a circle in the xy-plane has its center at 1,7 and has a radius of 3. an equation of this cirlcle is x2

Answer:

A. and F. and B.

:)

The change in thermal energy is 75.06 kJ.

To calculate the change in thermal energy, we need to use the specific heat capacity of water, which is 4.184 J/(g°C).

First, we need to calculate the change in temperature:

ΔT = 90°C - 12°C

ΔT = 78°C

Next, we can calculate the change in thermal energy:

ΔQ = m × c × ΔT

where m is the mass of water and c is the specific heat capacity of water.

ΔQ = 230 g × 4.184 J/(g°C) × 78°C

ΔQ = 75060.96 J or 75.06 kJ (rounded to two decimal places).

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(a) The Crossing-Graph Lemma states that if two continuous functions f and g are defined on an interval [a, b] and f(a) <= g(a) and f(b) >= g(b), then there exists some c in [a, b] such that f(c) = g(c).

(b) The Fixed-Points on [0, 1] Theorem states that if f is a continuous function from [0, 1] to [0, 1], then there exists some c in [0, 1] such that f(c) = c.

The lemma can be proved using the Intermediate Value Theorem. The IVT states that if a function f is continuous on an interval [a, b] and N is between f(a) and f(b), then there exists some c in (a, b) such that f(c) = N.

In the case of the Crossing-Graph Lemma, we can set N = g(a). Since f(a) <= g(a), the IVT guarantees that there exists some c in (a, b) such that f(c) = g(a).

But since g is also continuous, we know that g(c) = g(a). Therefore, we must have f(c) = g(c).

Here is a more detailed explanation of the Fixed-Points on [0, 1] Theorem:

We can use the Crossing-Graph Lemma to prove this theorem by setting g(x) = x. Since f(x) is continuous on [0, 1], we know that f(0) <= 0 and f(1) >= 1. Therefore, the Crossing-Graph Lemma guarantees that there exists some c in [0, 1] such that f(c) = g(c) = c.

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Using percentage to determine the ounce of iceberg lettuce in the salad from the pie chart, we have 15.2 ounces

A pie chart is a circular chart that is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area), is proportional to the quantity it represents. Pie charts are very useful for displaying data and are most commonly used to show percentages or proportional values of different categories relative to the whole.

We can use the concept of percentage to determine the number of ounces of iceberg lettuce present.

In the pie chart, the percentage of ice berg lettuce is 40% and the quantity of salad bought is 38 ounce

40 / 100 = x / 38

0.4 = x / 38

x = 38 * 0.4

x = 15.2 ounces

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A basketball player jumps straight upward to shoot the ball from beyond the three-point line. The player jumped approximately 7.874 feet or 94.488 inches.

To determine the height the player jumped, we can use the kinematic equation: h = (1/2)gt², where h is the height, g is the acceleration due to gravity, and t is the time.
Given that the player was in the air for 0.7 seconds, we can substitute the values into the equation.
h = (1/2)(9.8 m/s^2)(0.7 s)²
h = (1/2)(9.8)(0.49)
h = 2.401 m
Therefore, the player jumped approximately 2.401 meters.
To convert this into feet or inches, we can use the conversion factors:
1 meter = 3.281 feet
1 foot = 12 inches
Converting 2.401 meters to feet:
2.401 m * 3.281 ft/m = 7.874 ft
Converting 7.874 feet to inches:
7.874 ft * 12 in/ft = 94.488 in
So, the player jumped approximately 7.874 feet or 94.488 inches.

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Answer:

4 +5 _7

Step-by-step explanation:

The approximate solution to x^3 - 5x^2 - 9 = 0, to 2 decimal places, is x = 5.19.

It should be noted that to use the iterative process to find an approximate solution to x^3 - 5x^2 - 9 = 0, we can use the following formula:

x[n+1] = x[n] - f(x[n]) / f'(x[n])

First, let's find the derivative of the function:

f(x) = x^3 - 5x^2 - 9

f'(x) = 3x^2 - 10x

Next, let's plug in x = 5 to get our first approximation:

x[1] = 5 - (5^3 - 5(5)^2 - 9) / (3(5)^2 - 10(5))

x[1] = 5 - (125 - 125 - 9) / (75 - 50)

x[1] = 5 + 0.12

x[1] = 5.12

Now we can use this value as our new approximation and repeat the process:

x[2] = 5.12 - (5.12^3 - 5(5.12)^2 - 9) / (3(5.12)^2 - 10(5.12))

x[2] = 5.12 - (134.78 - 131.19 - 9) / (79.76 - 52.06)

x[2] = 5.12 + 0.064

x[2] = 5.184

x[3] = 5.184 - (5.184^3 - 5(5.184)^2 - 9) / (3(5.184)^2 - 10(5.184))

x[3] = 5.184 - (139.55 - 135.92 - 9) / (82.87 - 53.64)

x[3] = 5.184 + 0.005

x[3] = 5.189

Therefore, an approximate solution to x^3 - 5x^2 - 9 = 0, to 2 decimal places, is x = 5.19.

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Answer:

Step-by-step explanation:

if we need to combine the like terms

-4p+(-6p)=-4p-6p=-10p

choice b

The regular expression is ^(a(aa)*b)$.

To create a regular expression for the language L = {w = {a,b}* | w has an odd number of 'a's and ends with 'b'}, we can use the following expression:

^(b|(a(aa)*b))$

Breaking it down:

^ indicates the start of the string.

(b|(a(aa)*b)) matches either 'b' or a sequence of 'a's followed by an odd number of 'a's and 'b'.

(aa)* matches zero or more pairs of 'a's.

$ indicates the end of the string.

This regular expression ensures that the string starts with 'b' or a sequence of 'a's, followed by an odd number of 'a's, and ends with 'b'. Any additional characters or sequences in between are not allowed.

Please note that regular expressions can have different notations and conventions depending on the context or programming language you're using. The expression provided here follows a general pattern that should work in most cases.

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The function f(x, y ,z) and u(u1, u2, u3) are unit vectors, then;

Duf = ▽f.u = ∂f/∂x u1 + ∂f/∂y u2 + ∂f/∂z u3

The directional derivative is the rate at which any function changes in a fixed direction at a particular point. It is the vector form of any derivative. It characterizes the instantaneous rate of variation of a function.

Since we know that the gradient is defined for the function f(x, y) is as;

▽f = ▽f(x, y) = ∂f/∂xi + ∂f/∂ yj

It can be calculated by assigning the vector operator r to f(x, y) as a scalar function. This vector field is called gradient vector field.

If we have a function f(x, y ,z) and u(u1, u2, u3) are unit vectors, then;

Duf = ▽f.u = ∂f/∂x u1 + ∂f/∂y u2 + ∂f/∂z u3

It is clear that, if we take a dot product of the gradient and the given unit vector, then we get the directional derivative of the function.

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Hey buddy I am here to help!

5. y = ax + b

-5 = a*4 + b

-5 = 4a + b

If we take a as -2

-5 = 4*-2 + b

-5 = -8 + b

b = -5 - (-8)

b = -5 + 8

b = 3

so... a = -2 and b = 3

6. (i) y = 5x - 2

(1,7)

y = 7 & x = 1

7 = 5*1 -2

7 = 5 - 2

7 = 3

so this point (1,7) is wrong

(ii) y = 5x -2

we can take any value for x...

e.g. x = 2

y = 5*2 - 2

y = 10 -2

y = 8

SO answer in this case would be (2,8)

Plz mark my answer brainliest

For the function f(x)=1/2sin(2x-4)+3, the Domain: (-∞, ∞) and the Range: [2.5, 3.5].

The range of values that can be plugged into a function is known as its domain. In a function like f, this range corresponds to the x values (x).

The collection of values that the function assumes is known as its range. Following the insertion of an x value, the function outputs this set of values. The values of y are those.

An assembly line's machines can be compared to functions in this way. The machine in the middle performs the function. On one end of the assembly line are a few screws and bolts, and on the other end is a car.

Given that

F(x)=1/2sin(2x-4)+3

For the given function graph is sinewave (see attachment)

For which

Range: [2.5, 3.5]

Domain: (-∞, ∞)

Thus, For the function f(x)=1/2sin(2x-4)+3, the Domain: (-∞, ∞) and the Range: [2.5, 3.5].

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Since there are four tellers, the capacity of the bank in customers per hour = 4 x 7.5 = 30.

Valley Bank has four tellers. It takes a teller 8 minutes to serve one customer.

The correct option is D. 30.

We are given that

Valley Bank has four tellers. It takes a teller 8 minutes to serve one customer.

To calculate the capacity of the bank in customers per hour, we need to find how many customers each teller can serve in an hour. To do this, we first need to convert the time taken to serve one customer from minutes to hours.

1 minute = 1/60 hoursSo, time taken to serve one customer

= 8 minutes

= 8/60 hours

= 2/15 hours

One teller can serve one customer in 2/15 hours.In one hour, the number of customers one teller can serve = 1/(2/15) = 15/2 = 7.5 (customers/hour)

Therefore, the capacity of one teller in customers per hour is 7.5.

Now, we need to find the capacity of the bank in customers per hour. Since there are four tellers, the capacity of the bank in customers per hour = 4 x 7.5 = 30.

So, the correct option is D. 30.

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Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 2 mm

pi ( π ) = 3.14

Finding the area of circle having radius of 2 mm

Area of circle \( \sf{ = \pi \: {r}^{2} }\)

plug the values

⇒\( \sf{3.14 \times {2}^{2} }\)

Evaluate the power

⇒\( \sf{3.14 \times 4}\)

Multiply the numbers

⇒\( \sf{12.56 \: {mm}^{2} }\)

Hope I helped!

Best regards!!

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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Answer:

48

Step-by-step explanation:

Given

7x² - 3x - 6 ← substitute x = 3 into the expression

= 7(3)² - 3(3) - 6

= 7(9) - 9 - 6

= 63 - 15

= 48

Answer: No, the triangle sum theorem is not true for a sphere surface.

