PLEASE HELP 50POINTS!!!!!


Can you always use synthetic division for dividing polynomials?

The answer is 1.25 ft-lb. This can be calculated by multiplying 15 ft-lb by (9 in. / 12 in. per ft), which equals 1.25 ft-lb. The amount of work needed to stretch a spring 9 inches beyond its natural length is 1.25 ft-lb.

1. Convert 9 in. to feet by dividing 9 in. by 12 in. per ft.

2. Multiply the result (0.75 ft) by 15 ft-lb, which equals 1.25 ft-lb.

The amount of work needed to stretch a spring 9 inches beyond its natural length is 1.25 ft-lb. This can be found by taking the given work required to stretch the spring 1 foot (15 ft-lb) and multiplying it by the ratio of the desired distance (9 in.) to 1 foot (12 in. per ft). First, the desired distance of 9 inches must be converted to feet by dividing it by the conversion factor of 12 inches per foot. This results in 0.75 feet. This number is then multiplied by the given work of 15 ft-lb to yield 1.25 ft-lb of work. This is the amount of work needed to stretch the spring 9 inches beyond its natural length.

Learn more about amount here

https://brainly.com/question/8082054

#SPJ4

a)The energy stored when the extension is 5 cm is given by A = 675 Joules

b) The extension when the energy is 36 Joules is x = ( 2/√3 ) cm

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The energy E stored in an elastic band varies as the square of the energy stored extension x

So , the equation is E = kx²

And , when x = 3 cm , E = 243 Joules

Substituting the values in the equation , we get

243 = k ( 3 )²

9k = 243

k = 27

a)

Now , when the extension x = 5 cm

The energy stored when the extension is E = kx²

On simplifying , we get

E = 27 ( 5 )²

E = 27 x 25

E = 675 Joules

b)

When the energy is E = 36 Joules

E = kx²

36 = 27 ( x )²

On simplifying , we get

x² = ( 36 / 27 )

Taking square roots on both sides , we get

x = ( 6/3√3 ) cm

x = ( 2/√3 ) cm

Hence , the equation is E = kx²

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Yes, this sample of the trees in the county likely to be representative if each forest is the same size.

Representative sample, the sample must accurately reflect the population studied in demographics and characteristics of the chosen subjects.

For example, a representative sample will reflect only those within the study population and should not extend to those outside the study. If Jose is interested in studying the exercise habits of college athletes, only the population of college athletes should be considered for the selection of a representative sample. Jose will not choose athletes from high school or career athletes as part of his representative sample.

To know more about sampling

https://brainly.com/question/16228015

#SPJ4

Answer:jjj

Step-by-step explanation:because

By using only the positive exponents , the answer of the expression (2x⁻²y³/3xy⁻⁴) is  (2y⁷)/(3x³)  .

The Exponents, are defined as a shorthand way of representing the repeated multiplication of a base number by itself. The exponent is the small raised number that indicates how many times the base number is multiplied by itself.

For example, in the expression 2⁴, the base number is 2 and the exponent is 4,

We use the law of exponents to simplify the expression :

the expression is : (2x⁻²y³/3xy⁻⁴) ;

by using the rule that : a⁻ⁿ = 1/aⁿ  ;

we get ;

⇒ (2y³y⁴)/(3xx²) ;

On adding the exponents having the same base ,

we get ;

⇒ (2y⁷)/(3x³)  ;

Therefore , the simplified value of (2x⁻²y³/3xy⁻⁴) is (2y⁷)/(3x³) .

Learn more about Exponents here

https://brainly.com/question/29565624

#SPJ4

The given question is incomplete , the complete question is

Write answer only using positive exponents , (2x⁻²y³/3xy⁻⁴) .

The nth term of the given quadratic sequence is expressed as; aₙ = 2n²

To find the nth term, we have to find the relation between the given terms.

