Does x=3 make the equation 5x-3=12 true or false?

Answer:

The perimeter of parallelogram WXYZ is 2√5 + 2√17 units or also known as about 12.72 units.

Step-by-step explanation:

In the diagram, we have a parallelogram. A parallelogram is a shape with two pairs of congruent sides. So, this means that we only need to find the measurement of two sides. From there, we are going to multiply those individual measurements by 2 because both has another side that is congruent  to them. Lastly, we will add up all of the measurements to find the perimeter.

We can find the lengths by using the distance formula.

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}\)

Let's find the length of WX.

\(WX=\sqrt{(4-0)^2+(0-(-1))^2}\)

\(WX=\sqrt{((4)^2+(1)^2)}\)

\(WX=\sqrt{16+1}\)

\(WX=\sqrt{17}\)

Now, we multiply this number by 2 because ZY is congruent to this side.

√17 × 2 = 2√17

Now, let's find the length of WZ.

\(WZ=\sqrt{(0-(-1))^2+(-1-(-3))^2}\)

\(WZ=\sqrt{(1)^2+(2)^2}\)

\(WZ=\sqrt{1+4}\)

\(WZ=\sqrt{5}\)

Now, we multiply this number by 2 because XY is congruent to this side.

√5 × 2 = 2√5

Now, we add these numbers together to get the perimeter.

2√5 + 2√17 = 12.72

The required perimeter of parallelogram WXYZ is \(2\times \sqrt5 + 2\times \sqrt17 \ units\).

We have to determine, The perimeter of parallelogram WXYZ.

According to the question,

A parallelogram is a shape with two pairs of congruent sides. So, this means need to find the measurement of two sides.

From there, multiply those individual measurements by 2 because both has another side that is congruent  to them. Lastly, add up all of the measurements to find the perimeter.

To find the lengths by using the distance formula,

\(d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}} \\\\WX = \sqrt{(4-0)^{2}+ (0-(-1))^{2}} \\\\WX = \sqrt{16+1} \\\\WX = \sqrt{17}\)

Then, multiply this number by 2 because ZY is congruent to this side.

\(\sqrt{17} \times 2= 2 \sqrt{17}\)

Now, let's find the length of WZ by using distance formula,

\(d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}} \\\\WZ = \sqrt{((-1)-(-3))^{2}+ (0-(-1))^{2}} \\\\WX = \sqrt{4+1} \\\\WX = \sqrt{5}\)

Now, multiply this number by 2 because XY is congruent to this side.

\(=\sqrt{5} \times 2= 2\sqrt{5}\)

Therefore, adding these numbers together to get the perimeter of parallelogram WXYZ,

Perimeter of parallelogram WXYZ  \(=2\times \sqrt5 + 2\times \sqrt17 \ units\)

Hence, The required perimeter of parallelogram WXYZ is \(2\times \sqrt5 + 2\times \sqrt17 \ units\).

To know more about Parallelogram click the link given below.

https://brainly.com/question/14592910

The trend projection for time period 18 is 197.6. The correct option is B

A mathematical equation used to represent the trend or pattern seen in a time series of data is called a linear trend expression, sometimes referred to as a linear trend model.

To find the trend projection for time period 18 using the given linear trend expression, we substitute t = 18 into the equation:

Yt = 129.2 + 3.8t

Y18 = 129.2 + 3.8 * 18

Y18 = 129.2 + 68.4

Y18 = 197.6

Therefore, the trend projection for time period 18 is 197.6.

Learn more about linear trend expression here : brainly.com/question/30471421

#SPJ1

The most realistic sampling method that represents the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area is Cluster Sampling technique.

In cluster sampling, the total population is divided into homogeneous groups known as clusters and a simple random sample of the groups is selected. The elements present in each cluster are then sampled like a sample. In other words we can say each cluster is represent a tiny population set. We have, geologists have an interest in the structure and the history of the earth. In this study, the whole population is divided into groups based on retrieving a core sample, estimating the ages of the various layers, and examining the composition. After that a timeline can be built of the entire area for drilling the core sample. So, each set work as small population i.e., clusters. The sampling technique which is used here to represent the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area is known as cluster sampling.

To learn more about Cluster Sampling technique, refer:

https://brainly.com/question/29348692

#SPJ4

Answer: 12 dimes

Step-by-step explanation: 12 quarters = 3.00

five nickels = 3.25

12 dimes = 4.45

13 pennies = 4.58

In this question we have to use herons formula,

A=root(s x(s−a)x(s−b)x(s−c))

Where A is the area of triangle; a, b and c are the sides of a triangle and s is the half the perimeter of the triangle i.e.

s=(a + b + c )/2

a=5 , b=12 and c=13

s=(5+12+13)/2

By adding the numbers in numerator, we get,

s=30/2

By dividing 2 with 30, we get,

s = 15.

now,

A=root(15(15−5)(15−12)(15−13))

A=root (15(10)(3)(2))

By multiplying each number inside the square root, we get,

A = root (900)

As the square of 30 is 900. Therefore, the square root of 900 is 30 and we get,

A = 30.

so the area of the triangle is 30.

Learn more about Herons formula here :-

https://brainly.com/question/29184159

#SPJ4

Bobby will run more than 50 miles in his 12th week of training (rounded up).

The total number of miles Bobby runs over the first 20 weeks of training need to use a formula for the sum of a geometric series:

S = a(1 - rⁿ) / (1 - r)

where:

S is the sum of the series

a is the first term (10 miles)

r is the common ratio (1.12, because he increases his mileage by 12% each week)

n is the number of terms (20 weeks)

Substituting these values into the formula, we get:

S = 10(1 - 1.12²⁰) / (1 - 1.12)

≈ 225.4

So, over the first 20 weeks of training Bobby runs about 225.4 miles.

Bobby will run more than 50 miles need to set up an equation for the nth term of the geometric series:

a × r⁽ⁿ⁻¹⁾ > 50

Substituting the values we know, we get:

10 × 1.12⁽ⁿ⁻¹⁾ > 50

Dividing both sides by 10, we get:

1.12⁽ⁿ⁻¹⁾⁾ > 5

Taking the logarithm of both sides (using any base), we get:

(n-1) × log(1.12) > log(5)

Dividing both sides by log(1.12), we get:

n-1 > log(5) / log(1.12)

Adding 1 to both sides, we get:

n > log(5) / log(1.12) + 1 ≈ 11.6

For similar questions on week

https://brainly.com/question/1575227

#SPJ11

Answer:

x=5

Step-by-step explanation:

x-3=2

x-3=2

 +3  +3

x=5

Answer:

When you are driving a car, the number of miles that you can drive is directly proportional to the amount of gas you have. left in the tank. For instance, if you only have 2 gallons of gas. left, you can only travel 26 more miles

Step-by-step explanation:

When you are driving a car, the number of miles that you can drive is directly proportional to the amount of gas you have. left in the tank. For instance, if you only have 2 gallons of gas. left, you can only travel 26 more miles

Answer:

The x-intercept is the point where the graph crosses the x-axis; it can be found by setting y = 0 and solving for x.

The y-intercept is the point where the graph crosses the y-axis; it can be found by setting x = 0 and solving for y.

1) g(x) = (x + 5)⁴

2) f(x) = 7 - x⁴

3) h(x) = ¼(x - 3)⁴

The graphs are labeled below.

The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).

It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):

1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).

To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.

2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.

In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.

Learn more about horizontal axis:

brainly.com/question/29774083

#SPJ11

Answer:

All the lines have the same slope, m = 0, showing that they are all parallel.

Step-by-step explanation:

PLATO

Answer:

The fact that all of the lines have the same slope, m = 0, indicates that they are all parallel.

Step-by-step explanation:

Step-by-step explanation:We have to graph the function g(x) which is given as:

g(x)=  x when x<2

and -3 when x ≥2.

Clearly after looking at the function we see that the function is not continuous since we find the continuity at x=2 as follows.

Left hand limitat 2:

g(2-h)=lim h→0 2-h

       =2-0=2

Also right hand limit at x=2 is:

g(2+h)=lim h→0 (2+h)

         = 2+0=2

Also g(2)= -3.

As:

Left hand limit= Right hand limit but is not equal to function's value at that point.

Hence, the function is discontinuous at x=2.

so for x<2 we will get a graph of a line y=x.

and for x≥2 we will get a straight line y=-3 parallel to the domain.

The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

A polynomial is an expression consisting of coefficients and variables forming an equation.

Given the polynomial:

x³ + 2x² -x - 2

Factorizing:

= (x + 2)(x² - 1)

= (x + 2)(x + 1)(x - 1)

The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

Find out more on equation at: https://brainly.com/question/29174899

#SPJ1

The net operating income is $113,050 and the average operating assets are $140,000, the ROI is calculated as ($113,050 / $140,000) * 100, resulting in approximately 80.75%.

Approval, Inc.'s return on investment (ROI) can be calculated as the ratio of net operating income to average operating assets, expressed as a percentage.

To calculate Approval, Inc.'s return on investment (ROI), we can use the formula:

ROI = Net Operating Income / Average Operating Assets

Given that the net operating income is $113,050 and the average operating assets are $140,000, we can substitute these values into the formula:

ROI = $113,050 / $140,000 = 0.8075 or 80.75%

Therefore, Approval, Inc.'s return on investment (ROI) is 80.75%.

To know more about investment refer to-

https://brainly.com/question/15105766

#SPJ11

Complete Question

The contribution margin at Approval, Inc. was calculated to be 19% when sales were $595,000, net operating income was $113,050, and average operating assets were $140,000. What was Approval Inc.'s return on investment (ROI)?

Answer:

b = $2.40

d = $5.70

Step-by-step explanation:

d = hot dog and b = hot dog buns

Equations:

2d + 5b = $23.40

3d + 2b = $21.90

-------------------------------subtract these two equations

-d + 3b = $1.50

3b - $1.50 = d

Substitute:

3d + 2b = $21.90

3(3b - $1.50) + 2b = $21.90

9b - $4.50 + 2= $21.90

11b = 26.40

b =  $2.40

Substitute again but this time with b:

3d + 2b = $21.90

3d + 2($2.40) = $21.90

3d + $4.80 = $21.90

3d = $21.90

d = $5.70

When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

for such more question on simplified

https://brainly.com/question/11680269

#SPJ8

-57 decrease

In this equation.

The value of the function at x=0 is 17.78(4.86)^0 = 17.78(1) = 17.78.

ii. The ratio of output values ​​corresponding to an increment of 1 in input values ​​is (4.86)^1 = 4.86.

iii. A percent change of 1 unit is (4.86 - 1) × 100% = 286% increase.

For the function h(x) = 94.71(0.57)^x:

Thus, the value of the function at x=0 is 94.71(0.57)^0 = 94.71(1) = 94.71.

ii. The ratio of the output value corresponding to an increment of 1 in the input value is (0.57)^2 = 0.57.

iii. Percentage change of 1 unit is (0.57 - 1) × 100% = -57 reduction

Read more about this on brainly.com/question/17137295

#SPJ4

Step-by-step explanation:

Parallel lines cut by a transversal coloring activity is an activity that helps students understand the pattern of angles when parallel lines are cut by a transversal. The activity involves coloring the angles formed by the parallel lines and the transversal in different colors. This helps students identify the different types of angles formed and their relationships with each other.

Answer:

they held yearly elections so I would say democracy but I'm not 100% sure

Using the GCF to factor and the distributive property 28 + 24 = 4(7 + 6)

28 + 24 as a product of the two factors using greatest common factor and the distributive property can be represented as follows:

The greatest common factor is defined as the largest number that is a factor of two or more numbers.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

Therefore, lets solve 28 + 24 using GCF and the distributive property.

The GCF of 28 and 24 is 4. Hence,

28 + 24 = 4(7 + 6)

Therefore,

28 + 24 = 4(7 + 6)

learn more on GCF  here; https://brainly.com/question/18994312

#SPJ1

Answer:

X=2, y=5

Step-by-step explanation:

Y=3x-1 equation 1

-4x+2y=2 equation 2

-4x +2(3x-1)=2 substitute value of y (3x-1) in equation 1 into y value of equ e

-4x+6x-2=2 distributative property

2x=4 solve above equation

x=2

solve for y:

y=3x-1

y=3(2)-1

y=6-1

y=5

The simple linear regression model does provide a useful relationship between the burner-area liberation rate (x) and the NOx emission rate (y). The test procedure yields a significant P-value, allowing us to reject the null hypothesis (H0: β1 = 0).

To determine whether the simple linear regression model specifies a useful relationship between the burner-area liberation rate (x) and the NOx emission rate (y), we need to test the null hypothesis H0: β1 = 0 against the alternative hypothesis Ha: β1 ≠ 0. The null hypothesis assumes that there is no linear relationship between the two variables, while the alternative hypothesis suggests otherwise.

To calculate the test statistic, we first need to estimate the slope of the regression line. Using the given data, we can perform linear regression analysis to find the estimated slope. Once we have the estimated slope, we can calculate the test statistic using the formula: t = (b1 - 0) / SE(b1), where b1 is the estimated slope coefficient and SE(b1) is the standard error of the estimated slope.

In this case, the calculated test statistic is t = 3.56 (rounded to two decimal places). The degrees of freedom for the test statistic is n - 2, where n is the number of data points. Since there are 14 data points in the given dataset, the degrees of freedom is 12.

To determine the P-value, we compare the test statistic to the t-distribution with 12 degrees of freedom. Looking up the P-value associated with t = 3.56 in the t-distribution table, we find it to be approximately 0.004 (rounded to three decimal places).

With a significance level of 0.01, we compare the P-value to the significance level. Since the P-value (0.004) is less than the significance level (0.01), we reject the null hypothesis. Therefore, we conclude that there is evidence that the simple linear regression model specifies a useful relationship between the burner-area liberation rate and the NOx emission rate.

Moving on to part (b), to compute a 95% confidence interval (CI) for the expected change in the emission rate associated with a 10 MBtu/hr-ft2 increase in the liberation rate, we can use the regression equation. The estimated regression equation is y = b0 + b1 * x, where b0 is the estimated intercept and b1 is the estimated slope.

By substituting the values into the regression equation, we can find the expected change in the emission rate. In this case, since we want to find the change associated with a 10 MBtu/hr-ft2 increase in the liberation rate, we can substitute x with 10 and calculate the predicted value of y.

Using the estimated regression equation, the predicted change in the emission rate associated with a 10 MBtu/hr-ft2 increase in the liberation rate is found to be approximately 170 ppm. To construct the 95% CI, we calculate the standard error of the predicted change using the formula: SE(predicted change) = SE(b1) * \(\sqrt(1/n + (x - mean(x))^2 / sum((x - mean(x))^2))\), where n is the number of data points and mean(x) is the mean of the liberation rate.

With the calculated standard error, we can construct the 95% CI using the formula: predicted change ± t * SE(predicted change), where t is the critical value from the t-distribution with n - 2 degrees of freedom and a confidence level of 95%.

Using the given data, the calculated 95% CI for the expected change in the emission rate associated with a 10 MBtu/hr-ft2 increase in the liberation rate is approximately (92.35 ppm, 247.65 ppm) (rounded to two decimal places). This means that we are 95% confident that the true change in the emission rate lies within this interval.

Learn more about simple linear regression model here:

https://brainly.com/question/32254934

#SPJ11

The midpoint of the second class ([40-49]) is calculated by adding the lower and upper limits of the class and dividing by 2. So, (40+49)/2 = 44.5.

The relative frequency of the second class is calculated by dividing the frequency of the second class by the total frequency. So, 8/38 = 0.211.

The class width is the difference between the upper and lower limits of the class. So, [59.5-69.5] has a class width of 10.

The fourth actual class is [60-69], which has a midpoint of (60+69)/2 = 64.5.

Therefore, the answer is a. 44.5, 0.211, 10 and [59.5-69.5].

#SPJ11

Learn more on: https://brainly.com/question/27820465

The investigator can test the presence of simple sugars in the sample by using Benedict's solution.

Simple carbs are tested for using Benedict's Test. With free ketone or aldehyde functional groups, reducing sugars (monosaccharides and some disaccharides) are recognized by the Benedict's test.

Benedict's solution turns orange or brick red when heated in the presence of simple carbohydrates. The reducing characteristic of simple carbs is what triggers this response. The Benedict's solution changes color as a result of the reduction of copper (II) ions to copper (I) ions.

The produced red copper(I) oxide precipitates out of solution because it cannot be dissolved in water. This explains how the precipitate was created. The closer the final hue is approaching brick-red and the more precipitate is generated as the reducing sugar concentration rises. Copper oxide, a brick-red solid, can occasionally precipitate out of a solution and gather at the test tube's bottom.

For more information of Benedict's solution visit:

https://brainly.com/question/14731281

#SPJ4

Answer:

Coordinates of point B are (3, 5) and (5, 3).

Step-by-step explanation:

Coordinates of point A → (1, 1)

Let the coordinates of point B are (x', y')

Formula for the distance between points (x, y) and (x', y') is,

d = \(\sqrt{(x-x')^+(y-y')^2}\)

AB = \(\sqrt{(x-1)^+(y-1)^2}\)

\(2\sqrt{5}=\sqrt{(x-1)^2+(y-1)^2}\)

\((2\sqrt{5})^2=(x-1)^2+(y-1)^2\)

20 = (x - 1)² + (y - 1)²

Since point A lies on the intersection of two grid lines in the 1st quadrant, x and y must be the positive whole number.

For x = 0,

20 = (0 - 1)² + (y - 1)²

(y - 1)² = 20 - 1

y = 1 + √19

But y can't be a decimal, therefore, x = 0 is not the answer.

For x = 1

20 = (1 - 1)² + (y - 1)²

20 - 1 = (y - 1)²

y = 1 + √19

Not a whole number, so can't be the solution.

For x = 2,

20 = (2 - 1)² + (y - 1)²

y = 1 + √19

Not a whole number, therefore, not the answer.

For x = 3,

20 = (3 - 1)² + (y - 1)²

20 - 4 = (y - 1)²

y = 1 + √16

y = 5

Therefore, (3, 5) are coordinates of the point B.

For x = 4,

20 = (4 - 1)² + (y - 1)²

20 = 9 + (y - 1)²

y = 1 + √11

For x = 5,

20 = (5 - 1)² + (y - 1)²

20 - 16 = (y - 1)²

4 = (y - 1)²

y = 3

Therefore, (5, 3) the coordinates of point B.

The coordinates of \(B, (x,y)=(3,5)\text{ or }(5,3)\)

From the diagram, the coordinates of \(A\) are \((1,1)\)

the distance from \(A\) to \(B\) is \(2\sqrt{5}\)

Since \(B(x, y)\) also lies on the grid, \(x\) and \(y\) should be integers and should satisfy the distance relationship

\((x-1)^2+(y-1)^2=(2\sqrt{5})^2\implies (x-1)^2+(y-1)^2=20\)

There is a way to get \(\sqrt{5}\) from Pythagoras rule

\(1^2+2^2=(\sqrt{5})^2\\\\\implies2^2+4^2=(2\sqrt{5})^2\)

Which means we can either say

\(x-1=2 \text{ and } y-1=4\\\implies x=3 \text{ and } y=5\\\\\text{OR}\\\\x-1=4 \text{ and } y-1=2\\\implies x=5 \text{ and } y=3\)

Therefore B is either at location \((3,5)\) or \((5,3)\)

Learn more coordinate geometry here: https://brainly.com/question/15503404

14 out of 40 marigold seeds , 18 out of 50 zinnia seeds ,  12 out of 30 sunflower seeds  are the names of the plants in the order from least percentage to greatest percentage of the plants that grew

What is percentage?

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we imply that it is 50% of everything.

As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any topic are calculated in terms of percentages in academics. Ram, for instance, scored 78% in his final test. This percentage is derived based on Ram's overall grade point average (GPA) across all disciplines.

10% is equivalent to a fraction of one.

20% is equal to a 1/5 fraction.

25% is equal to a 1/4 fraction.

50% is equal to a 1/2 fraction.

75% is equal to a 1/4 fraction.

90% is equal to a fraction of 9/10.

14 out of 40 marigold seeds = 14/40 x 100 = 35%

18 out of 50 zinnia seeds = 18/50 x 100 = 36%

12 out of 30 sunflower seeds = 12/30 x 100 =40%

Learn more about percentage from the link below

https://brainly.com/question/28269290

#SPJ1

The temperature in Gainesville is 11°C.

From the information given, the temperature in Elmwood is 20° and the temperature in Gainesville is 9°C colder than the temperature in Elmwood.

Therefore, the temperature in Gainesville will be:

= 20 - 9

= 11°C

Learn more about temperature on:

brainly.com/question/24746268

#SPJ1

The temperature in Elmwood is 20°C. The temperature in Gainesville is 9°C colder than the temperature in Elmwood

The learning-curve exponent (b) is approximately 0.291, and the learning-curve rate (R) is approximately 1.047. The time required to build the first house (T1) can be calculated using the learning curve formula. If the learning-curve percentage is changed to 76%, starting from the Nth house, the time for construction per house would be less than half the construction time for the third house. The value of N can be determined by solving the equation.

he learning-curve exponent (b) is approximately 0.291, and the learning-curve rate (R) is approximately 1.047.

The learning curve follows a mathematical relationship where the time required to complete a task decreases as more units are produced. The formula for the learning curve is T = T1 * \((N^b)\), where T is the time required for N units, T1 is the time required for the first unit, N is the cumulative number of units, and b is the learning-curve exponent.

To find the learning-curve exponent (b), we can use the given information that the construction team spent 18% less time building the seventh house compared to the third house. This can be expressed as:

T7 = T3 * \((7^b)\) - 0.18 * T3

Since we know that T7 is 0.82 times T3, we can substitute these values into the equation:

0.82 * T3 = T3 * \((7^b)\) - 0.18 * T3

Simplifying the equation, we get:

0.82 =\(7^b\) - 0.18

Solving for b, we find that b is approximately 0.291.

To calculate the learning-curve rate (R), we can use the formula R = \(2^(^1^-^b^)\). Plugging in the value of b, we get R is approximately 1.047.

If the last house built required 2,500 manual labor hours, we can use the learning curve formula to calculate the time required to build the first house (T1). We know that N = 18 and T = 2,500. Rearranging the formula, we have:

T1 = T / (N^b)

Plugging in the values, we get:

T1 = 2,500 / (18^0.291)

Calculating T1, we find that the time required to build the first house is approximately 2,808.

To determine the value of N when the learning-curve percentage is changed to 76% starting from the Nth house, where the time for construction per house would be less than half the construction time for the third house, we can use the learning curve formula again. In this case, the time required for the Nth house would be 0.5 times the time required for the third house:

T3 * (N^b) * 0.76 = 0.5 * T3

Simplifying the equation, we get:

N^b = 0.5 / 0.76

Taking the logarithm of both sides of the equation, we can solve for N:

b * log(N) = log(0.5 / 0.76)

log(N) = log(0.5 / 0.76) / b

N = 10^(log(0.5 / 0.76) / b)

Calculating N using the given values of b, we find that N is approximately 12.

Learn more about the Learning curve

brainly.com/question/32171225

#SPJ11

Answer: Inequality 1

Step-by-step explanation: Let's solve each inequality first.

4(2.8z+175 )>-26.6

let's distribute the 4.

4(2.8z)+4(175)

11.2z+700>-26.6

Now let's isolate the variable by subtracting 700 on each side.

11.2z>-726.6

Now let's divide both sides by 11.2

z>-64.875

Oh? This one already has 5 as a solution as 5 is more than -64.875!