What is an equation of the line that contains the point (0, -5) and a slope of 1/4

Answer:

y = -2 the line intersects with y asis in the point -2

y = 4 the line intersects with y asis in the point 4

x = -1 the line intersects with x asis in the point -1

Step-by-step explanation:

i can only see those three lines

Answer:

-8

Step-by-step explanation:

a. The population variance is unknown.

The t-distribution should be used when estimating the population mean using a small-sample confidence interval if the population variance is unknown and the sample size is small (typically n < 30). If the population variance is known, then the normal distribution can be used instead of the t-distribution.

If the sample variance is large, it may indicate that the underlying population distribution has a high degree of variability. However, this alone does not determine whether to use the t-distribution or normal distribution for the confidence interval calculation.

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Answer:£500

Step-by-step explanation: 600 ÷ 1.05

Answer:

£500

Step-by-step explanation:

The number of many different outfits Sophia has to choose from should be 16.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Here, we have

Given: Sophia is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes.

She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes.

So here the number of distinct outfits should be like

= 2 × 4 × 2

= 16

Hence, the number of many different outfits Sophia has to choose from should be 16.

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Answer:16

Step-by-step explanation:Total outcomes

=

Total outcomes=

2‾

pants

×

2‾

t-shirts

×

4‾

shoes

pants

2

​

​

×

t-shirts

2

​

​

×

shoes

4

​

​

Fundamental counting principle

=

=

16

Answer:

3x-1 >x

Step-by-step explanation:

greater than number itself >x. one less is -1. product of number and 3 is 3x

Here all three are the factor. {a+b} will be the sum and 1/2 is the term

Hopefully i am right

All the best ！！

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

At the end of 46 week the city will have: 132 streetlight + (4 streetlight/ week * 46 weeks)

At the end of 46 week the city will have: 132 streetlight  + 184 streetlight

At the end of 46 week the city will have: 316 streetlight

232 streetlight at the end of the week = (232 streetlight - 132 streetlight) / 4 streetlight /week

232 streetlight at the end of the week = 100 streetlight /4 streetlight /week

232 streetlight at the end of the week = 25 weeks

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Correctly written question:

A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed. The city will have (blank) streetlights at the end of 46 weeks. The city will have 232 streetlights at the end of (blank) week

The exact area of each hexagonal shape is 181.5sqrt(3) cm^2. Option B

To determine the exact area of each hexagonal shape formed by the equilateral triangles, we need to calculate the area of one equilateral triangle and then multiply it by the number of triangles that make up the hexagon.

The formula to calculate the area of an equilateral triangle is:

Area = (sqrt(3) / 4) * side^2

Given that the side of each tile measures 11 cm, we can substitute this value into the formula to find the area of one equilateral triangle:

Area = (sqrt(3) / 4) * (11 cm)^2

= (sqrt(3) / 4) * 121 cm^2

= 121sqrt(3) / 4 cm^2

Now, since the hexagon is formed by six equilateral triangles, we can multiply the area of one triangle by 6 to find the total area of the hexagon:

Hexagon Area = 6 * (121sqrt(3) / 4 cm^2)

= 726sqrt(3) / 4 cm^2

= 181.5sqrt(3) cm^2

Therefore, the exact area of each hexagonal shape is 181.5sqrt(3) cm^2.

The correct answer is B: 181.5√3 cm^2.

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Answer:

23

Step-by-step explanation:

Answer:

324

Step-by-step explanation:

Answer:

(2^6)(x^9^6) /  1814

Simplifies to:

1 /  5856458868470016^ x531441

=

1 /  5856458868470016 ^x531441    

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

2x−3-x+4=3

combine like terms:

x + 1 = 3

x = 2

The equation is true for the value of x = 2.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given equation is as given below.

2x − 3 - x + 4 = 3

We have to operate the like terms together.

Here 2x and x are like terms and 3 and 4 are like terms.

(2x - x) - 3 + 4 = 3

x - 3 + 4 = 3

x + 1 = 3

Subtracting 1 on both sides,

x = 3 - 1

x = 2

Hence the equation is true for x = 2.

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Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

The answer is , the conditional probability that an even-numbered card is picked given that the 2 is picked is 1/2 or 0.5.

The conditional probability that an even-numbered card is picked given that the 2 is picked can be calculated using the formula for conditional probability.

Let's assume there are 52 cards in the deck, with half of them being even-numbered (26 cards) and 4 of them being twos (2 of which are even-numbered).

To find the conditional probability, we need to divide the number of favorable outcomes (even-numbered cards that are twos) by the total number of possible outcomes (all twos).

Therefore, the conditional probability can be calculated as:

Conditional Probability = Number of favorable outcomes / Number of possible outcomes

Conditional Probability = 2 / 4

Simplifying the fraction, we get:

Conditional Probability = 1/2

So, the conditional probability that an even-numbered card is picked given that the 2 is picked is 1/2 or 0.5.

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The median is not affected by an extreme value in the data set, while the standard deviation, range, and mean can all be influenced by extreme values.

An extreme value refers to a data point that significantly deviates from the other values in a data set. When considering the impact of extreme values, it is important to understand their effect on different statistical measures.

The median, which represents the middle value in a sorted data set, is not affected by extreme values. The median only considers the position of the data points and is not influenced by their actual values. Therefore, even if there are extreme values present, the median will remain unchanged.

On the other hand, the standard deviation, range, and mean can all be affected by extreme values. The standard deviation measures the dispersion of data points around the mean. Extreme values can significantly impact the spread of the data, leading to a larger standard deviation. The range, which is the difference between the maximum and minimum values in a data set, is directly influenced by extreme values. A single extreme value can greatly expand the range. Additionally, the mean, or the average of all data points, is sensitive to extreme values. Since the mean considers the actual values, extreme values can skew the average towards higher or lower values, depending on the nature of the extreme value.

Therefore, the correct answer is option c. The median is not affected by an extreme value in the data set, while the standard deviation, range, and mean can all be influenced by extreme values.

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The binary representations are a) 0.11000110, b) 0.10000010 and c) 0.10100000.

Let's convert the given real numbers to binary with 8 binary places after the radix point.

A. 0.11:

To convert 0.11 to binary, we can use the following steps:

Multiply 0.11 by 2:

0.11 × 2 = 0.22

Take the integer part of the result, which is 0, and write it down.

Multiply the decimal part of the result by 2:

0.22 × 2 = 0.44

Again, take the integer part (0) and write it down.

Repeat steps 3 and 4 until you reach the desired precision (8 binary places after the radix point).

0.44 × 2 = 0.88 (integer part: 0)

0.88 × 2 = 1.76 (integer part: 1)

0.76 × 2 = 1.52 (integer part: 1)

0.52 × 2 = 1.04 (integer part: 1)

0.04 × 2 = 0.08 (integer part: 0)

0.08 × 2 = 0.16 (integer part: 0)

0.16 × 2 = 0.32 (integer part: 0)

0.32 × 2 = 0.64 (integer part: 0)

Write down the integer parts obtained in step 4 and 5, in order:

0.11000110

Therefore, the binary representation of 0.11 with 8 binary places after the radix point is 0.11000110.

B. 0.51:

To convert 0.51 to binary, we can use the same steps:

Multiply 0.51 by 2:

0.51 × 2 = 1.02

Take the integer part of the result, which is 1, and write it down.

Multiply the decimal part of the result by 2:

0.02 × 2 = 0.04

Again, take the integer part (0) and write it down.

Repeat steps 3 and 4 until you reach the desired precision (8 binary places after the radix point).

0.04 × 2 = 0.08 (integer part: 0)

0.08 × 2 = 0.16 (integer part: 0)

0.16 × 2 = 0.32 (integer part: 0)

0.32 × 2 = 0.64 (integer part: 0)

0.64 × 2 = 1.28 (integer part: 1)

0.28 × 2 = 0.56 (integer part: 0)

0.56 × 2 = 1.12 (integer part: 1)

0.12 × 2 = 0.24 (integer part: 0)

Write down the integer parts obtained in step 4 and 5, in order:

0.10000010

Therefore, the binary representation of 0.51 with 8 binary places after the radix point is 0.10000010.

C. 0.625:

To convert 0.625 to binary, we can use the same steps:

Multiply 0.625 by 2:

0.625 × 2 = 1.25

Take the integer part of the result, which is 1, and write it down.

Multiply the decimal part of the result by 2:

0.25 × 2 = 0.50

Again, take the integer part (0) and write it down.

Repeat steps 3 and 4 until you reach the desired precision (8 binary places after the radix point).

0.50 × 2 = 1.00 (integer part: 1)

0.00 × 2 = 0.00 (integer part: 0)

0.00 × 2 = 0.00 (integer part: 0)

0.00 × 2 = 0.00 (integer part: 0)

0.00 × 2 = 0.00 (integer part: 0)

0.00 × 2 = 0.00 (integer part: 0)

0.00 × 2 = 0.00 (integer part: 0)

0.00 × 2 = 0.00 (integer part: 0)

Write down the integer parts obtained in step 4 and 5, in order:

0.10100000

Therefore, the binary representation of 0.625 with 8 binary places after the radix point is 0.10100000.

