Hannah bought a grandfather clock online. It cost $898 plus3 0%shipping and handling. What was the total cost?

f(x) = (x - 3)/(x + 2)

As the equation is basically a fraction the only thing that can be out of domain is if the denominator is equal to 0, so let's see when the denominator can be 0

x + 2 = 0

x = -2

So -2 is out of domain and all the other numbers are inside the domain.

Answer:

\(-2 \implies \sf no\)

 \(0 \implies \sf yes\)

 \(3 \implies \sf yes\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{x-3}{x+2}\)

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

A rational function is not defined when its denominator is zero.

Therefore, to find when the given function f(x) is not defined, set the denominator to zero and solve for x:

\(x+2=0 \implies x=-2\)

Therefore, the domain is restricted to all values of x except x = -2.

This means that the domain of f(x) is (-∞, 2) ∪ (2, ∞).

In conclusion:

The radius of the circle will be \(\sqrt{22}\).

In our question, we shall first extend QRS to the circle's point T.

According to the power of a point.

\(QP^{2}\)  =  QR*QT

\(6^{2}\)  =  3*QT

QT = 12

Since QR = 3, RT = 9.

Since RS = 3, ST = 6.

Draw OT and OR, creating a triangle(TSO) and triangle(RSO).

OT and OR are radii, Let the radius be r.

Use the Law of Cosines on these two triangles.

OT2  =  \(r^{2}\)  =  \(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)

OR2  =  r2  =  \(3^{2}\) + \(2^{2}\) - 2*3*2*cos(RSO)

Since these are equal:

\(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)  =  \(3^{2}\) + \(2^{2}\) - 2*3*2*cos(RSO)

40 - 24*cos(TSO)  =  13 - 12*cos(RSO)

Since angle(RSO) is supplementary to angle(TSO),  cos(RSO) = - cos(TSO)

40 - 24*cos(TSO)  =  13 + 12*cos(TSO)

27  =  36*cos(TSO)

0.75  =  cos(TSO)

Since  \(OT^{2}\)  =  \(r^{2}\)  =  \(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)

\(r^{2}\)  =  40 - 24*0.75  

\(r^{2}\)  =  22

r  =  \(\sqrt{22}\)

Hence the radius of the given circle will be \(\sqrt{22}\).

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Answer:

I am not sure if this is correct but I think it is A

Step-by-step explanation:

Answer:

25y^2 -20iy + 4i^2

Step-by-step explanation:

Theres an acronymn called Foil (first, ouside, inside, last) for expanding an expression like that

For this expression:

= (5y - 2i) (5y - 2i)

= 25y^2 - 10iy - 10iy + 4i^2

= 25y^2 -20iy + 4i^2

This is assuming that "i" is not the imaginary number "i"

Answer:

I guess the answer is x=0.2/45

Answer:

bom é a soma dos algarismos se for matemática

The approximate probability that the sample mean will be greater than 63 is 0.0885, rounded off to the second decimal place.

What is Central Limit Theorem?

The Central Limit Theorem (CLT) is a fundamental concept in statistics and probability theory. It states that, under certain conditions, the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To find the approximate probability that the sample mean will be greater than 63, we can use the Central Limit Theorem. The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution.

In this case, since the sample size is 58 (which is reasonably large), we can use the normal distribution to approximate the probability.

First, we need to calculate the standard error of the sample mean, which is the standard deviation of the population divided by the square root of the sample size:

Standard Error (SE) = Standard Deviation (σ) / √Sample Size (n)

SE = 17 / √58 ≈ 2.2271

Next, we can standardize the sample mean using the formula:

Z = (Sample Mean - Population Mean) / Standard Error

Z = (63 - 60) / 2.2271 ≈ 1.3488

Now, we need to find the probability of Z being greater than 1.3488 using the standard normal distribution table or a statistical calculator. Looking up the corresponding probability, we find that it is approximately 0.0885.

Therefore, the approximate probability that the sample mean will be greater than 63 is 0.0885, rounded off to the second decimal place.

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Answer:

The angles are adjacent. x = 100°

Step-by-step explanation:

x + 80 = 180

x = 100

Answer:

10y^2 + 39y + 35

Step-by-step explanation:

Simplify using FOIL

We can see here that the ratio of  raccoons to total animals is: B. 4:6

We can define ratio in mathematics as a division-based comparison of two numbers or quantities. It conveys how big or much one quantity is in proportion to another.

A fraction is a common way to express ratios, with the first number denoting how much of the first quantity there is, and the second number denoting how much of the second quantity there is.

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The required line representing the equation part of the constraint is go through (0, 4) and (7,0).

