Determine the equation of a line that has a slope-angle of 150° and goes through (4,0).

Answer:

Step-by-step explanation:

convert 3 5/6 and 3 3/5 into a improper fraction

x=23/6 and y = 18/5

23/6 ÷ 18/5 multiply both sides by 6 to cancel it out

23 ÷ 108/5 multiply both sides by 5 to cancel it out

answer 115/108

Answer:

1 1/45

Step-by-step explanation:

The expected probability that the next flip is a head given the results of the previous 25 coin flips is 0.6 or 60%.

The expected probability of a head coming up next given the results of the 25 coin flips is 15/25 = 0.6.

This is due to the fact that 15 of the 25 flips were heads, so the probability of the next head is 15 out of the 25 total flips which is equal to 0.6 or 60%.

However, since the probability of heads (m) is unknown, the expected probability of a head coming up next is still unknown.

Therefore, the expected probability that the next flip is a head given the results of the previous 25 coin flips is 0.6 or 60%.

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The common ratio for infinite geometric series with first term -3/2 and sums twice the common ratio is -1/2.

First keep in mind the common ratio must -1 < r < 1 for geometric series converges.

Common ratio can be calculated using standard formula for infinite geometric series converges which is Sum = a/(1-r) with a as first term and r as common ratio. So,

Since sum is twice the common ratio, so the equation is

2r = a/(1-r)

we can substitute (1-r). So,

2r(1-r) = a

2r-2r^2 = -3/2

we can multiple all by two. So,

4r-4r^2 = -3

0 = 4r^2-4r-3

0 = (2r-3)(2r+1)

So the result is either r = 3/2 or r = -1/2. as previously mentioned above, r result only in -1 < r < 1. So, the result of r = 3/2 is rejected.

Thus, the common ratio is -1/2.

You question is incomplete, but most probably your full question was

An infinite geometric series has first term -3/2 and sums to twice the common ratio. Find the sum of all possible values for the common ratio.

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Answer:

80

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

knowing a parallelogram, EJ = JQ

4w + 4 = 2w + 22

4w – 2w = 22 – 4

2w = 18

w = 9

then, substitute w=9 into 4w + 4

4(9) + 4 = 40

Solution:

As we can see according to the coordinate diagram, the length of the rectangle is 5 unit long in the negative x axis and negative 3 in the y axis, now with one vertex at origin.

Therefore there is 1 vertex that have their y coordinate as zero and other whose x coordinate is 0.

Hence, the value of two vertex that are on line with the axis are (-5, 0) and (0.-3).

To the value of x and y we use the coordinates (-5, 0) and (0, -3), as we can see the value of x axis is -5 and the value of y =3.  

Hence, the value of (x, y) = (-5, 3).  

And the other coordinates are (-5, 0) , (0,-3) and (0, 0)  

Answer:  (-5, -3)

Step-by-step explanation:

First, you need to understand where Quadrant III lies.

               Quadrant II ↓ ← ← ← ← ← ← Quadrant I

                                   ↓

                                   ↓

              Quadrant III ↓ → → → → → → Quadrant IV

Since the vertex lies in the bottom left corner of the graph with distance from the origin (0, 0) of 5 on the x-axis and 3 on the y-axis, we end up with (-5, 0) on the x-axis and (0, -3) on the y-axis.  To form a rectangle, the remaining vertex lies at (-5, -3).

         (-5, 0) o-----------------------o (0, 0)

                    |                            |

                    |                            |

                    |                            |

       (-5, -3) o-----------------------o (0, -3)

Answer:

Step-by-step explanation:

Answer:

  2 ft, 7 ft

Step-by-step explanation:

We are interested in the values of x such that g(x) = h(x). These will be solutions of the difference g(x) -h(x) = 0. Hence the x-intercepts of a graph of g(x) -h(x) will be solutions to the problem.

__

The graph shows the difference between the paths will be zero at distances of 2 feet and 7 feet.

The sample size required is 182 families should be interviewed.

To calculate the number of families that should be interviewed to obtain the desired precision and degree of confidence, one must first determine the minimum sample size required to achieve the desired degree of confidence. As the standard deviation of the sample was computed to be $400 with the mean of $60,000.

Sample size formula: n = (Z² * s²) / E²

The formula for the degree of confidence: Z = 2.576

Sample size formula: n = (Z² * s²) / E²

Substituting the values, we get n = (2.576² * $400²) / $90²= 181.49 = 182 families. The sample size required is 182 should be interviewed families.

