Suppose 3 < a <5 and 5 < b < 7. Find all possible values of each expression.
-2a + b​

a. The value of the mean is µ = 15

The value of the standard deviation is 2.74

b. Values of 9.52 girls or greater are significantly low.

Values of 20.48 girls or greater are significantly high

c.  The result of 25 girls is significantly high because it is greater than 20.48.

a. The mean for the number of girls in a group of 30 births is:

a. µ = np

= 30(0.5)

The value of the mean is µ  = 15

The standard deviation is:

a. σ = √(np(1-p))

= √(30(0.5)(0.5))

The value of the standard deviation = 2.74 (rounded to two decimal places)

b. Using the range rule of thumb, we can say that significantly low results are those that are less than 15 - 2.74(2) = 9.52, and significantly high results are those that are greater than 15 + 2.74(2) = 20.48.

c. The result of 25 girls is significantly high because it is greater than 20.48. This suggests that the method may be effective in increasing the likelihood of having a girl.

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The value of x, y and z in the line is as follows:

x = 55°

y = 125°

z = 55°

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, let's use the angle relationship to find the angles x, y and z in the line.

Hence,

y = 125 degrees(vertically opposite angles)

Therefore,

x = 180 - 125(angles on a straight line)

x = 55 degrees

Therefore,

x = z(vertically opposite angles)

Vertically opposite angles are congruent.

Hence,

z = 55 degrees.

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The norm or magnitude of 2v is 11.66. To find the norm, we first need to calculate 2v, which is 10i-6j. Then, we use the formula ||2v|| = [tex]\sqrt{ (100i^2 + 36j^2)[/tex] to find the magnitude of vector 2v, which simplifies to √136 or 11.66 when rounded to two decimal places.

To take care of this issue, we first need to comprehend what the vectors I and j address. In two-layered Cartesian space, I and j are unit vectors along the x-hub and y-hub, separately. That is, I = (1, 0) and j = (0, 1).

Presently, we can communicate the vector v as 5i-3j, and that implies that it has a greatness of √[tex](5^2 + (- 3)^2)[/tex] = √34.

Then, we really want to track down the standard or size of 2v, which is two times the vector v. That is,

2v = 2(5i-3j)

= 10i-6j

To track down the extent of 2v, we can utilize the equation ||2v|| = √( [tex](10i)^2 + (- 6j)^2[/tex] ).

Figuring out the two terms and disentangling, we get

||2v|| = √([tex]100i^2 + 36j^2[/tex])

Since [tex]i^2[/tex] = 1 and[tex]j^2[/tex] = 1, this streamlines to

||2v|| = √(100+36)

= √136

= 11.66 (adjusted to two decimal spots)

Hence, the standard or extent of 2v is 11.66.

To sum up, we began with the vector v = 5i-3j and viewed its greatness as √34. Then, at that point, we multiplied this vector to get 2v = 10i-6j and utilized the equation ||2v|| = √[tex]( (10i)^2 + (- 6j)^2 )[/tex] to find its size, which ended up being 11.66.

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The complete question is:

Let v = 3i-2j and w = 5i+j. Find 2v-w. None of the given answers o 11i-5j oi-5j o i-3; 0 7i+4j

The values of L and K which maximize production will be 18 and 216 respectively.

Production simply means the process of combining various inputs, both material and immaterial in order to create output. Ideally this output will be a good or service which has value and contributes to the utility of individuals

In this case, a company has 2700 dollars to invest, which must be divided between capital expenditures and labor and each unit of labor costs the company 10 dollars, and each unit of capital costs 10 dollars.

Hence, the values of L and K which maximize production will be 18 and 216 respectively.

Check the attachment.

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The equation written in point-slope form is:

y + 50 = (-1/3)*(x - 80)

A linear equation with a slope a that passes through a point (x₁,y₁) is written in the point-slope form as:

y -  y₁ = a*(x - x₁)

And the slope for a line that passes through  (x₁,y₁) and (x₂, y₂) is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can identify the points (-70, 0) and (80, -50)

Then the slope is:

a = (-50 - 0)/(80 + 70) = -50/150 = -1/3

Using the red point (80, -50)

We can write the equation as:

y + 50 = (-1/3)*(x - 80)

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The required, Tyshawn would need to sell 9 computers to make $225 on a given day.

