N(t) = 8950 Times (0.7)^2t (2024)

a) The coordinates of the center is (2 ,-3)

b) The radius of the circle is 3

c) The diameter of the circle is twice the radius = 2(3) = 6

Now, According to the question:

a) The equation of a circle is given by

[tex](x-h)^2 + (y-k)^2 =r^2[/tex]

where (h, k) is the center and r is the radius

(x - 2)² + (y+3)² = 9

(x - 2)² + (y- -3)² = 3^2

The coordinates of the center is (2 ,-3)

b) The radius of the circle is 3

c) The diameter of the circle is twice the radius = 2(3) = 6

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The complete question is this:

For the circle with equation (x - 2)² + (y+3)² = 9 , answer each question.

(a) What are the coordinates of the center?

(b) What are the radius of the circle?

(c) What is the diameter of the circle?

Answer:

541

Step-by-step explanation:

if you have a 1 in the ones place and a 4 in the tens place and a 5 in the hundreds place this will be your number

Answer:

70

Step-by-step explanation:

nk

The monthly payment for this difference would be $1,361.21. An Adjustable Rate Mortgage (ARM) is a type of mortgage in which the interest rate on the loan changes over time.

An Adjustable Rate Mortgage (ARM) payment is based on various factors such as the loan amount, interest rate, and the terms of the ARM. The interest rate is usually tied to a specific financial index, such as the U.S.

Here is the calculation format for the difference in payments between year 2 and year 3 for Bart and April's mortgage:

Total amount to be paid for the mortgage: $315,000

Rate of interest: 5.85% (Depreciating rate)

Time = 2 years:

a. Remaining amount to be paid after 2 years:

Principal × (1 - Rate/100)^time

= $315,000 × (1 - 5.85/100)²

= $315,000 × (1 - 0.0585)²

= $279,223.01

Time = 3 years:

a. Remaining amount to be paid after 3 years:

Principal × (1 - Rate/100)^time

= $315,000 × (1 - 5.85/100)³

= $315,000 × (1 - 0.0585)³

= $262,888.46

Difference in payments from year 2 to year 3:

= Remaining amount after 2 years - Remaining amount after 3 years

= $279,223.01 - $262,888.46

= $16,334.55

The monthly payment for this difference would be $1,361.21, which is calculated by dividing the difference in payments by 12:

$16334.546/12 = $1361.21

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The variable terms in the expression 3[tex]x^{3}[/tex]y + 5[tex]x^{2}[/tex] + y + 9 are [tex]x^{3}[/tex]y, [tex]x^{2}[/tex], and y.

The expression provided is

3[tex]x^{3}[/tex]y + 5[tex]x^{2}[/tex] + y + 9

In the expression, each variable is represented by a letter.

Let's look at the variables for each term.

The variable in the first term, 3[tex]x^{3}[/tex]y, is [tex]x^{3}[/tex]y.

The variable in the second term, 5[tex]x^{2}[/tex] , is [tex]x^{2}[/tex] .

Y is the variable in the third term.

There is no variable in term 9's final equation.

The variables in the expression are [tex]x^{3}[/tex]y, [tex]x^{2}[/tex] , and y.

As a result, the variables [tex]x^{3}[/tex] and y are the variable terms.

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The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

What is meant by discrete distribution?

If a random variable has a limited number of outcomes or a countable number, it is discrete (i.e. the integers are infinite, but are able to be counted).

The discrete distribution presented reveals that the expected value of Kelsie's time spent completing daily sales reports is 9.5 minutes.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(X) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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a. E(B) = 9.5

b. The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

c. Standard variable shows how much deviation from mean variable.

What do you understand by discrete distribution?

In statistics, a discrete distribution is a probability distribution that estimates the probability of a certain discrete, finite outcome. Simply put, as opposed to a continuous distribution, the discrete probability distribution aids in determining the probabilities of the occurrence of a specific event expressed in terms of positive, non-decimal, or whole integers.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(B) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.

