What do all products of the square of binomial have in common?

Answer: To solve this problem, we need to use the central limit theorem to find the distribution of the sample means. The central limit theorem states that if we take random samples of size n from a population with a mean μ and a standard deviation σ, the distribution of the sample means approaches a normal distribution with a mean of μ and a standard deviation of σ/√n, as n gets larger.

In this case, we have a population of healthy humans with a mean temperature of μ = 98.6 degrees and a standard deviation of σ = 0.8 degrees. We want to find the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher. The sample size is large enough to use the normal distribution to approximate the distribution of the sample means.

The z-score corresponding to a sample mean of 98.25 degrees is:

z = (98.25 - 98.6) / (0.8 / sqrt(130)) = -1.91

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -1.91:

P(Z > -1.91) = 0.9719

Therefore, the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher is approximately 0.9719 or 97.19%.

Step-by-step explanation:

Answer:

Jessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5.

The volume of the first prism is 35 cm^3. Since the second prism is a dilation of the first prism with a scale factor of 2.5, its volume will be (2.5)^3 = 15.625 times greater than that of the first prism. Therefore, the volume of the second prism will be 35 x 15.625 = 546.875 cm^3.

To make the second prism, Jessica needs an additional material of 546.875 - 35 = 511.875 cm^3.

So Jessica needs an additional material of 511.875 cm^3 to make the second prism.

Step-by-step explanation:

Michelle’s equations that is true for all values of x is 6x + 15 = x + x + x + x + x + x + 15.

Michelle’s equations that is false for all values of x is 6x + 15 = 6(x + 15).

Another equivalent expression for 6x + 15 is 3(2x + 5).

In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).

Michelle’s equations can be written for all values of x as follows;

6x + 15 = x + x + x + x + x + x + 15.

However, Michelle’s equations is false for all values of x when it is written as 6(x + 15).

Another equivalent expression is given by;

6x + 15 = 3(2x + 5).

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Answer:

Part A: The equation 6x + 15 = 6(x + 15) is true for all values of x because it distributes the 6 to both terms inside the parentheses and simplifies to the original expression. However, the equation 6x + 15 = x + x + x + x + x + x + 15 is false for all values of x. While it may be true for specific values of x, such as x = 1 or x = 2, it is not true for all values of x because the number of x terms changes depending on the value of x.

Part B: Another equivalent expression for 6x + 15 could be 3(2x + 5), which also simplifies to the original expression. This is because we can factor out a common factor of 3 from both terms and simplify to 3(2x + 5) = 6x + 15.

Step-by-step explanation:

Answer: Assuming that the proportion of patients cured by the drug is p = 0.6 and the sample size is n = 100, we can find the mean and standard error of the sampling distribution as follows:

Mean = p = 0.6

Standard error = sqrt[(p*(1-p))/n] = sqrt[(0.6*(1-0.6))/100] = 0.049

Rounding to three decimal places, the standard error is 0.049.

Step-by-step explanation:

The volume of Ganymede is approximately 3.48 times the volume of the Moon, based on the given diameters of the two moons and the formula for the volume of a sphere.

The volume of a sphere is the amount of space occupied by the sphere in three-dimensional space. It can be calculated using the formula V = (4/3)πr³, where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159. This formula states that the volume of a sphere is four-thirds of the product of pi and the cube of the sphere's radius.

In the given question,

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. Since we are given the diameters of the two moons, we can calculate their radii by dividing the diameters by 2. Therefore, the radius of Ganymede is 3,388/2 = 1,694 km, and the radius of the Moon is 1,245/2 = 622.5 km.

Now, we can calculate the volumes of the two moons:

V_Ganymede = (4/3)π(1694)³ ≈ 7.66 x 10^10 km³

V_Moon = (4/3)π(622.5)³ ≈ 2.2 x 10^10 km³

To find how many times larger Ganymede's volume is compared to the Moon's volume, we can divide the volume of Ganymede by the volume of the Moon:

V_Ganymede / V_Moon ≈ (7.66 x 10¹⁰) / (2.2 x 10¹⁰) ≈ 3.48

Therefore, the volume of Ganymede is approximately 3.48 times the volume of the Moon.

