Leonard conducts a study to see if the number of hawks in a park affects the number
of squirrels. What is the response variable in this study?
A.The number of hawks in the park
B.The number of squirrels in the park

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

Step-by-step explanation:

A

For a line with a slope a and a known point (h, k), the point-slope form is:

y = a*(x - h) + k

A general linear equation can be written in slope-intercept form as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that a line passes through a point (h, k), then the point-slope form of that line is:

y = a*(x - h) + k

Notice that particularly, the y-intercept can be written as (0, b), then the slope-intercept form is also a point-slope:

y = a*(x - 0) + b

y = a*x + b

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Answer:

The  95% confidence interval is  \(244.26 < \mu < 246.95\)  

The pivot function used is  

           \(t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }\)

Step-by-step explanation:

From the question we are told that

  The  data given is 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242

  The  sample  size is  \(n= 20\)

Given that the confidence level is 95% then the level of significance is

      \(\alpha = (100 - 95)\%\)

      \(\alpha = 0.05\)

The  degree of freedom is mathematically represented as

    \(df = 20 -1\)

    \(df = 19\)

From the student t-distribution table  the critical value of  \(\frac{\alpha }{2}\)  is  

          \(t_{\frac{\alpha }{2} , 19 } = 2.093\)

The mean is mathematically represented as

          \(\= x = \frac{\sum x_i}{ n}\)

         \(\= x = \frac{246+ 242 +248+245+ 250+ 244+252+ 248 +248 +247+ 250+ 248+ 246+ 242 +248 +244 +245 +246+ 250+ 242}{20}\)\(\= x = 246.6\)

The standard deviation is mathematically represented as

            \(\sigma = \sqrt{\frac{\sum (x_i - \= x )^2)}{n} }\)

           \(\sigma = \sqrt{\frac{(246- 246.6)^2 +(242- 246.6)^2 +(248- 246.6)^2 + (248- 245)^2+}{20} } \ ..\)

             \(\ ...\sqrt{\frac{(250-246.6 )^2+ (244- 246.6)^2+(252- 246.6)^2+ (248- 246.6)^2+ (248- 246.6)^2+}{20} } \ ...\)

              \(\ ..\sqrt{\frac{(247- 246.6)^2+ (250- 246.6)^2+ (248-246.6)^2+ (246-246.6)^2+ (242-246.6)^2+ (248-246.6)^2+ (244-246.6)^2+}{20} } \ ...\)       \(\sqrt{\frac{ (245-246.6)^2+ (246-246.6)^2+ ( 246-246.6)^2 + ( 250-246.6)^2+ ( 242-246.6)^2 +( 246-246.6)^2+ ( 242-246.6)^2 }{20} }\)\(\sigma = 2.87411\)

The margin of error is mathematically represented as

       \(E = t_{\frac{\alpha }{2} , 19} * \frac{\sigma }{\sqrt{n} }\)

      \(E = 2.093 * \frac{2.87411 }{\sqrt{20} }\)

      \(E = 1.345\)

The 95% confidence interval is mathematically represented as

       \(\= x - E < \mu < \= x + E\)

=>   \(245.6 - 1.345 < \mu <245.6 + 1.345\)

=>    \(244.26 < \mu < 246.95\)  

The pivot function used is  

           \(t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }\)

Using the z-distribution, it is found that the 95% confidence interval is (0.45 , 0.52), and it does not provide strong evidence against that belief.

A confidence interval of proportions is given by:

\(\pi\) ± \(z\sqrt{\frac{\pi (1-\pi )}{n} }\)

where \(\pi\) is the sample proportion, z is the critical value and n is the sample size.

In this problem, we have 95% confidence level, hence \(\alpha\) = 0.95, z is the value of Z that has a p-value of \(\frac{1+0.95}{2}\) = 0.975, so the critical value is z = 1.96

We have that a random sample of 860 births in a state included 423 boys, hence the parameters are given by:

n = 864, \(\pi =\frac{423}{860}\) = 0.49

Then the bounds of the interval are given by:

\(\pi\) + \(z\sqrt{\frac{\pi (1-\pi )}{n} }\) = 0.49 + \(1.96\sqrt{\frac{0.49(0.513)}{860} }\) = 0.52

\(\pi\) - \(z\sqrt{\frac{\pi (1-\pi )}{n} }\) = 0.49 - \(1.96\sqrt{\frac{0.49(0.513)}{860} }\) = 0.45

The 95% confidence interval estimate of the population of boys in all births is (0.45 , 0.52). Since the interval contains 0.513, it does not provide strong evidence against that belief.

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Answer:

I can tell you that #7 is 86.

Can’t help with 6

Step-by-step explanation:

Answer:

6. the answer is 2

7. the answer is 86

Step-by-step explanation:

6. 3/4+3/4= 6/4

6/4+1/4+1/4=8/4

Simplify that to 2

7. search on the calculator it's really simple math

Answer:

Sides:

Angles:

Step-by-step explanation:

Apply the law of sines to find the sine of \(\angle A\):

\(\displaystyle \frac{\sin{A}}{\sin{C}} = \frac{a}{c}\).

\(\displaystyle\sin A = \frac{a}{c} \cdot \sin{C} = \frac{103}{159} \times \left(\sin{104^{\circ}}\right) \approx 0.628556\).

Therefore:

\(\angle A = \displaystyle\arcsin (\sin A) \approx \arcsin(0.628556) \approx 38.9^\circ\).

The three internal angles of a triangle should add up to \(180^\circ\). In other words:

\(\angle A + \angle B + \angle C = 180^\circ\).

The measures of both \(\angle A\) and \(\angle C\) are now available. Therefore:

\(\angle B = 180^\circ - \angle A - \angle C \approx 37.1^\circ\).

Apply the law of sines (again) to find the length of side \(b\):

\(\displaystyle\frac{b}{c} = \frac{\sin \angle B}{\sin \angle C}\).

\(\displaystyle b = c \cdot \left(\frac{\sin \angle B}{\sin \angle C}\right) \approx 159\times \frac{\sin \left(37.1^\circ\right)}{\sin\left(104^\circ\right)} \approx 98.8\).

Answer: X=3

Step-by-step explanation:

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

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Answer:

130

Step-by-step explanation:

A straight like measures 180°

25+25=50

180-50=130

plz mark brainliest :)

Answer:

\(130^{\circ}\)

Step-by-step explanation:

A straight line can denote half a circle, each side having \(180^{\circ}\). Therefore, the sum of these three angles should be \(180^{\circ}\). Since the first two angles both measure \(25^{\circ}\), we can set up the following equation and solve:

\(25+25+m\angle 3=180,\\m\angle 3= \fbox{$130^{\circ}$}\).

Answer:

-36

Step-by-step explanation:

1. Lable the number from least to greatest.

-44, -41, -39, -33, -32, -27

2. Since there are an even number of options, take the two middle numbers, add them, and then divide the total by 2

-39 + -33 = -72

72/2  = -36

Your answer will be -36

The possible value of the side length of the plot of land that Abby owns, which is between 2200 and 2400 square meters is A. 48 meters.

The length is the quantitative measurement of a distance from one point to another position.

Length can also refer to the size of an object that has width or/and height.

The square of 2,200m² = 46.9 meters (√2,200)

The square of 2,400m² = 48.99 meters (√2,400)

The square of the median value of 2,200m² and 2,400m², which is 2,300m² is 48 meters approximateluy.

Thus, the possible value of the side length of the plot of land is A. 48 meters.

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A. 48 meters

B. 46 meters

C. 44 meters

D. 50 meters

Answer:

42 units

Step-by-step explanation:

Area of a trapezoid is always 1/2(b1+b2)*h

so here base 1 is 4 units, and base 2 is 10 units. When we add these we get 14, divided by 2 which is 7, and multiplied by height of 6, which is 42

Answer: DE = CE

Step-by-step explanation: AB is a continuous line so the distance from A to E could be different than the distance from D to E.

DE = CE is true.

A perpendicular bisector is a line that divides another line into two equal parts and is also perpendicular to it.

Here, we are given that AB is the perpendicular bisector of DC and DC is a perpendicular bisector of AB.

This means that AB and DC are the perpendicular bisectors of each other at the point of intersection, that is, E.

Now, since AB bisects DC at point E

⇒ DE = CE

and similarly, DC bisects AB

⇒ AE = BE

Apart from these two equalities, we cannot infer anything else from the given information.

Thus, out of the given options, we can see that only option 3, that is, DE = CE is true.

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Answer:

Step-by-step explanation:

Hence option B is correct.

a function of an arc or angle defined in terms of the ratios of pairs of sides of a right-angled triangle (such as sine, cosine, tangent, cotangent, secant, or cosecant).

In the figure it can be seen the perpendicular value =10 feet

and ,the base=3 feet,

tan(x)=10/3

tan(x)=3.33

x=73.3

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Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

Applying the two-tangent theorem, the length of AN is: 21 units.

The two-tangent theorem is a geometric theorem that states that if two tangents are drawn to a circle from a point outside the circle, then the lengths of the tangent segments are equal. This theorem is often used in geometry to find the length of tangent segments and to prove the existence of tangents to circles.

More formally, the two-tangent theorem states that if P is a point outside a circle with center O, and if PA and PB are tangents to the circle from point P, then PA = PB. In other words, the lengths of the two tangent segments are equal.

From the image above, AM and AN are two tangents from the same circle. Also, AN is also tangent with 29 - 2y.

This implies that the three tangents are congruent. Therefore:

6y - 3 = 29 - 2y

6y + 2y = 29 + 3

8y = 32

y = 32/8

y = 4

AN = 6y - 3

Plug in the value of y

AN = 6(4) - 3

AN = 21 units.

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See the attached picture for the answer:

Answer:

The maximum angle they can use the ladder is 65.38º

Step-by-step explanation:

Sine law allows sinA/a = sin B/b = sin C/c

Reference the drawing attached

sin 90/110m = sinB/100m

1/110m = sinB/100

multiply both sides by 100

100/110 = sinB

divide each side by 10

10/11 = sinB

find inverse sin of both sides

sin^-1(10/11) = B

65.38º = B

Given:

Log6 21.

We are asked to use change of base formula to determine form the options which is equivalent.

let's apply the base change formula:

For C:

Log10 10

Log10 21

Log10 10

Log10 6

Apply power law of logarithm to simplify the expression:

1

LOg10 21

1

Log10 6

ivide fraction by multiplying its reciprocal:

1 x Log10 6

Log10 21

Write as a single fraction:

Log10 6

Log10 21

Apply the base chande formula: log21 6

Check its equivalency: False.

Option A is False

Answer:

75 cents

Step-by-step explanation:

trust me pls and id its wrong i will paypal u 75 cents

Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

Answer:

4.5

Step-by-step explanation:

Probably too late for your RSM homework, but here is the solution:

6/(9-x) [Time they motored upstream] +6/x [Time it took the bottle to get back to the starting point] = 8/3 [Total Time]

Simplify to 54/(x(9-x))=8/3

Cross multiply: 162=(8x)(9-x)

Simplify -x^2+9x=20.25

Multiply both sides by negative one and move 20.25 to the other side. x^2-9x+20.25=0

Solve and get 4.5 :D!

The maximum amount of the original four numbers is 110.

What is the whole number?

A whole number is simply any positive number that does not include a fractional or decimal part. This means that, for example, the numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers.

Four whole numbers are each rounded to the nearest 10, which means each number can go +5 or -5.

The sum of the rounded numbers is 90, the maximum amount of the original four numbers is if +5 are added with each 4 original number.

So each number would have an extra +5.

And then the maximum number is 90 + (5 x 4) is equal to 110.

Or if the rounded-up no. were 10, 20, 30, 30.

The sum of these numbers is 90.

They can go up to 15,25,35,35.

So the sum of this is 110.

Hence, the maximum possible sum of the original four numbers is 110.

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how many different types of omlettes can be prepared with 10 ingredients? 7

Answer:

1024 omelets

Step-by-step explanation:

2^10 = 1024

Answer:

Option B,  two variables are measured and two groups are compared

Step-by-step explanation:

In a correlation study relationship between two variable is established.

The two variables represents two group.

For instance correlation study is conducted to determine the relationship between two variables X and Y

X and Y are variable

While X represents the group "number of cars passing through a lane"

Y represents the group "width of the road".

Hence, Option B is correct  

Answer:

The answer is The vertex of the graph of f(x) = |x – 3| + 6 is located at (3,6)

3

and

6

Step-by-step explanation:

Vertex of graph located at (3,6)

A mathematical object's vertex is a special point where two or more lines or edges typically meet. Angles, polygons, and graphs are the most common examples of vertices.

Given equation f(x) = |x - 3| +6

after simplifying there will be two equations they are

y = x - 3 + 6 = x +3...….(1)

and y = -(x-3) +6

y = 9 - x...…(2)      

substitute value of equation 2 in eq. 1

9 - x = x + 3

      x = 3 and

substitute value of x in eq. 1

y = x + 3 =3 + 3

y = 6

x = 3, y = 6

Hence the intersecting points of both equation are (3,6)

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