The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz?

Answer:

(3g-5)(2g+7)

Step-by-step explanation:

Compare

6g^2+11g-35 to

ag^2+bg+c.

We should see that a=6, b=11,c=-35.

It these is factoable over the rationals we should be able to find two numbers that multiply to be ac and add up to be b.

ac=6(-35)

b=11

Now I really don't want to actually find the product of 6(-35). I'm just going to play with the factors until I see a pair that adds up to 11.

6(-35)

30(-7)  Moved a factor of 5 around.

10(-21) Moved a factor of 3 around.

10 and -21 is almost it.  We just need to switch where the negative is because we want a sum of 11 when we add the numbers (not -11).

So b=-10+21 and ac=-10*21.

We are going to replace b in

6g^2+11g-35

with -10+21.

We can do this because 11 is -10+21.

Let's do it.

6g^2+(-10+21)g-35

6g^2+-10g+21g-35

Now we are going to factor the first two terms together and the second two terms together.

Like so:

(6g^2-10g)+(21g-35)

We are going to factor what we can from each pair.

2g(3g-5)+7(3g-5)

There are two terms both of these terms have a common factor of (3g-5) so we can factor it out:

(3g-5)(2g+7)

Answer:

The x-intercept is 5.

Some people prefer you right it as a point (5,0).

Step-by-step explanation:

The x-intercept can be found by setting y=0 and solving for x.

Just like to find the y-intercept you can set x=0 and solve for y.

Let's find the x-intercept.

So we will set y=0 and solve for x:

3x-9y=15

3x-9(0)=15

3x-0    =15

3x        =15

Divide both sides by 3:

 x         =15/3

 x          =5

So the x-intercept is (5,0).

Answer:

D.

Step-by-step explanation:

That would be D because there is a repetition of x = -6.

-6 maps to -6, 5 and -5 which is not allowed in a function.

Functions can be one-to-one or many-to-one but not one-to-many.

Answer: 5 units

Step-by-step explanation:

The formula to find the area of a triangle is given by :-

[tex]\text{Area}=\dfrac{1}{2}\text{ base * height}[/tex]

Given : The area of a triangle = 30 square units

The length of the base of the triangle = 12 units

Let h be the height of the triangle .

Then , we have

[tex]30=\dfrac{1}{2}12\times h\\\\\Rightarrow\ h=\dfrac{30}{6}\\\\\Rightarrow\ h=5\text{ units}[/tex]

Hence, the height of a triangle = 5 units

Answer:

  18.8 cm²

Step-by-step explanation:

Sometimes, as here, when the problem is not carefully constructed, the answer you get depends on the method you choose for solving the problem.

Following directions

Using the formula ...

  Area = (1/2)ab·sin(C)

we are given the values of "a" (BC=5.9 cm) and "b" (AC=7.2 cm), but we need to know the value of sin(C). The problem statement tells us to round this value to the nearest hundredth.

  sin(C) = sin(118°) ≈ 0.882948 ≈ 0.88

Putting these values into the formula gives ...

  Area = (1/2)(5.9 cm)(7.2 cm)(0.88) = 18.6912 cm² ≈ 18.7 cm² . . . rounded

You will observe that this answer does not match any offered choice.

__

Rounding only at the End

The preferred method of working these problems is to keep the full precision the calculator offers until the final answer is achieved. Then appropriate rounding is applied. Using this solution method, we get ...

  Area = (1/2)(5.9 cm)(7.2 cm)(0.882948) ≈ 18.7538 cm² ≈ 18.8 cm²

This answer matches the first choice.

__

Using the 3 Side Lengths

Since the figure includes all three side lengths, we can compute a more precise value for angle C, or we can use Heron's formula for the area of the triangle. Each of these methods will give the same result.

From the Law of Cosines, the angle C is ...

  C = arccos((a² +b² -c²)/(2ab)) = arccos(-38.79/84.96) ≈ 117.16585°

Note that this is almost 1 full degree less than the angle shown in the diagram. Then the area is ...

   Area = (1/2)(5.9 cm)(7.2 cm)sin(117.16585°) ≈ 18.8970 cm² ≈ 18.9 cm²

This answer may be the most accurate yet, but does not match any offered choice.

Answer:

Step-by-step explanation:

According to the problem

[tex]\angle N + \angle O =180\°[/tex]

[tex]\angle O + \angle P = 180\°[/tex]

[tex]\angle M + \angle P = 180\°[/tex]

Which means,

[tex]\angle N + \angle O = \angle O + \angle P\\\angle N = \angle P[/tex]

And,

[tex]\angle O + \angle P = \angle M + \angle P\\\angle O = \angle M[/tex]

Therefore, the right answer is the last choice.

Answer:

g = 28,000 - 700t

Step-by-step explanation:

This solution reads, in words,

"the amount of water remaining in the pool is equal to 28,000 gallons minus 700 gallons per hour", which is what your situation is asking you.  You start with 28,000 gallons and are pumping out (subtracting) 700 gallons per hour.

g is what remains

Answer: [tex]g=28000-700t[/tex]

Step-by-step explanation:

Given : A 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour.

i.e, Remaining gallons = 28,000- 700 × Number of hours.

Let g be the number of gallons remaining in the pool and t is the amount of time in hours the pool has been draining.

Then, the equation models this situation  will be :-

[tex]g=28000-700t[/tex]

Answer:

(B)  this is not binomial function

Step-by-step explanation:

Given data

sample card n = 4 cards

total card number N =  52 cards

red card = 26

black card = 26

to find out

X be the number of cards that are red. (A) Binomial(B) Not binomial

solution

we know that 4 is selected with out replacement from 52 cards

we can say that R item is as success , here R is Red card

so that  52 - R items will be as failures

and we know

failure = 52 - 26 = 26 that is equal to 26 black card

we know this is Hyper geometric function

so this is not binomial function

Answer:

156p

Step-by-step explanation:

13p×12

multiply the numbers

= 156p

The value of the permutation [tex]^{13}P_{12}[/tex] is 6,227,020,800.

We have,

To calculate [tex]^{13}P_{12}[/tex], we need to determine the value of 13 factorial (13!) divided by (13 - 12) factorial (1!).

The formula for factorial is n! = n * (n - 1) * (n - 2) * ... * 2 * 1.

So,

[tex]^{13}P_{12}[/tex]

= 13!/1!

= 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2

= 6,227,020,800.

Therefore,

The value of the permutation [tex]^{13}P_{12}[/tex] is 6,227,020,800.

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Answer:

sinB is correct

Step-by-step explanation:

Calculating each of cos/ sin for ∠B

cosB = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{3\sqrt{5} }[/tex] = [tex]\frac{2}{\sqrt{5} }[/tex] and

[tex]\frac{2}{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] = [tex]\frac{2\sqrt{5} }{5}[/tex] ≠ [tex]\frac{\sqrt{5} }{5}[/tex]

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

sinB = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{3\sqrt{5} }[/tex] = [tex]\frac{1}{\sqrt{5} }[/tex] and

[tex]\frac{1}{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] = [tex]\frac{\sqrt{5} }{5}[/tex]

Answer:sinB is correct

Step-by-step explanation

Step-by-step explanation:

Calculating each of cos/ sin for ∠B

cosB =  =  =  and

×  =  ≠

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

sinB =  =  =  and

×  =

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Answer with explanation:

Pre-image =Rectangle EFGH

Image = Rectangle E'F'G'H'

Stretch Factor = 2.5

Coordinates of Point H= (-2,0)

If Coordinate of any point is (x,y) and it is stretched by a factor of k , then coordinate of that point after stretching = (k x , k y).

So, Coordinates of Point H' will be=(-2×2.5,0×2.5)

                                      = (-5,0)

Answer: (-5,0)

Step-by-step explanation:

Given : Square EFGH stretches vertically by a factor of 2.5 to create rectangle  E?F?G?H?.

The square stretches with respect to the x-axis such that the point H is located at (-2, 0).

Since , we know that to find the coordinate of image , we multiply the scale factor to the coordinate of pre-image.

Then , the coordinate of H? is given by :-

[tex](-2\times2.5, 0\times2.5)=(-5,0)[/tex]

Answer:

The maximum area that can be obtained by the garden is 128 meters squared.

Step-by-step explanation:

A represents area and we want to know the maximum.

[tex]A(x)=-2x^2+32x[/tex] is a parabola.  To find the maximum of a parabola, you need to find it's vertex.  The y-coordinate of the vertex will give us the maximum area.

To do this we will need to first find the x-coordinate of our vertex.

[tex]x=\frac{-b}{2a}{/tex] will give us the x-coordinate of the vertex.

Compare [tex]-2x^2+32x[/tex] to [tex]ax^2+bx+c[/tex] then [tex]a=-2,b=32,c=0[tex].

So the x-coordinate is [tex]\frac{-(32)}{2(-2)}=\frac{-32}{-4}=8[/tex].

To find the y that corresponds use the equation that relates y and x.

[tex]y=-2x^2+32x[/tex]

[tex]y=-2(8)^2+32(8)[/tex]

[tex]y=-2(64)+32(8)[/tex]

[tex]y=-128+256[/tex]

[tex]y=128[/tex]

The maximum area that can be obtained by the garden is 128 meters squared.

By using the vertex formula to find the width that maximizes the area of Beth's garden, we determine that the maximum area she can enclose with 32 meters of fencing is 128 square meters when the width is set to 8 meters.

The question is about finding the maximum area that can be enclosed by Beth with 32 m of fencing for a garden, modeled by the function A(x) = -2x2 + 32x, where x is the width of the garden in meters. To find the maximum area, we need to determine the vertex of this quadratic equation since the coefficient of x2 is negative, indicating a maximum point for the area.

To find the vertex, we can use the formula x = -b / 2a, where a and b are the coefficients from the quadratic equation A(x). Thus, x = -32 / (2*(-2)) = 8 meters. Substituting x back into the function to find the maximum area, A(8) = -2(8)2 + 32(8) = -128 + 256 = 128 square meters.

This shows that the maximum area Beth can enclose with 32 meters of fencing for her garden is 128 square meters, by setting the width to 8 meters.

[tex]\bf 7~~,~~\stackrel{7+6}{13}......601\qquad \qquad \stackrel{\textit{common difference}}{d = 6} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=7\\ d=6\\ a_n=601 \end{cases} \\\\\\ 601=7+(n-1)6\implies 601=7+6n-6\implies 601=1+6n \\\\\\ 600=6n\implies \cfrac{600}{6}=n\implies 100=n \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ \cline{1-1} a_1=7\\ a_n=601\\ n=100 \end{cases}\implies S_{100}=\cfrac{100(7+601)}{2} \\\\\\ S_{100}=\cfrac{60800}{2}\implies S_{100}=30400[/tex]

Answer:

{2,8}

Step-by-step explanation:

This is the same thing as asking what element (in this case what number) is in all 3 sets.

0 isn't in all 3 sets because it isn't in B.

2 is in all 3 sets

3 isn't because it isn't in C

4 isn't in A.

6 isn't in C.

8 is in all 3 sets.

9 isn't in A

So the elements that are in the 3 sets are {2,8}.

Answer:

  rational: -3.786, 8/17, 8.23, 10.86731234, 0.75, √.49 = 0.7

  irrational: 3π, √11

Step-by-step explanation:

Any number that can only be represented completely using symbols, such as π or √, is an irrational number.

If the number can be expressed as the ratio of two integers, it is a rational number. Such numbers include proper and improper fractions, integers, any number you can write with a finite number of digits, and any repeating decimal, regardless of the length of the repeat.

The graph hits [tex]\fbox{\begin\\\ \dfrac{10}{T}+2\\\end{minispace}}[/tex] times over 2 feet for [tex]a>2[/tex].

Further explanation:  

The height of the wave is given by the equation as follows:  

[tex]y=asin\left(\dfrac{2\pi t}{T}\right)[/tex]                          ......(1)

Here, [tex]a[/tex] is amplitude, [tex]T[/tex] is period of wave in second and [tex]t[/tex] time in seconds.  

The height [tex]y[/tex] of the wave is given as 2 feet and time [tex]t[/tex] is given as 5 seconds.  

Substitute 2 for [tex]y[/tex] and 5 for [tex]t[/tex] in equation (1).  

[tex]2=asin\left(\dfrac{2\pi \times5}{T}\right)\\2=asin\left(\dfrac{10\pi}{T}\right)\\\dfrac{2}{a}=sin\left(\dfrac{10\pi}{T}\right)[/tex]

The above eqution is valid only for [tex]a\geq 2[/tex] because the maximum value of the term [tex]sin(10\pi /T)[/tex] is 1.  

If [tex]T[/tex] is the time period then in [tex]T[/tex] seconds the graph will hit at least 2 times over 2 feet for [tex]a>2[/tex].

T seconds[tex]\rightarrow[/tex]2 hits

1 seconds [tex]\rightarrow[/tex] [tex]\dfrac{2}{T}[/tex] hits

5 seconds [tex]\rightarrow\dfrac{2\times5}{T}[/tex]

5 seconds [tex]\rightarrow[/tex] [tex]\dfrac{10}{T}[/tex]

If [tex]T[/tex] is time period in 5 seconds then the graph will hit [tex][10/T][/tex] times in interval 0 to [tex]2\pi[/tex].

Thus, the graph hits [tex]\fbox{\begin\\\ \dfrac{10}{T}+2\\\end{minispace}}[/tex] times over 2 feet for [tex]a>2[/tex].

Learn more:  

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)  

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2. Which is the graph of f(x) = (x – 1)(x + 4)?  

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Answer details:  

Grade: High school.  

Subjects: Mathematics.  

Chapter: function.  

Keywords: Function, wave equation, height, amplitude, equation, period, periodic function, y=asin(2pit/T), frequency, magnitude, feet, height, time period, seconds, inequality, maximum value, range, harmonic motion, oscillation, springs, strings, sonometer.

Answer:

True

Step-by-step explanation:

Segments drawn to a circle from the same outside point are congruent.

Segments YZ and XY are tangent to circle E draw from outside point Y. The segments are congruent, so the statement is true.

Answer:

  6 2/3 minutes

Step-by-step explanation:

Their rates in "jobs per hour" are ...

  (60 min/h)/(15 min/job) = 4 jobs/h

and

  (60 min/h)/(12 min/job) = 5 jobs/h

So, their combined rate is ...

  (4 jobs/h) + (5 jobs/h) = 9 jobs/h

The time required (in minutes) is ...

  (60 min/h)/(9 jobs/h) = (60/9) min = 6 2/3 min

Working together, it will take them 6 2/3 minutes.

To find out how long it would take the two grandparents to clean the playroom together, we can use the concept of rates and set up an equation. Solving the equation, we find that it would take them 9 minutes to clean the playroom if they work together.

To solve this problem, we can use the concept of rates to find the combined rate at which the two grandparents clean. Let's assign the variable x to represent the time it takes for them to clean together.

The rate at which the first grandparent cleans is 1/15th of the playroom per minute, while the rate at which the second grandparent cleans is 1/12th of the playroom per minute. The combined rate when they work together is the sum of their individual rates, which is given by the equation (1/15)+(1/12)=(1/x).

To solve this equation, we can find a common denominator of 60 to simplify the equation to 4/60+5/60=1/x. Adding the fractions gives us 9/60=1/x. Multiplying both sides of the equation by 60 gives us 9=x. Therefore, it would take the two grandparents 9 minutes to clean the playroom if they work together.

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Answer:

  291.9518 T are required for completion

Step-by-step explanation:

The remaining 0.62 part is ...

  0.62 × 470.89 T = 291.9518 T

Answer:

291.9518 metric Ton

Step-by-step explanation:

Hello

according to the data provided by the problem.

Total Iron needed to build the railing (A)= 470.89 Ton

Total Iron purchased by the factory =0.38 of total

Total Iron purchased by the factory =0.38 *470.89

Total Iron purchased by the factory (B)=178.9382metric Ton

the difference between the total iron needed and the iron supplied by the factory will be the iron we need to get

A-B=iron we need to get(c)

C=A-B

C=470.89-178.9382

C=291.9518 metric Ton

Have a great day.

Answer:

shortest length of fence is 8485.2 ft

Step-by-step explanation:

Given data

area =  3,000,000 square feet

to find out

shortest length of fence

let length L and width is W

so area is L × W

W = 3 × [tex]10^{6}[/tex] /L    ............1

2W = 6 × [tex]10^{6}[/tex] /L

rectangular field and then divide it in half

so fencing will be 3 × L + 2 × W

i.e.  3 L + 2W

fencing =  3 L  + 6 × [tex]10^{6}[/tex] /L

fencing minimum = 3 L  -  6 × [tex]10^{6}[/tex] /L²

fencing minimum length will be zero

3 L  -  6 × [tex]10^{6}[/tex] /L² = 0

3 L² = 6 × [tex]10^{6}[/tex]

L² =  2 × [tex]10^{6}[/tex]

L  =  1414.2

so from equation 1

W = 3 × [tex]10^{6}[/tex] /L

W = 3 × [tex]10^{6}[/tex] /1414.2

W = 2121.3

so fencing will be  3 L +2 W

so fencing =   3 × 1414.2  +2 × 2121.3

fencing =  4242.6 +4242.6

fencing =  8485.2

shortest length of fence is 8485.2 ft

The shortest length of fence the rancher can use is approximately 6104 feet. This is derived by setting up the area and perimeter equations, differentiating to find the minimum perimeter, and substituting the values back into the equation.

This problem is a basic optimization problem in mathematics. Given that the area of the field to be fenced is 3,000,000 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the rancher wants to divide the field in two with a fence running parallel to one side, the total amount of fencing will be two lengths and three widths.

Let's denote the length of the rectangle as 'l' and the width as 'w'. The area is thus l*w = 3,000,000. The perimeter is defined as 2*l + 3*w. Given that the area is fixed, w can be expressed in terms of l as 3,000,000/l.

Therefore, the perimeter becomes 2*l + 3*(3,000,000/l). The minimum fence length or perimeter occurs when the derivative of this equation is zero. By differentiating and setting the equation to zero, we get l=sqrt(1,500,000), approximately 1224.74 feet. Substituting this value into the equation for w gives us w also as 1224.74 feet.

The shortest length of fence that the rancher can use is thus 2*l + 3*w = 2*1224.74 + 3*1224.74 = 6103.7 feet.

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Answer:

B)  Total price of cakes depend on the number of boxes.

Step-by-step explanation:

Given: Graph

To find : Based on the graph, which of the following statements is true.

Solution : We have given graph between total price of cupcakes and number of boxes.

We can see from the graph is linear graph that is straight line graph passing through the origin.

It shows the Directly relation between total price of cakes and number of boxes.

Number of boxes ∝Total price of cakes.

So, Total price of cakes depend on the number of boxes.

Therefore, B)  Total price of cakes depend on the number of boxes.

Answer:

only keeps-

cows=134-67-34-10=23

sheep=142-67-34-15=26

goats=76-10-34-15=17

no pets=205-23-17-26-67-10-16-34

Step-by-step explanation:

some have one pets some have two or three

total no. of family have cows is 134 then 134 minus by those with more will be no. of family only with cows

Answer:

The third side can be any length as long as it is greater than 4 in and less than 26 in

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x ----> the length of the third side

Applying the triangle inequality theorem

1) 11+15 > x

26 > x

rewrite

x < 26 in

2) 11+x > 15

x> 15-11

x > 4 in

therefore

Aziza's claim is incomplete

The third side can be any length as long as it is greater than 4 in and less than 26 in

Answer:

Aziza’s claim is not correct. The third side must be between 4 in. and 26 in.

Step-by-step explanation:

Answer:

D. 0.7611

Step-by-step explanation:

The area is:

P(z<1.60) − P(z<-0.90)

Looking up the values in a z-score table:

0.9452 − 0.1841

0.7611

Answer:

D. 0.7611

Step-by-step explanation:

We have been given a graph of a normal standard distribution curve. We are asked to find the area of the shaded region under the given standard distribution curve.

The area of the shaded region under the standard distribution curve would be area of a z-score of 1.60 minus area of a z-score of [tex]-0.90[/tex] that is [tex]P(-0.90<z<1.60)=P(z<1.60)-P(z<-0.90)[/tex]

Using normal distribution table, we will get:

[tex]P(-0.90<z<1.60)=0.94520-0.18406[/tex]

[tex]P(-0.90<z<1.60)=0.76114[/tex]

Therefore, the shaded area under the curve is 0.7611 and option D is the correct choice.

Answer:

  A.)  3

Step-by-step explanation:

In the equation g(x) = f(k·x), the factor k is a horizontal compression factor. Here the graph of g is the graph of f compressed by a factor of 3.

The point (3, 2) on the graph of f(x) becomes the point (1, 2) on the graph of g(x). The point (1, 2) is a factor of 3 closer to the y-axis than the point (3, 2).

It may be easier to think of k as the reciprocal of the horizontal expansion (dilation) factor. The function g is horizontally dilated by a factor of 1/3 from function f, so k = 1/(1/3) = 3.

To determine the value of k, we need to analyze the graphs of f(x) and g(x). By comparing the graphs, we can determine if k is greater or less than 1. The graph of g(x) is compressed horizontally, indicating that k is less than 1.

To determine the value of k, we need to analyze the relationship between the functions f(x) and g(x).

Since g(x) = f(k⋅x), we can compare the graphs of f(x) and g(x) to find the value of k.

If k is greater than 1, the graph of g(x) will be compressed horizontally compared to the graph of f(x).

If k is less than 1, the graph of g(x) will be stretched horizontally compared to the graph of f(x).

By analyzing the graphs of f(x) and g(x), we can see that the graph of g(x) is compressed horizontally, indicating that k is less than 1.

Therefore, the value of k is B.) 1/3.

Answer:

252

Step-by-step explanation:

y varies directly with x means y=kx where k is a constant.

A constant means it never changes no matter what the point (x,y) they give.

So y=kx means y/x=k (I just divided both sides by x here).

So we have the following proportion to solve:

[tex]\frac{y_1}{x_1}=\frac{y_2}{x_2}[/tex]

[tex]\frac{70}{10}=\frac{y_2}{36}[/tex]

70/10 reduces to 7:

[tex]7=\frac{y_2}{36}[/tex]

Multiply both sides by 36:

[tex]7(36)=y_2[/tex]

Simplify left hand side:

[tex]252=y_2[/tex]

So y is 252 when x is 36.

Answer: 0.1210

Step-by-step explanation:

Given : The length of country and western songs is normally distributed with [tex]\mu=170 \text{ seconds}[/tex]

[tex]\sigma=40\text{ seconds}[/tex]

Sample size : [tex]n=16[/tex]

Let x be the length of randomly selected country song.

z-score : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z=\dfrac{158.30-170}{\dfrac{40}{\sqrt{16}}}\approx-1.17[/tex]

The probability that a random selection of 16 songs will have mean length of 158.30 seconds or less by using the standard normal distribution table will be

= [tex]P(x\leq158.30)=P(z\leq-1.17)[/tex]

[tex]=0.1210005\approx0.1210[/tex]

Hence, the probability that a random selection of 16 songs will have mean length of 158.30 seconds or less is 0.1210

The probability that a random selection of 16 country and western songs will have a mean length of 158.30 seconds or less is approximately 12.10%. This is calculated using the concept of the Sampling Distribution of the Mean and a Z score.

To find the probability that a random selection of 16 songs will have a mean length of 158.30 seconds or less, we need to use the concept of the Sampling Distribution of the Mean. This is a statistical concept that involves probabilities and the distribution of sample means. We assume that the distribution of length of songs is normal.

In our case, the population mean (μ) is 170 seconds and the population standard deviation (σ) is 40 seconds. We are looking at samples of 16 songs, so the sample size (n) is 16.

The mean of the sampling distribution of the mean (also just the population mean) is μ. The standard deviation of the sampling distribution (often called the standard error) is σ/√n. Given our numbers, this would be 40/√16 = 10.

We want the probability that the sample mean is 158.30 or less. The Z score is a measure of how many standard errors our observed sample mean is from the population mean. To find the Z score we use the formula: Z = (X - μ) / (σ/√n).

Therefore: Z = (158.30 - 170) / 10 = -1.17

A Z score of -1.17 corresponds to a probability of about 0.1210 or 12.10% that a random selection of 16 songs will have a mean length of 158.30 seconds or less.

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Answer:

1_ scalene

2_isoscelous

Answer:

13a. scalene

13b. isosceles

13c. right

Step-by-step explanation:

i took geometry hope this helps

Answer:

  c. 130

Step-by-step explanation:

∠FAB is a vertical angle with the one that is marked, so is 50°. ∠FAE is the complement of that, so is 40°. ∠DAF is the sum of the right angle DAE and angle FAE, so is ...

  90° + 40° = 130° = m∠DAF

Answer:

Step-by-step explanation:

This is a combination problem from stats.  We have a total of 12 English books from which you have to 3.  The order in which you pick them doesn't matter, you only need to determine how many different combinations are available to you.  This is the combination formula, then:

₁₂C₃ = [tex]\frac{12!}{3!(12-3)!}[/tex]

I'm just going to simplify the right side and leave off the left side til the end of the algebra because it's easier.  The right side simplifies to

[tex]\frac{12*11*10*9!}{3*2*1*9!}[/tex]

The 9!'s cancel each other out, leaving you with

[tex]\frac{12*11*10}{3*2*1}=\frac{1320}{6}[/tex]

Therefore,

₁₂C₃ = 220 possible different combinations of English books from which to pick.

We'll do the same for History, which has a combination formula that looks like this:

₈C₂= [tex]\frac{8!}{2!(8-2)!}[/tex]

That right side expands to

[tex]\frac{8*7*6!}{2*1*6!}[/tex]

The 6!'s cancel each other out, leaving you with:

[tex]\frac{8*7}{2*1}=\frac{56}{2}[/tex]

Therefore,

₈C₂ = 28 possible different combinations of History books from which to pick.

You may or may not need to add those together to get the answer your teacher is looking for.