How is a circumference related to an arc

Answer:

I will assume that you mean solve for q.

q < -2

Step-by-step explanation:

-2q - 2 > 2

      +2  +2

Add 2 to both sides

2q > 4

/-2    /-2

Divide both sides by -2 (flip the sign if you multiply or divide by a negative number)

q < -2

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

The solution to the inequality is:

x ∈ (-∞, -21].

The correct option is F.

To solve the given inequality, we'll first simplify the expression:

23 < 3x - 3 ≤ -66

To simplify the inequality,

23 < 3x - 3 ≤ -66

Adding 3 to all parts of the inequality:

23 + 3 < 3x - 3 + 3 ≤ -66 + 3

Simplifying:

26 < 3x ≤ -63

Next, divide all parts of the inequality by 3:

26/3 < 3x/3 ≤ -63/3

Simplifying:

8.67 < x ≤ -21

Therefore, the solution to the inequality is:

x ∈ (-∞, -21]

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Answer:

160

Step-by-step explanation:

add the numbers together then divide by 8

Step-by-step explanation:

\( {2x}^{2} + 8x - 1 = 0 \\ {x}^{2} + 4x - \frac{1}{2} = 0 \\ {x}^{2} + 4x + {( \frac{1}{4} )}^{2} - \frac{1}{2} - { (\frac{1}{4} )}^{2} = 0 \\ {(x + \frac{1}{4}) }^{2} - \frac{9}{16} = 0 \\ {(x + \frac{1}{4}) }^{2} = \frac{9}{16} \\ x + \frac{1}{4} = ±( \frac{ 3}{4} ) \\ x = \frac{1}{2} \: or \: - 1\)

Answer:

Step-by-step explanation:

divide each term by 2 to begin with x²

x² + 4x - 1/2 = 0

now add 1 to each side

x² + 4x = 1/2

now divide 4 in half and square the result and add it to each side

x² + 4x + 4 = 1/2 + 4

(x + 2)² = 9/2

Answer:

85 Turkey sandwiches

Step-by-step explanation:

85% of 100 is 85

That means that the remaining 15% or 15 sandwiches that were made were ham.

The given lines of equations are not perpendicular to each other. Therefore, `θ = cos⁻¹(8/(4√10))` which is approximately `28.07°`.Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

Given lines of equations:

x = −2 + 2t, y = −6, z = 2 + 6tx=−1+t,y=1+t,z=t, t∈ R.

Firstly, we need to find the direction vectors of the two given lines.For the first equation,Let `t=1`, then the point on the line is `(-2+2(1), -6, 2+6(1))`=`(0, -6, 8)`.

Let `t=2`, then the point on the line is

\(`(-2+2(2), -6, 2+6(2))`=`(2, -6,\)14)`.T

herefore, direction vector `

\(v1 = (2, -6, 14)-(0, -6, 8)`=`(2, 0, 6)`\)

For the second equation, direction vector \(`v2 = (1, 1, 1)`.\\\)

Let the angle between the direction vectors `v1` and `v2` be `θ`.

Then, we know that `v1 • v2 = |v1||v2| cosθ`, where `•` represents the dot product of the vectors, and `|.|` represents the magnitude of the vector.

Thus, we have:

(2, 0, 6) • (1, 1, 1) = √(2²+0²+6²)√(1²+1²+1²) cosθ

=> 8 = √40√3 cosθ=> cosθ = 8/(4√10)

Therefore,

`θ = cos⁻¹(8/(4√10))`

which is approximately `28.07°`.

Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

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To compute the Laplace transform of the given function, we can use the linearity property of the Laplace transform and apply the transform to each term separately.