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Answer:

4th one

Step-by-step explanation:

18/6=3      3 units on the y-axis / vertical

That's the only one with (-4,-2)

The standard deviation of a sample proportion is given by the formula:

σ = sqrt((p * (1 - p)) / n)

where σ is the standard deviation, p is the sample proportion, and n is the sample size.

If we want the standard deviation to be one-half of what it was for a sample of size 100, we can write the following equation:

(sqrt((p * (1 - p)) / n)) / 2 = sqrt((p * (1 - p)) / 100)

To simplify the equation, we can square both sides:

((p * (1 - p)) / n^2) / 4 = (p * (1 - p)) / 100

Simplifying further:

100 * n^2 = 4 * 1

n^2 = (4 * 1) / 100

n^2 = 0.04

Taking the square root of both sides:

n = sqrt(0.04)

n = 0.2

Therefore, the sample size should be 0.2. However, since the sample size must be a positive integer, we round it up to the nearest whole number. Therefore, the sample size should be 1.

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According to the question For ( a ) the amount and concentration of salt at any time \(\(t\)\) can be \(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\) . For ( b ) the limiting concentration of salt in the tank is 0.25 kg/L.

To determine the amount and concentration of salt at any time in the tank, we need to consider the inflow of saltwater, outflow of water, and evaporation. Let's denote the time as \(\(t\)\) in hours.

a. Amount and Concentration of Salt at any time:

Let's denote the amount of salt in the tank at time \(\(t\) as \(S(t)\)\) in kg and the concentration of salt in the tank at time \(\(t\) as \(C(t)\) in kg/L.\)

Initially, the tank contains 100 L of water with a salt concentration of 0.1 kg/L. Therefore, at \(\(t = 0\)\), we have:

\(\[S(0) = 100 \times 0.1 = 10 \text{ kg}\]\)

\(\[C(0) = 0.1 \text{ kg/L}\]\)

Considering the inflow, outflow, and evaporation rates, the amount of salt in the tank at any time \(\(t\)\) can be calculated as:

\(\[S(t) = S(0) + \text{Inflow} - \text{Outflow} - \text{Evaporation}\]\)

The inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L. Thus, the amount of salt entering the tank per hour is:

\(\[\text{Inflow} = \text{Inflow rate} \times \text{Concentration} = 55 \times 0.2 = 11 \text{ kg/h}\]\)

The outflow rate is 44 L/h, so the amount of salt leaving the tank per hour is:

\(\[\text{Outflow} = \text{Outflow rate} \times C(t) = 44 \times C(t) \text{ kg/h}\]\)

The evaporation rate is 11 L/h, and as only water evaporates, it does not affect the salt concentration in the tank.

Therefore, the amount and concentration of salt at any time \(\(t\)\) can be expressed as follows:

\(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)

\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\)

b. Limiting Concentration:

The limiting concentration refers to the concentration reached when the inflow and outflow rates balance each other, resulting in a stable concentration. In this case, the inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L, and the outflow rate is 44 L/h. To find the limiting concentration, we equate the inflow and outflow rates:

\(\[\text{Inflow rate} \times \text{Concentration} = \text{Outflow rate} \times C_{\text{limiting}}\]\)

\(\[55 \times 0.2 = 44 \times C_{\text{limiting}}\]\)

\(\[C_{\text{limiting}} = \frac{55 \times 0.2}{44} = 0.25 \text{ kg/L}\]\)

Therefore, the limiting concentration of salt in the tank is 0.25 kg/L.

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Therefore, the correct inequality to find the domain is simply x - 3 < 0, which simplifies to x < 3.

To find the domain of a function, we need to determine all the values of the independent variable (usually represented by x) that the function is defined for. In this case, the function is defined as f(x) = x - 3, which means we can plug in any value of x into the expression x - 3 to get a corresponding value of f(x).

However, there are some values of x that would cause the expression x - 3 to be undefined. For example, if we were trying to find f(x) when x = 2, we would get f(2) = 2 - 3 = -1, which is a valid output. But if we were trying to find f(x) when x = 3, we would get f(3) = 3 - 3 = 0/0, which is undefined.

