Find the smallest positive value for θθ for which the tangent line to the curve r=3e1θr=3e1θ is horizontal θ =_________

Answer:

134.985cm

Step-by-step explanation:

firstly let's find area lf rectangle

20cm × 2cm = 40

secondly let's find area of the quarter circle

(11)^2×3.14 = 379.94 divide it by 4 which gives us the answer 94.985

and finally lets find the area of this figure

40+94.985 = 134.985

The scalar product of a vector is A · B = 35

Given data ,

The product of vectors is:

A · B = |A| |B| cos(θ)

where A and B are vectors, |A| and |B| are the lengths (magnitudes) of the vectors, and θ is the angle between the vectors.

In this case, the length of vector A is 7 and the length of vector B is 10. The angle between them is 60 degrees.

Substituting the given values into the formula, we have:

A · B = |A| |B| cos(θ)

= 7 * 10 * cos(60°)

= 70 * cos(60°)

The cosine of 60 degrees is 0.5, so we can simplify further:

A · B = 70 * cos(60°)

= 70 * 0.5

= 35

Hence , the scalar product of a vector of length 7 and a vector of length 10, which make an angle of 60 degrees with each other, is 35

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A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611

B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362

The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.

The formula for calculating the standard error of the mean is

SE = σ/√n

where SE is the standard error, σ is the population standard deviation, and n is the sample size.

For n = 30, SE = 4,000/√30 = 729.16

A. For a sample size of n = 60, SE = 4,000/√60 = 516.40

To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error.

For a range of +/- $500, the z-scores are

z = ($51,300 - $51,800) / 516.40 = -0.969

z = ($52,300 - $51,800) / 516.40 = 0.969

Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.

B. For a sample size of n = 120, SE = 4,000/√120 = 368.93

Following the same steps as above, the z-scores for a range of +/- $500 are

z = ($51,300 - $51,800) / 368.93 = -1.364

z = ($52,300 - $51,800) / 368.93 = 1.364

Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.

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Answer:

choice 1) x = 2,3

Step-by-step explanation:

2x/(x - 2) - (x + 3)/(x - 4) = -4x/(x² - 6x + 8)

Factor x² - 6x + 8 into (x - 2)(x - 4):

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

multiply both sides of the equation by (x - 2)(x - 4):

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

simplify:

2x² - 8x - x² + 2x - 3x + 6 = -4x

combine like terms:

x² -9x + 6 = -4x

add 4x to each side:

x² -5x + 6 = 0

factor:

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

x = 2, x = 3

Answer:

4w  −  14

Step-by-step Explanation:

This is the answer because:

1) First, we have to multiply the 4 with the -2. This equals -8

2) Now, we have the equation 4w - 8 - 6

3) Finally, do -8 - 6 which is -14

4) We simplified the equation to 4w - 14

Therefore, the answer is 4w - 14

Hope this helps!

The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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(i) The given function is f(x)=x∣x∣. Let us differentiate this function. We have,\[f(x)=\left\{\begin{matrix} x^{2} , x\geq 0\\ -x^{2} , x<0 \end{matrix}\right.\]The derivative of the function f(x) is given as\[f'(x)=\left\{\begin{matrix} 2x & x>0\\ -2x & x<0\\ Does\:not\:exist & x=0 \end{matrix}\right.\]Therefore,\[f'(x)>0 \Rightarrow f(x)\:\:is\:increasing\:on\:x>0\] \[f'(x)<0 \Rightarrow f(x)\:\:is\:decreasing\:on\:x<0\]From the above conditions, we can conclude that the function f(x) is neither increasing nor decreasing at x=0.

(ii) The given function is f(x)=sinx+∣sinx∣. Let us differentiate this function. We have,\[f(x)=2\sin x,\:\:x\in \left( \frac{(2n-1)\pi }{2},\frac{(2n+1)\pi }{2} \right)\]Here n is an integer. The derivative of the function f(x) is given as\[f'(x)=2\cos x\]The function is increasing in the interval \[0<\theta <\frac{\pi }{2}\]and decreasing in the interval \[\frac{\pi }{2}<\theta <\pi \]

(iii) The given function is f(x)=sinx(1+cosx). Let us differentiate this function. We have,\[f(x)=\sin x+\sin x\cos x\]The derivative of the function f(x) is given as\[f'(x)=\cos x+\cos x\cos x-\sin x\sin x\]or\

[f'(x)=\cos x+\cos ^{2}x-\sin ^{2}x\]or\[f'(x)

=\cos x+2\cos ^{2}x-1\]

This derivative equals 0 for the critical points of the function .We can also write,\[\cos x=1-2\sin ^{2}\frac{x}{2}\]

