type of measurement enables learners to quantify the measurement of an object, but differs in amount each time.

Answer:

3/4

Step-by-step explanation:

Answer:

The given expression is:

3x + 2 / (x + 1)(x² + x + 2)

To simplify this expression, we need to factor the denominator first:

x² + x + 2 = (x + 2)(x + 1)

So the expression becomes:

3x + 2 / (x + 1)(x + 2)(x + 1)

Next, we can use partial fraction decomposition to express the expression in terms of simpler fractions. Let's assume:

3x + 2 / (x + 1)(x + 2)(x + 1) = A/(x + 1) + B/(x + 2) + C/(x + 1)²

Multiplying both sides by the common denominator, we get:

3x + 2 = A(x + 2)(x + 1) + B(x + 1)² + C(x + 2)(x + 1)

Expanding the right side, we get:

3x + 2 = Ax² + 3Ax + 2A + Bx² + 2Bx + B + Cx² + 3Cx + 2C

Combining like terms, we get:

3x + 2 = (A + B + C)x² + (3A + 2B + 3C)x + (2A + B + 2C)

Since this equation holds for all values of x, the coefficients of each power of x must be equal on both sides. We can equate the coefficients of x², x, and the constant term to get a system of three equations for A, B, and C:

A + B + C = 0

3A + 2B + 3C = 3

2A + B + 2C = 2

Solving this system, we get:

A = 2/3

B = -1/3

C = -1/3

Substituting these values back into the partial fraction decomposition equation, we get:

3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²

Therefore, the simplified expression is:

3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²

Answer:

We can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + r)^(-n)) / r]

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of payments.

Substituting the given values, we have:

PV = $31.48 x [(1 - (1 + 0.152/12)^(-18)) / (0.152/12)]

PV = $31.48 x [(1 - 0.5159) / 0.0127]

PV = $1,007.97

Therefore, the equivalent cash price of the iPod is $1,007.97.

Answer:

2.75d+2t <= 40

Step-by-step explanation:

i may be wrong but I tried

Answer:

64, 69, 88, 88, 91, 92, 93, 95, 97, 97, 100

Median= 92

Mode= 88, 97

Mean= 88.55

Range= 36

Quartile 1= 88

Quartile 2= 92

Quartile 3= 97

Interquartile range= 9

Minimum= 64

Maximum= 100

Not sure if this helped but I hope it did

Answer:

  336 feet

Step-by-step explanation:

You want the change in elevation as a result of driving 4813 feet up a road with a 4° incline.

The sine function relates an angle to the ratio of the opposite side and the hypotenuse in a right triangle:

  Sin = Opposite/Hypotenuse

In this application, we have ...

  sin(4°) = (elevation change)/(distance along the road)

  elevation change = (4813 ft)·sin(4°) ≈ 336 ft

The driver's increase in altitude is about 336 feet.

Answer:

Let's start by finding the volume of water in the trough as a function of its depth.

At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:

V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm

Simplifying this expression, we get:

V(h) = (13/2000) h^2 m^3

Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:

dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)

At the moment when the water is 10 cm deep, we have:

h = 10 cm

dV/dt = 0.1 m^3/min

Plugging in these values, we get:

0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)

Solving for dh/dt, we get:

dh/dt = 0.1 m^3/min / (26/2000) / 10 cm

dh/dt ≈ 0.192 m/min

Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.

The solution to the given quadratic equation is expressed as:

x = (-1 ± √5)/2

The general form of expression of a quadratic equation is:

y = ax² + bx + c

Where the solution is given by the quadratic formula:

x = [-b ± √(b² - 4ac)]/2a

The given quadratic equation is expressed as:

-3x² + 1 = 3x - 2

Rearranging in standard form is:

3x² + 3x - 3 = 0

Thus, the solution is:

x = [-3 ± √(3² - 4(3 * -3))]/2(3)

x = [-3 ± √(9 + 36)]/6

x = (-1 ± √5)/2

Read more about Quadratic Equation Solution at: https://brainly.com/question/25841119

#SPJ1

Answer:

B

Step-by-step explanation:

The correct answer is B. The total number of people on the field trip must be a multiple of 9 (1 adult and 8 students).

A is not true because if there were only 9 people, there could not be both an adult and 8 students, and the ratio would not be 1:8.

C is not necessarily true. It is possible that there were more adults than students on the field trip, or that the ratio was not an exact 1:8.

D is not true because if there were 8 times as many students as adults, the ratio would be 1:64, not 1:8

The expression that represents the sum of the segments is:

AB + DC = 13x - 1

Here we have two segments defined as functions of a variable x, and we can write them as:

AB = 8x - 5

DC = 5x + 4

We want to find an expression that represents AB + DC, we can just replace the two expressions (for each of the segments) in the sum above, then we willget:

AB + DC = 8x - 5 + 5x + 4

Now we can simplify that sum to get:

AB + DC = 8x + 5x - 5 + 4

               = 13x - 1

That is the expression we wanted.

Learn more about segments at:

https://brainly.com/question/17374569

#SPJ1

The prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.

PrοbabiIity is a measure οf the IikeIihοοd οr chance οf an event οccurring, expressed as a number between 0 and 1, with 0 indicating impοssibiIity and 1 indicating certainty. It is used in variοus fieIds such as mathematics, statistics, science, ecοnοmics, and finance.

The prοbabiIity οf getting the true/faIse questiοn cοrrect is 1/2 οr 0.5. The prοbabiIity οf getting the muItipIe-chοice questiοn cοrrect is 1/4 οr 0.25. The prοbabiIity οf getting the Iast questiοn cοrrect is 1/2 οr 0.5.

Tο find the prοbabiIity οf getting aII 3 answers cοrrect, we muItipIy the prοbabiIities οf getting each questiοn cοrrect:

0.5 * 0.25 * 0.5 = 0.0625

Sο the prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.

To learn more about Probability from the given link

https://brainly.com/question/24756209

#SPJ1

In response to the stated question, we may state that As a result, we can triangle only state that angle A is congruent to angle P, angle B to angle Q, and angle C to angle R.

A triangle is a closed, two-dimensional geometric shape made up of three line segments called sides that intersect at three points called vertices. Triangles may be identified by their sides and angles. Based on their sides, triangles might be equilateral (all sides equal), isosceles, or scalene. Triangles are classed as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles more than 90 degrees) (all angles greater than 90 degrees). The area of a triangle may be calculated using the formula A = (1/2)bh, where A is the area, b is the base of the triangle, and h is the height of the triangle.

To demonstrate the similarity of two triangles, we must demonstrate that their respective angles are congruent and their corresponding sides are proportionate.

∆ABC ~ ∆PQR

We can see from the triangles that angle A is congruent with angle P, angle B is congruent with angle Q, and angle C is congruent with angle R. As a result, we have the angle-angle (AA) similarity:

∆ABC ~ ∆PQR

[tex]AC/PR = 13/16 \\AB/PQ = 5/8 \\BC/QR = 12/16 = 3/4 \\AC/PR = 13/16[/tex]

Because the matching side length ratios are not entirely equal, the triangles are not comparable according to the side-angle-side (SAS) similarity theorem. As a result, we can only state that angle A is congruent to angle P, angle B to angle Q, and angle C to angle R.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

This graph in the figure shows the no solutions to the inequalities

inequalities can be defined as if two real numbers or the algebraic expressions can be related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called inequalities.

For example, x>3 (x should be greater than 3)

system of inequalities y>3x+14 and y<3x+2

the system of inequalities have solutions only when the shaded part satisfies the given inequalities

We are given with the graph of inequalities . The given inequalities have 'and' in between.

so we look at the graph where both inequalities intersects

From the graph we can see that there is no intersection part of both shaded portions

So , we conclude that there is no solution.

to know more about real numbers, visit:

https://brainly.com/question/551408

#SPJ1

The complete question is:

This graph shows the solutions to the inequalities. does the system of inequalities y>3x+14 and y<3x+2. Does the system of inequalities have solutions? If so, which region contains the solutions?

Answer:

the chips are marked down by 12%.

Step-by-step explanation:

To calculate the percentage discount, you can use the formula:

percentage discount = (original price - sale price) / original price x 100%

Plugging in the values given in the problem, we get:

percentage discount = (6.00 - 5.28) / 6.00 x 100%

percentage discount = 0.72 / 6.00 x 100%

percentage discount = 0.12 x 100%

percentage discount = 12%

Answer:

The answer is 12%

Step-by-step explanation:

6 - 5.28 = 0.72

0.72/6 = 0.12

0.12 is a decimal, but written as a percent is 12%.

The completed text are:

Point of Tangency: A point of contact between a circle and its tangent line.

Secant segment: A segment that intersects a circle twice and has one endpoint on the circle and one endpoint outside of the circle.

Tangent Segment: A segment of a tangent line that has an endpoint at the point of tangency.

The concepts of chord, point of tangency, secant segment, and tangent segment are relevant in geometry, particularly in the study of circles.

They provide the foundation for understanding the relationships and properties of circles and their associated segments.

These concepts are essential in various fields such as engineering, physics, and architecture, where circular shapes are commonly used. They are also relevant in solving real-world problems that involve circles, such as determining the area and circumference of a circle.

Learn more about tangent line at:

https://brainly.com/question/23265136

#SPJ1

Answer:

asdf

Step-by-step explanation:

The completion of the bill showing the total cost for a dishwasher repair is as follows:

Description                Number      Unit Cost       Total

Filter                                1               £28.95       £28.95

Basket                            8                  £1.50       £12.00

Spray arm                      2                £10.45      £20.90

Labor charge 1¹/₂ hours at $18 per hour         £27.00

Total Cost                                                        £88.85

The total cost for the repairs can be computed using multiplication, division, and addition operations.

Multiplication and addition operations are three of the four basic mathematical operations.

Mathematical operations are techniques applied to solve mathematical problems.

Description                Number  Unit Cost                    Total

Filter                                1           £28.95                    £28.95

Basket                            8             £1.50                     £12.00 (£1.50 x 8)

Spray arm                      2           £10.45 (£20.90/2)  £20.90

Labor charge 1¹/₂ hours at $18 per hour                   £27.00

Total Cost                                                                   £88.85

Thus, the total cost for the dishwasher repair is £88.85.

Learn more about mathematical operations at https://brainly.com/question/4721701.

#SPJ1

Answer:

Step-by-step explanation:

294m

Maria and Ming will be 136 miles apart after 2 hours.

What is Distance?

Distance is the total length of a path an item or person takes to get from one place to another, ignoring the direction of motion. Given that it is a scalar number, it has only a magnitude and no direction. The most common units used to determine distance are meters, kilometers, miles, and feet. (ft).

The distance between Maria and Ming will grow at a rate that is equal to the sum of their speeds because they are traveling in opposite directions:

distance between them = (Maria's speed + Ming's speed) x time

                                         = (36 mph + 32 mph) x 2 hours

                                         = 68 mph x 2 hours

                                         = 136 miles

Therefore, Maria and Ming will be 136 miles apart after 2 hours.

To learn more about Distance

https://brainly.com/question/26046491

#SPJ9

Answer: Reflection in the y -axis:

Explanation: The rule for a reflection over the y -axis is (x,y)→(−x,y) .\

Answer:

  D.  ∠EBF = 40°

Step-by-step explanation:

You want the measure of angle EBF in a diagram in which right angle EBD is split by ray BF to form angle FBD = 50°.

The angle addition postulate tells you ...

  ∠EBD = ∠EBF +∠FBD

  90° = ∠EBF +50° . . . . use the given values

  40° = ∠EBF . . . . . . . subtract 50°

It must be true that ∠EBF = 40°.

Step-by-step explanation:

(a) If the order of the choices is relevant, we can choose the first object in 5 ways, and the second object in 4 ways (since we cannot choose the same object again). Therefore, the total number of ways to choose 2 objects without replacement and with order being relevant is:

5 x 4 = 20 ways

(b) If the order of the choices is not relevant, we need to use the combination formula, which is:

nCk = n! / (k! * (n-k)!)

where n is the total number of objects, and k is the number of objects we want to choose.

In this case, we want to choose 2 objects out of 5, so n = 5 and k = 2. Therefore, the number of ways to choose 2 objects without replacement and with order not being relevant is:

5C2 = 5! / (2! * (5-2)!) = 10 ways

Therefore, there are 20 ways to choose 2 objects without replacement and with order being relevant, and 10 ways to choose 2 objects without replacement and with order not being relevant.

the probability that they are both Democrats. round to the nearest thousandth if necessary is 0.194

The probability that BOTH is democrats means the probability of "one being democrat" AND "another also being democrat".

The AND means we need to MULTIPLY the individual probability of a person being a democrat.

The probability that a voter is democrat is 44% (0.44) -- stated in the problem

Now, the Probability of BOTH being Democrats is simply MULTIPLYING 0.44 with 0.44

Rounded to the nearest thousandth, 0.194

The last answer choice is correct.

the complete question is-

In one town 44% of all voters are Democrats if two voters are randomly selected for a survey find the probability that they are both Democrats. round to the nearest thousandth if necessary.

0.189

0.880

0.440

0.194

learn more about probability

https://brainly.com/question/30034780

#SPJ1

So the Greatest Common Factor of The given expressions is -63x²y, 9x³y³, and 90x³y is 9x²y.

In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a value or a quantity. Expressions can be simple or complex, and they can involve arithmetic operations, functions, and algebraic operations. Expressions can be evaluated, simplified, or manipulated using mathematical rules and techniques. They are used in many areas of mathematics, including algebra, calculus, and geometry, as well as in other fields such as physics, engineering, and economics.

Here,

To find the greatest common factor (GCF) of the given terms, we need to factor out any common factors of the coefficients and variables.

-63x²y = (-1) × 3² × 7 × x² × y

9x³y³ = 3² × x³ × y³

90x³y = 2 × 3² × 5 × x² × y

The common factors among these terms are 3², x², and y. Therefore, the GCF of the given terms is:

GCF = 3² × x² × y

= 9x²y

To know more about expression,

https://brainly.com/question/1859113

#SPJ1

Answer: 566.55 US dollars

Step-by-step explanation: i think, please give 5 stars

Answer:

Equation: y= -3/4x+15/2

Step-by-step explanation:

The points given: (-2,9) and (2,6)

Slope ,m=y2-y1/x2-x1=6-9/2-(-2)= -3/(2+2)

slope ,m= -3/4

Equation: y-y1=m(x-x1)

Equation: y-6= -3/4(x-2)

y-6= -3/4x+3/2

y= -3/4x+3/2+6

y= -3/4x+15/2

Learn more about equation of a line

here:

Brainly.com/question/23087740

#SPJ2

Answer:

11

Step-by-step explanation:

11 x 23 is 253