; A = 80 ft

Period = 60 ft

2)y = 80 sin ((π/30)x - 5π) + 80

3)y = 40 sin ((π/30)x - 5π) + 80

4)y = 40 sin ((π/30)x - 5π) + 40

5)y = -65sin ((π/30)x - 5π) + 80

Step-by-step explanation:

The general formula for sinusoidal wave equation is given by;

y = A sin (Bx - C) + D

Where;

A is amplitude = D_max or  D_min

Period = 2π/B

So; B = 2π/Period

Phase Shift = C/B  

So; C = B · Phase Shift

D: center

We are Given:

Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft

Thus; A = 80 ft

The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft

Thus; B = 2π/60 = π/30

Field is 300 ft wide and so the center is 300/2 = 150 ft

Thus; Phase Shift = 150.  

C = B × Phase Shift = π/30 · 150 = 5π

1) From the calculations above,

Amplitude; A = 80 ft

Period = 60 ft

2) As they begin to play, from the calculations above and y = A sin (Bx - C) + D, equation of the sine function is now;

y = 80 sin ((π/30)x - 5π) + 80

3) In this, since the sine wave is half as tall, then after the changes, we have;

y = 40 sin ((π/30)x - 5π) + 80

4) since they have moved closer, then equation is now;

y = 40 sin ((π/30)x - 5π) + 40

5) We are Given:

Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft

Since the first person forming the curve now stands at the 5 yard line, the minimum is at 5 yds (15 ft). Thus;

D_min = 80 - 15 = 65. Thus; A = 65 ft

The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft

Thus; B = 2π/60 = π/30

Field is 300 ft wide and so the center is 300/2 = 150 ft

Thus; Phase Shift = 150.  

C = B × Phase Shift = π/30 · 150 = 5π

The band ends down (at 15 feet) and thus A is negative

The equation is;

y = -65sin ((π/30)x - 5π) + 80

Part(1): The required values are,

Amplitude=[tex]80 ft[/tex] and Period: [tex]60 sec[/tex]

Part(2):

The equation of the sine function is

[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80[/tex]

Part(3):

The equation of the sine curve is,

[tex]y=40cos(\frac{\pi x}{30})+80[/tex]

Part(4):

The equation of the  sine curve representing the position of the band members after these changes is [tex]y=40cos(\frac{\pi x}{30})+40[/tex]

Part(5):

The required graph is attached below,

Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position

Part(1):

Amplitude=[tex]\frac{1}{2} width=80ft[/tex]

Period=[tex]2\times 30=60 sec[/tex]

Part(2):

Let the equation be,

[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80\\ y'=-\frac{8\pi}{3} sin((\frac{\pi x}{30}+\pi))[/tex]

Darla is at the point [tex]D(150,80)[/tex] which is on the graph at [tex]x=0[/tex] then,

[tex]80=80 cos(5\pi+\pi)=0\\y=-80 cos (\frac{\pi x}{30} )+80[/tex]

Part(3):

Since the wave is now [tex]\frac{160}{2} =80 ft[/tex] then,

Amplitude=40 ft

[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80\\y=40cos(\frac{\pi x}{30})+80[/tex]

Part(4):

The graph shifts downward 40 ft then,

[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80-40\\y=40cos(\frac{\pi x}{30})+40[/tex]

Part(5):

Start at:[tex]Y(x)=80sin (\frac{2\pi x}{60} )+80\\[/tex]

End at: [tex]Z(x)=80sin[ (\frac{2\pi }{60}(x-15) )]+80\\[/tex]

The graph is attached below:

Learn more about the topic of Simple harmonic motion:

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Answer:

Time taken = 6 sec (Approx)

Step-by-step explanation:

Given:

Total distance = 1/12 mi = 0.083333

Speed of train = 50 mph = 50 / 3600 = 0.01388889 mps

Find:

Time taken

Computation:

Time taken = Total distance / Speed

Time taken = Total distance / Speed of train

Time taken = 0.0833333 / 0.01388889

Time taken = 6 sec (Approx)

Answer:y=Mx+b

Step-by-step explanation:

Answer:

C) y = x + 5

Step-by-step explanation

Add 5 to both sides

Answer:The answer is c

Step-by-step explanation:

Answer:

its 9

Step-by-step explanation:

Answer:

c. 9i.

Step-by-step explanation:

[tex]\sqrt{-81}[/tex]

= [tex]\sqrt{-1 * 9 * 9}[/tex]

= [tex]\sqrt{-1 * 9^2}[/tex]

= [tex]9\sqrt{-1}[/tex]

The square root of -1 is the same thing as i.

= [tex]9i[/tex]

So, your answer is C.

Hope this helps!

Answer:

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

Step-by-step explanation:

You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as   "negation of a" or "  b" in mathematical terms is written like this

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

You can show that they are logically equivalent because they have the same truth table.

Answer:

3s-4bbb=17

Step-by-step explanation:

brother=4bbb

sister=3s

3s-4bbb=17

Answer:

the real deal is that you mistook if

cos(x)=y/z gives y=zcos(x)

Answer:

[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

Step-by-step explanation:

[tex]Volume = Base \ Area\ * Height[/tex]

[tex]Height = \frac{Volume}{Base \ Area}[/tex]

Where [tex]Volume = x^4+4x^3+8x+4[/tex] and [tex]Area = x^3+3x^2+8[/tex]

Putting in the formula

[tex]Height = \frac{x^4 + 4x^3 + 3x^2 + 8x + 4}{x^3 + 3x^2 + 8}[/tex]

Doing long division, we get

[tex]Height = x + \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

This is the simplifies form and it can't be further simplified.

Answer:

[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Step-by-step explanation:

[tex]volume=base \: area \times height[/tex]

[tex]height=\frac{volume}{base \: area}[/tex]

[tex]\mathrm{Solve \: by \: long \: division.}[/tex]

[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]

[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]

[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Answer:

y = x + 0.5

Step-by-step explanation:

This is a very trivial exercise, follow the steps below:

Step 1: Perform the implicit differentiation of the given equation

[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]

[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]

Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:

[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]

Step 3: Find dy/dx at the point (0, 0.5)

[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]

Step 4: The equation of the tangent line to a curve at a given point is given by the equation:

[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]

Answer:

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Step-by-step explanation:

The rate is -1 4/5 lbs  per hour

The time is 3 1/2 hours

Multiply to find the weight change

-1 4/5 * 3 1/2

Change to improper fractions

- ( 5*1 +4) /5 * ( 2* 3+1)/2

- 9/5 * 7/2

-63/10

Changing back to a mixed number

-6  3/10

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Answer:

-6 3/10 pounds

Step-by-step explanation:

The weight of ice sculpture changes -1 4/5 pounds every 1 hour.

In 3 1/2 hours, multiply the time with the weight.

-1 4/5 × 3 1/2

Multiply.

-9/5 × 7/2

-63/10 = -6 3/10