Find the area of a rectangle whose side lengths are 8x² feet and 8x³ feet.

A.The area of the rectangle is 16x² feet squared.

B. The area of the rectangle is 64x5 feet squared.

C.The area of the rectangle is 16x² + 16x³ feet squared.

D.The area of the rectangle is 16x5 feet squared.

She need 6 points to score in her 12th game in order to decrease the interquartile range by 1 point.

What is Interquartile range?

An Interquartile range is one of the measure of variability that measures the spread of middle 50% of the data.

Given that;

A basketball player recorded for 11 consecutive games her points as;

13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27

Now,

Since, We know that;

The formula for the interquartile range is,

⇒ IQR = Q₃ - Q₁

Where, Q₃ is the third quartile , Q₁ is the first quartile.

Here, We arrange the points in the increasing order as;

⇒ 13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27

The first quartile is calculated as;

Q₁ = (n + 1) / 4 th term

Where, n is number of terms.

Q₁ = (11 + 1) / 4

Q₁ = 3rd term

Q₁ = 17

The third quartile Q₃ is calculated as;

Q₃ = 3(n + 1) / 4

Q₃ = 3 x 3

Q₃ = 9th term

Q₃ = 24

Thus, The interquartile range is,

⇒ IQR = Q₃ - Q₁

⇒ IQR = 24 - 17

⇒ IQR = 7

So, The desired interquartile range is,

⇒ IQR = 7 - 1

⇒ IQR = 6

Therefore, She need 6 points to score in her 12th game in order to decrease the interquartile range by 1 point.

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Given that a table is 6 feet long and 3 feet wide. You extend the length of the table by inserting two identical table leaves. The extended table is rectangular with an area of (18+6x) square feet.

The area of a rectangle is the product of the width and the length

The required values are given as;

6 + 2x

Here x represents the width of the leaves

Total length = (6 + 2x) feet

Width = 3 feet

Area, A = (6 + 2x) ft. × 3 ft. = (18 + 6x) ft.²

The expression that represents the length of the table is 6 + 2x

The variable x represents the width of the leaves

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The vertex is (7, -27)

The line of symmetry is x = 7.

The minimum is y = -27

The domain is the set of all real numbers.

The range is y ≥ -27.

Given,

The quadratic equation is as follows:

f(x) = (x - 7)^2 - 27

The quadratic equation is in vertex form, hence if the vertex is (h, k), the vertex form will be as follows:

f(x) = (x - h)^2 + k

Then the vertex in this instance is (7, -27).

A line of the form x = h is the line of symmetry, and in this instance the line is x = 7.

The minimum of the quadratic equation is y = -27 since the function has a positive leading coefficient, indicating that the vertex is a minimum.

Finally, the domain is the set of all real numbers, much like the domain of any quadratic equation.

The range includes all real numbers that are greater than or equal to -27.

R = y ≥ -27.

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The given question is incomplete. Completed question is given below;

Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of the function. f(x)=(x-7)^(2)-27

Answer:  x > _5

Step-by-step explanation:

"1/2BH" represents the formula for finding out the area of the triangle.

What is the area of the triangle?

In a two-dimensional plane, the area of a triangle is the region enclosed by it. As we all know, a triangle is a closed shape with three sides and three vertices. Thus, the area of a triangle is the total space occupied by the triangle's three sides. The general formula for calculating a triangle's area is half the product of its base and height.

The given formula is 1/2BH

so this is the formula for finding out the area of the triangle where 'B' is the base of the triangle and H is the height of the triangle.

Hence, "1/2BH" represents the formula for finding out the area of the triangle.

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Answer:

-2,2

4

Step-by-step explanation:

The density function of area is is ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}}).

A random variable can be defined as a variable whose value is unknown or as a function that assigns numerical values to each of the outcomes of an experiment. It can also be defined as a rule that assigns a numerical value to each outcome in a sample space.

