find answer in terms of pi

Answer:

Step-by-step explanation:

y=10

To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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Given:

The data set is:

14, 15, 3, 15, 14, 14, 18, 15, 8, 16

To find:

The mean, median and mode of the given data set.

Solution:

We have,

14, 15, 3, 15, 14, 14, 18, 15, 8, 16

Arrange the data values in ascending order.

3, 8, 14, 14, 14, 15, 15, 15, 16, 18

Mean of the data set is:

\(Mean=\dfrac{\text{Sum of all observations}}{\text{Number of observation}}\)

\(Mean=\dfrac{3+8+14+14+14+15+15+15+16+18}{10}\)

\(Mean=\dfrac{132}{10}\)

\(Mean=13.2\)

The number of observation is 10 which is an even number. So, the median of the data set is:

\(Median=\dfrac{(\dfrac{n}{2})\text{th term}+(\dfrac{n}{2}+1)\text{th term}}{2}\)

\(Median=\dfrac{(\dfrac{10}{2})\text{th term}+(\dfrac{10}{2}+1)\text{th term}}{2}\)

\(Median=\dfrac{5\text{th term}+6\text{th term}}{2}\)

\(Median=\dfrac{14+15}{2}\)

\(Median=\dfrac{29}{2}\)

\(Median=14.5\)

Mode is the most frequent value of the data set.

In the given data set the highest frequency is 3 because 14 and 15 occurs three times.

So, the mode of the given data set is 14 and`15.

Therefore, the mean is 13.2, median is 14.5 and mode is 14 and 15.

The interval estimate that will estimate the true average time that people spend brushing their teeth is given by 42.3 ± 1.35

42.3 is the point estimate of the population mean, and 1.35 is the margin of error. The lower limit of the interval is given by subtracting the margin of error from the point estimate:

42.3 - 1.35 = 40.95

The upper limit of the interval is given by adding the margin of error to the point estimate:

42.3 + 1.35 = 43.65

Therefore, the 95% confidence interval estimate for the true average time that people spend brushing their teeth is (40.95, 43.65) seconds. This means that we are 95% confident that the true average time that people spend brushing their teeth falls within this interval.

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The information that a slope of 0.416 represents in the scatterplot is the crime index will increase 416 for every 1000 increment in the population.

The information that an intercept of -669.96 represents in the scatterplot is the value of the crime index when the population is zero.

A graph is a pictorial representation of data. It is used by as many fields that uses data. Graphs helps to make information that the data represents easier to understand the relationship existing within the variables

The graph plots the crime index against the population. The slope is the represents how the crime index will behave with respect to the population. While the intercept is the point where the graph intercept the y axis which represents the crime index

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Answer:

P = mgh

P/mg = h

We can divide both sides by mg, since both mass and gravity are being multiplied and not added.

Hope this helps!! :)

Step-by-step explanation:

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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The angle ∠DPB is cos(x/2)

We have the information from the question:

PN Is the perpendicular bisector of AB and is also the angle bisector of 4 CPD.

Since ∠CPD = x and segment PN is the angle bisector of this angle, therefore segment PN equally divides ∠CPD into two angles. Which means that:

∠CPN = ∠NPD = x / 2

If we segment PN which is the bisector of AB, it would create angle 90 and this would give us:

∠NPD + ∠DPB = 90°

x/2 + ∠DPB = 90°

∠DPB = 90° - x/2

Therefore:

sin ∠DPB = sin(90 – x/2)

However we know that the relationship of sin and cos is:

sin(π/2 - θ) = cos θ

Where,

π/2 = 90

θ = x/2

Therefore:

sin(90 – x/2) = cos(x/2)

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Correlation coefficients examine the relationship between variables.

They help in determining the strength and direction of the association between two continuous variables, making it easier to understand and interpret their connection.

Correlation coefficients are statistical measures used to examine the relationship between two or more variables. The correlation coefficient quantifies the degree to which the variables are related or associated with each other.

A positive correlation coefficient indicates that when one variable increases, the other variable also tends to increase, while a negative correlation coefficient indicates that when one variable increases, the other variable tends to decrease.

A correlation coefficient of zero indicates no relationship between the variables.

Correlation coefficients are often used in research studies to examine the strength and direction of the relationship between two variables.

For example, in a study examining the relationship between exercise and weight loss, a correlation coefficient could be calculated to determine how strongly exercise and weight loss are related.

It is important to note that correlation does not imply causation, and a strong correlation between two variables does not necessarily mean that one variable causes the other.

Correlation coefficients are simply used to describe the relationship between two variables and to identify patterns in the data.

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The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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Answer: 9/2, 2.63, -2.47, -5sqrt(3), -18

Step-by-step explanation:

Answer:

7.4

Step-by-step explanation:

Answer:

7.4

Step-by-step explanation:

Because we have the adjacent length and we are trying to find the opposite of the angle we will use tan.

Tan = \(\frac{opposite}{adjacent}\)

Rearrange this to find opposite...

Opposite = Tan * Adjacent

Opposite = tan(42) * 8.2

Opposite = 7.4 (rounded to the nearest tenth)

Answer:

Step-by-step explanation:

3x+23/54

Answer:

The last one is the answer

Answer: For each hour that Michelle drove, she travelled an additional 50 miles.

Step-by-step explanation:

Test each option to see its accuracy

Calculate the slope:

\((x_{1}, y_{1}) = (7, 0)\\(x_{2}, y_{2}) = (0, 350)\\ \\\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{350-0}{0-7} =\frac{350}{-7} =-50\)

This means that Michelle drove 50 miles per hour.

The other three options are wrong because if you bring in:

into your function- y = -50x + 350, you would not get the stated miles.

Answer:X would be -12

Step-by-step explanation: -12-10=-22

The future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

To find the future value of the fund on January 1, 2018, just after the third deposit, we can use the compound interest formula:

\(FV = P(1 + r/n)^{nt}\)

Where:

FV = Future Value

P = Principal amount (initial investment)

r = Annual interest rate (expressed as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

Let's calculate the future value step by step:

First deposit:

P = $16000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 4.333 years (from September 1, 2010, to March 1, 2015)

\(FV_1 = 16000(1 + 0.072/12)^{(12*4.333)}\\= 16000(1 + 0.006)^{52}\\= 16000(1.006)^{52}\\= 20,296.43\)

Second deposit:

P = $13000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 2.917 years (from March 1, 2015, to January 1, 2018)

\(FV_2 = 13000(1 + 0.072/12)^{(12*2.917)}\\= 13000(1 + 0.006)^{35}\\= 15,618.04\)

Third deposit:

P = $12000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 0.084 years (from January 1, 2018, to January 1, 2018)

\(FV3 = 12000(1 + 0.072/12)^{(12*0.084)}\\= 12000(1 + 0.006)\\= $12,072.00\\\)

Adding up the future values:

\(Total FV = FV_1 + FV_2 + FV_3\)

= $20,296.43 + $15,618.04 + $12,072.00

≈ $47,986.47

Therefore, the future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

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Answer:

Acute, right angle, obtuse, reflex

Step-by-step explanation:

Answer:

Acute

right angle

obtuse

reflex angle

Step-by-step explanation:

The volume of the solid generated by revolving the triangle about the -axis is (8π/3).

The region enclosed by the -axis, the line y = 2, and the curve y = -x is a triangle with base 2 and height 2.

To find the volume of the solid generated by revolving this triangle about the -axis, we can use the method of cylindrical shells.

The volume of each shell is given by the formula:

V = 2πr * h * δr

where r is the distance from the -axis to the shell, h is the height of the shell, and δr is the thickness of the shell.

We can express r as a function of y, since each shell corresponds to a vertical slice of the triangle:

r = y

The height of each shell is given by the difference between the -axis and the curve y = -x:

h = 2 - (-x) = 2 + x

Finally, the thickness of each shell is δr = dy.

Therefore, the volume of the solid is:

V = ∫[0,2] 2πy * (2 + y) dy

= 2π ∫[0,2] (2y + y^2) dy

= 2π [y^2 + (1/3)y^3] |[0,2]

= (8π/3)

Therefore, the volume of the solid generated by revolving the triangle about the -axis is (8π/3).

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Answer:

(3)=5-2

Step-by-step explanation:

5=2+3 or 5=3+2.