Using the Laplace transform pairs:

L{1} = 1/s

L{u(t)} = 1/(s+1)

L{e^(-6t)} = 1/(s+6)

L{cos(πt)} = s/(s^2+π^2)

Applying these transforms to the given function:

L{1 u^(5/2)(t) e^(-6t) cos(πt)} = L{1} * L{u^(5/2)(t)} * L{e^(-6t)} * L{cos(πt)}

Substituting the transform pairs:

= (1/s) * (1/(s+1)^(5/2)) * (1/(s+6)) * (s/(s^2+π^2))

Simplifying this expression, we can multiply the terms together:

= s / (s(s+1)^(5/2)(s+6)(s^2+π^2))

Therefore, the Laplace transform of the given function is:

L{1 u^(5/2)(t) e^(-6t) cos(πt)} = s / (s(s+1)^(5/2)(s+6)(s^2+π^2))

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step 1

Find the center of the circle

we have that

the center of the circle is the midpoint between the endpoints

sp

step 2

Find the radius of the circle

we have that

the distance between endpoints is equal to the diameter of circle

so

D=15-1=14 units -------> (difference of the y-coordinates)

Remember that the radius is half the diameter

r=D/2

r=14/2=7 units

step 3

Find the equation of the circle

(x-h)^2+(y-k)^2=r^2

where

*h,k) is the center

r is the radius

substitute

(x-9)^2+(y-8)^2=7^2

(x-9)^2+(y-8)^2=49

The ladder needs to be 34.3m long from tree you to get to get the cat.

We must determine the hypotenuse in this right triangle, which is the side that is opposite the triangle's 90° angle. When the neighboring side is 23 meters away, the elevation angle is  54°

Suppose Hypotenuse equals h.

Given, the base is 23m

Using trigonometry,

tan θ = Base / hypotenuse

tan 54° = 23 / h

⇒ 0.67 = 23 / h

⇒ h = 23 / 0.67

⇒ h = 34.3

So, the ladder needs to be 34.3m away in order to reach cat.

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We would need a sample size of at least 1073 children under age 6 in Washington to estimate the true proportion of children living in poverty with 95% confidence and a margin of error of 2%.

To estimate the true proportion of children under age 6 living in poverty in Washington with 95% confidence and a margin of error of 2%, we can use the formula:

n = (Z² * p * q) / E²

where:

Z = the Z-score corresponding to the desired confidence level (1.96 for 95% confidence)

p = the estimated proportion (0.17 based on the federal report)

q = 1 - p

E = the desired margin of error (0.02)

Plugging in these values, we get:

n = (1.96² * 0.17 * 0.83) / 0.02²

n = 1072.45

Rounding up to the next whole number, we would need a sample size of at least 1073 children under age 6 in Washington to estimate the true proportion of children living in poverty with 95% confidence and a margin of error of 2%.

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Answer:

58.03 ft

Step-by-step explanation:

To solve for the total circumference of circle F, we can create a ratio of section angle measure to circumference. We know that these two attributes of a circle have a linear relationship because the formula for arc length (\(S = 2\pi r \cdot \frac{\theta}{360\°}\)) relies proportionately on the radius and angle measure of the section.

angle measure : circumference

               290°   :   46.75 ft

We can multiply this ratio by \(\frac{360}{290}\) to get the corresponding circumference for a 360° section (which is the entire circle).

\(\frac{360}{290}(290\° : 46.75 \text{ ft})\)

\(= 360\° : \boxed{58.03 \text{ ft}}\)

Therefore, the circumference of circle F is approximately 58.03 ft.

Answer: 30 eggs

Step-by-step explanation:

Given

Mrs. Jones bought 120 eggs

She used two-third for baking cakes i.e.

\(\Rightarrow 120\times \dfrac{2}{3}=80\ \text{eggs}\)

Remaining eggs are \(120-80=40\ \text{eggs}\)

She used on-fourth of the remaining for baking cookies i.e.

\(\Rightarrow 40\times \dfrac{1}{4}=10\ \text{eggs}\)

Eggs left after baking cookies

\(\Rightarrow 40-10=30\ \text{eggs}\)

She is left with 30 eggs

Given the following question:

Graph 3 is the same as y = -3x + 1

For part B:

Answer:

1. r = -4

3. n=6

5. m = -5

7. x=0.66= \(\frac{2}{3}\)

Step-by-step explanation:

1.

-52=4(7+5r)

-52=28+20r

Subtract 20r from both sides

-20r-52=28

Add 52 to both sides

-20r=80

Divide both sides by -20

r = -4

3.

8(n-5)=-5n+38

8n-40=-5n+38

Add 5n to both sides

13n-40=38

Add 40 to both sides

13n=78

Divide both sides by 13

n=6

5.

-33+5m=2(1+6m)

-33+5m=2+12m

Subtract 12m from both sides

-33-7m=2

Add 33 to both sides

-7m=35

Divide both sides by -7

m=-5

7.

2(7x-2)=2(x+4)

14x-4=2x+4

Subtract 2x from both sides

12x-4=4

Add 4 to both sides

12x=8

Divide both sides by 12

x=0.66...

The equation of the plane that is normal to the function at the point P(4, 2) is 64x + 192y - 832 = 0.

The gradient vector of a function gives the direction of the steepest ascent at a particular point. To find the gradient vector, we need to compute the partial derivatives of the function with respect to x and y.  Taking the partial derivative of f(x, y) = \(x^2y^3\)with respect to x, we get ∂f/∂x = \(2xy^3\).

Taking the partial derivative of f(x, y) = \(x^2y^3\) with respect to y, we get ∂f/∂y = 3x^2y^2.  Now, we can evaluate the gradient vector at the point P(4, 2) by substituting x = 4 and y = 2 into the partial derivatives. The gradient vector at P(4, 2) is ∇f(4, 2) = (2 * 4 * \(2^3\), 3 * 4^2 * \(2^2\)) = (64, 192).

Since the gradient vector is normal to the plane, we can use it to form the equation of the plane. The equation of the plane becomes 64(x - 4) + 192(y - 2) = 0, which simplifies to 64x + 192y - 832 = 0.

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The number of weeks are 0 1 2 4 7 12

The balances are 24 32 40 56 80 120

The rate of change of the balance of the student's savings account in dollars and cents per week is also referred to as the slope of the graph that can be potted with these values. The formula for slope is expressed as

Slope = (y2 - y1)/(x2 - x1)

y1 and y2 would be consecutive values of the balance

x1 and x2 would be consecutive values of the number of weeks

When x1 = 0, y1 = 24

When x2 = 1, y1 = 32

Slope = (32 - 24)/(1 - 0)

Slope = 8

The rate of change of the balance of the student's savings account in dollars and cents per week is 8 dollars per week. Converting to cents, it would be 800 cents per week

Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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Answer:

Bottom Left

Step-by-step explanation:

Bottom Left

Answer:

thats a little complex

Step-by-step explanation:

advanced math?

Answer:

273.62

Step-by-step explanation:

Using translations, it is found that:

12. The representations are:

13. The representations are:

14. The coordinates are K(-5,0).

15. The coordinates are P(9,0).

A translation is when the graph of a function is moved either left, right, up or down.

The function keeps it congruence, orientation and inclination, the only change is in the position.

For item 12, we have that each vertex was moved:

Hence the coordinate rule is:

(x,y) -> (x + 4, y + 3).

The vector rule is:

(4,3).

For item 13, we have that each vertex was moved:

Hence the coordinate rule is:

(x,y) -> (x + 1, y - 7).

The vector rule is:

(1,-7).

For item 14, the rule is:

(x,y) -> (x - 3, y + 6).

After the translation, we have that K'(-8,6). Hence, applying the inverse translation, the original coordinates are as follows:

K(-8 + 3, 6 - 6) = K(-5,0).

For item 15, the rule is:

(x,y) -> (x - 8, y). -> due to the vector rule

After the translation, we have that P'(1,-2). Hence, applying the inverse translation, the original coordinates are as follows:

P(1 + 8, -2 + 0) = P(9,0).

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20 are the degrees of freedom for this study.

The 95% confidence interval for the mean chemical waste in g per mile is (120.487, 131.513) per mile.

We need to determine the degrees of freedom and construct a 95% confidence interval for the mean chemical waste.

(a) Degrees of freedom: In this study, we have a sample size of 20 water samples (n = 20).

Degrees of freedom (df) for a sample is calculated as df = n - 1. In this case, df = 20 - 1 = 19.

(b) Construct a 95% confidence interval for the mean chemical waste:

First, we need to find the standard error (SE) of the mean, which is calculated as SE = standard deviation (SD) / sqrt(n).

In this case, SD = 11.78 g and n = 20, so SE = 11.78 / sqrt(20) = 2.634.

Next, we need to find the critical value (t*) for a 95% confidence interval with 19 degrees of freedom.

You can find this value using a t-table or calculator. For this case, t* ≈ 2.093. Now, we can calculate the margin of error (ME) using the formula ME = t* * SE.

In this case, ME = 2.093 * 2.634 = 5.513.

Finally, we can calculate the lower and upper bounds of the 95% confidence interval as follows:

Lower bound = mean - ME = 126 - 5.513 = 120.487 g/mile

Upper bound = mean + ME = 126 + 5.513 = 131.513 g/mile

So, the 95% confidence interval for the mean chemical waste in g per mile is (120.487, 131.513) per mile.

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Answer:

Step-by-step explanation:

a. The probability that Miami will be hit by a hurricane in any given year can be calculated as the inverse of the historical frequency of hurricane hits, which is 1/25. Therefore:

Probability of Miami being hit by a hurricane in any given year = 1/25

b. The probability that Miami will be hit by hurricanes in both of the next two consecutive years can be calculated as the product of the individual probabilities, assuming that the occurrence of hurricanes in different years is independent. Therefore:

Probability of Miami being hit by hurricanes in both of the next two consecutive years = (1/25) * (1/25) = 1/625

c. The probability that Miami will be hit by hurricanes in either the next year or the year after can be calculated as the sum of the probabilities of each event occurring, minus the probability of both events occurring (since they are not mutually exclusive). Therefore:

Probability of Miami being hit by hurricanes in either the next year or the year after = (1/25) + (1/25) - [(1/25) * (1/25)] = 48/625

d. The probability that Miami will be hit by at least one hurricane in the next seven years can be calculated using the complement rule: the probability of no hurricanes in seven years is (24/25)^7, so the probability of at least one hurricane is 1 minus that value. Therefore:

Probability of Miami being hit by at least one hurricane in the next seven years = 1 - (24/25)^7 ≈ 23.071% (rounded to three decimal places)

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If the difference of 3 times a number(n) and 10 is 5 , then the number is n = 5  .

In the question ,

it is given that

the number is = n

and also the statement is given as  " the difference of 3 times of a number "n" and 10 is = 5 "

which means

3×n - 10 = 5    ...because times means × and difference means " - " .

3n - 10 = 5

on adding 10 to both sides of the equation and solving further ,

we get ,

3n = 5 + 10

3n = 15

n = 15/3

n = 5

Therefore , If the difference of 3 times a number(n) and 10 is 5 , then the number is n = 5  .

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data collected by imposing a treatment on a sample and examining the results is data collected as a result of computer modeling. Left skewed distribution is data collected that does not fairly represent the population.

Mode [ Choose ]

x  Continuous variable

n  N

σ  σ²

r  q = 1 – p

Mode  Most frequently occurring value in the date set

Left skewed distribution  Data is collected that does not fairly represent the population

Normal distribution  Data is collected by asking a series of questions

A measure of the spread or variability of the data set  Data is collected by watching

Data is collected by imposing a treatment on a sample and examining the results  Data is collected as a result of computer modeling

x is a continuous variable, n is N, σ is σ², r is q = 1 – p, mode is the most frequently occurring value in the date set, a left skewed distribution is data collected that does not fairly represent the population, a normal distribution is data collected by asking a series of questions, a measure of the spread or variability of the data set is data collected by watching the behavior of sample, and data collected by imposing a treatment on a sample and examining the results is data collected as a result of computer modeling.

x is a continuous variable, n is N, σ is σ², r is q = 1 – p, mode is the most frequently occurring value in the date set. Data collected by asking a series of questions is a normal distribution, data collected by watching the behavior of sample is a measure of the spread or variability of the data set, and data collected by imposing a treatment on a sample and examining the results is data collected as a result of computer modeling. Left skewed distribution is data collected that does not fairly represent the population.

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Answer: 191/2

Step-by-step explanation:

95.5 as a fraction is 191/2

so i divided 191/2 and the answer is 95.5

and so 95 1/2 is also equivalent to 191/2