The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?

Answer:

y = [tex]\frac{1}{2}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 10 ← is in slope- intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (10, 7 ) into the partial equation

7 = 5 + c ⇒ c = 7 - 5 = 2

y = [tex]\frac{1}{2}[/tex] x + 2 ← equation of perpendicular line

The correct answer is option D. 1/35. To count the number of rectangles that can be formed, we need to consider the two cases where the diagonals of the rectangle are parallel to the sides of the octagon, and where the diagonals are perpendicular to the sides of the octagon.

In the first case, there are four choices for which side the diagonals are parallel to, and once that side is chosen, there are two choices for which pair of vertices lie on that side. Therefore, there are $4 \cdot 2 = 8$ rectangles of this type.

In the second case, there are four choices for which vertex the diagonals intersect, and once that vertex is chosen, there are two choices for which pair of vertices lie on the same side of the intersection point as the chosen vertex. Therefore, there are $4 \cdot 2 = 8$ rectangles of this type.

Altogether, there are $8 + 8 = 16$ rectangles. Therefore, the probability that the quadrilateral formed by the four vertices is a rectangle is

                               = \frac{1}{{8 \choose 4}/16}

                               = \frac{1}{{8 \choose 4}/2^4}

                               = \frac{1}{{8 \choose 4}/2^4}

                               = \boxed{\text{(D) } 1/35}$.

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Therease should take her 7th dose on Friday at 9:00AM

What is time ?

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Time is defined by physicists as the flow of events from the past through the present and into the future. In essence, a system is timeless if it is unchanging. When describing events that take place in three-dimensional space, time can be thought of as the fourth dimension of reality.

The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.

If Theresa took her first dose at 9:00 AM on Monday,

Simply add 12 hours every time up to the 7th dose,

First dose  ----> 9:00 AM on Monday,

Second dose  ----> 9:00 PM on Monday,

Third dose  ----> 9:00 AM on Tuesday,

Fourth dose  ----> 9:00 PM on Tuesday,

Fifth dose  ----> 9:00 AM on Thursday,

Sixth dose  ----> 9:00 PM on Thursday,

Seventh dose  ----> 9:00 AM on Friday,

Hence, Theresa should take her 7th dose at 9:00 AM on Friday.

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Answer:

Therefore, the area of the triangle with vertices at A(2, 2), B(4, 5), and C(7, 5) is approximately 4.5, to the nearest tenth.

Step-by-step explanation:

To find the area of a triangle with vertices at A(2, 2), B(4, 5), and C(7, 5), you can use the Shoelace Theorem.

The Shoelace Theorem states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) is given by the following formula:

A = 1/2 * |(x1y2 + x2y3 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + ... + yn-1xn + ynx1)|

To apply the Shoelace Theorem to a triangle with vertices at A(2, 2), B(4, 5), and C(7, 5), you can plug in the coordinates of these vertices into the formula:

A = 1/2 * |(25 + 45 + 72) - (24 + 57 + 52)|

= 1/2 * |(10 + 20 + 14) - (8 + 35 + 10)|

= 1/2 * |44 - 53|

= 1/2 * |-9|

= 1/2 * 9

= 4.5

The correct option is (d) i.e. log [ √x × (x-1)^3 / ∛ (x+1)^2 ] is as the single logarithm.

What is logarithm?

Logarithm is a mathematical operation which is used to determine the exponential power of a number. It is the inverse operation of exponentiation. Logarithm is commonly used in calculus, algebra, and other areas of mathematics. It can also be used to solve problems involving exponents, roots, and powers. Logarithm is denoted by the symbol log, and is read as "log to the base". The base is the number which the logarithm is taken to. For example, log2 10 is the logarithm to the base 2 of 10. This is equivalent to saying "2 to the power of what equals 10?" The answer is that 2 raised to the power of 3 (2^3) would equal 10.

Given, log x / 2 + 3 [ log(x-1) - 2/9 log(x+1) ]

        = log √x + 3 log(x-1) - 2/3 log (x+1)            {∵ log x^a = a log x }

        = log √x + log (x-1)^3 - log (x+1)^2/3

        = log √x + log [(x-1)^3 / (x+1)^2/3]              {∵ log a - log b = log a/b }

        = log [√x × (x-1)^3 / (x+1)^2/3 ]

        = log [ √x × (x-1)^3 / ∛ (x+1)^2 ]

Hence, (d) is the correct option.

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The total area of the figure is equal to 192 square meters. The correct option is A.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Calculate the area of the rectangle by the formula written below,

Area of the rectangle = L x W

Area of the rectangle = 8 x 18

Area of the rectangle = 144 square meters

The area of the triangle will be calculated by the formula written as,

Area of triangle = 1/2 x B x H

Area of triangle = 1/2 x ( 18 - 6 ) x 8

Area of triangle = 1 / 2 x 12 x 8

Area of triangle = 48 square meters

Total area = 144 + 48

Total area = 192 square meters

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w=9/2 =4,5

Step-by-step:

:)

Answer:

3/2 or 1.5 or 1 1/2 in mix number

Answer:

  the product of 6 and 23 is more than 126

Step-by-step explanation:

You want to know how to tell that 6 is too high an estimate for the first digit of the quotient of 126 and 23.

When the trial quotient value of 6 is multiplied by the actual divisor of 23, we are computing 6(20 +3) = 120 +18. This is more than 126, so the trial quotient value is too large.

__

Additional comment

Another way to tell is to consider the dual problem that 120/20 = 6 represents: 120/6 = 20. It is easy to see that 126/6 = 21, so we know that a divisor of 23 (larger than 21) will give a quotient less than 6.

Answer:

y=12x+20

Step-by-step explanation:

Your question and a graph of picture are different. So I just considered your question.

m= (80-44)/(5-2) = 36/3=12

(y- y_1)=m(x-x_1)

(y-44)= 12(x-2)

y-44=12x-24

y= 12x-24+44

y=12x+20

Answer: -64

Step-by-step explanation:

To solve this equation, you need to isolate the b term on one side of the equation. You can do this by dividing both sides of the equation by 16. This will give you:

b/16 = (-4)

You can then divide both sides of the equation by -4 to get:

b/16 = -4

b/16 * -4 = -4 * -4

b = -64

Therefore, the solution to the equation is b = -64.

The following choices are binomial random variables: A. Take a random sample of 30 tours and let L = the number of tours that result in a sale. B. Take a random sample of 3 tours and let K = the number of tours that result in a sale.

Choice A is a binomial random variable because it represents the number of tours that result in a sale in a random sample of 30 tours. The trials are independent, as the results of one tour do not affect the results of other tours, and the probability of success (a sale) is constant at 5%.

Choice B is also a binomial random variable because it represents the number of tours that result in a sale in a random sample of 3 tours. The trials are independent and the probability of success is constant at 5%.

Choice C is not a binomial random variable because it represents the number of sales generated by a random sample of 3 tours, which is a continuous variable. Binomial random variables are always discrete, as they represent the number of successes in a sequence of trials.

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Five years ago, you acquired a 30-year loan of $130,750, charging 6.6% annual interest, compounded monthly,

a) You will be refinancing $122536.

b) New monthly payment be after refinancing is

$794.1858 or 79 418.58 cents.

We have given that

Initial loan amount = $ 130,750

Number of year of loan = 30 year

Nomber of month of loan "n" = 30x12= 360

Annual interest rate = 6.6%

monthly rate "r" = 6.6% /12 =

monthly payment on the loan is

PMT= loan× r / [1 - (1+r)⁻ⁿ]

= $ 130750 X 12/(1 - (1+ 6.6%/12)⁻³⁶⁰)

= $719,125/(1- (1+0.0055) ⁻³⁶⁰

= $835.046

Monthly payment, $835.046 on initial loan.

Now after 5 years refinishing is done . So, amount and remaining balance is for 30-5 = 25 years and 25×12 = 300 months . The present value of unpaid monthly payment is

= PMT× ( (1 - (1+r)⁻ⁿ)/r)

= $835.046( 1 - (1+6.6%/12)⁻³⁰⁰/ 6.6%/12]

= $835.046× 196.74179

= $122536

Hence, amount refinanced is $122536.

b) New monthly payment will be on loan =$122536

Annual rate = 2.1%

monthly rate, r' = 2.1%/12

Number of years for refinancing = 15 years

Number of months , n' = 15× 12 = 180

Using the formula new monthly payment is

PMT = new loan× r'/ [1 - (1+r')⁻ⁿ´ ]

= $122536× 2.1%/12[ 1 - (1+2.1%/12)⁻¹⁸⁰]

= $214.43826/0.2700104

= $794.1858

Hence, new monthly payment is $794.1858.

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From the values that we have here, the statement that can be said to be true here would be that: There is no constant relationship between the number of video games collected by Cooper and Maria. Last option

A relationship with a fixed ratio between two quantities is referred to as proportionate. The graph will therefore be linear, or straight.

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

The values between these two does not show any constant relationship hence the last option

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Answer: part a

cooper- 35 45 55 65

maria 15 23 31 39

part B

there is no constant relationship between the number of video games collected by coopeer and maria

Step-by-step explanation:

Answer:

since 12inches=1foot

x inches=34feet

34feet converted to inches =408inches

total inches=408+8

T=416inches

dividing 416 by 8 we have

52 inches left

converting back to feet we get

4ft 4in

The value of the function G(-5 + h) - G(-5) in the simplest form -5h.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

G(t) = 9 - 5t            (1)

To find the value of expression G(-5 + h) - G(-5),

First, find the value of G(-5 +h) by substituting t = -5+h in equation (1),

G(-5 + h) = 9 - 5(-5 + h)

               = 9 +25 -5h

               = 34 - 5h

The value of G(-5)

G(-5) = 9 - 5(-5)

        = 9 + 25

        = 34

The required value,

G(-5 + h) - G(-5) = 34 - 5h - 34 = -5h.

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The amount earned by Damian on Friday, if The function f(x) = 12 x + 10, and he works for 2.75 hours, is $43.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The function f(x) = 12 x + 10, where x is working hours,

Calculate the amount by putting the value of x = 2.75 in the function as shown below,

f(x) = 12 × 2.75 + 10

f(x) = 33 + 10

f(x) = $43

Thus, the amount earned is $43.

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Answer:

-6/6 or -1

Step-by-step explanation:

To find the equation of the line (or the slope, assuming that's what equation means, ) we need to write the formula Y1-Y2/X1-X2

So, we need to fill in the numbers, which gives us the fraction -6-0/-2-(-8)

When we solve for the numerator (-6-0), we get -6.

When we solve for the denominator (-2 - {-8}), we get 6.

So, we have -6/6, which, when simplified, is -1.

(If the problem is not asking for slope when it says equation, then sorry!)

The expression of (a + b + c) is equivalent to 16.5.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given are two circles intersecting at each others centers at D and E.

We can write the area of the common region as -

[A] = 4 x {(θ/180) x (πr²/2) - (1/2)r²sinθcosθ}

Now, we can write θ as -

cos(θ) = (3/6) = 1/2

θ = 60°

[A] = 4 x {(60/180) x (π(6)²/2) - (1/2)(6)²sin(60)cos(60)}

[A] = 4 x {(1/3 x 36π/2 - (1/2) x 36 x [tex]\sqrt{\frac{3}{2} }[/tex] x 1/2}

[A] = 4 x {6π - 9 [tex]\sqrt{\frac{3}{2} }[/tex] }

[A] = 24π + (-  9 [tex]\sqrt{\frac{3}{2} }[/tex])

So, on comparing, with the expression below -

aπ + b[tex]\sqrt{c}[/tex]

We get -

a = 24

b = - 9

c = 3/2

So, we get -

a + b + c

24 - 9 + 3/2

24 - 9 + 1.5

24 - 7.5

16.5

Therefore, the expression of (a + b + c) is equivalent to 16.5.

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In the factorization, the bottom triangular matrix L is the only one.

The exponent of a number indicates how many times it has been multiplied by itself.

Exponent-related issues can be solved using either exponent laws or exponent characteristics. When a number is repeated numerous times by itself, writing the product without the use of exponents becomes very difficult. Major exponentiation rules are also thought of as having these characteristics.

Given that A is a positively defined symmetric matrix with a Cholesky decomposition,

A = L[tex]L^{T}[/tex]  = [tex]R^{T} R[/tex]

Let A be our positive define symmetric matrix,

suppose A has Cholesky decomposition,

A = L₁L₂ = L₁L₂ , for L₁, L₂ lower triangular matrix with positive diagonal entries,

thus (A x ,x) = (Lx, Lx) = (Lx, Lx)

pick x = eₓ  the last coordinate vector,

then (Aₓ, x) = Axx = || L₁x||² = || L₂x||²

Given that L1, and L2 are lower triangular, which necessitates that their lower right entry be the same,

The Kth entry is currently the last row.

given by (L₁, eₓ, eₓ) = 1/√Axx (L₁eₓ, L₂eₓ) = 1/ Aₓ = (Aeₓ, eₓ)

so the last row of L₁, L₂ be the same,

we reduce our A to new (n - 1)x(n - 1) submatrix,

which will likewise be true, and then repeat the process to discover each row's unique value.

