The tail of a 1-mile long train exits a tunnel exactly 3 minutes after the front of the train entered the tunnel. If the train is moving 60 miles per hour, how long is the tunnel? Hint : How far does the front of the train move in 3 minutes?

In the series of a value of a(4)=216

What do the terms sequence and series mean?

Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of the elements in a sequence, which is a group of arranged elements that follow a pattern. The formulas for the nth term and the sum are typically included in the sequence and series formulas.

Given that:

a(1) = 8

a(n)= 3a(n-1)

so a(4) = 3a(3) = 72*3 = 216

a(3)= 3a(2) = 24*3 = 72

a(2)= 3a(1) = 3*8 = 24

Hence a(4) = 216

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Answer:208

Step-by-step explanation:

204+206+208.

Step-by-step explanation:

let the even numbers be :

x+(2+x)+(4+x)

so 3x+6=618

3x=618-6

3x/3=612/3

x=204

Answer:

4

Step-by-step explanation:

If I'm reading it correctly, x is multiplied by 6 to equal y.

So, 3(x) x 6 = 18(y)

Therefore, 24/6 = 4 OR,  4(x) x 6 = 24(y)

Answer:

90-15=75

75/90= 5/6

ans: 5/6

1/6

We can combine the two numbers together to get the fraction we are looking for:

15/90

By simplifying, we get:

1/6

We get this answer by dividing the highest possible number by both fractions. In this case, the number would be 15:

15 ÷ 15 = 1

90 ÷ 15 = 6

1/6

1/6

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The equation of the inequality graph with dashed line

The equation of the inequality graph with solid line

Using the slope intercept form of the straight line which is of the form

y = mx + c

The slope, m is the ratio of the change in the output to the change in the input. This is given by the formula

m = (y₀ - y₁) / (x₀ - x₁)

Slope calculation using the points (0, -4) and  (2, 0)

m = (-4 - 0) / (0 - 2)

m = 2

y intercept, c from the graph

c = -4

applying inequality representations

shading above the line is greater than and dotted lines means it does not have equal to

hence y > 2x - 4

for the solid line graph

the slope, m calculating using the points on the graph (0, 4) and  (4, 0)

m = (4 - 0) / (0 - 4)

m = (4) / (-4)

m = -1

y intercept, c from the graph

c = 4

The equation of the line is y = -x + 4

Solid lines indicate an equality in the inequality, while shading over the line indicates a greater than

hence y ≥ -x + 4

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There is an 8.1% probability that any given distance will exceed 212.50 cm.

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

I frequently remind kids that we can express probabilities as ratios, percentages, fractions, or decimals so they are aware of the variety of ways we express odds.

So, the probability that the individual distance is greater:

z = 212.50-200/8.9 = 1.4

Looking up 1.4 in the normal distribution table:

P(z>1.4) = 1 - 0.9192 = 0.0808

= 8.1%

Therefore, there is an 8.1% probability that any given distance will exceed 212.50 cm.

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Complete question:
The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.9 cm.

a. find the probability that an individual distance is greater than 212.50 cm.

The coefficient in the expression is 25.

Given is the following expression -

f(p, q) = 25pq

The coefficient in the expression is 25.

Therefore, the coefficient in the expression is 25.

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Answer:

25

Step-by-step explanation:

The measure of angle ∠C = 35°, 2x = 50° and x = 25°.

In Euclidean geometry, an angle is made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively.

Angles can be formed by two rays in the plane where they are placed.

Additionally, when two planes overlap, angles are created.

Dihedral angles are what they are called.

So, m∠ABC:

We know that ∠C in triangle ABC = 180 - 145 = 35°

Now, the measure of  m∠ABC:

95 + 35 + 2x = 180

130 + 2x = 180

2x = 180 - 130

2x = 50°

x = 50/2

x = 25°

Therefore, the measure of angle ∠C = 35°, 2x = 50° and x = 25°.

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Answer: 160

Step-by-step explanation: If I remember correctly, the formula for finding the rate is:

r = d/t

So, rate = 640/4

When I divided it, I got 160.

I hope this helped!

Answer:

25.6

Step-by-step explanation:

while i do not know how to do this is dod use a rate calculator so hopes this help!

The required parameters of a smaller surface area and a smaller amount of metal per can are a radius of 3.05 cm and a height of 6.09 cm.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. A three-dimensional shape's surface area is the sum of all of its faces. Finding the area of each face and adding them together gives us the surface area of a form.

Here,

V=πr²h

178=πr²h

πrh=178/r

S=2πr²+2πrh

S=2πr²+2*(178/r)

S=2πr²+356/r

S'=4πr-356/r²

S'=0

4πr=356/r²

r³=356/4π

r³=28.343

r=3.05 cm

h=178/πr²

h=178/(3.14*3.05*3.05)

h=178/29.23

h=6.09 cm

The dimensions needed for less surface area so each can uses less metal is radius as 3.05 cm and height as 6.09 cm.

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Answer:

2.94

Step-by-step explanation:

I just found 1%

Which is 0.98

then times that by 3 which is 2.94

hope that helps!

The number based on the information given is 3.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

In this case, three times the difference of four times a number and two decreased by the sum of the number and five equals 22.

Let the number be x

3(4x - 2) - (x + 5) = 22

12x - 6 - x - 5 = 22

11x - 11 = 22

11x = 22 + 11

11x = 33

Divide

x = 33 / 11

x = 3.

The number is 3

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Answer:

-----------------------------

Given three consecutive terms of a GP:

The middle term is the geometric mean of the other terms. Therefore:

The matching choice is D.

The value of the given expression, 67π × 7, is 1473.4

From the question, we are to determine the value of the given expression.

From the given information,

The given expression is

67π × 7

To determine the value of the expression, we will evaluate the expression step-wisely.

Evaluate 67π

67π = 210.4867

Multiply by 7

210.4867 × 7

= 1473.4069

≈ 1473.4

Hence, the value is 1473.4

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Answer:

A. Can be written in a fraction.

Step-by-step explanation:

Do you need any help..

Rational number can be any number that can also be wrote as a ratio or fraction of two integers would be commonly known as a rational number…

The probability that X is greater than 53

What is probability ?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Formula for calculating the standard score or z score:

z = x-μ/σ, where:

z is the standard score

x is the raw score

μ is the population mean

σ is the population standard deviation

In this question: μ = 61 and σ = 8

The score is greater than 53

Let’s calculate the z score, for x = 53 and then find the probability for x greater than 53

z = (53 - 61)/8

  = -8 / 8

  = -1

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The area of the circle with the given radius would be = 12.56m².

A circle is defined as the figure that do not posses any form of edges or corners and is known as a two dimensional figure with a center of 360°.

The area of the circle can be gotten when the radius is given.

The formula used for the calculation of the area of a circle = πr²

Where,

Pie (π) = 3.14 or 22/7

Radius (r) = 2 m

Area = 3.14 × 2²

= 3.14 ×4

= 12.56 m²

Therefore, the area of the given circle would be = 12.56m².

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Answer:

The slope of both equations is 7.  Yes, since the slopes are the same, the lines are parallel.

Step-by-step explanation:

For both equations, as the x increased by 1, the y increased by 7.

The speed of Zihao to open the door, when toilet is on 25 m in front of the door for 5 sec is 5m/sec.

The formula used to explain the relationship between speed, distance, and time is speed distance time. That is speed = distance time. Alternatively, you can calculate the time by dividing the distance traveled by the speed. You can figure out the third input if you know two of the inputs. For instance, the length of the line segment that connects two points equals the distance between them. The formula for finding the distance between two points in a two-dimensional plane—which can be expanded to discover the distance between two points in a three-dimensional plane as well—is derived using the Pythagoras theorem.

Given,

Distance=25m

Time=5sec

Speed?

We know that,

Speed=Distance/Time

Speed=25/5

Speed=5m/sec

Therefore, the speed of Zihao to open the door, when toilet is on 25 m in front of the door for 5 sec is 5m/sec.

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Answer: A.-20

Step-by-step explanation:

Since x=4

substitute in and solve

h(4)=-5(4)

h(4)=-20

Answer:

Step-by-step explanation:

when x=4, then h(x)=-5 * 4=-20

Therefore, choose A

After the substitution 2(3y - 17) +3y = -7 is the answer of the system of equation.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given system of the equation,

x = 3y - 17      {equation 1}

2x + 3y = -7         {equation 2}

Substitute the value of x from the equation 1 to equation2,

2 (3y - 17) + 3y = -7

Therefore, after the substitution 2(3y - 17) +3y = -7 is the answer of the system of equation.

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Answer:

486

Step-by-step explanation:

area of a cube =6x²

length= 9

area=6×9²

=6×81

=486

The value will be $371.39.

Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

The formula to calculate the compound amount after t years is given by :-

A =P [tex](1 + R)^{T}[/tex]

where the interest rate is r and P represents the principal amount.

Given: $150 is the principal sum.

Interest is charged at a rate of 12%/0.12

A = 150 will be the amount compounded after 8 years.

A = 150 [tex]( 1 + 12 )^{8}[/tex]

A =371.3944

A = $371.39

Hence, the value of $150 after eight years if you earn 12 percent interest per year would be $371.39.

option a. is right

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Congruence is a property between two or more shapes that proves that they are equal in all respect. The required proof in the given question is shown below:

Two or more figures are said to be congruent if and only if they have equal length of sides, or measure of interior angles.

A triangle is a plane shape bounded by three straight sides, with three interior angles. The series properties can be used to classify the types of triangles with respect to their sides and angles. Some types of triangles are; equilateral, isosceles, right angled, acute angles scalene etc.

Thus to prove that: ΔADE ≅ Δ CDF

                               ΔBDE ≅ ΔBDF

AD ≅ DC (congruent property of similar figures)

AE ≅ CF (similarity property)

DE ≅ DF (congruent property of similar figures)

Thus,

ΔADE ≅ ΔCDF (SSS congruent property)

Also,

EB ≅ FB (congruent property of similar figures)

BD (common side of congruent figures)

DE ≅ DF (congruent property of similar figures)

So that,

ΔBDE ≅ ΔBDF (SSS congruent property)

This implies that,

i ΔADE + ΔBDE = ΔABD

ii. ΔCDF + ΔBDF = CBD

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Answer:

A

Step-by-step explanation:

Option A is the only Option with the correct domain.

○ (ƒ − g)(x) = x² − 11x +4 is the correct Answer

Answer:

ƒ(x) = 4x² – 5

g(x) = 3x² + 6x − 4.

(ƒ – g)(x) = ƒ(x)–g(x)

= 4x² – 5 –(3x² + 6x − 4)

= 4x²–5x –3x²–6x+4

= 4x²–3x² –5x–6x +4

= x² − 11x +4

[tex] [/tex]

Thank you