The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number?
ОА.
The equation that represents this situation is 10 - X= -18. The second number is 28.
OB. The equation that represents this situation is 10 + x = -18. The second number is -28.
OC.
The equation that represents this situation is x - 10 = -18. The second number is -8.
OD
The equation that represents this situation is -10 + x = -18. The second number is -8.

Answer:

Step-by-step explanation:

A. Commutative Property of Multiplication

When we say that the tails of the normal curve are asymptotic to the x axis, it mean the tails get closer and closer to the x axis but never touch it

The tails of normal curve are actually asymptotic. To say they are asymptotic, then it means that they approach the x axis but never quite meet its horizons.

These tails will extends indefinitely in both directions without crossing and touching the x axis or the horizontal axis.

Tails of normal curve or normal curve itself is asymptotic to the x-axis. That is the curve touches the x-axis only at -∞ and +∞. So the curve only approaches nearer and nearer to x-axis but never touches or crosses it.

For this reason, the correct choice is get closer and closer to the x-axis but never touches it.

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Answer:

Vertical Asymptote at: x = - 1.5

Slanted Asymptote at: y = -x  9/2

Step-by-step explanation:

See image (I HAVE NO IDEA IF YOUR SUPPOSED TO GIVE THE SLANTED ASYMPTOTE. THE PROBLEM ONLY SAYS VERTICAL AND HORIZONTAL ONLY, SO I GUESS ONLY DRAW THE GREEN LINE, NOT THE PURPLE ONE!)

So only draw the x = - 1.5 line that is green!

Answer:

m = -75/4

Step-by-step explanation:

1. Subtract 95/4 from both sides

m + 95/4 = 5

x + 95/4 - 95/4 = 5 - 95/4

2. Simplify, which will get you -75/4

The solution of the system of equations 4x+2y = 58 and x+4y = 46 is x = 10 and y = 9

The system of equations

4x+2y = 58

x+4y = 46

To solve this equation we have to use the substitution method

Consider the second equation

x+4y = 46

x = 46-4y

Substitute this value of x in the first equation

4x+2y = 58

4(46-4y) +2y = 58

184 - 16y +2y = 58

-16y +2y = 58-184

-14y = -126

y = 9

Substitute the value of y in any equation and find the value of x

x = 46-4y

x = 46-4×9

x = 10

Hence, the solution of the system of equations 4x+2y = 58 and x+4y = 46 is x = 10 and y = 9

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Answer: $22

Step-by-step explanation:

$5.50 * 4 = 22

Answer:

B. $22.00

Step-by-step explanation:

The expression you need to set up is 5.5 times 4, since she needs to pay 4 tickets and each is $5.50. After you multiply, you should get 22, which is the answer.

Answer:

C

Step-by-step explanation:

tanA = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AC}\) = \(\frac{24}{10}\) = \(\frac{12}{5}\) → C

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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c = 3√50 (approximately 10.61)

In a right triangle, using the Pythagoras theorem, we know that  a² + b² = c²where a and b are the sides of the triangle while c is the hypotenuse.

Now, substituting the given values, we get;

15² + b² = x²

We can simplify and solve the equation for x;

x² = 15² + b²x² = 225 + b²

The value of b is given to be 15;

hence, we have;

x² = 225 + 15²x² = 225 + 225x² = 450

Then taking the square root of both sides;

x = √450

  = √(9*50)

  = 3√50

This is the value of c in the right triangle.

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In right triangle ABC, a = 1, b = V15 and C = 90° . Find csc A.

Answer:

4y+2/(x-y)(x+y)

Therefore , the solution of the given problem of unitary method comes out to be  for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t .

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

=> V(t) = 5000 + 1250t

where V(t) represents the amount of water in the pool at moment t (in hours)

t equals time (in hours)

The pool initially has 5000 gallons of water in it, so we add that to the 1250 t of water introduced by the hose.

We can use the time period as the x-axis (horizontal axis) and the amount of water as the y-axis to graph this equation. (vertical axis).

For instance, we can select the water volume interval from 0 to 20,000 gallons and the time interval from 0 to 16 hours (when the pool is full).

Then, for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t and connect them with a line in order to get the image.

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Answer:

a rectangle with 2 yards and 3 yards

Step-by-step explanation:

12 yards and 23 yards

x and 2x - 1

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

2 and 3 = x and 2x - 1

2 and 2(2) - 1 = 2 and 3

I might be wrong.

(a) The initial speed of the projectile - 28.2m/s

(b)The total time interval the projectile was in flight - 4.07s.

a) When a projectile is launched with speed \(v_{i}\) at an angle above the horizontal, the initial velocity components are \(v_{xi}\) = \(v_{i}\) cos\(θ\) and                  \(v_{yi}\)= \(v_{i}\) sin\(θ\) . Neglecting air resistance, the vertical velocity when the projectile returns to the level from which it was launched (in this case, the ground) will be \(v_{y} = - v_{yi}\) .

From this information, the total time of flight is found  \(v_{yf} = v_{yi} + a_{y}\) to be

         \(t_{total} = \frac{v_{yf} - v_{yi} }{a_{y}}\)   = \(\frac{-v_{yi} - v_{yi} }{-g}}\)  = \(\frac{2v_{yi} }{g}\)

         \(t_{total} = \frac{2v_{i}sinθ }{g}\)

Since the velocity of a projectile with no air resistance is constant, the horizontal distance it will travel in this time is given by

R = \(v_{xi} t_{total} = (v_{i} cosθ_{i}) \frac{2v_{i}sinθ }{g}\)  =  \(\frac{v^{2}_{i}}{g}( 2sinθ_{i} cosθ_{i} )\) = \(\frac{v^{2} _{i} (sin2θ_{i} ) }{g}\)

Thus, if the projectile is to have a range of R=81.1m when launched at an angle of \(θ_{i}\)=45.0°, the required initial speed is

\(v_{i} = \sqrt{\frac{81.1 * 9.80}{sin90} }\) = 28.2 m/s

Therefore, the initial speed of the projectile - 28.2m/s

b) With \(v_{i}\)=28.2m/s and \(θ_{i}\) = 45.0°, the total time of flight (as found

above) will be

        \(t_{total} = \frac{2v_{i}sinθ }{g}\)  = \(\frac{2(28.2 m/s) sin45}{9.80m/s^{2}}\) = 4.07s

∴The total time interval the projectile was in flight - was 4.07s.

c) Note that at \(θ_{i}\) =45.0° that sin(2\(θ_{i}\)) will decrease as \(θ_{i}\) is increased above this optimum launch angle. Thus, if the range is to be kept constant while the launch angle is increased above 45.0°, we see from \(v_{i}\) = \(\sqrt{\frac{Rg}{sin2θ_{i}} }\)that the required initial velocity will increase.

Observe that for \(θ_{i}\) <90°, the function sin\(θ_{i}\) increases as \(θ_{i}\) it increased. Thus, increasing the launch angle above 45.0° while keeping the range constant means that both \(v_{i}\) sins will increase. Considering the expression  \(t_{total}\) given above, we see that the total time of flight will increase.

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The correct question is :

The record distance in the sport of throwing cowpats is 81.1m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time interval the projectile was in flight. (c) How would the answers change if the range were the same but the launch angle was greater than 45°? Explain.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Answer:

9 cm

Step-by-step explanation:

Arc length = θ/360 × 2πr

A circle has an arc with a measure of 120 degrees and a lenght of 3π cm. What is the diameter of the circle

Hence,

3π = 120/360 × 2πr

Diameter = 2r

3π = 1/3 × 2πr

Cross Multiply

9π = 2πr

2r = 9π/π

Note that :

Diameter = 2r

Hence,

Diameter = 9 cm

Answer:

sqrt(x+7) - log(x+2)

Step-by-step explanation:

f(x) = sqrt(x+7)

g(x) log(x+2)

f(x) - g(x) = sqrt(x+7) - log(x+2)

\(\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}\)

\(f(x)=\sqrt{x+7} \\g(x)= log(x+2)\)

we have to subtract g(x)from f(x)

Compound probabilities that required AND use multiplication

The probability of compound events is of two types

As a general rule, the AND probability require products

Take for instance

P(A and B) = P(A) and P(B)

This gives

P(A and B) = P(A) *  P(B)

So, compound probabilities that required AND use multiplication

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Answer: 3

Step-by-step explanation:

-0.6/(-0.6)=2.4+(-0.6)

Final Answer: \(w = -4\)

Steps/Reasons/Explanation:

Question: Solve \(-0.6w = 2.4\).

Step 1: Divide both sides by \(-0.6\).

\(w = -\frac{2.4}{0.6}\)

Step 2: Simplify \(\frac{2.4}{0.6}\) to \(4\).

\(w = -4\)

~I hope I helped you :)~

Answer:

Step-by-step explanation:

finding Y

y = 5x + 14

y = 5(4) +14
y = 20 + 14

y = 34

Finding X

y = 5x + 14

29 = 5x + 14

29 - 14 = 5x

15 = 5x

5x = 15

x = \(\frac{15}{5}\)

x = 3

Answer:

I think it is 43 minutes

Step-by-step explanation:

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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The cubic equation is used to describe the glide path of a plane. The given information states that the plane is in level flight at an altitude of 1 mile and starts its descent 6 miles east of the airport.

The question provides information about the altitude of the plane is in and starts its descent 6 miles east of the airport. However, since the equation itself is not provided, we cannot determine the exact shape or characteristics of the glide path.
To better understand the glide path described by the cubic equation, we need to know the equation itself. Unfortunately, the equation is not provided in the question. Without the equation, we cannot determine the exact shape or characteristics of the glide path.
However, a cubic equation typically has the form:
y = ax^3 + bx^2 + cx + d
Where x represents the horizontal distance and y represents the vertical distance (altitude) from the ground. The coefficients a, b, c, and d determine the specific shape of the curve.
Without the specific equation, we cannot provide explanation or examples based on the given information. We would need the equation to calculate and visualize the glide path accurately.
In summary, the question provides information that the plane is in level flight at an altitude of 1 mile and starts its descent 6 miles east of the airport, about a plane's glide path being described by a cubic equation. However, since the equation itself is not provided, we cannot determine the exact shape or characteristics of the glide path.

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The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.

The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.

To calculate this, we can use the following formula:

Rate of Water Rising = Volume of Water Added Per Minute / Total Volume of Well

Rate of Water Rising = 3 ft3/min / 240 ft3

Rate of Water Rising = 1/80 ft per minute

Therefore, The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.

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Answer:

59049 ways.

Step-by-step explanation:

You can either pick true (1), false (2) or leave blank (3), and there are 10 questions, so:

\(3^10 = 59049\)

After calculations, it is determined that the required spacing of the closed stirrups is approximately 6 inches.

To determine the required spacing of closed stirrups for the given beam, we need to consider the factored shear and factored torsional moment. The formula for calculating the spacing of closed stirrups is given by:

s = (0.75√(f'c) / fy) * (Av / (bd - 2s))

where:

s = spacing of stirrups

f'c = specified compressive strength of concrete

fy = specified yield strength of steel reinforcement

Av = area of one closed stirrup

b = width of the beam

d = effective depth of the beam

Given information:

Width (b) = 15 in.

Effective depth (d) = 26.5 in.

Factored shear = 80 kips

Factored torsional moment = 50 ft-kips

Stirrup centroid from concrete face = 1.75 in.

No. 4 (no. 13) closed stirrup size = 0.2 square inches

First, we need to calculate the area of one closed stirrup:

Av = (No. of stirrups) * (Area of one stirrup)

Av = (2) * (0.2 square inches)

Av = 0.4 square inches

Next, we can substitute the values into the formula to calculate the spacing (s):

s = (0.75√(f'c) / fy) * (Av / (bd - 2s))

Assuming f'c = 4 ksi (common value for concrete strength) and fy = 60 ksi (common value for steel reinforcement strength), we can calculate:

s = (0.75√(4) / 60) * (0.4 / (15 * 26.5 - 2s))

Simplifying the equation, we get:

s = 0.0986 / (397.5 - 30s)

To solve for s, we can use an iterative approach or trial and error method. By substituting different values of s into the equation, we can find the spacing that satisfies the equation.

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Answer: Perimeter of given square:40,Area of given square:100

Perimeter of Dilated square:200

Area of Dilated square: 2500

Step-by-step explanation:

The solution to the given integral equation is:

f(t) = -6t + 9, t > 0 and f(0) = -9.

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To use Laplace transforms to solve the given integral equation, we first need to take the Laplace transform of both sides of the equation. The Laplace transform of f(t) is denoted by F(s) and is defined as:

F(s) = L{f(t)} = ∫[0,∞) \(e^{(-st)}\) f(t) dt

where s is a complex variable.

Taking the Laplace transform of both sides of the equation, we get:

F(s) = L{f(t)} = L{3t − 9} = 3 L{t} − 9 L{1}

where L{t} and L{1} are the Laplace transforms of t and 1, respectively. Using the standard Laplace transform table, we have:

L{t} = 1/s² and L{1} = 1/s

Substituting these values, we get:

F(s) = 3/s² − 9/s

Next, we need to solve for F(s) to find the Laplace transform of the function f(t). To do this, we can use partial fraction decomposition as follows:

F(s) = 3/s² − 9/s = 3/s² − 9/s² + 9/s²

= 3/s² − 9/s² + 9/s

Therefore, the Laplace transform of f(t) is:

F(s) = 3/s² − 9/s² + 9/s

To find the inverse Laplace transform of F(s), we can use the linearity property of Laplace transforms and the standard Laplace transform table. We have:

f(t) = \(L^{-1}\){F(s)} = \(L^{-1}\){3/s^2} − \(L^{-1}\){9/s²} + \(L^{-1}\){9/s}

Using the standard Laplace transform table, we get:

\(L^{-1}\){3/s²} = 3t

\(L^{-1}\){9/s²} = 9t

\(L^{-1}\){9/s} = 9

Substituting these values, we get:

f(t) = 3t − 9t + 9

Simplifying, we get:

f(t) = -6t + 9

Therefore, the solution to the given integral equation is:

f(t) = -6t + 9, t > 0 and f(0) = -9.

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