a random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces. in this problem, what is the 0.7?

The probability will be 0.9940.

The provided parameters are

p = 0.05  (the true proportion or the mean )

n = 269   ( sample size )

we can calculate standard deviation as follows

σ = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

σ = 0.0132

Now the values that 'x' can take are

x = [tex]x_{1}[/tex] ±  [tex]x_{2}[/tex]

x = 0.05 + 0.03, 0.05 - 0.03

x = 0.08 , 0.02

Also the z-score is

z = (x - μ)/σ

z = [tex]\frac{0.08-0.05}{0.0132}[/tex]  , [tex]\frac{0.02-0.05}{0.0132}[/tex]

z = 2.27 , -2.27

we now find the p-values for the z-scores

p values are = 0.9970 , 0.0030

The difference in these values will give the probability

∴ P = 0.9970 - 0.0030

P =  0.9940

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Answer:

Length would be 6ft

Width would be 4ft

Step-by-step explanation:

24ft^2 is the area as we know 6x4 = 24 and 4 is two less than 6, therefor your answer is 4 and 6.

Answer:

  875 cm³

Step-by-step explanation:

You want the volume of the 15 cm high frustum of a 30 cm high pyramid with a 10 cm square base.

The volume of a pyramid is given by the formula ...

  V = 1/3Bh

Where B is the area of the base:

  B = s²

For the given pyramid, the volume is ...

  V = 1/3(10 cm)²(30 cm) = 1000 cm³

The volume of the frustum is the volume of the whole pyramid, less the volume of the part that is cut off. The part that is cut off has dimensions that are 1/2 of those of the whole pyramid, so its volume is ...

  V = (1/2)³ × (1000 cm³) = 125 cm³

Then the volume of the remaining frustum is ...

  1000 cm³ -125 cm³ = 875 cm³

The volume of the frustum is 875 cm³.

__

Additional comment

The volume can also be calculated from the areas of the two bases of the frustum and its height.

  V = (1/3)(B₁ +B₂ +√(B₁B₂))h

The top base is 5 cm square, so this evaluates to ...

  V = (1/3)(100 cm² +25 cm² +√(100·25) cm²)(15 cm) = 1/3(175 cm²)(15 cm)

  V = 875 cm³

Answer:

x=10

Step-by-step explanation:

3(4x-12)=84

12x-36=84

   +36. +36

12x=120

/12.  /12

x=10

Hopes this helps please mark brainliest

Answer:

No

Step-by-step explanation:

The value that corresponds with the other value on a data (34 to 2, 51 to 3, 68 to 5 etc.) needs to have the same quotient (or ratio) when you compare them.

34/2 = 51/3 ? Yes (but you can't stop here because you need to test ALL the values, what I mean is ALL the values UNTIL you found one that is not equal to each other, if all of them are equal, then the data are proportional.

34/2 = 68/5 ? No (Now you can stop here and say it's not proportional because we already found one pair that are not equal).

Answer:

the options are wrong

Step-by-step explanation:

Answer:

C. 8

Step-by-step explanation:

2 x 8 = 16

16 - 16 = 0

2 x 0 = 0

The larger bulldozer would take about 30 minutes.

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y-intercept: (0,60)

This is given in the table.

Slope: [tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

Using (1,50) and (2,40):

   [tex]m = \dfrac{40 - 50}{2-1} = \dfrac{-10}{1} = -10[/tex]

The slope is -10.

Using the slope-intercept form (y=mx+b) and the fact that we found m=-10 and b=60 from the table, the equation is:

   y = -10x + 60

Answer:

2x+4=52

2x+19=67

2x+13=61

(I gotta be honest I can’t fully remember how to name the angles but to not set you astray I just put the equation each angle goes to)

x=24

Step-by-step explanation:

the sum of all three angles is equal to 180 degrees

So we can add all of these angles and set it equal to 180 like this

(2x+19)+(2x+4)+(2x+13)=180

Simplify by adding common terms

6x+36=180

   -36.  -36

6x=144

/6.  /6

x=24

So now to find the angles we just fill in x with 24

2(24)+4

48+4

52

2(24)+19

48+19

67

2(24)+13

48+13

61

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The range of the function g, given the premises for f(x) = |x| and a < 0 while b ≠ 0 is; the set of all real numbers.

It follows from the task content that the range of the function g(x) = a|x| + b is to be determined given the parameters as in the task content.

Since the function f(x) = |x| has a range of y ≥ 0, and a is a negative number ( < 0), it therefore means that the a|x| is always a number less than 0 (<0).

However, the possible values of constant, b include all real numbers except 0.

On this note, the function g(x) = a|x| + b has a range which is the set of all real numbers. This is so because, g(x) > 0 when a|x| < b and g(x) < 0 when a|x| > b.

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Answer:

[tex](x + 4)(2x + 5) - (x + 3)(x + 2) = 79 \\ 2x {}^{2} + 5x + 8x + 20 - {x}^{2} - 2x - 3x - 6 = 79 \\ {x}^{2} + 8x + 14 = 79 \\ {x}^{2} + 8x - 65 = 0 \\ {x}^{2} + 13x - 5x - 65 = 0 \\ x(x + 13) - 5( x + 13) = 0 \\ (x - 5)(x + 13) = 0[/tex]

x-5=0

x=5

the length of smaller rectangle= 8 m

and breadth of s. rectangle= 7 m

l x b = 8 x 7

[tex]56 {m}^{2} [/tex]

hopefully this will u

Answer:

[tex]x^2+3x-10[/tex]

Step-by-step explanation:

To expand you must do this:

[tex]x*x+(-2x)+(5x)-10\\x^2-2x+5x-10\\x^2+3x-10[/tex]

The answer to be entered in the boxes for the area model is 17, 0 and 17

An area model is a rectangular diagram or model used for solving multiplication and division problems, in which the quotient and divisor define the length and width of the rectangle

Given:

    ....60.....1.............

36|2160 | 36 | 17

2160 ÷ 36 = 60 R 0

36 ÷ 36 = 1 R 0

17  ÷ 36 =  0 R 17

Note:  (0 x 36) + 17 = 17

Therefore, the answer to be entered in the boxes is 17, 0 and 17 respectively

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The expression that represents the distance between -3/4 and -0.2 on a number line is |-3/4 + 0.2|

The distance between points on a number line is the number of units or points between these points

From the question, we have the following parameters that can be used in our computation:

Distance between -3/4 and -0.2 on a number line

This means that

Endpoints = -3/4 and -0.2

These endpoints can be represented as

Endpoint 1 = -3/4

Endpoint 2 = -0.2

The distance between these endpoints is then calculated as

Distance = |Endpoint 1 - Endpoint 2|

Substitute the known values in the above equation, so, we have the following representation

Distance = |-3/4 - -0.2|

Evaluate the difference

Distance = |-3/4 + 0.2|

Hence, the distance expression is |-3/4 + 0.2|

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The solution to the equation given as √|x|² = x is x ≥ 0

From the question, the representation of the equation is given as

√|x|² = x

To start with;

We evaluate the square root expression in the equation

So, we have the following representation

|x| = x

The above implies that the absolute value of a number equals the number

As a general rule of absolute values, the absolute value of a number is positive

This can be represented as

x ≥ 0

Hence, the solution to the equation is x ≥ 0

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Answer: -19 49/50 ==> a

Step-by-step explanation:

(−5 2/5) ⋅ 3 7/10=

(−5 - 2/5) ⋅ (3 + 7/10)=

(−25/5 - 2/5) ⋅ (30/10 + 7/10)= ==> make the terms have like denominators

((-25-2)/5) ⋅ ((30+7)/10)=

-27/5 ⋅ 37/10 =

-27 ⋅ 37 / (5 ⋅ 10) =

-999/50=

(-950-49)/50=

-950/50 - 49/50=

-19 - 49/50=-19 49/50 ==> a

The product of the improper fraction 3 1/4 and 1/2 is 1 5/8.

What is mixed fraction?

 A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. a fraction when the denominator (bottom number) and the numerator (top number) are both more than or equal (the bottom number). When the numerator is equal to or more than the denominator, the fraction is said to be improper fraction. It always has a value of one or higher.

Here the given fraction 3 1/4 convert into 13/4.

Now the product of the fractions is

=> 13/4 × 1/2

=> 13/8

=> 1 5/8.

Therefore product of the given fraction is 1 5/8.

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Answer:

sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1

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

Explanation:

Part A)  Find P(-2)

We'll divide P(x) over (x+2) to get a quotient Q(x) and remainder 8 like so

P(x)/(x+2) = quotient + remainder/(x+2)

P(x)/(x+2) = Q(x) + 8/(x+2)

When multiplying both sides by (x+2), it clears out the fractions and we're left with this

P(x) = (x+2)*Q(x) + 8

From here, plug in x = -2 and simplify

P(x) = (x+2)*Q(x) + 8

P(-2) = (-2+2)*Q(-2) + 8

P(-2) = (0)*Q(-2) + 8

P(-2) = 0 + 8

P(-2) = 8

Luckily we don't need the value of Q(-2) since it cancels out with the zero.

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

Part B) Find P(2)

This time we'll plug in x = 2 and we'll get...

P(x) = (x+2)*Q(x) + 8

P(2) = (2+2)*Q(2) + 8

P(2) = 4*Q(2) + 8

P(2) = 4*5 + 8

P(2) = 20+8

P(2) = 28

Answer:16/25 :D

Step-by-step explanation:does that help :3

Answer:

Step-by-step explanation:

16/(2+6)

16/8=2

Answer:

Step-by-step explanation:

y = ¼x + (-7/4) is the standard form for the line that passes through (3, −1) and (−5, −3)

What is Slope intercept form?

y=mx=c is the slope intercept form of a line, m is the slope.

We need to find equation of line passing through (3, −1) and (−5, −3)

First we need to calculate slope 'm'.

slope m = y2- y1 / x2-x1

y2=-3, y1=-1, x2=-5, x1=3

m= -3 - (-1)/(-5)-3 = -2/-8=1/4

Equation of line, y=mx+c

find C in the equation (y=mx+c)

C = y-mx

C = -1-1/4(3)= -7/4

now replace the values you find in the equation (y=Mx+C)

y =1/4x-7/4

Hence y =1/4x-7/4 is the equation of line  passes through (3, −1) and (−5, −3).

Answer:

yes it is

atleat i think

Answer:

[tex]x=12, y=0[/tex]

Step-by-step explanation:

[tex]22+\frac{1}{5}yi=2x-2 \\ \\ (24-2x)+\frac{1}{5}yi[/tex]=0[/tex]

Setting the real and imaginary parts of the left hand side equal to 0,

[tex]24-2x=0 \implies x=12 \\ \\ \frac{1}{5}y=0 \implies y=0[/tex]

If Two planes are parallel and each plane contains a line, the two lines are  not skew because In the event that any two lines fall on a single plane, they will either intersect or be parallel to one another. Both instances violate the concept of a skew line because the skew lines are neither parallel nor intersect.

Infinitely many lines cross through, yet only one of them is parallel to. Lines that never intersect and are in distinct planes are known as skew lines. Parallel lines and skew lines are distinguished by the fact that they both reside in the same plane, whereas skew lines do not.

The two lines would overlap at some point if the two planes on which they are located weren't parallel, which again defies the definition of skew lines.

Therefore, The skew lines are thus present if and only if both lines fall on a pair of parallel planes.

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The absolute value equation graphed is defined by the rule given as follows:

y = |x - 3| + 6.

The function graphed is an absolute value equation, due to it's v format.

The equation that represents an absolute value function with vertex (h,k) is given by the rule presented as follows:

y = |x - h| + k.

On the graph, this vertex is the turning point of the absolute value function.

For the graphed function, the coordinates of the vertex are given as follows:

Then the coordinates of the vertex are:

(3,6).

The equation of the graphed absolute value function is:

y = |x - 3| + 6.

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