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Answer: Answer: A

Explanation:

Just plug in numbers since you know the unknown values,

x + r = 4 + 5

4 + 5 = 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you want to find the equation of line with a given a slope of which goes through the point (-4,5), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---

where is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute  

Multiply and to get

Add -1 to both sides to isolate y

Combine like terms and to get the answer

So the equation of the line with a slope of which goes through the point (-4,5) is:

which is now in y=mx = b form where the slope is m=-4/5  and the y-intercept is b=1

The number of teams she can make is 10.

Division is the process of putting a number into equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other basic mathematical operations include addition, subtraction, multiplication.

The number of teams that can be made can be determined by dividing the total number of friends by the total number of players in each team. The whole number that is derived from the division process is the number of teams teams that can be made given the total number of friends and the number of people that have to be in each group.

Number of teams she can make = total number of friends / number of people in each group

31 / 3 = 10 remainder 1

So, only 10 teams can be made. one person would not be on any team.

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Option D is the correct.

The given function f: R → R with the rule f(x) = 3x + 2. Let R represent the set of all real numbers.

What is a function?

A function is defined as the set of ordered pairs in which each first element of the ordered pair maps to one unique second element of the ordered pair.

What is an injective function?

A function f(x) is called one-to-one or an injective function, if and only if each and every element of the function domain is paired with exactly one element of the function range.

What is a surjective function?

A function f(x) is called onto or a surjective function, if and only if each and every element of the function range is paired with at least one element of the function domain.

What is a bijective function?

A function f(x) is called a bijection or a bijective function if it is both injective and surjective.

The given function is a function because for every x in R, there is exactly one image (3x+2) in R.

Let x₁, x₂ be two distinct real numbers in R, then3x₁ + 2 ≠ 3x₂ + 2, which implies f is injective or one-to-one.

Therefore, the given function f is both an injective function and a surjective function.

So, the function is a Bijective function

Option D is the correct choice. The given function f: R → R with the rule f(x) = 3x + 2 is Bijective function.

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i don't speak russian bro

The statement that It is sufficient to test an analogy by asking what are its relevant similarities is false.

Analogy refers to the process of comparison of two or more items such that it explains some idea, or classification or familiarity and representativeness. Studying the analogies helps in enhancing, strengthening and reinforcing the skills in areas such as reading comprehension, homophones, deductive reasoning and logic.

Testing an analogy only by relevant similarities will produce partial results which might not be suitable to fully explain the reason. Hence, both relevant similarities and differences are to be considered for more detailed review. Different kind of analogies used to explain the differences or similarities are synonym and antonym, symbol and reference, degree of differences.

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A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

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The required cost of the meal given as a hot dog is of $6 and the hamburger is of $8.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Let's call the cost of a hot dog meal "x" and the cost of a hamburger meal "y".

From Mrs. Hammond's purchase, we know that:

x + 3y = 30   -- - - - - -(1)

From Mr. Weber's purchase, we know that:

3x + 3y = 42 - - - - - -(2)

We can use substitution to solve for one of the variables in terms of the other. If we substitute the first equation into the second equation:

3x + 3y = 42

3x + 3(30 - x)/3 = 42

3x + 30 - x = 42

2x = 12
x = 6

now,
6 + 3y = 30
3y = 24
y = 8

Thus, the required cost of the meal given as a hot dog is of $6 and a hamburger is $8.

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The slack of activity B, given its duration of 12 days, earliest finish of 22 days, and latest start of 15 days, is -7 days.

Now, let's calculate the slack of activity B. Slack represents the amount of time an activity can be delayed without affecting the overall project schedule. Mathematically, slack can be calculated as the difference between the latest start (LS) and the earliest finish (EF) of an activity:

Slack = LS - EF

In our case, the latest start (LS) of activity B is 15 days, and the earliest finish (EF) is 22 days. Therefore, the slack of activity B can be calculated as follows:

Slack = LS - EF

Slack = 15 - 22

Slack = -7

The slack value of -7 indicates that activity B is already delayed by 7 days, considering the project schedule. Negative slack values imply that the activity is behind schedule, and any further delay will directly impact the project completion date.

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Answer:

D. 5

Step-by-step explanation:

Applying,

cos∅ = adjacent/Hypotenuse

From the diagram,

Given: ∅ = 45°, adjacent = s, hyptenuse = 5√2

Therefore,

cos45° = s/5√2

make s the subject of the equation

s = cos45°×5√2

s = (1/√2)(5√2)

s = 5

Hence the right answer is D. 5

Answer:

48

Step-by-step explanation:

The bowl started with x number of pieces of candy.

