In which quadrant does the point P(-2 , 4) lie

Answer:

25, 125, 3125, 78125, 1953125

Answer:

-1 ; 1/5 ; -1/25

Step-by-step explanation:

125 : (-5) = -25

-25 : (-5) = 5

5 : (-5) = -1

-1 : (-5) = 1/5

1/5 : (-5) = -1/25

Answer:

Amount earned in 1 hour \(=\$9.750\)

Amount earned in 1 hour \(=\$10\)

Step-by-step explanation:

Total amount earned by Dawn = $97.50

Dawn earned $97.50 for 10 hours of work

Amount earned in 1 hour \(=\frac{97.50}{10}=\$9.750\)

Total amount earned by Amy in 12 hours = $120

Amy earned $120 in 12 hours of work

Amount earned in 1 hour \(=\frac{120}{12}=\$10\)

The explicit formula and a recursive formula using n for the day and Vn for the number of days will be;

⇒ Vn = 100 (2)ⁿ⁻¹

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The table is shown in figure.

Now,

Let n for the day and Vn for the number of days.

Clearly, The table is in geometric sequence as;

⇒ Common ratio = 200/100

                           = 2

And, The first term = 100

So, The explicit formula and a recursive formula will be;

⇒ Vn = 100 (2)ⁿ⁻¹

Where,  'n' for the day and 'Vn' for the number of days.

Thus, The explicit formula and a recursive formula using n for the day and Vn for the number of days will be;

⇒ Vn = 100 (2)ⁿ⁻¹

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The slope intercept form of the line that passes through the point (1, 4) and has the slope 6 is y = 6 x - 2.

The point that the line passes through is:

(1, 4)

The slope of the line is:

m = 6

The slope intercept form of the line is:

y - y₁ = m (x - x₁)

Substitute the values in the equation, we get that:

y - 4 = 6 ( x - 1)

y - 4 = 6 x - 6

y = 6 x - 6 + 4

y = 6 x - 2

Therefore, we get that, the slope intercept form of the line that passes through the point (1, 4) and has the slope 6 is y = 6 x - 2.

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To calculate the electric flux through each side of the box, we need to use Gauss's Law, which states that the electric flux through a closed surface is proportional to the total charge enclosed by that surface.

Given the magnitudes of the electric field on each side of the box, we can calculate the electric flux through each side using the formula:

Electric Flux = Electric Field * Area * Cos(θ)

where:

Electric Field is the magnitude of the electric field on a particular side of the box

Area is the area of that side of the box

θ is the angle between the electric field vector and the surface normal (which is 0 degrees for a perpendicular field)

Given the dimensions of the box, we can calculate the areas of each side:

Area of the right side = w * h

Area of the top and bottom sides = L * w

Area of the front and back sides = L * h

Area of the left side = w * h

Now, we can calculate the electric flux through each side:

Electric Flux through the right side = E₁ * Area of the right side * Cos(0°)

Electric Flux through the top side = E₂ * Area of the top side * Cos(0°)

Electric Flux through the bottom side = E₂ * Area of the bottom side * Cos(0°)

Electric Flux through the front side = E₂ * Area of the front side * Cos(0°)

Electric Flux through the back side = E₂ * Area of the back side * Cos(0°)

Electric Flux through the left side = E₃ * Area of the left side * Cos(0°)

To calculate the total charge enclosed by the Gaussian box, we use the formula:

Total Charge Enclosed = Electric Flux through the right side + Electric Flux through the left side

Now, let's calculate the values:

Area of the right side = w * h = 56.1 cm * 13.6 cm = 763.96 cm²

Electric Flux through the right side = 1156 N/C * 763.96 cm² * Cos(0°)

Area of the top and bottom sides = L * w = 89.5 cm * 56.1 cm = 5023.95 cm²

Electric Flux through the top side = 2842 N/C * 5023.95 cm² * Cos(0°)

Electric Flux through the bottom side = 2842 N/C * 5023.95 cm² * Cos(0°)

Area of the front and back sides = L * h = 89.5 cm * 13.6 cm = 1216.2 cm²

Electric Flux through the front side = 2842 N/C * 1216.2 cm² * Cos(0°)

Electric Flux through the back side = 2842 N/C * 1216.2 cm² * Cos(0°)

Area of the left side = w * h = 56.1 cm * 13.6 cm = 763.96 cm²

Electric Flux through the left side = 4484 N/C * 763.96 cm² * Cos(0°)

Total Charge Enclosed = Electric Flux through the right side + Electric Flux through the left side

Now, you can plug in the values and calculate the electric flux and total charge enclosed using the given magnitudes of the electric fields.

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The volume of the conical mound of gravel is approximately 159.12 cubic feet.

To calculate the volume of the mound of gravel in the shape of a cone, we can use the formula:

\(V=\frac{1}{3} *\pi *r^2*h\)

where:

V is the volume,

π is a mathematical constant approximately equal to 3.14,

r is the radius of the cone's base, and

h is the height of the cone.

In this case, the radius is given as 4.24 ft, and the height is twice the radius, which is 2 * 4.24 ft.

Plugging in the values, we have:

\(V=(\frac{1}{3} ) * 3.14 * (4.24 ft)^2 * (2 * 4.24 ft)\)

\(V = (\frac{1}{3} ) * 3.14 * 17.9776 ft^2 * 8.48 ft\)

\(V = 0.3333 * 3.14 * 152.490624 ft^3\)

\(V = 159.12 ft^3 (rounded to two decimal places)\)

Therefore, the volume of the mound of gravel is approximately 159.12 cubic feet.

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The mistake Sofia did will doing survey is mentioned in option A, B, and D.

Survey:

In human research, a survey is a list of questions designed to extract specific data from a specific group of people. Surveys can be conducted by phone, email, internet, street corner or shopping mall. Surveys are used to gather or generate insights in areas such as social surveys and demographics.

Research studies are commonly used to assess thoughts, opinions, and feelings. Research can be specific and narrow, or it can set more global and broad goals. Psychologists and sociologists often use surveys to analyze behavior, but they also serve the more practical needs of the media, such as evaluating political candidates, public health officials, professional organizations, and advertising and marketers. It is also used to meet Research studies are also used in various medical and surgical fields to gather information about the practice patterns of health care workers and their attitudes towards various clinical problems and diseases. Health professionals who may participate in research studies include, but are not limited to, physician nurses and physical therapists. A questionnaire consists of a series of pre-determined questions for a sample. A representative sample, that is, a sample representative of the larger population of interest, can be used to describe the attitudes of the population from which the sample was drawn. Additionally, you can compare the attitudes of different population groups and look for changes in attitudes over time. Proper sample selection is very important as it allows the sample results to be generalized to the population. This is the overall purpose of the research study. Additionally, it is important to ensure that the survey questions are not biased. B. Use of Obscene Language. This prevents survey results from being inaccurate.

According to the Question:

The survey included 40 children.

The movie Sofia chose was " Three Little Princesses"

The mistake in the way she selected her sample was:

Option A: The sample of 40 children is too small to represent all kindergartners.

Option B: The sample was taken at a specific movie, which will skew data towards that type of movie.

Option D: The sample should include the adults with the children instead of only children.

Therefore, the mistake Sofia did will doing survey is mentioned in option A, B, and D.

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Answer:

Step-by-step explanation:

a) Men = 4/9 × 27 = 12

Women = 7/12 × 60 = 35

Total =  35 + 12 = 47

b) 60 + 27 = 87

87 - 47 = 40

P(no glasses) = 40/87

The number of people in the choir who do not wear glasses is 40 and the number of people who wear glasses is equal to 47

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes.

Given here P(a man is wearing a glasses) = 4/9 and P(A woman wearing glasses)= 7/12

Now using the formula for probability and total man is 27 hence

P(man) = 4/9

            = 4× 3/9×3

            = 12/27

thus the number of men that wear glasses is equal to 12 and man who do not is 27-12=15

Similarly for woman P(woman) = 7×5/12×5

                                                   = 35/60

therefore woman who wear glasses = 35 and woman who do not = 25

Hence total number of people who wear glasses is 47 and people who do not wear glasses is equal to 40

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This is a classic river crossing puzzle. To safely get all three across take the goat across, leave the goat, take the lion across, take the cabbage across,  return with the empty boat, Take the goat across to reunite with the cabbage and lion

Here's one possible solution:

By following these steps, you will have successfully transported all three items across the river without violating the rules.

