Identify the type of curve given by each equation.
r2 = 49sin 2θ

The probability of a defect is 5.7330 x \(10^{-5}\) and the number of defects is 5.73.

To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.

First, we need to standardize the weight limits as follows -

\(Z_{lower}\) = (9.75 - 10) / 0.25 = -4

\(Z_{upper}\) = (10.25 - 10) / 0.25 = 4

Next, we will find the area under the standard normal curve that lies outside of these limits as follows -

P(Defect) = P(Z < -4) + P(Z > 4)

Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x   \(10^{-5}\)  and P(Z > 4) = 2.8665 x  \(10^{-5}\) .

So, the total probability of a defect is -

P(Defect) = 2.8665 x  \(10^{-5}\)  + 2.8665 x  \(10^{-5}\)  = 5.7330 x  \(10^{-5}\)

Finally, we will find the number of defects for a 1,000-unit production run as follows -

The number of defects = 1000 * 5.7330 x  \(10^{-5}\)  = 5.73 (rounded to the nearest whole number).

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Answer:

Rs. 7245

Step-by-step explanation:

Given parameters:

Cost price  = Rs. 6300

Percentage profit  = 15%

Unknown:

Selling price = ?

Solution:

If profit is made on a trade, the selling price is higher than the cost price.

 Profit  = Selling price  - Cost price

To find the selling price simply;

  Selling price  =( 1 + \(\frac{15}{100}\))  x cost price

  Selling price  = 1.15 x 6300  = Rs. 7245

Answer:

8,415

Step-by-step explanation:

2+2+2+2+20+41+20+8252+74 = 8,415

Answer:

8,415

Step-by-step explanation:

Copy and pasted into a calc

look it up dum dum this app got me a f+ >:(

Answer:

The answer is "0.3206".

Step-by-step explanation:

\(H_0: p_1 = p_2\\\\H_a: p_1 \neq p_2\\\\\hat{p_1} = \frac{X_1}{N_1} = \frac{53}{400} = 0.1325\\\\\hat{p_1}= \frac{X_2}{N_2} = \frac{78}{500}= 0.156\\\\\hat{p} = \frac{(X_1 + X_2)}{(N_1 + N_2)} = \frac{(53+78)}{(400+500)} = 0.1456\)

Testing statistic:

\(z = \frac{(\hat{p_1}- \hat{p_2})}{\sqrt{(\hat{p} \times (1-\hat{p}) \times (\frac{1}{N_1} + \frac{1}{N_2}))}}\)

\(=\frac{(0.1325-0.156)}{\sqrt{(0.1456\times (1-0.1456)\times (\frac{1}{400} + \frac{1}{500}))}}\\\\ = -0.99\)

Calculating the P-value Approach

\(\text{P-value}= 0.3206\)

The measures of the angles are a = 38, b = 52, c = 104 and d = 90 degrees

From the question, we have the following parameters that can be used in our computation:

The circle and its properties

The angle in a semicircle is 90 degrees

So, we have

d = 90

Using the properties of angles, we have

a = 1/2 * 76

a = 38

Also, we have

a + b + d = 180 --- sum of angles in a triangle

So, we have

38 + b + 90 = 180

This gives

b = 52

Using the properties of angles, we have

b = 1/2 * c

52 =  1/2 * c

c = 104

Hence, the measures of the angles are a = 38, b = 52, c = 104 and d = 90 degrees

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Answer:

It would cost Jeremy $66 for 6 CDs

Step-by-step explanation:

3 CDs for $33

3(2)=6

$33(2)=$66

Answer:

A’(-5,4)

B’ (1, 4)

c’ (1,1)

d’ (-5, 1)

Step-by-step explanation:

Hi 

let call "a number" X.

then we have: 4-13X = X + 8 ..

Answer:

12.7  ==> distance of RS

24.2 ==> distance of RT

Step-by-step explanation:

Distance is always positive. So if you get a negative value, take the absolute value of the negative number:

For example, between point R and S:

-17.2 - (-4.5) =

-17.2 + 4.5 =  ==> subtracting a negative number is equivalent to adding a

                           positive number

-(17.2 - 4.5) = -12.7

-12.7 ==> |-12.7| = 12.7  ==> distance of RS

For RT:

-17.2 - 7 =

-(17.2 + 7) = -24.2

-24.2 ==> |-24.2| = 24.2 ==> distance of RT

The given expression is

=ab+cd+ef+gh

The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction,  Multiplication and Division.

→The expression consists of four terms which are, ab, cd, ef, and gh.

→Each term contains

Two factors.

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The weighted total is obtained by multiplying the data value by its corresponding frequency,

Solve for the weighted total for each data point as,

The mean of the data is calculated as,

Thus, the mean number of cups of coffee drank yesterday is

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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The points on a parabola with the focal axis parallel to the abscissa axis, of parameter p and A, B is -12.

Since A and B are points on the parabola, write two equations using the general form of the parabolic equation:

(x - h)² = 4p(y - 1)

The focal axis is parallel to the x-axis, so the distance from the vertex to the focus is equal to p. Therefore, use the distance formula to write an equation for the distance between the vertex and point A:

√((13 - h)² + (a - 1)²) = p

Similarly, write an equation for the distance between the vertex and point B:

√((4 - h)² + (b - 1)²) = p

A and B lie on the line 2x - y - 13 = 0, so substitute the x and y coordinates of A and B into this equation and solve for a and b:

2(13) - a - 13 = 0

2(4) - b - 13 = 0

Solving these equations gives us a = 3 and b = -5.

Now three equations and three unknowns (a, b, and h):

√((13 - h)² + 4) = p + 1

√((4 - h)² + 36) = p + 1

2h - 3 - 13 = 0

The third equation simplifies to 2h = 16, or h = 8.

Substituting this value of h into the first two equations and squaring both sides:

(13 - 8)² + 4 = (p + 1)²

(4 - 8)² + 36 = (p + 1)²

Simplifying these equations and solving for p gives us p = 3.

Finally, find a" + bP by substituting the values found for a, b, and p:

a" + bP = 3 + (-5)(3) = -12

Therefore, the solution is a" + bP = -12.

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Hi small cats and cats and dogs have a great experience with the evening of the evening of 6th century the morning of this

Answer:

$1710

Step-by-step explanation:

let me know if you want an explanation :))

Answer:

IV

Step-by-step explanation:

Answer:

The Quadrent it would be in would be the bottom right.

Step-by-step explanation:

Go over 6 units on the x axis, then go down 4 (because it is a negative).

Answer:

x = 15

Step-by-step explanation:

the segment inside the triangle is an angle bisector and divides the side opposite the bisected angle into segments that are proportional to the other two sides, that is

\(\frac{x}{21-x}\) = \(\frac{25}{10}\) ( cross- multiply )

10x = 25(21 - x)

10x = 525 - 25x ( add 25x to both sides )

35x = 525 ( divide both sides by 35 )

x = 15

The correct option is

D. (x-4)^2 + (y-2)^2 = 9

The equation of a circle that has center in a point P = (h, k) is:

Where r is the radius. In this case the center is in (4, 2). Then we can rplace h and k:

All that is left is replace r by the radius. In this case r = 3 then r^2 = 9

Now we can complete the equation:

And that's option D.

Answer:

2.120 kg= 2.12 kg.

Step-by-step explanation:

As you can clearly tell, 2.120 is equal to 2.12, because the 0 to the right of all the numbers and the period doesn't add or substract anything from the number.

Therefore, 2.120 kg= 2.12 kg.

Answer:

Option A

Step-by-step explanation:

       Pick any two points on the line.

       (3 , 0) ⇒ x₁ = 3 & y₁ = 0

        (0,-2) ⇒ x₂ = 0 & y₂ = -2

Find the slope using the formula,

      \(\boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}\)  

                   \(\sf =\dfrac{-2-0}{0-3}\\\\\\=\dfrac{-2}{-3}\\\\\\=\dfrac{2}{3}\)

      Slope-point form of a line: y - y₁ = m(x - x₁)

Substitute slope and the point in the above equation,

              \(y - 0 = \dfrac{2}{3}(x - 3)\\\\ ~~~~~~ y= \dfrac{2}{3}x-\dfrac{2}{3}*3\\\\\\~~~~~~\boxed{ y = \dfrac{2}{3}x-2}\)

This is in slope intercept form: y = mx + b.

Answer:

about 1.32 pounds for 1 dollar

Step-by-step explanation:

simply do 50÷38 then you get your answer

Answer:

rounded up to 1.32 pounds for 1 dollar

Step-by-step explanation:

Simply take 50 and divide it by 38 to get your answer

The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.

The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.

(8 x 4) : 30

32 : 30

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Answer: A. 8 strawberries: 30 blueberries

Step-by-step explanation:

As no digram attached you can solve it by yourself

Formula is given by

\(\\ \rm\rightarrowtail \dfrac{1}{2}(a+b)h\)

Where

Answer:m

Step-by-step explanation: