if a/3 =b/2 what are the following ratios a+b=4a

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer:

To represent -17/4 on a number line, we first need to find its approximate decimal equivalent. To do that, we divide -17 by 4:

-17 ÷ 4 ≈ -4.25

So, -17/4 is approximately -4.25. To plot it on a number line, we can start by locating -4, which is four units to the left of 0. Then, we can estimate a little bit to the left of -4 to represent -4.25. The resulting point should be closer to -4 than to -5.

Step-by-step explanation:

Hope this helps you~

The values of expressions are:

(a) 1(6×2) + 2 = 14,

(b) 3(0.30 × 2) + 4 = 5.80,

(c) (2 × 1)/(9 × 2) = 1/9.

Part (a) : To calculate the value of the expression 1(6×2) + 2, we perform the multiplication first: 6×2 = 12. Then we multiply the result by 1: 1×12 = 12. Finally, we add 2 to the product: 12 + 2 = 14. So, value of expression is 14.

Part (b) : For the expression 3(0.30 × 2) + 4, we first calculate the multiplication inside the bracket: 0.30 × 2 = 0.60.

Then we multiply the result by 3, 3 × 0.60 = 1.80. Finally, we add 4 to the product: 1.80 + 4 = 5.80.

Thus, the value of the expression is 5.80.

Part (c) : In the expression (2 × 1)/(9 × 2), we calculate the multiplications first: 2 × 1 = 2 and 9 × 2 = 18.

Then we divide the first result by the second: 2/18 = 1/9. Hence, the value of the expression is 1/9.

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The given question is incomplete, the complete question is

Calculate the value of the following expressions here:

(a) 1(6×2) + 2

(b) 3(0.30 × 2) + 4

(c) (2 × 1)/(9 × 2)

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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Answer:

3

Step-by-step explanation:

With a total of 15 grams of mass and 5 mL of volume, the simple formula of \rho ={\frac {m}{V}} would solve into the density being 3.

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z1 = (4 - 8.35) / 2.5 = -1.74
z2 = (12 - 8.35) / 2.5 = 1.46
P(-1.74 < z < 1.46) = 0.8711 - 0.0428 = 0.8283
Therefore, the probability that a household views television between 4 and 12 hours a day is 0.8283 (or 82.83% when expressed as a percentage).

To find the probability that a household views television between 4 and 12 hours a day, we will use the normal probability distribution.
1. To solve this problem, we can use the normal probability distribution formula:
z = (x - μ) / σ
where z is the z-score, x is the value we are interested in (in this case, between 4 and 12 hours), μ is the mean (8.35 hours), and σ is the standard deviation (2.5 hours).

2. We will find the Z-scores for the lower and upper bounds (4 and 12 hours, respectively) using the following formula: Z = (X - µ) / σ.

For the lower bound (4 hours):
Z1 = (4 - 8.35) / 2.5 = -1.74

For the upper bound (12 hours):
Z2 = (12 - 8.35) / 2.5 = 1.46

3. Now, we will use a Z-table or a calculator with a normal distribution function to find the probabilities corresponding to these Z-scores.

P(Z1) = P(Z < -1.74) ≈ 0.0409
P(Z2) = P(Z < 1.46) ≈ 0.9222

4. Finally, to find the probability that a household views television between 4 and 12 hours a day, subtract P(Z1) from P(Z2).

P(4 < X < 12) = P(Z2) - P(Z1) = 0.9222 - 0.0409 = 0.8813

So, the probability that a household views television between 4 and 12 hours a day is approximately 0.8813, or 88.13% (rounded to four decimal places).

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Solution

For this case we have the following, the sum of the angles needs to be 360 since we have a circumference:

10a-4 +6a-2 +8a+6=360

Regrouping we have:

10a +6a +8a -4 -2 +6= 360

24a= 360

a= 360/24= 15

Life Insurance Corporation (LIC) issued a policy in his favor charging a lower premium than what it should have charged if the actual age had been given. the optimal solution of the primal problem is (x1,x2,x3)=(5,0,10) and the objective function value is 45,000.

The optimal value of the given LP problem is 45,000. In this problem,  x1 = 5,

x2 = 0 and

x3 = 10.

Therefore, the objective function value = 7x1 + 5x2 + 9x3 will be 45,000, which is the optimal value.

problem is Minimize z = 7x1 + 5x2 + 9x3

subject to the constraints: i. 2x1 + x2 – 0.5x3 ≤ 5ii. 0.9x1 - 0.1x2 - 0.1x3 ≤ 10iii. x1 ≤ 14iv. x2 ≤ 20v. x3 ≤ 10vi. 3x1 + x2 + 2x3 ≤ 50

Duality: Maximize z = 5y1 + 10y2 + 14y3 + 20y4 + 10y5 + 15,000y6

subject to the constraints:2y1 + 0.9y2 + y3 + 3y6 ≥ 7y1 - 0.1y2 + y4 + y6 ≥ 0.5y1 - 0.1y2 + y5 + 2y6 ≥ 0y3, y4, y5, y6 ≥ 0 Now, we will solve the dual problem using the Simplex method. Using Excel Solver, As per complementary slackness theorem, the value of the objective function of the dual problem = 45,000, which is same as the optimal value of the primal problem. Therefore, the optimal solution of the primal problem is (x1,x2,x3)=(5,0,10) and the objective function value is 45,000.

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Answer:

The perimeter of triangle XYZ is 54 cm

Step-by-step explanation:

∵ Δ ABC is similar to Δ XYZ

∵ The longest side in Δ XYZ is 25.2 cm

→ That means its corresponding side in Δ ABC is the longest side

∵ AB = 18 cm, BC = 30 cm, CA = 42 cm

∴ The longest side in Δ ABC is CA

∴ CA is the corresponding side of the side of length 25.2 cm

∴ The ratio of similarity = \(\frac{25.2}{42}\) = 0.6 ⇒ (r)

∵ The perimeter of Δ ABC = AB + BC + CA

∴ The perimeter of Δ ABC = 18 + 30 + 42

∴ The perimeter of Δ ABC = 90 cm

→ Use the 2nd fact above

∵ P of Δ XYZ = r × P of Δ ABC

∵ r = 0.6 and P of Δ ABC = 90

∴ The perimeter of Δ XYZ = 0.6 × 90

∴ The perimeter of Δ XYZ = 54 cm

After conversion, B) 5 mL is 0.005 L milliliters

The quantity given = 0.005 L

Using a unit conversion, the same property is stated in a different unit of measurement. Minutes can be used to measure time instead of hours, and feet, kilometres, or any other measurement method can be used to measure distance in place of miles.

To convert from litres to millilitres, it is required to multiply the quantity by 1000. This is because there are 1000 millilitres in one litre.

Therefore, converting the given value-

= 0.005 L x 1000 mL/L

= 5

Thus, the resultant value after conversion is 5mL

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(-4,4) (4,-2)

m = (y2-y1)/(x2-x1)

m = ( -2-4)/(4-(-4))

m = -6/8

m = -3/4

Answer:

(4,3)

Step-by-step explanation:

Pick the 2 closest points that are perfectly on the line [(0,1) and (4,-2)]. Start at the first point (0,1) count to the right (From (0,1) to (4,1)) and that's our "x" number (4). Count down from that point (4,1) to the other predetermined point (4,-2) and you get your "y" number (3), thus (4,3)

Answer:

he would be left with 8.4meters

The statement "If the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent" is true.

Let's understand why?

Explanation:

An argument with a tautology conclusion is an argument that arrives at a conclusion that is always true, regardless of the truth values of the premises. In other words, it is impossible for the premises to be true while the conclusion is false.

This means that any attempt to find a counterexample that disproves the conclusion will always fail, as there is no possible scenario in which the conclusion is false.

The counterexample set of an argument is the set of all possible scenarios in which the premises are true but the conclusion is false. If the conclusion is a tautology, then there is no possible scenario in which the conclusion is false, and thus the counterexample set is empty. An empty counterexample set is equivalent to an inconsistent counterexample set, as it means that there is no consistent scenario in which the conclusion is false.

Therefore, if the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent.

Hence, the statement is true.

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The equation in slope intercept form for a line that passes through (10,-1) and a y intercept of -6 is y = -1/10x - 6.

Equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions that are separated by an equals sign (=), and the equation is true if and only if both expressions have the same value.
Slope intercept form is a way to express a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y intercept. In this equation, m is equal to -1/10 (the slope of the line between the two given points) and b is equal to -6 (the given y intercept). This equation can be used to describe the line that passes through (10,-1) and has a y intercept of -6.

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Answer:

To simplify the ratio, you can put it into a fraction and divide both the numerator and the denominator

Both numbers can be divided by 7

21/7= 3

35/7= 5

3 lizards: 5 frogs

Step-by-step explanation:

Hope this helps!

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Inequalities are used to represent the unequal expressions

The complete inequality of the range is \(-2 \le y < 5\)

The domain and the range are given as:

Rewrite properly as:

[-4,-2] to (4,5)

Remove the x values

[-2] to (5)

Square brackets represent >= or <= while brackets represent > or <.

So, we have the following range:

\(-2 \le y < 5\)

Hence, the complete inequality of the range is \(-2 \le y < 5\)

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Answer:less than or equal to and less than

Step-by-step explanation:

The points at which the banner should be attached to the archway are (1.5, 5.62) and (3.5, 6.12).Therefore, the correct answer is option D, (1.5, 5.62) and (3.5, 6.12).

The equation of the archway of the main entrance of a university is given as y = -*2 + 6x.

The equation of the angle the university is hanging its banner is 4y = 21 - x.We need to find the points at which the banner should be attached to the archway.Solution

Step 1: We need to solve the equation of the angle for y.4y = 21 - xy = (21 - x) / 4

Putting the value of y in the equation of the archway, we get y = -*2 + 6x.

Hence, we can write-*2 + 6x = (21 - x) / 4

Multiplying both sides by 4, we get-4x2 + 24x = 21 - x4x2 + 25x - 21 = 0The quadratic formula is used to find the roots of the equation.

Using the quadratic formula, we getx=\frac{-b\pm\sqrt{b^2-4ac}}{2a}a = -4, b = 25 and c = -21.

Substituting these values in the formula, we getx=\frac{-25\pm\sqrt{(25)^2-4(-4)(-21)}}{2(-4)}x = 1.5 or x = 3.5

So, the points at which the banner should be attached to the archway are (1.5, 5.62) and (3.5, 6.12).

Therefore, the correct answer is option D, (1.5, 5.62) and (3.5, 6.12).

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There is no such a number whose absolute value is -2. This is because the absolute value of any number is its distance from 0 irrespective of the direction.

An absolute value of a number is the distance of the number from 0 on a number line irrespective of the direction.

Consider the number "x".

Then its absolute value is written as

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

For example x = -9; then its absolute value is

|(-9)| = -(-9) = 9; (Since x = -9 < 0; we applied |x| = -x)

So, we can conclude that irrespective of the direction (positive or negative), the absolute value of any number remains positive.

We know that the absolute value of any number is calculated by

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

And the absolute value of any number irrespective of its direction on the number line remains positive.

So, no such number has a negative absolute value.

Hence, the answer is none for the given question.

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Answer:

points A, B and D are all in the same plane but not all are on the same line

Step-by-step explanation:

points A, C, D are all collinear which means they must also be coplanar

Answer: 53

Step-by-step explanation:

False. An n × n matrix that is orthogonally diagonalizable does not necessarily have to be symmetric. A matrix is said to be orthogonally diagonalizable if it can be expressed as PDP^T, where P is an orthogonal matrix and D is a diagonal matrix.

For a matrix to be symmetric, it must satisfy the condition A = A^T, where A^T denotes the transpose of A. While it is true that symmetric matrices are always orthogonally diagonalizable, the converse is not necessarily true. There exist non-symmetric matrices that can still be orthogonally diagonalized. An example of such a matrix is the following:

  [1  2]

A = [3 4]

This matrix is not symmetric, as A^T is:

  [1  3]

A^T = [2 4]

However, it is still orthogonally diagonalizable. The matrix A can be diagonalized as:

A = PDP^T, where P = [0.8507 -0.5257]

[0.5257 0.8507]

          and D = [-0.3723   0     ]

                    [ 0      5.3723]

Therefore, it is not necessary for an n × n matrix that is orthogonally diagonalizable to be symmetric.

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Part a:  [In⁻]/[HIn] = 4.0 × 10⁻⁶

Part b: [In⁻]/[HIn] = 50.11, for the given phenolphthalein solution.

Using the Henderson-Hasselbalch equation to determine the indicator's pH  is as follows:

pH = pKa + log[In⁻]/[HIn]

In which,

Ka = dissociation constant of acid.

As the stated value-

Part a:

pKa = 9.7

pH = 5.3

Thus,

5.3 = 9.7 + log[In⁻]/[HIn]

log[In⁻]/[HIn]  = - 4.4

[In⁻]/[HIn] = Antilog (-4.4)

[In⁻]/[HIn] = 4.0 × 10⁻⁶

Part b:

pKa = 9.7

pH = 11.4

Thus,

11.4 = 9.7 + log[In⁻]/[HIn]

log[In⁻]/[HIn]  = 1.7

[In⁻]/[HIn] = Antilog (-4.4)

[In⁻]/[HIn] = 50.11

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9514 1404 393

Answer:

  all are functions except Relation 2

Step-by-step explanation:

If any input value (first of an ordered pair) is used more than once, the relation is not a function. Output values can be used as often as you like.

Only Relation 2 is not a function.

The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).

Mean time that employees spend on personal issues each week(M) = 4.9 hours

Standard deviation = 0.35 hours

The following formula is used to get the confidence interval for the sample mean and standard deviation given:

μ = M ± t(sM)

where; M = sample mean

t = T-statistic based on confidence interval

Degree of freedom = n - 1

From the question, n = 55

Degree of freedom = 55 - 1

Degree of freedom = 54

(Standard errors)sM = √(s^2/n)

Now putting the value

sM = √(0.352/55)

sM = 0.05

t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)

Now the confidence interval

μ = M ± t(sM)

μ = 4.9 ± 2.005 × 0.05

μ = 4.9 ± 0.095

μ = (4.9 - 0.095, 4.9 + 0.095)

μ = (4.805, 4.95)

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The population of bacteria after 672 hours is 36000.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to the given question we have

The number of bacteria double is 336 hours.

And, the current population of bacteria is 9,000.

Therefore,

The population of bacteria after 336 hours = 9,000×2 = 18,000

⇒ the population of bacteria after 672 hours  = 18000 × 2 = 36000  

Hence, the population of bacteria after 672 hours is 36000.

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The area of the surface generated by revolving y=5−2x on [1,7] about the y-axis is approximately 96π square units.

To find the area of the surface generated by revolving the curve y = 5 - 2x on the interval [1, 7] about the y-axis, we can use the formula for the surface area of revolution. The formula states that the surface area is given by A = 2π∫[a,b] y(x) √(1 + (dy/dx)²) dx.

In this case, y(x) = 5 - 2x and the interval is [1, 7]. We need to find dy/dx, which is -2. Substituting these values into the formula, we have A = 2π∫[1,7] (5 - 2x) √(1 + (-2)²) dx.

Simplifying the equation, we get A = 2π∫[1,7] (5 - 2x) √5 dx. Evaluating this integral gives A = 2π√5 [x - (2/3)x²] evaluated from 1 to 7.

Evaluating the expression at the upper and lower limits and simplifying, we find that the area is approximately 96π square units.

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Answer:

Revolution traveled by me = 30π ft.

Revolution traveled by my friend = 20π ft.

Difference between revolutions = 10π ft.

Step-by-step explanation:

In one revolution, I travel 2π(15) = 30π ft., and my friend travels 2π(10) = 20π ft., so my revolution is 30π - 20π, or 10π, ft. longer than my friend's revolution.

i believe it is

8x+9 because it doesnt give a lot of info to solve for x  

The required probability of completing the color transformation when the textural transformation is not complete is 0.600.Given data,Total color transformation Yes: 212 No: 26.Total Textural transformation Yes: ?No: ?We are required to find the probability that it will complete the textural transformation when a leaf completes the color transformation.

We know that there are 212 cases of color transformation out of which, we need to find out the cases where textural transformation is also there.P(Completes the textural transformation | Completes the color transformation) =\($\frac{212}{212+26}$=0.891\) (Rounding to three decimal places, we get 0.891)

b) We are required to find the probability of completing the color transformation when the textural transformation is not complete.Given data,Total color transformation Yes: 212 No: 26 Total Textural transformation Yes: ?No: ?We can find out the cases where color transformation is complete but the textural transformation is not complete as follows,P(Completes the color transformation | Does not complete the textural transformation) = \($\frac{18}{18+12}$=0.600\)(Rounding to three decimal places, we get 0.600)

Hence, the required probability of completing the color transformation when the textural transformation is not complete is 0.600.

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