Which set of ordered pairs is a function?
{(1,3).(2,4),(3,5),(4,3)}
{(1,3),(1,4),(1,5),(1,3)}
{(2,5),(2,4).(3.4).(4.3)}
{(1,3).(2,8).(3.-6),(1,3)}

Answer:

x = 10.

Step-by-step explanation:

Because the angles are the same, the two triangles are similar. So, we can set up a proportion.

\(\frac{x}{5} = \frac{x-4}{3}\)

5(x - 4) = 3 * x

5x - 20 = 3x

2x = 20

x = 10

Sorry this is really late, but hope it helps!

Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

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Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

Answer:

The Answer is D

Step-by-step explanation:

Answer:

20 ringgits.

Step-by-step explanation:

Ratio of $1:4 ringgits

5 * 4=20

Answer:

0.03215.

Step-by-step explanation:

The exponential function g(x) can be written as g(x) = a ⋅ b^x, where a and b are constants. The table represents the values of x and g(x).

To complete the equation for g(x), we need to find the values of a and b based on the given table. From the table, we can observe that when x = 0, g(x) = 1, and when x = 1, g(x) = 2. Substituting these values into the equation g(x) = a ⋅ b^x, we get:

1 = a ⋅ b^0

2 = a ⋅ b^1

The first equation simplifies to a = 1, since any number raised to the power of 0 is equal to 1. Plugging this value into the second equation, we have:

2 = 1 ⋅ b^1

2 = b

Therefore, the completed equation for g(x) is g(x) = 1 ⋅ 2^x, or simply g(x) = 2^x. This means that the exponential function g(x) is equal to 2 raised to the power of x.

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Answer:

1.5 inches ; 2 inches ; 2.5 inches

Step-by-step explanation:

Given that the original measurement of the triangular sail is :

6 inches, 8 inches and 10 inches

Scale factor = 1/4

Hence, scaled diagram of the triangular sail :

1/4 * (6 inches, 8 inches, 10 inches)

1/4 * 6 = 1.5 inches

1/4 * 8 = 2 inches

1/4 * 10 = 2.5 inches

Answer: Non-collinear, Shows, Are

Answer:

125 sweets

Step-by-step explanation:

Let the total # of sweets the teacher bought be the variable, x.

We can set up this equation to find the # of sweets she bought:

40 · 3 + 5 = x

Because she gave 3 sweets each to her 40 students, we have to multiply these two numbers to get the # of sweets the teacher gave out.

120 + 5 = x

Then, since there's 5 extra sweets left, we can add it to the # of sweets the teacher gave out to get the total amount of sweets she bought.

125 = x

x = 125

125 sweets

Answer:

Total sweets = 125

Step-by-step explanation:

Number of sweets given to each student = 3

Number of sweets given to 40 students = 40*3 = 120

Number of sweets left with the teacher = 5

Total sweets = 120 + 5 = 125

Answer:

2

Step-by-step explanation:

p/2-5

You can use PEMDAS to help:

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

So, first we have to substitute 14 for p to get:

14/2-5

Next, comes division before subtraction, so we can rewrite the equation as this:

(14/2)-5

7-5

=2

Answer:

D

Step-by-step explanation:

Cos(D) = adjacent / hypotenuse

The adjacent side is the one making up angle  D

adjacent side = f

hypotenuse = e

Cos(D) = f/e

D = cos-1(f/e)

The ratio of LM to FG is 3:4, so correct option is A.

A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.

The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.

Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.

Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.

If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).

So we have:

LMN / FGH = 18 / 32

(x²) = 18 / 32

x² = 9 / 16

x = (3 / 4)

Therefore, the ratio of LM to FG is 3:4, which is option A.

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The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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Answer:

Step-by-step explanation:

A)0.000421m^2

C)25000L^2

B)9300000g^2

D)0.001439km^2

The equation or system of equations that can be used to determine the number of cats and dogs Bea has in her pet shop is d = 2c - 5 d + 3 = c + 3. We can solve the system of equations using substitution and plug it back into either equation to find the value of d, which is 8 cats and 10 dogs.

The equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop is:

d = 2c - 5

d + 3 = c + 3

No, Bea's Pet Shop could not initially have 15 cats and 20 dogs. This is because the equation or system of equations states that the number of dogs is five less than twice the number of cats, which would mean that 15 cats would result in 25 dogs, which is not equal to 20.

To determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop, we can use the equation or system of equations that we previously created.

d = 2c - 5

d + 3 = c + 3

We can solve the system of equations using substitution:

d = 2c - 5

d + 3 = c + 3

d + 3 = c + 3

d = c + 3

2c - 5 = c + 3

2c = c + 8

c = 8

Once we determine the value of c, we can plug it back into either equation to find the value of d:

d = 2(8) - 5

d = 15 - 5

d = 10

Therefore, Bea initially had 8 cats and 10 dogs in her pet shop.

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The complete question is: At Bea's Pet Shop, the number of dogs, d, is initially five less than twice the number of cats, c. If she decides to add three more of each, the ratio of cats to dogs will be – Write an equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop. Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning. Determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop.​

Answer:

Step-by-step explanation:

Inverse relationship equation:

1)

2)

Required equation:

Use the initial values to find the value of k:

Find a when b = 4:

Option C

3)

Required equation:

Find k:

Find x when y = 3:

Option D

4)

Required equation:

Find k:

Find a when b = - 15:

Option C

5)

Required equation:

Find k:

Find t when N = 16:

Option B

The answer to the given question is true. A chart where the data is arranged in vertical columns is called Column Chart, and this chart is useful for showing data changes over time or illustrating comparisons among items.

What is column chart?

Column chart is a type of chart that compares different object levels over time using a vertical format. It is a chart in which the data is arranged in columns and this is useful for showing data changes over a period of time or for illustrating comparisons among items.

Data that is arranged in columns or rows on a worksheet can be plotted in a column chart. In column charts, categories are typically organized along the horizontal axis and values along the vertical axis. Column charts are useful to show how data changes over time or to show comparisons among items.

Column charts are not useful when there are a lot of categories. Catagories organized along the x-axis, while numbers or numerical values ligned in the y-axis.

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The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer:

slope = - \(\frac{3}{2}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (- 6, - 5 ) and (x₂, y₂ ) = B (- 4, - 8 )

m = \(\frac{-8-(-5)}{-4-(-6)}\) = \(\frac{-8+5}{-4+6}\) = \(\frac{-3}{2}\) = - \(\frac{3}{2}\)

The equation that represents n; the number of pages Steph read on Monday is B (52 − 16) × 2 = n

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.

The following can be deduced:

Lara read 52 pages.

Jack read 16 fewer pages than Lara.

Steph read 2 times as many pages as Jack.

The pages for Steph will be:

= 2(52 - 16)

In conclusion, the correct option is B.

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Answer: C. 512

Step-by-step explanation:

V= s^3

V= 8 x 8 x 8 = 512 cubic inches

Therefore, the absolute maximum value of f on the interval [−1, 5] is approximately 5 - 3√5, and the absolute minimum value does not exist (it is not a real number).

To find the absolute maximum and absolute minimum values of the function f(t) = t - 3√t on the interval [−1, 5], we need to evaluate the function at critical points and endpoints.

Critical points:

We find the critical points by taking the derivative of the function and setting it equal to zero:

f'(t) = 1 - (3/2)√t^(-1/2) = 0

Solving for t:

(3/2)√t^(-1/2) = 1

√t^(-1/2) = 2/3

t^(-1/2) = 4/9

t = (9/4)^2

t = 81/16

However, we need to check if this critical point falls within the given interval [−1, 5]. Since 81/16 is greater than 5, we discard it as a critical point within the interval.

Endpoints:

Evaluate the function at the endpoints of the interval:

f(-1) = -1 - 3√(-1) ≈ -1 - 3i

f(5) = 5 - 3√5

Now, we compare the values obtained at the critical points and endpoints to determine the absolute maximum and minimum values.

f(-1) ≈ -1 - 3i (Not a real number)

f(5) ≈ 5 - 3√5

Since f(5) is a real number and there are no critical points within the interval, the absolute maximum and absolute minimum occur at the endpoints.