A linear equation is precisely what?

The algebraic equation y=mx+b stands in for a linear equation. The slope is m, and B is the y-intercept. The last phrase referred to a "simple formula with two elements" where both y and x are variables. Bivariate linear equations are calculations involving two variables. Here are a few examples: The outcomes are 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3. If the answer to a mathematical equation is in the form y=mx+b, where m denotes the slope and b the y-intercept, the equation is said to be linear.

Here,

Given :

According to parallelogram laws

adjacent side sum is 180 degree

=> 4y + 3x-18 = 180

=> 4y+3x = 162

and

2x+12+3z = 180

=> 2x + 3z = 168

and

=> 3x+3z = 162

=> x + z =54

=> z = 54-x

So,

2x + 3(54-x) = 168

=> 162 - 3x+2x =168

=> -x = 6

or x =-6

and

z = 60

and

y = 162 - 3x /4

=> y= 162 +18 /4

=> y =180/4

=> y = 45

Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.

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The dy for the given values of x and dx is dy = 0.5632, and their difference to the nearest thousandth is 0.0005.

The difference between dy and Δy can be determined by subtracting dy from Δy and taking the absolute value. In this case, dy approximates Δy to the nearest thousandth with a difference of 0.0005. This is a very small difference, indicating that dy is an accurate approximation for Δy.

The accuracy of dy can be attributed to the fact that the function f(x) = ln(1 + x^2) is a smooth function, meaning that the rate of change at a point (i.e., the derivative) is nearly constant. This allows dy to accurately approximate the change in y, Δy, over a small interval of x. Furthermore, the choice of dx = 0.2 is a small enough value that it does not significantly affect the accuracy of the approximation.

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By dividing we can get proper fraction is 9/10.We can find answer by dividing two fractions.

What is proper fraction with example?

A proper fraction is a fraction which has its numerator value less than the denominator. For example, ⅔, 6/7, 8/9, etc. are proper fractions.. We simplify fractions because it is always to work or calculate when the fractions are in the simplest form.

How do you divide fractions?

To divide a fraction with a whole number we multiply the given whole number with the denominator of the fraction. Here, 8/5 ÷ 5 = 8/5 × 1/5 = 8/25. Therefore, 8/5 ÷ 5 = 8/25. Because multiplication is easier than division and because division by itself does not always produce whole numbers.

Now we get

1/2 divide 5/9

1/2 * 9/5

9/5

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Answer:

Step-by-step explanation:6

joyce's painting rate in window frames per hour is 1.6 and her painting rate in hours per window frame 0.625.

What is the unit rate?

A unit rate is a ratio between two separate units with one as the denominator. Examples include miles/hour, kilometers/hour, meters/sec, salaries/month, etc. The most fundamental and historically significant field of mathematics is arithmetic, which is also the one we use the most frequently in daily life.

Given, Joyce painted 8 window frames in 5 hours while earning money for college.

Her painting rate in window frames per hour is = 8 /5

Her painting rate in window frames per hour is = 1.6

Her painting rate in hours per window frame is = 5/8

Her painting rate in hours per window frame is = 0.625

therefore, The rate at which Joyce paints is 1.6 window frames per hour and 0.625 hours per window frame.

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An inequality that represents the number of signatures Ali needs to collect in each of the remaining weeks so that he will have enough signatures to submit the petition: 520 + 6m ≥ 1000

and the minimum number of signatures he needs to collect = 80

Given that Ali wants to collect the same number of signatures each week.

Assume that Ali collects m number of signatures each week.

He has 6 weeks to collect the remaining signatures he needs.

So, by unitary method in 6 weeks the number of signatures he would collect:

6 × m

He currently has 520 signatures and he needs a total of at least 1,000 signatures before he can submit the petition.

so, we get an inequality.

520 + 6m ≥ 1000

We solve above inequality.

6m ≥ 1000 - 520

m ≥ 480/6

m ≥ 80

Ali needs to collect at least 80 signatures, so that he will have enough signatures to submit the petition.