Here we see that;

1st term = 2 = 2 × 1 × 1 = 2 × 1²

2nd term = 8 = 2 × 2 × 2 = 2 × 2²

3rd term = 18 = 2 × 3 × 3 = 2 × 3²

4th term = 32 = 2 × 4 × 4 = 2 × 4²

5th term = 2 × 5² = 2 × 50 = 100

Thus, we clearly see a pattern that can represent the nth term as;

aₙ = 2 × n²

aₙ = 2n²

Read ore about quadratic sequence at; https://brainly.com/question/28697348

#SPJ1

The amount of time it require to water all the parts of her lawn is, 63 minutes

Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.

We denote division by '÷' this symbol.

Given that,

Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn.

Each station runs for an equal amount of time

it takes 49 minutes for the first 7 stations to water

The amount of time it require to water stations = ?

First, we need to calculate time required to water 1 station,

t =  Total time taken / Total station watered

  =   49 / 7

  =   7  minutes/station

So

Time for water all parts = 7 x 9

                                       = 63 minutes

Hence, the required time is 63 minutes

To know more about division check:

https://brainly.com/question/21416852

#SPJ9

A minimum score of 182 is required to stay out of the bottom 1.5% of students and avoid going to summer school.

To find the minimum score required to avoid going to summer school, we need to determine the score that separates the bottom 1.5% of students from the rest of the distribution. This score is also known as the cutoff or the critical value.

We know that the test scores have a normal distribution with a mean of 400 and a standard deviation of 100. To find the critical value, we can use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can standardize the test scores using the z-score formula:

z = (x - mu) / sigma

where x is the test score, mu is the mean, and sigma is the standard deviation.

Substituting the given values, we get:

z = (x - 400) / 100

To find the z-score corresponding to the bottom 1.5% of the distribution, we can use a standard normal table or a calculator. The area to the left of this z-score is 0.015, which corresponds to a z-score of approximately -2.17.

Now we can solve for x, the minimum score required to stay out of the bottom 1.5%:

-2.17 = (x - 400) / 100

x = -2.17 * 100 + 400

x ≈ 182

To learn more about score click on,

https://brainly.com/question/6762121

#SPJ4

Answer:

the answer is 4

Step-by-step explanation:

hope this helps

The value for A∪B in probability form is 3/4. The value for A∪B in data set form is {5, 6, 8}.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The event U has data - U = {1, 2, 3, 4, 5, 6, 7, 8}

The event A has data - A = {6, 8, 10}

The event B has data - B = {5, 6, 9, 12}

The event C has data - C = {1, 3, 7}

The probability formula is -

Probability = No. of outcomes that is favorable / Total number of outcomes

The value for A∪B is -

A∪B = 3/4

The value of A∪B in data set is the values that are present in U data set and in A and B data set.

So, the value is - {5, 6, 8}

Therefore, the value is 3/4 or {5, 6, 8}.

To learn more about probability from the given link

https://brainly.com/question/23286309

#SPJ1

Step-by-step explanation:

use the pythagors theorm b square = h2 -p2

then the 10 cm is parallel so use area of right angled triange =1/2 b×p

The sine, cosine, cosecant, and secant functions have a period 2π;

the tangent and cotangent functions have period π.

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.

If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. The period is the interval between two occurrences of the wave.

The complete question is-

The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.

Learn more about period ,

brainly.com/question/16061498

#SPJ4

Answer: x=4

Step-by-step explanation: as you saw everything is multiplied by 5 this means the 4 became a 20.

3x+8=20

-8 on both sides

3x=12

divide both sides by 3

x=4

Step-by-step explanation:

36 - 7p = -7(p-5)

= 36 - 7p = -7p + 35

= 36 - 35 = - 7p + 7p

= 1 = 0

am confused at the last part

I don't know if p= 1 or it 0 = 1

A possible explanation for why female characters in Latin American myths and legends often represent evils that inflict harm on men is the patriarchal nature of those societies.

In such societies, women were often seen as weaker and more vulnerable than men, and their perceived subservience reinforced the idea that they were not to be trusted. In addition, women were often seen as a threat to male power and authority, and as a result, they were often depicted as malevolent figures who used their cunning and sexuality to manipulate men.

Another explanation is that the portrayal of female characters as evils in these myths and legends was a way of maintaining social order and control. By demonizing women, men were able to justify their own actions and maintain their position of power and control over women.

Find out more on Latin American myths at https://brainly.com/question/17896847

#SPJ1

Answer:

a: Angle 1 and Angle 3

b: Angle 8 and Angle 5

c: Angle 2 and Angle 9

d: Angle 5 and Angle 3

e: none of the above

Answer:

144 egg sandwiches

Step-by-step explanation:

[tex]25\% + 45\% = 70\%[/tex], and [tex]100\% - 70\% = 30\%.[/tex] Thus, [tex]30\%[/tex] of the [tex]480[/tex] sandwiches are egg sandwiches. Since "of" means multiply, we have [tex]30\% \cdot 480.[/tex] We know [tex]30\% = \frac{30}{100} = \frac{3}{10},[/tex] so we can rewrite it as [tex]\frac{3}{10} \cdot 480.[/tex] We cancel [tex]480[/tex] with [tex]10[/tex] which is [tex]480 \div 10 = 48.[/tex] We multiply [tex]48[/tex] by the numerator, [tex]3,[/tex] to get [tex]48 \cdot 3 = 144.[/tex] Thus, Lillian makes [tex]\boxed{144 \text{ egg sandwiches.}}[/tex]

The equation represents how many grams of the compound will remain after 4 hours m(4) = 0.285m₀

Radiation and decay are important concepts in nuclear physics. The rate at which radioactive compounds decay is measured in terms of half-life and the decay constant.

To solve this problem, we can use the exponential decay equation, which describes the rate of decay of a radioactive substance.

In this scenario, we are interested in finding the remaining mass of the radioactive compound, which can be obtained by multiplying the number of remaining atoms by the atomic mass of the substance. The equation for the remaining mass is:

m(t) = N(t) x m

where:

m(t) represents the mass of the radioactive substance remaining at time t.

N(t) is the number of radioactive atoms remaining at time t.

m is the atomic mass of the substance.

To determine the values of N0 and λ for our radioactive compound, we can use the decay rate given in the problem. If the compound decays at a rate of 27% per hour, it means that the remaining fraction of the substance after each hour is 0.73 (i.e., 100% - 27% = 73%). Therefore, the decay constant can be calculated as follows:

ln(0.73) = -λ

λ = 0.312

Next, we can use the initial mass of the compound (320 grams) and the exponential decay equation to find the remaining number of atoms at 4 hours:

[tex]N(4) = N_0 \times e^{-0.312 x 4}[/tex]

N(4) = N₀ x 0.285

Since we don't know N₀, we can express it in terms of the initial mass and the atomic mass:

N₀ = m₀ / m

where:

m₀ is the initial mass of the radioactive compound.

m is the atomic mass of the substance.

Substituting this into the previous equation, we get:

N(4) = (m₀ / m) x 0.285

Finally, we can use the equation for the remaining mass to find the answer:

m(4) = N(4) x m

m(4) = (m₀ / m) x 0.285 x m

m(4) = 0.285m₀

To know more about equation here.

https://brainly.com/question/10413253

#SPJ4

If Kirk had worked for 7 hours he would have made 42 kg of dough.

A unit rate means a rate for one of something.

Given that, Kirk prepared 24 kilograms of dough after working 4 hours, we need to find the amount of dough if he worked for 7 hours.

Calculating the unit rates,

Since, he worked for 4 and made 24 kg,

So, in 1 hour = 24/4 = 6 kg

Therefore, in 1 hour he will make 6 kg

Therefore, in 7 hours he will make = 7x6 = 42 kg

Hence, If Kirk had worked for 7 hours he would have made 42 kg of dough.

Learn more about unit rate, click;

https://brainly.com/question/20920959

#SPJ1

18 pattern block trapezoids would be needed to create 3 hexagons.

Pattern block trapezoids are geometric shapes used for pattern block activities.

Each hexagon is typically made up of 6 pattern block trapezoids.

To determine the number of pattern block trapezoids required to create 3 hexagons, multiply the number of hexagons by the number of trapezoids in each hexagon.

Number of trapezoids = Number of hexagons × Number of trapezoids in each hexagon

                                    = 3 × 6

                                    = 18

Therefore, 18 pattern block trapezoids would be needed to create 3 hexagons.

Learn more about Trapezoid here:

https://brainly.com/question/31380175

#SPJ6

The expression which represents the perimeter of the rectangle is 2x + 14

The following expressions represent the descriptions respectively;

6x

(x - 5)

(x + 2.99)

The total cost of membership of each gym is represented by;

Gym A total cost = 80 + 25m

Gym B total cost = 40m

Length= x + 3

Width = 4

Perimeter of a rectangle= 2(length + width)

= 2{(x + 3) + 4}

= 2(x + 3 + 4)

= 2(x + 7)

Perimeter of the rectangle = 2x + 14

Area of the rectangle= length × width

= (x + 3) × 4

Area of the rectangle = 4x + 12

If x = 7

Area of the rectangle = 4x + 12

= 4(7) + 12

= 28 + 12

= 40 square units

If x is the cost of each apple, the total cost of 6 apples = 6x

Adam is x years old. John is 5 years younger.

So, John's age = (x - 5) years

Ben spent x dollars on a book and $2.99 on a pack of pencil.

Ben spent a total of x + 2.99

Gym A total cost:

80 + 25m

Gym B total cost:

40m

Where,

number of months= m

If m = 6 months

Gym A total cost:

80 + 25m

= 80 + 25(6)

= 80 + 150

= $230

Gym B total cost:

40m

= 40(6)

= $240

Therefore, the gym which is the best deal for 6 months is gym A

Read more on algebraic expression:

https://brainly.com/question/4344214

#SPJ1

The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'y' is given by the tangent of the angle 27°. Then we have

tan 27° = y / 350

y = 350 tan 27°

y = 178.3

The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

#SPJ1

The missing diagram is given below.

According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.

The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.

By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.

To know more about average visit:

https://brainly.com/question/15344468

#SPJ1

The system of the equations are:

y = 10 + 4x

y = 25 + x

The height of tree is 30 inches tall.

The graph is given below.

The solution is (5, 30).

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation

We have,

Maple tree:

The maple tree that is 10 inches tall is

growing 4 inches per month,

This can be written as,

y = 10 + 4x _____(1)

Where y is the height of the tree.

Oak tree:

The oak tree is 25 inches tall and is growing 1 inch per

month.

This can be written as,

y = 25 + x ______(2)

Where y is the height of the tree.

Now,

From (1) and (2),

In a few months, the two trees will be the same height.

So,

10 + 4x = 25 + x

4x - x = 25 - 10

3x = 15

x = 5

Now,

y = 10 + 4x = 10 + 4 x 5 = 10 + 20 = 30

y = 25 + x = 25 + 5 = 30

Thus,

The height of tree is 30 inches tall.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ9

The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.

Regression analysis is a powerful statistical tool used to estimate the relationship between two or more variables. The ordinary least squares (OLS) method is the most commonly used regression method. However, the OLS method is sensitive to outliers in the data.

LAD regression is a robust alternative to OLS regression because it minimizes the sum of the absolute vertical differences between the regression line and the data points. This method is also known as L1 regression.

Let's consider an example of a simple linear regression model with n observations, where Y is the dependent variable and X is the independent variable.

The OLS method estimates the parameters of the regression line by minimizing the sum of the squared vertical differences between the observed data points and the predicted values of the regression line.

In mathematical terms, the OLS method can be represented as follows:

minimize the sum of squared vertical differences,

min(β₀, β₁) ∑ (yₐ - β₀ - β₁ xₐ)²

However, if the data contains outliers, the OLS method may produce biased estimates of the parameters of the regression line, leading to incorrect predictions. On the other hand, LAD regression minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line.

In conclusion, the LAD regression is an alternative to OLS that reduces the sensitivity to outliers. The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.

To know more about regression here.

https://brainly.com/question/14184702

#SPJ4

The z-score for a weight of 13 ounces for a bird living in the northern region is 1 and in the southern region is -1.2.

A z-score, also known as a standard score, is a statistical measure that indicates how many standard deviations an observation or data point is above or below the mean of the distribution.

z = (x - μ) / σ

where

x  = value of the variable

μ = mean of the distribution

σ = standard deviation of the distribution.

In northern region, x = 13 ounces, μ = 10 ounces, σ = 3 ounces

z - score = (13 - 10) / 3

               = 1

In southern region, x = 13 ounces, μ = 16 ounces, σ = 2.5 ounces

z - score = (13 - 16) / 2.5

              = -1.2

Learn more about z-score of revenue from the link below:

https://brainly.com/question/15016913

#SPJ4

The joint distribution of X(t) and Y(t) is P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)

The joint distribution of customers remaining and having left can be expressed using the Poisson process as follows:

Let N(t) be the number of customers that arrive in the time interval [0, t], and let S₁, S₂, S₃, ... be the sequence of service times for each customer, where S_i is the time the i-th customer spends in the system (i.e., waiting and being served). Let Y(t) be the number of customers who have left the system by time t, and let X(t) be the number of customers who are still in the system at time t.

The joint distribution of X(t) and Y(t) can be written as:

P(X(t) = k, Y(t) = n) = P(N(t) = k + n) * P(sum of S_i for i = 1 to k + n > t) * P(sum of S_i for i = 1 to k + n - 1 <= t)

where the first term on the right-hand side represents the probability that k + n customers arrive in the time interval [0, t], the second term represents the probability that the sum of service times for the first k + n customers exceeds t (i.e., there are still k + n customers in the system at time t), and the third term represents the probability that the sum of service times for the first k + n - 1 customers is less than or equal to t (i.e., the first k + n - 1 customers have left the system by time t).

The distribution of X(t) and Y(t) can be quite complex, depending on the distribution of service times and the arrival rate of customers. However, in some special cases, closed-form expressions for the joint distribution can be derived. For example, if the service times have an exponential distribution and the arrival rate of customers is constant, then the joint distribution of X(t) and Y(t) is given by the following formula:

P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)

where μ is the rate parameter for the exponential distribution of service times.

Learn more about exponential distribution here https://brainly.com/question/22692312

#SPJ4

The population mean, 9,009, 10,585 employees, and 9,009, 10,585 steps are the solution.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency.

The term "activity tracker" refers to gadgets, including watches and bands, that record your physical activity, such as walking, jogging, and skipping. They only count your steps and inform you of your daily objectives. They are quite useful for tracking blood pressure and other things.

The 95% confidence interval between 9,009 and 10,585 steps was used to estimate the mean number of steps taken by City employees.

The likelihood of the various values may be estimated using the confidence interval. It may be utilised to derive conclusions about the population mean.

To know more about mean visit:

https://brainly.com/question/30094057

#SPJ1

The height of the building is approximately 79.22 meters, rounded to the nearest meter.

To calculate the angle of elevation, we use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle.

We know that the pole is 3.5 meters tall, and its shadow is 1.77 meters long. We can use this information to calculate the angle of elevation of the sun's rays, which is the angle formed between the horizontal line and the line of sight from the top of the pole to the sun.

In this case, the opposite side is the height of the pole (3.5 meters), and the adjacent side is the length of the shadow (1.77 meters). Therefore, we have:

tan(angle of elevation) = opposite/adjacent = 3.5/1.77

Using a calculator, we can find that the angle of elevation is approximately 63.24 degrees.

Now, we can use this angle to find out the height of the building. We know that the shadow of the building is 43.5 meters long, and we want to find its height, which is the opposite side of the right triangle formed by the angle of elevation and the length of the shadow. Therefore, we have:

tan(63.24 degrees) = opposite/43.5

Solving for the opposite, we get:

opposite = 43.5 * tan(63.24 degrees) = 79.22 meters

To know more about angle of elevation here.

https://brainly.com/question/21137209

#SPJ4