We can use the values from the table to find the slope of the linear relationship between x and P. We know that the relationship is linear because the table shows a constant increase in P as x increases by the same amount each time.

To find the slope, we can choose any two pairs of values from the table and use the formula:

slope = (change in P) / (change in x)

Using the first and second pairs of values, we get:

slope = (165 - 135) / (5 - 3) = 15

This tells us that Tyshawn's pay increases by $15 for each additional computer he sells.

Now we can use the point-slope form of the equation of a line to find the number of computers he would need to sell to make $225. We know that his pay starts at a base amount and increases by $15 for each computer sold, so the equation is:

P = 15x + b

where b is the base pay amount. We can find b by using one of the pairs of values from the table. Using the first pair, we get:

135 = 15(3) + b

b = 90

So the equation for Tyshawn's pay is:

P = 15x + 90

To find how many computers he needs to sell to make $225, we can substitute P = 225 into the equation and solve for x:

225 = 15x + 90

x = 9

Therefore, Tyshawn would need to sell 9 computers to make $225 on a given day.

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There are 56 ways for a group of 10 people to form a committee with at least 8 people on it.

To find the number of ways that a group of 10 people can form a committee with at least 8 people on it, we can use combinations.

First, we can find the number of ways to choose 8 people from the 10 available, which is:

C(10, 8) = 45

Next, we can find the number of ways to choose 9 people from the 10 available, which is:

C(10, 9) = 10

Finally, we can find the number of ways to choose all 10 people, which is:

C(10, 10) = 1

To get the total number of ways to form a committee with at least 8 people on it, we can add up these three cases:

45 + 10 + 1 = 56

Therefore, there are 56 ways for a group of 10 people to form a committee with at least 8 people on it.

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Answer:

g(x) = x^2 + 5

Step-by-step explanation:

You notice that g(x) is essentially just f(x) but moved upwards.

Using the formula a(x-h)^2 + k, you know that there is no vertical or horizontal stretch, so a is 1. You also know that h is 0 because there is no horizontal movement.

Lastly, you have k. Because the graph is moved up by 5, k = 5.

The equation is g(x) = x^2 + 5.

The combination of transformation that results in the image WXYZ from the pre-image QRST are:

In mathematics, rotation is a notion that originated in geometry. Any rotation is a movement of a specific space that retains at least one point. It can, for example, explain the motion of a rigid body around a fixed point.

A translation is a geometric transformation in Euclidean geometry that moves every point in a figure, shape, or space by the same distance in the same direction. A translation may alternatively be understood as the addition of a constant vector to each point or as altering the coordinate system's origin.

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The maximum value of f is (√2)/2, and the point (x, y) at which f has the maximum value on the constraint curve is (x, y) = (√2, -√2/2).

We have,

We set up the equation as:

L(x, y, λ) = f(x, y) - λg(x, y)

= x + y - λ(x² - 2y² - 4)

Then, we need to find the partial derivatives of L with respect to x, y, and λ, and set them equal to zero:

∂L/∂x = 1 - 2λx = 0

∂L/∂y = 1 + 4λy = 0

∂L/∂λ = x² - 2y² - 4 = 0

Solving the first two equations for x and y.

x = 1/(2λ)

y = -1/(4λ)

Substituting these values into the third equation.

(1/(2λ))² - 2(-1/(4λ))² - 4 = 0

Simplifying this equation.

λ² = 1/8

Taking the positive square root.

λ = 1/√8 = √2/4

Substituting this value of λ into the equations for x and y.

x = √2

y = -√2/2

To confirm that this is a maximum point, we need to check that it is indeed a maximum by checking the second partial derivative of L.

The second partial derivative of L.

∂²L/∂x² = -2λ

∂²L/∂y² = 8λ

∂²L/∂x∂y = 0

Substituting the value of λ into these expressions.

∂²L/∂x² = -√2/2 < 0

∂²L/∂y² = √2 > 0

Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, this confirms that the point (x, y) = (√2, -√2/2) is a maximum point.

