(03.02, 03.03, 03.04 MC)
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 0.69(1.03)*
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below
hows the price f(t), in dollars, of product B after t years:
t (number of years)
1
2
3
f(t) (price in dollars) 10,100 10,201 10,303.01
4
10,406.04

For the given distribution the mean is 20.74  , the variance is  1.652   and the standard deviation is 1.2853   .

In the question ,

probabilities are given ,

the mean is given by the formula,

mean = [tex]\sum[/tex]x*p(x) ,

we get ,

mean = 19*0.21 + 20*0.23 + 21*0.30 + 22*0.13 + 23*0.13

= 3.99 + 4.6 + 6.3 + 2.86 + 2.99

= 20.74

For calculating the Variance we need to subtract the mean for every value x, then we square the result and multiply it by the respectively probability .

19 - 20.74 = -1.74 = (-1.74)²× 0.21 = 0.6357

20 - 20.74 = -0.74 = (-0.74)²× 0.23 = 0.1259

21 - 20.74 = 0.26 = (0.26)²× 0.30 = 0.0202

22 - 20.74 = 1.26 = (1.26)²× 0.13 = 0.2063

23 - 20.74 = 2.26 = (2.26)²× 0.13 = 0.6639

The variance = 0.6357 + 0.1259 + 0.0202 + 0.2063 + 0.6639

= 1.652

the standard deviation = √variance

= √1.652

= 1.2853

Therefore , the values are mean is 20.74  , the variance is 1.652  and standard deviation is 1.2853 .

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There is  no error by Margaret identifying the different transformations of graphs

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations, it is a typical kind of algebraic problem.

Reflections, rotations, and translations are the three fundamental rigid transformations. Dilation is a fourth frequent transition.

Vertical Reflection: Mirror images are produced by reflections. Imagine the graph "folding" over the x-axis.

Horizontal reflection: Mirror images make up reflections. Imagine the graph "folding" over the y-axis.

Vertical Shift: This translation "slides" up or down in a straight line.

• The graph is translated upward by k units if k > 0.

• If k is less than 0, the graph descends by k units.

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Answer:

infinite solutions

Step-by-step explanation:

4x=2(2x-3)+6

4x=4x-6+6

4x=4x

these are the same lines so there are infinitely many solutions

hopes this helps

The required volume of the given cylinder is 1005 ft³.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry.

In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

So, the volume of cylinder formula:

V=πr²h

We have,

Height of 20 ft and diameter of 8 ft.

The radius will be 8/2 = 4 ft.

Now, calculate the volume as follows:

V=πr²h

V=π(4)²20

V=1005.30965

Rounding off: 1005 ft³

Therefore, the required volume of the given cylinder is 1005 ft³.

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Answer:

the mark up is 2$

Step-by-step explanation:

each shirt was baught for 18$ divide 7200 by 400

The other two points on the line are (2, 7) and (4, 14).

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

Given, Sonya walks on a treadmill at a constant rate of 3.5 miles per hour

it is the slope.

∴ The equation of this line passing through point (1, 3.5) is,

3.5 = 3.5(1) + b.

b = 0.

So, y = 3.5x.

Now the other points can be obtained by choosing some integer values of x.

When x = 2, y = 7 ⇒ (2, 7).

When x = 4, y = 14 ⇒ (4, 14).

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Answer: 8 years for her salary to be the same at both companies.

Step-by-step explanation:

To solve this problem, we can set up a system of linear equations to represent the salaries at each company. Let's say that the first company's salary is represented by the variable x, and the second company's salary is represented by the variable y. Since the first company offers a starting salary of $28,000 with a raise of $3,000 each year, we can represent this with the equation x = 28,000 + 3,000 * t, where t represents the number of years. Similarly, the second company offers a starting salary of $36,000 with a raise of $2,000 each year, so we can represent this with the equation y = 36,000 + 2,000 * t.

Since we want to find the number of years it will take for Joanne's salary to be the same at both companies, we can set the two equations equal to each other and solve for t:

x = 28,000 + 3,000 * t

y = 36,000 + 2,000 * t

x = y

28,000 + 3,000 * t = 36,000 + 2,000 * t

We can solve this equation by combining like terms on both sides of the equation:

28,000 + 3,000 * t = 36,000 + 2,000 * t

-8,000 = -1,000 * t

Dividing both sides of the equation by -1,000, we get:

8,000 = t

Thus, it will take Joanne 8 years for her salary to be the same at both companies.

