Raquel builds a model train that has 4 equal-sized rail cars. Each rail car has a passenger section and a cargo section. The cargo section for each rail car is 4 inches long. The total length of the model train is 48 inches. What is the length of the passenger section in each rail car?

Answer: BELOW

Step-by-step explanation:

m<1 62°

m<2 39°

m<3 26°

m<4 55°

m<5 55°

m<6 35

A triangle is equal to 180° so you keep adding angles till you have all your answers.

Answer:

68

Step-by-step explanation:

The formula for finding the are of a right triangle is

A= 1/2bh

( area = base times height divided by 2)

17 is the base and 8 is the height, 8*17=136

136÷2=68

Answer:

45 degrees

Step-by-step explanation:

BD bisects the angle so divide it by two

Answer:

The right answer is 45 degrees .

Answer:

x=-5, x=-9

Step-by-step explanation:

Use zero product property to set each term to 0: x+5=0, x+9=0.

x=-5, x=-9

Answer:

x=-5 and x=-9

Step-by-step explanation:

First you use the first bracket to give you:

x+5=0

so x=-5

Then you use the second bracket to give you:

x+9=0

so x=-9

Answer:

y= -4/3x - 1/2 is the perpendicular line to y= 3/4x -1/2

Step-by-step explanation:

The slope would be the negative reciprocal of your current slope :)

+3/4 would turn into -4/3 and you wouldnt change the y intercept

hope this helps

Answer: The angle of depression would be 26.57°

Step-by-step explanation: Please refer to the attached picture for further details.

What harry has done has effectively led to the formation of a right angled triangle. As shown in the diagram, the camera has been mounted at a height of 8 feet above the ground. Also he mounts the camera at a horizontal from the entrance, which puts the camera at 16 feet away from the entrance (not from the ground). In order to capture every movement at the entrance, the camera range would be determined by an angle which covers everything from top to bottom of the entrance. That gives you the angle of depression which is at the point labelled CAMERA in the triangle.

Having determined two sides and an angle (unknown) in a right angled triangle, we shall use the trigonometric ratios as follows;

Tan ∅ = Opposite/Adjacent

Where the opposite is 8 (side facing the reference angle) and the adjacent is 16 (side that lies between the reference angle and the 90 degree angle)

Tan ∅ = 8/16

Tan ∅ = 0.5

By use of a calculator,

∅ = 26.5650

∅ ≈ 26.57

Therefore the angle of depression of the surveillance camera should be 26.57°

Answer:

the answer is 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

3 ÷ 3 = 1

6 ÷ 3 = 2

9 ÷ 3 = 3

12 ÷ 3 = 4

Hope it helps and have a great day! =D

~sunshine~

The equation of the line in fully simplified slope-intercept form is y = -x + 3

From the question, we are to write the equation of the line in fully simplified slope-intercept form

The slope-intercept form of the equation of a straight line is given as

y = mx + b

Where m is the slope of the line

and b is the y-intercept

From the graph,

The y-intercept is 3

∴ b = 3

Now, we will determine the slope, m, of the line

Given any two points (x₁, y₁) and (x₂, y₂) on a line, the slope, m, of the line is

m = (y₂ - y₁)/(x₂ - x₁)

Picking the points, (0, 3) and (2, 1)

m = (1 - 3)/(2 - 0)

m = -2/2

m = -1

Putting in the slope, m, and the y-intercept, b into the equation of a line

y = mx + b

We get

y = -1(x) + 3

Simplify

y = -x + 3

Hence, the equation of the line in fully simplified slope-intercept form is y = -x + 3

Learn more on Writing equation of a line here: https://brainly.com/question/25041573

#SPJ1

Answer:

Option A is correct.

Step-by-step explanation:

Between B and C, the value of height (y) remains constant, as shown as a horizontal line on the graph.

The probability that two randomly generated strings of length 9 in the DNA alphabet is 729.

We have to find the probability that two randomly generated strings of length 9 in the DNA alphabet (a, c, g, t) are identical.

Probabilities are based on occurrences, and events can result from one or more observations or experiment results.

The total number of alphabet in word DNA is 3.

So, the probability that two randomly generated strings of length 9 in the DNA alphabet = 9 × 9 × 9

The probability that two randomly generated strings of length 9 in the DNA alphabet = 729

To learn more about probability link is here

brainly.com/question/14210034

#SPJ4

The ratio of the horizontal change to the vertical change of a line would not be used to describe a slope. Thus the correct option is option C.

The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) of a line.

Slope=Vertical Change/Horizontal Change

This is also represented as the "ratio of rise to run of a line".

Slope=Rise/Run

In the given question, however, option C states that the "ratio of the horizontal change to the vertical change of a line".

Horizontal Change/ Vertical Change= 1/slope

This is an incorrect statement since the ratio of the horizontal change to the vertical change of a line is the reciprocal of the correct ratio.

To know more about the slope of a line:

https://brainly.com/question/14459038

Where is the Graph.

Step-by-step explanation:

LOL

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

P = 1

Step-by-step explanation:

-7p-10=-8p-9p

-7p + 8p + 9p = 10

10p = 10

p = 10/10

p = 1

The probability from the odds is 3/7

The value of the odds is given as

Odds = 3 to 4

Represent the odds as a fraction

So, we have the following representation

Odds = 3/4

To convert the odds to probability, we make use of the following equation

Probability = Odds/(1 + Odds)

Substitute the known values in the above equation, so, we have the following representation

Probability = (3/4)/(3/4 + 1)

Evaluate the sum

Probability = (3/4)/(7/4)

Evaluate the quotient

Probability = 3/7

Hence, the probability is 3/7

Read more about odds and probability at

brainly.com/question/9760260

#SPJ1

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

Learn more about cylinder current total cost https://brainly.com/question/25109150

#SPJ11

Answer:

9(3+5)

Step-by-step explanation:

GCF is 9, because thats the highest common number that both numbers can be divided by.

27/9 = 3

45/9 = 5

so,

9(3+5)

Answer: It takes 3 cups of sugar for 4 cups of cranberry

Step-by-step explanation:

12 cups of sugar, 16 cups of cranberry

Divide both numbers by 4

12/4=3

16/4=4

It takes 3 cups of sugar for 4 cups of cranberry

Answer:

Step-by-step explanation:

|x-a|≤b

-b≤x-a≤b

add a

a-b≤x≤a+b

put a-b=-8

a+b=-4

add

2a=-12

a=-12/2=-6

-6+b=-4

b=-4+6=2

so |x+6|≤2

The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:

\(V(x) = x(10-2x)(16-2x)\)
Taking the derivative with respect to x:
\(V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x\)
Setting V'(x) = 0 and solving for x:
\(10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0\)
Solving for x using the quadratic formula:
\(x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07\)
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.

Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106

Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.

Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

learn more about extreme values

https://brainly.com/question/1286349

#SPJ11

a) The extreme values of V are:

Minimum value: V(0) = 0

Relative maximum value: V(3) = 216

Absolute maximum value: V(4) = 128

b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.

a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of V(x), we get:

\(V'(x) = 48x - 36x^2 - 4x^3\)

Setting this equal to zero and solving for x, we get:

\(48x - 36x^2 - 4x^3 = 0\)
4x(4-x)(3-x) = 0

So the critical points are x = 0, x = 4, and x = 3.

We now need to test these critical points to see which ones correspond to maximum or minimum values of V.

We can use the second derivative test to do this. Taking the derivative of V'(x), we get:

\(V''(x) = 48 - 72x - 12x^2\)

Plugging in the critical points, we get:

V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)

To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:

V(0) = 0
V(3) = 216
V(4) = 128

So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
for such more question on extreme values

https://brainly.com/question/30886356

#SPJ11

Answer:

x = 20

Explanation:

(3x + 1)° + 29° = 90°

3x + 1 + 29 = 90

3x + 30 = 90

3x + 30 − 30 = 90 − 30

3x = 60

3x / 3 = 60 / 3

The system described by the equation y(t) = √x(t²) is linear, fixed, dynamic, and causal. The response of the system to the input x(t) = δ(t) is:

y(t) = ∫_{-∞}^{∞} δ(τ) h(t - τ) dτ = ∫_{-∞}^{∞} √τ² dτ

Linear: The system is linear because the output is a linear combination of the inputs. For example, if x(t) = 2 and y(t) = √4 = 2, then if we double the input, x(t) = 4, the output will also double, y(t) = √16 = 4.

Fixed: The system is fixed because the output depends only on the current input and not on any past inputs. For example, if x(t) = 2 at time t = 0, then the output y(t) = √4 = 2 at time t = 0, regardless of what the input was at any previous time.

Dynamic: The system is dynamic because the output depends on the input at time t, as well as the input's history up to time t. For example, if x(t) = 2 at time t = 0, then the output y(t) = √4 = 2 at time t = 0, but if x(t) = 4 at time t = 1, then the output y(t) = √16 = 4 at time t = 1.

Causal: The system is causal because the output does not depend on future inputs. For example, if x(t) = 2 at time t = 0, then the output y(t) = √4 = 2 at time t = 0, regardless of what the input will be at any future time.

Problem #2: The response of the system to the input x(t) = δ(t) can be determined using the convolution integral:

y(t) = ∫_{-∞}^{∞} x(τ) h(t - τ) dτ

where h(t) is the impulse response of the system. In this case, the impulse response is h(t) = √t². Therefore, the response of the system to the input x(t) = δ(t) is:

y(t) = ∫_{-∞}^{∞} δ(τ) h(t - τ) dτ = ∫_{-∞}^{∞} √τ² dτ

The integral cannot be evaluated in closed form, but it can be evaluated numerically.

To learn more about linear combination click here : brainly.com/question/30341410

#SPJ11

Answer:

1/2 × 10 + 7

=5+7

=12

..................

Answer:

12

Step-by-step explanation:

1/2a+b=

1/2*10 + 7 =

5+7= 12

Answer:

60.57

Step-by-step explanation:

The angle L can be found using the inverse sine function.

L=arcsin(opp/hyp )

L=arcsin(2.7/3.1)

L =60.57129282

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

To learn more about the parallel line from the given link

https://brainly.com/question/24607467

#SPJ4

The probability of obtaining a sample mean between 4.1 and 4.11 in a random sample of size 511 is 0.

To calculate the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in a discrete uniform population with x = 2.4, we can use the properties of the sample mean and the given population.

In a discrete uniform population, all values are equally likely. Since the mean of the population is x = 2.4, it implies that each value in the population is 2.4.

The sample mean is calculated by summing all selected values and dividing by the sample size. In this case, the sample size is 511.

To find the probability, we need to calculate the cumulative distribution function (CDF) for the sample mean falling between 4.1 and 4.11.

Let's denote X as the value of each individual in the population. Since X is uniformly distributed, P(X = 2.4) = 1.

The sample mean, denoted as M, is given by M = (X1 + X2 + ... + X511) / 511.

To find the probability P(4.1 < M < 4.11), we need to calculate P(M < 4.11) - P(M < 4.1).

P(M < 4.11) = P((X1 + X2 + ... + X511) / 511 < 4.11)
           = P(X1 + X2 + ... + X511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(X1 + X2 + ... + X511 < 4.1 * 511)

Since each value of X is 2.4, we can rewrite the probabilities as:

P(M < 4.11) = P((2.4 + 2.4 + ... + 2.4) < 4.11 * 511)
           = P(2.4 * 511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(2.4 * 511 < 4.1 * 511)

Now, we can calculate the probabilities:

P(M < 4.11) = P(1224.4 < 2099.71) = 1 (since 1224.4 < 2099.71)
P(M < 4.1) = P(1224.4 < 2104.1) = 1 (since 1224.4 < 2104.1)

Finally, we can calculate the probability of the sample mean falling between 4.1 and 4.11:

P(4.1 < M < 4.11) = P(M < 4.11) - P(M < 4.1)
                 = 1 - 1
                 = 0

Therefore, the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in the given discrete uniform population is 0.

Learn more about Probability click here :brainly.com/question/30034780

#SPJ11

Answer:

b. one solution

Step-by-step explanation:

hope this helps :)

Answer:

B. One solution

Step-by-step explanation:

Hope this helps!!

$3,000 in an account that earns 4% compound interest after 6 years.

\(p = 3000\)

\(r = 4\)

\(t = 6years\)

\(interest = \frac{prt}{100} \)

\( = \frac{3000 \times 6 \times 4}{100} \)

\( = 720\)

therefore, $720 is the current amount of interest.

Amount of money he get in change is, $2.51

We have to given that;

Olivia buys a University of Florida sweatshirt that costs $37.49.

And, She pays with two $20 bills.

Hence, Amount of money he get in change is,

⇒ 2 x 20 - 37.49

⇒ $40 - $37.49

⇒ $2.51

Thus, Amount of money he get in change is, $2.51

Learn more about the subtraction visit:

https://brainly.com/question/17301989

#SPJ1