the dollar value v (t) of a certain car model that is t years old is given by the following exponential function

v (t) = 27,500(0.84)^t

find the initial value of the car and the value after 12 years. round your answer to the nearest dollar necessary.

There is a 15.47% chance of selecting a red marble from the urn without looking.

The probability of choosing a red marble from the urn is expressed by the following formula:

P(Red Marble) = Number of Red Marbles / Total Number of Marbles

In this case, we are dealing with 13 red marbles, 33 blue marbles, and 38 yellow marbles. Therefore, the probability of choosing a red marble is 13/84, or 15.47%. We can calculate this by dividing the number of red marbles (13) by the total number of marbles (84). This means that there is a 15.47% chance of selecting a red marble from the urn without looking.

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In complex number,  that x ranges from -5 to -1/2 and the correct option is (-∞, -1/2)

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation [tex]{\displaystyle i^{2}=-1};[/tex]

every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes.

Given that,

|P| = 3x + 2

|Q| = 2x + 1

P+Q = -2

We know that, from Cauchy inequalities

|P| + |Q| > |P+Q|

3x + 2 + 2x + 1 > - 2

5x + 3 > - 2

subtract both side by 3

5x > -5

Divide both side by 5

x > -1 first condition

Note that,

|P| > 0

Then,

3x + 2 > 0

3x > -2

x > -2/3

Also,

|Q| > 0

2x + 1 > 0

2x > -1

x > -1/2

So, comparing the three conditions

We see that x ranges from -5 to -1/2, this range covers all the other ranges

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The transformations are composed so that the sides of triangles are in the ratio of 1/2 and the angles are equal.

Similarity transformations are a sort of mathematical transformation that preserves the length ratios of related lines in a figure. Among these transformations are:

A translation is the movement of a figure in a given direction without affecting its size or shape. The combination of two translations results in a single translation equal to the total of the distances travelled.

A rotation is a transformation that involves turning a figure around a fixed point known as the center of rotation. The combination of two revolutions results in a single rotation equal to the total of the angles of rotation.

A reflection is a transition that occurs when a figure is flipped over a line known as the line of reflection. The combination of two reflections is simply a single 180-degree rotation.

Dilation: A dilation is a transformation that enlarges or reduces a figure by a given scale factor, centered at a fixed point. The product of two dilations is a single dilation equal to the product of the scale factors.

Here,

The sides of triangles are in ratio.

4/8=6/3=1/2

The composition of transformations is the sides of triangles are in ratio of 1/2 and angles are equal.  

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The probability that both cards are aces is 0.45%.

Given that,

A standard 52-card deck is used to deal two cards. In other words, two cards are uniformly and randomly sampled without being replaced.

There are four aces in the deck of 52 cards. The likelihood of drawing an ace when you draw a card is 4/52=1/13.

There are only 51 cards left when the second card is drawn, and since an ace has already been drawn, just 3 of those cards are still in the deck. Therefore, there is a 3/51 chance of drawing the second ace. The likelihood that both of these events occur is 1/13 x 3/51 = 0.00452. (approx). Thus, there is a 0.45% chance of drawing two aces.

Combinations and permutations offer a different perspective on this. There are 52C2 different methods to choose two cards from a deck. The entire sample space is shown here.

Therefore, the probability that both cards are aces is 0.45%.

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A carousel with a 45-foot diameter makes 3 revolutions per minute. (a) The angular speed is 6π rad/minute. (b) The linear speed is 424 feet per minute.

Information available in the problem:

diameter of the carousel = d = 45 feet

The carousel makes 3 revolutions per minute.

a) 1 revolution = 360⁰ = 2π radians

angular speed = 3 rev/minute

angular speed = 3 x 2π radians/minute = 6π rad/minute

b) the distance travelled in a revolution is equal to the circumference of the carousel.

Circumference of carousel = πd = 45π feet

Linear speed = 3 rev/minute = 3 x 45π  feet/minute

Linear speed = 424 feet per minute.

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The 85% confidence interval for the mean time at lunch is (31.84, 39.36) minutes.

