which coordinates represent a translation of B (1,2) 3 units to the left and 2 units up

The initial equation is:

So if we use the distribution propertie, we have to multiply the 4 for all term in the parenthesis so:

and then we simplify:

So is option D)

Answer:

(a+6)(a-2)=a^2-4a-12

Step-by-step explanation:

Answer:

2/5 is the slope of the line

Step-by-step explanation:

To get to the point at (3,1) from point (-2,-1), you would need to go up 2 units and right 5 units.

Hope this helps.

Answer:

y=8y=8? y^2 -y-2 y 2 −y−2.

Step-by-step explanation:

Thats the answer to it

Answer:

The answer is 135 in 3.

Step-by-step explanation:

To find the volume of a square pyramid, first you need to find the base and height. In this case,

a = 9

h = 5

Now we use the formula (1/3 a^2 h) To find the volume.

I will use )( To show numbers being multiplied, example: 3)(4 = 12

=1/3)(9 cm^2)(5 cm

=1/3)(81 cm)( 5 cm

= 135 in. 3

The value of P(1.41 < Z < 2.85)  is 0.0771.

Hence, the correct answer is d.

A normally distributed random variable with mean μ= 0 and standard deviation σ= 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Because the Standard Normal Distribution is a probability distribution, the area under the curve between two points indicates the likelihood that variables will take on a range of values.

The whole area under the curve is one, or one hundred percent.

The mean and variance of a normal distribution are governed by two factors.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

The probability that a standard normal random variable Z is between 1.41 and 2.85 can be found using a standard normal table with a standard normal cumulative distribution function.

The answer is approximate:

P(1.41 < Z < 2.85)

= P(Z < 2.85) - P(Z < 1.41)

= 0.9927 - 0.9185

= 0.0742

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The 27th term of the sequence -11, -5, 1, , , is 145.In this sequence, we can observe that each term is obtained by adding 6 to the previous term.

So, the pattern is an arithmetic sequence with a common difference of 6.

To find the 27th term, we can use the formula for the nth term of an arithmetic sequence:

nth term = first term + (n - 1) * common difference

In this case, the first term is -11 and the common difference is 6. Plugging these values into the formula, we have:

27th term = -11 + (27 - 1) * 6

Simplifying the expression, we get:

27th term = -11 + 26 * 6

Calculating the value, we have:

27th term = -11 + 156

Therefore, the 27th term of the sequence is 145.

Main answer: The 27th term of the sequence -11, -5, 1, ... is 145.
The sequence follows an arithmetic pattern where each term is obtained by adding 6 to the previous term. To find the 27th term, we used the formula for the nth term of an arithmetic sequence and substituted the given values. After simplifying the expression, we found that the 27th term is 145.

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Answer:

4.35

Step-by-step explanation:

-4.35. Step-by-step explanation: You multiply three eights times .4 which gives you .15, then you subtract that from 4.5 which gives you 4.35

Answer: I would say 80 but I don't think that's right so sorry I don't really think I can help you with this question.

Step-by-step explanation:

Answer:

Each biker gets 3 19/32 of the mix.

Step-by-step explanation:

In the questions, we are told that a trail mix consist

7 3/4 oz of sunflower seeds,

9 1/4 oz of raisins

4 1/4 oz of walnuts

7 1/2 oz of soybeans

Step 1

Add up every element in the trail mix

We have are given mixed numbers which is made up of whole number and a proper fraction

7 3/4 oz + 9 1/4 oz + 4 1/4 oz + 7 1/2 oz

So we add up the whole numbers first

27 + ( 3/4 oz + 1/4 oz + 1/4 oz + 1/2 oz)

Next, We find the lowest common multiple of the denominators of the proper fractions which is 4

= 27 + ((3×1) + (1×1) + (1×1) +(1×2)/4)

27 + (3+1+1+2) / 4

27 + 7/4

27 + 1 3/4

27 + 1 + 3/4

Total mix = 28 3/4

Step 2

If the mix is split equally between eight hikers, how much would each one get?

We would convert 28 3/4 into an improper fraction and divide it by 8 bikers

115/4 ÷ 8

115/ 4 × 1/8

= 115/32

Turning it into a mixed fraction, we have:

3 19/32

Therefore, each biker gets 3 19/32 of the mix.

The depth of water in the second cup is 9 cm when the water is transferred from a cylindrical cup with a radius of r cm and a depth of 36 cm.

Given that,

Depth of water in the first cylindrical cup with radius r: 36 cm

Transfer of water from the first cup to another cylindrical cup

Radius of the second cup: 2r cm

The first cup has a radius of r cm and a depth of 36 cm.

The volume of a cylinder is given by the formula:

V = π r² h,

Where V is the volume,

r is the radius,

h is the height (or depth) of the cylinder.

So, for the first cup, we have:

V₁ = π r² 36.

Now, calculate the volume of the second cup.

The second cup has a radius of 2r cm.

Call the depth or height of the water in the second cup h₂.

The volume of the second cup is V₂ = π (2r)² h₂.

Since the water from the first cup is transferred to the second cup, the volumes of the two cups should be equal.

Therefore, V₁ = V₂.

Replacing the values, we have

π r² 36 = π (2r)² h₂.

Simplifying this equation, we get

36 = 4h₂.

Dividing both sides by 4, we find h₂ = 9.

Therefore, the depth of the water in the second cup is 9 cm.

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a) A formula for the mean is:

mean = (Σx) / n

where Σx is the sum of all values and n is the number of values.

b) mean = 42.44

c) The probability of a person picked at random from the group weighing below 150 lb is 0.0228 or 2.28%.

a) In the case of outliers in a dataset, the measure of central tendency that would be used is the median. This is because outliers can skew the mean, making it an inaccurate representation of the center of the data. The median is less affected by extreme values and represents the middle of the data when arranged in order. Two other measures of central tendency are the mode and the mean. The mode is the value that appears most frequently in the dataset, while the mean is the sum of all values divided by the number of values.

Hence, A formula for the mean is:

mean = (Σx) / n

where Σx is the sum of all values and n is the number of values.

b) To compute the mean of the given sample values, we add them up and divide by the number of values:

mean = (157 + 40 + 21 + 8 + 10 + 73 + 24 + 41 + 8) / 9

mean = 382 / 9

mean = 42.44

To show that Σ(x−X) = 0, we need to calculate the deviations of each value from the mean and add them up. The formula for deviation is:

deviation = x - X

where x is the value and X is the mean.

So, the deviations for each value are:

157 - 42.44 = 114.56 40 - 42.44 = -2.44 21 - 42.44 = -21.44 8 - 42.44 = -34.44 10 - 42.44 = -32.44 73 - 42.44 = 30.56 24 - 42.44 = -18.44 41 - 42.44 = -1.44 8 - 42.44 = -34.44

If we add up all these deviations, we get:

Σ(x - X) = 0

This means that the sum of all deviations from the mean is zero, as expected.

Given that the mean weight of a large group of people is 180 lb and the standard deviation is 15 lb, we can use the normal distribution to find the probabilities of a person weighing between certain weight ranges.

a) To find the probability that a person picked at random from the group will weigh between 160 and 180 lb, we need to standardize the values using the formula:

z = (x - μ) / σ

where x is the weight, μ is the mean weight, and σ is the standard deviation.

For x = 160 lb:

z = (160 - 180) / 15 = -1.33

For x = 180 lb:

z = (180 - 180) / 15 = 0

Using a standard normal distribution table or calculator, we can find the area under the curve between z = -1.33 and z = 0, which is the probability of a person weighing between 160 and 180 lb.

P(160 < x < 180) = P(-1.33 < z < 0) = 0.4082

Therefore, the probability of a person picked at random from the group weighing between 160 and 180 lb is 0.4082 or 40.82%.

b) To find the probability that a person picked at random from the group will weigh above 200 lb, we standardize the value:

z = (200 - 180) / 15 = 1.33

Using a standard normal distribution table or calculator, we can find the area under the curve to the right of z = 1.33, which is the probability of a person weighing above 200 lb.

P(x > 200) = P(z > 1.33) = 0.0918

Therefore, the probability of a person picked at random from the group weighing above 200 lb is 0.0918 or 9.18%.

c) To find the probability that a person picked at random from the group will weigh below 150 lb, we standardize the value:

z = (150 - 180) / 15 = -2

Using a standard normal distribution table or calculator, we can find the area under the curve to the left of z = -2, which is the probability of a person weighing below 150 lb.

P(x < 150) = P(z < -2) = 0.0228

Therefore, the probability of a person picked at random from the group weighing below 150 lb is 0.0228 or 2.28%.

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Answer:

Triangles B and C

Step-by-step explanation:

Im not 100% sure i cant really explain because i did this in my head sorry im 60% sure its right sorry its my bad if you get it wrong

Triangles A and B are similar because they have the same equal pair of corresponding angles. Thus, the correct answer is option (D).

As per the shown figure, In triangles A and B have:

Same angle = 67°

Same angle = 23°

Same angle = 90°°

As we know that similar triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

Here, triangles A and B have corresponding angles that are the same.

Thus, triangles A and B are similar.

Therefore, the correct answer is an option (D).

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Since the null hypothesis was rejected, we can conclude that there is enough evidence to suggest that the mean weight of adult German shepherd dogs is greater than 75 pounds.

However, we cannot conclusively state that the mean weight is exactly 75 pounds, only that it is likely greater than that value. The alternative hypothesis (Hi: μ > 75) supports this conclusion, indicating that the true mean weight is likely higher than the claimed value of 75 pounds.

It is important to note that further research and analysis may be necessary to determine a more precise estimate of the mean weight of adult German shepherds.

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The solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112

what is trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

We can use the trigonometric identity:

cos(a)cos(b)sin(a)sin(b) = (1/4)sin(2a)sin(2b)

Applying this identity, we have:

cos(6x)cos(5x)sin(6x)sin(5x) = (1/4)sin(12x)sin(10x)

So, our equation becomes:

(1/4)sin(12x)sin(10x) = 1

Multiplying both sides by 4, we get:

sin(12x)sin(10x) = 4

Now, let's consider the function f(x) = sin(12x)sin(10x) - 4. We want to find the zeros of this function on the interval [0,2).

Using a graphing calculator or some analysis, we can see that the function has two zeros on this interval, one between x=0 and x=1, and another between x=1 and x=2.

Using numerical methods such as the bisection method or Newton's method, we can approximate the zeros to four decimal places:

The first zero is approximately 0.2071.

The second zero is approximately 1.4112.

Therefore, the solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112.

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1. P-adic Numbers:

P-adic numbers are a specialized alternative not commonly used as a continuity strategy in mathematics. They are an extension of the real numbers that provide a different way of measuring and analyzing numbers. P-adic numbers are based on a different concept of distance, known as the p-adic metric. This metric assigns a measure of closeness or distance between numbers based on their divisibility by a prime number, p. P-adic numbers have unique properties and can be useful in number theory, algebraic geometry, and other branches of mathematics. However, they are not typically employed as a continuity strategy in practical applications.

2. Nonstandard Analysis:

Nonstandard analysis is a mathematical framework that provides an alternative approach to calculus and analysis. It introduces new types of numbers called "infinitesimals" and "infinite numbers" that lie between the standard real numbers but are infinitely smaller or larger than any real number. Nonstandard analysis allows for more rigorous treatment of infinitesimal quantities and provides a different perspective on limits, continuity, and differentiation. While nonstandard analysis has theoretical implications and can provide valuable insights in mathematical research, it is not commonly used as a continuity strategy in practical applications where standard analysis and calculus are more prevalent.

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Option C: \(y=2x+1\) is the correct option.

Answer:

C

Step-by-step explanation:

The area is calculated as width × length , that is

\(\frac{50\sqrt{3} }{\sqrt{2} }\) × \(\frac{80\sqrt{5} }{\sqrt{3} }\) ( cancel \(\sqrt{3}\) on numerator/ denominator

= \(\frac{50}{\sqrt{2} }\) × 80\(\sqrt{5}\)

= \(\frac{4000\sqrt{5} }{\sqrt{2} }\)

To rationalise the denominator multiply numerator/denominator by \(\sqrt{2}\)

= \(\frac{4000\sqrt{6} }{\sqrt{2} }\) × \(\frac{\sqrt{2} }{\sqrt{2} }\)

= \(\frac{4000\sqrt{10} }{2}\)

= 2000\(\sqrt{10}\) → C

Answer: The answer is C!

Step-by-step explanation:

Hope this helps, can I please have brainliest?

Answer:

x=3

Step-by-step explanation:

x^3=27

x^3=3^3

x=3

The solution to this question is  27 units the perimeter of kite OBDE.

The perimeter of a shape is the entire length of the shape's boundary as used in geometry. A form's perimeter can be calculated by adding the lengths of all of its sides and edges. In order to calculate it, linear distances such as centimeters, meters, inches, or feet are used.

Here

This is because 15x15 =225

8x8 = 64

225+64=289 and

the square root of 289 is 17 and that is the diameter of the circle and the hypotenuse of the triangle and since the kite has two congruent sides which are both radii or  can be written as half of a diameter times two would be the same as the length of the diameter which is17+the two bottom sides (which are both 5 and 5 )

So 5+ 5 = 10 and

10 + 17 =27 or the perimeter of the kite.

Therefore ,the perimeter of kite OBDE is 27 units.

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Answer:

The coordinates of point S are (5, 9) will make line PQ // line RS ⇒ A

Step-by-step explanation:

Parallel lines have  the same slopes

The slope of a line = Δy/Δx, where

Let us first find the slope of the line PQ.

∵ P = (-2, -2) and Q = (0, 7)

∴ Δx = 0 - (-2) = 0 + 2 = 2

∴ Δy = 7 - (-2) = 7 + 2 = 9

∴ The slope of PQ = 9/2

∵ Line PQ // line RS

∴ The slope of line PQ = the slope of line RS

∴ The slope of line RS =9/2

∵ Point R = (3, 0) and point S = (x, y)

∵ The slope of line RS = 9/2

∵ The slope = Δy/Δx

∴ Δy/Δx = 9/2

→ That means Δy = 9 and Δx = 2

∵ Δy = y - 0

∵ Δy = 9

∴ 9 = y

∵ Δx = x - 3

∵ Δx = 2

∴ 2 = x - 3

→ Add 3 to both sides

∴ 2 + 3 = x - 3 + 3

∴ 5 = x

∴ The coordinates of point S are (5, 9) will make line PQ // line RS

Answer:

its 87

Step-by-step explanation:

The approximate volume of the sphere is 6.01 ft³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the surface area of the sphere is 16 square feet.

First, we determine the radius r:

Surface area = 4πr²

Hence

16 = 4πr²

Dividing both sides by 4π, we get:

r² = 16/4πr

r = √( 16/4πr )

r = 1.128 ft

Plugging in the value of r that we just found, we get:

Volume =  (4/3)πr³

Volume =  (4/3) × 3.14 × (1.128 ft)³

Volume =  6.01 ft³

Therefore, teh volume is 6.01 ft³.

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4 cups of water would need 16 tablespoons of olive oil.

Each cup of water uses 2 2/3  cups of flour, while each cup of flour he uses, Amir needs to use 1 1/2  tablespoons of olive oil. Hence for 4 cups of water:

4 cups of water = 2 2/3  cups of flour × 4 cups = 32/3 cups of flour

32/3 cups of flour = 1 1/2  tablespoons of olive oil * 32/3 = 16 tablespoons of olive oil

4 cups of water would need 16 tablespoons of olive oil.

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the area under the standard normal curve between z = -2.9 and z = 0.28 is approximately 0.0014 (rounded to four decimal places).

The given values for z are z = -2.9 and z = 0.28. We need to find the area under the standard normal curve between these values.

To find this area, we can use the standard normal distribution table. This table lists the areas under the standard normal curve for different z-values. However, we need to make some adjustments to use this table because our values are negative.

Let's first find the area between z = 0 and z = 2.9, and then subtract this area from 0.5 to get the final answer.0.5 - P(0 ≤ z ≤ 2.9) = 0.5 - [0.49865] (from the standard normal distribution table)

= 0.00135

Therefore, the area under the standard normal curve between z = -2.9 and z = 0.28 is approximately 0.0014 (rounded to four decimal places).

Hence, the correct option is, Area ≈ 0.0014.

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The matrix A represents the linear transformation that reflects points across the line y=x in the Cartesian plane.

To find the eigenvalues of A, we solve the characteristic equation:

det(A - λI) = 0

where I is the identity matrix and λ is an eigenvalue of A.

A - λI =

[1-λ 0]

[0 1-λ]

det(A - λI) = (1-λ)(1-λ) - 0*0 = (1-λ)^2

Setting this expression equal to zero and solving for λ, we find:

(1-λ)^2 = 0

1-λ = 0

λ = 1

So the only eigenvalue of A is 1.

To find the eigenvectors corresponding to λ=1, we solve the system of equations:

(A - λI)v = 0

where v is an eigenvector of A.

For λ=1, we have:

(A - I)v =

[0 0]

[0 0]

which implies that any non-zero vector in the plane (i.e., any non-zero vector in R^2) is an eigenvector of A corresponding to the eigenvalue 1.

Therefore, the eigenspace corresponding to the eigenvalue 1 is all of R^2, and any non-zero vector in R^2 can be taken as an eigenvector.

In summary, the eigenvalue of A is 1, and the eigenspace corresponding to this eigenvalue is all of R^2. Any non-zero vector in R^2 can be taken as an eigenvector.

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