what is the value of X
​

Answer:

[tex]y=3x^2-12x-135[/tex]

Step-by-step explanation:

The standard form of a quadratic is  [tex]y=ax^2+bx+c[/tex]

We will use the x and y values from each of our 3 points to find a, b, and c.  Filling in the x and y values from each point:

First point (-5, 0):

[tex]0=a(-5)^2+b(-5)+c[/tex] and

0 = 25a - 5b + c

Second point (9, 0):

[tex]0=a(9)^2+b(9)+c[/tex] and

0 = 81a + 9b + c

Third point (8, -39):

[tex]-39=a(8)^2+b(8)+c[/tex] and

-39 = 64a + 8b + c

Use the elimination method of solving systems on the first 2 equations to eliminate the c.  Multiply the first equation by -1 to get:

-25a + 5b - c = 0

81a + 9b + c = 0

When the c's cancel out you're left with

56a + 14b = 0

Now use the second and third equations and elimination to get rid of the c's.  Multiply the second equation by -1 to get:

-81a - 9b - c = 0

64a + 8b + c = -39

When the c's cancel out you're left with

-17a - 1b = -39

Between those 2 bolded equations, eliminate the b's.  Do this by multiplying the second of the 2 by 14 to get:

56a + 14b = 0

-238a - 14b = -546

When the b's cancel out you're left with

-182a = -546 and

a = 3

Use this value of a to back substitute to find b:

56a + 14b = 0 so 56(3) + 14b = 0 gives you

168 + 14b = 0 and 14b = -168 so

b = -12

Now back sub in a and b to find c:

0 = 25a - 5b + c gives you

0 = 75+ 60 + c so

0 = 135 + c and

c = -135

Put that all together into the standard form equation to get

[tex]y=3x^2-12x-135[/tex]

Answer:

  f(x) = 3x^2 -12x -135

Step-by-step explanation:

The given zeros tell you that two factors are (x +5) and (x -9). Then the function can be written ...

  f(x) = a(x +5)(x -9)

We can find "a" from ...

  f(8) = -39 = a(8 +5)(8 -9) = -13a

  3 = a . . . . . . divide by -13

Expanding the above form, we get the standard form ...

  f(x) = 3x^2 -12x -135

Answer:  New Mean = $40,920

                New Median = $38,500

Step-by-step explanation:

5 employee's salaries are as follows in order from least to greatest:

       $32,000 - unknown - $38,500 - unknown - unknown

The median (middle number) is: $38,500

The mean (average) of the 5 salaries is: $40,300

If $3,100 is added to the $32,000 salary, then the mean(average) is increased by [tex]\dfrac{\$3100}{5\ salaries}=\$620[/tex].

Old Mean + increase = New Mean

$40,300  +  $ 620    = $40,920

The median (middle number) does not change. It is still $38,500

Answer:

0.999

Step-by-step explanation:

At least 1 correct means, 1 correct, 2 correct, 3 correct ... until 10 correct. That would be a long process to calculate.

Instead we use the complement rule to calculate.

[tex]P(x\geq1)=1-P(x<1)[/tex]

So we need to find P(x<1). So this is getting 0 answers correct, or 10 incorrect.

In true false question, probablity of correct is 1/2 and incorrect is 1/2, hence,

Probability of 10 incorrect is (1/2)^10

Thus,

[tex]P(x\geq1)=1-(\frac{1}{2})^{10}=0.999[/tex]

So the answer is 0.999 (rounded to nearest thousandth)

An unprepared student's probability of guessing at least one correct answer in a ten-question true-false quiz is 0.999, found by calculating the complement of all answers being incorrect.

To find the probability that an unprepared student makes at least one correct guess on a ten-question true-false quiz, we start by recognizing that each question has two possible answers (true or false), so the probability of guessing correctly on a single question is 0.5.

The complement of guessing at least one correct answer is guessing all answers incorrectly. The probability of guessing one question incorrectly is also 0.5. Therefore, the probability of guessing all ten questions incorrectly is (0.5)¹⁰.

