The makers of Mini-Oats cereal have an automated packaging machine that is set to fill boxes with 24.3 ounces of cereal (as labeled on the box). At various times in the packaging process, we select a random sample of 100 boxes to see if the machine is (on average) filling the boxes as labeled. On Tuesday morning, at 7:45 a.m., a random sample of 100 boxes produced an average amount of 23.6 ounces. Which of the following is an appropriate statement of the null hypothesis?
A) The machine fills the boxes with the proper amount of cereal.
B) The average is 24.3 ounces (H0: μ = 24.3)
C) The machine is not filling the boxes with the proper amount of cereal (H0: μ ≠ 24.3 ounces).
D) The machine is not putting enough cereal in the boxes.
E) The average is less than 24.3 ounces (H0: μ < 24.3).
F) The machine fills the boxes with an average of 23.6 ounces (H0: μ = 23.6).

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

- 3y + 4x = 9

3y = 4x - 9

Divide both sides by 3

y = 4/3x - 3

Comparing with the above formula

Slope / m = 4/3

Since the lines are parallel their slope are also the same

So slope of the parallel line l is also 4/3

Equation of the line using point (-12 , 6) is

y - 6 = 4/3(x + 12)

Multiply through by 3

That's

3y - 18 = 4(x + 12)

3y - 18 = 4x + 48

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

cosФ=0 then the angle=π/2=90 degrees

sinФ==1     sin 90=1

12) the original price of the console  that Amanda bought :

240+(240*50%)=360 dollars

the price before the tariffs:

360-(360*50^)=180 dollars

Answer:

The divisor and dividend have the same signs.

Step-by-step explanation:

Let's look at all of the possible outcomes of dividing with different signs.

Positive / positive = positive

Positive / negative = negative

Negative / positive = negative

Negative / negative = positive

We can see that whenever the signs are the same, the quotient is positive.

Answer:

If it is warm outside, then it is summer

Step-by-step explanation:

To find the converse, interchange the hypothesis and the conclusion

"If it is summer, then it is warm outside"

If it is warm outside, then it is summer

Answer:

A. If it is warm outside, then it is summer

Step-by-step explanation:

statement "If it is summer, then it is warm outside" : warm=summer

A. If it is warm outside, then it is summer. : warm = summer ✓

B. If it is not warm outside, then it is summer. : not warm = summer x

C. If it is warm outside, then it is not summer. : warm =not  summer x

D. If it is not warm outside, then it is not summer. : not warm = not summer x

Answer:

El reloj está marcando:

las 4:00 horas

Step-by-step explanation:

El reloj avanzó a su mismo ritmo pero en sentido contrario a partir de las 6:45

si ahora son las 9:30 el reloj marca:

9:30 = 9horas 30minutos = 9h 30'

6:45 = 6horas 45minutos = 6h 45´

1 hora = 60'

9h 30' = 8h + 60' + 30' = 8h + 90' = 8h 90'

entonces:

 8h 90'

- 6h 45'

= 2h 45

entonces el reloj está marcando 2h 45' menos que la hora en que se dañó.

por tanto:

 6h 45'

- 2h 45'

= 4h 00'

El reloj ahora está marcando las

4 horas en punto.

Answer:

its simplest form for the question is 2:1

Answer:

200°

Step-by-step explanation:

<2 = 90° (right angle)

<3 = 70° (vertically opposite angles)

<4 + <3 = 180° ( angles on a straight line)

<4 + 70 = 180°

<4 = 180° - 70°

<4 = 110°

<2 + < 4

= 90 ° + 110° = 200°

Answer:

(-4, -8)

Step-by-step explanation:

Let the coordinates of common point of the given lines are (x, y),

Thus, the slope of the line passes through the points (a, b) and R(4,2) is,

       2 - b

m1 = ------

        4 - a

Again, the slope of the line passes through two points P(-6,4) and Q(4,-4),

      -4 - 4          -8           -8          -4

m2 = ------  =   --------- = --------- = ---------

        4- (-6)       4 + 6         10        5

= m1 * m2 = -1

  2 - b      -4

= -------   x ---- =  -1

   4 - a      5

        8 - 4b

=     -----------   = 1

        20 - 5a

= 8 - 4b  = 20 - 5a

= 5a - 4b = 12 --------- equation 1

For a = -6   and b = -10

5 x -6  - 4  x  10 = -70 ≠ 12

For a = -4   and b = -8

5 x -4  - 4  x  - 8  = 12 = 12

For a = 0  and b = -1

5 x 0 - 4 x -1 = 4 ≠ 12

For a = 2 and b = 4

5 x 2 - 4 x 4 = -6 ≠ 12

therefore Second is correct

hope it helps and i get the brainliest.

The point lies on the line that passes through point R and is perpendicular to line PQ will be (-4, -8). Then the correct option is B.

If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The points are P(-6, 4), Q(4, -4), and R(4, 2). Then the slope of the line PQ is calculated as,

m = (4 + 4) / (-6 - 4)

m = - 4/5

The slope of the perpendicular line is calculated as,

⇒ -1/m

⇒ -1/(-4/5)

⇒ 5/4

The equation of the perpendicular line is written as,

y - 2 = (5/4)(x - 4)

y - 2 = (5/4)x - 5

y = (5/4)x - 3

Let's check which option satisfies the equation. Then we have

a) For, x = -6 and y = 10, then we have

10 = (5/4) (-6) - 3

10 ≠ - 10.5

b) For, x = -4 and y = -8,

-8 = (5/4) (-4) - 3

-8 = -8

c) For, x = 0 and y = -1,

-1 = (5/4) (0) - 3

-1 ≠ - 3

d) For, x = 2 and y = 4,

4 = (5/4) (2) - 3

4 ≠ - 0.5

The point lies on the line that passes through point R and is perpendicular to line PQ will be (-4, -8). Then the correct option is B.

More about the equation of a perpendicular line link is given below.

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Answer:

2

Step-by-step explanation:

opposite angles are the same

the shape opposite to 'z' is labelled with 2

which means that, that angle is 2 degrees

which also means that z would be 2 aswell.

Answer:

The radius of the circle is 40.44 cm

Step-by-step explanation:

We can use the formula for the arc of a circle of radius R and central angle [tex]\theta[/tex], where [tex]\theta[/tex] is given in radians (we therefore convert [tex]17^o[/tex] into radians with [tex]17^o\,\pi/180^o=0.2967[/tex] radians)

[tex]arc=R\,\theta\\12\,cm= R\,\theta\\12\,cm=R\,(0.2967)\\R=\frac{12}{0.2967} \,cm\\R=40.44\,cm[/tex]

Answer: Center D I think

Step-by-step explanation:

Answer:

The amount in 2001 is 8400

Step-by-step explanation:

Let x be the amount in 2001

There is an increase of 25% to get to the amount in 2002

x+ .25x = 1.25 x

1.25x = 10500

Divide each side by 1.25

1.25x / 1.25 = 10500/1.25

x =8400

The amount in 2001 is 8400

119°

Step-by-step explanation:

for this angle A has to be found for that you can use the theorem that states sum of interior angles is equal to the sum of opp exterior angle

51 + A = 112

A = 112 - 51

A = 61°

THEN WE CAN FIND THE B angle

they are angles on a straight line

so 61 + B = 180

B = 119°

Answer:

5 ≤ The number of packages Renna can remove

Step-by-step explanation:

The allowable mass on the elevator is given as 450 kg

The mass of Renna and the packages = 620 kg

The mass of each package = 37.4 kg

The mass Renna should remove from the elevator to meet the mass requirement = 620 - 450 = 170 kg

Therefore, the number of packages, n, Renna should remove can be found from the following inequality

170 ≤ n × 37.4

We note that since the mass of the packages are known, 5 packages weigh 187 kg which is > 170 kg

Therefore, the number of packages to be removed is 170 ≤ n × 37.4 < 187

Dividing by 37.4, we get;

Number of packages to be removed = 4.55 ≤ n < 5 ≈ 5 packages

Given that there whole number packages, we have;

5 ≤ n, which is , 5 ≤ The number of packages Renna can remove.

Answer:

37.4p  ≥ 170

Step-by-step explanation:

5 are in total packages.

Trust me this is the answer because I did this before

Hope this helps ;)

Answer:

2065.5

Step-by-step explanation:

You have to approximate the following calculation 3.5^6

The binomial theorem is given by:

[tex](a+b)^n=\Sigma_{k=0}^{k=n}\left[\begin{array}{c}n&k\end{array}\right] a^{n-k}b^k[/tex]      (1)

You can express the number 3as follow:

[tex]3.5^6=(3+0.5)^6=(3+\frac{1}{2})^6[/tex]          (2)

by comparing the equation (1) with the equation (2) you have

a = 3

b = 1/2

To calculate the first three terms of the binomial theorem you use k=3. You replace the values of a, b, n and k in the equation (1):

[tex](3+\frac{1}{2})^6=\Sigma_{k=0}^{k=6}\left[\begin{array}{c}6&k\end{array}\right] (3)^{6-k}b^k[/tex]

You only take the first three terms:

[tex](3+\frac{1}{2}^6)\approx(1)(3)^6(\frac{1}{2})^0+(6)(3)^5(\frac{1}{2})^1+\frac{6\cdot 5}{1\cdot 2}(3)^4(\frac{1}{2})^2\\\\(3+\frac{1}{2}^6)\approx729+729+\frac{1215}{2}=2065.5[/tex]

By using the first three terms of bynomial theorem you obtain 2065.5

Answer -3(2m-3n+4)

Step-by-step explanation:

Answer:  B) as x → -5  from the left, y → -∞

                    as x → -5 from the right, y → +∞

Step-by-step explanation:

[tex]g(x) =\dfrac{x^2+15x+56}{x+5}\quad =\dfrac{(x+7)(x+8)}{x+5}\\\\\\\text{Evaluate from the left. Let x = -6}\rightarrow \dfrac{(-)(-)}{(-)}=-\\\\\\\text{Evaluate from the right. Let x = -4}\rightarrow \dfrac{(-)(-)}{(+)}=+[/tex]

Refer to the graph which confirms that

Answer:

The term inside the box should be 3 x.

Step-by-step explanation:

Given the equation:

- (x - 1) + 5 = 2 (x + 3) - T

(where T is the missing term in Leonardo's equation)

we can work with the given terms and accumulate all of them on one side of the equal sign (let's pick the right side for that, and move the tremt T to the left):

- x + 1 + 5 = 2 x + 6 - T

- x + 6 = 2 x + 6 - T

0 = 3 x - T

T = 3 x

For such equation to render infinite number of solutions, the term T on the left must equal "3 x". that way, the equation would be verified for any possible value x.

Answer:

3x

Step-by-step explanation:

i did the test and got it right, hope this helps!

Answer:

158.73 yd

Step-by-step explanation:

A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.

Let use the formula of the law of cosine:

c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem

Let the third side be c, we replace:

c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °

c ^ 2 = 198225 - 173027.10

c ^ 2 = 25197.9

c = 158.73

So the distance is 158.73 yd

Answer: the right answer is 195.4

Step-by-step explanation: this guy does not what's happening

Answer: The equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .

The solution of the system is (3,6).

Step-by-step explanation:

Linear equation: [tex]y=mx+c[/tex]  , where m= slope

c = y-intercept.

In the first table, the y-intercept = 5     [ y-intercept = value of y at x=0.

Slope for first table  = [tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{6-5}{3-0}=\dfrac{1}{3}[/tex]

The equation that represents the first table:

[tex]y=\dfrac{1}{3}x+5[/tex]

So, the equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .

Also, the solution of the system is the common point (x,y) that satisfy both equations in the system.

Here, x=3 and y=6 is the common value in both tables.

So, the solution of the system is (3,6).

The linear equation of the first table is y = 1 / 3 x + 5

The solution to the system of equation is (3, 6)

where

m = slope

b = y-intercept

Therefore, y = - 1 /3 x + 7 is the equation for the second table.