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Answer:

is it from a text book

Step-by-step explanation:

Let L = length, W = width and P =Perimeter

L = 3W

and

P + 2(L + W) = 120

L + W = 60

Substitute

3W + W = 60

4W=60

W=60/4

W=15

L+W=60

L+15=60

L=60-15

L=45

The graph of the exponential function y = 2(9/5)ˣ is attached below

The graph of an exponential function has the general form of y = a^x, where "a" is the base of the exponential function and "x" is the exponent. The graph of an exponential function has some distinctive features:

1. The domain of the function is all real numbers.

2. The range of the function is positive real numbers.

3. The graph of an exponential function always passes through the point (0, 1), because any number raised to the power of zero is one.

As x approaches negative infinity, the graph of the function approaches the x-axis, but never touches it.

As x approaches positive infinity, the graph of the function approaches the y-axis, but never touches it.

4. The graph of an exponential function is always increasing or always decreasing, depending on whether the base "a" is greater than one or less than one, respectively.

5.The graph of an exponential function becomes steeper and steeper as it moves away from the y-axis, indicating that the function is growing or decaying at an increasing rate.

The graph of y = 2(9/5)ˣ is attached below using the table of values given;

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a) We have shown an example where A[t] · V[t] = 0, indicating that the speed is not changing at that specific time, but the velocity is changing.

b) We have proved that dy/dt = "the scalar component of A[t] in the direction of V[t]" for this particular motion where the speed is constant.

To demonstrate that a motion could have A[t] · V[t] = 0, where A[t] represents acceleration and V[t] represents velocity, we can consider an example where the motion occurs along a curved path.

Let's assume the motion of an object on a circle with a constant radius r.

In polar coordinates, we can express the position vector as x[t] = r(cos(t), sin(t)), where t is the parameter representing time. Taking the derivative of x[t] with respect to time, we obtain the velocity vector:

v[t] = (dx/dt, dy/dt)

     = (-r sin(t), r cos(t)).

The speed, denoted by v[t], is the magnitude of the velocity vector:

|v[t]| = \(\sqrt{((-r sin(t)}^2 + (r cos(t))^2) = \sqrt{(r^2 (sin^2(t) + cos^2(t)))}\)

                                                    = r.

As we can see, the speed is constant and equal to r, which means it does not change with time.

Now let's calculate the acceleration vector A[t]:

A[t] = (dv/dt)

      =\((d^2x/dt^2, d^2y/dt^2).\)

Differentiating the velocity vector v[t] with respect to time, we obtain:

(dv/dt) = (-r cos(t), -r sin(t)).

The dot product of A[t] and V[t] is given by:

A[t] · V[t] = (-r cos(t), -r sin(t)) · (-r sin(t), r cos(t))

              = \(r^2\) (cos(t) sin(t) - cos(t) sin(t))

              = 0.

Therefore, we have shown an example where A[t] · V[t] = 0, indicating that the speed is not changing at that specific time, but the velocity is changing.

Now let's prove the derivative of speed satisfies dy/dt = "the scalar component of A[t] in the direction of V[t]."

We have already established that the speed v[t] is constant (let's denote it as v) in this case. So, we can write:

v[t] = v.

Differentiating both sides with respect to time, we get:

dv[t]/dt = 0.

Now, let's express the velocity vector v[t] in terms of its components:

v[t] = (dx/dt, dy/dt).

Taking the derivative of v[t] with respect to time, we have:

dv[t]/dt = \((d^2x/dt^2, d^2y/dt^2)\).

The magnitude of the acceleration vector A[t] is the derivative of speed:

|A[t]| = \(\sqrt{((d^2x/dt^2)^2 + (d^2y/dt^2)^2)}\)

Since we know that dv[t]/dt = 0 (from the constant speed), the acceleration vector A[t] is orthogonal to the velocity vector V[t].

Now, let's consider the scalar component of A[t] in the direction of V[t]. We can calculate it by taking the dot product of A[t] and V[t] and dividing it by the magnitude of V[t]:

(A[t] · V[t]) / |V[t]| = (A[t] · V[t]) / v.

But we have established that A[t] · V[t] = 0, so the numerator is zero:

(A[t] · V[t]) / |V[t]| = 0 / v = 0.

Thus, we have shown that the derivative of speed, dy/dt, is equal to the scalar component of A[t] in the direction of V[t], which is 0 in this case.

Therefore, we have proved that dy/dt = "the scalar component of A[t] in the direction of V[t]" for this particular motion where the speed is constant.

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Complete Question:

let x[t] be a parametric motion and denote speed v[t]=|V[t]|=\(\sqrt{[v[t].v[t]]}\), where velocity is v[t]=\(x^{'}[t]\).                                                                                                                                                                                           a) Show by example that a motion could have A[t] V[t] = 0, so the speed is not changing (at least at that time), but the velocity is changing (at that time.)

b) Prove that the derivative of speed satisfies dy/dt = "the scalar component of A[t] in the direction of V[t]"

The high temperature for today using a 3-day moving average is 92 degrees.

To calculate the high temperature for today using a 3-day moving average, we take the average of the temperatures from the past three days, including today.

Given the daily high temperatures in St. Louis for the last week:

92, 92, 93, 95, 95, 86, 95 (yesterday)

To find the 3-day moving average for today's high temperature, we consider the temperatures from yesterday, the day before yesterday, and three days ago.

(95 + 86 + 95) / 3 = 92

Therefore, the high temperature for today, calculated using a 3-day moving average, is approximately 92 degrees Fahrenheit, rounded to one decimal place.

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Answer:

0.8,0.91,1/10,3/100

0.6,0.9,0.21,0.35,7/10,11/100

0.2,0.5,1/10,0.44,8/100

Step-by-step explanation:

Answer:

0.8,0.91,1/10,3/100

0.6,0.9,0.21,0.35,7/10,11/100

0.2,0.5,1/10,0.44,8/100Step-by-step explanation: IVE DONE THIS BEFORE TOO

Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

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Answer:

18

Step-by-step explanation:

Answer:

18 or 19 or 21 or 27

Step-by-step explanation:

(a) To show that y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem dy/dt = e⁻ᵗ², y(0) = 0, we differentiate y(t) with respect to t and substitute the given differential equation and initial condition.

(b) To approximate the integral ²∫₀ e⁻ᵘ² du using the Euler Method with h = 1/2, we divide the interval [0, 2] into subintervals of width h and approximate the integral using the formula: ∑[f(u(i))*h], where f(u(i)) represents the function evaluated at each subinterval.

(a) To show that y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem dy/dt = e⁻ᵗ², y(0) = 0, we first differentiate y(t) with respect to t. Using the Fundamental Theorem of Calculus, we have:

dy/dt = d/dt [ᵗ∫₀ e⁻ᵘ² du]

Applying the Leibniz rule for differentiating under the integral sign, we obtain:

dy/dt = ∫₀ e⁻ᵘ² du

Now we substitute the given differential equation dy/dt = e⁻ᵗ² and the initial condition y(0) = 0:

e⁻ᵘ² = e⁻ᵗ²

Since e⁻ᵘ² and e⁻ᵗ² are equal, the given function y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem.

(b) To approximate the integral ²∫₀ e⁻ᵘ² du using the Euler Method with h = 1/2, we first divide the interval [0, 2] into subintervals of width h = 1/2. In this case, we will have four subintervals: [0, 1/2], [1/2, 1], [1, 3/2], and [3/2, 2].

Using the Euler Method, we approximate the integral within each subinterval by evaluating the function e⁻ᵘ² at the left endpoint of the subinterval and multiplying it by the width of the subinterval. Then, we sum up these approximations for all subintervals.

For example, in the first subinterval [0, 1/2], the approximation would be:

Approximation for

[0, 1/2] = e⁻⁰² * (1/2) = (1/2)

Similarly, we can calculate the approximations for the other subintervals:

Approximation for

[1/2, 1] = e⁻¹/₂² * (1/2) ≈ (0.60653/2)

Approximation for

[1, 3/2] = e⁻¹² * (1/2) ≈ (0.13534/2)

Approximation for

[3/2, 2] = e⁻³/₂² * (1/2) ≈ (0.18394/2)

Finally, we sum up these approximations:

Approximation for

²∫₀ e⁻ᵘ² du ≈ (1/2) + (0.60653/2) + (0.13534/2) + (0.18394/2)

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