Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother’s height minus sister’s height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (–0. 76, 4. 34). What was the sample mean difference from these 24 pairs of siblings?



–0. 76 inches


0 inches


1. 79 inches


4. 34 inches

Answer:

Part A  The 4th bubble y= -55x+1630

Part B 1630

Part C 55

Step-by-step explanation:

Part A Use slope to find answer. In this example, points (1,599) and (4,1430).

Next use equation y1-y2/x1-x2. In this example, 1599-1430/1-4  which equals 169/-3 and that equals -56.3333333333333333333333.  Since y= -55x+1630 is closer, choose that answer.

Part B use y intercept. The y intercept is 1630

Part C Use the slope -55. It decreases by 55.

The values of a and b are 60 and 120 degrees respectively

We can see that the angles a to b are on a straight line and thus supplementary to each other.

Note that supplementary angles sum to 180 degrees

Let the angle a be x

Let the angle b be 2x

Then, we have;

x + 2x = 180

add the like terms

3x = 180

Make 'x' the subject of formula, we get;

3x/3 = 180/3

Divide the values

x = 60

Learn about supplementary angles at: https://brainly.com/question/2046046

#SPJ1

Answer:

72 lawns

Step-by-step explanation:

if the students could mow 12 lawns in 3 hours, then we can turn it into a ratio of 12:3, which we can simplify to 4:1.

to find how many lawns they can mow in 18 hours, we can multiply the numbers in our ratio by 18.

4x18=72

1x18=18

our new ratio is 72:18

we can translate this to:

they can mow 72 lawns in 18 hours

Using the substitution partial fraction method to find the indefinite integral, we have: \(\mathbf{\dfrac{1}{2}x^2-x+ In(|(x-1)(x+2)|)+C}\)

The method of solving partial fractions using the substitution method is called partial fraction decomposition. The steps in evaluating the indefinite integral are as follows:

Given that:

\(\int (\dfrac{x^3-x+3}{x^2+x-2})dx\)

We need to remove the parentheses in the denominator and write the fraction by using the partial fraction decomposition.

\(\int \dfrac{x^3-x+3}{x^2+x-2}dx\)

\(\int x-1+\dfrac{1}{x-1}+\dfrac{1}{x+2}dx\)

Now, this process is followed by splitting the two integrals into multiple integrals.

\(\int xdx + \int-1dx +\int \dfrac{1}{x-1}dx + \int \dfrac{1}{x+2 }dx\)

By using the power rule, the integral of x with respect to x is \(\dfrac{1}{2}x^2\)

\(\dfrac{1}{2}x^2+C+ \int-1dx +\int \dfrac{1}{x-1}dx + \int \dfrac{1}{x+2 }dx\)

Now, Let's apply the constant rule

\(\dfrac{1}{2}x^2+C-x+C +\int \dfrac{1}{x-1}dx + \int \dfrac{1}{x+2 }dx\)

Such that; \(u_1 = x - 1\), Then \(du_1 = dx\). So, we can now rewrite it as \(u_1 \ and \ du_1\).

\(\dfrac{1}{2}x^2+C-x+C +\int \dfrac{1}{u_1}du_1 + \int \dfrac{1}{x+2 }dx\)

Furthermore, taking the integral  of \(\dfrac{1}{u_1}\) with respect to \(u_1\) is \(\mathbf{In (|u_1|)}\)

\(\dfrac{1}{2}x^2+C-x+C +In(|u_1|)+C + \int \dfrac{1}{x+2 }dx\)

Now, let \(u_2 = x +2\) such that \(du_2 = dx\). So, we can now rewrite it as \(u_2 \ and \ du_2\).

\(\dfrac{1}{2}x^2+C-x+C +In(|u_1|)+C + \int \dfrac{1}{u_2 }du_2\)

The integral  of \(\dfrac{1}{u_2}\) with respect to \(u_2\) is \(\mathbf{In (|u_2|)}\)

\(\dfrac{1}{2}x^2+C-x+C +In(|u_1|)+C + In(|u_2|)+C\)

By simplifying the above process;

\(\dfrac{1}{2}x^2-x+ In(|u_1*u_2|)+C\)

Now, using the substitution method to substitute back in for each integration substitution variable, we have:

\(\mathbf{\dfrac{1}{2}x^2-x+ In(|(x-1)(x+2)|)+C}\)

Learn more indefinite integral here:

https://brainly.com/question/27419605

#SPJ1

Answer:

6

Step-by-step explanation:

3/4 x 8 = 3 x 8 / 4 x 1 = 24/4 = 6

Answer:

2 000 000 \(cm^{2}\)

Step-by-step explanation:

100 \(km^{2}\) = 1 000 000 000 000 \(cm^{2}\)

the scale of 1:500000 means that 1 cm in the map represents 500000 cm in reality

So on the map this pond's area would be

\(\frac{1 000 000 000 000}{500000}\) = 2 000 000 \(cm^{2}\)

Answer: they are 3

Step-by-step explanation:

3x3x3

To find a basis for the subspace W spanned by set S, we can perform Gaussian elimination on the matrix formed by the vectors in S. The basis vectors will be the non-zero rows in the reduced row-echelon form of the matrix.

a) s = [1 1 -2], [-1 -2 3], [1 0 -1], [2 -1 0]

Let's form a matrix using the given vectors:

```

[1  1  -2]

[-1 -2  3]

[1  0  -1]

[2 -1  0]

```

Perform Gaussian elimination to obtain the reduced row-echelon form:

```

[1  0  -1]

[0  1  -1]

[0  0  0]

[0  0  0]

```

The non-zero rows correspond to the basis vectors:

[1 0 -1] and [0 1 -1].

Therefore, the basis for W is {[1 0 -1], [0 1 -1]}.

The dimension of W (dim(W)) is equal to the number of basis vectors, which in this case is 2.

b) s = [1 2 -1 1], [3 1 1 2], [-1 1 -2 2], [0 -2 1 2]

Let's form a matrix using the given vectors:

```

[1  2 -1  1]

[3  1  1  2]

[-1 1 -2  2]

[0 -2  1  2]

```

Perform Gaussian elimination to obtain the reduced row-echelon form:

```

[1  0  1  0]

[0  1 -1  0]

[0  0  0  1]

[0  0  0  0]

```

The non-zero rows correspond to the basis vectors:

[1 0 1 0], [0 1 -1 0], and [0 0 0 1].

Therefore, the basis for W is {[1 0 1 0], [0 1 -1 0], [0 0 0 1]}.

The dimension of W (dim(W)) is equal to the number of basis vectors, which in this case is 3.

To know more about Gaussian elimination refer here

https://brainly.com/question/30400788#

#SPJ11

Answer: 60

Step-by-step explanation:

Find the total number of students.

In this case, there are 8 total students. Multiply 60 * 8 = 480

Add all the numbers up.

85 + 65 + 36 + 48 + 75 + 39 + 72 = 420

480 - 420 = 60

x = 60

Step-by-step explanation:

2x+26=2(5-3x)

2x+26=10-6x

combination of like terms

2x+6x=10-26

8x= -16

x= -16/8

x= -2

The conditional probabilities are as follows: P(B | C) = 0.295, P(C | B) = 0.371, P(A | B) = 0.371, P(B | A) = 0.333, P(A | C) = 0.273, and P(C | A) = 0.308. These probabilities represent the likelihood of one event occurring given that another event has already occurred.

To determine the conditional probabilities, we can use the formula:

P(X|Y) = P(X ∩ Y) / P(Y)

where X and Y are events.

1. P(B | C):

P(B | C) = P(B ∩ C) / P(C)

P(B ∩ C) = P(B n C) = 0.13

P(C) = 0.44

P(B | C) = 0.13 / 0.44 = 0.295

2. P(C | B):

P(C | B) = P(C ∩ B) / P(B)

P(C ∩ B) = P(B n C) = 0.13

P(B) = 0.35

P(C | B) = 0.13 / 0.35 = 0.371

3. P(A | B):

P(A | B) = P(A ∩ B) / P(B)

P(A ∩ B) = P(A n B) = 0.13

P(B) = 0.35

P(A | B) = 0.13 / 0.35 = 0.371

4. P(B | A):

P(B | A) = P(B ∩ A) / P(A)

P(B ∩ A) = P(A n B) = 0.13

P(A) = 0.39

P(B | A) = 0.13 / 0.39 = 0.333

5. P(A | C):

P(A | C) = P(A ∩ C) / P(C)

P(A ∩ C) = P(A n C) = 0.12

P(C) = 0.44

P(A | C) = 0.12 / 0.44 = 0.273

6. P(C | A):

P(C | A) = P(C ∩ A) / P(A)

P(C ∩ A) = P(A n C) = 0.12

P(A) = 0.39

P(C | A) = 0.12 / 0.39 = 0.308

Therefore, the conditional probabilities are:

P(B | C) = 0.295

P(C | B) = 0.371

P(A | B) = 0.371

P(B | A) = 0.333

P(A | C) = 0.273

P(C | A) = 0.308

To know more about conditional probabilities refer here:
https://brainly.com/question/32171649#

#SPJ11

The 15 units lengths of the sides of the triangle, MN and NR, and 3·√2  length of the side MR, which is 3·√2, indicates that MNR is an isosceles triangle;

An isosceles triangle is a triangle that has a pair of congruent sides and congruent base angles.

The distance formula indicates that we get;
√((x₂ - x₁)² + (y₂ - y₁)²)

Therefore; √((k - (-2))² + (-8 - 4)²) = √((k - (-5))² + (-8 - 1)²)

((k - (-2))² + (-8 - 4)²) = ((k - (-5))² + (-8 - 1)²)

k² + 4·k + 148 = k² + 10·k + 106

Subtracting k², from both sides, we get;

4·k + 148 = 10·k + 106

10·k - 4·k = 148 - 106

6·k = 42

k = 42/6 = 7

k = 7

The length of the third side of the triangle, MR, can be found to determine the type of triangle that triangle ΔMNR is as follows;

MR = √(((-5) - (-2))² + (1 - 4)²) = 3·√2

The length of MN = √((7 - (-2))² + (-8 - 4)²) = 15

NR = MN = 15

The congruent lengths of the sides MN and MR, which are both 15 units and the length of  MR of 3·√2, indicates that the triangle is an isosceles triangle.

Learn more on isosceles triangles here: https://brainly.com/question/27437134

#SPJ1

Answer:

A

Step-by-step explanation:

Given

f(x) = \(\frac{2}{3x+2}\)

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the value that x cannot be.

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - \(\frac{2}{3}\) ← excluded value

Then

domain is ( - ∞ , - \(\frac{2}{3}\) ) U ( - \(\frac{2}{3}\), ∞ ) → A

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

its true

they are both already right triangles so if both have acute angles that are congruent then the right triangles are similar

if one of the acute angles of a right triangle is congruent to an acute angle of another right triangle then by angle angle Similarity the triangles are similar

Option B : The height of the square pyramid must be larger than the height of the triangular pyramid.

To compare the heights of the pyramids, we need to use the formula for the volume of a pyramid. The volume of a square pyramid is given by:

V = (1/3) \(Bh\), where B is the area of the base and h is the height.

The volume of a triangular pyramid is given by:

V = (1/3)\(Bh\), where B is the area of the base and h is the height.

Since the base area of both pyramids is 36 square inches, we can write:

\(V_square\) = (1/3) * 36h_square

\(V_triangular\) = (1/3) * 36h_triangular

And since the volume of the square pyramid is twice as large as that of the triangular pyramid, we can write:

2V_triangular = \(V_square\)

Substituting the expressions for \(V_square\) and \(V_triangular\) into the equation above, we get:

2(1/3) * 36h_triangular = (1/3) * 36h_square

Solving for \(h_square\) and \(h_triangular\), we get:

2h_triangular =\(h_square\)

To learn more about square pyramid please click on below link        

https://brainly.com/question/27350043

#SPJ4

To approximate the integral ∫2.4 to 2 f(x) dx using Simpson's rule, we divide the interval [2, 2.4] into subintervals and approximate the integral within each subinterval using quadratic polynomials.

Given the data points (x, f(x)) = (2, 0.6931), (2.2, 0.7885), and (2.4, 0.8755), we can use Simpson's rule to approximate the integral.

Step 1: Determine the step size, h.

Since we have three data points, we can divide the interval [2, 2.4] into two subintervals, giving us a step size of h = (2.4 - 2) / 2 = 0.2.

Step 2: Calculate the approximations within each subinterval.

Using Simpson's rule, the integral within each subinterval is given by:

∫f(x)dx ≈ (h/3) * [f(x₀) + 4f(x₁) + f(x₂)]

where x₀, x₁, and x₂ are the data points within each subinterval.

For the first subinterval [2, 2.2]:

∫f(x)dx ≈ (0.2/3) * [f(2) + 4f(2.1) + f(2.2)]

≈ (0.2/3) * [0.6931 + 4(0.7885) + 0.8755]

For the second subinterval [2.2, 2.4]:

∫f(x)dx ≈ (0.2/3) * [f(2.2) + 4f(2.3) + f(2.4)]

≈ (0.2/3) * [0.7885 + 4(0.4545) + 0.8755]

Step 3: Sum up the approximations.

To obtain the approximation of the total integral, we sum up the approximations within each subinterval.

Approximation ≈ (∫f(x)dx in subinterval 1) + (∫f(x)dx in subinterval 2)

Calculating the values, we get the final approximation of the integral ∫2.4 to 2 f(x) dx using Simpson's rule.

To learn more about Simpson's rule click here:

brainly.com/question/30459578

#SPJ11

Answer:

\(m= \frac{6}{5}\)

Step-by-step explanation:

Slope can be calculated using following formula

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Here

\((x_1, y_1) = (-5, -1) \ \ and \ \ (x_2, y_2) = (5, 11)\)

Slope m is given as

\(m=\frac{11-(-1)}{5-(-5)}\)

\(m=\frac{12}{10}\\m=\frac{6}{5}\)

Answer:

3

Step-by-step explanation:

You would do 3/5 =6 then do 13/7 = 18/6=3

\(\text{Given that,}\\\\\text{Width,}~ w = 3x-2\\\\\text{Length,}~ l = x+5 \\\\\\\text{Perimeter} =2(w+l) = 2(3x-2+x+5) = 2(4x +3) = 8x +6\)

In trigonometry, it should be noted that the value of sin(-5pi/6) is -0.5.

In order to find the value, we can use the following steps:

Draw a unit circle and mark an angle of -5pi/6 radians.

The sine of an angle is represented by the ratio of the opposite side to the hypotenuse of the triangle formed by the angle and the x-axis.

In this case, the opposite side is 1/2 and the hypotenuse is 1.

Therefore, sin(-5pi/6) will be:

= 1/2 / 1

= -0.5.

We can also use the following identity to find the value of sin(-5pi/6):

sin(-x) = -sin(x)

Therefore, sin(-5pi/6)

= -sin(5pi/6)

= -0.5.

Learn more trigonometry on

https://brainly.com/question/24349828

#SPJ1

Answer:

The grade of this sixth and (final) test would be 91.

Step-by-step explanation:

This is an arithmetic series since each time the data is increasing by the common difference of 4, and we already know a₁ which is the first term in the sequence is 71, therefore we can say:

a₁ = 71

r = 4

a₆ = the sixth term that needs to be found out

n = 6

Formula of an arithemetic series:

aₙ = a₁ + r(n - 1)

a₆ = 71 + 4(6 - 1)

a₆ = 71 + 4(5)

a₆ = 71 + 20

a₆ = 91

Hence, the grade of this sixth and (final) test would be 91.

Hope this helps!

Feldman investigated how the rate of bar pressing by rats was affected by the type of injection they received, with two levels (saline and drug).

a. The dependent variable in this study is the rate of bar pressing by rats.

b. The independent variable in this study is the type of injection administered to the rats (saline-injection condition vs. drug-injection condition).

c. The independent variable has two levels: saline-injection condition and drug-injection condition.

d. A controlled extraneous variable in this study could be the environment in which the rats were tested. Since only one Skinner box was used and the same assistant handled all the animals, it suggests that the environment and handling conditions were kept constant to minimize their potential influence on the dependent variable.

a. Dependent variable: Rate of bar pressing by rats.

b. Independent variable: Type of injection administered.

c. Levels of the independent variable: Saline-injection condition and drug-injection condition.

d. Controlled extraneous variable: Environment and handling conditions.

Feldman investigated how the rate of bar pressing by rats was affected by the type of injection they received, with two levels (saline and drug). The study controlled for extraneous variables such as the environment and handling conditions.

For more such questions on rate

https://brainly.com/question/25720319

#SPJ8

That is, limₙ→∞ enⁿ⁶ = ∞. Hence, the limit does not exist, and the sequence diverges.

Given: Sequence aₙ = enⁿ⁶. To determine whether the sequence converges or diverges, we need to consider the value of e and the exponent n. Here, e is a positive constant and n is the index of the sequence. Hence, let us examine the behavior of the sequence by taking a few terms: when n = 1, a₁ = e;when n = 2, a₂ = e²;when n = 3, a₃ = e³;and so on. By observing the first few terms, we can notice that the sequence is increasing rapidly.

Hence, the terms of the sequence diverge to infinity. Therefore, the given sequence is divergent. Hence, the answer is Diverges. We could have also used the limit test to confirm this.

To know more about Sequence Visit:

https://brainly.com/question/30262438

#SPJ11

Answer:

439

Step-by-step explanation:

1700/4=425

15-1=14

425+14=439

By taking the difference between the y-intercepts, we conclude that the distance between the lines is 3 units.

A general linear equation is:

y = a*x + b

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

Two linear equations are parallel if and only if both lines have the same slope and different y-intercepts.

And the distance is given by the difference between the y-intercepts.

Here the lines are:

y = -3*x + 1

y = -3*x + 4

The difference between the y-intercepts gives:

4 - 1 = 3

That is the distance between the lines.

Learn more about distances:

https://brainly.com/question/7243416

#SPJ1

The Area Of The Circle Is 452.16

The Circumference Of The Circle Is 75.36

Answer:

The question is not asked correctly

Step-by-step explanation:

Answer:

x = 9.33

Step-by-step explanation:

7/13 = x/(x+8)

7x + 56 = 13x

6x = 56

x = 9.33