Answer:

8 years

Step-by-step explanation:

y = salary

x = years

1st company: y = 3,000x + 28,000

2nd company: y = 2,000x + 36,000

3000x + 28000 = 2000x + 36000

subtract 2000x on both sides

1000x + 28000 = 36000

subtract 28000 on both sides

1000x = 8000

divide 1000 on both sides

x = 8

The number of gray squares for 15 white squares based on the given ratio will be 25.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

Number of white squares = 3

Number of gray squares = 5

The ratio of gray squares to white = 5/3

With maintaining the same ratio,

Let's say the number of gray squares for 15 white squares will be x.

The ratio of gray squares to white will be as x/15

Both ratios must be the same for the same pattern.

x/15 = 5/3

x = (5/3)15 = 25

Hence "On the basis of the specified ratio, there will be 25 gray squares for every 15 white squares.".

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The value of x will be;

⇒ x = 1

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3 (6x - 2) = 2 (3x + 3)

Now,

Since, The expression is,

⇒ 3 (6x - 2) = 2 (3x + 3)

Solve for x as;

⇒ 18x - 6 = 6x + 6

⇒ 18x - 6x = 6 + 6

⇒ 12x = 12

⇒ x = 12/12

⇒ x = 1

Thus, The value of x = 1

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Answer:

x = 1

Step-by-step explanation:

Given equation,

→ 3(6x - 2) = 2(3x + 3)

Now the value of x will be,

→ 3(6x - 2) = 2(3x + 3)

→ (3 × 6x) - (3 × 2) = (2 × 3x) + (2 × 3)

→ 18x - 6 = 6x + 6

→ 18x - 6 - 6x = 6

→ 12x = 6 + 6

→ 12x = 12

→ x = 12/12

→ [ x = 1 ]

Let's check the value of x,

→ 3(6x - 2) = 2(3x + 3)

→ 3(6(1) - 2) = 2(3(1) + 3)

→ 3(6 - 2) = 2(3 + 3)

→ 3 × 4 = 2 × 6

→ 12 = 12

→ [ LHS = RHS ]

Hence, the value of x is 1.

Answer:

The amount of carbon-14 in the fossil is 15% of the amount of carbon-14 in a living beetle.

This means that the amount of carbon-14 in the fossil is 0.15 * the amount of carbon-14 in a living beetle.

The age of the fossil can be found by dividing the half-life of carbon-14 by the logarithm of the ratio of the amount of carbon-14 in the fossil to the amount of carbon-14 in a living beetle.

This means that the age of the fossil is 5715 years / log(0.15).

The age of the fossil is approximately 5715 years / -1.1761.

Therefore, the age of this fossil is approximately <<4895.4683=4895>>4895 years.

Answer:

Step-by-step explanation:

1) 3(2x + 9) = 24, find x?

→ 3(2x + 9) = 24

→ 6x + 27 = 24

→ 6x = 24 - 27

→ x = -3/6

→ [ x = -1/2 ]

Hence, value of x is -1/2.

2) 4x - 2 = 10x + 1, find x?

→ 4x - 2 = 10x + 1

→ 4x - 10x = 1 + 2

→ -6x = 3

→ x = -3/6

→ [ x = -1/2 ]

Hence, value of x is -1/2.

3) 3x - 4(2x + 1) = 10, find x?

→ 3x - 4(2x + 1) = 10

→ 3x - 8x - 4 = 10

→ -5x = 10 + 4

→ [ x = -14/5 ]

Hence, value of x is -14/5.

4) 3x + 10 = 19, find x?

→ 3x + 10 = 19

→ 3x = 19 - 10

→ x = 9/3

→ [ x = 3 ]

Hence, value of x is 3.

The probability that the child is not affected by  the disorder is \frac{5}{6}

Probability is simply the likelihood of something occurring.

It is an autosomal recessive disorder because all of the defective ones are recessive. So, when a 2nd generation 3rd individual marries a 2nd generation 4th individual, the probability of their child having a genetic disease is [tex]\frac{1}{6}[/tex]. The parents must be heterozygous for the child to be diseased, and the probability of an individual being heterozygous is [tex]\frac{2}{3}[/tex]. 2nd generation, 3rd individual, and the probability of disease in the child is [tex]\frac{1}{4}[/tex], so [tex]\frac{2}{3} *\frac{ 1}{4} = \frac{1}{6}[/tex].

As a result, the probability of a child having a genetic disorder is [tex]\frac{1}{6}[/tex].

then the probability of child not having any genetic disorder is [tex]1-\frac{1}{6} =\frac{5}{6}[/tex].

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Answer:Yes

Step-by-step explanation:If two triangles have the same size and shape they are called congruent triangles.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Substituting into the slope formula, [tex]m=\frac{-2-3}{-4-6}=\frac{1}{2}[/tex].

Answer:

1/2

Step-by-step explanation:

Answer: If you wanted to know what 13x13, or the square of something is, then the value is 169. Or if you wanted to know the square root of 13, it would be about 3.606.

Step-by-step explanation: A square number is any number multiplied by itself = that number. For example, 12x12 = 144, which means the square root of 144 is 12, and the square number of 12 is 144.

When they decide to bid the same then the probability of Barney getting the car is 1/3. The expected profit by Barney will be the difference amount of SL and SH.

Given:

if arnie, barney and carny agree to always bid $l,

, then on any given day, what is the probability that barney gets the car for $l when it is actually worth $l to him = ?

When they choose to place identical bids, Barney has a 1/3 chance of winning the automobile. The difference between SL and SH will represent Barney's anticipated profit.

Hence we get the required answer.

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Answer:

8

Step-by-step explanation:

solve the 2 cube first = 8

then solve the .2 with 8 = 16

then minus 24

24-8.2

24-16

8

The system of equations y = 2x + 4 when graphed have a solution that y = − (1/3)x − 1 is (3, - 2)

A straight line's general equation is -

y = (m)x + c

where -

The slope of the line, [m], indicates the unit rate at which [y] changes in relation to [x].

The y-intercept, or the place where the graph crosses the [y] axis, is represented by [c].

A straight line's equation can also be expressed as -

Ax + By + C = 0

By = - Ax - C

y = [tex](\frac{A}{B} - \frac{B}{C})x - \frac{A}{C}[/tex]

The set of equations is as follows:

y = − 2x + 4

AND

y = − [tex](\frac{1}{3} )[/tex]x − 1

Draw the graphs for these two equations. The answer to this system of equations would be near the intersection. Please see the following graph. These lines come together at (3, - 2)

As a result, y = 2x + 4 and is the system of equations that has been solved.

y = − [tex](\frac{1}{3} )[/tex]x − 1 is (3, - 2)

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By using the concept of distance, it can be calculated that

Veronica's mistake was that the number of animals seen per kilometer was not calculated by her. Arrangement was made on the basis of animals seen

What is distance?

Distance is the length of the path travelled by an object during its motion.

Here,

For River Edge

Number of animals seen = 8

Length of hike =  3 km

Number of Animals seen per km = [tex]8 \div3[/tex] = 2.67

For Wooden Marsh

Number of animals seen = 24

Length of hike =  8 km

Number of Animals seen per km = 24 [tex]\div[/tex] 8 = 3

For Canyon Creek

Number of animals seen = 35

Length of hike =  15 km

Number of Animals seen per km = [tex]35 \div 15[/tex] =2.33

Number of animals in ascending order are 2.33, 2.67, 3

Canyon Creek, River Edge, Marshy Land is the required arrangement from the least to the greatest.

Veronica's mistake was that the number of animals seen per kilometer was not calculated by her. Arrangement was made on the basis of animals seen

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Complete Question

Veronica went on three hikes. On each hike, she saw the following numbers of animals:

Rivers Edge 3 8

Wooded Marsh 8 24

Canyon Creek 15 35Veronica tried to order the hikes from least to greatest by number of animals seen per kilometer, but she made a mistake. Here's her work:

least greatest

8 24 35

rivers edge wooded marsh canyon creek

What was Veronica's mistake?

The graph of the piece-wise function containing Andres's data is given by the image at the end of the answer.

A piece-wise function is a function that has different definitions, based on it's input.

The variables in this problem are given as follows:

At 6 a.m., the temperature was 60° F, hence the intercept is of:

(0,60).

For the next 9 hours, the temperature rose 2° every 3 hours, hence a line is traced connecting these two points:

(0, 60) and (9, 66).

For the next 2 hours, it rose 2° per hour, hence these two points are connected:

(9, 66) and (11,70).

The temperature then stayed steady until 6 p.m, hence these two points are connected:

(11,70) and (12,70).

For the next 2 hours, the temperature dropped 1° per hour, hence the points at:

(12,70) and (14,68).

The temperature then dropped steadily until the temperature was 66° at midnight, then the points are:

(14,68) and (18,66).

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Answer:

5 necklaces and 10 bracelets

Step-by-step explanation:

Let N and B stand for the numbers of necklaces(N) and bracelets(B) sold.  The total sales would be:

 Total Sales = 6.25B + 12.50N, whcu we are told amounted to $125:

  $125 = 6.25B + 12.50N

We know that B + N = 15.

Rearrange this to isolate B:  B = 15-N

Now use this definition of B in the first equation:

$125 = 6.25B + 12.50N

$125 = 6.25(15-N) + 12.50N

$125 = 93.75-6.25N + 12.50N

31.25 = 6.25N

N = 5 necklaces

From B+N = 15, we can find B:

  B = 15 - 5

  B = 10 bracelets

Check:  Do 5 necklaces and 10 bracelets add up to $125??

 5*($6.25) + 10*($12.50) = $62.50 + $62.50 = $125  YES

The number of bracelets and the number of necklaces if, Sophia sells each bracelet for $6.25 and each necklace for $12.50, and the total number of items sold is 15, are 10, and 5 respectively.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

Sophia sells each bracelet for $6.25 and each necklace for $12.50,

Total number of items sold = 15,

Total income made = $125,

Write the equation as shown below,

x + y = 15

Here, x is the number of bracelets and y is the number of necklaces,

6.25x + 12.5y = 125

Solve the equations by elimination method as shown below,

y = 5 and x = 15 - 5 = 10

Thus, the number of bracelets is 10 and the number of necklaces is 5.

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At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

The speed of an object is the ratio of distance and time it takes for the object to travel that distance.

Mathematically,

S = D/T

where

S is velocity

D is the distance traveled or distance traveled

T is the time it takes to travel that distance

Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.

If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.

Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.

Mathematics,

a = v/t

When an object is in motion, its acceleration is never zero.

When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.

Given in the question:

First the plane was travelling at a constant rate of 250  miles per hour.

Initial height was 20000 feet

Now,

As the speed increases and travels at a constant rate of 400 miles per hour.

Now,

   (400 /250 ) × 20000

=  1.6 × 20000

= 32000 feet

Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

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Answer:

442 ÷ (12+5) = 26

26 × 12 = 312, 312 ppl think yoda was cuter

26 × 5= 130, 130 ppl think Porg was cuter

Answer:

w = 39

Step-by-step explanation:

3w + 9 + 2w - 24 = 180 , that is

5w - 15 = 180 ( add 15 to both sides )

5w = 195 ( divide both sides by 5 )

w = 39

Answer:

Read carefully each step for your fully understand it.

Step-by-step explanation:

To find the equation of a line that is perpendicular to the line y = 2x - 3 and contains the point (-5, 3), we need to find the slope of the perpendicular line.

To find the slope, we use the negative reciprocal of the slope of the given line. The slope of the given line is 2, so the slope of the perpendicular line is -1/2.

We can then use the point-slope formula to find the equation of the line that is perpendicular to y = 2x - 3 and contains the point (-5, 3).

The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get:

y - 3 = -1/2 (x + 5)

We can then simplify this equation to get the final equation:

y = -1/2 x - 11/2

Therefore, the equation of the line that is perpendicular to y = 2x - 3 and contains the point (-5, 3) is y = -1/2 x - 11/2.

Answer: (1,2)

Step-by-step explanation:

1)

x+y=3

y=-x+3

x | 0 | 3 |

y | 3 | 0 |

2)

3x+y=5

y=-3x+5

x | 0 | 2 |

y | 5 | -1 |

To find Q1 and Q3, you must first arrange the data in numerical order. Once the data is in order, you will need to determine the median of the data set.

To calculate the median, count the total number of data points, divide it by two, and round down to the nearest whole number under numerical order. This number will be the median.Q1 is the median of the lower half of the data set, while Q3 is the median of the upper half of the data set. To calculate these, divide the data set into two halves, calculate the median of each half, and then take the median of those two numbers.

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The pace or speed of Debbie during rides with her bike is greater on the way of going to home from School.

So, her pace is faster on the way of going to home .

We have given that,

Debbie ride 1.5 miles to school in 10 minute

As we know that 10 minute = 10/60⇒1/6 hour

As we know that

Speed = distance /time or S = D/T

So, the speed at which Debbie ride to school with first route,

S=1.5/1/6 => 9 mile per hour

Now, On her way home, she took other route and

she rides, 3 mile in 15 minutes,

As 15 minutes = 15/60 => 1/4 hour

Speed of Debbie of her way home

S' = 3/1/4 => 12miles per hour

As we see that S' > S

So, Debbie rides faster on her way to home.

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Answer:

[tex]u(w(2) = 19[/tex]

Step-by-step explanation:

let's evaluate w(2) first

[tex]w(2) = - 2(2) {}^{2} - 1 = - 9[/tex]

at this point let's replace thia value in u(x)

[tex]u( - 9) = - 2( - 9) + 1 = 19[/tex]