Lucy runs at an average speed of 3.5 miles per hour. John runs 2 miles per hour faster than Lucy. How far will John run (r) he runs x number of hours?​

Step-by-step explanation:

I cannot draw here but f(x) + y simply means everything moves up by 6 units.

the line is parallel to the original line and goes now through the points (0, 4) and (1, 8).

The utility function u(x, y) = xy represents monotone and convex preferences.

To prove that the utility function u(x, y) = xy represents monotone and convex preferences, we need to show that it satisfies the conditions of monotonicity and convexity.

Monotonicity:

Monotonicity means that as the quantities of both goods increase, the utility also increases or remains the same.

Let's consider two bundles of goods (x1, y1) and (x2, y2) such that x1 ≥ x2 and y1 ≥ y2.

u(x1, y1) = x1y1

u(x2, y2) = x2y2

Since x1 ≥ x2 and y1 ≥ y2, it follows that x1y1 ≥ x2y2.

Therefore, u(x1, y1) ≥ u(x2, y2), which satisfies the condition of monotonicity.

Convexity:

Convexity means that the average of two bundles of goods yields at least as much utility as any individual bundle in between them.

Let's consider three bundles of goods (x1, y1), (x2, y2), and (x3, y3) such that x1 ≥ x2 ≥ x3 and y1 ≥ y2 ≥ y3.

We need to show that u((x1+x3)/2, (y1+y3)/2) ≥ (u(x2, y2) + u(x3, y3))/2.

First, calculate the utility for each bundle:

u((x1+x3)/2, (y1+y3)/2) = ((x1+x3)/2)((y1+y3)/2)

u(x2, y2) = x2y2

u(x3, y3) = x3y3

Now, let's compare the utility values:

(u((x1+x3)/2, (y1+y3)/2) + u(x3, y3))/2

= (((x1+x3)/2)((y1+y3)/2) + x3y3)/2

= ((x1+x3)(y1+y3) + 2x3y3)/4

= (x1y1 + x3y3 + x1y3 + x3y1 + 2x3y3)/4

= (x1y1 + x3y3 + (x1y3 + x3y1)/2 + x3y3)/4

= (x1y1 + x3y3 + (x1y3 + x3y1 + 2x3y3)/2)/4

= (x1y1 + x3y3 + x3(y1+y3 + 2y3)/2)/4

= (x1y1 + x3y3 + x3(y1+3y3)/2)/4

Since x1 ≥ x2 ≥ x3 and y1 ≥ y2 ≥ y3, it follows that x1y1 + x3y3 + x3(y1+3y3)/2 ≥ x2y2 + x3y3 + x3(y2+3y3)/2.

Therefore, (u((x1+x3)/2, (y1+y3)/2) + u(x3, y3))/2 ≥ (u(x2, y2) + u(x3, y3))/2, which satisfies the condition of convexity.

Hence, the utility function u(x, y) = xy represents monotone and convex preferences.

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Answer:

c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Manjiro is not only brave, but also he is extremely resourceful and one day dreams of becoming a samurai.

The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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No, the assertion made by your buddy is false. It is impossible to utilize the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate itself. You must employ known facts and theorems rather than the theorem you are attempting to show in order to prove a theorem.

If your buddy is utilizing the SSS congruence theorem (Thm. 5.8) and the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate the theorem, they are not offering a proper proof since they are employing the theorem they are attempting to demonstrate as part of the proof itself. This results in a circular argument and is invalid as evidence

The parallelogram opposing sides theorem has to be proven using other well-known facts and theorems, like the definition of a parallelogram, the definition of congruent figures, and other relevant theorems and postulates from geometry.

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Answer:

Reminder: \(log _a x\) answers the question: "what power do I have to raise a to in order to get x?"

Thus said.

\(1. \ 64= 2^6 = 4^3 \implies log_464=3\\2. \ 5^1 = 5 \implies log_55 = 1\\3.\ 3^1=3; \ 2^1=2 \implies Log_33 + log_22 = 1+1=2\\4.\ 5^1=5; \ 8^1=8 \implies log_55 - log_88=1-1=0\\5. \ 8=2^3; 32=2^5 \implies log_28+log_232 = 3+5=8\)

Last one, if you already talked about log properties, can be handled as:

\(log_28+log_232= log_2(8\times32) = log_2256 =8\ (256=2^8)\)

The least-squares regression line is used to predict the values of one variable based on the values of the other variable. In this case, the Verbal score can be predicted from the Math score.

The formula for the least-squares regression line is: Verbal = a + b * Math, where a is the intercept and b is the slope. The least-squares regression line for predicting Verbal score from Math score can be determined using a calculator or a statistical software package.

Once the least-squares regression line has been determined, it can be used to make predictions about the Verbal score for a given Math score. For example, if a student scores 600 on the Math portion of the SAT, the least-squares regression line can be used to predict their Verbal score.

The least-squares regression line is a useful tool for analyzing the relationship between two variables. It can be used to identify patterns and trends, and to make predictions about future values.

However, it is important to remember that correlation does not equal causation, and that other factors may be influencing the relationship between the two variables. The least-squares regression line should be used as a starting point for further analysis, rather than as a definitive answer.

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On solving the provided question, we have the followings roots of the equations as -  x3 - 23x2 + 142x - 120 = (x - 1) (x - 10) (x - 12) and (x-1)(x-2)(x-3)=0

f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real integers and a 0. The cubic function is the cubic polynomial function. The higher cube function, or the fundamental cubic function, is defined as f(x) = x3.

x3 – 6x2 + 11x – 6 = 0.

(x-1)(x-2)(x-3)=0

x3 – 23x2 + 142x – 120.

first factorize

\(x3 - 23x2 + 142x - 120 = (x - 1) (x2 - 22x + 120)\\ But x2 - 22x + 120 = x2 - 12x - 10x + 120\\ = x (x - 12) -10(x - 12)\\ = (x - 12) (x - 10)\\ Therefore,\\ x3 - 23x2 + 142x - 120 = (x - 1) (x - 10) (x - 12)\)

Equate each factor to zero to get;

x = 1

x = 10

x = 12

The roots of the equation are x = 1, 10 and 12.

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Recall that the point-slope form of a line is of the form y=mx+b. We are told that the point (4,1) is on our line and that the slope is 4. This means that m=4. So far, we have the equation

So it only suffices to find the value of b.

Since (4,1) is on this line, it should happen that if we replace x by 4, it must happen that y is 1.

Then, we have the following

So, if we subtract 15 on both sides, we get

Then the equation of the line is

Answer:

x = a³b + b²/ab + 1

Step-by-step explanation:

x = a² + b²/ab + 1

x = a² × (ab + 1) + b²/ab + 1

x = a³b + a² + b²/ab + 1

x = a³b + b²/ab + 1

The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.

An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.

Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.

Angle ABC = Angle ABD + Angle ACD

replacing the specified values:

110° = Angle ABD + 75°

Simplifying:

Angle ABD = 110° - 75°

Angle ABD = 35°

Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:

AC / CD = AB / BD

replacing the specified values:

AC / 10 = 16 / 8

Simplifying:

AC = 20

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Complete Question:

Find the angle ∠ABD jn the given figure

Answer:

its -1

Step-by-step explanation:

cuz

Answer: it’s -1

Step-by-step explanation:

I just did the test

Let's simplify each expression shown in the exercise:

Option a

Given:

You can apply the Product of powers property. This states the following:

Where "b" is the base and "n" and "m" are exponents.

Then, you get:

By definition:

Therefore:

The expression given in Option a is equal to 1.

Option b

Knowing that any number or expression with exponent zero is equal to 1, you get that:

The expression given in Option b is equal to 1.

Option c

Given:

You can notice that the numerator and the denominator are equal, then:

The expression given in Option c is equal to 1.

Option d

Given:

You can simplify it using the Quotient of powers property, which states that:

Then, you get:

The expression given in Option d is not equal to 1.

The answer is: Option d.

Answer:

40

Step-by-step explanation:

The area of the second triangle is 200 square unit.

Given:

the area of the first triangle, A = 8 square unit

let the base of the first triangle = b

let the height of the first triangle = h

then, base of the second triangle = 5b

height of the second triangle = 5h

To find:

the area of the second triangle

The area of the first triangle is given as;

\(A = \frac{bh}{2} \\\\2A = bh\\\\2(8) = bh\\\\16 = bh ---- (1)\)

The area of the second triangle is calculated as;

\(A = \frac{5b \times 5h}{2} \\\\A = \frac{25bh}{2} \\\\recall, bh = 16\\\\A = \frac{25 \times 16}{2} \\\\A = 200 \ unit^2\)

Thus, the area of the second triangle is 200 square unit.

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Answer:

(0,7/2)    (1,17/4)    (2,5)

Step-by-step explanation:

The first two are suppose to be fractions but, I can't make a fraction so yeah...

Good Luck!!!! :) :) :) :)

The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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Answer:

3x+15\(\leq\)7

Step-by-step explanation:

The equation form of the given statement would be 3n + 15 ≤ 7.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

The given statement is "Fifteen more than three times a number is

at most 7"

Let the unknown number be n.

So, the equation form;

3n + 15 ≤ 7

Where n =unknown number

Hence, the equation form of the given statement would be 3n + 15 ≤ 7.

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Answer:

Equation : y = -0.5x − 8

Step-by-step explanation:

because i grabbed two points and plugged them in im not very good at explaining but im 99% sure thats right

The percent of students in grade 8 those who like to join dance club is equal to 25%.

Total number of students in grade 8 = 20

Total number of students of grade 8  join in dance club = 5

Percent of students of grade 8 prefer to join dance club

= ( total number of students prefer dance club ) / ( Total number of students in grade 8 ) × 100

Substitute the value in the formula we get,

⇒ Percent of students of grade 8 prefer to join dance club

= ( 5 ) / ( 20 ) × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 0.25 × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 25%

Therefore, percent of grade 8 students who preferred to join dance club is equal to 25%.  

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The above question is incomplete, the complete question is:

What percent of students in grade 8 prefer to join a dance club?

                      Dance club      Hiking club     Total

Grade 7               15                       15                 30

Grade 8               5                        15                  20

Total                    20                     30                    50

Answer:

The function f(x)= 16-4x forms an arithmetic sequence when x=1,2,3,...

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always the same.

The function f(x) = 16 - 4x forms an arithmetic sequence when x = 1, 2, 3, ...

When x = 1, f(x) = 16 - 4(1) = 12

when x = 2, f(x) = 16 - 4(2) = 8

when x = 3, f(x) = 16 - 4(3) = 4

As you can see, the difference between any two consecutive terms is 4, which is the same for all terms, therefore the function f(x) = 16 - 4x forms an arithmetic sequence when x = 1, 2, 3, ...

On the other hand, the function f(x) = 8 (2)^x increases exponentially, so the values obtained would be not part of an arithmetic sequence. The function f(x) = x^2/5 has no common difference between the consecutive terms, so it is not an arithmetic sequence. The function f(x) = 4/x -2 is not an arithmetic sequence either, due to the division of 4 by x and the subtraction of 2.

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Answer: I see acute, obtuse, and right angle.

Step-by-step explanation:

Answer:

89

Step-by-step explanation:

The y intercept is the value when x = 0

Even when you have 0 hours you still have to pay the service fee

The equation is

y = 35x+89

The y intercept is 89

Answer:

k=f(x)-ab^x-h

h=x-ln(f(x)/a-k/a)/ln(b)

a=f(x)/b^x-h - k/b^x-h

If the scale is

R.F.= 1/2000000

=1/2x 10000x100

1cm=20000m

The scale of a map is given as= 1/2000000

Two town are 4 cm apart on the map.

the actual distance between two towns

=4x 20000

=80000 m

=80000/1000 Km

=80Km

I hope this help you

Answer:

7^4

Step-by-step explanation:

to divide exponents we just subtract what the exponent is so we can write it like this

7^5/7^1= 7^5-1=7^4

Hopes this helps please mark brainliest

Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept

We can use the data given in writing out our equation

390.6 = 14x

If 14 gallons = 390.6 miles

 1 gallon = x miles

x = 390.6 / 14

x = 27.9 miles

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Answer:

x=-8

Step-by-step explanation:

Answer:

D) 32,357mm^3

Step-by-step explanation:

Given

\(Quarters = 40\)

\(Thickness = 1.75mm\)

\(diameter = 24.26mm\)

First, we calculate the volume of 1 roll.

The volume of the cylinder is:

\(V = \pi r^2h\)

Where

\(r = \frac{1}{2} * diameter\)

\(r = \frac{1}{2} * 24.26mm\)

\(r = 12.13mm\)

And the thickness represents the height.

So:

The volume is:

\(V = 3.142 * 12.13^2 * 1.75\)

\(V = 809.03mm^3\)

The volume of the 40 is:

\(Roll= 40 * 809.03mm^3\)

\(Roll=32361.20mm^3\)

The closest option is (d):