A pulley is on the edge of a dock, 10 feet above the water level. A rope is being used to pull in a boat. The rope is attached to the boat at water level. The rope is being pulled in at the rate of 3 feet per second. Find the rate at which the boat is approaching the dock at the instant the boat is 2 feet from the dock.

Answer:

independent

Step-by-step explanation:

Answer:

Multiply the numbers inside the parenthesis with the number outside. In the case of the negative, use -1

Step-by-step explanation:

5(x-4)+3x-9x=6-(2x+5)+8x

5(x)- 5(4) +3x-9x=6 -(2x)-(5)+8x

5x-20+3x-9x=6-2x-5+8x

-x-20=6x+1

-x-6x=20+1

-7x=21

-7x/-7=21/-7

x=-3

a. In the Psychology exam Carl do best relative to the other student. Because Carl has the highest z-score in this exam. Percentile rank for his best exam is 94%.

b. In the History exam Carl do worst relative to the other student. Because Carl has the lowest z-score in this exam. Percentile rank for his Worst exam is 12%.

a. To determine on which exam Carl did best relative to the other students, we need to calculate the z-score for his grade on each exam, using the class mean and standard deviation.

z-score = (Carl's grade - Class mean) / Class SD

Exam | Class mean | Class SD | Carl's grade | z-score

French \(| 70.4 | 6.3 | 68.2 | -0.35\)

History\(| 88.2 | 4.1 | 83.4 | -1.17\)

Psychology \(| 83.6 | 3.5 | 89.2 | 1.60\)

Statistics \(| 75.4 | 8.6 | 82.5 | 0.83\)

From the table, we see that Carl did best relative to the other students on the Psychology exam, as his z-score for this exam is the highest. To find Carl's percentile rank for this exam, we can use a standard normal distribution table or calculator. Carl's z-score of 1.60 corresponds to a percentile rank of approximately 94%.

b. To determine on which exam Carl did the worst relative to the other students, we again look at the z-scores for his grades on each exam.

Exam | Class mean | Class SD | Carl's grade | z-score

French \(| 70.4 | 6.3 | 68.2 | -0.35\)

History \(| 88.2 | 4.1 | 83.4 | -1.17\)

Psychology \(| 83.6 | 3.5 | 89.2 | 1.60\)

Statistics \(| 75.4 | 8.6 | 82.5 | 0.83\)

From the table, we see that Carl did the worst relative to the other students on the History exam, as his z-score for this exam is the lowest. To find Carl's percentile rank for this exam, we again use a standard normal distribution table or calculator. Carl's z-score of -1.17 corresponds to a percentile rank of approximately 12%.

for such more question on z-score

https://brainly.com/question/25638875

#SPJ4

is it uh x=16.25 or 16 and y=7.87 or just 7? I dont know to be honest

Answer

The quadratic model for this data

n = -2t² + 24t + 10

Explanation

Quadratic functions are given as

y = ax² + bx + c

where y = n, t = x and a, b and c are constants.

n = at² + bt + c

when t = 1, n = 32

32 = a(1)² + b(1) + c

32 = a + b + c

when t = 3, n = 64

64 = a(3)² + b(3) + c

64 = 9a + 3b + c

when t = 4, n = 74

74 = a(4)² + b(4) + c

74 = 16a + 4b + c

Combining the three equations

a + b + c = 32

9a + 3b + c = 64

16a + 4b + c = 74

We can then solve this simultaneously and obtain that

a = -2

b = 24

z = 10

So, the quadratic model for this data

n = -2t² + 24t + 10

Hope this Helps!!!

To calculate the total number of samples in the sample space when randomly sampling 3 objects in order from among 42 objects, we need to consider the concept of permutations.

A permutation is an arrangement of objects in a specific order. In this case, we are interested in the number of permutations when selecting 3 objects from a pool of 42 objects.

The formula to calculate permutations is given by nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being selected.

In our case, n = 42 (total objects) and r = 3 (objects being selected). Therefore, the total number of samples in the sample space can be calculated as 42P3.

By substituting the values into the formula, we have 42P3 = 42! / (42 - 3)!

To know more about permutations: brainly.in/question/43149189

#SPJ11

Answer:

− 23

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify it.

Hope this helps!

Answer:

2500 m long

Step-by-step explanation:

Answer:

2,500 meters

Step-by-step explanation:

There are 1000 meters in a kilo meter so just multiply 2.5 x 1000

Answer:

152

Step-by-step explanation:

Substitute the given value for x.

\(8(3(6)+1)\\8(18+1)\\8(19)\\152\)

Answer:

152

Step-by-step explanation:

8(3x+1)

Let x = 6

8(3*6+1)

Multiply inside the parentheses

8(18+1)

Add inside the parentheses

8(19)

Multiply

152

A binomial is an algebraic expression that has two terms. Maclaurin series is a special case of Taylor series, where the expansion is made at 0 (i.e., a=0). To find the first four nonzero terms of the Maclaurin series for the binomial (1+x)^n.

A binomial is an algebraic expression that has two terms. Maclaurin series is a special case of Taylor series, where the expansion is made at 0 (i.e., a=0).

To find the first four nonzero terms of the Maclaurin series for the binomial (1+x)^n we use the formula:

(1+x)^n = C(n,0) x^0 + C(n,1) x^1 + C(n,2) x^2 + C(n,3) x^3 + ... + C(n,r) x^r + ...

where C(n,r) denotes the binomial coefficient of n and r.

C(n,0) = 1 for all n.

C(n,1) = n for all n.

C(n,2) = n(n-1)/2 for n>1.

C(n,3) = n(n-1)(n-2)/6 for n>2.

C(n,4) = n(n-1)(n-2)(n-3)/24 for n>3.

Therefore, the first four nonzero terms of the Maclaurin series for the binomial (1+x)^n are:

First nonzero term = C(n,0) x^0 = 1x^0 = 1.

Second nonzero term = C(n,1) x^1 = nx^1.

Third nonzero term = C(n,2) x^2 = n(n-1)/2 x^2.

Fourth nonzero term = C(n,3) x^3 = n(n-1)(n-2)/6 x^3.

Thus, the first four nonzero terms of the Maclaurin series for the binomial (1+x)^n are 1, nx, n(n-1)/2 x^2, and n(n-1)(n-2)/6 x^3.

These terms can be used to approximate (1+x)^n for small values of x, where the higher-order terms can be neglected.

The binomial expansion is one of the most useful expansions in mathematics. It allows us to find the powers of any binomial expression with ease. It finds its application in various fields of mathematics, including probability, algebra, and combinatorics.

To know more about Maclaurin series visit: https://brainly.com/question/31745715.

#SPJ11

Answer:

has been saving is the correct answer I believe

Answer:

"has been saving" is the right answer.

Solution:

Given the parallelogram below:

According to the properties of a parallelogram, the opposite sides are parallel and equal in dimensions.

Thus,

A) Height of the parallelogram:

The length BE is the height of the parallelogram, which is evaluated using the Pythagorean theorem.

According to the Pythagorean theorem,

Where

To evaluate h, we need to determine the value of EC.

Recall that

Thus, we have

We can now determine the value of h.

From the Pythagorean theorem,

Answer:

7x+y, when x+4 and y+5

7(4) + 5=

28+5=

33

Step-by-step explanation:

Hope this helps. :)

Answer:

16,891 pennies

$168.91

Step-by-step explanation:

The quadratic equation x2 - 4x + 3 = 0 has two roots. The roots are given by the quadratic formula as x = [4 ± √(16 - 12)]/2, which gives x = [4 ± 2√3]/2. Therefore, the roots are x = 2 ± √3.
The quadratic equation x^2 - 4x - 3 = 0 has two roots.

To find the roots of this equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 1, b = -4, and c = -3. Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-3)))/(2(1))
x = (4 ± √(16 + 12))/2
x = (4 ± √28)/2
x = (4 ± 2√7)/2

Simplifying further, we get:
x = 2 ± √7

Therefore, the two roots of the equation are x = 2 + √7 and x = 2 - √7.

Learn more about quadratic equation here: brainly.com/question/24349828

#SPJ11

Answer:

(C) x=50

Step-by-step explanation:

\(\frac{3}{5 }x -7=23\)

\(\frac{3x}{5} -7=23\)

\(\frac{3x}{5} -7+7=23+7\)

\(\frac{3x}{5}=30\)

\(3x=30* 5\)

\(3x=150\)

\(x=50\)

Answer:

(C) X = 50

Step-by-step explanation:

(3/5)*x-7 = 23 // - 23

(3/5)*x-23-7 = 0

3/5*x-30 = 0 // + 30

3/5*x = 30 // : 3/5

x = 30/3/5

x = 50  (Sorry if it's wrong)

The perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm  and 28 inches respectively.

We need to find the perimeter of given figures.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

4) Now, sum of all the sides

= 5+3.5+1.5+3.5+5+3.5+1.5+3.5 m

= 27 m

5) Here, radius = Diameter/2 = 17 cm

Perimeter = 2 semicircles+2(17) cm

= 2 × 1/2 πr + 2×17

= 2 × 3.14 × 17 + 34

= 140.76 cm

6) In the given figure here, there are 4 similar triangles

= 4(4+3) inches

= 4 × 7

= 28 inches

Therefore, the perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm  and 28 inches respectively.

To learn more about the perimeter visit:

https://brainly.com/question/6465134.

#SPJ1

Answer:

Seems to be no correlation at all.

Answer:

anges between -1 and +1 and quantifies the direction and strength of the linear association between the two variables. The correlation between two variables can be positive (i.e., higher levels of one variable are associated with higher levels of the other) or negative (i.e., higher levels of one variable are associated with lower levels of the other).

The sign of the correlation coefficient indicates the direction of the association. The magnitude of the correlation coefficient indicates the strength of the association.

For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association. A correlation close to zero suggests no linear association between two continuous variables.

It is important to note that there may be a non-linear association between two continuous variables, but computation of a correlation coefficient does not detect this. Therefore, it is always important to evaluate the data carefully before computing a correlation coefficient. Graphical displays are particularly useful to explore associations between variables.

The figure below shows four hypothetical scenarios in which one continuous variable is plotted along the X-axis and the other along the Y-axis.

Step-by-step explanation:

The  surface area over the given region is 864π square units.

To find the surface area of the given region, we can use the formula:

A = ∫∫ ||r_u × r_v|| dA

where r(u,v) is the vector-valued function that defines the surface, r_u and r_v are the partial derivatives of r with respect to u and v, and dA is the differential area element.

First, we need to find the partial derivatives of r(u,v):

r_u = 6cos(v)i + 6sin(v)j + 2uk
r_v = -6usin(v)i + 6ucos(v)j

Next, we can calculate the cross product of r_u and r_v:

r_u × r_v = det( [i  j  k], [6cos(v)  6sin(v)  2u], [-6usin(v)  6ucos(v)  0] )
          = (-12u^2cos(v))i + (-12u^2sin(v))j + (36u)k

Now, we can find the magnitude of r_u × r_v:

||r_u × r_v|| = sqrt[(-12u^2cos(v))^2 + (-12u^2sin(v))^2 + (36u)^2]
              = 6u sqrt[6^2 + u^2]

Finally, we can set up the double integral to find the surface area:

A = ∫∫ ||r_u × r_v|| dA
 = ∫[0,2π] ∫[0,6] 6u sqrt[6^2 + u^2] du dv

Using a computer algebra system, we can evaluate this integral to get:

A = 864π

Therefore, The  surface area over the given region is 864π square units.

Visit to know more about Area:-

brainly.com/question/25292087

#SPJ11

When p=4 and t=24 then substituting these values into the equation 6p + 3q = t we get q=0.

To find the value of q in the equation 6p + 3q = t when p = 4 and t = 24, you can substitute the given values into the equation and solve for q. First, replace p with 4 and t with 24

6(4) + 3q = 24

Simplify the left side of the equation

24 + 3q = 24

Subtract 24 from both sides

3q = 0

Divide both sides by 3

q = 0

Therefore, when p = 4 and t = 24, q is equal to 0.

To know more about Substitution:

https://brainly.com/question/24518649

#SPJ4

Answer:

EKH and FKG

Step-by-step explanation:

vertical angles are angles that are directly vertical from each other.

Answer:

C

Step-by-step explanation:

EKH AND FKG THEY ARE VERTICLE (SAME ANGLES)

Answer:

Step-by-step explanation:

We are to find the greatest common factor of x^7, x^3 and x^5

x^7 = x^3 * x^4

x^3 = x^3 * 1

x^5 = x^3 * x^2

From both factors, we cam see that x^3 is common to the three, hence the GCF is x^3

Answer:

83.33%

Step-by-step explanation:

300 - 50 = 250

250/300 = .8333 or 83.33%

Answer:

83.33%Step-by-step explanation:300 - 50 = 250250/300 = .8333 or 83.33%Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number of male and female be 3x and 5x

There are twelve more females than males

According to the above problem,

\(5x - 3x=12\\ 2x = 12\\ x = \frac{12}{2} \\ \boxed{x = 6}\)

Therefore, the numbers of male is

\(3x = 3 \times 6 = 18\)

and number of female is

\(5x = 5 \times 6 = 30\)

Hence, total number of people are

\((30 + 18) = 48\)

There are 48 people in the party.

Answer:

35

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

3 + 2(13 - 17)²

Step 2: Parenthesis subtraction

3 + 2(-4)²

Step 3: Exponent

3 + 2(16)

Step 4: Parenthesis multiplication

3 + 32

Step 5: Add

35

All the missing angles of the given image are;

(a) = 145°

(b) = 35°

(c) = 145°

(d) = 35°

(e) = 145°

(f) =35°

The line transversal theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Thus, angle e is a corresponding angle to 145°

Angle f is a corresponding angle to 35°

Similarly, angle b is an opposite angle to 35° while angle c is an opposite angle to 135°

Angle a is opposite to angle e and as such angle a = 145°

Angle d is opposite to angle f and as such angle d = 35°

Read more about Missing Angles at; https://brainly.com/question/28293784

#SPJ1

Answer: i think it may be b

Step-by-step explanation:

Answer:

r = 10

Step-by-step explanation:

just rearrange the equation to find r

Answer:

x=1

Step-by-step explanation: