Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line

Answer:

a. The probability that the finished product selected is defective is 2.45%.

b. The probability that product chosen randomly was defective and made by machine B3 is 20.41%.

Step-by-step explanation:

Let A represents the defective product.

We also have the following from the question:

P(B1) = Probability or percentage of the made by machine B1 = 30%, or 0.30

P(B2) = Probability or percentage of the made by machine B2 = 45%, or 0,45

P(B3) = Probability or percentage of the made by machine B3 = 25%, or 0.25

P(A/B1) = Probability or percentage of product B1 that is defective = 2%, or 0.02

P(A/B2) = Probability or percentage of product B2 that is defective = 3%, or 0.03

P(A/B3) = Probability or percentage of product B3 that is defective = 2%, or 0.02

We can therefore proceed as follows:

A. Suppose that a finished product is randomly selected. What is the probability that it is defective?

To determine this, the rules of elimination is applied and we have:

P(A) = (P(B1) * P(A/B1)) + (P(B2) * P(A/B2)) + (P(B3) * P(A/B3)) ………… (1)

Where;

P(A) = Probability that the selected product is defective = ?

Substitutes the values defined above into equation (1), we have:

P(A) = (0.30 * 0.02) + (0.45 * 0.03) + (0.25 * 0.02)

P(A) = 0.006 + 0.0135 + 0.005

P(A) = 0.0245, or 2.45%

Therefore, the probability that the finished product selected is defective is 2.45%.

B. If a product were chosen randomly and found to be defective, what is the probability that it was made by machine B3.

To calculate this, the Bayes’ rule is employed as follows:

P(B3/A) = (P(B3) * P(A/B3)) / [(P(B1) * P(A/B1)) + (P(B2) * P(A/B2)) + (P(B3) * P(A/B3))] = (P(B3) * P(A/B3)) / P(A)  ………….... (2)

Where;

P(B3/A) = The probability that product chosen randomly was defective and made by machine B3 = ?

Also, from the values already defined and obtained in part A, we have:

P(B3) = 0.25

P(A/B3) = 0.002

P(A) = 0.0245

Substituting the values into equation (2), we have:

P(B3/A) = (0.25 * 0.02) / 0.0245

P(B3/A) = 0.005 / 0.0245

P(B3/A) = 0.2041, or 20.41%

Therefore, the probability that product chosen randomly was defective and made by machine B3 is 20.41%.

Answer:

The answer is D. 4(sqrt(5))

Step-by-step explanation:

To find this we use the Pythagorean Theorem a^2+b^=c^2

So making 4 = to a, and 8 = to, and x = to, we do

4^2+8^2= 80

Then we take the square root of 80 to find the missing side, which is equal to 4(sqrt(5)

Good luck!

The probability that in a given game the lions will score less than 3 goals is 0.80.

The probability distribution for the number of goals the lions soccer team makes per game is given below:

number of goals probability 0 0.30 1 0.35 2 0.15 3 0.10 4 0.10. The probability that in a given game the lions will score less than 3 goals is 0.80.

To find the probability that in a given game the lions will score less than 3 goals, we need to add up the probabilities for scoring 0, 1, or 2 goals.

P(Less than 3 goals) = P(0 goals) + P(1 goal) + P(2 goals)

We have the following probabilities:

P(0 goals) = 0.30

P(1 goal) = 0.35

P(2 goals) = 0.15

Therefore,

P(Less than 3 goals) = P(0 goals) + P(1 goal) + P(2 goals)

                                 = 0.30 + 0.35 + 0.15

                                 = 0.80

Thus, the probability that in a given game the lions will score less than 3 goals is 0.80.

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∑\((k^2)\) for k = 1 to 6 is the sum in sigma notation for this series of terms.

The series is 1 + 4 + 9 + 16 + 25 + 36. The lower limit of summation is 1, which means, the sum starts at the initial term in the series.

The index of summation is k, which implies, the ongoing term in the series is represented by the variable k.

In the expression \(k^2\)  which implies that we are adding up the square of the index of summation.