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The line representing the equation 7x1 + 4x2 = 28 is a boundary line that separates the feasible solutions from the infeasible solutions in a linear programming problem.

The line passes through two points, which can be determined by substituting the x1 and x2 values into the equation. By substituting the values (4,0) and (7,0) into the equation, we can see that both points satisfy the constraint.

This means that any point on the line also satisfies the constraint, and any point above or to the right of the line would be infeasible as they would not meet the requirement of the constraint.

Understanding the position and shape of the constraint lines is important in solving linear programming problems and finding the optimal solution.

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The value of $5,000 after 5 years with a 5% interest rate compounded quarterly will be approximately $6,381.41.

To calculate the future value of an investment with compound interest, we can use the formula: FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount (P) is $5,000, the interest rate (r) is 5% (or 0.05), the compounding is done quarterly, so n is 4, and the investment period (t) is 5 years. Plugging these values into the formula, we get FV = 5000(1 + 0.05/4)^(4*5) ≈ $6,381.41.

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Answer:

y = 0x - 5 or just y = -5

Step-by-step explanation:

use the slope intercept equation

y2 - y1

x2 - x1

- 5 - 9 = 14

-3 + 3 = 0

14 / 0 = 0

so the slope is undefined

take one of the points (let's use -3, -5) and plug that in the slope intercept form (y = mx+b)

so -5 = 0(-3)+b

0 • 3 = 0 so the b (or y intercept) equals -5

so the equation is y = -5

Answer:

Step-by-step explanation:

To solve this problem, we can start by analyzing the forces acting on the barge. There are two forces involved: the tension in the tow ropes and the resistance to motion.

1. Tension in the first tow rope:

The tension in the first tow rope is given as 1800 N, and it makes an angle of 20° with the direction of motion. Let's call this angle θ1 = 20°.

2. Tension in the second tow rope:

The tension in the second tow rope is given as 1650 N, and it makes an angle of xº with the direction of motion. Let's call this angle θ2 = xº.

Now, let's analyze the forces along the direction of motion:

1. Tension force along the first tow rope:

The component of the tension force along the direction of motion is T1cos(θ1).

2. Tension force along the second tow rope:

The component of the tension force along the direction of motion is T2cos(θ2).

The net force along the direction of motion is equal to the mass of the barge multiplied by its acceleration:

Net force = mass × acceleration

Since the acceleration is given as 0.6 m/s² and the mass is 4 tonnes (which is equivalent to 4000 kg), we have:

Net force = 4000 kg × 0.6 m/s²

Net force = 2400 N

Now, we can equate the net force to the sum of the tension forces along the direction of motion:

T1cos(θ1) + T2cos(θ2) = 2400 N

Substituting the given values:

1800cos(20°) + 1650cos(xº) = 2400

Simplifying the equation, we can solve for x:

1800cos(20°) + 1650cos(xº) = 2400

cos(xº) = (2400 - 1800cos(20°)) / 1650

xº = arccos((2400 - 1800cos(20°)) / 1650)

Using a calculator, we can find the value of xº.

To find the resistance to motion of the barge, we need to find the total force opposing the motion, which is the sum of the tension forces perpendicular to the direction of motion:

1. Tension force perpendicular to the first tow rope:

The component of the tension force perpendicular to the direction of motion is T1sin(θ1).

2. Tension force perpendicular to the second tow rope:

The component of the tension force perpendicular to the direction of motion is T2sin(θ2).

The resistance to motion is equal to the sum of these perpendicular tension forces:

Resistance = T1sin(θ1) + T2sin(θ2)

Substituting the given values, we can calculate the resistance to motion.

Step 1

Multiple both fractions

Step 2

Multiply numerator with numerator and denominator with denominator.

Final answer

Answer 1:

D. 24 sq feet

The formula to find surface area of a cube is \(a=6a^{2}\)

Substitute 2 for a, \(2^{2} = 4\)

6 x 4 = 24, so 24 sq feet

Answer 2:

B. 62 sq feet

The formula to find surface area of a rectangular prism is \(a = 2(wl+wh+hl)\)

Substitute 3 for w, 5 for l, 2 for h and multiply

a = 62 sq feet

Answer 3:

C. 1296 sq inches

The formula to find surface area of a rectangular prism is \(a = 2(wl+wh+hl)\)

Substitute 24 for w, 12 for l, 10 for h and multiply

a = 1296 sq inches

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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The area of the region bounded by the graphs of x = y2 - 2 and x = y - 2 on the interval [-2, -1] is:

Based on the options provided, the closest approximation is: 0.15 sq units

To find the area of the region bounded by the graphs of the given equations on the interval [-2, -1], we need to calculate the definite integral of the difference of the two equations over that interval.

Let's proceed with the calculation:

First, let's find the points of intersection between the curves x = y² - 2 and x = y - 2.

Setting the equations equal to each other:

y² - 2 = y - 2

Rearranging the equation:

y² - y = 0

Factoring out y:

y(y - 1) = 0

This equation gives us two solutions: y = 0 and y = 1.

Now, we need to integrate the difference of the two equations over the interval [-2, -1] to find the area:

Area = ∫[-2, -1] (f(x) - g(x)) dx

Here, f(x) = y² - 2 and g(x) = y - 2.

To express the equations in terms of x, we solve for y:

From the first equation:

x = y² - 2

y² = x + 2

y = ±√(x + 2)

From the second equation: x = y - 2

y = x + 2

Now, let's calculate the area:

Area = ∫[-2, -1] ((√(x + 2)) - (x + 2)) dx

Evaluating this integral will give us the area of the region bounded by the two curves on the given interval.

This integral does not have a simple closed-form solution and requires numerical methods for evaluation.

Using numerical methods like the trapezoidal rule or Simpson's rule, we can approximate the area.

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Answer:36 weeks

Step-by-step explanation:

1757/50=35.1

Answer:

18 x 9 = 162

Step-by-step explanation:

Based solely on the mileage of the Eurovan, it is likely to be in above-average condition.

The condition of a vehicle is influenced by several factors, including mileage, maintenance history, usage, and overall care. While high mileage can generally indicate wear and tear on a vehicle, it does not necessarily imply poor condition. Eurovans are known for their durability and reliability, so even with 81,718 thousand miles, it is possible for the van to be in above-average condition.

To determine the true condition of the Eurovan, additional information beyond mileage is required. Factors such as regular maintenance, service records, and the overall care provided by the previous owner(s) play a crucial role in assessing the van's condition. If the van has been well-maintained, with routine servicing and repairs, it is more likely to be in above-average condition despite the higher mileage. Additionally, the overall usage of the van should be considered. If the majority of the mileage consists of long highway trips rather than stop-and-go city driving, it can contribute to less wear and tear on the engine and components. Furthermore, factors such as storage conditions, accident history, and the quality of the driving surface can also impact the condition of the Eurovan.

In summary, while the mileage of the Eurovan may initially suggest a below-average condition, it is essential to consider additional factors such as maintenance history, usage patterns, and overall care to make a more accurate assessment. Without this additional information, it is reasonable to assume that the Eurovan is likely to be in above-average condition based on its reputation and durability.

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Answer: 8

Step-by-step explanation: in this problem n=3 so you are to substitute 3 in for the variable n.

3*2+2

3*2=6

6+2=8

g(3)=8

Hope this helps (^_^)

Answer:

8

Step-by-step explanation:

g(3) means to plug 3 in as the n-value

g(3)= (3)2+2

=6+2

g(3)=8

\(\text {Hello! The answer to your problem is j=-13}\)

\(\text {Subtract 4j:}\\\text {6j+16-4j=4j-10-4j}\\\text {2j+16=-10}\)

\(\text {Subtract 16:}\\\text {2j+16-16=-10-16}\\\text {2j=-26}\)

\(\text {DIVIDE both sides by 2:}\\\text {2j/2=-26/2}\\\text {x=-13}\)

\(\text {Hope this helps!}\\\\\text {-LimitedX}\)

Answer:

It equals poop in the face.

Step-by-step explanation:

Good-Bye poopy face.

To determine if the experimental probability for getting a 6 is close to the theoretical probability, we need to compare the observed frequency of rolling a 6 to the expected probability based on a fair six-sided die.

In the given list of rolls, we have a total of 20 rolls. To calculate the experimental probability of rolling a 6, we count the number of times a 6 appears and divide it by the total number of rolls.

From the list, we can see that a 6 appears 6 times. Therefore, the experimental probability of rolling a 6 is:

Experimental probability = Number of 6's / Total number of rolls = 6/20 = 0.3

Now let's compare this experimental probability to the theoretical probability. In a fair six-sided die, each face has an equal chance of occurring, so the theoretical probability of rolling a 6 is 1/6 ≈ 0.1667.

Comparing the experimental probability of 0.3 to the theoretical probability of 0.1667, we can see that the experimental probability is higher than the theoretical probability for rolling a 6.

Therefore, the statement "the experimental probability for getting a 6 is close to the theoretical probability" is false. The experimental probability is higher than the theoretical probability in this case.

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Answer:  Graph D (bottom right corner)

======================================================

Explanation:

The equation y = 3x+3 is in slope intercept form y = mx+b

m = 3 = slope

b = 3 = y intercept

In this case, both the slope and y intercept are the same (though in general they tend not to be).

The positive slope value means the line goes uphill as you move from left to right. The positive y intercept means the diagonal line crosses the y axis somewhere above the horizontal x axis. Specifically, it crosses the y axis at y = 3

Graph D is the only graph that has such a line on it. Graphs A, B and C have the positive slope line where they have a negative y intercept, so we can rule them out.

You can use graphing tools such as Desmos or Geogebra to help confirm this answer. You could also make a table of values, and plot each point, to form the lines. Two points is the minimum amount needed to form any line.

Answer:

Step-by-step explanation:

Answer:

See picture attached below.

Step-by-step explanation:

To graph the system, graph each line separately.

y = 3x + 3 ha slope 3 and y-intercept 3.

Start at 3 on the y-axis and mark a point. Then from this point move up 3 units and to the right 1 unit. Mark a point and connect.

y=-x - 3 has slope -1 and y-intercept -3.

Start at -3 on the y-axis and mark a point. Then from this point move down 1 unit and to the right 1 unit. Mark a point and connect.

This graph is represented in the picture attached.

...............................................................................................................................................

Which graph represents the following system of equations?

y = 3x + 3

y = –x – 3

...............................................................................................................................................

y=x−8

​y=12x−5​

...............................................................................................................................................

Graph of 2 lines that intersect at one point. Both lines are solid. One line passes through (-2,2) and (0,3) and is shaded below the line.

y < = 1/2x + 3...(-2,2)                y < = 1/2x + 3....(0,3)

2 < = 1/2(-2) + 3                        3 < = 1/2(0) + 3

2 < = -1 + 3                                3 < = 0 + 3

2 < = 2 (correct)                        3 < = 3 (correct)

The other line passes through points (0,1) and (1,-2) and is shaded above the line.

y > = -3x + 1...(0,1)            y > = -3x + 1...(1,-2)

1 > = -3(0) + 1                   -2 > = -3(1) + 1

1 > = 0 + 1                         -2 > = -3 + 1

1 > = 1 (correct)                 -2 > = -2 (correct)

...............................................................................................................................................

we have

using a graph tool

see the attached figure

The solution of the system is the shaded area

we know that

The line is solid

The line passes through points  and  and is shaded above the line.

The line is solid

The line passes through points  and  and is shaded below the line

The two lines intersect at one point

therefore

the answer is the option

B) Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.

Answer:

a d

Step-by-step explanation:

maybe

The parameters to the Poisson distribution, to find the probability of exactly 3 arrivals in one thousandth of a​ minute, are given as follows:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute, hence the mean of the distribution is given as follows:

μ = 6000/13719.

The parameter x represents the number of arrivals in each thousandth of a minute, hence it is given as follows:

x = 3.

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The statement which is true about the two equilateral triangles is b)The two triangles are the same shape but not the same size. So, correct option is b.

In calculation, a symmetrical triangle is a triangle where every one of the three sides have a similar length. In the natural Euclidean calculation, a symmetrical triangle is likewise equiangular; that is, every one of the three inward points are additionally compatible to one another and are each 60°. It is likewise an ordinary polygon, so it is additionally alluded to as a normal triangle.

Some of hypotheses which are made sense of utilizing symmetrical triangle:

The side length of the primary symmetrical triangle is 3 inches.The side-length of the second symmetrical triangle is 4 inches.Since both the triangles are symmetrical triangles, in this way they have same shape.

Be that as it may, the two triangles have different side lengths in this way they have different size.

Hence, option b is correct.

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(Complete question) is:

on a piece of paper, use a protractor and a ruler to construct two equilateral triangles: one with a side length of 3 inches and one with a side length of 4 inches. which statement is true about the two triangles?

a. The two triangles are the same size but not the same shape.

b. The two triangles are the same shape but not the same size.

c. The two triangles are the same size and same shape.

d. It is impossible to construct equilateral triangles with these side lengths.

Answer:

  f(–6) = 10

Step-by-step explanation:

Each ordered pair represents the pair (x, f(x)).

The domain (set of possible x-values) is the list of first numbers in the pairs:

  {8, 0, 1, 2, -6}

Any number not on this list will not appear as x in f(x). This eliminates f(-3) and f(3).

The pair for f(8) is (8, -3), so f(8) = -3, not 0.

The pair for f(-6) is (-6, 10), so f(-6) = 10, as shown in the last answer choice.

Answer:

D           f(–6) = 10

Step-by-step explanation:

I took the test and wanted to help people who are struggling.

(–6, 10)} matches f(–6) = 10 therefor it is correct