The life in hours of a 75-watt light bulb is known to be normally distributed with σ=25hours. A random sample of 20 bulbs has a mean life of ¯x=1014 hours.Construct a 95% two sided confidence interval on the mean life.Construct a 95% lower confidence bound on the mean life.

Answer: y = 0.5x - 10

Step-by-step explanation:

2x + y = -4

y = -2x - 4

perpendicular, so slope = 1/2

y + 6 = (1/2)(x - 8)

y = (1/2)x - 10

a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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Answer:

\(1\frac{1}{2}\)

Step-by-step explanation:

The first step to solving this problem is to convert these into improper fractions.

\(7\frac{2}{3} =\frac{21+2}{3}=\frac{23}{3}\)

\(5\frac{1}{9} =\frac{45+1}{9}=\frac{46}{9}\)

The second step is to determine the reciprocal of the second term.

Reciprocal of \(\frac{46}{9} =\frac{9}{46}\)

The third step is to multiply the first term by the reciprocal of the second term.

\(\frac{23}{3}*\frac{9}{46}=\frac{207}{138}\)

The fourth step is to reduce this fraction.

\(\frac{207}{138}=\frac{3(69)}{3(46)}=\frac{23(3)}{23(2)}=\frac{3}{2}=1\frac{1}{2}\)

Answer:

1 1/2 or 3/2

Step-by-step explanation:

First you need to make your fractions improper.

7 times 3 + 2 = 23, so the fraction is 23/3

5 times 9 + 1 = 46, so the fraction is 46/9

Since this is division, flip the second fraction.

So instead of 46/9, it's now 9/46

Now you can multiply.

23/3 + 9/46 = 207/138

207/138 simplified is 3/2, or  1  1/2

Hope this helped! Leave a comment if it did. :)

Answer:

large = 12

medium = 18

Step-by-step explanation:

L + M = 30 => L = 30-M

4L+3M =102

substitute : L with M

=> 4(30-M)+3M =102

120-4M+3M = 102

- M = 102-120

-M = -18

=========> M = 18, L = 12

It can be deduced from the information given that the value of angle F in the quadrilateral is 90°.

From the complete information given, ABCD is the baseball "diamond," a square measuring 90 feet on a side and points A, B, E, H are collinear.

In this case, in a cyclic quadrilateral, the sum of a pair of opposite angles is 180° since it's supplementary. Therefore,

F + 90° = 180°

F = 180° - 90°

F = 90°

In conclusion, F is 90°.

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The  product of the given matrices is \(AB=\left[\begin{array}{ccc}9\\18\end{array}\right]\)

Matrix multiplication is a binary operation that produces a matrix from two matricesThe given matrices are \(A=\left[\begin{array}{ccc}1\\2\end{array}\right]\) and \(B=\left[\begin{array}{ccc}4&5\end{array}\right]\)

To perform product of two matrices, we should make sure that the number of columns in the 1st matrix is equal to the rows in the 2nd matrix

AB=\(\left[\begin{array}{ccc}1\\2\end{array}\right].\left[\begin{array}{ccc}4&5\end{array}\right]\)

\(AB=\left[\begin{array}{ccc}4+5\\8+10\end{array}\right]\)

\(AB=\left[\begin{array}{ccc}9\\18\end{array}\right]\)

Hence, the  product of the given matrices is \(AB=\left[\begin{array}{ccc}9\\18\end{array}\right]\)

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Answer:

C. 0.5..................

The number of ways Chris can arrange the three cards is 6

What is a Set?

A set is the mathematical model for a collection of different things.

Given data ,

Number of cards Chris has S = { 5 , 9 , 0 }

Now from the set S , the number of ways the 3 numbers can be arranged is given be

E = {{5 , 9 , 0 } , { 5 , 0 , 9 } , { 9 , 5 , 0 } , { 9 , 0 , 5 } , { 0 , 5 , 9 } , { 0 , 9 , 5 }}

E denotes the total list of all the numbers Chris can make using the cards.

Hence , the number of ways Chris can arrange the three cards is 6

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The function is expanding to the right of x = 3.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

Given graph of a quadratic function,

to find where function is increasing,

The maximum value or minimum value of a quadratic function are located at its vertex, which is shaped like a U. The quadratic function's axis of symmetry crosses the function (a parabola) at its vertex.

here vertex  is at x = 3,

the increasing and decreasing of graph is shown by vertex,

the shape of curve is parabola so,

In parabolas, the rate of increase (the slope or rate of change) isn't consistent. If the parabola opens up, it will increase as you move towards the right; if the parabola opens down, it will decrease.

The function is increasing to the right side of 3

The parabola's apex can be found at (3, 2) Therefore, all real numbers make up the domain, and the range is y ≥  2. As can be seen in the figure, the function is expanding to the right of x = 3 and contracting to the left of x = 3

Hence the function is increasing to right at x = 3.

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Answer:

About $3.28

Step-by-step explanation:

Divide 24.33 by 7.4

Answer:

3.28783783784...

Step-by-step explanation:

You're description could turn into 24.33 : 7.4.

You turn 7.4 into 1, and divide 7.4 / 1.

(It is 7.4)

Then, you divide 24.33 / 7.4.

It is 3.28783783784.......

or, If you want you're answer close to an natural number, It is 3.

Answer:

GCF = 3

Factor = 3(x^2-100)=0

Solutions are: x = 10, -10

Step-by-step explanation:

You have to factor out GCF which is 3 which then makes the equation 3(x^2-100)=0. After that you basically have (x^2-100)=0. Which then you solve for x which is a difference of squares and the answers are 10 and -10 for x.

Therefore , the solution to the given problem of function comes out to be the drone and toy rocket are at the same 20-foot height there.

Variables and their variations, formulas and related structures, locations of forms and forms themselves are all included in the field of mathematics. The term "function" describes the connection between a group of inputs, of which each has a corresponding output. A function is an association between outputs and inputs where equation results in a single, unique output. A realm and a made the request, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The entry is an x. On activities, one-to-one functions, many-to-one features, within features, and on functions are the four basic categories of functions that are available.

Here,

R(2)>D(2) is true because, on the graph, R = 45 and D = 20 when time is 2 seconds.

The drone has a 20-foot height.

R=0 at 5 seconds is where that is. D=20 at 5 seconds,

t=4.25 at R(t)=D (t).

The drone and toy rocket are at the same 20-foot height there.

Therefore , the solution to the given problem of function comes out to be the drone and toy rocket are at the same 20-foot height there.

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On Saturday, Alex ate 3/10 of the original pizza he had on Friday  

Let's represent the amount of pizza Alex had on Friday as a whole unit. Since he had 3/5 of the pizza left over, we can divide the pizza into 5 equal parts and represent 3 parts as the leftovers. Now, we need to determine how much pizza he ate on Saturday, which is 1/2 of the leftovers from Friday.
To find 1/2 of the leftovers, we divide the 3 parts (leftovers) into 2 equal parts. Each part represents 1/2 of the leftovers. Therefore, each part represents 3/2 divided by 2, which is 3/4.
Since we need to find how much pizza Alex ate on Saturday, we take 1 part (representing 1/2 of the leftovers) from the 3 parts (leftovers). Thus, Alex ate 1/4 of the original pizza on Saturday.
In conclusion, on Saturday, Alex ate 1/4 of the pizza he had on Friday. In fraction form, it can also be expressed as 3/10 of the original pizza.

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The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.

For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".

Using quantifiers and logical connectives, we can express the given fact as follows:

∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))

Explanation:

- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r

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Answer:

1/12

Step-by-step explanation:

1/4*3

Answer:

x = -3

Step-by-step explanation:

If not, let me know. If so, brainliest??

Answer:

x = - 3

Step-by-step explanation:

Substitute -22 for y in y=5x-7

Add -5x to both sides

Add 22 to both sides

Divide both sides by -5

x= -3 y= -22

Answer:

6(x-5)2+288

Step-by-step explanation:

6x2-60x+438  Factor out a 6 from the first 2 terms.

6(x2-10x     )+438  Do (b/2)2 to find the c term.  (-10/2)2 = 25

6(x2-10x+25)+438-150   Adding 25 inside the parenthesis is really like adding 6(25)=150 to that side of the equation.  To keep the equation in balance, you have to subtract 150 from the other term.  Simplify

6(x-5)2+288

Answer:

6x2-60x+438  Factor out a 6 from the first 2 terms.

6(x2-10x     )+438  Do (b/2)2 to find the c term.  (-10/2)2 = 25

6(x2-10x+25)+438-150   Adding 25 inside the parenthesis is really like adding 6(25)=150 to that side of the equation.  To keep the equation in balance, you have to subtract 150 from the other term.  Simplify

6(x-5)2+288

Step-by-step explanation:

The surface area painted blue will be 1,488 square cm.

The correct option is: (D)

Surface area is the amount of space covering the outside of a three-dimensional shape.

We have, The plan is to paint 40% of the total surface area.

The surface area is :

Surface Area = (17 + 17 + 18 + 30 + 18) x 24 + 8 x 30 + 2 x 30 x 18

Surface Area  = 100 x 24 + 8 x 30 + 60 x 18

Surface Area = 2400 + 240 + 1080

Surface Area = 3720 square cm

Blue paint will be applied to 40% of the overall surface area of the doorstop, including the bottom face then

= 0.40 x 3720

= 1488 square cm

Therefore, the surface area painted blue will be 1,488 square cm.

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The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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The required probability of given mean and standard deviation for chloride concentration equals 109,  is less than 109 and is at most 109 is

given by 0, approximately 0.6915 and 0.6915 respectively.

Blood chloride concentration has a normal distribution,

Mean μ = 108

Standard deviation σ = 2.

Probability that chloride concentration equals 109 is,

Since the distribution is continuous, the probability that chloride concentration equals 109 is zero.

As the probability of obtaining any single value in a continuous distribution is zero.

Probability that chloride concentration is less than 109 is,

Area under the normal distribution curve to the left of x = 109.

Use the standard normal distribution and the z-score formula ,

Convert this to a standard normal variable Z,

Z = (X - μ) / σ

  = (109 - 108) / 2

  = 0.5

Using a standard normal table ,

Probability of a standard normal variable being less than 0.5 is approximately 0.6915.

Probability that chloride concentration is at most 109,

Area under the normal distribution curve to the left of x = 109, including the probability of x = 109.

Probability of obtaining any single value in a continuous distribution is zero,

Use the same approach,

Probability that chloride concentration is less than 109.

Add the probability that chloride concentration equals 109 to get the probability that chloride concentration is at most 109,

P(X ≤ 109)

= P(X < 109) + P(X = 109)

≈ 0.6915 + 0 = 0.6915

Therefore, the probability that chloride concentration is equals 109 , less than 109 and at most 109 is zero, approximately 0.6915 and 0.6915 respectively.

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The above question is incomplete, the complete question is:

Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 108 and standard deviation 2. what is the probability that chloride concentration equals 109? is less than 109? is at most 109? (round your answers to four decimal places.)

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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mass (m) = 5.4g

Volume (V) = 2 cm^3

To find the density (p), we have to apply the next formula:

p= m/v

Replacing:

p´= 5.4/2 = 2.7 g/cm^3

Answer:

Set two equations:

\(\left \{ {{x+y=50} \atop {\frac{x}{y}=\frac{7}{11} }} \right.\)

Rearrange one of the equations to find the value of a variable:

\(x+y=50\\x=50-y\)

Substitute in that value into the other equation:

\(\frac{50-y}{y}=\frac{7}{11}\)

Cross-multiply & solve for y:

\(7y=11(50-y) \\7y=550-11y\\7y+11y=550\\18y=550\\y=\frac{550}{18}=\frac{275}{9}\)

Substitute in the value to the original equation to find x:

\(\frac{x}{\frac{275}{9}}=\frac{7}{11} \\\frac{9x}{275}=\frac{7}{11} \\9(11)x=275(7)\\99x=1925\\x=\frac{1925}{99} =\frac{175}{9}\)

Therefore, the answer will be:

You can check your answers by:

\(\frac{175}{9} +\frac{275}{9} =\frac{450}{9} =50\)

\(\frac{\frac{175}{9} }{\frac{275}{9} } =\frac{175}{9} *\frac{9}{275} =\frac{175}{275}=\frac{7}{11}\)

Answer:

x = 175/9

y = 275/9

Step-by-step explanation:

Let the larger number be 'x' and smaller number be 'y'

sum of two numbers is 50.

x +y = 50 --------(I)

      x = 50 - y   -------------(II)

The larger number is divided by the smaller number we get 7/11.

\(\frac{x}{y}=\frac{7}{11}\\\\\)

Cross multiply,

11x = 7y

11x - 7y = 0 ------------(III)

Substitute x = 50 -y in equation (III)

11*(50-y) - 7y = 0  

11*50 - 11*y - 7y  = 0             {Distributive property}

550 - 11y - 7y = 0  

550 - 18 y = 0        {Combine like terms}

Subtract 550 from both sides

- 18y = -550

Divide both sides by (-18)

y = -550/-18

y = 275/9

substitute y = 275/9 in equation (III)

\(11x - 7*(\frac{275}{9})=0\\\\11x-\frac{1925}{9}=0\\\\11x =\frac{1925}{9}\\\\x=\frac{1925}{9*11}\\\\x=\frac{175}{9}\)

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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The months with temperature below 0° is August and October.

GIven,

T(m) = 4 sin (π/6 m)₊2

In the above equation, T(m) is the average temperature in a month in degrees Fahrenheit, and m is the month of the year.

T(8) = 4 sin (8π/6 m)₊2

       = 4 sin (4π/3 )₊2

       = 4 sin (π₊π/3 )₊2

       = ₋4 sin π/3 ₊2

       = ₋4×√3/2 ₊2

       = ₋2√3 ₊ 2 <0

The function for the average monthly temperature, in m months from january is given by

T(0) = 4 sin(10π/6) ₊ 2

       = 4 sin(5π/3) ₊ 2

       = 4 sin(2π ₋ π/3) ₊ 2

       = - 4sin π/3 ₊ 2 = ₋4 × √3/2 ₊ 2

        = ₋2√3 ₊2<0

we can notice that after january, from august till october the months will face temperature below 0 degrees.

So the answer is August and October.

Your question is incomplete. Please find the missing content here.

The average monthly temperature T(m), in degrees Celsius, in a particular city varies according to the model T of m equals 4 times sine of the quantity pi over 6 times m end quantity plus 2 comma where m represents the months of the year and January begins at m = 0. Between what months will the temperature be below 0°C?

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Answer:

1.27777777778

Step-by-step explanation:

i think

Answer:

60 ounces

Step-by-step explanation:

Answer:

i belive its 60

Step-by-step explanation:

1 pound = 16 ounces

3/4 pound = 12 ounces

3 3/4 x 16 = 60

Answer:

\(\frac{29,x\leq 250}{29+0.35(x-250)x\geq 250}\)

Step-by-step explanation:

Let x represent the total time spent calling and f(x) represent the charges.

Since Tracy is charged $29 for 250 free minutes, hence:

For x ≤ 250, f(x) = $29

Tracy is charged an extra $0.35 per minute for calls over 250 minutes, hence:

For x ≥ 250, f(x) = 29 + 0.35(x - 250)

Therefore this can be represented by the piecewise function:

f(x)=  \(\frac{29,x\leq 250}{29+0.35(x-250)x\geq 250}\)

The equation of a line passing through (10,10) that is perpendicular to the line with equation 5x + 8y = -9 is y - 10 = (8/5)(x - 10) or y = (8/5)x - 6.

Get the slope of the line 5x + 8y = -9 by rewriting it in slope-intercept form. Subtract 5x from both sides and divide by 8.

y = (-5/8)x - (9/8)

The slope of this line is -5/8. The negative reciprocal of -5/8 is 8/5. Therefore, the slope of the line that is perpendicular to 5x + 8y = -9 is 8/5.

Using point-slope form, determine the equation of the line.

y - y₁ = m(x - x₁)

y - 10 = (8/5)(x - 10)

or using the slope-intercept form,

y = mx + b

y = (8/5)x + b

10 = (8/5)10 + b

b = -6

y = (8/5)x - 6

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