The quality which a taylor polynomial have that the tangent line does not necessarily have is that Taylor polynomial has a far better approximation of f(x) near x = a than is the tangent line

Taylor polynomial function simply refers to an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

So therefore, the quality which a taylor polynomial have that the tangent line does not necessarily have is that Taylor polynomial has a far better approximation of f(x) near x = a than is the tangent line

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Answer:

1,2 and 5

Step-by-step explanation:

hope, it will help

Answer:

16

Step-by-step explanation:

20*80/100 use this formula to find it

Answer:

IF and GH are parallel

Step-by-step explanation:

This is because both lines are side by side, do not meet at any point and they are equal.

Objects that float typically have densities less than or equal to the density of the liquid they are placed in, while objects that do not float have densities greater than the density of the liquid.

The principle behind floating and sinking lies in the concept of density. Density is defined as the mass of an object divided by its volume. When an object is placed in a liquid, such as water, it experiences an upward buoyant force equal to the weight of the liquid it displaces.

If the density of the object is less than the density of the liquid, the buoyant force will be greater than the weight of the object, causing it to float. In the case of wood floating on water, wood has a lower density than water, allowing it to float.

On the other hand, if the density of an object is greater than the density of the liquid, the buoyant force will be less than the weight of the object, causing it to sink. Objects with densities higher than that of water will sink in water because their weight exceeds the buoyant force exerted by the water.

Based on the given information about water's density, which is approximately 0.0361 pounds/cubic inch, we can conclude that objects with densities less than or equal to 0.0361 pounds/cubic inch will float on water, while objects with densities greater than 0.0361 pounds/cubic inch will sink.

In summary, the densities of objects that float are generally less than or equal to the density of the liquid they are placed in, while objects that do not float have densities greater than the density of the liquid.

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Answer:

M=10

n=1

Happy learning,

Applepi101

Answer:

4 pieces

Step-by-step explanation:

Total length of lumber = 9 feet

How many 2 1/4 foot pieces can you cut from this piece of lumber

To find the number of 2 1/4 foot pieces of lumber in a 9 feet of lumber, we will divide the total length of lumber by the length of each piece of lumber

9 ÷ 2 1/4

= 9 ÷ 9/4

= 9 × 4/9

= 36/9

= 4 pieces of lumber

Therefore, 4 pieces of 2 1/4 foot of lumber can be gotten from 9 feet of lumber

Answer: 336.80 miles, \(15.85^{\circ}\) North of east

Step-by-step explanation:

Given

Plane lands at a point 324 miles east and 92 miles north

Distance is given by using Pythagoras theorem

\(\Rightarrow d=\sqrt{324^2+92^2}\\\\\Rightarrow d=\sqrt{113,440}\\\\\Rightarrow d=336.80\ \text{miles}\)

Direction is given by using figure i.e.

\(\Rightarrow \tan \theta=\dfrac{92}{324}\\\\\Rightarrow \tan \theta=0.2839\\\\\Rightarrow \theta=15.85^{\circ}\)

Direction is \(15.85^{\circ}\) North of east

Answer:

1/3n-3÷6

Step-by-step explanation:

3 is subtraced form 1/3

Answer:

n < 27

Step-by-step explanation:

1/3n - 3

1/3n - 3 < 6

Add 3 to each side.

1/3n - 3 + 3 < 6 + 3

Combine like terms.

1/3n < 9

Divide each side by 1/3.

1/3n ÷ 1/3 < 9 ÷ 1/3

Combine like terms.

n < 27

The given equation, 63 - 63x = (8x + 1)(x - 1), can be rewritten in factored form as (8x + 1)(x - 1) = 0. To solve the equation, we set each factor equal to zero and solve for x.

To solve the equation by factoring, we start with the factored form: (8x + 1)(x - 1) = 0. According to the zero-product property, if a product of factors is equal to zero, then at least one of the factors must be equal to zero.

Setting each factor equal to zero, we have two equations:

8x + 1 = 0 and x - 1 = 0.

Solving the first equation, we subtract 1 from both sides:

8x = -1,

x = -1/8.

Solving the second equation, we add 1 to both sides:

x = 1.

Therefore, the solutions to the equation are x = -1/8 and x = 1. These are the values of x that make the equation (8x + 1)(x - 1) equal to zero.

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Answer: SYSTEMS OF EQUATIONS in TWO VARIABLES. A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The equations in the system can be linear or non-linear.

Step-by-step explanation:

Answer:

Gwen's and Tristan's. Keith already has the same equation as Gwen, so it won't help us find out the cost of the entry fee and the cost of each ticket.