Biscuits are made in a factory. On Monday, machine A produced 2400 biscuits. 22 of these were broken. On Monday, 0.8% of the biscuits produced by machine B were broken. Which machine had the smaller proportion of broken biscuits? Show working to support your answer.

if possible I need the answer asap​

The correct answer is (a) No, the function for model A is a quadratic function that decreases faster than the function for model B, which is a decreasing exponential function.

To determine if model B will ever be lower than model A, we compare the decrease rates for both models.

Model A is represented by the quadratic function y = -0.5x^2 + 125, where x is the number of units produced. As x increases, the quadratic function decreases, but at a slower rate. This means that the cost decreases, but the rate slows down over time.

Model B is represented by the exponential function y = 250(0.95)^x, where x is the number of units produced. As x increases, the exponential function decreases faster. This means that the cost decreases, and the rate accelerates over time.

Looking at the costs given for the first 7 units produced, we can see that model A costs more initially than model B. However, as the number of units increases, the cost of Model A decreases at a slower rate than Model B.

Based on the patterns observed and the nature of the functions representing both models, the cost of model B will not be lower than model A. Model A, being a quadratic function, will eventually reach a point where the decrease in cost becomes minimal. In contrast, the exponential function of model B will continue to decrease faster. Therefore, option (a) is the correct answer.

To determine whether the cost of model B will ever be lower than the costs of model A, we can compare the cost patterns of both models as the number of units produced increases.

Looking at the given table, we can see that for each corresponding number of units produced, the cost of model B is consistently lower than the cost of model A. This pattern indicates that as the number of units produced increases, model B remains less expensive than model A.

Furthermore, we can analyze the cost functions for both models:

- Model A: y = -0.5x^2 + 125 (quadratic function)

- Model B: y = 250(0.95)^x-1 (decreasing exponential function)

From the cost functions, we can observe that the quadratic function for model A decreases at a faster rate as x increases, while the decreasing exponential function for model B decreases at a slower rate. This implies that model A's cost decreases more rapidly than model B's cost.

Based on the given information and the characteristics of the cost functions, we can conclude that the cost of model B will never be lower than the costs of model A. Therefore, the correct answer is:

b) No, the function for model B is a quadratic function that decreases at a slower rate than the function for model A, which is a decreasing exponential function.

Answer:The correct answer is d. Neither the normal nor the t distribution applies.

The corresponding rectangular equation for the polar equation is:

(x - 4)² + y² = 16

To convert polar equation to rectangular equation. Use the following relations:

x = rcosθ

y = rsinθ

r² = x² + y²

We have:

r = 8cos θ

r² = 8rcosθ (Multiply both sides by r)

x² + y² = 8x   (Remember: x = rcosθ)

x² - 8x + y² = 0

Using completing the square method:

x² - 8x + (-4)² + y² = 0 +  (-4)²

(x - 4)² + y² = 0 + 16

(x - 4)² + y² = 16

Therefore, the rectangular equation is (x - 4)² + y² = 16

Learn more about polar equation on:

brainly.com/question/14965899

#SPJ1

The volume V can be obtained by evaluating the integral of (2π)(5)((2 - (x^2 + 1)^(-2)) - ((x^2 + 1)^(-2))) with respect to y from 0 to 1.

To apply the Shell Method, we consider vertical cylindrical shells within the region. Each shell has a radius equal to the distance from the y-axis to the curve, and a height equal to the difference between the y-values of the two curves.

First, we need to find the limits of integration for the y-values. The curves intersect at y = 1, so we integrate from y = 0 to y = 1.

The radius of each shell is given by the x-coordinate of the curve. From the equation x = 5, we can see that the shell radius is always 5.

The height of each shell is the difference between the y-values of the curves. Thus, the height is (2 - (x^2 + 1)^(-2)) - ((x^2 + 1)^(-2)).

The volume of each shell is given by the product of the circumference (2π) and the radius times the height. Integrating this expression over the range of y = 0 to y = 1 will give us the total volume.

Therefore, the volume V can be obtained by evaluating the integral of (2π)(5)((2 - (x^2 + 1)^(-2)) - ((x^2 + 1)^(-2))) with respect to y from 0 to 1.

Performing this integration will yield the final result for the volume V.

Learn more about volume here;

https://brainly.com/question/28058531

#SPJ11

There is no value of c for integrals with f(x), g(x) in the interval [0, 1] that satisfies the Mean Value Theorem for integrals for f(x) = x and g.

To find the value of c that satisfies the Mean Value Theorem for integrals, we need to determine if there exists a value c in the interval [0, 1] such that the average rate of change of f(x) and g(x) over that interval is equal to the derivative of the antiderivative of g(x) minus the antiderivative of f(x) evaluated at c.

a) For f(x) = x and g(x) = x:

The average rate of change of f(x) and g(x) over [0, 1] is:

(f(1) - f(0)) / (1 - 0) = (1 - 0) / 1 = 1.

The antiderivative of g(x) minus the antiderivative of f(x) is:

∫[0,1] (g(x) - f(x)) dx = ∫[0,1] (x - x) dx = ∫[0,1] 0 dx = 0.

Since 1 is not equal to 0, there is no value of c that satisfies the Mean Value Theorem for integrals for f(x) = x and g(x) = x.

b) For f(x) = x² and g(x) = x:

The average rate of change of f(x) and g(x) over [0, 1] is:

(f(1) - f(0)) / (1 - 0) = (1² - 0²) / 1 = 1.

The antiderivative of g(x) minus the antiderivative of f(x) is:

∫[0,1] (g(x) - f(x)) dx = ∫[0,1] (x - x²) dx = [x²/2 - x³/3] evaluated from 0 to 1 = (1/2 - 1/3) - (0/2 - 0/3) = 1/6.

Since 1 is equal to 1/6, there exists a value of c in the interval [0, 1] that satisfies the Mean Value Theorem for integrals for f(x) = x² and g(x) = x.

c) For f(x) = x and g(x) = e^x:

The average rate of change of f(x) and g(x) over [0, 1] is:

(f(1) - f(0)) / (1 - 0) = (1 - 0) / 1 = 1.

The antiderivative of g(x) minus the antiderivative of f(x) is:

∫[0,1] (g(x) - f(x)) dx = ∫[0,1] (e^x - x) dx.

Finding the antiderivative of e^x gives us e^x, and the antiderivative of x is (1/2)x².

Evaluating the integral from 0 to 1, we have:

∫[0,1] (e^x - x) dx = [e^x - (1/2)x²] evaluated from 0 to 1 = (e - 1/2) - (1 - 0) = e - 3/2.

Since 1 is not equal to e - 3/2, there is no value of c that satisfies the Mean Value Theorem for integrals for f(x) = x and g(x) = e^x.

There is no value of c that satisfies the Mean Value Theorem for integrals for f(x) = x and g

To know more about Mean Value Theorem, click here: brainly.com/question/30403137

#SPJ11

Answer:

There will be 3 full 4.2-yd pieces plus a 2.02-yd leftover piece.

Step-by-step explanation:

Divide 14.62 yd by 4.2.  Determine the remainder as a decimal fraction:

14.62 yd

------------- = 3 full 4.2 yd pieces, plus 0.5 piece left over.

4.2 yd

Note that "0.5 piece" would be 0.48(4.2) yds long, or 2.02 yds.

Then you'd have three pieces of length 4.2 yds and 1 leftover piece of length 2.02 yd.

Louise has 132 points after hitting the blue target first, then the red target.

Adam also has 132 points after hitting the red target first, then the blue target.

Louise hits the blue target first, then the red target:

Starting score: 100 points

Hitting the blue target increases the score by 10%

100 + (10/100) × 100

= 100 + 10

= 110 points

Hitting the red target increases the score by 20%:

110 + (20/100) × 110 = 110 + 22 = 132 points

b) Adam hits the red target first, then the blue target:

Starting score: 100 points

Hitting the red target increases the score by 20%: 100 + (20/100) × 100 = 100 + 20 = 120 points

Hitting the blue target increases the score by 10%: 120 + (10/100) × 120 = 120 + 12 = 132 points

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

Answer:132 each

Step-by-step explanation:

Answer:

447

Step-by-step explanation:

We know that :

[tex] \sf2x + 15 + x + 10 + 3x + 5 = 180[/tex]

[tex] \sf6x + 30 = 180[/tex]

[tex] \sf6x = 180 - 30[/tex]

[tex] \sf6x = 150[/tex]

[tex] \sf \: x = 25[/tex]

Answer:

Question 1:   <BAC = 35 degrees

Question 2:   <ABC =  80 degrees

Question 3:  <ACB = 65 degrees

Step-by-step explanation:

Angle Sum Theorem:

<ABC + <ACB + <BAC = 180 degrees

(3x + 5) ^degrees + (2x + 15)^degrees +  (x + 10)^degrees = 180 degrees

<ABC = (3x + 5)^degrees

<ACB = (2x + 15)^degrees into <ABC + <ACB + <BAC = 180 degrees

x = 25

<BAC = (25 + 10)^degrees

<BAC = 35 degrees

Answer = <BAC = 35 degrees

<ABC + <ACB + <BAC = 180 degrees

(3x + 5) ^degrees + (2x + 15)^degrees +  (x + 10)^degrees = 180 degrees

<ABC = (3x + 5)^degrees

<ACB = (2x + 15)^degrees into <ABC + <ACB + <BAC = 180 degrees

x = 25

<ABC = (3 * 25 + 5)^degrees

<ABC = 80 degrees

Answer = <ABC =  80 degrees

Question 3:  Angle Sum Theorem

<ABC + <ACB + <BAC = 180 degrees

(3x + 5) ^degrees + (2x + 15)^degrees +  (x + 10)^degrees = 180 degrees

<ABC = (3x + 5)^degrees

<ACB = (2x + 15)^degrees into <ABC + <ACB + <BAC = 180 degrees

x = 25

<ACB = (2 * 25 + 15) ^degrees

<ACB = 65 degrees

Answer = <ACB = 65 degrees

Hope this helps!

Among the given options, the most reasonable conclusion that can be made when a facility employs mostly healthcare workers certified by the Association of Safe Patient Handling Professionals (ASPHP) is:

a. The facility will save money from reduced employee injuries.

Certification by ASPHP indicates that the healthcare workers have received specialized training in safe patient handling techniques. This training aims to prevent injuries to both the healthcare workers and the patients. By employing certified workers, the facility can expect a reduction in employee injuries, leading to potential cost savings associated with workers' compensation claims, medical expenses, and lost productivity.

It is important to note that while this conclusion is likely, it does not guarantee that all injuries will be eliminated or that the facility will be completely injury-free. However, employing certified healthcare workers is a positive step towards promoting a safer working environment.

Know more about Association of Safe Patient Handling Professionals here:

https://brainly.com/question/30831413

#SPJ11

The complex amplitudes are

1.  A = 21*e^(-j15°).

2. A = 60*e^(j10°).

3. A = 120*e^(-j50°).

4.  A = 8*e^(j70°).

To find the complex amplitudes in polar format, we can express the given sinusoidal signals as complex numbers of the form A*e^(jθ), where A is the magnitude (amplitude) and θ is the phase angle.

1. v(t) = 21 cos(4t - 15°) V:

The complex amplitude is A = 21*e^(-j15°).

2. v(t) = -60 cos(30t + 10°) V:

The complex amplitude is A = 60*e^(j10°).

3. v(t) = 120 sin(10t - 50°) V:

The complex amplitude is A = 120*e^(-j50°).

4. v(t) = -8 sin(10t + 70°) V:

The complex amplitude is A = 8*e^(j70°).

Note: In the polar format, the magnitude A represents the amplitude of the signal, and the angle θ represents the phase shift of the signal. The exponential term e^(jθ) represents a phasor with magnitude 1 and phase angle θ.

To know more about amplitude visit:-

brainly.com/question/8662436

#SPJ11

To determine the optimum production cycle, we need to calculate the production run sizes (Q) for each item. Here's how you can fill in the table:

1. Unit Demand (Di): This is the annual demand divided by the number of working days: RF1: 2,500 / 250 = 10

RF2: 10,000 / 250 = 40

RF3: 5,000 / 250 = 20

RF4: 4,000 / 250 = 16

RF5: 15,000 / 250 = 60

2. Production Run Size (Qi): The production run size is calculated using the economic production quantity formula: Qi = sqrt((2 * Di * Ci) / Hi)

RF1: sqrt((2 * 10 * $200) / $1.50) ≈ 73

RF2: sqrt((2 * 40 * $250) / $0.60) ≈ 223

RF3: sqrt((2 * 20 * $250) / $1.00) ≈ 89

RF4: sqrt((2 * 16 * $100) / $2.50) ≈ 25

RF5: sqrt((2 * 60 * $400) / $1.00) ≈ 110

3. Production Cycle Length: The production cycle length is the sum of all production run sizes:

73 + 223 + 89 + 25 + 110 = 520 units

4. Slack Time per Run: The slack time per run is the total number of working days divided by the number of production runs:

250 / 5 = 50 days

To determine the optimum production cycle, we calculate the production run sizes for each item using the economic production quantity formula. This formula considers the annual demand, holding cost, and production run cost to find the optimal production quantity. Once we have the production run sizes for each item, we sum them up to determine the length of the complete production cycle. In this case, it amounts to 520 units. The slack time per run is then calculated by dividing the total number of working days by the number of production runs, which is 50 days in this scenario. This information helps in planning the production schedule efficiently.

LEARN MORE ABOUT production  here: brainly.com/question/32196896

#SPJ11

A regression model was developed to predict the state burglary rate per 100,000 people for 2005 using median age, number of bankruptcies, federal expenditures per capita, and high school graduation percentage as predictors.

To build a regression model to predict the state burglary rate per 100,000 people for 2005 using the four state predictors (X1, X2, X3, X4), you can follow these steps:

Collect the data: Gather data for the predictors (X1, X2, X3, X4) and the target variable (Y) for multiple states in 2005. Ensure that you have a sufficient number of data points for a reliable analysis.

Preprocess the data: Clean the data by handling missing values, outliers, and any other data quality issues. Normalize or standardize the predictors if necessary to ensure they are on a similar scale.

Split the data: Divide the dataset into a training set and a testing set. The training set will be used to train the regression model, while the testing set will be used to evaluate its performance.

Choose a regression algorithm: Select an appropriate regression algorithm based on your specific requirements and the nature of the data. Common choices include linear regression, polynomial regression, or even more advanced algorithms like random forest regression or support vector regression.

Train the model: Fit the regression model using the training data. Provide the model with the predictor variables (X1, X2, X3, X4) and the corresponding target variable (Y).

Evaluate the model: Use the testing set to assess the performance of the trained regression model. Calculate evaluation metrics such as mean squared error (MSE), root mean squared error (RMSE), or R-squared to measure how well the model fits the data.

Interpret the results: Analyze the coefficients of the regression model to understand the relationship between the predictors (X1, X2, X3, X4) and the target variable (Y). Determine which predictors have a significant impact on the burglary rate.

Make predictions: Once you are satisfied with the model's performance, use it to make predictions on new, unseen data. Provide the model with the predictor values (X1, X2, X3, X4) for the desired state(s) and obtain the predicted burglary rate (Y).

Remember that building an accurate regression model involves iterative processes of refining the model, feature selection, and evaluation. It's essential to explore the data, understand its characteristics, and adjust the model accordingly to improve its predictive capabilities.

The complete question should be :

A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage.

To learn more about regression model visit : https://brainly.com/question/28178214

#SPJ11

Answer:

  C.  1.875 J

Step-by-step explanation:

You want the work done stretching a spring from 25 cm to 30 cm, given that the force required to stretch it to 25 cm from its natural length of 15 cm is 30 N.

In newtons per meter, the spring constant is ...

  k = (30 N)/(0.25 m -0.15 m) = 300 N/m

Work is the product of force and distance. When the force is a function of distance, the work can be found by integrating:

  dW = k(x -0.15)dx

  [tex]\displaystyle W=\int_{0.25}^{0.30}300(x-0.15)dx = \dfrac{300}{2}((0.30-0.15)^2-(0.25-0.15)^2)\\\\=150(0.0125)=1.875\quad\text{joules}[/tex]

The work required to stretch the spring to 30 cm is 1.875 J.

__

Additional comment

The units of work (energy) used here are newton-meters (joules), so the distance dimensions need to be in meters. 15 cm = 0.15 m, for example.

<95141404393>

The correct match of each dilation to its function is:

g (x) = 4/3 x² ; vertical stretch

h (x) = (5x)²; horizontal compression

We have to given that;

Functions are,

g (x) = 4/3 x²

And, h (x) = (5x)²

Now, We get;

For g (x) = 4/3 x²;

g(x) = x²: This is the parent function, and it is not dilated in any way. Its graph is a parabola that opens upwards and has a vertex at the origin.

For h (x) = (5x)²;

This function is a horizontal compression of the parent function, because the constant factor of 2 inside the x^2 causes the function to be compressed horizontally by a factor of 1/5.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

The value of Hypotenuse (x) of triangle is,

⇒ x = 80

Since, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In a triangle,

Hypotenuse of triangle = x

Adjacent side of triangle = 48

Hence, By definition of trigonometry formula we get;

⇒ sin θ = Adjacent / Hypotenuse

Substitute all the given values, we get;

⇒ sin 37° = 48 / x

⇒ 0.60 = 48 / x

⇒ x = 48 / 0.6

⇒ x = 80

Hence, The value of Hypotenuse of triangle is,

⇒ x = 80

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer: True

Step-by-step explanation:    

The missing numbers are,

⇒ 18, and 17

We have to given that;

A pairs of equivalent expressions is shown with one in standard form and the other in factored form.

Here, Expressions are,

⇒ (x + 1) (x + 17)

And, x² + _x + _

Now, WE can simplify the factor form of expression as;

⇒ (x + 1) (x + 17)

⇒ x² + 17x + x + 17

⇒ x² + 18x + 17

By comparing, we get;

The missing numbers are,

⇒ 18, and 17

Learn more about the quadratic equation visit:

brainly.com/question/1214333

#SPJ1

The Factored form of 3x^2 - 11x + 6 is (x - 3)(3x - 2).

The quadratic expression 3x^2 - 11x + 6, we can use the method of factoring by grouping. Here's the step-by-step process:

Step 1: Multiply the coefficient of x^2 (3) by the constant term (6) in the expression.

  3 * 6 = 18.

Step 2: Find two numbers that multiply to give 18 and add up to the coefficient of x (-11).

  The numbers -2 and -9 fit this criteria because -2 * -9 = 18 and -2 + (-9) = -11.

Step 3: Split the middle term (-11x) into two terms using the numbers found in step 2.

  3x^2 - 2x - 9x + 6.

Step 4: Group the terms and factor out the greatest common factor (GCF) from each group.

  (3x^2 - 2x) - (9x - 6).

  x(3x - 2) - 3(3x - 2).

Step 5: Notice that the terms (3x - 2) are common in both groups. Factor it out.

  (x - 3)(3x - 2).

So, the factored form of 3x^2 - 11x + 6 is (x - 3)(3x - 2).

To know more about  Factored form.

https://brainly.com/question/30284656

#SPJ11

Answer:

  (a)  It can always be written as a fraction.

Step-by-step explanation:

You want to know what can be said of the sum of rational numbers.

The set of rational numbers is closed under addition. The sum of any pair of rational numbers is a rational number.

A rational number can always be written as a fraction.

__

Additional comment

As a decimal, it will either be terminating or repeating. Any given rational number will be one or the other. Rationals in general will not always terminate, or always repeat.

<95141404393>

Answer:

D. 6x^2– x – 12​

Step-by-step explanation:

The area of a rectangle is the product of its length and width.

In this case, the length is given as 2x-3 and the width is given as 3x+4.

Therefore, the area of the rectangle is (2x-3) * (3x+4) = 6x^2-x-12.

To find the area of a rectangle in general, you can use the formula A = L * W where A is the area, L is the length and W is the width of the rectangle

Hope this helps!

a 21.8 g sample of osmium would occupy a volume of approximately 0.9646 cm³.

To calculate the volume occupied by a sample of osmium, we can use the formula:

Volume = Mass / Density

Given:

Mass = 21.8 g

Density = 22.6 g/cm³

Substituting these values into the formula:

Volume = 21.8 g / 22.6 g/cm³

Simplifying:

Volume = 0.9646 cm³

what is volume?

Volume is a measure of the amount of space occupied by a three-dimensional object or substance. It quantifies the extent or capacity of an object or substance in terms of how much space it occupies.

In mathematical terms, volume is typically measured in cubic units (such as cubic meters, cubic centimeters, or cubic inches). It is calculated by multiplying together the three dimensions of the object (length, width, and height) or by using specific formulas depending on the shape of the object.

For example, the volume of a rectangular box can be calculated by multiplying its length, width, and height. The volume of a cylinder can be calculated using the formula πr²h, where r is the radius of the base and h is the height.

Volume is an essential measurement in various fields such as physics, engineering, chemistry, and everyday life. It helps determine capacities, quantities, displacements, and the amount of space occupied by objects or substances.

to know more about Density visit:

brainly.com/question/30636123

#SPJ11

True, we can conclude that an interval computed as 112.5-118.4 has a probability of .95 of bracketing the population mean.

When we compute the 95% confidence limits on the mean, we are essentially creating an interval within which the true population mean is likely to fall. In this case, the interval is 112.5-118.4. The probability of this interval bracketing the true population mean is .95, which means that there is a 95% chance that the population mean lies within this interval.

Therefore, it is true that an interval computed in this way has a probability of .95 of bracketing the population mean.


The statement is true because when we compute 95% confidence limits on the mean, it means that we are 95% confident that the true population mean lies within the given interval. In this case, the interval is 112.5-118.4. So, there is a 0.95 probability that the true population mean is within this range.

Based on the 95% confidence interval, we can conclude that it is highly probable (95% probability) that the true population mean lies between 112.5 and 118.4.

To learn more about interval visit;

https://brainly.com/question/11051767

#SPJ11

Both A and B should be classified as discrete data.

In the given options, both A and B should be classified as discrete data.

A. The letter grades earned in a Statistics course are discrete data because they are categorical and have distinct categories such as A, B, C, etc. These categories cannot be subdivided into smaller units.

B. The number of books on a shelf is also discrete data because it represents a countable quantity. You can only have whole numbers of books, and you cannot have a fractional or continuous value for the number of books.

Discrete data consists of distinct and separate values that cannot be subdivided, unlike continuous data which represents a range of values.

To learn more about “fractional” refer to the https://brainly.com/question/78672

#SPJ11

The power series representation for ln((1+x)/(1-x)) is given by: ln[tex]((1+x)/(1-x)) = 2(x + (x^3)/3 + (x^5)/5 + (x^7)/7 + ...)[/tex], This representation is valid for |x| < 1, as it is derived using the power series expansion of ln(1+x) and ln(1-x), which have a convergence radius of 1.

To find the power series representation of ln((1+x)/(1-x)), we'll use the properties of the natural logarithm function and the geometric series.

First, we'll rewrite the expression using the properties of logarithms:

ln((1+x)/(1-x)) = ln(1+x) - ln(1-x)

Now, let's find the power series representation for ln(1+x) and ln(1-x) separately.

Power series representation of ln(1+x):

We know that the power series representation of ln(1+x) is given by: [tex]ln(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...[/tex]

Power series representation of ln(1-x):

Similarly, the power series representation of ln(1-x) is given by:

[tex]ln(1-x) = -x - (x^2)/2 - (x^3)/3 - (x^4)/4 - ...[/tex]

Now, we'll subtract the series representation of ln(1-x) from ln[tex](1+x): ln((1+x)/(1-x)) = (x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...) - (-x - (x^2)/2 - (x^3)/3 - (x^4)/4 - ...) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ... + x + (x^2)/2 + (x^3)/3 + (x^4)/4 + ... = 2(x + (x^3)/3 + (x^5)/5 + (x^7)/7 + ...)[/tex]

Learn more about Power series

brainly.com/question/29896893

#SPJ11

The possible units digits for the multiples of 6 are:

{0, 2, 4, 6 ,8}

A multiple of 6 is any number that can be written as a product between an integer and 6.

Remember that 6 is an even number, and thus, all the products between an even number and an integer is also an even number.

Then the units digits of the possible multiples of 6 will be the set of even numbers:

{0, 2, 4, 6 ,8}

These are all the possible options.

6*10 = 60

6*2 = 12

6*4 = 24

6*1 = 6

6*3 = 18

Learn more about multiples at:

https://brainly.com/question/10749076

#SPJ1

Rounded to four decimal places, the estimated area using left endpoints is approximately 8.2925.

(a) To estimate the area under the graph of f(x) = 2√x from x = 0 to x = 4 using four approximating rectangles and right endpoints, we can use the right Riemann sum.

The width of each rectangle is Δx = (4 - 0) / 4 = 1, since we are dividing the interval [0, 4] into four equal parts.

The right endpoints for the four rectangles are x = 1, 2, 3, and 4.

To find the height of each rectangle, we evaluate f(x) = 2√x at the right endpoints:

f(1) = 2√1 = 2

f(2) = 2√2 ≈ 2.8284

f(3) = 2√3 ≈ 3.4641

f(4) = 2√4 = 4

The area of each rectangle is the product of the width and height.

Area of first rectangle = 1 * 2 = 2

Area of second rectangle = 1 * 2.8284 ≈ 2.8284

Area of third rectangle = 1 * 3.4641 ≈ 3.4641

Area of fourth rectangle = 1 * 4 = 4

The estimate of the area under the graph is the sum of the areas of the four rectangles:

R4 = 2 + 2.8284 + 3.4641 + 4 ≈ 12.2925

Rounded to four decimal places, the estimated area is approximately 12.2925.

(b) To estimate the area under the graph using left endpoints, we use the left Riemann sum.

The left endpoints for the four rectangles are x = 0, 1, 2, and 3.

Using the same calculations as in part (a), we find the heights of the rectangles:

f(0) = 2√0 = 0

f(1) = 2√1 = 2

f(2) = 2√2 ≈ 2.8284

f(3) = 2√3 ≈ 3.4641

The area of each rectangle is the product of the width and height:

Area of first rectangle = 1 * 0 = 0

Area of second rectangle = 1 * 2 = 2

Area of third rectangle = 1 * 2.8284 ≈ 2.8284

Area of fourth rectangle = 1 * 3.4641 ≈ 3.4641

The estimate of the area under the graph using left endpoints is the sum of the areas of the four rectangles:

L4 = 0 + 2 + 2.8284 + 3.4641 ≈ 8.2925

To know more about graph visit:

brainly.com/question/17267403

#SPJ11

[tex]\stackrel{\widehat{FI}}{85}~~ + ~~\stackrel{\widehat{IH}}{(50+x)}~~ + ~~\stackrel{\widehat{HG}}{(-9x-10)}~~ + ~~\stackrel{\widehat{GF}}{(-15x+5)}~~ = ~~360 \\\\\\ 130-23x=360\implies 130=360+23x\implies -230=23x\implies \cfrac{-230}{23}=x \\\\\\ -10=x\hspace{9em}\stackrel{\widehat{GF}}{-15(-10)+5}\implies \text{\LARGE 155}^o[/tex]

Answer:

A. y = (x + 3)^ 2 - 1

Step-by-step explanation:

To represent the transformation of a horizontal shift left 3 and a vertical shift down 1 applied to the function y = x^2, you can use the following equation:

y = (x + 3)^2 - 1

In this equation, the term (x + 3) represents the horizontal shift left 3, and the term -1 represents the vertical shift down 1. The squared term remains the same as in the original function, y = x^2.