Therefore,\[f'(x)=\cos x+2\cos ^{2}x-1\]\

[f'(x)=1-2\sin ^{2}\frac{x}{2}+2-2\sin ^{2}\frac{x}{2}-1\]\

[f'(x)=4\cos ^{2}\frac{x}{2}-3\]or\[

f'(x)=4\sin ^{2}\frac{x}{2}-1\]

The critical points of f(x) are given as\[4\sin ^{2}\frac{x}{2}-1=0\]\[\Rightarrow \sin \frac{x}{2}=\pm \frac{1}{2}\]or\[

x=2n\pi \pm \frac{\pi }{3}\]The intervals of increase and decrease are :Increase: \[x\in \left( 2n\pi -\frac{\pi }{3},2n\pi +\frac{\pi }{3} \right)\]Decrease: \[x\in \left( 2n\pi +\frac{\pi }{3},2n\pi +\frac{2\pi }{3} \right)\]where n is an integer.

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Answer: B&D

Step-by-step explanation:

Answer:

17/12= 1 5/12

Step-by-step explanation:

make the denominator the same as 12

_______  -9/12 =8/12

so add 8+9 to get 17.then keep the denominator as 12. last simpfie it to 1 5/12

False.  We cannot use the normal distribution to approximate the sampling distribution of the average (x) for a small sample (n<30) if our sample has clear outliers.

The sampling distribution of the average, also known as the sampling distribution of the mean, is the distribution of all possible sample means that could be obtained from a population. In order to use the normal distribution to approximate the sampling distribution of the average, certain assumptions need to be met. One of these assumptions is that the data should follow a normal distribution or at least be approximately normally distributed.

If the sample contains clear outliers, it indicates that the data deviates significantly from the assumptions of normality. Outliers can affect the shape and properties of the distribution, making it non-normal. In such cases, using the normal distribution to approximate the sampling distribution of the average would not be appropriate because the underlying assumptions are violated. Alternative approaches, such as non-parametric methods, may be more suitable for analyzing data with outliers.

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Answer:

É necessário dividir por 3 para calcular a média simples das 3 notas.

Média = 7.

Step-by-step explanation:

O resultado deve ser dividido por três porque três notas com pesos iguais (projeto, prova e trabalho em grupo) foram somadas, portanto para calcular a média bimestral de Laura, a soma das três notas deve ser dividida por 3. A média de Laura é:

\(M=\frac{5,0+6,5+9,5}{3}\\ M=7\)

Let's calculate the total cost of all the items purchased by the computer club:

Cost of 14 portfolios = 14 * $24.59

Cost of 14 binders = 14 * $12.92

Cost of 14 school sweatshirts = 14 * $14.00

Cost of 14 music cases = 14 * $1.25

Cost of 14 phone cases = 14 * $1.99

Cost of 14 mouse pads = 14 * $2.14

Total cost of all items = Cost of 14 portfolios + Cost of 14 binders + Cost of 14 school sweatshirts + Cost of 14 music cases + Cost of 14 phone cases + Cost of 14 mouse pads

Plugging in the given values:

Total cost of all items = (14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14)

Now, the computer club will pay for 40% of the total cost. To calculate this, we can multiply the total cost by 40% (or 0.40):

Club's payment = 0.40 * Total cost of all items

The remaining cost will be divided equally among the 14 members:

Remaining cost per member = (Total cost of all items - Club's payment) / 14

Plugging in the values and calculating:

Club's payment = 0.40 * ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14))

Remaining cost per member = ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14) - Club's payment) / 14

So, each member of the computer club will owe the calculated value for "Remaining cost per member".

Hope this is good

The value of r=-0.854 indicates a stronger correlation than r=0.835.

To determine which value of r indicates a stronger correlation, r=0.835 or r=-0.854, we need to compare their absolute values.

Step 1: Find the absolute values of both correlation coefficients.
|r=0.835| = 0.835
|r=-0.854| = 0.854

Step 2: Compare the absolute values.
0.835 < 0.854

The value of r=-0.854 indicates a stronger correlation than r=0.835.

This is because the absolute value of -0.854 (0.854) is greater than the absolute value of 0.835 (0.835), meaning that the correlation is stronger, regardless of the negative sign.

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Answer:

5.00 + 0.25p

Step-by-step explanation:

The probability that a randomly selected customer likes hot or iced coffee is 0.83.

What is probability?

To find the probability that a randomly selected customer likes hot or iced coffee, we need to add the probability of liking hot coffee and the probability of liking iced coffee, while subtracting the probability of liking both (since we don't want to count those customers twice).

So, P(H or I) = P(H) + P(I) - P(H and I)

We are given that P(H) = 0.75, P(I) = 0.30, and P(H and I) = 0.22 (from the venn diagram).

Therefore, P(H or I) = 0.75 + 0.30 - 0.22 = 0.83

So the probability that a randomly selected customer likes hot or iced coffee is 0.83.

Therefore, the answer is 0.83.

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Complete question is: according to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like iced coffee, and 22% like both hot and iced coffee. the venn diagram displays the coffee preferences of the customers. a venn diagram titled coffee preferences. one circle is labeled h, 0.53, the other circle is labeled i, 0.08, the shared area is labeled 0.22, and the outside area is labeled 0.17. a randomly selected customer is asked if they like hot or iced coffee. let h be the event that the customer likes hot coffee and let i be the event that the customer likes iced coffee. the probability that a randomly selected customer likes hot or iced coffee is 0.83.

Answer:

one circle has a total angle of 360. Hence, 360-101= 3x+2+x-35

259=4x-33

292=4x

x=73 degrees

Answer: 1.25

Step-by-step explanation:

-1.25+2.5=

2.5-1.25=1.25

Answer:

Step-by-step explanation:

IF U ADD -1.25+2.25 U WILL GET A ANSWER 1.25

Answer:

1. ひよこ     は     ちいさい     。

2. おおかみ     は     どうくつ     に     すんでいます     。

3. せんせい     は     どうぶつたち     を     みます     。

Answer: No

Step-by-step explanation:

Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:

9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.

Answer:

Rotation is the answer to your problem.

Step-by-step explanation:

the curve has a vertical tangent line.

The given parametric equation is given as follows:

x(t) = t² + 2ty(t) = 4t² + t

Differentiate each equation to find the tangent lines.

dy/dx = (dy/dt) / (dx/dt)= (8t + 1) / (2t) = 4 + 1/2t

Therefore, to obtain the horizontal tangent line we need to make the numerator 0.8t + 1 = 0t = -1/8

Therefore, when t = -1/8, the curve has a horizontal tangent.

To find the vertical tangent lines, differentiate each equation with respect to yx'(t) = 2ty'(t) = 8t + 1

The slope of the tangent line will be undefined (i.e., vertical) if the denominator of the slope is zero.

8t + 1 = 0t = -1/8

Substituting t = -1/8 in the given equation,

the curve has a vertical tangent line.

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Answer:

i hope im right but have u tried restarting your phone or getting it checked out?

Step-by-step explanation:

Part (a)

Focus on triangle PSQ. We have

angle P = 52

side PQ = 6.8

side SQ = 5.4

Use of the law of sines to determine angle S

sin(S)/PQ = sin(P)/SQ

sin(S)/(6.8) = sin(52)/(5.4)

sin(S) = 6.8*sin(52)/(5.4)

sin(S) = 0.99230983787513

S = arcsin(0.99230983787513)

S = 82.889762826274

Which is approximate

------------

Use this to find angle Q. Again we're only focusing on triangle PSQ.

P+S+Q = 180

Q = 180-P-S

Q = 180-52-82.889762826274

Q = 45.110237173726

Which is also approximate.

A more specific name for this angle is angle PQS, which will be useful later in part (b).

------------

Now find the area of triangle PSQ

area of triangle = 0.5*(side1)*(side2)*sin(included angle)

area of triangle PSQ = 0.5*(PQ)*(SQ)*sin(angle Q)

area of triangle PSQ = 0.5*(6.8)*(5.4)*sin(45.110237173726)

area of triangle PSQ = 13.0074347717966

------------

Next we'll use the fact that RS:SP is 2:1.

This means RS is twice as long as SP. Consequently, this means the area of triangle RSQ is twice that of the area of triangle PSQ. It might help to rotate the diagram so that line PSR is horizontal and Q is above this horizontal line.

We found

area of triangle PSQ = 13.0074347717966

So,

area of triangle RSQ = 2*(area of triangle PSQ)

area of triangle RSQ = 2*13.0074347717966

area of triangle RSQ = 26.0148695435932

------------

We're onto the last step. Add up the smaller triangular areas we found

area of triangle PQR = (area of triangle PSQ)+(area of triangle RSQ)

area of triangle PQR = (13.0074347717966)+(26.0148695435932)

area of triangle PQR = 39.0223043153899

------------

This value is approximate. Round however you need to.

===========================================

Part (b)

Focus on triangle PSQ. Let's find the length of PS.

We'll use the value of angle Q to determine this length.

We'll use the law of sines

sin(Q)/(PS) = sin(P)/(SQ)

sin(45.110237173726)/(PS) = sin(52)/(5.4)

5.4*sin(45.110237173726) = PS*sin(52)

PS = 5.4*sin(45.110237173726)/sin(52)

PS = 4.8549034284642

Because RS is twice as long as PS, we know that

RS = 2*PS = 2*4.8549034284642 = 9.7098068569284

So,

PR = RS+PS

PR = 9.7098068569284 + 4.8549034284642

PR = 14.5647102853927

-------------

Next we use the law of cosines to find RQ

Focus on triangle PQR

c^2 = a^2 + b^2 - 2ab*cos(C)

(RQ)^2 = (PR)^2 + (PQ)^2 - 2(PR)*(PQ)*cos(P)

(RQ)^2 = (14.5647102853927)^2 + (6.8)^2 - 2(14.5647102853927)*(6.8)*cos(52)

(RQ)^2 = 136.420523798282

RQ = sqrt(136.420523798282)

RQ = 11.6799196828694

--------------

We'll use the law of sines to find angle R of triangle PQR

sin(R)/PQ = sin(P)/RQ

sin(R)/6.8 = sin(52)/11.6799196828694

sin(R) = 6.8*sin(52)/11.6799196828694

sin(R) = 0.4587765387107

R = arcsin(0.4587765387107)

R = 27.3081879220073

--------------

This leads to

P+Q+R = 180

Q = 180-P-R

Q = 180-52-27.3081879220073

Q = 100.691812077992

This is the measure of angle PQR

subtract off angle PQS found back in part (a)

angle SQR = (anglePQR) - (anglePQS)

angle SQR = (100.691812077992) - (45.110237173726)

angle SQR = 55.581574904266

--------------

This value is approximate. Round however you need to.

The linear function that goes through the points (2,-4) and (-4,2) is:

y = -x + 2.

A linear function is modeled by:

y = mx + b

In which:

A linear function going through the points (2,-4) and (-4,2) would intersect the parabola at these points, hence these points would be the solution for the system of equations.

The slope of the line is:

m = (-4 - 2)/(2 - (-4)) = -1.

The line goes through point (2,-4), that is, when x = 2, y = -4, which we use to find the y-intercept b.

y = -x + b

-4 = -2 + b

b = -2.

Hence the equation is:

y = -x + 2.

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Answer:

A: 1

B: 17

C: 26

D: 42

E: 57

Step-by-step explanation:

hola buenas tardes como está el día de hoy ? yo estoy bien gracias por preguntar, espera...hablas español verdad...?

Answer: All real numbers

Step-by-step explanation: It is pretty simple. Just see if the x can be undefined. In this case x works with every number. So, it's all real numbers

Answer:

D

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

For a pentagon with n = 5 , then

sum = 180° × 3 = 540° , thus

x = 540° ÷ 5 = 108

For an octagon with n = 8, then

sum = 180° × 6 = 1080° , thus

y = 1080° ÷ 8 = 135

Thus

x + y = 108 + 135 = 243 → D

The mode can indicate the most frequently occurring values in a data set, it may not be the most suitable measure of central tendency for continuous data like math test scores. Considering other measures like the mean or the median would provide a more informative representation of the data.

To determine if the mode is a good measure of central tendency for the given data set, we need to understand the characteristics of the data and the purpose of using a measure of central tendency.

The mode is the value that appears most frequently in a data set. It can be a useful measure of central tendency when dealing with categorical or discrete data, where identifying the most common category or value is meaningful. However, for continuous data, such as math test scores in this case, the mode may not always provide a comprehensive representation of the data.

In the given data set of math test scores for 20 students, there are multiple values that occur with the same highest frequency, such as 100, 90, and 85, each appearing three times. Therefore, we have multiple modes in this data set. While the mode can tell us which scores are most common, it does not provide information about the overall distribution of the scores or the spread of the data.

For this reason, in this particular scenario, the mode alone may not be the best measure of central tendency. It would be more appropriate to consider other measures, such as the mean or the median, which can provide a more comprehensive understanding of the data set by considering the average score or the middle score, respectively.

In summary, while the mode can indicate the most frequently occurring values in a data set, it may not be the most suitable measure of central tendency for continuous data like math test scores. Considering other measures like the mean or the median would provide a more informative representation of the data.

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Answer:

DFG = 28⁰

because DEFG is a rhombus

=> DF is a bisector of angle EFG

=> EFD = DFG

we also have: EG is perpendicular with DF

EG cuts DF at O

=> EOF is a right triangle at O

=> EFD = 90⁰ - 62⁰ = 28⁰

=> DFG = 28⁰