The equation for the first table can be solved using (0, 5)(3, 6) from the table. Therefore,

m = 6 - 5 / 3 - 0 = 1 / 3

let's find b using (0, 5)

5 = 1 / 3(0) + b

b = 5

Therefore, the equation of the first table is as follows:

The solution to the system of equation can be calculated as follows:

y + 1 /3 x  = 7

y - 1 / 3 x  = 5

2y = 12

y = 12 / 2

y = 6

6 - 1 / 3 x = 5

- 1 / 3 x = 5 - 6

- 1 / 3 x = - 1

x = 3

Therefore, the solution to the system of equation is (3, 6)

learn more on linear equation here: https://brainly.com/question/2263981?referrer=searchResults

Answer: C) 12.2

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

Explanation:

We have a known adjacent side (10) and an unknown hypotenuse (x). The cosine rule ties the two sides together.

cos(angle) = adjacent/hypotenuse

cos(35) = 10/x

x*cos(35) = 10

x = 10/cos(35)

x = 12.2077458876146 approximately

x = 12.2

Make sure your calculator is in degree mode.

Answer:

[tex]\boxed{12.2}[/tex]

Step-by-step explanation:

cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

The hypotenuse of the triangle is x.

cos (35) = [tex]\frac{10}{x}[/tex]

x = [tex]\frac{10}{cos(35)}[/tex]

x = 12.20774588...

x ≈ 12.2

Answer:

2

Step-by-step explanation:

|a+x|/2-|a-x|/2

Plug in the values.

|-2+-6|/2-|-2- -6|/2

Evaluate.

|-8|/2-|4|/2

Apply rule : |-a| = a

8/2 - 4/2

4 - 2

Subtract.

= 2

Answer:

9 cm.

Step-by-step explanation:

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

= 1/3 * h * s^2      where s is the length of a side of the square base.

= hs^2/3 cm^3

Volume of the cuboid:

= s^2(15 - h).

So we have:

hs^2/ 3 = 300.......................(1)

s^2(15 - h) = 600..................(2)

From  equation (1) :

h s^2 = 900

s^2 = 900/h

Now substitute for s^2 in  equation (2) :

(900/h)(15 - h) = 600

Multiply through by h:

900(15 - h) = 600h

13500 - 900h = 600h

1500h = 13500

h = 9 cm (answer).

If the total height of the solid is 15 cm. If the volume of the pyramid and cuboid are 300 cm and 600 cm respectively, then height of pyramid is 9cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

300= 1/3 ×h×s²  

300= hs²/3

hs²=900

Volume of the cuboid:

600= s² (15 - h).

600=15s²-hs²

600=15s²-900

600+900=15s²

1500=15s²

100=s²

s=10

Now substitute s value in hs²=900

h(100)=900

Divide both sides by 100

h=9cm

Hence height of the pyramid is 9cm.

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Answer:

Step-by-step explanation:

Let x be the height of the box . x will be cut at four corners .

each side of the box = 6 - 2x

volume of box V = ( 6 - 2 x )² x

V = ( 36 + 4 x² - 24 x ) x

V = 4x³ - 24 x ² + 36 x

For maximum volume

dV / dx = 12 x² - 48 x + 36 = 0

x² - 4 x + 3 = 0

( x - 3 ) ( x - 1 ) = 0

x = 1 , x = 3 ( not possible )

Possible solution x = 1

Volume  , for x = 1

V = V = ( 6 - 2 x )² x

V = 4² x 1

= 16 m³.

Answer:

Everything but B

Step-by-step explanation:

When solving you can not have the degrees on the top

Answer:

A. The domain is (1,∞), and the range is (-7,∞)

Step-by-step explanation:

Well lets graph it first,

Look at the image below ↓

By looking at the image we move it 3 units right and 3 units down.

Then it will be located at the point (1,-7).

Meaning for the domain it starts at 1 and goes on for infinity.

And For the range it starts down at -7 and goes down for infinity.

Thus,

the correct answer is choice A.

Hope this helps :)

Answer:

A

Step-by-step explanation:

Solution:-

- First we will go through the guidelines that are followed when a given function [ f ( x ) ] is translated in a cartesian coordinate system domain.

Horizontal shifts:

Where, the constant ( a ) denotes the magnitude of shift  

Vertical shifts:

Where, the constant ( b ) denotes the magnitude of shift  

- The generalized form of a translated function is defined by the combination of both horizontal and vertical shifts as follows:

                    General: f ( x ) -> f ( x ± a ) ± b

Where, (a) and (b) are constants of respective translation shifts.

- We are given a function H ( x ) is to be translated 3 units to right and 3 units down. Use the above guidelines to determine the translated function H* ( x ) as follows:

                    [tex]H ( x ) = \sqrt{x+2} - 4\\\\H^* ( x ) = H ( x - 3 ) - 3[/tex]

- Substitute ( x - 3 ) in place of all ( x ) in the given function H ( x ) and subtract ( 3 ) from H ( x ) as follows:

                   [tex]H^* ( x ) = \sqrt{x-3 + 2} -4 - 3\\\\H^* ( x ) = \sqrt{x-1} -7\\[/tex]

- Now we will look for any transcendental functions in the translated function H*(x). These are " Radicals, fractions, Logs, trigonometric ratios "

- We have a radical - > " square root " in H* ( x ). To find the domain of H*(x) we need to determine for what real values of x is the function H*(x) is defined.

- The square root exist for all only positive numbers. So the terms under the square root must be positive; hence,

                     [tex]x - 1 \geq 0\\\\x \geq 1[/tex]

- Since the square root is the only transcendental in the given function H*(x) we have a one sided closed interval for the domain of the translated function.

                    Domain: [ 1 , ∞ )       ... Answer  

- The range of the function is the corresponding output of function H*(x) for the domain established above. We can determine this by plugging in the end-points of the defined domain in the translated function H*(x) as follows:

                    [tex]H^* ( 1 ) = \sqrt{1 - 1} - 7 = -7\\\\H^* ( inf ) = \sqrt{inf - 1} - 7 = inf - 7 = inf\\\\[/tex]

Therefore the range of the function is also a one sided closed interval bounded by x = 1.

                    Range: [-7 , ∞ )       ... Answer

Answer: d. 0.0047

Step-by-step explanation: The p-value is the calculated value used to compare to the significance level to determine if you reject or fail to reject the null hypothesis.

To find p-value, first find the z-score:

z = [tex]\frac{x-\mu}{SE}[/tex]

x is sample mean

μ is population mean

SE is standard error calculated by [tex]\frac{s}{\sqrt{n} }[/tex]

SE = [tex]\frac{10}{\sqrt{50} }[/tex]

SE = 1.414

z = [tex]\frac{24-28}{1.414}[/tex]

z = - 2.83

The hypotheses ([tex]H_{0}, H_{a}[/tex]) are if sample mean is equal or different from the average given, so, p-value will be the value of z from z-table multiplied by 2:

p-value = 0.00233*2

p-value = 0.0047

The p-value for this test is 0.0047

Answer:

88 inches

Step-by-step explanation:

We are finding the perimeter of the stop sign, therefor we have to either multiply or add the value of 11. Since this sign is an octagon we will have to multiply by eight or add 11 eight times. This will give you an answer of 88 inches.

Answer:

88 inches

Step-by-step explanation:

The stop sign is in the shape of an octagon. An octogon has 8 sides. If each side is 11 inches you multiply 11 * 8 which is 88.

Answer:

The password is weakest if it uses a single symbol for all 7 characters.

The strength of password increases with an increase in the number of symbols.

There are 7 possible symbol options per character to produce a password of strength of 7 bits.

Step-by-step explanation:

The password strength is determined by the usage of symbols and upper case and lower case letters along with a numeric character. The strength of password increases when different symbols are used. It is considered as weak password if only single symbol is used for all the 7 characters. The strong passwords are not easy to break and decode.

Answer:

The three correct options are:

The password is weakest if it uses a single symbol for all 7 characters.

The password is stronger with an increase in the number of symbols.

There are 2 possible symbol options per character to produce a password of strength of 7 bits.