The density function (1.4-5)P(x) = an exp(-ax), if x0,0, if x>0, where an is any positive real number, defines the exponential random variable.

radius R has df f(r) ={\lambdae}^{-\lambdar}

area Y= *r2

r = \pm (Y/(\pi))1/2

hence P(Y<y) =F(Y) =P( *r2<y) =P(r<+/- (Y/( ))1/2 ) = \int_{{-y/\pi}^{1/2}}^{{(y/\pi)}^{1/2}}{\lambdae}^{-\lambdar} dr

= e^{{\lambda(y/\pi)}^{1/2}}- e^{{-\lambda(y/\pi)}^{1/2}}

Therefore P(df of y) = f(y) = d/dyf(y) =(d/dy) (e^{{\lambda(y/\pi)}^{1/2}}- e^{{-\lambda(y/\pi)}^{1/2}})

= ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}})

Therefore the density function of area is ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}})

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hello here is number 4 & 6

6:

the graph for number 6 is listed below.

table:

(-2,5)

(-1,0)

(0,-3)

(1,-4)

(2,-3)

4:

all of them can be, look at the listed images below.

The domain of the given function h(x) = 1 - 3x is {-2, 1, -2, -5}.

The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.

The function is given in the question as:

h(x) = 1 - 3x    ....(i)

Here domain= {1, 0, 1, 2}

The range includes all possible y values of a set of ordered pairs.

Substitute the values of the domain i.e. x = 1, 0, 1, 2 in the equation (i),

h(x) = 1 - 3(1)

h(x) = 1 - 3

h(x) = -2

h(x) = 1 - 3(0)

h(x) = 1

h(x) = 1 - 3(1)

h(x) = 1 - 3

h(x) = -2

h(x) = 1 - 3(2)

h(x) = 1 - 6

h(x) = -5

Therefore, the domain of the given function is {-2, 1, -2, -5}.

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The appropriate transformation to increase the hourly wage is a vertical stretch of the function.

The payment function, as a function of the number of hours worked, is a linear function with definition given as follows:

P(h) = mh + b.

In which the coefficients of the payment function are listed as follows:

To increase the hourly pay, the slope needed to be increased, meaning that the slope m has to be multiplied by a constant k, and this multiplication is a transformation called a vertical stretch by a factor of k.

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The appropriate transformation to increase the hourly wage is a vertical stretch of the function.

What is the definition of the payment function?

The payment function, as a function of the number of hours worked, is a linear function with definition given as follows:

P(h) = mh + b.

In which the coefficients of the payment function are listed as follows:

m is the slope of the linear function, which is equivalent to the hourly pay of the students.

b is the intercept of the linear function, which is equivalent to the fixed pay of the students.

To increase the hourly pay, the slope needed to be increased, meaning that the slope m has to be multiplied by a constant k, and this multiplication is a transformation called a vertical stretch by a factor of k.

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 To prove that given is perpendicular we have show that one make right angle, i.e. 90 degree.

A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with that other line. In other words, two lines become perpendicular to one another if they connect at a right angle.

For proof of perpendicular-

Theorm 1 : If two lines intersect to form a pair of lines with a "congruent angle," then the lines are perpendicular to one another. Angles that are equivalent to one another are known as congruent angles.

Theorm 2 : Four right angles will be formed if two perpendicular lines cross.

Theorm 3 : The "adjacent acute angles" are complimentary if two of their sides are perpendicular. As you presumably remember, acute angles are angles that are fewer than 90 degrees, whereas adjacent angles are angles that are next to one another.

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The given statement "a path diagram allows you to determine the effect of one variable upon another both directly and indirectly through an intervening variable. " is true.

Given that,
To justify the given statement whether it is true or not.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,

According to the question,
Let the two interdependent numbers be x and y,
y ∝ x
y = kx
Or
x = y/k

Thus, a path diagram allows you to determine the effect of one variable upon another both directly and indirectly through an intervening variable.

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Answer:

  $1400

Step-by-step explanation:

You want the value of a car 18 years on if its initial value was $14,000 and its value is cut in half every 5.5 years.

The value of the car can be modeled by the exponential equation ...

  value = (initial value) × (growth factor)^(t/(growth period))

where "growth period" is the period applicable to the "growth factor."

Here, the problem statement tells us ...

So, our exponential model is ...

  value = 14,000·(1/2)^(t/5.5)

When t=18 years, this is ...

  value = 14,000(1/2)^(18/5.5) = 14000(1/2)^(36/11) ≈ 14000·0.103469 ≈ 1449

The value after 18 years is about $1400.

The value of x using the Pythagoras Theorem is 6.08 cm.

What is Pythagoras' Theorem?

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares. The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC,is present. The base in this equation is AB, the height is AC, and the hypotenuse is BC.

In the given figure, we have:

A right angles triangle.

So, the Hypotenuse meaure is 14.2 cm;

The measure of the base side is 3.6 + 9.7 cm = 13.3 cm;

So, we can find the perpendicular side length using the Pythagorean Theorem

So, using the Pythagoras theorem,

[tex]c^{2} = x^{2} + y^{2}[/tex]

[tex](14.2)^{2} = (13.3)^{2} + x^{2}[/tex]

201.64 = 176.89 + [tex]x^{2}[/tex]

24.75 = [tex]x^{2}[/tex]

So, x = 4.97

So, The perpendicular side is 4.97 cm;

Now using the Pythagoras theorem again in the smaller triangle, we get:

[tex](3.6)^{2} + (4.9)^{2} = x^{2}[/tex]

12.96 + 24.01 = [tex]x^{2}[/tex]

36.97 = [tex]x^{2}[/tex]

So, The value of x is 6.08 cm;

Hence,

The value of x is 6.08 cm;.

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The minimum dimensions to minimize the amount of material is 15.87 x 15.87 x 15.87 inch.

We need to know about the minimum function to solve this problem. The minimum function can be defined as the minimum value of the variable. It can be calculated by the derivative of the function. The minimum function can be written as

f'(s) = 0

where f'(s) is the derivative function

From the question above, the given parameter is

V = 4000 inch³

The cubic volume can be written as

s² x h = 4000

where s is the length of the base area and h is the height of the box.

the minimum value of the  box refer to its surface area, hence

f(s) = 4sh + 2s²

f'(s) = 4h + 4s

4h + 4s = 0

h = s

It means that the length of the base area and the height must have the same dimension. The minimum volume should have a cube shape

V = s³

s³ = 4000

s = 15.87 inch

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Answer:

Since we need your monthly bill we will call it the variable B for now, (Unless you have the bill, if so replace it with the variable)

Multiply 1.64 x B since the exchange rate is different than the US bill,

For example, say your bill is $100 in the U.S.

You do 1.64 x 100 = A monthly bill of $164 if you lived in Britain

Step-by-step explanation:

Answer:

Step-by-step explanation:

11 2/3

The equation of line possible solution sets of the equation are all the points that lie on the graph of this function.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is the line y = 6x - 11

Plot the graph on the equation. The coordinates on the line plotted represents all the coordinates that are the solution for the equation -

y = 6x - 11

Therefore, the equation of line possible solution sets of the equation are all the points that lie on the graph of this function.

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Answer:

2.9 days

Step-by-step explanation:

Need days / mile

 67 days / 600 mi = .1116666  day/mile

.1116666 day/mi  * 26.4 mi  = 2.948 day    ~ 2.9 days

OR

Miles per day

  600 mi / 67 day = 8.9552 mi / day

   26.4 mi  /  (8.9552 mi/day) = 2.948     ~ 2.9 day

Answer:

The answer is: y = x + 7

Step-by-step explanation:

happy learning

0.86  is the probability that a randomly selected patient is admitted for something other than coronary care.

What is probability ?

Let H denotes the patients are admitted for heart disease.

Let C denotes the patients are admitted for cancer treatment.

We are given:

 P(H) = 0.16

 P(C) = 0.26

P( H ∩ C ) = 0.8

P(Hc ) = 1 - P(H) = 1 - 0.16  =  0.86

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Equation shows  identity property of multiplication is (a + bi) × 1 = (a + bi)

What is Identity property of multiplication?

The identity property of multiplication says that the product of 1 and any number is that number.

We know, Identity property of multiplication states that

"the product of 1 and any number is that given number".

We know that every complex number have two parts one is real and other is imaginary.

If a is real number and b is imaginary  part then by definition

(a + bi) × 1 = (a + bi).

1. Uses Distributive Property of Multiplication.

2. Zero product property.

3. Commutative property of multiplication

4. Identity property of multiplication.

Hence, equation shows identity property of multiplication is (a + bi) × 1 = (a + bi)

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The probability that nadia randomly picks up a reference book and then without replacing it picks up a nonfiction book is 5/136.

Given:

17 total number books out of which 10 are fiction books,2 are reference books , 5 non fiction books.

Number of ways of picking reference book = [tex]2_C_1[/tex]

Probability of picking a reference book = [tex]2_C_1/17_C_1[/tex]

= 2/17

The total number of books left on the shelf is 16.

The number of ways in which a non fiction book can be picked after a reference book is already picked = [tex]5_C_1/16_C_1[/tex]

= 5/16.

Total probability = 2/17*5/17

= 10/272

= 5/136.

Therefore The probability that nadia randomly picks up a reference book and then without replacing it picks up a nonfiction book is 5/136.

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Answer:

5x2=10. 7x2=14. 10+14=24.

Step-by-step explanation:

The amount that Ms. Takata has left to spend is $100.26  .

In the question ,

it is given that ,

total amount that Ms. Takata can spend on redecorate her room = $480

the cost of 1 curtain is = $48.25

the cost for 3 curtain = 3*48.25 = 144.75

the cost of dresser = $234.99

the amount left to spend can be represented by

the amount left to spend = total amount - ( cost of 3 curtain + cost of dresser)

= 480 - (144.75 + 234.99)

= 480 - 379.74

= 100.26

Therefore , The amount that Ms. Takata has left to spend is $100.26  .

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Answer:2.4

Step-by-step explanation:

Based on the information given the unit rate per pound is 2.4.

Using this formula

Unit rate per pound=Costs/Pounds

Where:

Cost=$3.36

Pounds=1.4 pounds of grapes

Let plug in the formula

Unit rate per pound=$3.36/1.4

Unit rate per pound=2.4

the unit rate per pound is 2.4.

A survey of 600 students yielded the following information: 129 were seniors, 249 were commuters, and 68 were seniors and commuters.

The answer provided below has been developed in a clear step by step manner.

Step: 1

Total number of students are 600

n(T) = 600

The number of seniors are:

n(S) = 129

The total number of commuters are:

n(C) = 249

The total number of seniors and commuters are:

n(S∩C) = 68

Total number of seniors or commuters is:

n(S∪C) = n(S)+n(C) - n(S∩C)

n(S∪C) = 129+249-68

            = 310

Explanation:

The given information has been shown as.

Step: 2

Calculate the total value of n(S∪C):

So the total number of seniors and commuters are 310.

Now we have to calculate the students who are neither seniors nor commuters are:

Total students - n(S∪C)

S∪C = 600 - 310

        = 290

Hence the students that are neither senior nor commuters are 290.

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The general form of a Confidence Interval Estimate for a population mean is

      Sample mean ± Critical Value × Standard Error of statistics.

Confidence intervals are one type of statistical interference. They allow us to range values where we can be relatively confident the true value will be. In this case, we are constructing a confidence interval for a population mean. For example: - Suppose that our sample has a mean of X bar = 10 and have constructed the 90% confidence interval.

From the above discussion, we get to know that:

It is reasonable to use a one sample t confidence interval to estimate the population mean since all freshman at a  mid western university where surveyed.

It is reasonable to use a one sample t confidence interval to estimate the population mean since the sample size is at least 30.

It is reasonable to use a one sample t confidence interval to estimate the population mean since the sample size is the sample is representative of the population.

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