Tthe maximum value of f(x, y) = x + y subject to the constraint g(x, y) = x² - 2y² = 4.

f(√2, -√2/2) = √2 - √2/2 = (√2)/2

Thus,

The maximum value of f is (√2)/2, and the point (x, y) at which f has the maximum value on the constraint curve is (x, y) = (√2, -√2/2).

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The area of the right triangle, using the two formula gave the same result as (25√3)/2 squre units.

A right triangle is a triangle in which one angle is a right angle.

Area of a triangle can be calculated using:

A = 1/2 × b × h

Where b and h are base and height respectively.

From the diagram:

Base b = 5

Height h = 5√3

Area = ?

Plug these values into the above formula and solve for area.

A = 1/2 × b × h

A = 1/2 × 5 × 5√3

A = (25√3)/2

Now, using a second formula to verify if we get the same result.

A = 1/2 × ab × sinC

From the image:

a = 5√3

b = 5

Angle C = 90

Plug in the values:

A = 1/2 × ab × sinC

A = 1/2 × 5√3 × 5 × sin( 90° )

A = 1/2 × 5√3 × 5 × 1

A = (25√3)/2

Therefore, the area of the triangle is (25√3)/2 squre units.

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The true statement is, The difference between the mean is about 2 times the mean absolute deviation of the data sets.

Mean absolute deviation (MAD) is defined as the average value of the absolute deviations from the mean.

Difference of the means is found by subtracting the two means.

Each mean is found by adding the data points and then dividing by the number of data sets.

The relationship between the difference of means and the MAD of two sets is,

The difference between the mean is about 2 times the mean absolute deviation of the data sets.

Hence the correct option is B.

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The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

If Lydia had ²/₃ of a bag of flour and she used ³/₅ of it to make loaves of bread, the fraction of the whole bag that she used was ²/₅.

A fraction is a portion or part of a whole.

Fractions are classified into proper, improper, and complex fractions, depending on the value of the numerator and denominator.

The fractional value of the bag of flour = ²/₃

The fraction of the bag that she used to make bread = ³/₅ of ²/₃

Comparatively, the proportion of the bag that she used was = ²/₅ (³/₅ of ²/₃)

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Answer:

Step-by-step explanation:

The answer is -3 because when you add a positive number with a negitive number you subtract not add

Answer:

its step A

Step-by-step explanation:

it wants you to add instead of subtracting witch is trying to fool you

Yw and have a good day! :)

The graph that represents the function f(x) = [tex]\frac{1}{x - 3} - 2[/tex]  is shown below.

We are given a function f(x) = [tex]\frac{1}{x - 3} - 2[/tex] and we have to plot a graph that represents this function.

The function we have is f(x) = [tex]\frac{1}{x - 3} - 2[/tex]  . We will now find the domain of the function. A set of input values for which the function is real and has defined values is called the domain of the function. So, The given function will be undefined at x = 3

Therefore, the domain is x < 3  or x > 3.

Now, we will look for the range of the given function. The range is the set of values of the dependent variable for which the function is defined. If we inverse the given function, we get

y = [tex]\frac{(3x + 7)}{(x + 2)}[/tex]

We will find the domain of this inverse function. The domain is f(x)  < -2 or f(x) > -2. Now, we will find x-intercepts and y-intercepts. The x-intercept is the point where y = 0 and the y-intercept is where x= 0

Let f(x) = y

Then y = [tex]\frac{1}{x - 3} - 2[/tex]

Put x = 0

thus y-intercept is (0, -7/3)

Now put y = 0

Then  x-intercept is (7/2, 0)

Now, we will calculate the horizontal and vertical asymptotes.

Vertical asymptotes,

Now, we will go over every undefined point and check if at least one of these statements is satisfied.

[tex]lim_{x - > a^{-}} f(x) = \pm\infty[/tex]

[tex]lim_{x - > a^{+}} f(x) = \pm\infty[/tex]

Therefore, the vertical asymptotes are x = 3

and For horizontal asymptotes,

Check if  [tex]x - > \pm\infty[/tex] the function y = [tex]\frac{1}{x - 3} - 2[/tex] behaves as a line y = mx + b.

Therefore, we have y = -2 as horizontal asymptotes.

The plotted graph that represents the given function is shown below.

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The complete question is "Which graph represents the function f(x)=1/x+3-2 "

The critical value based on the information will be zα/2 = -2.58

We want to find the critical values zα/2 and -zα/2 that correspond to these tail probabilities.

Using the standard normal distribution table for negative z scores, we can find the value that corresponds to a tail probability of 0.005. This is -2.58.

Using the standard normal distribution table for positive z scores, we can find the value that corresponds to a tail probability of 0.005. This is 2.58.

Therefore, the critical values are zα/2 = -2.58 and -zα/2 = 2.58.

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After considering the given values we can come to the conclusion that the annual installment that has to be made to the investment fund to retire within the age of 40 with enough money to draw $75,000 per year until age 90, assuming a risky investment that earns 8% per year, is approximately $16,431.

To evaluate the equal annual installment that you need to make from age to age 40, we need to use the present value of an annuity formula:

PMT = (PV × r) / (1 - (1 + r)⁻ⁿ)

Here,

PMT= equal annual installment,

PV =present value of the investment fund at age 40,

r = expected annual rate of return on the fund,

n = number of years over which the payments will be made.

We can proceed by evaluating the present value of the investment fund that we need at age 40, based on the assumption that we will draw per year for the next years.

Let's call this present value PV2. Assuming an interest rate of r2 for the period from age 40 to age, we can calculate PV2 using the present value of a perpetuity formula:

PV2 = PMT2 / r2

Here,

PMT2 = annual draw we plan to make from age to age .

Next, we need to evaluate the present value of the investment fund at age, which we will call PV1. Now we can apply the future value of an annuity formula:

FV = PMT × ((1 + r)ⁿ⁻¹) / r

Here,

FV = future value of the annuity at age,

PMT = equal annual installment,

r = expected annual rate of return on the fund,

n = number of years over which the payments will be made (in this case, the number of years from age to age ).

We can then apply the present value formula to evaluate PV1:

PV1 = FV / (1 + r)ⁿ

Finally, we can apply substitution the values we have evaluated into the PMT formula to find the equal annual installment:

PMT = (PV1 × r) / (1 - (1 + r)⁻ⁿ)

Once we have calculated PMT, we can start making annual payments into the investment fund starting at age and continuing until age 40.

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The word that best describes line segment ID in the image given showing a circle is: a chord.

A chord can simply be described as a line segment in a circle that connects two points on the circumference of a circle to each other.

The largest chord in a circle is a the diameter. A circle can have as many chords as possible.

Considering the image given above, ID is a line segment which connects points I and D which are on the circumference of the circle together. Therefore, ID can best be described as a chord.

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The expected number of hits

= ∑x P (X=x) = 0.96

Here, we have, to solve

Let X be a Binomial random variable that denotes the number of hits

where the parameters are n = 3, p = 0.320

P(X = x) , x = 0,1,2,3

(a) The probability distribution of X is

P(X = 0) = 0.3144

P(X = 1) = 0.4439

P(X = 2) = 0.2089

P(X = 3) = 0.0328

X 0 1 2 3

P(X = x) 0.3144 0.4439

0.2089

0.0328

(c) Expected number of hits

= ∑x P (X=x) = 0.96

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complete question:

Percents (round to 1. Jing has a .320 on-base percentage. Over the course of a 3-game series, Jing will bat 14 times. Assume that the chance of getting on base a fixed number of times is a binomial distribution. *tel Is the distribution for Jing getting on base symmetric, skewed right or skewed left?

Answer:4/5 minute

Step-by-step explanation:Fastest girl time = 21/10 Slowest girl time = 34/10 difference = (34-21)/10 = 13/10 (3) Total time = 33/10 + 28/10 + 34/10 + 21/10 = 116/10 Previous record = 12 2/5 = 62/5 = 124/10 As the time taken by girls (116/10) is lower than the previous record (124/10) Therefore these girls are faster by (124-116)/10 = 8/10 minutes = 4/5 minutes

There are three primary sorts of operations done on sets in a set theory, such as:

Sets' union (∪)

Sets intersecting (∩)

Set difference (- )

Sets help in the identification of related groupings of objects. Set operations such as relations and functions are used to connect and manipulate sets.