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The various statements regarding the given scatter plot is checked and found to be true or false.

What is a scatter plot?

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.

1)The equation of the line is y = 2500x - 125.

From the graph we can take two points on the line,

( 2,2250) and ( 10,1250)

Standard equation of line is y = mx + b

where b is y - intercept and m is slope

m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125

From graph, b = 2500

Equation of line is

y = -125x + 2500

Therefore the given equation is false.

2) The group of hikers descends about 250 feet every minute.

From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.

So the hikers descend 250 feet every minute.

Therefore the given statement is true.

3) The hikers began at the elevation of 2500 feet.

The x-intercept of the graph is 2500 feet.

So the beginning elevation is 2500 feet.

Therefore the statement is true.

4) The graph shows a negative association.

Since the line in the graph is going down and the slope is negative, the graph shows a negative association.

Therefore the statement is true.

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The solution of the given system of equations is x = -7/3 and y = 7.

The given system of equations is given as,

3x + 2y = 7

y = 3x + 11

To solve this system of equations, we need to eliminate one of the variables. We can eliminate y by subtracting the second equation from the first.

3x + 2y = 7

y = 3x + 11

⇒ 3x + 2y - y = 7 - 11

⇒ 3x + 2y - 3x - 11 = -4

⇒ 2y - 11 = -4

⇒ 2y = -4 + 11

⇒ 2y = 7

Now, substitute the value of y in the first equation to find the value of x.

3x + 2(7) = 7

⇒ 3x + 14 = 7

⇒ 3x = 7 - 14

⇒ 3x = -7

⇒ x = -7/3

Therefore, the solution of the given system of equations is x = -7/3 and y = 7.

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Answer:

Step-by-step explanation:

The ratio of the volume of the pyramid to the volume of the prism is 1.so, the option A. is correct.

Let the base of the base of a prism is b and the height of the prism is h.

so, the volume of the prism-

V= [tex]b^{2}[/tex] h

also, given that base of the given pyramid is also b and the height of the pyramid is three times the height of the prism.

h'=3h

so, the volume of the square pyramid-

V'=[tex]\frac{1}{3}[/tex][tex]b^{2}[/tex]h'

V'=[tex]\frac{1}{3}[/tex][tex]b^{2}[/tex](3h)

V'=[tex]b^{2}[/tex]h

so, now-

[tex]\frac{V'}{V}[/tex]=[tex]\frac{b^{2}h }{b^{2}h }[/tex]

[tex]\frac{V'}{V}[/tex]= 1

so. the ratio of the volume of the pyramid to the volume of the prism is 1.

Answer:

Step-by-step explanation:

No, some people don't like certain things. It like saying that you pick five random people who are at a science fair and ask them if they like science, the answer would be yes, but if you went to Walmart and asked five random people if they liked science your answers would most likely end up being no. It's the same way looking at the magazines.

Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

The definition of a linear equation.

A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : (X-5)-1

Thus,

after substituting the value of x with 9

We get,

=> (X-5) -1

=>(9-5)-1

=> 4 -1

=> 3

Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

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The type of quadrilateral is ABCD is parallelogram.

There are some properties of parallelogram:

If Two pairs of opposite sides are parallel and equal in length.The two pairs of opposite angles are equal in measure and one pair of opposite sides is parallel and equal in length.The diagonals bisect each other, and the adjacent angles are supplementary.Each diagonal divides the quadrilateral into two congruent triangles, with the sum of the squares of the sides equals the sum of the squares of the diagonals.

The coordinate of quadrilateral ABCD are A=(2,4) B=(5,6) C=(4,3) D=(1,1)

By using the coordinates we can find the slope:

slope=y2-y1/x2-x1

the slope of AB =6-4/5-2

AB=2/3

the slope of AD =1-4/1-2

AD=3/1

the slope of CD =1-3/1-4

CD=2/3

the slope of BC =3-5/3-6

BC=2/3

The slope indicates that the slope of AB is equal to BC and the slope of AD is equal to CD

Therefore, as per the properties, quadrilateral ABCD is Parallelogram

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15 degrees by eye i think

Answer: The odds of an event happening are the ratio of the number of ways the event can happen to the number of ways it cannot happen.

