Five units were defective in a sample of 70 units. Obtain a 95% confidence interval for the population proportion of defective units a. [0.064 , 0.078 ] b. [-0.432 , 0.574 ] c. [0.011 , 0.131 ] d. [0.040 0.102 ]

Answer:

There is a 40% chance that it will rain Tuesday and Friday.

Step-by-step explanation:

This is a good way to check you've done it correctly. Rains on Tuesday + doesn't rain on Friday: 40%⋅50%=20%

Answer:

60 percent chance

Step-by-step explanation:

First you multiply the two together. Then move the decimal to get a percent! HOpe this helps

If b be a subset of a where |a| = n and |b| = k, then the number of subsets of a whose intersection with b has exactly one element is k × (n-k) C(k-1)

Let's first choose the one element that must be in the intersection of any subset of A with B. Since B has k elements, there are k choices for this element.

Now, we need to choose the remaining (k-1) elements of the subset from A - B, which has n-k elements. There are (n-k) choose (k-1) ways to do this.

Therefore, the total number of subsets of A whose intersection with B has exactly one element is

k × (n-k) choose (k-1)

Alternatively, we can write this as

k × (n-k)C(k-1)

where nCk represents the number of ways to choose k items from a set of size n using combinations.

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Answer:

you forgot to add the statements

Answer:

c = - 4

Step-by-step explanation:

Nothing else matters except that the number associated with the y value in equation one = 1 and the number in front of x is known in equation 1. Then we'll get around to looking at c

Add 2y to both sides of equation 1 (the top equation)

3x - 2y + 2y = 3 + 2y

3x = 2y + 3        

Now divide both sides of the equation by 2

3x/2 = y + 3/2

What's in front of x? It is (3/2)

So divide both sides of 6x + cy = 4       by c

6x/c + y = 4/c

Now put 6x/c on the right hand side so y is by itself.

y = -6x/c + 4/c

What do you have to do now?

You must equate -6x/c = 3/2x

Why?

The slopes have to be the same so the lines are parallel and never cross. That will give no solutions.

-6x/c = 3x / 2     Divide both sides by x

-6/c = 3/2           Cross multiply

3c = - 6 * 2        Combine

3c = - 12             Divide by 3

c = - 12/3

c = - 4

Answer:

\(\frac{4}{54}\) feet (0.07407407407 feet)

Step-by-step explanation:

For this problem, we must just keep dividing by six.

At the drop, it is at 96 feet.

Divide that by six after the first bounce we have 16 feet.

Divided again we have 2\(\frac{2}{3}\) feet for the second bounce, (or 2.666666)

The third bounce we have \(\frac{4}{9}\) feet (0.4444444444)

and finally for the fourth bounce \(\frac{4}{54}\) feet (0.07407407407)!

Answer:

Step-by-step explanation:

1 + 2 + 4 = 7

7x = 1400

x = 1400/2 = 200

1(200) + 2(200) + 4(200) = 1400

Sand:  200 kg

Gravel:  400 kg

Cement:  800 kg

You would need 200 kg of sand, 400 kg of gravel, and 800 kg of cement to make 1400 kg of dry concrete using the ratio 1:2:4,

Let's assign variables to represent the quantities:

Let x be the quantity of sand.

Let y be the quantity of gravel.

Let z be the quantity of cement.

According to the given ratio, the quantities will be as follows:

Sand: x

Gravel: 2x (twice the amount of sand)

Cement: 4x (four times the amount of sand)

The total weight of the dry concrete is the sum of the weights of the individual components:

x + 2x + 4x = 1400 kg

Combining like terms:

7x = 1400 kg

Dividing both sides of the equation by 7:

x = 200 kg

Now that we know the quantity of sand, we can find the quantities of gravel and cement:

Gravel: 2x = 2 × 200 kg = 400 kg

Cement: 4x = 4 × 200 kg = 800 kg

Therefore, you would need 200 kg of sand, 400 kg of gravel, and 800 kg of cement.

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Answer:

(x - y - 3)(x + 1/2 y + 3/2) = 0

or  (x - y - 3)(2x + y + 3) = 0

Step-by-step explanation:

see attached for step-by-step

The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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The angles at each corner of the rhombus are approximately 56 degrees. To find this, we can use the fact that the diagonals of a rhombus bisect each other at a 90-degree angle and that the diagonals of a rhombus are perpendicular bisectors of each other's sides.

Let's label the rhombus ABCD, with AB = BC = CD = DA = 10 cm. Let's also label the shorter diagonal as AC, where AC = 7 cm. Since the diagonals of a rhombus bisect each other at a 90-degree angle, we can draw a perpendicular line from A to line segment CD, which we will label as E. This creates two right triangles, AEC and AED, where AE is half of the diagonal AC (since it bisects the diagonal) and AD and DC are both 5 cm (half of the side length).

Using the Pythagorean theorem, we can find that EC = $\sqrt{AC^2 - AE^2} = \sqrt{7^2 - 5^2} = \sqrt{24} = 2\sqrt{6}$. Since the diagonals of a rhombus are perpendicular bisectors of each other's sides, we know that EC is also half of BD, the longer diagonal. Therefore, BD = 2EC = $4\sqrt{6}$.

Now we can look at triangle ABD. We know that AB = DA = 10 cm, and BD = $4\sqrt{6}$ cm. To find the angle at B, we can use the law of cosines, which states that $c^2 = a^2 + b^2 - 2ab\cos(C)$, where a, b, and c are the side lengths of a triangle and C is the angle opposite side c. Let's label angle ABD as angle C in this equation.

We want to solve for angle C, so we rearrange the equation to get $\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$. Plugging in the values we know, we get $\cos(C) = \frac{10^2 + 10^2 - (4\sqrt{6})^2}{2(10)(10)} = \frac{80}{200} = 0.4$. Taking the inverse cosine of 0.4, we get that angle C is approximately 56 degrees. Since all four corners of the rhombus are congruent, we know that all four angles are approximately 56 degrees.

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There would be 22 red chips in the bucket containing 66 total chips.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let us assume the ratio of red chips to blue chips is 1:2.

Hence, if there 44 blue chips in the bucket:

(2/3) * total chips = 44

Total chips = 66

Number of red chips = (1/3) * 66 = 22

There would be 22 red chips in the bucket containing 66 total chips.

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29,060,000

When writing this out, it is important to make sure you include the commas and the exact amount of zero's by the way.

Answer:29,060,000

Step-by-step explanation:

with every three zeros your number grows bigger 100,00= One hundred thousand. 29,000,000 = thwenty-nine million

answer: 8

i added all the numbers and divided them by how much numbers there are

Answer:

400

Step-by-step explanation:

Answer:3600

\

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x-3)^2 + (y+2)^2 = 7^2

Answer:

\( (x - 3)^{2} + { (y + 2)^{2} = 49\)

Step-by-step explanation:

Center of the circle = (3, - 2) = (h, k)

Therefore, h = 3, k = - 2

Radius r = 7

Equation of circle in centre radius form is given as:

\((x - h)^{2} + {(y - k)}^{2} = {r}^{2} \\ \therefore \: (x - 3)^{2} + { \{y - ( - 2) \}}^{2} = {7}^{2} \\ \red{ \boxed{ \bold{\therefore \: (x - 3)^{2} + (y + 2)^{2} = 49}}}\)

Therefore , the solution of the given problem of quadrilateral comes out to be  EFHG is dilation of figure ABCD.

A quadrilateral is a four-sided shape with four corners that is used in mathematics. The term is either derived from the Latin words "quad" or "portfolio of inventive (meaning "side"). The three factors of a rectangle are four corners, four regions, and four corners. The two main types of concave and convex shapes are convex and concave. The subcategories of trapezoids, rectangular shapes, angles, rhombuses, but also squares are also considered to be convex quadrilaterals.

Here,

A transition that changes a figure's size is a dilation. Each point's coordinates are multiplied by a scale factor, which is a fixed value higher than zero, to achieve this.

A magnification occurs when the scale factor is higher than 1; a reduction occurs when the scale factor is between 0 and 1. (a reduction). The spot around which the figure is resized is the centre of dilation.

Figure ABCD is enlarged from position Q in this instance.

This indicates that the corresponding point in the dilated figure is created by multiplying each point in EFHG  by a scale factor.

The amount of scaling is determined by the scale factor. The dilated figure will be bigger than ABCD if the scale factor is greater than 1, and smaller than ABCD if the scale factor is between 0 and 1.

So,  EFHG is dilation of figure ABCD.

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The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.

According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.

To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.

Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.

Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.

Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.

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The minimum number of student tickets that the drama club must sell is 40.

Let's assume the drama club sells 'x' student tickets to meet the show's expenses.

The revenue from selling student tickets is given by: Revenue from student tickets = 6.50 * x

We know that the revenue from selling adult tickets is $10.50 per ticket and 44 adult tickets were sold. Therefore, the revenue from selling adult tickets is: Revenue from adult tickets = 10.50 * 44 = $462

The total revenue from ticket sales (student and adult tickets) must be at least $720 to cover the show's costs. Therefore, we can write the following equation:

Revenue from student tickets + Revenue from adult tickets ≥ 720

6.50 * x + 462 ≥ 720

Now, let's solve this equation to find the minimum number of student tickets 'x' needed:

6.50 * x ≥ 720 - 462

6.50 * x ≥ 258

x ≥ 258 / 6.50

x ≥ 39.69 (rounded up)

Since we cannot sell a fraction of a ticket, the drama club must sell a minimum of 40 student tickets in order to meet the show's expenses.

Therefore, the minimum number of student tickets that the drama club must sell is 40.

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Answer:

The answer to this is B. y=32.55

Answer:

The variable expression equation of the situation is;

x + 5 + x + 3·x - 7 = $73

The amount of money Jadah collects = $15

The amount of money Martez collects = $20

The amount of money Roana collects = $38

Step-by-step explanation:

The given parameters are;

The total amount of money they collect together = $73

The amount of money Martez collects = 5 + The amount of money Jadah collects

The amount of money Roana collects = 3 × The amount of money Jadah collects - 7

Let x represent the amount of money Jadah collects

Therefore, we have;

The amount of money Martez collects = 5 + x

The amount of money Roana collects = 3 × x - 7

The variable expression equation of the situation is given as follows;

The total amount of money the three collected = x + 5 + x + 3 × x - 7 = $73

∴ 5 × x - 2 = $73

5 × x - 2 = 73

5 × x  = 73 + 2 = 75

x = 75/5 = 15

x = 15

The amount of money Jadah collects = x = $15

The amount of money Martez collects = 5 + x = 5 + 15 = 20

The amount of money Martez collects = $20

The amount of money Roana collects = 3 × x - 7 = 3 × 15 - 7 = 38

The amount of money Roana collects = $38

On solving the provided question, we can say that volume of cylinder  =  \(\pi r^2h\) = 13564.8

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

volume of cylinder  =  \(\pi r^2h\)

\(\pi\) = 3.14

r = 15 cm\

h = 18 cm

V = \(3.14*15*16*18\) = 13564.8

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Answer:

Lateral Surface Area = 472 m²

Total Surface Area = 486m²

Step-by-step explanation:

The above prism is a Triangular prism

a) Lateral Surface Area = Perimeter of the Base × H

H = 29m

Perimeter of the Base = (7m + 7.28m + 2m)

= 16.28m

Lateral Surface Area = 16.28m × 29m

= 472.12 m²

Approximately to the nearest whole number = 472 m²

b) Total Surface Area

Triangular prism =

2 Triangles and 3 Rectangles

1st Triangle = 1/2 × base × Height

= 1/2 × 2m × 7m

= 7m²

2nd Triangle = 1/2 × base × height

= 1/2 × 2m × 7m

= 7m²

1st Rectangle = Length × Width

= 29m × 2m = 58m²

2nd Rectangle =

Length × Width

= 29m × 7.28m = 211.12m²

Length × Width

= 29m × 7m = 203m²

Total surface area = 7m² + 7m² + 58m² + 211.12m² + 203m²

= 486.12m²

Approximately to the nearest whole number = 486 m²

Option A is the correct option

Answer: (2,7) does not satisfy the system:

x - 2y ≤ -16

6x - y < 5

We can substitute the point (2,7) into the inequalities and see if they are true:

2 - 2*7 ≤ -16

-10 ≤ -16 which is false

6*2 - 7 < 5

5 < 5 which is also false

Since (2,7) does not satisfy both inequalities of the system, it is the correct answer.

Step-by-step explanation:

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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(a) The probability that a randomly chosen vehicle is traveling at a legal speed is 3.01%.

(b) If police are instructed to ticket motorists driving 120 km/h or more, the percentage of motorists targeted would be approximately 15.87%.

(a) The mean speed of vehicles on the highway is 115 km/h, with a standard deviation of 9 km/h. We are given that the speed limit is 100 km/h. To calculate the probability of a vehicle traveling at a legal speed, we need to determine the proportion of vehicles that have a speed of 100 km/h or less.

Using the properties of a normal distribution, we can convert the given values into a standardized form using z-scores. The z-score formula is (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation.

For a vehicle to be traveling at a legal speed, its z-score should be less than or equal to (100 - 115) / 9 = -1.67. We can consult a standard normal distribution table or use a statistical calculator to find the corresponding cumulative probability.

From the standard normal distribution table or calculator, we find that the cumulative probability for a z-score of -1.67 is approximately 0.0301, or 3.01% (rounded to two decimal places).

(b) To calculate this, we first need to find the z-score for the speed of 120 km/h using the formula: z = (x - μ) / σ, where x is the value we want to calculate the probability for, μ is the mean, and σ is the standard deviation. In this case, we want to find the probability for x ≥ 120 km/h.

Using the formula, we calculate the z-score as follows: z = (120 - 115) / 9 = 0.56.

To find the probability, we need to calculate the area to the right of the z-score of 0.56 in a standard normal distribution table or using statistical software. This area corresponds to the probability that a randomly chosen vehicle is traveling at a speed of 120 km/h or higher. This probability is approximately 0.2939 or 29.39%.

Since the question asks for the percentage of motorists targeted, we subtract this probability from 100% to find the percentage of motorists not adhering to the speed limit. 100% - 29.39% = 70.61%.

Therefore, the percentage of motorists targeted for ticketing by the police would be approximately 15.87%.

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Hi!1200 centimetres are equal to 12 meters.

Answer:

1200cm

Step-by-step explanation:

1m = 100cm

12m = 1200cm

Answer:

19:

4  <   third side    <   14  

20:

3  <   third side    <   13  

Step-by-step explanation:

hint: go to http://www.17 28.org/trianinq.htm

(fix the space between 17 and 28)

you're welcome xx

B: no, bc the side lengths ans angles arent similar

The measurement of the angle OP is 39

The given parameters that will help us to answer the question are

R is mid point of OQ

S is mid point of PQ

RS = 3x + 38

OP = 4x- 14

R is mid point of OQ and S is mid point of PQ;

By using mid point theorem

[1/2][OP] = RS

This implies that So,

[1/2][3x + 38] = [4x- 14]

[3x+38] = 2[4x- 14]

Opening the brackets we have

3x+38=8x-28

Collecting like terms

3x-8x=-28-38

-5x=-66

Making x the subject of the relation we have

x = -66 / -5

x = 13.2

Therefore RS = 3(13.2) + 38 = -11.4

OP = 4(13.2)- 14=38.8

Measurement of OP = 39 approximately

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Answer:

Step-by-step explanation:

perpendicular (p)= 7.7

hypotenuse (h)= 9.7

now

sin x = p / h

sin x = 7.7/9.7

x = sin ^-1( 7.7/9.7)

x = 53°