So, the sigma notation for this series of terms is ∑\((k^2)\)  for k = 1 to 6, which means, we are adding up the squares of the numbers from 1 to 6 (1, 4, 9, 16, 25, and 36)

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Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry

The ratio of neon fish to all the fish in the aquarium is 3 : 4   .

In the question ,

it is given that

in Mrs. Jone's class room there are angel fish and neon fish

number of angel fish in the aquarium = 14 fish

number of neon fish in the aquarium is = 42 fish

So, the total number of fish in the aquarium = number of angel fish + number neon fish

total number of fish = 14 + 42

= 56

the ratio of neon fish to all the fish in the aquarium is  

= number of neon fish : total number of fish

= 42 : 56

since the ratio is written in simplest form ,

we get

= 6 : 8

= 3 : 4

Therefore , The ratio of neon fish to all the fish in the aquarium is 3 : 4   .

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Answer:

Sphete B have a surface area of 48 square feet

Step-by-step explanation:

Two spheres of

Sphere A the smallest and sphere B the biggest has a scale factor of 1/3

Sphere A has surface area of 16 square feet.

Let's determine the surface area of sphere B.

Sphere A /sphere B = 1/3

Sphere A = 16

16/sphere B = 1/3

3*16= sphere B *1

48 = sphere B

Sphete B have a surface area of 48 square feet

Using the t-distribution, it is found that:

a. The margin of error is of 4.7 homes.

b. The 98% confidence interval for the population mean is (19.3, 28.7).

The information given in the text is:

We are given the standard deviation for the sample, which is why the t-distribution is used to solve this question.

The confidence interval is:

\(\overline{x} \pm M\)

The margin of error is:

\(M = t\frac{s}{\sqrt{n}}\)

Item a:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 23 - 1 = 22 df, is t = 2.508.

Then, the margin of error is:

\(M = t\frac{s}{\sqrt{n}} = 2.508\frac{9}{\sqrt{23}} = 4.7\)

Item b:

The interval is:

\(\overline{x} - M = 24 - 4.7 = 19.3\)

\(\overline{x} + M = 24 + 4.7 = 28.7\)

The 98% confidence interval for the population mean is (19.3, 28.7).

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The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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Answer:

3000

Step-by-step explanation:

50 flaps per second x 60 seconds in a minute = 3000 flaps

Answer:

Heyyyyy

Step-by-step explanation:

Answer:

yess

Step-by-step explanation:

Answer:

BC =  27

Step-by-step explanation:

The point B is the midpoint of AC

=> AB = BC

=> 4x - 5 = 11 + 2x

Let's calculate x to work out BC

Transferring the components containing x to the left side, and other components to the right side:

=> 4x - 2x = 11 + 5

Simplifying both sides:

=> 2x = 16

=> x = 8

Working out BC:

=> BC = 11 + 2x = 11 + 2(8) = 11 + 16 = 27

Hope this helps!

Using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem.

In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

A second-order equation of the form ax² + bx + c = 0 denotes a quadratic equation, where a, b, and c are real number coefficients and a 0.

So, we have the equation:

x²-3x+ 5 = 0

Now, solve it using the quadratic formula as follows:

x²-3x+ 5 = 0

a = 1

b = -3

c = 5

x = -(-3)±√(-3)² -4*1*5/2

Solve this further:

x = 3±√11/2

Therefore, using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.

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Correct question:

Solve x²-3x+ 5 = 0.

A.3+√-29 +VE/2 and 3- 2-29

B. 3+√29 and 3-√29

C. 3+√-11 and 3-√-11/2

D. 3+√11/2 and 3-√11/2

Answer:

6 + 40 *3 = 126

Step-by-step explanation:

first is 6 and you add 3 in every step

Answer:

126 smileys

Step-by-step explanation:

\(a_{1} =\) First term

    = 6

\(d =\) Common difference

  = 3

\(n =\) \(n^{th} term\)

  = Step number

Arithmetic sequence will be applied:

\(a_{n} = a_{1} + (n - 1)d\)

For n = 2:

\(a_{2} = 6 + (2 - 1)(3)\)

    \(= 6 + (1)(3)\)