Aaliyah took half: now there are x/2 pieces of candy

Tehgan took half of the remaining: now there are x/4 pieces of candy

Juliette took half of the remaining: now there are x/8 pieces

After Juliette took, there were 6 pieces left.

That means that x/8 equals 6.

x/8 = 6

Multiply both sides by 8.

x/8 × 8 = 6 × 8

x = 48

Answer: 48

Answer:

30x - 18

Step-by-step explanation:

6(5x - 3)

30x - 18

6(5x) = 30x

6(-3) = -18

Combined:

30x - 18

Rounding this approximation to the nearest whole number, we get:

V_metal ≈ 157 cubic inches. None of the given options match this estimation.

To estimate the amount of metal in the tank, we need to calculate the surface area of the metal and then multiply it by the thickness of the metal.

The surface area of the top and bottom of the tank can be calculated as the area of a circle, which is given by the formula A = πr². Since the radius of the tank is 10 inches, the area of each circular end is:

A_top_bottom = π(10)² = 100π square inches

The surface area of the side of the tank can be calculated as the lateral surface area of a cylinder, which is given by the formula A = 2πrh, where r is the radius and h is the height. In this case, the height is 20 inches, and the radius is 10 inches. Therefore, the lateral surface area is:

A_side = 2π(10)(20) = 400π square inches

The total surface area of the metal is the sum of the top, bottom, and side surface areas:

A_total = A_top_bottom + A_side = 100π + 400π = 500π square inches

Since the thickness of the metal is 0.1 inches, we can estimate the volume of the metal by multiplying the surface area by the thickness:

V_metal = A_total × 0.1 = 500π × 0.1 = 50π cubic inches

To find a numerical approximation for the volume, we can use the value of π as 3.14159:

V_metal ≈ 50 × 3.14159 ≈ 157.0795 cubic inches

Rounding this approximation to the nearest whole number, we get:

V_metal ≈ 157 cubic inches

None of the given options match this estimation. It seems there might be an error in the available options.

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Answer:

The matrix that represents the number of each type of house available in Tampa is D) Matrix with 1 row and 3 columns consisting of elements 24, 12, and 18. This matrix shows that there are 24 1-bedroom houses, 12 2-bedroom houses, and 18 3-bedroom houses available in Tampa.

The probability that a randomly selected customer at the restaurant orders both an appetizer and dessert is 30%.

Let's denote the event of ordering an appetizer as A and the event of ordering dessert as D. We are given that P(A) = 0.55 (55% order an appetizer) and P(D) = 0.52 (52% order dessert). We are also given that P(A ∪ D) = 0.77 (77% order an appetizer or dessert, or both).

To find the probability of a customer ordering both an appetizer and dessert, we need to calculate the intersection of events A and D, denoted as P(A ∩ D).

Using the inclusion-exclusion principle, we have:

P(A ∪ D) = P(A) + P(D) - P(A ∩ D)

We can rearrange this equation to solve for P(A ∩ D):

P(A ∩ D) = P(A) + P(D) - P(A ∪ D)

         = 0.55 + 0.52 - 0.77

         = 0.3

The probability that a randomly selected customer at the restaurant orders both an appetizer and dessert is 30%. This means that approximately 30% of the customers who order an appetizer also order dessert, and vice versa.

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The measure of angle AEB is determined as 9.5⁰.

The measure of angle AEB is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠AEB = ¹/₂( CD + AB)

Also, m∠AEB = m∠DEC (vertical opposite angles are equal)

Substitute the given values and solve for x;

3x + 5 = ¹/₂ (7x + 4  +  2x²)

6x + 10 = 7x + 4 +  2x²

0 =  2x² + x - 6

Factorize the above equation;

2x² + 4x - 3x - 6 = 0

2x(x + 2) - 3(x + 2) = 0

(2x - 3)(x + 2) = 0

2x = 3  or  x = -2

x = 3/2 or - 2

The measure of angle AEB is calculated as follows;

m∠AEB = 3x + 5

when x = 3/2

m∠AEB  = 3(3/2) + 5

m∠AEB = 9.5⁰

when x = -2

m∠AEB = 3(-2) + 5

m∠AEB = -1⁰  (the value of angle cannot be negative)

So the value of m∠AEB is 9.5⁰.

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