Thus, the inductive process shows that L1 = L2.

As a result, the factorization's bottom triangular matrix L is exclusive.

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There are several reasons why researchers might not use the normal distribution to model real data which are due to assumptions of normal distribution.

First, the normal distribution assumes that the data is symmetric and is distributed around the mean. However, in some cases, the data may be skewed, making the normal distribution an inappropriate model.

Second, the normal distribution assumes that the data is homoscedastic, meaning that the variance is constant across the sample. However, in some cases, the variance may be heteroscedastic, meaning that the variance changes across the sample. This makes the normal distribution an inappropriate model for this type of data.

One situation in which researchers should not use the normal distribution approximation is when modeling financial data. Financial data often follows a power-law distribution, which is not normal. Therefore, researchers should use a power-law distribution to model this type of data.

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1.  The average difference between the two values on the two stacks of cards is expected to be about 0 minutes best describes the outcome of the randomization test.

This randomization test was conducted to test whether the average difference of 32 minutes between the two groups could be attributed to chance. The test essentially involved shuffling the index cards containing the minutes slept by each subject and then dealing them into two equal-sized groups.

This process allows for a fair comparison between the two groups and ensures that any differences in the average minutes slept are due to chance. Since the cards are shuffled randomly, the average difference between the two stacks of cards is expected to be about 0 minutes.

If meditation is effective, then the difference between the values on the two stacks of cards would be expected to be more than 32 minutes.

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Answer:No

Step-by-step explanation:

When we substitute x=6 into the first equation we get

y=1/6 *6+5=6 so we get (6, 6)

When we substitute x=6 into the second equation we get

y=5/6*6+3=8  so we get (6, 8) . it works for the second equation but not the first. It must be true for both equations

Answer:

75.5

Step-by-step explanation:

The amount invested in the account that earns 8% interest is $6500

The amount invested in the account that earns 12% interest is $8500

a + b = $15,000 equation 1

0.08a + 0.12b = $1540 equation 2

Where:

a = amount invested in the account that earns 8% interest

b = amount invested in the account that earns 12% interest

The elimination method would be used to determine the required values:

Multiply equation 1 by 0.08

0.08a + 0.08b = 1200 equation 3

Subtract equation 3 from equation 2

0.04b = 340

Divide both sides of the equation by 0.04

b = 340 / 0.04

b = $8500

a + 8500 = 15,000

a = $15,000 - $8,500

a = $6500

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Answer:

52 is range

Step-by-step explanation:

Range is the 'y' values the function can have

 from 0 to 10 books would give a range of 0 - 52

Domain is the x-values  0, 1,2,3,4,56,7,8,9,10

    discrete, because you cannot have anything but the whole numbers listed for the values of 'x'

Answer:

The domain is the input.  It is the number of books.  You can have 0-10 books.  These would be the domains.  

The range is the outputs.  The outputs can be from 0 to 52 pounds.

The domain is discrete.  The domain is the number of books.  We cannot have half or a book or 3/4 of a book.  So this will be discrete.  The number of books can only be whole numbers up to 10.

Step-by-step explanation:

The z-test statistic is used to test the claim that the proportions of the two populations differ. A normal test statistic, the z-test statistic can also be used to measure the proportion of a single population.

Let's say that:

p1: Liberal voters' proportion of the population who smoked cannabis, p. 2:

Conservative voters' proportion of the population who smoked cannabis The null hypothesis is H 0:

The alternative hypothesis is H 0: p 1 = p 2.

p 1 p 2 P-value = 0.00001 The P-value is less than the significance level of 1%. The null hypothesis is rejected at the 1% significance level.

We can conclude that conservative voters had a lower percentage of voters who regularly smoked cannabis.

Two distinct hypotheses are tested by all analysts using a random population sample: the alternative hypothesis and the null hypothesis. Typically, the null hypothesis is a hypothesis that all population parameters are equal; For instance, a null hypothesis might assert that the population mean return is zero.

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The value of x in the inequality, -13x < 65, is simplified as, x > 5.

Any inequality given can be solved by find the value of the variable in the inequality, which will make it a true statement. To do this, isolate the given variable to make it stand alone on one side.

Given the inequality, -13x < 65, solve as shown below:

-13x < 65 [given]

Divide both sides by -13:

-13x/-13 < 65/-13

x > -65/13 {the sign changes from < to > because we divided both sides by a negative quantity]

x > 5

The value of x is simplified as x > 5.

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