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The coordinates of triangle A'B'C' after a dilation centered at the origin with a scale factor of 2 are:

A' (-10, -14).

B' (12, -6).

C' (4, 14).

In Geometry, a dilation is a transformation that is typically used for changing the dimension (size) of a geometric figure, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 2 that is centered at the origin as follows:

Ordered pair A (-5, -7) → Ordered pair A' (-5 × 2, -7 × 2) = Ordered pair A' (-10, -14).

Ordered pair B (6, -3) → Ordered pair B' (6 × 2, -3 × 2) = Ordered pair B' (12, -6).

Ordered pair C (2, 7) → Ordered pair C' (2 × 2, 7 × 2) = Ordered pair C' (4, 14).

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A level 0.95 confidence interval is a range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time. So, the correct answer is C).

A level 0.95 confidence interval is a statistical measure used to estimate the true value of a population parameter based on a sample of data. It provides a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.

The level of confidence, in this case 0.95, means that if the same sampling method and data analysis were repeated multiple times, the resulting confidence intervals would contain the true population parameter in 95% of cases.

The width of the interval, or margin of error, is influenced by factors such as sample size, variability, and level of confidence. So, the correct option is C).

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Based on the information, we can infer that the most accurate method would be method 3 because it randomly selects the participants without any preference.

The most appropriate method for this survey would be method three (option D) because it will have a group of people who were chosen randomly. This means that people can have different ranges of age, gender, preferences, among others.

This is important because they will represent all the diversity of characteristics of the public, which will allow a study in this population to be more accurate.

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The surface area of the right rectangular prism 280 yd².

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The surface area of a rectangular prism is expressed as;

S.A = 2( wl + hl + hw )

Where w is the width, h is height and l is length.

From the diagram:

Length l = 6 yd

Width w = 5 yd

Height = 10 yd

Plug the values into the above formula:

S.A = 2( wl + hl + hw )

S.A = 2( 5×6 + 10×6 + 10×5 )

S.A = 2( 30 + 60 + 50 )

S.A = 2( 90 + 50 )

S.A = 2( 140 )

S.A = 280 yd²

Therefore, the surface area is 280 square yards.

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The ratio for sin A, written as a fraction in simplest form, is 3 / (2√3).

The sine function is a mathematical function that takes an angle as its input and returns the ratio of the length of the side opposite to the angle to the length of the hypotenuse in a right triangle

In a right triangle, the sine of an angle A is defined as the ratio of the length of the side opposite to angle A to the length of the hypotenuse. Therefore, we have:

sin A = Opposite / Hypotenuse

Substituting the given values, we get

sin A = CB / AB = 8√3 / 16 = √3 / 2

To simplify this fraction further, we can multiply both the numerator and denominator by √3:

sin A = (√3 / 2) × (√3 / √3) = 3 / (2√3)

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The given question is incomplete, the complete question is:
Which is the ratio for sin A, written as a fraction in simplest form?

Answer:

409 > 1.008

Step-by-step explanation:

409 is greater than 1.008

Step-by-step explanation:

Refer the attachment!!~

Answer:

Step-by-step explanation:

As Almay walks through a local park and passes an old man in pain, the presence of many other walkers in the park will most likely increase the probability that Almay will experience the "bystander effect."

As Almay walks through the local park and comes across an old man who is in pain, the presence of many other walkers in the park will most likely increase the probability that Almay will seek help for the man.

This is because the bystander effect, which is the tendency for individuals to be less likely to intervene in an emergency situation when others are present, is less likely to occur when there are more people around. With more people present, Almay may feel a greater sense of responsibility to act and seek help for the man.

Additionally, the presence of other walkers may also make it easier for Almay to quickly locate someone who can assist with medical attention or call for emergency services.