Calculation:

The probability of guessing at least one correct answer is the complement of this probability:

1 - 0.0009765625 = 0.9990234375

Rounding to the nearest thousandth, the probability that the student guesses at least one correct answer is 0.999.

Answer:  3

Step-by-step explanation:

Let E be the event of that student pierces ear and N be the event of that student pierces nose.

Given: [tex]n(E\cup N=50)[/tex]

[tex]n(E)=46\\\\n(N)=7[/tex]

For any two event A and B, we have

[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]

Similarly , [tex]n(E\cup N)=n(E)+n(N)-n(E\cap N)[/tex]

[tex]50=46+7-n(E\cap N)\\\\\Rightarrow\ n(E\cap N)=53-50=3[/tex]

Hence, 3 students have piercings both on their ears and their noses.

Answer:it is 18*20 effective every year

Step-by-step explanation:

To find the effective annual rate for an 18% yearly interest compounded daily, the formula (1 + i/n)^(n*t) - 1 is used.

For a yearly rate, 'n' equals 365 and 't' equals 1, while for a semi-annual rate, 't' is 0.5. These calculations show the true interest earnings per period.

To calculate the effective annual rate (EAR) for an 18% per year, compounded daily interest rate, we use the formula for the EAR, which is:

EAR = (1 + i/n)^(n*t) - 1

Where i is the nominal interest rate, n is the number of compounding periods per year, and t is the number of years. For daily compounding, n = 365, as there are 365 days in a year.

The calculation for a yearly (annual) effective rate would be:

EAR = (1 + 0.18/365)^(365*1) - 1

For a semi-annual effective rate, we consider the compounding effect over half a year, so t = 0.5:

EAR semi-annual = (1 + 0.18/365)^(365*0.5) - 1

These calculations give you the effective rate of interest for each compounding period.

let's recall that on the III Quadrant sine/y is negative and cosine/y is negative, now, the hypotenuse/radius is never negative, since it's just a radius unit.

[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-1}}{\stackrel{hypotenuse}{2}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{2^2-(-1)^2}=a\implies \pm\sqrt{4-1}=a\implies \pm\sqrt{3}=a\implies \stackrel{\textit{III Quadrant}}{-\sqrt{3}=a} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(\theta )=\cfrac{\stackrel{opposite}{-1}}{\stackrel{adjacent}{-\sqrt{3}}}\implies \stackrel{\textit{rationalizing the denominator}}{tan(\theta )=\cfrac{-1}{-\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} }\implies tan(\theta )=\cfrac{\sqrt{3}}{3}[/tex]

Answer:

Conclusion:

Based on the law of syllogism, if a triangle is equilateral, then all the angles are congruent.

Step-by-step explanation:

The law of syllogism, also called reasoning by transitivity, is a valid argument form of deductive reasoning that follows a set pattern. It is similar to the transitive property of equality, which reads: if a = b and b = c then, a = c.

In syllogism, we combine two or more logical statements into one logical statement.

Statement 1:

If a triangle is equilateral, then all the sides in the triangle are congruent.

Statement 2:

If all the sides in a triangle are congruent, then all the angles are congruent.

Concluded Statement using law of syllogism:

Based on the law of syllogism, if a triangle is equilateral, then all the angles are congruent.

Answer:

Based on the law of syllogism, if a triangle is equilateral, then all the angles are congruent.

Step-by-step explanation:

took test and made 100. law of syllogism shows this to be true

Answer: 5/36

Step-by-step explanation: We know that A U B means all the possible combinations that make event A or event B true. As we know, the only combinations that can make 4 is 1+3, 2+2, or 3+1, and the only combinations that can maker 11 is 5+6 and 6+5. This leaves us with a total of 5 combinations, and with a total of 36 combinations, that means that there is a 5/36 chance that the combinations of the dice add to either 4 or 11.

Final answer:

The sample points in event A ∪ B are (1, 4), (2, 3), (3, 2), (4, 1), (5, 6), (6, 5).

Explanation:

The sample points in the event A ∪ B are the points that belong to either event A or event B. To find the sample points in A ∪ B, we combine the sample points from A and B.

The sample points in event A are (1, 4), (2, 3), (3, 2), (4, 1), (5, 6), (6, 5) and the sample points in event B are (2, 3), (5, 6), (6, 5). When we combine these sample points, we have the following sample points in A ∪ B: (1, 4), (2, 3), (3, 2), (4, 1), (5, 6), (6, 5).

Answer: 91.2%

Step-by-step explanation:

Of the 1% of women that have breast cancer, 90% of those are tested positive with 8% of those being false positive. 8% of 90% is 8.8% so 91.2% chance.

Answer: 0.688

Step-by-step explanation:

Given: Mean : [tex]\mu = 481 \text{ millimeters}[/tex]

Standard deviation : [tex]\sigma=871\text{ millimeters}[/tex]

Sample size : [tex]n=1600[/tex]

We assume these lengths are normally distributed.

Then the  formula to calculate the z score is given by :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X=501

[tex]z=\dfrac{501-481 }{41}=0.487804878049\approx0.49[/tex]

The p-value of z =[tex]P(z<0.49)=0.6879331\approx0.688[/tex]

Now, the probability of the newborns weighed between 1492 grams and 4976 grams is given by :-

Hence, The proportion of six-year-old rainbow trout are less than 501 millimeters long = 0.688

Final answer:

To determine the proportion of six-year-old rainbow trout less than 501 millimeters long, we calculate the z-score and then find the corresponding proportion in the standard normal distribution.

Explanation:

The question asks for the proportion of six-year-old rainbow trout in the Arolik River in Alaska that are less than 501 millimeters long, given a mean length of 481 millimeters and a standard deviation of 41 millimeters, with lengths normally distributed. To find this proportion, we need to calculate the z-score for 501 millimeters.

First, we calculate the z-score using the formula:

z = (X - μ) / σ

where X is the value we are evaluating (501 millimeters), μ is the mean (481 millimeters), and σ is the standard deviation (41 millimeters).

Plugging the values in, we get:

z = (501 - 481) / 41

z = 20 / 41

z ≈ 0.49

Next, we consult the standard normal distribution table or use statistical software to find the proportion of values below a z-score of 0.49.

This will give us the proportion of six-year-old rainbow trout that are less than 501 millimeters long.

Answer:

The Miller Family used the sprinkler for 40 hours.

The Washington Family used the sprinkler for 30 hours.

Step-by-step explanation:

First write an equation.

M = Miller Family's Output Rate

W = Washington Family's Output Rate

30M + 15W = 1650

M + W = 70

Using simultaneous equations:

1) Make one of the coefficients the same value.

We will make both W's 15.

Multiply the second equation by 15.

15M + 15W = 1050

2) Subtract the equations to remove the coefficient.

(30M + 15W = 1650) - (15M + 15W = 1050)

(30M + 15W) - (15M + 15W) = 1650 - 1050

15M = 600

3) Divide to find the value of 1 M

15M = 600

M = 600/15

M = 40

4) Substitute M into either equation to find the value of W.

30M + 15W = 1650

30(40) + 15W = 1650

1200 + 15W = 1650

15W = 1650 - 1200

15W = 450

W = 450/15

W = 30

M + W = 70

40 + W = 70

W = 70 - 40

W = 30

Answer:

Miller family's sprinkler was used for 40 hours and Washington family's sprinkler was used for 30 hours.

Step-by-step explanation:

 Set up a system of equations.

Let be "m" the time Miller family's sprinkler was used and "w" the time Washington family's sprinkler was used.

Then:

[tex]\left \{ {{m+w=70} \atop {30m+15w= 1,650}} \right.[/tex]

You can use the Elimination method. Multiply the first equation by -30, then add both equations and solve for "w":

[tex]\left \{ {{-30m-30w=-2,100} \atop {30m+15w= 1,650}} \right.\\.................................\\-15w=-450\\w=30[/tex]

 Substitute w=30 into an original equation and solve for "m":

[tex]m+30=70\\m=70-30\\m=40[/tex]

Answer:

New mean = $40920

New Median = $38500 (Same as old)

Step-by-step explanation:

Given

Mean = $40300

Median = $38500

The formula for mean is:

Mean = Sum/No. of Values

According to the formula,

40300 = Sum/5

40300*5 = Sum

Sum of Salaries = 201500

If the salary of lowest employee is raised 3100, then sum will be 204600.

The new mean will be:

Mean = 204600/5

Mean =$40920

The median will remain unchanged as it is the middle value of 5 quantities. 2 values are greater than median and two are less than median. Even after the raise in salary, the salary becomes $35100 which is still less than median. So the median will be same as old ..

With the raise, the new mean salary of the employees is $40920, while the median salary is likely to remain $38500 unless the raise causes a rearrangement in the salary sequence.

Assuming there have been no other changes to the employees' salaries, we can calculate the new mean and new median as follows:

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[tex]|\Omega|=5^3=125\\|A|=2\cdot3\cdot1=6\\\\P(A)=\dfrac{6}{125}=\dfrac{48}{1000}=0.048[/tex]

Answer: D) As a semicircle, a trapezoid, and two rectangles.

Step-by-step explanation:

In order to find the area of the composite figure provided, it is necessary to descompose it.

Observe the image attached.

You can observe that it can descomposed as:

1- A semicircle, whose area can be calculated with this formula:

[tex]A=\frac{\pi r^2}{2}[/tex]

Where r is the radius.

2- A trapezoid,  whose area can be calculated with this formula:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where h is the height, B is the larger base and b is the minor base.

3- Rectangle.

4- Rectangle.

The formula for calculate the area of a rectangle is:

[tex]A=lw[/tex]

Where l is the lenght and w is the width.

The area of the composite figure consists of a semicircle, a trapezoid, and two rectangles

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

The figure consists of a semicircle, a trapezoid, and two rectangles

So , the area of semicircle C = πr² / 2

The area of trapezoid T = ( ( a + b ) h ) / 2

And , the area of 2 rectangles R = 2 x L x B

Hence , the area of composite figure A = πr² / 2 + ( ( a + b ) h ) / 2 + 2 x L x B

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Answer:

The area of the rectangle is 12 cm² ⇒ in 2 significant figures

Step-by-step explanation:

* Lets talk about the significant figures

- All non-zero digits are significant

# 73 has two significant figures

- Zeroes between non-zeros digits are significant

# 105.203 has six significant figures

- Leading zeros are never significant

# 0.00234 has three significant figures

- In a number with a decimal point, zeros to the right of the last

 non-zero digit are significant

# 19.00 has four significant figures

- Lets make a number and then approximate it to different significant

∵ 12.7360 has 6 significant figures

∴ 12.736 ⇒ approximated to 5 significant figures

∴ 12.74 ⇒ approximated to 4 significant figures

∴ 12.7 ⇒ approximated to 3 significant figures

∴ 13 ⇒ approximated to 2 significant figures

∴ 10 ⇒ approximated to 1 significant figure

- Another number with decimal point

∵ 0.0546700 has 6 significant figures

∴ 0.054670 ⇒ approximated to 5 significant figures

∴ 0.05467 ⇒ approximated to 4 significant figures

∴ 0.0547 ⇒ approximated to 3 significant figures

∴ 0.055 ⇒ approximated to 2 significant figures

∴ 0.05 ⇒ approximated to 1 significant figures

* Lets solve the problem

∵ The width of the rectangle is 2.1 cm

∵ The length of the rectangle is 5.6 cm

- Area of the rectangle = length × width

∴ Area of the rectangle = 2.1 × 5.6 = 11.76 cm²

- Approximate it to two significant figures

∴ Area of the rectangle = 12 ⇒ to the nearest 2 significant figures

* The area of the rectangle is 12 cm² ⇒ in 2 significant figures

Answer:

c. 28

Step-by-step explanation:

Congruence means that all the sides and angle of the triangles which are said to be congruent are equal.