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Answer:

b.is the answer to your question

The inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Ms. Jerome wants to buy identical boxes of art supplies for her 25 students. If she can spend no more than $375 on art supplies

Let's suppose b is the price of each box of supplies.

Total cost for a 25 number of boxes = $25b

25b ≤ 375

Thus, the inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.

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Answer:

6h = 36ft + 3h

The height h of each floor is 12ft

Step-by-step explanation:

From the question,

The two buildings have the same total height.

Let the total height of each building be H, that is

H (for one building) = H (for the other building)

Also,

For one building, there are 6 floors each with height h, that is

H = 6h

For the other building, there is a ground floor of 36 ft and 3 other floors each with  height h, that is

H = 36ft + 3h

To find the height h of each floors,

Since the two buildings have the same total height, we can write that

H (for one building) = H (for the other building),

Then,

6h = 36ft + 3h

This is an equation that could be used to find height h.

To solve for h,

6h = 36ft + 3h

Then,

6h - 3h = 36ft

3h = 36ft

h = 36ft / 3

h = 12ft

Hence, the height h of each floor is 12ft

Applying the centroid theorem, the length of QK in the triangle is: 10.

The centroid of a triangle is the point of intersection of the three medians of the triangle. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposing side. T

The Centroid Theorem states that the centroid of a triangle is located two-thirds of the distance from each vertex to the midpoint of the opposite side.

In other words, if G is the centroid of triangle ABC, then AG = (2/3)AD, BG = (2/3)BE, and CG = (2/3)CF, where D, E, and F are the midpoints of sides BC, AC, and AB, respectively.

Therefore, given that:

Q is the centroid of ΔJKL

PQ = 5

Thus, PQ = 1/3(PK) [according to the centroid theorem]

Substitute:

5 = 1/3(PK)

15 = PK

PK = 15

QK = PK - PQ

QK = 15 - 5

QK = 10 units

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a. the population in 1790 was 3.93 million. b. the population in 1820 can be expressed as N = 3.93 x 1.03^t, where t is the number of years since 1790. c. the population of the United States in 1820 was approximately 31.12 million.

(a) To find the population in 1790, we plug in t = 0 into the given formula:

N = 3.93 x 1.03^0 = 3.93

Therefore, the population in 1790 was 3.93 million.

(b) To express the population in 1820 using functional notation, we plug in t = 30 into the given formula:

N = 3.93 x 1.03^30

Therefore, the population in 1820 can be expressed as N = 3.93 x 1.03^t, where t is the number of years since 1790.

(c) To calculate the value of the population in 1820, we plug in t = 30 into the formula and round to two decimal places:

N = 3.93 x 1.03^30 ≈ 31.12

Therefore, the population of the United States in 1820 was approximately 31.12 million.

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The statements that are true about the family of t distributions are A. t distributions have fatter tails and narrower centers than Normal models. B. As the degrees of freedom increase, the t distributions approach the Normal distribution. C. t distributions are symmetric and unimodal is not accurate, as they can be asymmetric and have multiple modes depending on the degrees of freedom.

The following statements are true about the family of t distributions:

A. t distributions have fatter tails and narrower centers than Normal models.

B. As the degrees of freedom increase, the t distributions approach the Normal distribution.

A. t distributions have fatter tails and narrower centers than Normal models:

In comparison to Normal distributions, t distributions have fatter tails. This means that t distributions have a higher probability of extreme values, or outliers, in the tails of the distribution compared to Normal distributions. The fatter tails of t distributions indicate that they are more spread out in the tails, leading to a greater probability of observing extreme values. Additionally, t distributions have narrower centers or peaks compared to Normal distributions. This narrower center indicates that the values in the middle of the distribution are concentrated more closely together, resulting in a taller and narrower peak.

B. As the degrees of freedom increase, the t distributions approach the Normal distribution:

The degrees of freedom (df) in a t distribution refer to the number of independent observations used to estimate a population parameter. As the degrees of freedom increase, the t distributions become more similar to the Normal distribution. Specifically, as the sample size increases, the t distribution becomes closer to a Normal distribution in terms of its shape, center, and spread. When the degrees of freedom are very large (e.g., greater than 30), the t distribution closely approximates the Normal distribution. In other words, as the sample size increases, the t distribution becomes less dependent on the assumptions of the underlying population, and the shape of the distribution approaches the bell-shaped, symmetric shape of the Normal distribution.

C. t distributions are symmetric and unimodal:

The statement that t distributions are symmetric and unimodal is not accurate. Unlike the Normal distribution, which is symmetric and unimodal, t distributions can be asymmetric and have multiple modes. The symmetry and unimodality of a distribution depend on the specific values of the degrees of freedom. When the degrees of freedom are larger, the t distribution tends to become more symmetric and approach a unimodal shape. However, for smaller degrees of freedom, t distributions can exhibit asymmetry and have multiple peaks, resembling a shape different from the typical bell curve.

In summary, the statements that are true about the family of t distributions are:

A. t distributions have fatter tails and narrower centers than Normal models.

B. As the degrees of freedom increase, the t distributions approach the Normal distribution.

C. t distributions are symmetric and unimodal is not accurate, as they can be asymmetric and have multiple modes depending on the degrees of freedom.

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Given the graph of a line

As shown : the line passes with points (0 , 3 ) and ( 4 , -1 )

The general slope intercept form is : y = m * x + b

Where m is the slope and b is y- intercept

The point of y- intercept is = ( 0 , 3 )

Substitute with m and b at the general form

So, the equation of the line will be :

So ,the answer is the first option: y = -1x + 3

Answer:

-360 degrees celcius

Step-by-step explanation:

Answer:

All pairs of corresponding sides are congruent

Step-by-step explanation:

∠A≅∠D

∠B≅∠E

∠C≅∠F

The total cost of the principal and interest after 30 years is $788,489.94 (approx). The correct option is D. $788,489.94.

Here, Principal = $315,000

Interest rate = 7.35%

Term of mortgage = 30 years

Total cost of the principal and interest can be found using the formula; T = (P x (r/n) x (1 + r/n)(n x t))/(1 + r/n)(n x t) - 1

Where, T = Total cost of the principal and interest

P = Principal

r = Rate of interest per annum

n = Number of payments per year

T = Term of the mortgage

In this question, P = $315,000

r = 7.35%/yr = 0.0735/y

rn = 12/yr (12 monthly payments in a year)

t = 30 years

Substituting all the values in the formula, T = ($315,000 x (0.0735/12) x (1 + 0.0735/12)(12 x 30))/(1 + 0.0735/12)(12 x 30) - 1≈ $788,489.94

Hence, D is the correct option.

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The lateral surface area of the square is 784mm².

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

If the square has a side length of 14 mm, then all sides are equal in length.

The lateral surface area of a square is simply the perimeter multiplied by the height of the shape. Since a square has equal length and width, the perimeter of the square is simply 4 times its side length. Therefore, we have:

Perimeter = 4 × 14 mm = 56 mm

The height of the shape is the same as the length of any of its sides, which is also 14 mm. Therefore, we have:

Lateral Surface Area = Perimeter × Height = 56 mm × 14 mm = 784 mm^2

Therefore, the lateral surface area of the square is 784mm².

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find the lateral surface area of a square box with dimensions 14 mm, 13mm and 6 mm.

Answer:

-2 is the slope

Step-by-step explanation:

Hello there, I am here to help you!

The equation of this line is written in slope-intercept form. In case you do not know what it looks like, I will tell you.

It looks like so:

y=mx+b

Where

m is the slope and b is the y-intercept.

Therefore, the slope is -2. Hope it helps. Use the comment section to clarify your doubts, and sorry for the late response.

Answered by

~A cheerful teen who helps others with joy

Good luck.

Answer:

The 11th term is 295,245.

Step-by-step explanation:

We are given the sequence:

\(5, 15, 45, 135...\)

And we want to find the 11th term.

First, let's determine whether this is an arithmetic sequence or a geometric sequence.

Arithmetic sequences have common differences, while geometric sequences have common ratios.

We can determine that our sequence is a geometric sequence because each subsequent term is triple the previous term: our common ratio is 3.

To find the 11th term, we can write an explicit formula for our sequence. The explicit formula for a geometric sequence is given by:

\(x_n=ar^{n-1}\)

Where a is the initial term, r is the common ratio, and n is the nth term.

Since initial term is 5, and the common ratio is 3. Thus:

\(x_n=5(3)^{n-1}\)

To find the 11th term, substitute 11 for n:

\(x_{11}=5(3)^{11-1}\)

Evaluate. Thus, the 11th term is:

\(x_{11}=5(59049)=295245\)

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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Answer:

Option A

Step-by-step explanation:

The set of values for which y is a function of x is the set where each x-value has exactly on y-value. No x-value has more than 1 y-value.

✅Option A: y is A FUNCTION of x because it has exactly one y-value assigned to each x-value.

❌Option B: y is NOT a function of x because there are two y-values, 4 and 2, that are assigned to one x-value, -1.

❌Option C: y is NOT a function of x because there are two y-values, 10 and 12, that are assigned to one x-value, 1.

❌Option D: y is NOT a function of x because there are two y-values, 2 and 4, that are assigned to one x-value, -1.

Answer:

Step-by-step explanation:

1). In ΔTPW and ΔGHD,

  Triangles will be congruent by the properties of congruence,

  1). SSS - (Sides - Side - Side) property of congruence

  2). SAS - (Side - Angle - Side) property of congruence

  3). ASA - (Angle - Side - Angle) property of congruence

2). ΔABE ≅ ΔMNP

   ∠A ≅ ∠M

   ∠B ≅ ∠N

   ∠E ≅ ∠P

   Side AB ≅ Side MN

   Side AE ≅ Side MP

   Side BE ≅ Side NP

   Another way to write the congruency statement → ΔAEB ≅ ΔMPN

3). ΔQRY ≅ ΔJLS

   ∠Q ≅ ∠J

   ∠R ≅ ∠L

   ∠Y ≅ ∠S

   Side QR ≅ Side JL

   Side RY ≅ Side LS

   Side QY ≅ Side JS

   Anthe way to write the congruency statement → ΔQYR ≅ ΔJSL

If the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.

Let's go through the problem step by step to find the area of the rectangle.

Let's assume that the length of the rectangle is represented by the variable "x" (as stated in the question). According to the given information, the width of the rectangle is 58 units less than its length.

If the width is 58 units less than the length, we can represent the width as (x - 58). This means that the length minus 58 gives us the width.

Now, to find the area of the rectangle, we use the formula:

Area = Length × Width

Substituting the values we have:

Area = x × (x - 58)

Expanding the equation:

Area = x² - 58x

So, the area of the rectangle is given by the expression x² - 58x.

To summarize, if the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.

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Answer:6

Step-by-step explanation:i’ve done this answer before

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of x is 6.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example:

2 + 3x + 4y = 7 is an expression.

3x = 4 is an expression.

3x + 4x - 4 is an expression.

We have,

The sum of the measures of angle P and angle S is 140°.

The measure in degrees of angle P is represented by the expression.

=  (5x + 30)

The measure of angle S.

= 80°

Now,

5x + 30 + 80 = 140

5x + 110 = 140

Subtract 110 on both sides.

5x = 140 - 110

5x = 30

Divide both sides by 5.

x = 6

Thus,

The value of x is 6.

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The coffee shop owner should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian coffee to make the 150-pound blend.

To solve this problem, we can use a system of equations. Let x be the number of pounds of Brazilian coffee and y be the number of pounds of Colombian coffee. We can set up the following equations:

x + y = 150 (the total amount of coffee is 150 pounds)
10x + 14y = 11(150) (the total cost of the coffee is $11 per pound)

Now we can use the first equation to solve for one of the variables. Let's solve for y:

y = 150 - x

Now we can substitute this into the second equation:

10x + 14(150 - x) = 11(150)

Distribute the 14:

10x + 2100 - 14x = 1650

Combine like terms:

-4x = -450

Divide by -4:

x = 112.5

Now we can substitute this back into the first equation to solve for y:

112.5 + y = 150

y = 37.5

So the coffee shop owner should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian coffee to make the 150-pound blend.

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