    \(= 9\)

For n = 3:

\(a_{3} = 6 + (3-1)(3)\)

    \(= 6 + (2)(3)\)

    \(= 6 + 6\)

    \(= 12\)

∴For n = 41:

\(a_{41} = 6 + (41 - 1)(3)\)

     \(= 6 + (40)(3)\)

     \(= 6 + 120\)

     \(= 126\)

∴There will be 126 smiley faces in Step 41

167-149= The answer is 18

Answer:

$223,787

Step-by-step explanation:

r = 0.02

C = 191,000

t = 8

S = 191,000 (1 + 0.02)⁸

Follow order of operations (PEMDAS).

S = 191,000 (1.02)⁸

S = 191,000 (1.171659381)

S = 223,786.9

(We want to round to the nearest dollar, which is the ones place, so ignore all digits after the tenths place.)

Rounding, S = 223,787

An expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes is (0.55 + (n - 5) x 0.07) dollars.

Given:

Long Distance Rates Time (minutes) Cost5 $0.556 $0.627 $0.698 $0.769 $0.8310 $0.90We need to find an expression that can be used to find the cost of an n-minute long-distance call, where n is at least 5 minutes.

The cost of making a long-distance call is given for 5 minutes, 6 minutes, 7 minutes, 8 minutes, 9 minutes, and 10 minutes.

We can observe from the above table that for every increase of 1 minute, the cost increases by $0.07.

We can conclude that the cost of n minutes long-distance call is given by: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes.

Therefore, the required expression is: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes. The above expression is based on the pattern in the table provided for long-distance call rates. We can use this expression for values of n greater than or equal to 5.

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Bookworm publications can expect 2599.74 sales. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

It is believed that the four fundamental operations, often known as "arithmetic operations," may explain all real numbers. The four mathematical operations that produce the quotient, product, sum, and difference are division, multiplication, addition, and subtraction.

We are given that the sales in second year vary according to

S(x) = A₀ - (x + 600) / x²

Now, we are given that A₀ = 2600 and x = 50.

On substituting these values in the equation, we get

⇒S(50) = [2600 - (50 + 600)] / 50²

⇒S(50) = 2600 - (650 / 2500)

⇒S(50) = 2600 - 0.26

⇒S(50) = 2599.74

Hence, Bookworm publications can expect 2599.74 sales.

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Step-by-step explanation:

\( \sf{\dfrac{5( \fbox{41} - 32)}{9} = C}\)

\( \sf{\dfrac{5( \fbox{9})}{9} = C}\)

\( \sf{ \dfrac{45}{9} = C}\)

\( \sf{C = 5 }\)

So,

41° F = [5]°C

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

A and C

Step-by-step explanation:

A. Like terms have the same variable like -6y and 7y. If it was -6y squared and 7y, they would NOT be like terms.

B. 6 is a coefficient (number), not a variable.

C.  5 is the coeffecient (it 's being multiplied by x)

D. A constant term is a number.

Answer:

2,0

Step-by-step explanation:

Answer:

9.5 x 10^-3

Step-by-step explanation:

Move the decimal place until the leading digit is between 1 and 10, about three places to the right.

The exponent we use to notate our movement is negative, as we moved it to the right, so since we moved it three places to the right, it is -3.

Write it in the notation form m x 10^n, where m is that number between 1 and 10, and n is the exponent.

Your answer is 9.5 x 10^-3

Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

Answer:

x<4

Step-by-step explanation:

4*6-2=22

For number 5 - .3 ( 3.60 ÷ 12 = .3)

For number 6 - .32 ( 2.56 ÷ 8 = .32)

For number 7 - 2 ( 2.36 ÷ 2 = 1.18)

The value of angle ADB in the parallelogram given is 19°

Using the parallelogram laws :

Supplementary angles adds up to 180°, Hence we can use that to find CDA :

The sum of angles ∠ ADB + ∠ CDB should add up to 42°

∠ ADB + ∠ CDB = 42°

∠ ADB + 23° = 42°

∠ ADB = 19°

Hence, ADB is 19°

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