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The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

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The module of x is equal to 9, this means that x has two possible values "9" or "-9"

Answer:

see explanation

Step-by-step explanation:

Given

3 < 5 + 6h < 10 ( subtract 5 from each interval )

- 2 < 6h < 5 ( divide each interval by 6 )

- \(\frac{1}{3}\) < h < \(\frac{5}{6}\)

The answers are a) Derive growth rate equation: Pt = 139722 + 38900(t-1), b) Population growth is crucial for wastewater treatment planning, c) Population in 2015: 748,722 people and d) Time for population to increase 10-fold: Approximately 32.62 years.

a) Derive the growth rate equation when assuming linear growth rate. Population growth can be assumed to be linear if it grows by a constant number each year. If we let the population grow at a constant rate of increase k, the equation for population in year t can be written as: Pt=P0+k(t-1)

Where: Pt is the population in year tP0 is the population in year zero (in this case, the population in year 2000)k is the constant rate of increase(t-1) is the number of years since the initial population was recorded in year 2000.

Using the values provided in the question: P0 = 139722, P5 = 305580, P10 = 528000We can find the rate of increase k as follows:

Using P5 and P0: k = (P5 - P0)/(5 - 0) = (305580 - 139722)/5 = 33216

Using P10 and P5: k = (P10 - P5)/(10 - 5) = (528000 - 305580)/5 = 44584

The average of these two rates of increase is: \(k_{avg}\) = (33216 + 44584)/2 = 38900

Therefore, the equation for population growth assuming linear growth is: Pt = 139722 + 38900(t-1)

b) Why is population growth and forecasting important for wastewater treatment?

Population growth and forecasting are important for wastewater treatment for several reasons. First, an increase in population means an increase in demand for clean water, which can put a strain on existing water treatment infrastructure.

Second, as the population grows, so does the amount of wastewater produced, which requires treatment to prevent pollution and protect public health. Accurate population forecasting can help wastewater treatment plants plan for future capacity needs and ensure that they have the necessary resources to meet demand.

c) Calculate the population in 2015.

Assuming the population grows at a constant rate of increase of 38900 people per year, we can use the linear growth equation to find the population in 2015 (15 years after 2000):

P15 = 139722 + 38900(15-1) = 748722

Therefore, the population in 2015 was 748722 people.

d) How long will it take for the population to increase 10-fold from 2000?

To find how long it will take for the population to increase 10-fold from 2000, we need to solve for t in the equation P = 10P0.

This gives us:10P0 = P0 + k(t-1)

Simplifying: 9P0 = k(t-1)

Substituting the value of \(k_{avg}\) from part a:

9(139722) = 38900(t-1)

Solving for t:t-1 = 31.62t = 32.62

Therefore, it will take approximately 32.62 years (or 32 years and 7 months) for the population to increase 10-fold from 2000.

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Answer:

x intercept= -1

y intercept= 2

Answer:  The correct symbol is '<'.

Step-by-step explanation:

Given: In triangle GHJ

\(m\angle H=85^{\circ}\) and \(m\angle G=60^{\circ}\)

Here angle H is opposite to side JG and angle G is opposite to side HJ

We know that,

The side opposite to the greater angle of a triangle is greater.

Since \(m\angle H> m\angle G\)

Then, JG > HJ

Hence, HJ     <       JG

Answer:

(a)V=36πh

Explanation:

• Radius = 6 meters

Part A

An equation that represents the volume V as a function of the height h is:

Part B

Using 3.14 as an approximation for π

The graph of the function is attached below: (V is on the y-axis and h is on the x-axis).

Part C

The initial equation for volume is:

When h=1

If you double the height of a cylinder, h=2:

We observe that when the height is doubled, the volume of the cylinder is also doubled.

Part D

The initial equation for volume is:

If the height of the cylinder is multiplied by 1/3, we have:

The volume of the cylinder will be divided by 3.

Using the graph, we observe a horizontal stretch of the graph by 1/3.

Answer:

946

Step-by-step explanation:

To find the area, you can split the figure into 2 rectangles. The one on the left has a width of 7 and a height of 28. Multiply 28 * 7 to get the area of the first rectangle, which is 196 in.

The second rectangle has a width of 25 and a length of 30. Multiply 30 by 25 to get the area, which is 750 in.

To find the area of the entire figure, add the areas of both rectangles.

196 + 750 = 946 square inches.

Given:

Entrance fee per student: $5(29)

Lunch costs: $4(29 + 6)

Bus fees: $25 + 8($2 + $3)

Total cost: 5(29) + 4(35) + 25 + 8(5)

To find:

The equivalent expressions of the total cost that use the properties of operations to simplify the math.

Solution:

We have,

Total cost = 5(29) + 4(35) + 25 + 8(5)

To simply this expression, we need to write 29 and 35 in the expand form or as the sum of their place values because it is easy to multiply a number with multiply of 10 and single digit.

Total cost = 5(20+9) + 4(30+5) + 25 + 40

Therefore, the correct option is B.

Answer:

Entrance fee per student: $5(29) Lunch costs: $4(29 + 6) Bus fees: $25 + 8($2 + $3) Total cost: 5(29) + 4(35) + 25 + 8(5) To find: The equivalent expressions of the total cost that use the properties of operations to simplify the math. Solution: We have, Total cost = 5(29) + 4(35) + 25 + 8(5) To simply this expression, we need to write 29 and 35 in the expand form or as the sum of their place values because it is easy to multiply a number with multiply of 10 and single digit. Total cost = 5(20+9) + 4(30+5) + 25 + 40 Therefore, the correct option is B.

Step-by-step explanation:

copy me above :)))

The correct step that involved in proving if x is a real number, then [x] [x] = 1 if x is not an Integer and [x] [x] = 0 if x is an Integer are:

a. If x is not an integer, then [x] is the integer just larger than x

b. If x is not an integer, then [x] is the integer just smaller than x

c. It is clear that if x is not an integer, then [x] and [] differ by 0.

d. It is clear that if x is not an integer, then [x] and [x] differ by 1.

e. If x is an integer, then [x] and [x] are equal, so [x-x=x-x=0. f. If x is an integer, then [x] and [x] are different, so [x] [x] = 0.

Since if x is not an integer, then [x] is the integer just smaller than x and [x] + 1 is the integer just larger than x.

Thus, we can write x as x = [x] + {x} where {x} is the fractional part of x.

[x] is an integer, {x} = x - [x].T

Now, we have [x] [x] = [x]([x]+{x}) = [x]^2 + [x]{x}.

Thus we can see that [x]^2 is an integer, and [x]{x} is a fraction, so it is between 0 and 1.

Hence, [x] [x] = 1 if x is not an Integer. If x is an Integer, then [x] and [x] are equal, so [x] [x] = 0.

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Greetings from Brasil....

As stated in the statement of the question, EF is a bisector of CD, so point G is the median point of CD, so CG = GD

5X - 1 = 7X - 13

X = 6

EF = EG + GF

6X - 4 = EG + 13      x = 6, so

6·6 - 4 = EG + 13

(see attachment)

A line segment is also a line but the line with finite length and having fixed endpoints. The length of the line segment EG is 19 unit.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

Given that EF bisects CD at point G, therefore, the line segment CD will be divided into two equal parts, CG and GD. Therefore, we can write,

CG = GD

5x - 1 = 7x - 13

-1 + 13 = 7x - 5x

12 = 2x

x = 12/2

x = 6

Further, the length of segment EG will be,

EG = EF - GF

     = 6x - 4 - (13)

     = 6x - 4 - 13

     = 6x - 17

     = 6(6) - 17

     = 36 - 17

     = 19

Hence, the length of the line segment EG is 19 unit.

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It is impossible to construct an equilateral triangle with three vertices with integer coordinates.

Suppose ABC is an equilateral triangle with integer coordinates.

Then its area by the formula \(\frac{1}{2} (x_{1} (y_{2} -y_{3})+x_{2}(y_{3} -y_{1})+x_{3} (y_{1} -y_{2}))\) is an integer.

Let a be the length of a side. Then \(a^{2}\) is a positive integer. The area of the equilateral triangle is \(\sqrt{\frac{3}{4} } a^{2}\) which is irrational.

Hence we get a contradiction.

Therefore an equilateral triangle cannot have all its vertices integer coordinates.

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It is impossible to construct an equilateral triangle with three vertices with integer coordinates because the distance between any two points with integer coordinates is also an integer. In an equilateral triangle, all three sides must have equal length. However, if the distance between two points with integer coordinates is an integer, then the distance between the third point and either of the first two points will not be an integer in most cases. This means that it is not possible to find three points with integer coordinates that are equidistant from each other.

The distance between two points with integer coordinates can be calculated using the Pythagorean theorem. If we consider two points with coordinates (x1, y1) and (x2, y2), the distance between them is √((x2-x1)²+(y2-y1)²). If the distance between two points is an integer, it means that the difference between the x-coordinates and the y-coordinates is also an integer. In an equilateral triangle, the distance between any two points must be the same. However, it is impossible to find three points with integer coordinates that are equidistant from each other.

In conclusion, it is not possible to construct an equilateral triangle with three vertices with integer coordinates because the distance between any two points with integer coordinates is also an integer. In an equilateral triangle, all three sides must have equal length. However, if the distance between two points with integer coordinates is an integer, then the distance between the third point and either of the first two points will not be an integer in most cases. This means that it is not possible to find three points with integer coordinates that are equidistant from each other.

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Answer:

the third and fourth one is correct

Answer:

i did5.32-11.5 =-6.18

Step-by-step explanation:

Answer:

Find 5.32 - 11.5= -6.18

Step-by-step explanation: