A camera has a list price of
$
459.99
before tax. If the sales tax rate is
7.25
%
,
find the total cost of the camera with sales tax included.

Round your answer to the nearest cent, if necessary.

The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.

To find the solution to the initial value problem, we first need to solve the differential equation.

Taking the derivative of y(t), we get:

y'(t) = -2t + a

Taking the derivative again, we get:

y''(t) = -2

Substituting y''(t) into the differential equation, we get:

y''(t) + 2y'(t) + 10y(t) = 20sin(3t)

Substituting y'(t) and y(t) into the equation, we get:

-2 + 2a + 10(-2t + a) = 20sin(3t)

Simplifying, we get:

8a - 20t = 20sin(3t) + 2

Using the initial condition y(0) = 2, we get:

y(0) = -2(0) + a = 2

Solving for a, we get:

a = 2

Using the other initial condition y'(0) = 21, we get:

y'(0) = -2(0) + 2(21) + B = 21

Solving for B, we get:

B = -21

Therefore, the solution to the initial value problem is:

y(t) = -t^2 + 2t + 3sin(3t) - 1

Thus, we have e(t) = y(t) - 8, so

e(t) = -t^2 + 2t + 3sin(3t) - 9

and a = 2, B = -21.

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_____The given question is incomplete, the complete question is given below:

Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =

The given prescription lacks important information about the frequency and route of administration. Knowing how often a medication should be taken and how it should be administered is crucial for ensuring that patients receive the appropriate dose and achieve the desired therapeutic effect.

Without the frequency information of how (e.g., orally, intravenously, etc.) and when  (e.g., daily, twice daily, etc.)  to take medicine on prescription, patients may take the medication incorrectly or miss doses, potentially leading to ineffective treatment or adverse effects.

Healthcare providers should always provide clear and complete instructions for medication use to ensure patient safety and optimal treatment outcomes.

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The chance that both numbers drawn are even numbers is 8/21.

The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.

The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.

By the multiplication rule of probability, the probability of drawing an even number from both boxes is

(4/7) × (2/3) = 8/21

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Answer: c

Step-by-step explanation: i dont have one

1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .

An expression, as used in computer programming, is a grouping of values, variables, operators, and/or function calls that the computer evaluates to produce a final value. For instance, the equation 2 + 3 combines the numbers 2 and 3 using the + operator to produce the number 5. Similar to this, the equation x * (y + z) produces a value based on the current values of the variables x, y, and z by combining the variables x, y, and z with the * and + operators.

given

In terms of numbers, the phrase "one-half the difference of 6 and 8 hundredths and 2" is expressed as follows:

1/2 x (6.08 - 2) (6.08 - 2)

1/2 x (6.08 - 2) (6.08 - 2) is the correct numerical expression for "one-half the difference of 6 and 8 hundredths and 2 " .

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Answer:

971.8

Step-by-step explanation:

The expression (x < y) && (y == 5) is an alternative way of writing the original expression, and it will be true only if two conditions are met: first, x is smaller than y, and second, y is equal to 5.

The expression !(!(x < y) || (y != 5)) is equivalent to:

(x < y) && (y == 5)

To see why, let's break down the original expression:

!(!(x < y) || (y != 5))

= !(x >= y && y != 5) (by De Morgan's laws)

= (x < y) && (y == 5) (by negating and simplifying)

So, the equivalent expression is (x < y) && (y == 5). This expression is true if x is less than y and y is equal to 5.

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Complete question:

Assume that x and y have been defined and initialized as int values. The expression

!(!(x < y) || (y != 5))

is equivalent to which of the following?

(x < y) && (y = 5)

(x < y) && (y != 5)

(x >= y) && (y == 5)

(x < y) || (y == 5)

(x >= y) || (y != 5)

The experimental probability of winning the contest based on the data of all 3 games is 0.432.

What is experimental probability ?

Experimental probability is a measure of the likelihood of an event occurring based on the results of an experiment or observation. It is determined by dividing the number of times the event occurred by the total number of trials or observations. The more trials or observations conducted, the more accurate the experimental probability will be. Experimental probability is often used in situations where the probability of an event cannot be determined theoretically or where the theoretical probability is difficult to calculate. It is also commonly used in scientific experiments, market research, and other fields where the results of an experiment or observation can be used to make predictions or inform decisions.

Finding the experimental probability of winning the contest :
In this case, the event is winning the contest by choosing a marble from a bag, and the trials are the three games played by Hal.

Total number of players in all three games = 123 + 155 + 172 = 450

Total number of winners in all three games = 52 + 63 + 65 = 180

Experimental probability of winning the contest = Number of winners / Total number of players = 180/450 = 0.432

Therefore, the experimental probability of winning the contest based on the data of all 3 games is 0.432.

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The frequency in hertz of electromagnetic radiation which has a wavelength of 585nm is 5.13×10¹⁴ Hz.

The frequency(f) of electromagnetic radiation is related to its wavelength (λ) by the equation : f = c/λ;

Where, c = the speed of light in a vacuum, which is  3.00×10⁸ m/s.

So, to calculate the frequency of radiation with a wavelength of 585.0 nm, we need to convert the wavelength to meters:

⇒ 585.0 nm = 585.0×10⁻⁹ m;

Substituting the value in the above formula,

We get,

⇒ f = c/λ = 3.00×10⁸/(585.0×10⁻⁹)

⇒ 5.13×10¹⁴ Hz.

Therefore, the frequency of electromagnetic radiation is approximately 5.13 × 10¹⁴ Hz.

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In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.

In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v

We use the following formula to create a confidence interval around the population mean u:

CI = x ± z*(s/√n)

where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.

Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.

CI = 18.1 ± 1.96*(4.1/√34)

CI = 18.1 ± 1.96*(0.704)

CI = 18.1 ± 1.38

Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.

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By answering the presented question, we may conclude that Therefore, 1  expressions cm on the map corresponds to a real distance of 3.2 km. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Scale 1:

320000 means that 1 unit on the map represents his 320000 units in the real world.

To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.

1 kilometer = 100000 cm

So,

1 unit on the map = 320000 units in the real world

1 cm on the map = (1/100000) km in the real world

Multiplying both sides by 1 cm gives:

1 cm on the map = (1/100000) km * 320000

A simplification of this expression:

1 cm on the map = 3.2 km

Therefore, 1 cm on the map corresponds to a real distance of 3.2 km. 

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The cylindrical has a surface area of 414 square units due to its 9-unit radius and 14-unit height.

A cylinder is a three-dimensional geometric form made up of two circular bases that are parallel to one another and are joined by a curved lateral surface. It can be pictured as a solid item with a constant circular cross-section along its entire length. The measurements of a cylinder, such as the radius and height of the circular bases, affect its characteristics. The surface area, volume, and horizontal surface area of a cylinder are some of its typical characteristics. Mathematical formulas can be used to determine these properties.

given

The following algorithm determines a cylinder's surface area:

[tex]A = 2\pi r^2 + 2\pi rh[/tex]

where r is the cylinder's base's radius, h is the cylinder's height, and (pi) is a mathematical constant roughly equivalent to 3.14.

Inputting the numbers provided yields:

[tex]A = 2\pi (9)^2 + 2\pi (9)(14)\\[/tex]

A = 2π(81) + 2π(126) 

A = 162π + 252π

A = 414π

The cylindrical has a surface area of 414 square units due to its 9-unit radius and 14-unit height.

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Answer:

[tex]a = \frac{20}{3}[/tex]

Step-by-step explanation:

Answer:

the answer would be 100 I guess

There are 792 strings across a,b, and 27,720 in a,b,c.

(a) We must select five slots for a's in an alphabet of "a,b" before filling the remaining spaces with "b's." Hence, the binomial coefficient is what determines how many strings of length 12 that include precisely five as:

C(12,5) = 792

As a result, there are 792 distinct strings of length 12 that include exactly five a's across the letters a, b.

(b) We may use the same method as before for an alphabet consisting of the letters "a,b,c." The first five slots must be filled with a's, followed by three b's, and the final four positions must be filled with c's. The number of strings of length 12 that contain exactly five a's across the letters "a," "b," and "c" is thus given by:

C(12,5) * C(7,3) = 792 * 35 = 27720

Thus, there are 27,720 distinct strings.

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Answer: 37.5

Step-by-step explanation:

75 - 180 = 105

105 degrees = the obtuse angle, bottom triangle.

75/2= 37.5 (since both sides of the bottom triangle are equal angles)

The value of the equation (fxg)(-1) is 10.

An equation is a mathematical statement that shows that two expressions are equal. It usually includes variables, which are represented by letters or symbols, and constants, which are fixed values.

There are several types of equations in mathematics. Here are some of the most common types:

Linear equation: An equation of the form "ax + b = c", where "a", "b", and "c" are constants and "x" is the variable. The graph of a linear equation is a straight line.Quadratic equation: An equation of the form "ax² + bx + c = 0", where "a", "b", and "c" are constants and "x" is the variable. The graph of a quadratic equation is a parabola.

Cubic equation: An equation of the form "ax³ + bx² + cx + d = 0", where "a", "b", "c", and "d" are constants and "x" is the variable. The graph of a cubic equation is a curve that can have one or two humps.

In the given question,

To find (f x g)(-1), we need to evaluate the product of f(-1) and g(-1).

First, we find f(-1):

f(-1) = -3(-1) - 1 = 2

Next, we find g(-1):

g(-1) = -1 - 4 = -5

Now, we can find the product (f x g)(-1):

(f x g)(-1) = f(-1) x g(-1) = 2 x (-5) = -10

Therefore, (f x g)(-1) = -10.

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Answer:

3:30

Step-by-step explanation:

We know

Jeni put a cake in the oven at 2:30. The cake takes 1 hour to bake.

What time should it be taken out of the oven?

We take

2:30 + 1 = 3:30

So, it should be taken out of the oven at 3:30

Answer:

x²

Step-by-step explanation:

[tex]{ \tt{ \frac{ {x}^{ - 3} . {x}^{2} }{ {x}^{ - 3} } }} \\ \\ \dashrightarrow{ \tt{x {}^{( - 3 + 2 - ( - 3))} }} \\ \dashrightarrow{ \tt{ {x}^{( - 3 + 2 + 3)} }} \: \: \: \: \\ \dashrightarrow{ \boxed{ \tt{ \: \: \: \: {x}^{2} \: \: \: \: \: \: }}} \: \: \: \: [/tex]

Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.

The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.

To calculate the percentage difference, we can use the formula:

% difference = (difference ÷ original value) x 100%

In this case, the difference is $1.50, and the original value is $10.00.

% difference = ($1.50 ÷ $10.00) x 100%

% difference = 0.15 x 100%

% difference = 15%

Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.

Step-by-step explanation:

The required probability of W being greater than 6 is 0.065 or 6.5%.

A probability value represents the likelihood that an occurrence will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.

The complement of an event A is the event that A does not occur. In this case, the event A is "W ≤ 6", and its complement is "W > 6".

We are given that P(W ≤ 6) = 0.935. Using the complement rule of probability, we can find the probability of W > 6 as follows:

[tex]$$P(W > 6) = 1 - P(W \leq 6)$$[/tex]

Substituting the given value, we have:

P(W > 6) = 1 - 0.935 = 0.065

Therefore, the probability of W being greater than 6 is 0.065 or 6.5%.

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Answer:

57

57

123

123

57

57

123

that's all.

Answer:

m<1 = 57°

m<2 = m<1 = 57°

m<3 = x = 123°

m<4 = x = 123°

m<5 = m<1 = 57°

m<6 = m<5 = 57°

m<7 = m<4 = 123°

Step-by-step explanation:

[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]

As the two triangles are congruent to each other, using that we can get the value of x = 13 and y = 9.

Whether two or more triangles are congruent depends on the size of the sides and angles. As a result, a triangle's three sides and three angles determine its size and shape.

Two triangles are said to be congruent if their respective side and angle pairings are both equal.

Now in the given question,

The triangles are congruent so,

ED = QR

5y -7 = 38

⇒ 5y = 38+7

⇒ y = 45/5

⇒ y = 9

Now as the sum of angles in a triangle are 180°,

∠E +∠D +∠F = 180°

⇒ ∠F = 180 - 123 - 29

⇒ ∠F = 28°

As per congruency,

(2x+2) ° = 28°

⇒ 2x = 28-2

⇒ x = 26/2

⇒ x = 13

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The complete question is:

Find the values of x and y. ADEF = AQRS

(5y-7) ft

D

E

123⁰

F

S

S

(2x + 2)° R

= 0, y =

Q

38 ft

P

Answer:

30, rational

Step-by-step explanation:

[tex]3\sqrt{20}\cdot\sqrt{5}=3\sqrt{4}\sqrt{5}\cdot\sqrt{5}=(3\cdot2)\cdot5=6\cdot5=30[/tex]

The result is rational because it can be written as a fraction of integers.

Answer:

V=lwh

=2×2×2=8

720÷8=90

90 cubes

In the diagram given IJK≅LJK ,the length cannot be negative, the only valid solution is g = 6. Therefore, the length of the segment KJ is 6 meters.

Length is a physical dimension that measures the distance between two points or the size of an object along one dimension.

It is commonly measured using standard units of length such as meters, feet, inches, and centimeters.

Given that KM is the bisector line of line IM and J is the bisector point on line IL. Two triangles are formed, △IJK and △LJK, on line IL in the upward and downward direction, respectively. We are given the lengths of IK, JN, LM, and KJ, and we need to find the value of g such that IJK≅LJK.

Since the two triangles are similar, their corresponding sides are proportional. Using the side proportionality theorem, we have:

KJ/LM = IJ/JL

Substituting the given values, we get:

g/10 = 5/(4+g)

Cross-multiplying, we get:

g(4+g) = 50

Expanding and simplifying, we get:

g²+ 4g - 50 = 0

Using the quadratic formula, we get:

g = (-4 ± √(4² + 4(50)))/2

g = (-4 ± √(256))/2

g = (-4 ± 16)/2

g = -10 or g = 6

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Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value of the annuity

PMT = payment (or deposit) made at the end of each compounding period

r = annual interest rate

n = number of compounding periods per year

t = number of years

In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:

Marcia wants to retire in 15 years (when she is 65), so t = 15

The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2

Marcia wants to have $90,000 in her retirement account

Substituting these values into the formula, we get:

$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)

Simplifying the formula, we get:

PMT = $90,000 / [(1.025)^30 - 1] / 0.025

PMT = $90,000 / 19.7588

PMT = $4,553.39 (rounded to the nearest cent)

Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.

Answer:

To multiply a whole number and a fraction, we can simply multiply the whole number with the numerator of the fraction and keep the denominator the same.

So, 3 x 3/5 = (3 x 3)/5 = 9/5

Therefore, 3 x 3/5 = 9/5.

Answer:

Step-by-step explanation:

9x/5

Step-by-step explanation:

Please mark as brainliest

The set of all x-values that are at a distance of 13 or less from the number 8 in the interval notation is given by  [ -5, 21 ].

The distance between x and 8 is |x - 8|.

Find all the values of x such that |x - 8| ≤ 13.

This inequality can be rewritten as follow,

|x - 8| ≤ 13

⇒ -13 ≤ x - 8 ≤ 13

Now,

Adding 8 to all sides of the inequality we get,

⇒  -13 +  8 ≤ x - 8 + 8 ≤ 13 + 8

⇒ -5 ≤ x ≤ 21

Therefore, all the x-values which are at a distance of 13 or less from the number 8 represented in the interval notation as [ -5, 21 ].

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Answer:

A

Step-by-step explanation:

because___________________________________

Answer:

B) True

Step-by-step explanation:

SSS or Side-Side-Side is used to prove two triangles are congruent.