In a random sample of fourteen people, the mean time at lunch was 35.6 minutes.

Standard deviation of 8.2 minutes.

A common method to calculate the confidence interval for the mean of a normal distribution is to use the Z-score. For a 85% confidence interval, the Z-score is 1.44. Therefore, the confidence interval can be calculated as:

The confidence interval formula in statistics is used to describe the amount of uncertainty associated with a sample estimate of a population parameter.

Where,

n= Number of terms

[tex]$\overline{\mathrm{x}}[/tex]= Sample Mean

[tex]$\sigma[/tex]=Standard Deviation

[tex]$z_{\alpha / 2}[/tex]= Value corresponding to a2 in z table

[tex]$t_{\alpha / 2}[/tex]= Value corresponding to a2 in t table

[tex]$\alpha[/tex]=(1 - Confidence Level /100)

So for the given data, the confidence interval would be:

35.6 ± 1.44 * 8.2 / √14

35.6 ± 1.44 * 8.2 / 3.74

35.6 ± 3.76

Therefore, the 85% confidence interval for the mean time at lunch is (31.84, 39.36) minutes.

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Answer:

60.83 percent hope it helps

The function represents the exponential decay. And the rate of change is 20%.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

y = a (1 ± r)ˣ

The exponent function is given below.

[tex]\rm m(t) = \left ( \dfrac{4}{5} \right)^t[/tex]

Compare the equation with the standard form. Then we have

If the value of the 1 - r is less than 1, then the rate is decaying.

1 - r = 4/5

r = 1 - 4/5

r = 1/5

r = 0.20 or 20%

The function represents the exponential decay. And the rate of change is 20%.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Square inches formula is: }\\\\\large\boxed{\mathsf{l}\rm{ength}\times\mathsf{h}\rm{eight} = \mathsf{s}\rm{quare \ inches}}}}}}}[/tex]

[tex]\huge\text{So, your equation should look like:}[/tex]

[tex]\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}[/tex]

[tex]\huge\text{Now let us solve for your answer to this problem:}[/tex]

[tex]\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}[/tex]

[tex]\large\boxed{\mathsf{24\ inches\times 14\ inches = square\ inches^2}}[/tex]

[tex]\large\boxed{\mathsf{336 = square\ inches^2}}[/tex]

[tex]\huge\text{Therefore, your answer SHOULD be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ D. \ 336}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Below

Step-by-step explanation:

3/8 h = - 9    multiply both sides of the equation by   8/3

h = - 9 * 8/3 = - 24

The right answer is C, which means "number of square feet in area equals number of feet in perimeter."

A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. A rectangle is a quadrilateral with equal and parallel opposite sides. It is a four-sided polygon with four angles of 90 degrees. A rectangular form is two-dimensional. A rhombus is a quadrilateral with all sides the same length and both pairs of opposing sides parallel. The term rhomb is occasionally used instead of rhombus, and a rhombus is also known as a diamond.

Here,

area=6*3

=18 units

perimeter=2*(6+3)

=18 units

area=perimeter

The correct option is C that is "number of square feet in area is equal to number of feet in perimeter."

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Converting the binary (base-10) number 77₁₀ to decimal (base-2) gives 1001101₂.

In Mathematics, there are four (4) main types of number system and these include the following:

In this exercise, you're required to convert the given number in base 10 to base 2 and this can be done as follows:

2 | 77

2 | 38 R 1

2 | 19 R 0

2 | 9 R 1

2 | 4 R 1

2 | 2 R 0

2 | 1 R 0

2 | 0 R 1

Next, you would read the decimal number (base-2) upward and this gives:

77₁₀ = 1001101₂.

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When the potential costs of production are constant, the cost of creating one thing remains constant regardless of how much of that good is produced. This is also known as continuous returns to scale.

The term "constant" has several meanings in mathematics. It refers to non-variance as an adjective; as a noun, it has two meanings: A constant and well-defined integer or other mathematical object that does not change. A constant is a value or number whose expression never changes; it is always the same.

Here,

In this case, increasing the production of one good will result in a proportionate rise in the overall cost of production rather than an increase or decrease in the opportunity cost of producing that good. For example, if a corporation manufactures chairs and tables and the opportunity cost of manufacturing one chair is always two tables, the cost of making two chairs is four tables, the cost of producing three chairs is six tables, and so on.

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Functions f(x) and g(x) has same vertex and axis of symmetry. Therefore, option C and D are the correct answers.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(x)= -1/2 x² and f(x)=x².

Graph of g(x):

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex: (0,0)

Focus: (0,-1/2)

Axis of Symmetry: x=0

Directrix: y=1/2

Graph of f(x):

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (0,0)

Focus: (0,1/4)

Axis of Symmetry: x=0

Directrix: y= -1/4

Therefore, option C and D are the correct answers.

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Step-by-step explanation:

24×-1=

-24ans

and that's the answer

The area of the sector is 12π square units.

Given data:

To find the area of the sector, use the formula:

[tex]\text{Area of Sector} = \frac{\text{Central Angle} }{ 360^\circ} * \pi * r^2[/tex]

Given that the central angle is 120° and the radius is 6 units.

Substitute these values into the formula:

[tex]\text{Area of Sector} = \frac{120^\circ }{ 360^\circ} * \pi * 6^2[/tex]

[tex]A = \frac{1}{3} * \pi * 36[/tex]  square units

A = 12π square units

Hence, the area of the sector is 12π square units.

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a) The distance of the boat from its starting point is 20 km.

b. The nearest degree  is 63°

c. The bearing g that the boat should travel on to return to the starting point is 360° - 63° = 297°.

To find the distance of the boat from its starting point, we can use the Pythagorean theorem.

x^2 + y^2 = d^2

Substituting the values for x and y, we get:

12^2 + 16^2 = d^2

d^2 = 144 + 256

d^2 = 400

d = 20

Hence, the distance of the boat from its starting point is 20 km.

b) To find the bearing that the boat should travel on to return to the starting point, we must calculate the angle between the two legs of the journey.

b = arctan (y / x) = arctan (16 / 12) = 63.43°

To the nearest degree  is 63°.

c) The bearing that the boat should travel on to return to the starting point is the opposite direction of the angle formed by the two legs of the journey. Therefore, the bearing is 360° - 63° = 297°.

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A fashionable deck of cards trendy deck of playing cards carries fifty two playing cards, of which 26 are crimson and 26 are black, thirteen are of every match. The probablity of selecting two spades in a row = 3

A wellknown deck of cards incorporates 52 cards and consequently there are 52 feasible outcomes.

# of viable outcomes =

52

four of the 52 cards in a standard deck of cards are aces and accordingly there are 4 favorable results.

# of favorable outcomes

=

four

# of favorable consequences=4

The opportunity is the wide variety of favorable results divided by using the variety of possible outcomes:

�(Ace)=

# of favorable effects =4

# of feasible consequences =52

P(Ace)=

# of viable outcomes

# of favorable results =

fifty two

4​

=

13

1

​

The anticipated variety of aces is then acquired through multiplying the variety of draws via the opportunity.

Prediction = range of attracts × (Ace) = 39 × 1 = 39

=three Prediction = wide variety of draws×P(Ace)

13* 1 = 13

39×1 = 39

=3

thus we expect that three of the drawn cards will be aces.

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Answer:

-3(2x-5y+8)

Step-by-step explanation:

Answer:

435 cubic yards.

Step-by-step explanation:

Length x width x height.

Cut the shape into 2 parts.

Calculate the length for each.

13 yd - 5 yd = 8 yd

5 × 5 × 11 = 275

8 × 4 × 5 = 160

275 + 160

435 cubic yards

$6,820 is the total tax owned by William.

percentage, a relative value indicating hundredth parts of any quantity.

Given that William earned $52,000 last year.

he first $30,000 is taxed at 11%

Let us find the 11% of 30000

30000×11/100

$3,300.

The tax owed on 30000 amount is $3,300.

The balance amount is 52000-30000

$22000

The above amount has a tax of 16%.

Now let us find the 16% of 52000

16/100×52000

$3520

The total tax owed by William is $3,300 + $3,520 = $6,820.

Hence, $6,820 is the total tax owned by William.

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The correct response is d. 4.6 years. The company is replacing at most 10% of their toasters sold 4.6 years.

To handle problems using samples that have a normal distribution, utilize the z-score formula.

The z-score of a measure X in a collection with mean and standard deviation is given by:

Z= x−μ/σ

The measure's standard deviations from the mean are determined by the [tex]Z-[/tex]score. We examine the p-value linked with the [tex]Z-[/tex]score in the [tex]Z-[/tex]score table after computing the [tex]Z-[/tex]score. This p-value is the probability that the measure's value is smaller than [tex]X[/tex], or the percentile of [tex]X[/tex]. The likelihood that the value of the measure exceeds [tex]X[/tex] is calculated by deducting [tex]1[/tex] from the pvalue.

This issue involves that:

Mean, μ[tex]=5.8[/tex]

Standard deviation,σ[tex]=0.9[/tex]

Only those who rank in the bottom 10% will be replaced.

So, if Z has a p value of 0.10, the warranty is equal to the value of X.

So it is X when

[tex]Z=-1.28[/tex]

Z= x−μ/σ

x=Z∗σ+μ

[tex]x=-1.28*0.9+5.8\\x=4.6[/tex]

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Using Algebra, we concluded, there are 36 children.

The study of variables and the procedures for modifying variables in formulas is known as algebra, and it is the subject that underlies almost all of mathematics. All applications of mathematics require knowledge of elementary algebra since it deals with manipulating variables as though they were numbers.

In algebra, the fundamental concepts are numbers, variables, constants, expressions, equations, linear equations, and quadratic equations. Additionally, it requires adding, subtracting, multiplying, and dividing basic arithmetic operations within the algebraic formulas.

If there are X children at first

[tex]\frac{360}{x}+2=\frac{360}{x-6}[/tex]

360(x-6)+2x(x-6)=360x

360x-2160-12x=0

(X+30)(x-36)=0

So,x+30=0  x-36=0

X=-30, x=-36

Because X Great than or equal to 0

X=36

So there are 36 children at first.

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The probability of any one person visiting a particular station is 1/3. Since there are three people in the family, the probability that they would all visit the same station is 1/3 x 1/3 x 1/3, which is equal to 1/27.

The probability that all three members of the family visit the same station at the medical clinic is 1/27 (1/3 x 1/3 x 1/3). This is because each person has an equal chance of being assigned to any of the three stations and since there are three people in the family, the probability that they would all visit the same station is 1/3 multiplied by itself three times, which is equal to 1/27. The experiment is recording the station number for each member and since the incoming individuals are assigned to any of the three stations randomly, the probability that all three members visit the same station is 1/27.

The complete question is :

A family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that all three members visit the same station?

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The proportion is solved to give s = 3

Proportion can simply be described as an equation made equal to each other.

Also, algebraic expression are defined as expression that are comprised of terms, variables, factors, coefficient and constants.

They are also made up of arithmetic operations, such as;

From the information given, we have that;

s + 1/4 = 4/8

cross multiply

8(s + 1) = 16

Divide both sides by 8, we get;

s + 1 = 2

collect like terms

s = 3

Hence, the value is 3

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The probability that he or she has a visa card is 40%.

Probability is a mathematical concept that describes the likelihood of an event happening. In this case, the event is the selected individual having a visa card.

Let's assume that the individual has a total of n cards and v of those are visa cards. The probability of the individual having a visa card is given by the formula:

P(Visa) = v/n

This formula expresses the ratio of the number of successful outcomes (having a visa card) to the total number of possible outcomes (having any type of card).

The probability is expressed as a decimal or a percentage. If the individual has 5 cards and 2 of them are visa cards, then the probability of them having a visa card is

=> 2/5 = 0.4 or 40%.

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