Explanation:

Consider 3 cities A,B,C at the following locations

The placement of C is important because this then allows angle ABC to be 90 degrees. Angles BAC and BCA are also 90 degrees each because B is directly north of both A and C (all northerly roads lead to the north pole at point B). This bizarre triangle has all three angles of 90 degrees. The angles here sum to 90+90+90 = 270 degrees.

No, the triangle sum theorem is not true on the surface sphere.

The triangle sum theorem states that, the sum of the three interior angles of any triangle is always 180°.

Given that, is the triangle sum theorem true on the surface sphere or not, so in relation to Euclid's geometry,

A statement that is equivalent to the parallel postulate is that there exists a triangle whose angles add up to 180°. Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere. The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.

Hence, there exists no such triangle on the surface of a sphere.

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Answer:

Step-by-step explanation:

f(4)=5

f(-1)=0

f(0)=1

F(2)=3

This problem is a classic example of applying the stars and bars combinatorial method.

To solve this problem, we need to distribute 23 identical objects into 7 distinct containers so that none of the containers is empty. Let's start by assuming that each container has at least one object. This means we have distributed 7 objects, leaving 16 objects to be distributed.

We can now use the stars and bars method to distribute these 16 objects. Imagine placing all 16 objects in a line, and placing 6 dividers between them to separate them into 7 groups (one for each container). Each group will then receive the objects that are to the left of the divider.

For example, if we have the sequence OO|OOO|O|OOO|OO|OO|O, this corresponds to 2 objects in the first container, 3 objects in the second container, 1 object in the third container, and so on.

The number of ways to place the 6 dividers in the sequence of 16 objects is the same as the number of ways to choose 6 positions out of 16 to place the dividers. This can be computed using the formula for combinations:

$${16 \choose 6} = \frac{16!}{6!(16-6)!} = 8008$$

Therefore, there are 8008 ways to distribute 23 identical objects into 7 distinct containers so that no container is empty.

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The area of the region enclosed by the curves y = 1, y = x, y = x^2, and x > 0 is 1/6 square units.

To find the area of the region enclosed by the given curves, we need to determine the points of intersection.

First, we find the intersection points of y = 1 and y = x^2. Setting these equations equal to each other, we have:

1 = x^2

Solving for x, we find x = 1.

Next, we find the intersection points of y = x and y = x^2. Setting these equations equal to each other, we have:

x = x^2

Rearranging the equation, we get x^2 - x = 0. Factoring out an x, we have x(x - 1) = 0. This gives us two solutions: x = 0 and x = 1.

Therefore, the region is bounded by x = 0, x = 1, y = 1, and y = x^2. To find the area of this region, we integrate the difference of the upper and lower curves with respect to x. The integral is given by:

A = ∫[0, 1] (x^2 - 1) dx

Evaluating this integral, we get A = 1/6 square units.

Hence, the area of the region enclosed by the given curves is 1/6 square units.

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Answer:

divide

Step-by-step explanation:

Answer: 3 ovals and 3 rectangles and an even amount of rectangles and ovals

Answer:

They are parallel

Step-by-step explanation:

You can tell that they are parallel because if you find the slope of it, you can see that they both have a slope of 2.

Hope this is the answer you were looking for. :)

Applying the equation of the model, y = 123.1(1.069)^x:

a. 150.4 thousand students

b. 467.5 thousand students

In the above problem given, we are told that the equation that models the the number of college students who studied abroad each year is: y = 123.1(1.069)^x, where:

The number of students from a country in thousands is represented as y

The number of years after 1998 is represented as x in the equation.

We can apply the equation for this model to solve the given problem as explained below:

a. 1998 to 2001 is 3 years. x = 3. Therefore, substitute x = 3 into y = 123.1(1.069)^x:

y = 123.1(1.069)^3

y = 150.4

Therefore, the number of students that are studying abroad in 2001 is about: 150.4 thousand.

b. 1998 to 2018 is 20 years. x = 20, therefore, substitute x = 20 into y = 123.1(1.069)^x:

y = 123.1(1.069)^20

y = 467.5

Number of students studying abroad in 2018 (y) is therefore about 467.5 thousand.

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Answer:

x= -11

Step-by-step explanation:

You would distribute the 2 to x and 3 which would make the equation 2x+6=-16. next, you would subtract 6 from both sides making it 2x=-22. you would then divide both sides by 2 to get x=-11

Answer:

x = -11

Step-by-step explanation:

I decided to start off by thinking, "What number multiplied by 2 equals -16?"

In this case, -8 would be the answer to that question.

Then, I solved the equation x + 3 = -8.

In this case, x would equal -11.

To check my answer, I solved the equation with x as -11.

-11 + 3 = -8, multiplied by 2, which equals -16.

Hope this helps.

Answer:

its d

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

The "quotient" is what you get after you divide 2 number, and in this case, you are dividing m/6.