What is the approximate value for tan C?

Answer:

\(10a - 41\)

Step-by-step explanation:

We can represent the area of the shaded section with the equation:

\(A_\text{shaded} = A_\text{rect} - A_\text{square}\)

First, we can solve for the area of the large enclosing rectangle:

\(A_\text{rect} = l \cdot w\)

↓ plugging in the given side lengths

\(A_\text{rect} = (a+4)(a-4)\)

↓ applying the difference of squares formula ... \((a + b)(a - b) = a^2 - b^2\)

\(A_\text{rect} = a^2 - 16\)

Next, we can find the area of the non-shaded square.

\(A_\text{square} = l^2\)

↓ plugging in the given side length

\(A_\text{square} = (a-5)^2\)

↓ applying the binomial square formula ... \((a - b)^2 = a^2 - 2b + b^2\)

\(A_\text{square} = a^2 - 10a + 25\)

Finally, we can plug these areas into the equation for the area of the shaded section.

\(A_\text{shaded} = A_\text{rect} - A_\text{square}\)

↓ plugging in the areas we solved for

\(A_\text{shaded} = \left[\dfrac{}{}a^2 - 16\dfrac{}{}\right] - \left[\dfrac{}{}a^2 - 10a + 25\dfrac{}{}\right]\)

↓ distributing the negative to the subterms within the second term

\(A_\text{shaded} = \left[\dfrac{}{}a^2 - 16\dfrac{}{}\right] + \left[\dfrac{}{}-a^2 + 10a - 25\dfrac{}{}\right]\)

↓ applying the associative property

\(A_\text{shaded} = a^2 - 16 -a^2 + 10a - 25\)

↓ grouping like terms

\(A_\text{shaded} = (a^2 -a^2) + 10a + (- 16 - 25)\)

↓ combining like terms

\(\boxed{A_\text{shaded} = 10a - 41}\)

Answer:

1/6 for number 1

4/6 but 1/6 for number 2

Answer:

3

Step-by-step explanation:

So they said to find what the number will stop on and they told you that it need to be less then 5 and it land on the gray and the number 3 my favorite number is gray and it is less than 5.

Answer:

D (-4, -9)

Step-by-step explanation:

midpoint formula:

(x₁ + x₂) / 2 , (y₁ + y₂) / 2

plug in C (2,7)

(2 + x₂) / 2 , (7 + y₂ ) / 2 = (-1, -1)

(2 + x₂) / 2 = -1

multiply each side by 2

2 + x₂ = -2

subtract 2 from both sides

x₂ = -4

(7 + y₂) / 2 = -1

multiply each side by 2

7 + y₂ = -2

subtract 7 from both sides

y₂ = -9

D (-4, -9)

The  correct relation symbol

1. LN < RN

2.  LR > LN

3. RN > LN

4. m∠L < m∠N

5. m∠N = m∠R

To determine the correct relation symbols in the given situations, we need to compare the given values in the triangle ∆LRN.

A. In ∆LRN, m∠L = 61° and m∠R = 48°.

LN < RN: The measure of ∠L is greater than the measure of ∠R. By the angle-side relationship, this indicates that the side opposite ∠L (LN) is shorter than the side opposite ∠R (RN). Therefore, LN < RN.

LR > LN: The sum of the measures of ∠L and ∠R is greater than 180° (61° + 48° = 109°), indicating that ∆LRN is an obtuse triangle. In an obtuse triangle, the longest side is the one opposite the obtuse angle, which is LR. Therefore, LR > LN.

RN > LN: In a triangle, the length of any side is greater than the length of the side opposite the smaller angle. Since ∠L is greater than ∠R, the side opposite ∠L (LN) is shorter than the side opposite ∠R (RN). Therefore, RN > LN.

B. In ∆LRN, LN = 8cm, RN = 12cm, and LR = 15cm.

m∠L < m∠N: In a triangle, the measure of any angle is larger than the measure of the angle opposite the shorter side. Since LN is the shortest side, the angle opposite LN (∠L) will have a smaller measure than the angle opposite the longer side, which is ∠N. Therefore, m∠L < m∠N.

m∠N = m∠R: In an isosceles triangle, the angles opposite the equal sides are congruent. Since LR = LN, it indicates that ∆LRN is an isosceles triangle, and therefore, m∠N = m∠R.

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Answer:

x=26/5

Step-by-step explanation:

2(x - 5) = 9 - 3x + 7.

2x-10=9-3x+7

+3x         +3x

5x+-10=16

     +10=+10

5x=26

divide by 5x

x=26/5

Given:

Number of winter coats = 2

Number of hats = 4

Number of scarves = 3

To find:

The total number of different outfit combinations.

Solution:

Number of winter coats is 2. So, the number of ways to select a winter coat from 2 coats is 2.

Number of hats is 4. So, the number of ways to select a hat from 4 hats is 4.

Number of scarves is 3. So, the number of ways to select a scarf from 3 scarves is 3.

So, the total number of ways is:

\(2\times 4\times 3=24\)

Therefore, Helen have 24 different outfit combinations.

To find the point on the surface \(\(2x + y - 1 = 0\)\) closest to the point \(\((9, 3, -7)\)\) using Lagrange multipliers, we need to minimize the distance between the two points. The distance between two points \(\((x, y, z)\)\) and \(\((9, 3, -7)\)\) can be expressed as:

\(\[d = \sqrt{(x - 9)^2 + (y - 3)^2 + (z + 7)^2}\]\)

We also need to consider the constraint equation \(\(2x + y - 1 = 0\).\) Let's define a Lagrangian function \(\(L\)\) as:

\(\[L(x, y, z, \lambda) = (x - 9)^2 + (y - 3)^2 + (z + 7)^2 + \lambda(2x + y - 1)\]\)

where \(\(\lambda\)\) is the Lagrange multiplier.

To find the closest point, we need to find the values of \(\(x\), \(y\), \(z\)\), and \(\(\lambda\)\) that satisfy the following equations:

\(\[\frac{\partial L}{\partial x} = 0\]\)

\(\[\frac{\partial L}{\partial y} = 0\]\)

\(\[\frac{\partial L}{\partial z} = 0\]\)

\(\[2x + y - 1 = 0\]\)

Differentiating \(\(L\)\) with respect to each variable, we have:

\(\[\frac{\partial L}{\partial x} = 2(x - 9) + 2\lambda\]\)

\(\[\frac{\partial L}{\partial y} = 2(y - 3) + \lambda\]\)

\(\[\frac{\partial L}{\partial z} = 2(z + 7)\]\)

Setting these partial derivatives equal to zero, we can solve the system of equations to find the values of \(\(x\), \(y\), \(z\), and \(\lambda\).\) Substituting these values into the original constraint equation, we can find the closest point on the surface.

Solving the system of equations, we find:

\(\[\lambda = -\frac{65}{19}, \quad x = \frac{1}{19}, \quad y = \frac{27}{19}, \quad z = -\frac{139}{19}\]\)

Therefore, the point on the surface \(\(2x + y - 1 = 0\)\) closest to the point \(\((9, 3, -7)\) is \(\left(\frac{1}{19}, \frac{27}{19}, -\frac{139}{19}\right)\).\)

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Answer:

Just QT and UX

Step-by-step explanation:

QT and TX intersect and are not parallel.

QU and ST are not parallel or intersecting.

QT and WX are not parallel or intersecting.

QT and UX are parallel.

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.

(a) The given units can be converted as follows: 6 glints = 1 filn...

(1)12 grees = 1 zool...

(2)2 grees = 10 twibbs...

(3)5 grees = 1 bic...

(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:

7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord

(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.

1 mega = 106

Thus 1 megafiln = 106 filn

16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.

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The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour. (option 1)

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operation.

If the total drop in temperature over 4 hours is −20∘F, in order to determine the temperature drop each hour, divide −20∘F by 4.

Drop each hour = −20∘F / 4 = −5∘F

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The value of the iterated integral ∫∫R (5x - 2y) dy dx over the region R given by 0 ≤ x ≤ 6 and 0 ≤ y ≤ x/2 is 81.

The iterated integral ∫∫R (5x - 2y) dy dx over the region R given by 0 ≤ x ≤ 6 and 0 ≤ y ≤ x/2 is:

∫[0,6]∫[0,x/2] (5x - 2y) dy dx

We can integrate with respect to y first:

∫[0,6]∫[0,x/2] (5x - 2y) dy dx = ∫[0,6] [5xy - y^2]⌈y=0⌉⌊y=x/2⌋ dx

= ∫[0,6] [(5x(x/2) - (x/2)^2) - (0 - 0)] dx

= ∫[0,6] [(5/2)x^2 - (1/4)x^2] dx

= ∫[0,6] [(9/4)x^2] dx

= (9/4) * (∫[0,6] x^2 dx)

= (9/4) * [x^3/3]⌈x=0⌉⌊x=6⌋

= (9/4) * [(6^3/3) - (0^3/3)]

= 81

Therefore, the value of the iterated integral ∫∫R (5x - 2y) dy dx over the region R given by 0 ≤ x ≤ 6 and 0 ≤ y ≤ x/2 is 81.

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The confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent. These two methods provide a range of plausible values (confidence interval) for the difference between two population proportions and involve the calculation of critical values to determine the margin of error.

On the other hand, the p-value method is not equivalent to the confidence interval and critical value methods. The p-value method involves calculating the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the sample data, assuming the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the difference between two population proportions.

To summarize:

- Confidence interval method: Provides a range of plausible values for the difference between two population proportions.

- Critical value method: Uses critical values to determine the margin of error in estimating the difference between two population proportions.

- P-value method: Determines the statistical significance of the observed difference between two population proportions based on the calculated p-value.

Hence, the confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

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Answer:

12 ft

Step-by-step explanation:

Note that you have a right triangle here, with hypotenuse 13 ft, and base 5 ft.  Using the Pythagorean Theorem, we find the height of the upper tip of the ladder as follows:

(13 ft)^2 = y^2 + (5 ft)^2.  Then y^2 = 144 ft^2, and y =height= 12 ft

Step-by-step explanation:

p(x) = 15x-(2000+4x)

profit is going to be the difference between how much money you get from sales less the cost to make the items

the money you make in this case is $15 times the number of cds you sell, we will call the number of cds x

so 15x is the money from sales

the costs you have are 2000 to create the master and then $4 for every cd you create, so your costs will be 2000+4x

so profit is sales minus costs, therefore we get

p(x) = 15x - (2000+4x)

now to find specifically the profit when we create and sell 2800 cds, x = 2800, so we substitute that value in for x

p(2800) = 15(2800) - (2000+4(2800))

= 42000 - (2000+11200)

= 42000 - 13200

= 28800

The profit of selling 2800 additional DVDs is 28800 dollars.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, The profit function is P, and let no. of DVDs sold is x and the profit on each additional disc is,

= $(15 - 4).

= $11.

∴ The profit function p is,

P = 11x - 2000.

So, the profit by selling 2800 additional discs is,

P = 11(2800) - 2000.

P = 30800 - 2000.

P = 28800 dollars.

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Based on the given scatter plot, Vaughn's survey results suggest a positive correlation between the number of days exercised and the number of days fruit was eaten among his 9 surveyed classmates.

Based on the given scatter plot, it appears that Vaughn surveyed his 9 classmates about their fruit consumption and exercise habits. The x-axis represents the number of days exercised, and the y-axis represents the number of days fruit was eaten. Each data point on the scatter plot corresponds to a classmate's response.

Let's examine the scatter plot and analyze the survey results:

Data point A has a value of 2 on the x-axis (number of days exercised) and a value of 3 on the y-axis (number of days fruit was eaten).

Data point B has a value of 3 on the x-axis and a value of 4 on the y-axis.

Data point C has a value of 4 on the x-axis and a value of 5 on the y-axis.

Data point D has a value of 5 on the x-axis and a value of 4 on the y-axis.

Since we are only given four data points, we can't make any definitive conclusions about the overall trends in the survey results. However, we can observe that as the number of days exercised increases, there is a slight tendency for the number of days fruit was eaten to increase as well. This positive correlation can be seen in the general upward trend of the data points.

It's important to note that with only 9 data points, this scatter plot may not accurately represent the entire population of Vaughn's classmates. To draw more robust conclusions about the relationship between exercise and fruit consumption, a larger sample size would be required.

Based on the given scatter plot, Vaughn's survey results suggest a positive correlation between the number of days exercised and the number of days fruit was eaten among his 9 surveyed classmates.

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The state income tax owed on a $90,000 per year salary is $4950.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

From the given information we conclude that the percentage tax for

a $90,000 per year salary is 5.5%.

Therefore, The amount to be paid is,

= $(5.5/100)×90000.

= $4950.

So, An amount of $4950 has to be paid for an annual income of $90000.

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Answer: that the people he is addressing appreciate intellectualism

Step-by-step explanation: found it on quizlet

Answer:

That the people he is addressing have researched philosophy

Step-by-step explanation:

i said so

Answer:

a. To determine the percentage of finishers with times between 50 and 75 minutes, we need to find the proportion of finishers with times in that range and convert it to a percentage. From the cumulative frequency table, we see that the number of finishers with times between 50 and 75 minutes is 75 - 45 = 30. The total number of finishers is 100. Therefore, the proportion of finishers with times between 50 and 75 minutes is 30/100 = 0.3. To convert this to a percentage, we multiply by 100 and get 30%.

Approximately 30% of finishers had times between 50 and 75 minutes.

b. To determine the percentage of finishers with times less than 80 minutes, we need to find the proportion of finishers with times less than 80 minutes and convert it to a percentage. From the cumulative frequency table, we see that the number of finishers with times less than 80 minutes is 95. The total number of finishers is 100. Therefore, the proportion of finishers with times less than 80 minutes is 95/100 = 0.95. To convert this to a percentage, we multiply by 100 and get 95%.

Approximately 95% of finishers had times less than 80 minutes.

c. The 40th percentile is the value that separates the lowest 40% of the finishers from the highest 60%. From the cumulative frequency table, we see that the value corresponding to the 40th percentile is between 45 and 50 minutes. To find the exact value, we can use linear interpolation.

First, we find the position of the 40th percentile in relation to the cumulative frequency of 45 minutes (which is 25). The percentile lies in the range between the cumulative frequencies of 45 and 50 minutes, which correspond to positions 25 and 45 in the data set. The 40th percentile is 15% of the way from position 25 to position 45. Therefore, the position of the 40th percentile is:

25 + 0.15(45 - 25) = 30

This means that the 40th percentile corresponds to the time taken by the 30th finisher in the race. We can estimate this time by averaging the times of the 29th and 30th finishers:

(48 + 50) / 2 = 49

Therefore, the 40th percentile is 49 minutes.

Interpretation: The 40th percentile tells us that 40% of the finishers completed the race in 49 minutes or less, while 60% took longer than 49 minutes to complete the race.

give thanks po! and rate5*! your welcome!

Answer:

y = 10(1.01)^60

Step-by-step explanation:

The general equation of exponential growth is

y = ab^x

b has to do with the rate of growth.

b = 1 + r, so in this case, b = 1 + 1% = 1 + 0.01 = 1.01.

Now we have

y = a(1.01)^x

a is the initial value, so now we have

y = 10000(1.01)^x

where y is the number of books after x months

Since you need the number of books after 5 years, we must convert 5 years into months.

5 years * (12 months)/year = 60 months

The problem wants the expression in thousands of books, so we divide the initial value by 1000.

Answer: y = 10(1.01)^60

   Expression representing the number of books after 5 years,              

                           \(A(60)=10000(1.01)^{60}\)

          \(A(t)=A_0(1+r)^t\)

          Here, \(A(t)=\) Final amount

          \(A_0=\) Initial amount

           \(r=\) Growth rate

           \(t=\) Duration or time

Given in the question,

Substitute these values in the expression,

\(A(t)=A_0(1+r)^t\)

\(A(60)=10000(1+0.01)^{60}\)

      Therefore, expression representing the number of books after 5 years will be → \(A(60)=10000(1.01)^{60}\)

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Answer:

Um. There is no equation?

Step-by-step explanation:

Answer:

4 <(less than or Equal to) y (less than or Equal to) 13

Step-by-step explanation:

Answer:

Hey there!

We are trying to find the difference between 4 and -7

We can write -7+x=4, where x is the difference we are trying to find.

Solving for x, we get that the difference is 11.

Let me know if this helps :)

The difference between the high and low temperatures is 11 degrees.

Given :

The high temperature Monday was 4 degrees.

The low temperature was -7 degrees.

We need to find the difference between high and low temperatures .

To find the difference ,we subtract low temperature from high temperature

High temperature - low temperature

\(High - low \; temperature \\4-(-7)\\4+7\\11\)

The difference between the high and low temperatures is 11 degrees.

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Answer: See explanation

Step-by-step explanation:

A. Find the current sale price. Round to the nearest cent if necessary.

B) Members of the stores loyalty club can and additional 10% off their computer purchases. How much do club members pay for the computer with their discount.

A. Current sales price will be:

= $954 - (20% × $954)

= $954 - (0.2 × $954)

= $954 - $190.80

= $763.20

B. Club members will pay:

= $763.20 - (10% × $763.20)

= $763.20 - (0.1 × $763.20)

= $763.20 - $76.32

= $686.88

Answer:

it’s 15x+30y-220

Step-by-step explanation:

Because you distribute and then you add the like terms

Answer:

no

Step-by-step explanation:

-7 is bigger

Answer:

no, its less

Step-by-step explanation:

because in negatives the higher the number is (ex: -10) the less the value is, so its the opposite of positive numbers

Answer:

f = √2-2x

Step-by-step explanation:

vshsgshbeeyvecv

Step-by-step explanation:

Hoping I didnt take it wrong from the question!

Answer:

10 m

Step-by-step explanation:

We are given that the relationship between intensity of sound and distance from the source is given by

Intensity (I)=\(\frac{k}{d^2}\)

Where I=Intensity

d=Distance of sound from the source

If distance d=1m

Intensity, I=0.1\(w/m^2\)

We have to find how close she can to the stage if vanessa does not want the sound intensity to be more than 0.001(w)/(m^(2)).

Using the formula

\(0.1=\frac{k}{1}\)

\(k=0.1\)

\(\frac{0.1}{d^2}\leq 0.001\)

\(\frac{0.1}{0.001d^2}\leq 1\)

\(\frac{0.1}{0.001}\leq d^2\)

\(100\leq d^2\)

\(10\leq d\)

\(d=10 m\)

Hence, she can sit 10 m away from the stage.