Bowls, glasses, cups, and saucers are kept separate from plates, while pans and utensils have their own compartments. Cooking utensil sets and other collections are separated in storage. As seen above, there are countless examples of sets in our daily lives.

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The height of the building to the nearest foot is: 235 ft

We are given the parameters as:

Height of building = 94.7 ft

The angle of elevation of the top of the flagpole = θ₁ = 35.2°

The angle of elevation of the bottom of the flagpole = θ₂ = 26.7°

Let,

Height of building = x

Distance from observation point to base of building = y

Thus:

tan 26.7 = x/y

y = x/tan 26.7

tan 35.2 = (94.7 + x)/y

Thus:

tan 35.2 =(94.7 + x)/(x/tan 26.7)

Rearranging this gives:

x = 94.7/((tan 35.2/tan 26.7) - 1)

x = 235.23 ft

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Answer:

To encourage more people to purchase tickets while still raising at least $4000 for the organization, I would make several changes to the raffle game. Firstly, I would reduce the ticket price to a more affordable amount, such as $5 per ticket, to make it accessible to more people. Secondly, I would increase the number of tickets available for purchase, possibly to 2000 tickets, to increase the chances of winning and make it more appealing to potential buyers.

Thirdly, I would adjust the prize amounts to make them more enticing, such as offering a grand prize of $2000, a second prize of $1000, and several smaller prizes of $100 each. By increasing the prize amounts and offering more prizes, it will make the raffle more attractive to people who are looking for a chance to win big while still supporting a good cause.

Additionally, I would use social media platforms and email marketing to promote the raffle to a wider audience, highlighting the prizes and the charitable cause to increase awareness and encourage people to buy tickets. By implementing these changes, the raffle would become more accessible, offer more attractive prizes, and be promoted to a wider audience, ultimately increasing the likelihood of selling more tickets and achieving the fundraising goal of at least $4000 for the organization.

Answer: 0.3 and 3/10

Step-by-step explanation:

its 3 tenths

The measure of the angle ABC is 84 degrees and other measures are listed below

Here, we have

8n - 38 = 5n - 8

So, we have

3n = 30

n = 10

So, we have

ABC = 8n - 38 + 5n - 8

ABC = 8(10) - 38 + 5(10) - 8

ABC = 84

So, the measure of the angle ABC is 84 degrees

Here, we have

2k + 28 = 6k - 20

So, we have

4k = 8

k = 2

So, we have

CBW = 2k + 28

CBW = 2(2) + 28

CBW = 32

So, the measure of the angle CBW is 32 degrees

The interior angle is calculated as

Angle = 180 * (n - 2)/n

Regular 18-gon

Angle = 180 * (18 - 2)/18

Angle = 160

Regular 24-gon

Angle = 180 * (24 - 2)/24

Angle = 165

Here, we have

3x - 10 = x + 8

So, we have

2x = 18

x = 9

So, we have

YA = MA = 9 + 8

YA = MA = 17

Hence, the measures of YA and MA are 17

Here, we have

4x - 15 = 2x - 3

So, we have

2x = 12

x = 6

So, we have

NY = 2(6) - 3

NY = 9

NV = 2 * 9

NV = 18

Hence, the measures of NY and NV are 9 and 18, respectively

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The values of angle x is 140⁰.

The values of angle y is 108⁰.

The values of angle x and angle y is calculated by applying intersecting chord theorem.

The intersecting chord theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.

Angle opposite arc 50 = ¹/₂ x 50 = 25⁰

Angle opposite arc 50 = ¹/₂ x 30 = 15⁰

angle x = 180 - (25 + 15) ( sum of angles in a triangle )

x = 140⁰

The value of angle y is calculated as follows;

minor arc = y

major arc = 50 + 30 + 140 = 220⁰

56 = ¹/₂ (220 - y)

2(56) = 220 - y

112 = 220 - y

y = 108⁰

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Answer:

Step-by-step explanation:

It’s not clear what you’re referring to by “surveying”. However, here are some questions that you can ask yourself while reading to help you better understand what you’re reading1: