Using the quadratic formula, solve the
equation below to find the two possible
values of t.
6x^2-35=-11x
Give each value as a fraction in its
simplest form.

a. The probability that exactly one is defective is 0.2025

b. The probability that none will be defective is 0.0769

c. The probability rate that should be used is 2%

d. The modified production process is better.

The question has to do with binomial probability.

Binomial probability is probability in which the event can only have two values or is binary.

Given the binomial probability formula,

P(X = x) = ⁿCₓpˣ(1 - p)ⁿ ⁻ ˣ

where

For the probability that exactly one is defective, x = 1

So, P(x = 1) = ⁵⁰C₁p¹(1 - p)⁵⁰ ⁻ ¹

= ⁵⁰C₁p(1 - p)⁴⁹

= ⁵⁰C₁(0.05)(1 - 0.05)⁴⁹

= ⁵⁰C₁(0.05)(0.95)⁴⁹

= 50(0.05)(0.95)⁴⁹

= 50(0.05)(0.081)

= 0.2025

So, the probability that exactly one is defective is 0.2025

For the probability that exactly one is defective, x = 0

So, P(x = 0) = ⁵⁰C₀p⁰(1 - p)⁵⁰ ⁻ ⁰

= ⁵⁰C₀(1 - p)⁵⁰

= ⁵⁰C₀(1 - 0.05)⁵⁰

= ⁵⁰C₀(0.95)⁵⁰

= 1 × (0.95)⁵⁰

= 0.0769

So, the probability that none will be defective is 0.0769

Since the modified result results in a defective rate of one out of 50 pens.

The probability rate that should be used is p = number of defective pens/total number of pens = 1/50

= 1/50 × 100 %

= 2%

The probability rate that should be used is 2%

Since the defective rate of the modified production process is 2% which is less than that of the previous production process which is 5%, the modified production process is better.

So, the modified production process is better.

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Answer:

n = 2.6

Step-by-step explanation:

Hello!

We can create an equation with equivalent fractions. Remember that a ratio can also be represented as a fraction.

We can create two fractions that are equivalent to each other given the ratios.

The value of n is 2.6.

The number of years based on the equation is 24 years.

The information is incomplete. An overview will be given. Let the income equation be represented as I = 60 + 10x where x represents the years taken.

Therefore i = 60 + 10x

60 + 10x = 300

10x = 300 - 60

10x = 240

x = 240/10

x = 24

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If the length,breadth, height of cuboid are 16 m, 5 m,4 m , slant height of pyramid is 10m,  height be 6 m then the surface area of composite figure be 444 [tex]m^{2}[/tex].

Given that the length,breadth,height of cuboid are 16m,5 m, 4m and slant height be 10 m and height be 6 m.

Surface area is basically sum of area of all the sides of a figure.

Surface area of composite figure =  area of cuboid less area of common side + area of 2 slant sides of pyramid+area of two triangles.

=2(lb+bh+hl)-(lb)+2(slant height*breadth of cuboid)+2[1/2* length of cuboid* height of triangle)

=2(16*5+5*4+4*16)-16*5+2(10*5)+2[1/2*16*6]

=2(80+20+64)-80+2*50+2(48)

=2(164)-80+100+96

=328-80+196

=248+196

=444[tex]m^{2}[/tex]

Hence the surface area of composite figure having a cuboid and pyramid on top is 444[tex]m^{2}[/tex].

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Answer:

75%

Step-by-step explanation:

9 divided by 12 is 0.75, so 9 is 75 percent of 12.

I hope this helps, have a good day!

Hence, the standard deviation for these data is 7.1 sessions

In statistics, the standard deviation is a measure of the volatility or variance of a set of values. [1] A low standard deviation indicates that the values ​​tend to be close to the mean of the set (also known as the mean), and a high standard deviation indicates that the values ​​are more widely distributed. indicate.

Standard deviation can be abbreviated as SD, and in mathematical texts and equations, it is most commonly represented by the Greek lower σ (sigma) for population standard deviation or the Latin letter s for sample standard deviation. It is a target.

The standard deviation of a random variable, sample, population, dataset, or probability distribution is the square root of its variance. It's algebraically simple, but it's actually less robust than mean absolute deviation. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.

Expression

\ sigma = {\ sqrt {\ frac {\ sum (x_ {i}-{\ mu}) ^ {2}} {N}}}

\ sigma = Population standard deviation

N = size mother Population

x_i = Arbitrary value from population

\ mu = Population mean

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The examples of sinusoids include sound and water waves.

Simple harmonic motion such as that of a pendulum or a weight attached to a spring results in a sinusoidal relationship between position and time.

The angle will be formed after t time of the starting of the motion.

θ = wt = 2πt/20 = πt/10

Radius of the wheel = 30/2 = 15 feet

Distance from the ground = (15 - 15cosθ) + 8 = (15 - 15cosπt/10) + 8

= 23 - 15cos(πt/10)

As we know the minimum value of the cos is -1

-1 ≤ cos(πt/10) ≤ 1

8 ≤ 23 - 15cos(πt/10) ≤ 38

The lowest distance = 8 feet

It should be always greater than zero as the lowest point of what should be above the ground.

d = 23 - 15cos(πt/10)

Plug t = 3 in the above equation:

d(3) = 14.18 feet

For t = 8

d(8) = 35.13 feet

For t = 15

d(15) = 23 feet

For t = 19

d(19) = 8.73 feet

Thus, the lowest distance is 8 feet, and the lowest point of what should be above the ground and the equation is d = 23 - 15cos(πt/10).

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Answer: Option (1)

Step-by-step explanation:

[tex]\angle DMA[/tex] is another name for angle 3, but not [tex]\angle DME[/tex].

Answer:

x = [tex]\frac{4}{25}[/tex]

Step-by-step explanation:

1 : x = 6 [tex]\frac{1}{4}[/tex] ← change to improper fraction

1 : x = [tex]\frac{25}{4}[/tex] , then

[tex]\frac{1}{x}[/tex] = [tex]\frac{25}{4}[/tex] ( cross- multiply )

25x = 4 ( divide both sides by 25 )

x = [tex]\frac{4}{25}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation a.}[/tex]

[tex]\rm{2x^2 - 162 = 0}[/tex]

[tex]\huge\textbf{Solving for:}[/tex]

[tex]\rm{2x^2 - 162 = 0}[/tex]

[tex]\huge\textbf{Add \boxed{\bf 162} to both sides:}[/tex]

[tex]\rm{2x^2 - 162 + 162 = 0 + 162}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{2x^2 = 0 + 162}[/tex]

[tex]\rm{2x^2 = 162}[/tex]

[tex]\huge\textbf{Divide \boxed{\bf 2} to both sides:}[/tex]

[tex]\rm{\dfrac{2x^2}{2} = \dfrac{162}{2}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x^2 = \dfrac{182}{2}}[/tex]

[tex]\rm{x^2 = 81}[/tex]

[tex]\huge\textbf{Take the square root of \boxed{\bf 81}}[/tex]

[tex]\rm{x = \pm \sqrt{81}}[/tex]

[tex]\rm{x = 9\ or\ x = -9}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{x = } \frak{9\ or } \ \textsf{x = }\frak{-9}}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation b.}[/tex]

[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]

[tex]\huge\textbf{Solving for:}[/tex]

[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]

[tex]\huge\textbf{Simplify both sides of your equation:}[/tex]

[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} = -2}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf -2} to both sides:}[/tex]

[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} - (-2) = -2 - (-2)}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{- \dfrac{1}{2}x^2 + 3x - \dfrac{5}{2} = 0}[/tex]

[tex]\huge\textbf{Now, we can convert the equation to:}[/tex]

[tex]\rm{-0.5x^2 + 3x - 2.5 = 0}[/tex]

[tex]\large\text{When we changed the equation entirely, we made it easier to solve}\uparrow[/tex]

[tex]\huge\textbf{Use the quadratic formula to solve.}[/tex]

[tex]\large\textsf{The quadratic formula:}[/tex]

[tex]\mathsf{x= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\huge\textbf{Here are your labels:}[/tex]

[tex]\text{a = }\rm{-0.5}\\\\\text{b = }\rm{ 3}\\\\\rm{c = }\rm{\ -2.5}[/tex]

[tex]\huge\textbf{Your new equation:}[/tex]

[tex]\rm{x = \dfrac{-(3) \pm \sqrt{3^2 - 4(-0.5)(-2.5)}}{2(-0.5)}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{-3 \pm \sqrt{4}}{-1}}[/tex]

[tex]\rm{x = 1\ or \ x = 5}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\textsf{x = }\frak{1}\ \textsf{or x = }\frak{5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

[tex]a)\ x_1=-9,\ x_2=9\\\\b)\ x_1=1,\ x_2=5[/tex]

Given equations:

[tex]a)\ 2x^2 - 162 = 0\\\\b) -\dfrac{1}{2}(x-3)^2=-2[/tex]

A) 2x² - 162 = 0

Step 1: Divide both sides by 2.

Step 2: Take the square root of both sides (using both the positive and negative roots).

[tex]\\\implies \sqrt{x^2}=\sqrt{81}\\\\\implies x=\pm\ 9[/tex]

Step 3: Separate into two cases.

[tex]\implies x_1 = -9,\ x_2 =-9[/tex]

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

B) -1/2(x - 3)² = -2

Step 1: Multiply both sides by -2.

[tex]\\\implies -2\left(-\dfrac{1}{2}(x-3)^2\right)=-2(-2)\\\\\implies (x-3)^2=4[/tex]

Step 2: Take the square root of both sides (using both the positive and negative roots).

[tex]\\\implies\sqrt{(x-3)^2}=\sqrt{4}\\\\\implies x-3=\pm\ 2[/tex]

Step 3: Separate into two cases and solve each one.[tex]1)\ x-3=-2\implies x=-2+3\implies \boxed{x=1}\\\\2)\ x-3=2\implies x=2+3\implies \boxed{x=5}[/tex]

Answer:

40 units

Step-by-step explanation:

lengths:

12+12=24

width:

8+8=16

perimeter:

2l+2w

2(12)+2(8)

24+16=40

The equation of the line in slope intercept form is y = 7x - 2

The equation of the line can be solved with the following equation.

y = mx + b

where

Therefore,

m = -2  - 5 / 0 - 1 = -7 / -1

m = 7

Hence, using (1, 5)

y = 7x + b

5 = 7(1) + b

5 - 7 = b

b = -2

Therefore,

y = 7x - 2

Hence, the equation of the line in slope intercept form is y = 7x - 2

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The answer is . one-to-one.

(a) The function is onto because a, b, c, and d are members of its codomain. All points are converted into various points, making it a one-to-one relationship. The response is that it is one-to-one and onto ( A and C).

(b) It is onto because a, b, c, and d are members of the function's codomain. All points are converted into various points, making it a one-to-one relationship. The response is that it is one-to-one and onto (A and B).

(C) The element b is not onto since it is not a part of the function's codomain. All points are converted into various points, making it a one-to-one relationship. One-to-one is the right response.

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The complete question is -

Determine if each of the following functions from {a,b,c,d} to itself is one-to-one and/or onto.

Check ALL correct answers.

(a) f(a)=d,f(b)=a,f(c)=c,f(d)=b

A. onto.

B. neither one-to-one nor onto.

C. one-to-one.

f(a)=b,f(b)=a,f(c)=c,f(d)=d

A. one-to-one.

B. onto.

C. neither one-to-one nor onto.

f(a)=c,f(b)=d,f(c)=a

A. one-to-one.

B. onto.

C. neither one-to-one nor onto.

Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:

"Zero, because the discriminant is negative".

A quadratic equation is a polynomial of degree 2, in a single variable x.

The standard form of a quadratic equation is ax² + bx + c = 0.

The quadratic formula is used to find the solution(s)/root(s) of this equation.

The quadratic formula is:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

In this formula, [tex]b^2-4ac[/tex] is called the discriminant (D).

The solution(s)/root(s) of the equation, depends on this discriminant value as follows:

In the question, we are given that the simplest form of Quincy's equation in the radical form was,

[tex]x = \frac{-3 \pm \sqrt{-19} }{2}[/tex].

Comparing this to the quadratic formula,

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

we get the discriminant (D) = -19.

Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:

"Zero, because the discriminant is negative".

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For complete question, refer to the attachment.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \: \angle1 \cong \angle2[/tex]

( by corresponding angle pair )

[tex]\qquad❖ \: \sf \: \angle2 \cong \angle3[/tex]

( given in the question )

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle1 \cong \angle3[/tex]

The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

The cosine rule is given as;

[tex]c = \sqrt{a^2 + b^2 - 2ab cos \alpha }[/tex]

c = length of the diagonal

a = base length = 22 feet

b = 7 feet

[tex]c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}[/tex]

[tex]c = \sqrt{533 - 308 * 0. 7660}[/tex]

[tex]c = \sqrt{533 - 235. 93}[/tex]

[tex]c = \sqrt{297. 072}[/tex]

[tex]c = 17. 24[/tex] feet

Using sine rule

[tex]\frac{a}{sin A } = \frac{c}{sin C}[/tex]

[tex]\frac{a}{sin 70} = \frac{17. 24}{sin 40}[/tex]

Cross multiply

[tex]a[/tex] × [tex]sin 60[/tex] = [tex]c[/tex] × [tex]sin 70[/tex]

[tex]a[/tex] × [tex]0. 8660[/tex] = [tex]17. 24[/tex] × [tex]0. 9397[/tex]

[tex]a = \frac{16. 20}{0. 8660}[/tex]

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

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Answer:

See below

Step-by-step explanation:

Take fox across

go back to get goose

  take goose across

  take fox BACK

  grab dog.....take dog across

   go back get grain and take it across

    go back get fox and take it across

The relationship that represents the law of cosines if the measure of the included angle between the sides a and b is D. area of square c² = area of square a² area of squareb² area of defect1 area of defect2

It should be noted that the cosine law is simply used to solving triangles.

The law simply states that c² = a² + b² - 2abcosC.

The correct option that illustrates this is D.

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Answer:

c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation \#1.}[/tex]

[tex]\mathsf{|-8| + 9 = }[/tex]

[tex]\huge\textbf{Random note:}[/tex]

[tex]\textsf{The additive inverse of }\mathsf{|-8|}\textsf{ is positive 8.}[/tex]

[tex]\huge\textbf{Solving for the equation:}[/tex]

[tex]\mathsf{|-8| + 9}[/tex]

[tex]\mathsf{= \bold 8 + 9}[/tex]

[tex]\mathsf{= 17}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{17}}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation \#2.}[/tex]

[tex]\mathsf{|-8 + 9| =}[/tex]

[tex]\huge\textbf{Random note:}[/tex]

[tex]\textsf{We will convert your equation to }\mathsf{-8 + 9}\textsf{ because it can make the equation}\\\textsf{a lot easier to solve.}[/tex]

[tex]\huge\textbf{Solving for the equation:}[/tex]

[tex]\mathsf{|-8 + 9|}[/tex]

[tex]\mathsf{= -8 + 9}[/tex]

[tex]\text{Start at }\rm{-8}\text{ and go \boxed{up} 9 spaces to the right and you have your answer.}[/tex]

[tex]\mathsf{= 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The other fraction is [tex]1\frac{1}{55}[/tex].

Provided that ,

One fraction = [tex]9\frac{3}{7}[/tex] = [tex]\frac{66}{7}[/tex]

The product of their fraction = [tex]9\frac{3}{5}[/tex] = [tex]\frac{48}{5}[/tex]

We have to find out the other fraction.

When one fraction and their product are given, the formula to find out another fraction = product / one fraction

So, the other fraction = [tex]\frac{48}{5}[/tex] / [tex]\frac{66}{7}[/tex]

= [tex]\frac{48}{5} * \frac{7}{66}[/tex]

= 336/330

= 56/55 [divided both the numerator & denominator by 6]

= [tex]1\frac{1}{55}[/tex]

Therefore it is concluded that the other fraction is [tex]1\frac{1}{55}[/tex] .

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Answer:

  D.  264 in³

Step-by-step explanation:

The missing edge dimension can be found using the Pythagorean theorem. Then the volume can be found using the appropriate formula.

The missing dimension and the two given for the top triangle will satisfy the Pythagorean theorem. If the missing dimension is represented by 'a', then we have ...

  a² +8² = 10²

  a = √(100 -64) = 6 . . . . inches

The area of the top triangle is ...

  A = 1/2bh . . . . where b and h are the base and height dimensions

  A = 1/2(6 in)(8 in) = 24 in²

The volume of the triangular prism is ...

  A = Bh . . . . . where B is the area of the triangular base, and h is the prism height

  A = (24 in²)(11 in) = 264 in³

The volume of the triangular prism shown is 264 in³.

The sample standard deviation of sample 1 is 11.54,  of sample 2 is 10.21,  of sample 3 is 11.25,  of sample 4 is 14.15.

Given

Data point      sample 1     sample 2           sample 3                sample 4

1                          37                38                       16                             19          

2                          15                31                        21                             10

3                          43                12                       45                             45

4                          25                19                        32                            37

5                          21                 28                       25                             22

We have to find the sample standard deviation of each sample.

We have to first mean of each sample.

Sample mean of 1=141/5=28.2

Sample mean of 2=128/5=25.6

Sample mean of 3=139/5=27.8

Sample mean of 4=133/5=26.6

Sample standard deviation=[tex]\sqrt{}[/tex]∑[tex](x-x bar)^{2}/n-1[/tex]

∑[tex](x-x bar)^{2}[/tex] is calculated in the figure.

Sample standard deviation of sample 1=[tex]\sqrt{532.8/4}[/tex]

=[tex]\sqrt{133.2}[/tex]

=11.54

Sample standard deviation of sample 2=[tex]\sqrt{417.2/4}[/tex]

=[tex]\sqrt{104.3}[/tex]

=10.21

Sample standard deviation of sample 3=[tex]\sqrt{506.8/4}[/tex]

=[tex]\sqrt{126.7}[/tex]

=11.25

Sample standard deviation of sample 4=[tex]\sqrt{801.2/4}[/tex]

=[tex]\sqrt{200.3}[/tex]

=14.15.

Hence the sample standard deviation of sample 1 is 11.54, sample standard deviation of sample 2 is 10.21, sample standard deviation of sample 3 is 11.25, sample standard deviation of sample 4 is 14.15.

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Answer:

1/2 pounds

Step-by-step explanation:

3/4 * 2/3 = 1/2 pounds

The probability that two of three football games will go to into overtime is 0.08

From the question, we have the following parameters about the probability

Sample size, n = 3

Proportion that goes to overtime, p = 18%

Number that goes into overtime, x = 2

The probability that two of three football games will go to into overtime is calculated using the following binomial probability

P(x) = nCx * p^x * (1 - p)^(n -x)

Substitute the known values in the above equation

P(2) = 3C2 * (18%)^2 * (1 - 18%)^(3 -2)

Express 18% as decimal

P(2) = 3C2 * (0.18)^2 * (1 - 0.18)^(3 -2)

Evaluate the difference

P(2) = 3C2 * (0.18)^2 * (0.82)^1

Evaluate the combination expression

P(2) = 3 * (0.18)^2 * (0.82)^1

Evaluate the exponent

P(2) = 3 * 0.0324 * (0.82)

Evaluate the product

P(2) = 0.079704

Approximate

P(2) = 0.08

Hence, the probability that two of three football games will go to into overtime is 0.08

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Answer:

Step-by-step explanation:

A = 4 ft

B = 10 ft

C = 8 ft

D = 6 ft

b) Area of rectangle = length * width

Area of 2 triangle = base * height

Area of right triangular prism = area of 2 triangles +area of left rectangle + area of middle rectangle + area of right rectangle

  = 6 * 8  + 4* 6 + 4 * 10 + 4 * 8

  = 48 + 24 + 40 + 32

  = 144 ft²

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Formulas:}[/tex]

[tex]\huge\text{Area of rectangle is: }\huge\boxed{\rm{\bold{w}idth \times \bold{h}eight = \bold{a}rea}}[/tex]

[tex]\huge\text{Area of triangle is: }\huge\boxed{\rm{\dfrac{1}{2} \times \bold{b}ase \times \bold{h}eight = \bold{a}rea}}[/tex]

[tex]\huge\textbf{Now, that we have that out of the}\\\\\huge\textbf{way, we can label your given equation:}[/tex]

[tex]\rm{A \rightarrow 4\ \boxed{\rm{ft}}}\\\\\rm{B \rightarrow 10\ \boxed{\rm{ft}}}\\\\\rm{C \rightarrow 8 \ \boxed{\rm{ft}}}\\\\\rm{D \rightarrow 6\ \boxed{\rm{ft}}}[/tex]

[tex]\huge\textbf{What should your equation look like?}[/tex]

[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]

[tex]\huge\textbf{What should it look like when we're}\\\huge\textbf{solving for the answer?}[/tex]

[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]

[tex]\rm{= 48 + 4\times6 + 4\times10 + 4\times8}[/tex]

[tex]\rm{= 48 + 24 + 4 \times 10 + 4\times8}[/tex]

[tex]\rm{= 72 + 4\times 10 + 4\times8}[/tex]

[tex]\rm{= 72 + 40 + 4\times8}[/tex]

[tex]\rm{= 112 + 4\times8}[/tex]

[tex]\rm{= 112 + 32}[/tex]

[tex]\rm{= 144}[/tex]

[tex]\huge\textbf{What is the answer?}[/tex]

[tex]\huge\boxed{\textsf{Answer: }\boxed{\frak{144\ ft^2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

1/12

Step-by-step explanation:

Landing on the 5 is a 1/6 chance, landing on tails is a 1/2 chance, multiply, and you get 1/12

The number of observation given in the following data set 14. This is also called the size of the population.

It is important to note that the above data possess the minimum value of 12 and the maximum value of 25. As indicated in the attached image, the data set is normally distributed.

The measures of central tendency are given as follows;

Q1 --> 15

Q2 --> 18.5

Q3 --> 22
IQR  = 7

Mean Absolute Deviation (MAD) = 3.5

Min = 12

Max = 25.

It is to be noted that the above indictors are called Descriptive Statistics.

The features of a sample or data set, such as a variable's mean, standard deviation, or frequency, are described or referred to as descriptive statistics.

We can better grasp a data sample's constituent parts by using inferential statistics.

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The solution for the questions is mathematically given as

a)

t-distribution.

b)

the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952, 7.3048 )

c) the value of the [tex]\mu_0[/tex] is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_0; otherwise, reject H _0.

d)

you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

Generally, the equation for is mathematically given as

a.

In this case, the standard deviation of the population is unknown.

As a result, we make use of the t-distribution.

b)

We wish to generate a confidence interval with a 98 percent likelihood for the mean.

Because of this,

[tex](\bar{X}-t_{n-1,\alpha/2}\frac{s}{\sqrt{n}},\bar{X}+t_{n-1,\alpha/2}\frac{s}{\sqrt{n}})[/tex]

[tex](6.85-t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}},6.85+t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}})[/tex]

[tex](6.85-t_{147,0.01}\frac{2.12}{12.1655},6.85+t_{147,0.01}\frac{2.12}{12.1655})[/tex]

(6.3952,7.3048)

Therefore, the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952 , 7.3048 )

c )

If the value of the mu _0 is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_o; otherwise, reject H_0.

d . Here, we want to determine the sample size

Therefore,

[tex]n=t_{n-1,\alpha/2}^2\frac{s^2}{E^2}[/tex]

[tex]n=t_{148-1,0.05/2}^2\frac{2.12^2}{0.5^2}[/tex]

[tex]n=t_{147,0.025}^2\frac{2.12^2}{0.5^2}[/tex]

[tex]n=2.6097^2\frac{2.12^2}{0.5^2}[/tex]

n=122.4364

In conclusion, you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

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14 of the $1.50/lb type will you need to obtain the desired mixture.

According to the statement

Chocolate A that sells for $1.50/lb

Chocolate B that sells for $6.50/lb

Then in equation form the quantity of mixture will

A + B = X

then

$1.50A + $6.50(10) = X

1.50A + 65 = X -(1)

after solving the equation the value of a and b will become

A = 14.

So, 14 of the $1.50/lb type will you need to obtain the desired mixture.

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Answer:

Yes. If the squares of the 2 short sides add up to the square of the hypotenuse, the triangle contains a right angle. Hope this helped.