Odds = (probability of success) / (probability of failure)

In this case, the event is that a carton of eggs will have at least one cracked egg.

The probability of success (the event happening) is 2.5%

The probability of failure (the event not happening) is 100% - 2.5% = 97.5%

so we can find the odds by dividing the probability of success by the probability of failure.

Odds = 2.5 / 97.5 = 0.025/0.975 = 1/39

So the odds that a carton of eggs will have at least one cracked egg is 1:39, meaning that for every 39 cartons that are free of cracked eggs, one carton will have at least one cracked egg.

It means that it's 1 in 39 chance that a carton of eggs will have at least one cracked egg

Step-by-step explanation:

Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:

y = 24*3 + 12 = 72 + 12 = 84

So the matching pairs are:

a ⇔ 4, b ⇔ 2,c ⇔ 3,d ⇔ 1 .

The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.

What is the probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.

In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.

To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.

So the probability of the intersection of the two diagonals lying inside the nonagon is:

P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3

Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.

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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.

What is the probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.

In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.

To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.

So the probability of the intersection of the two diagonals lying inside the nonagon is:

P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3

Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.

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The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numerical expression is given below.

⇒ 12 × [6.3 + 3 × (1.9)]

Simplify the numerical expression, then we have

⇒ 12 × [6.3 + 3 × (1.9)]

⇒ 12 × [6.3 + 5.7]

⇒ 12 × 12

⇒ 144

The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

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On solving the provided question, we can say that by the help of unitary method total 28 + 40 = $ 68

What is unitary method ?

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

One package of chicken costs = $7

steaks cost = $4 per pound.

cost of 4 chicken = 4 * 7 = $28

cost of 10 steaks = 4*10 = $40

total 28 + 40 = $ 68

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a = 13. b^0 = 1, y=a(1), 13 = a 325 = 13(b)^2 b^2 = 325/13 = 25

b = sqr25 = 5 y=13(5)^x is the exponential equation going through the two given points

What is Exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.The graphs of all exponential functions have these characteristics. They all contain the point (0, 1), because a0 = 1. The x-axis is always an asymptote. They are decreasing if 0 < a < 1, and increasing if 1 < a. If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variable

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Three examples of perfect squares is 1) 9, as it is equal to 3 x 3.2) 16, as it is equal to 4 x 4.3) 25, as it is equal to 5 x 5.

What is perfect squares?

Similarly, 9 is a perfect square because it is equal to 3 x 3. Perfect squares can be easily identified by their square root, which is the number that can be multiplied by itself to produce the perfect square.

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X=6
Y=-3
Step: Solve
x
=
6
y
+
24
for x:
x
=
6
y
+
24

Step: Substitute
6
y
+
24
for
x
in
2
x
+
3
y
=
3
:
2
x
+
3
y
=
3
2
(
6
y
+
24
)
+
3
y
=
3
15
y
+
48
=
3
(Simplify both sides of the equation)
15
y
+
48
+
−
48
=
3
+
−
48
(Add -48 to both sides)
15
y
=
−
45
15
y
15
=
−
45
15
(Divide both sides by 15)
y
=
−
3

Step: Substitute
−
3
for
y
in
x
=
6
y
+
24
:
x
=
6
y
+
24
x
=
(
6
)
(
−
3
)
+
24
x
=
6
(Simplify both sides of the equation)

Answer:
x
=
6
and
y
=
−
3

The easiest way to find this is touse the library's catalog. Depending on the integrated library system (or ILS) the library subscribes to, the process might be slightly different. Generally, you can use a catalog system on a computer to search by title, author, subject, and more.

Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.

What is the ghost?

Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.

Here, we have,

Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.

Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.

Therefore, option B is the correct option.

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