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The volume of the prism with given dimensions in the figure is equal to 612√3 cubic millimeter.

The dimensions of the triangular prism are,

Base of the triangle  'B' = 12mm

let us consider 'h' be the height of the triangle base.

Which intersect base at midpoint

height of the triangle 'h' = √ 12² - 6²

                                        = √108

                                        = 6√3mm

Side length of the prism 'l' = 17mm

Volume of the triangular prism

= ( 1/2 ) × Base × height × length of the side

= ( 1/2 ) × B × h × l

Now , substitute the values we have,

⇒ Volume of the triangular prism  = (1/2) × 12 × 17 × 6√3

⇒ Volume of the triangular prism  = 612√3 cubic millimeter.

Therefore, the volume of the triangular prism is equal to 612√3 cubic millimeter.

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Answer:

Step-by-step explanation:

4

The probability that the vehicle Bob chooses is new or is a car is [tex]\frac{31}{37}[/tex]

To determine the probability that the vehicle Bob chooses is new or is a car at Bob's Auto Plaza, follow these steps:

1. Calculate the total number of vehicles:
  15 new cars + 7 used cars + 9 new trucks + 6 used trucks = 37 vehicles

2. Calculate the number of new vehicles:
  15 new cars + 9 new trucks = 24 new vehicles

3. Calculate the number of cars (both new and used):
  15 new cars + 7 used cars = 22 cars

4. Since we have already counted the new cars in both categories, we need to subtract the number of new cars once to avoid double counting:
  24 new vehicles + 22 cars - 15 new cars = 31 vehicles that are either new or cars

5. Finally, calculate the probability:
  Probability = (number of vehicles that are new or cars) / (total number of vehicles)
  [tex]Probability = \frac{31}{37}[/tex]

So, the probability that the vehicle Bob chooses is new or is a car is [tex]\frac{31}{37}[/tex]  .

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Answer: Let's call the total amount of grass that Austin collected "G" in kilograms. We know that he collected 30 9/10 kilograms, which can be written as a mixed number or an improper fraction:

30 9/10 = 309/10

So, we have:

G = 309/10

We also know that 2/3 of the grass he collected was blue grass. So, let's call the amount of blue grass "B" in kilograms. We can set up an equation based on the information given:

B = (2/3)G

Substituting G = 309/10, we get:

B = (2/3)(309/10)

B = 206/5

B = 41 1/5

Therefore, the total amount of blue grass Austin collected was 41 1/5 kilograms.

Step-by-step explanation:

Answer:

To perform McNemar's test, we need to find the number of discordant pairs, i.e., the pairs of individuals who change their response from before to after college. In this case, there are 23 students who said "yes" before college but "no" after college, and 11 students who said "no" before college but "yes" after college. Therefore, there are 23 discordant pairs.

The test statistic for McNemar's test is calculated as:

z = (|b-c| - 1) / √(b+c)

where b is the number of discordant pairs who responded "yes" before college, and c is the number of discordant pairs who responded "no" before college.

In this case, b = 23 and c = 11, so:

z = (|23-11| - 1) / √(23+11)

z = 1.96

Therefore, the test statistic is 1.96

She rewrites the given equation in the following way as: (x + 10)² = 82.

An equation is a mathematical statement that shows the equality between two expressions. It contains one or more variables, which represent unknown values, and may involve mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. The goal of an equation is to find the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, physics, engineering, and other sciences to model and solve various real-world problems.

Here,

We can complete the square as follows:

x² + 20x + 18 = 0

x² + 20x = -18

(x + 10)² - 100 = -18 (adding and subtracting 100 to the left-hand side)

(x + 10)² = 82

Taking the square root of both sides, we get:

x + 10 = ±√(82)

x = -10 ± √(82)

So the correct answer is: (x + 10)² = 82.

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The first-grade teacher could take several steps to improve her students' understanding of expanded form. she could use manipulatives to help students visualize the concept of place value.

For example, she could use base-ten blocks or colored chips to represent the value of each digit in a number. This would help students see that the value of the 7 in 74 is actually 7 tens or 70.

Second, she could provide more examples and practice problems that gradually increase in difficulty. This would help students build their understanding of expanded form and allow them to apply the concept to a variety of numbers.

Third, she could use real-world examples that students can relate to, such as money or counting objects in a classroom. This would make the concept of expanded form more meaningful and engaging for students.

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For the given data, The correct statement is: A refrigerator with 3.75 ft³ of refrigerator space will have 1.5 ft³ of freezer space.

We can compute the refrigerator space ratio for each model by dividing the refrigerator space by the freezer space:

[tex]\text{For Model A: Space ratio = Refrigerator space / Freezer space} = 15.75 \;ft^3 / 6.3 ft^3 \approx 2.5[/tex]

[tex]\text{For Model B: Space ratio = Refrigerator space / Freezer space }= 10.25 ft^3 / 4.1 ft^3\approx 2.5\\\\\text{For Model C: Space ratio = Refrigerator space / Freezer space }= 15.25 ft^3 / 6.1 ft^3 \approx 2.5[/tex]

We can use this ratio to compute the freezer space for a particular refrigerator with a known refrigerator space because all refrigerators have the same space ratio of around 2.5.

Now for given statements:

Using the space ratio of 2.5, if a refrigerator has 3.25 ft³ of refrigerator space, the freezer space will be= [tex]3.25 ft^3 / 2.5 \approx 1.3 ft^3[/tex], not 1.2 ft³. So, statement a is not true.

Using the space ratio of 2.5, if a refrigerator has 3.25 ft³ of refrigerator space, the freezer space will be [tex]3.25 ft^3 / 2.5 \approx 1.3 ft^3[/tex], not 1.5 ft³. So, statement b is not true.

Using the space ratio of 2.5, if a refrigerator has 3.75 ft³ of refrigerator space, the freezer space will be [tex]3.75 ft^3 / 2.5 \approx 1.5 ft^3[/tex], not 1.2 ft³. So, statement c is not true.

Using the space ratio of 2.5, if a refrigerator has 3.75 ft³ of refrigerator space, the freezer space wii be[tex]3.75 ft^3/ 2.5 \approx 1.5 ft^3[/tex] So, statement d is true.

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The value of r/s is equal to 9.

There exists a theorem that states that the square of a hypotenuse in a right-angled triangle is equal to the sum of squares of the perpendicular side and the base side.  This theorem is known as Pythagoras theorem. By applying Pythagoras' theorem in this right-angled triangle formed in our image, we obtain the given formula

[tex]H^2 = P^2 + B^2[/tex]

[tex](r + s)^2 = (r - s)^2 + (r - 3s)^2[/tex]

[tex]r^2 + 2r.s + s^2 = 2r^2 - 8r.s + 10.s^2[/tex]

[tex]r^2 - 10.r.s + 9s^2 = 0[/tex]

(r - 9s) (r - s) = 0

Now we will equate these two factors to 0.

By equating, we get r/s = 9 and r/s = 1.

r/s = 1 does not apply to the geometry in this question.

So, r/s = 9 is the solution for the given equation.

Therefore, our answer is 9.

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The complete question is -

"Three circles of radius s are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the x-axis, and the third is tangent to the first circle and the y-axis. A circle of radius r>s is tangent to both axes and to the second and third circles. What is r/s? "

Answer:

27 inches

Step-by-step explanation:

1 ft = 12 inches, therefore 2 ft = 24 inches because (12)(2)=24. Then you need to add the other 3 inches to 24, and 24 + 3 = 27 in.

The height of the tree is 44.4 feet.

Height is the vertical distance between two points.

To calculate the height of the tree, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The speed of boat is 5/6 meter per second and height of boat is 50[tex]\sqrt{3}[/tex] meter.

An angle is a shape created by two rays or lines that meet at the same terminal. The Latin word "angulus" (which means "corner") is where the term "angle" first appeared. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle between the two beams.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

After solving the figure:

The speed of boat is 5/6 meter per second and height of boat is 50[tex]\sqrt{3}[/tex] meter.

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The speed of the boat from point C to point B is approximately 10.82 meters per second.

What is speed ?

Speed is a measure of how fast an object is moving. It is the rate at which an object covers distance.

We can use trigonometry to solve for h and the speed of the boat. Let's start with h:

From the right triangle CLB, we have:

tan 30° = h / CB

where CB is the distance between points C and B, which is given as 50 meters. Solving for h, we get:

h = CB * tan 30° = 50 * tan 30° ≈ 28.87 meters

So the height of the lighthouse is approximately 28.87 meters.

Now let's find the speed of the boat. We know that the boat travels from point C to point B in 1 minute, which is equivalent to 60 seconds. Let's define the speed of the boat as v, in meters per second. Then we have:

v = CB / t

where t is the time it takes for the boat to travel from point C to point B. We can find t using the distance formula:

[tex]CB = \sqrt{(x_B - x_C)^2 + (y_B - y_C)^2[/tex]

where x and y are the coordinates of each point. From the diagram, we can see that:

[tex]x_C = 0[/tex]

[tex]y_C = 0[/tex]

[tex]x_B = BL * cos \theta[/tex]

[tex]y_B = BL * sin \theta[/tex]

where BL is the distance from point B to the foot of the lighthouse, which is equal to h / tan θ. Therefore:

CB [tex]= \sqrt{((BL * cos \theta)^2 + (BL * sin \theta)^2)[/tex]

     [tex]= \sqrt{(BL^2 * (cos^2 \theta + sin^2 \theta))[/tex]

     [tex]= BL = h / tan \theta[/tex]

Substituting the values we have found, we get:

v = CB / t = (h / tan θ) / 60 ≈ 10.82 meters per second

Therefore, the speed of the boat from point C to point B is approximately 10.82 meters per second.

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The value of x for the angles of the quadrilateral is: x = -4

We know that the sum of angles in a quadrilateral is 360 degrees.

The angles are given as:

(11x + 140)°

(13x + 143)°

(4x + 98)°

(11x + 135)°

Thus:

(11x + 140)° + (13x + 143)° + (4x + 98)° + (11x + 135)° = 360°

Thus:

39x + 516 = 360

39x = 360 - 516

39x = -156

x = -156/39

x = -4

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The probability of exactly 17 successes in a binomial distribution with p=0.20 and n=60, using normal approximation to the binomial, is approximately 0.0129.

To use the normal approximation to the binomial, we need to check if the conditions for the approximation are met

np = 60 x 0.20 = 12 ≥ 10

n(1-p) = 60 x 0.80 = 48 ≥ 10

Both conditions are met, so we can use the normal approximation to the binomial.

The mean of the binomial distribution is μ = np = 12, and the standard deviation is σ = √(np(1-p)) = √(60 x 0.20 x 0.80) ≈ 2.19.

To find the probability of exactly 17 successes, we can use the normal distribution with mean μ = 12 and standard deviation σ ≈ 2.19, and approximate the discrete binomial distribution with a continuous normal distribution

P(X = 17) ≈ P(16.5 < X < 17.5)

where X is a continuous random variable that follows a normal distribution with mean μ = 12 and standard deviation σ ≈ 2.19.

Using the standard normal distribution, we can calculate the z-scores for 16.5 and 17.5

z1 = (16.5 - 12) / 2.19 ≈ 1.83

z2 = (17.5 - 12) / 2.19 ≈ 2.28

Using a standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores

P(1.83 < Z < 2.28) ≈ P(Z < 2.28) - P(Z < 1.83) ≈ 0.0129

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Answer: 24

Step-by-step explanation:

n = 12^2

n + 1 = 13^2

2n = 12

Transpose the 2 on the other side, you get -

n = 12*2

Therefore, n = 24