In the given triangle, all three angles of GEF and HEF will be equal.

Using the property, we can see that in triangle GEF the angle is 60 degree and in HEF the corresponding congruent angle of it is 2(x+2)

So,

Putting them equal

2(x+2) = 60

Now, it is a simple equation to solve.

2x+4=60

2x+4-4 = 60-4

2x = 56

2x/2 = 56/2

x = 28 degrees

So, option C is the correct answer ..

Step-by-step explanation:

The energy required to stretch a spring a distance x is:

E = ½ kx²

where k is the stiffness constant.

If spring B has a constant k and is stretched a distance of b:

E = ½ k b²

If spring A has a constant of 4k and is stretched a distance of a:

E = ½ (4k) a²

E = 2 k a²

If the energies are the same:

½ k b² = 2 k a²

b² = 4 a²

b = 2a

So spring B is stretched twice as far as spring A.

When the same amount of energy is applied to both Spring A and Spring B, Spring B which has a lower spring constant stretches more than Spring A. The spring constant has an inverse relationship with the amount of displacement for a given energy.

The problem deals with the physics concept of potential energy stored in springs. When equal amounts of energy are applied to multiple springs, different amounts of displacement or extension will result, depending on the spring constant (k) of each spring.

Based on Hooke's law, the potential energy (U) stored in a spring is given by the equation U = 1/2 kx², where x represents the displacement or extension of the spring.

For Spring A, which has a spring constant four times that of Spring B, while the same amount of energy is applied to both, less displacement will occur compared to Spring B. This is because a spring with a higher spring constant is stiffer and therefore resists displacement more.

So to answer your question, Spring B will stretch more than Spring A when the same amount of energy is applied to both.

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Answer:

The variable "a number" stands for 9.

Step-by-step explanation:

Rewrite the problem as 2 * (6 + x) = 30

Divide 30 into 2. 30/2 = 15

That means that the variable that is added to 6 must make the number 15.

15 - 6 = 9

The variable x is 9 so the equation would be:

2 * (6 + 9) = 30

Answer:

Step-by-step explanation:

[tex]n-the\ number\\\\\text{two times the sum of 6 and the number}\ n:\ 2(6+n)\\\\\text{The equation:}\\\\2(6+n)=30\qquad\text{divide both sides by 2}\\\\\dfrac{\not2(6+n)}{\not2}=\dfrac{30\!\!\!\!\!\diagup^{15}}{\not2_1}\\\\6+n=15\qquad\text{subtract 6 from both sides}\\\\6-6+n=15-6\\\\n=9[/tex]

Answer:

g(x)

Step-by-step explanation:

-4/-4 = aops

aops = 1

f(1) = 5

f(x)'s max = 5

g(x)'s = 6

(pls give brainliest)

Answer: [tex]x<2[/tex]

Step-by-step explanation:

Given the inequality [tex]2x + 1 < 5[/tex] you can follow these steps to solve it:

- The first step is:

Subtract 1 from both sides on the inequaltity.

Then:

[tex]2x + 1-(1) < 5-(1)\\\\2x < 4[/tex]

- The second  and final step is:

Divide both sides of the inequality by 2.

Therefore, you get:

[tex]\frac{2x}{2}<\frac{4}{2} \\\\(1)x<2\\\\x<2[/tex]

Answer:

A

Explanation:

For functions to be inverse, it must be true that f( g(x) ) = x and g( f(x) ) = x.

But for F( G(x) ), we have √( G(x) - 3 ) + 8

= √( (x+8)² - 3 - 3 ) + 8

= √( (x+8)² - 6 ) + 8

This -6 part should be cancelled out for functions to work out but we cannot do that, therefore F(x) and G(x) are not inverse.

The given function is not an inverse function across the domain [3,+∞)

We have given that the functions F(x) and G(x)

We have to determine the functions F(x) and G(x) inverse function across the domain  [3,+∞)

For functions to be inverse, it must be true that f( g(x) ) = x and g( f(x) ) = x.

The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by[tex]{\displaystyle f^{-1}.}[/tex]

But for F( G(x) ), we have √( G(x) - 3 ) + 8

[tex]= \sqrt{( (x+8)^2} ( - 3 - 3 ) + 8= \sqrt ( (x+8)^ {- 6} ) + 8[/tex]

This -6 part should be canceled out for functions to work out but we cannot do that, therefore F(x) and G(x) are not inverse.

Therefore the given function is not an inverse function across the domain [3,+∞).

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Answer:

[tex]H0 : \muD = 0\\\\ H_A : \mu D \neq0 \text{ with }\ \mu D = \mu2- \mu1[/tex]

Step-by-step explanation:

Let [tex]\mu_1[/tex] and  [tex]\mu_2[/tex] are the mean costs raised by workshop I and workshop II respectively.

Given claim :The costs raised by workshop I were greater than workshop II.

i.e. [tex]\mu_1>\mu_2\ or\ \mu_1-\mu_2>0[/tex]

Since it does not contain equals sign therefore we consider it as the alternative hypothesis.

The null hypothesis will be just opposite of this.

i.e.  [tex]H_0:\mu_1-\mu_2\leq0[/tex]

Hence, The decision of the right hypothesis to prove the given suspicion:-

[tex]H_0:\mu_1-\mu_2\leq0\\\\H_1:\mu_1-\mu_2>0[/tex]

[tex]\text{If }\ D=\mu_1-\mu_2[/tex], then

[tex]H0 : \mu D = 0\\\\ H_A : \mu D \neq0 \text{ with }\ \mu D = \mu_2- \mu_1[/tex]

Answer with explanation:

It is given that z is an irrational complex number.

Z= x + i y

Where x is real part and y is Imaginary part.x and y can be any Real number.

If z is an irrational complex number , then both real part and imaginary part should be a complex number.That is x, y ∈Q, then ,Q= Set of Irrationals.

It means , x and y both should be an irrational number.

So, if x is any irrational number then, [tex]\sqrt{x}[/tex] will be also an irrational number.

Answer: 7.7055

Step-by-step explanation:

Given: Sample size : [tex]n= 38> 30\text{ i.e. Large sample}[/tex]

Sample Mean : [tex]\overline{x}=12.15[/tex]

Standard deviation : [tex]\sigma =0.12[/tex]

Claim : The population mean is [tex]\mu=12[/tex]

We assume the contents of cans of Coke have a normal distribution .

We know that the test-static for population mean for larger sample is given by :-

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

[tex]\Rightarrow z=\dfrac{12.15-12}{\dfrac{0.12}{\sqrt{38}}}=7.70551750371\approx7.7055[/tex]

Hence, the value of the test statistic z for the claim that the population mean is μ=12 is 7.7055.

The calculated z-score is approximately 77.72, for which sample mean = 12.15, standard deviation = 0.12, and population mean =12.

To determine the value of the test statistic z for the given data, follow these steps:

The test statistic z is approximately 77.72, indicating how many standard errors the sample mean is from the population mean.

Answer:

-2.333

Step-by-step explanation:

In a certain normal distribution of scores, the mean is 30 and the standard deviation is 3. Find the z-score corresponding to a score of 23.

The z-score corresponding to an observed value in a normal distribution is calculated as;

z-score = (observed value - mean)/(standard deviation)

Our observed score is 23, the mean is 30, and the standard deviation is 3. The z-score will thus be;

z-score = ( 23 - 30)/( 3)

z-score = -2.333

Answer:

- 2.333

Step-by-step explanation:

The formulae to apply here is;

z= (x-μ) / δ------------where x is the score, μ is the mean and δ is the standard deviation

Given x=23, μ=30 and δ= 3

z= (23-30) / 3 z= - 7/3 z=  -2.333

The 6th term of the geometric sequence is:

                  [tex]a_6=-1458[/tex]

We know that the nth term of a geometric sequence is given by the formula:

          [tex]a_n=a_1\cdot r^{n-1}[/tex]

where [tex]a_1[/tex] is the first term of the sequence and r is the common ratio of the sequence and [tex]a_n[/tex] is the nth term of a sequence.

Also,

[tex]a_=-6[/tex]

and [tex]r=3[/tex]

Hence, we get:

[tex]a_6=-6\times (3)^{6-1}\\\\\\a_6=-6\times 3^5\\\\\\a_6=-1458[/tex]

           Hence, the answer is:

                         -1458

Answer with explanation:

(a)

Mean number of flight hours for Continental Airline pilots = 49 hours per month

Total Sample Size =100

Standard Deviation =11.5 Hours

Margin of error for a 95% confidence interval

        [tex]=Z_{95 \text{Percent}}\times \frac{\sigma}{\sqrt{n}}\\\\=0.8365 \times \frac{11.5}{\sqrt{100}}\\\\=\frac{9.61975}{10}\\\\=0.961975\\\\=0.97(\text{Approx})[/tex]

(b)

The Range of values for a 95% confidence interval

 ⇒     Mean number of flight  + Margin of Error  ≤  Confidence interval ≤    Mean number of flight  - Margin of Error      

⇒ 49+0.97  ≤  Confidence interval ≤ 49-0.97

⇒ 49.97  ≤  Confidence interval ≤48.03

Upper Bound = 49.97

Answer:

zero

Step-by-step explanation:

The inheritance tax is paid by the estate. The heirs have no tax liability on the amount inherited.

Final answer:

The heir's tax liability for an estate valued at $7.36 million, after applying a 40% tax rate to the amount above the estate tax exemption of $5.43 million (assumed for 2017), would be $772,000.

Explanation:

To calculate the heir's tax liability for an estate valued at $7.36 million with a tax rate of 40%, we need to determine if the estate's value exceeds the estate tax exemption threshold. According to the Center on Budget and Policy Priorities, in 2015, the exemption limit was $5.43 million. Since the date of death is 2017, the exemption amount may have been different, but for this calculation, we’ll assume it is the same.

Here's how to calculate the tax liability:

Subtract the exemption limit from the total estate value: $7,360,000 - $5,430,000 = $1,930,000. This is the taxable amount.

Multiply the taxable amount by the tax rate: $1,930,000 * 40% = $772,000.

Therefore, the heir's tax liability would be $772,000.

Answer: 0.1353

Step-by-step explanation:

Given : The mean of failures =  0.025 per hour.

Then  for 8 hours , the mean of failures = [tex]\lambda=8\times0.25=2[/tex] per eight hours.

Let X be the number of failures.

The formula to calculate the Poisson distribution is given by :_

[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]

Now, the probability that the instrument does not fail in an 8-hour shift :-

[tex]P(X=0)=\dfrac{e^{-2}2^0}{0!}=0.1353352\approx0.1353[/tex]

Hence, the the probability that the instrument does not fail in an 8-hour shift = 0.1353

Answer: 0.2789

Step-by-step explanation:

Given: Mean : [tex]\mu=10.00\ mm [/tex]

Standard deviation : [tex]\sigma =0.03\ mm[/tex]

The formula to calculate z-score is given by :_

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 9.96 mm, we have

[tex]z=\dfrac{10-9.96}{0.03}\approx1.33[/tex]

For x= 10.01 mm, we have

[tex]z=\dfrac{10.01-10}{0.03}\approx0.33[/tex]

The P-value = [tex]P(0.33<z<1.33)=P(z<1.33)-P(z<0.33)[/tex]

[tex]= 0.9082408- 0.6293=0.2789408\approx0.2789[/tex]

Hence, the probability that a randomly selected gear has a diameter between 9.96 mm and 10.01 mm =0.2789

Answer:

Pr=0.2894

Step-by-step explanation:

given mean diameter =10 mm

standard deviation=0.03 mm

z equation is

z=x-μ/σ

The problem has two values of x

for x=9.96

z=-1.33

for x-10.01

z=0.33

from Probability table we have

Pr(-1.33<z<0.33)=pr(z<0.33)-pr(z>-1.33)

Pr=0.2894