4. A rectangular plate has a perimeter of 28cm. determine the dimensions of the plate that give the maximum area​

Answer:-0.36

Step-by-step explanation:

Answer: C. -0.36

Step-by-step explanation:

The tangent vector  → \(r(t)=〈4cos(2t),4sin(2t),5t〉\), normal vector at t=0 is given by →N(0) = 〈-1,0,0〉, and binormal vector at t=0 is given by →\(B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector, normal vector, and binormal vector of the given curve are as follows:

Given curve:

→ \(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0

To find: Tangent vector, the Normal vector, and the Binormal vector (→T, →N and →B) at the point t=0

Tangent vector: To find the tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0,

we need to differentiate the equation of the curve with respect to t.t = 0, we have:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉→r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

Differentiating w.r.t t:→\(r(t) = 〈4cos(2t),4sin(2t),5t〉 → r'(t) = 〈-8sin(2t),8cos(2t),5〉t = 0\),

we have:

→\(r'(0) = 〈-8sin(0),8cos(0),5〉= 〈0,8,5〉\)

Therefore, the tangent vector at t = 0 is given by

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Normal vector:To find the normal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to differentiate the equation of the tangent vector with respect to t.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating w.r.t t:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉t = 0\),

we have:

→\(T'(0) = 〈-16cos(0),-16sin(0),0〉= 〈-16,0,0〉\)

Therefore, the normal vector at t = 0 is given by

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Binormal vector: To find the binormal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to cross-product the equation of the tangent vector and normal vector of the curve.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉\)

The cross product of two vectors:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the binormal vector at t = 0 is given by→B(0) = 〈0, -0.441, -0.898〉

Hence, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are as follows:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The given curve is

→\(r(t)=〈4cos(2t),4sin(2t),5t〉 at the point t=0.\)

We are asked to find the tangent vector, the normal vector, and the binormal vector of the given curve at t=0.

the tangent vector at t=0. To find the tangent vector, we need to differentiate the equation of the curve with respect to t. Then, we can substitute t=0 to find the tangent vector at that point. the equation of the curve Is:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉\)

At t = 0, we have:

→\(r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

We can differentiate this equation with respect to t to get the tangent vector as:

→\(r'(t) = 〈-8sin(2t),8cos(2t),5〉\)

At t=0, the tangent vector is:

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Next, we find the normal vector. To find the normal vector, we need to differentiate the equation of the tangent vector with respect to t. Then, we can substitute t=0 to find the normal vector at that point.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating this equation with respect to t, we get the normal vector as:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉\)

At t=0, the normal vector is:

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Finally, we find the binormal vector. To find the binormal vector, we need to cross-product the equation of the tangent vector and the normal vector of the curve.

At t=0, we can cross product →T(0) and →N(0) to find the binormal vector.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

The normal vector is:

→N(0) = 〈-1,0,0〉Cross product of two vectors →T(0) and →N(0) is given as:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0 is given by →\(T(0) = 〈0.000,0.898,0.441〉.\)

The normal vector at t=0 is given by →N(0) = 〈-1,0,0〉.

The binormal vector at t=0 is given by →B(0) = 〈0, -0.441, -0.898〉.

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Answer:

none

Step-by-step explanation:

Answer:

235

Step-by-step explanation:

470 ÷ 2 = 235

The line which has an undefined slope among the answer choices given in the task content as described is; the line R which is a vertical line.

It follows from the task content that the line which has an undefined slope is to.be determined among the answer choices.

Since, the slope of a graph is the rate of change in the vertical axis to that in the horizontal axis; it follows that the slope of vertical lines is undefined.

The statement above is true because, no change is recorded in the X axis of vertical lines. Hence, the denominator in the slope formula is; 0 and ultimately, the slope is undefined.

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Answer:

Step-by-step explanation:

The answer is R

1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)

To find the common ration, multiply thus;

⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)

⇒ \(\frac{256}{25}\)

= 10. 24

1b. (5/7)^2 × (5/7)^1

= \(\frac{25}{49}\) × \(\frac{5}{7}\)

= \(\frac{125}{343}\)

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= \(\frac{8}{125}\) × \(\frac{4}{25}\)

= \(\frac{32}{3125}\)

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)

Take the inverse of the denominator

= \(\frac{1}{4}\) × \(\frac{8}{5}\)

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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Answer:

1. 7

2. 12

3. 31

4. 1

Step-by-step explanation:

In this case, we are given only a partial list of observations. To determine if the process is in control, we would need the complete set of observations to evaluate their values in relation to the control limits.

To construct a control chart and determine if the process is in control, we need to calculate the control limits using the given observations.

Let's start by calculating the average (x(bar)) and standard deviation (σ) of the observations:

Observations: 10, 3, 9, 9, 8, 4

Step 1: Calculate the average (x(bar)):

x(bar) = (10 + 3 + 9 + 9 + 8 + 4) / 6 = 43 / 6 ≈ 7.17

Step 2: Calculate the standard deviation (σ):

1. Calculate the squared deviation for each observation:

\((10 - 7.17)^2, (3 - 7.17)^2, (9 - 7.17)^2, (9 - 7.17)^2, (8 - 7.17)^2, (4 - 7.17)^2\)

= 6.9129, 18.9129, 2.5929, 2.5929, 0.6889, 10.5889

2. Calculate the average of the squared deviations:

(6.9129 + 18.9129 + 2.5929 + 2.5929 + 0.6889 + 10.5889) / 6 ≈ 7.9198

3. Calculate the square root of the average squared deviation:

σ = √(7.9198)

≈ 2.81

Now that we have the average (x(bar)) and standard deviation (σ), we can construct the control chart using two sigma limits. The control limits are calculated as follows:

Upper Control Limit (UCL) = x(bar) + (2 * σ)

Lower Control Limit (LCL) = x(bar) - (2 * σ)

UCL = 7.17 + (2 * 2.81)

≈ 12.79

LCL = 7.17 - (2 * 2.81)

≈ 1.55

Based on the control chart, if any of the observations fall above the UCL or below the LCL, it would indicate an out-of-control process.

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Answer:

There are 10 cards in the stack, and 5 of them are odd (1, 3, 5, 7, and 9). There are 3 cards (1, 2, and 3) that are less than 4. Since we are replacing the first card before selecting the second, the outcomes are independent and we can multiply the probabilities of each event.

The probability of selecting an odd card on the first draw is 5/10, or 1/2.

The probability of selecting a card less than 4 on the second draw is 3/10, since there are 3 cards that meet this condition out of a total of 10.

Therefore, the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is:

(1/2) x (3/10) = 3/20

So the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is 3/20.

Step-by-step explanation:

Answer:

3/20.

Step-by-step explanation:

To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is:

5/10 x 3/10 = 15/100

We can simplify this fraction by dividing both the numerator and denominator by 5:

15/100 = 3/20

So, the final answer is 3/20.

Received message. To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is: 5/10 x 3/10 = 15/100 We can simplify this fraction by dividing both the numerator and denominator by 5: 15/100 = 3/20 So, the final answer is 3/20.

Answer:

A \(1.3 - 5.6 = - 4.3\)

Step-by-step explanation:

\(1.3 - 5.6 = - 4.3\)

Hope this helps! Pwease mark me brainliest! Have a great day!

−xXheyoXx

Answer:

just answering so you can give the other person brainliest :D

Step-by-step explanation:

The mean is 172, the variance is 34.4, and the standard deviation is 5.86.

The United States has a system of bicameralism, which means that each state has two chambers in its legislature: a lower chamber (such as the Assembly or House of Representatives) and an upper chamber (such as the Senate).

The number of constituents per district in each chamber varies from state to state, and it is usually determined by the state's constitution or by a state redistricting commission.

As of the 2010 census, Texas had about 811,147 constituents per state senate district.

However, this is not the highest number of constituents per senator among all the states.

In fact, the state with the highest number of constituents per senator is California.

According to the U.S. Census Bureau, as of the 2010 census, California had a population of approximately 37.3 million people.

The state's constitution provides for 40 state senators, which means that each senator represents approximately 933,000 constituents.

This is significantly higher than the number of constituents per senator in Texas.

The high number of constituents per senator in California can be attributed to the state's large population and the fact that the number of state senators has not kept up with population growth.

The last time the number of state senators in California was increased was in 1973, when the state's population was around 20 million people.

In conclusion, while Texas has a high number of constituents per state senate district, it is not the only state with a high number of constituents per senator.

California has a significantly higher number of constituents per senator, due to its large population and the fact that the number of state senators has not kept up with population growth.

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Answer:

17%

Step-by-step explanation:

5 out of 30 is 17%

5/30 = 5 ÷ 30 = .16.  rounds to .17 =17%

On solving this trigonometry, we find that (a) sec(sin⁻¹ \(\frac{12}{13}\)) = \(\frac{13}{5}\) and (b) tan(sin⁻¹ \(\frac{12}{13}\)) = \(\frac{12}{5}\)

(a) To find the exact value of sec(sin⁻¹ \(\frac{12}{13}\)), we can use the fact that sec(x) = \(\frac{1}{cos}\)(x). Let's draw a right triangle with opposite side 12 and hypotenuse 13. Using the Pythagorean theorem, we can find the adjacent side:

a² + b² = c²

a² + 12² = 13²

a² = 169 - 144

a = √25

a = 5

So our triangle has sides of length 5, 12, and 13. Now we can find cos(sin⁻¹  \(\frac{12}{13}\)) by looking at the adjacent/hypotenuse ratio in this triangle:

cos(sin⁻¹ \(\frac{12}{13}\)) =  \(\frac{5}{13}\)

Therefore, sec(sin⁻¹(12/13)) = 1/cos(sin⁻¹ \(\frac{12}{13}\))

                                            = 1/\(\frac{5}{13}\)

                                            = \(\frac{13}{5}\).

So the exact value of sec(sin⁻¹ \(\frac{12}{13}\)) is \(\frac{13}{5}\).

(b) To find the exact value of tan(sin⁻¹ \(\frac{12}{13}\)), we can use the fact that tan(x) = sin(x)/cos(x). Let's use the same right triangle as before.

Then sin(sin⁻¹ \(\frac{12}{13}\))=  \(\frac{12}{13}\) and cos  \(\frac{12}{13}\)) = \(\frac{5}{13}\)  , so

tan(sin⁻¹ \(\frac{12}{13}\)) = sin(sin⁻¹ \(\frac{12}{13}\))/cos(sin⁻¹\(\frac{12}{13}\))

                        = \(\frac{12}{13}\) / \(\frac{5}{3}\)

                        = \(\frac{12}{5}\)

So the exact value of tan(sin⁻¹ \(\frac{12}{13}\)) is \(\frac{12}{5}\).

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Answer:

Step-by-step explanation:

Using Trigonometry: SOH CAH TOA,

Cross multiplying:

x = tan (47°) × 35

  =  37.5329

  = 37.53 to two decimal places

Answer:

62.83

Step-by-step explanation:

Circumference=2 pi r

diameter=20

20*pi= about 62.83

so it sould be around 62.83

The two triangles are similar by the Angle- Angle and also SIde -Side postulates.

A postulate is defined as a statement that is assumed to be true without any proof.

A theorem is defined as a true statement and is supported by a proof (or can be proven).

Here, two triangles can be said to be similar through many postulates :

1. △ABC and △DEF are similar if

angle ABC is equal to angle DEF; and

angle BCA is equal to angle EFD

(or any other two corresponding angles are same)

This can be said that △ABC and △DEF are similar with Angle- Angle (AA) postulate.

2.  △ABC and △DEF are similar if

side AB/ BC is proportional to side DE/ EF;

(or ratio of two corresponding sides are similar)

This can be said that △ABC and △DEF are similar with Side Side (SS) postulate.

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Answer:

Step-by-step explanation:

d

Answer:

D

Step-by-step explanation:

Answer:

  (b)  Both vertical and horizontal reflection

Step-by-step explanation:

The figure will be a horizontal reflection of itself about any vertical line through two of the smaller 6-pointed stars.

The figure will be a vertical reflection of itself about any horizontal line through two of the smaller 6-pointed stars.

  the pattern has both vertical and horizontal reflection

__

Additional comment

A pattern will have horizontal reflection if there exists a vertical line about which the pattern can be reflected to itself. That is, there exists one (or more) vertical lines of symmetry.

Similarly, the pattern will have vertical reflection if there is a horizontal line about which the pattern can be reflected to itself. Such a line is a horizontal line of symmetry.

A confidence interval cannot instantly lead to rejecting the null hypothesis in a hypothesis test. In the given case the null hypothesis is either rejected or rejected based on test statistics.

α = 0.05

μ = 2

If the confidence interval is 1.0 or 2.0, then the null hypothesis value of 2 drops exceeds the interval, this makes the data contradict the null hypothesis and may reject the null hypothesis.

This alone would not be good to decline the null theory - the conclusion to reject or not reject the null hypothesis is determined by the test statistic and the alternate p-value.

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Answer:

ln(28.1) ≈ 3.336

log(2/5) ≈ -0.398

Step-by-step explanation:

In this question, we are asked to find the natural log of 28.1 and the log base 10 of 2/5, rounded to the nearest thousandth.

The natural log of a number x is what power the constant e is raised to to get x.

For example,

ln(e²) = 2

We can approximate ln(28.1) by inputting it into a calculator.

ln(28.1) ≈ 3.33576957634

Then, we can round this to the nearest thousandth.

ln(28.1) ≈ 3.336

Notice how the 7 in the ten-thousandths place is greater than or equal to 5, so we round the thousandths place digit up to 6.

__

The log base 10 of a number x is what power the number 10 is raised to to get x. However, note that since log base 10 is the "common log" the base of 10 is not always specified.

log(2/5) ≈ -0.398

Notice how the output is negative, since 2/5 is less than 1 (and any number to the zeroth power is 1).

7680 bats are expected to be in the colony after 8 years

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

The formula for exponential growth

\(y=ab^{t}\)

Given,

After 2 years, there were 120 bats.

120=ab²...1

After 5 years, there were 960 bats.

960=ab⁵....2

Hence:

120/960 = ab²/ab⁵

1/8 = b²/b⁵

1/8 = 1/ b³

1/2³ =1/ b³

2³=b³

b=2

We solve for a

120 = ab²...... Equation 1

120 = a × 2²

120 = 4a

a = 120/4

a = 30

Now put a, b and t value in the formula

y = 30 × 2⁸

y = 7680 bats

Hence, 7680 bats are expected to be in the colony after 8 years

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If segment BD is congruent to segment BC, and BD = 4x - 18, BC = x + 3, and AC = 34, then AB = 31/x.

Let the equation be AB + BC = AC

substitute the values in the above equation, we get

AB + x + 3 = 34

simplifying the value of x,

Subtract A B from both sides AB + x + 3 - AB = 34 - A B

x + 3 = 34 - AB

Subtract 3 from both sides,

x + 3 - 3 = 34 - AB - 3

x = -AB + 31

Plug in this value of x into the line segments to find BC and AC.

Where, BC = x + 3

substitute the value of x in the above equation, we get

BC = [-AB + 31 ] + 3

BC = -AB + 34

Then, AB + BC = AC

x = -AB + 31

AB = 31/x

Hence, If segment BD is congruent to segment BC, and BD = 4x - 18,

BC = x + 3, and AC = 34, then AB = 31/x.

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Answer:

I think the answer is 11 in my opinion

Answer:

C 1 5

Step-by-step explanation:

that's ur answer I hope it's correct

the expression is

so the correct answer is d = -16

The chord of the sphere is represented by OT.

The geometrical equivalent of a two-dimensional circle in three dimensions is a sphere. The collection of points in three-dimensional space that are all located at the same r distance from one another is known as a sphere.

The line segment connecting any two locations on a circle's circumference is referred to as the chord of the sphere. It should be emphasized that the diameter is the circle's longest chord, which runs through its center.

So, if L, M, and N lie on the surface of a sphere with its center at point O. Point T lies in the interior of the sphere, then OT would connect two points on the circumference of the sphere.

Hence, the chord of the sphere is represented by OT.

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Answer:

If you are trying to simplify the expression, the answer is -14x^2+8x-37

Step-by-step explanation:

First, keep removing the parentheses.

(x-1)(2-x)+(x^2+5)(x-7) -x^2(x+6)

Next, try expanding the expression.

3x - x^2 - 2+ (x^2+5)(x-7)-x^2(x+6

3x-x^2-2+x^3-7x^2+5x-35-x^2(x+6

3x-x^2-2x^3-7x^2+5x-35-x^3-6x^2

Finally, simplify the expression.

-14x^2 8x-37

I hope this helped to answer your question.

The probability that exactly 7 customers are very satisfied is 0.75.

So, the probability that exactly 7 customers are satisfied.

We know that a total of 93% of customers are satisfied.

Then, get 93% of 10:

10/100 × 93

0.1 × 93

9.3

Probability formula: P(E) = Favourable events/Total events

F(E) = 7 and T(E) = 9.3

Now, calculate as follows:

P(E) = Favourable events/Total events

P(E) = 7/9.3

P(E) = 0.75

Therefore, the probability that exactly 7 customers are very satisfied is 0.75.

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Correct question:
Use excel to find the following binomial distribution probabilities. a hotel claims that 93% of its customers are very satisfied with its service. complete parts a through e below based on a random sample of 10 customers. (4 points) a) what is the probability that exactly 7 customers are very satisfied?

Answer:

x = 98; y = 112

Step-by-step explanation:

Opposite angles of an quadrilateral inscribed in a circle are supplementary. That means that the sum of their measures is 180 deg.

x + 82 = 180

x = 98

y + 68 = 180

y = 112

The constant of proportionality in a graph, table or ordered pairs is divide y by x

Ising a graph, the constant of proportionality is the constant value of the ratio obtained from two proportional quantities.

How to obtain a constant of proportionality?

The constant of proportionality is the slope of the graph of a straight line.

The slope of a graph of a straight line is determined by:

Slope = rise /run or increase in y/increase in x or decrease in y/decrease in x

In conclusion, rise in y/run in x determines the constant of proportionality.

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The value of simplified form of the expression is,

⇒ √2 (13 - √3)

We have to given that;

The expression is,

⇒ 3√2-√6+10√2

Now, We can simplify as;

⇒ 3√2 - √6 + 10√2

⇒ 3√2 - √2 × √3 + 10√2

⇒ 13√2 - √2 × √3

⇒ √2 (13 - √3)

Thus, The value of simplified form of the expression is,

⇒ √2 (13 - √3)

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