Mario start collecting stamps in January and buys 12 stamps each month.Karen starts collecting stamps in July and buys 18 starts each month. how many months after Karen starts collecting stamps will she have the same number of stamps as Mario?

Answer:

(p,r) = (1/3, 2/9)

Step-by-step explanation:

Here, we want to solve a system of equations

We can rewrite the second equation by dividing through by 2

So we have;

4p + 3r = 2

and

5p - 3r = 1

Add both equations:

9p = 3

p = 3/9

p = 1/3

Recall ;

5p - 3r = 1

3r = 5p - 1

Substitute the value or p here

3r = 5(1/3)-1

3r = 5/3 - 1

3r = 2/3

r = 2/9

So we have the solution set as;

(p,r) = (1/3 , 2/9)

\(\huge\text{Hey there!}\)

\(\mathsf{\dfrac{3}{4} + \dfrac{1}{2}}\)

\(\mathsf{= \dfrac{3}{4} + \dfrac{1\times2}{2\times2}}\)

\(\mathsf{= \dfrac{3}{4} + \dfrac{2}{4}}\)

\(\mathsf{= \dfrac{3 + 2}{4 + 0}}\)

\(\mathsf{= \dfrac{5}{4}}\)

\(\mathsf{= 1 \dfrac{1}{4}}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{5}{4}\ or \ 1 \dfrac{1}{4}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

567

Step-by-step explanation:

t = 4.5x

t = 4.5 (126)

t = 567

Answer:

t is equal to 567

A medium-sized orange contains 68 calories. Which is one-fifth the number of calories in a slice of cheese pizza.

If one slice of cheese pizza contains 340 calories, and a medium-size orange has one-fifth that number of calories, we can find the number of calories in a medium-size orange by dividing 340 by 5. Calories in a medium-sized orange = \(\frac{340}{5}\) calories = 68 calories. The division is an arithmetic operation used to find out how many times one number is contained within another number. The result of a division operation is called the quotient.

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Answer:

digit 3 has a value of 30

Step-by-step explanation:

In the number eight hundred thirty-nine thousand, six hundred seven, the digit 3 has a value of 30, because it is in the tens place. It is not the value of the digit 3 in the number 839607.

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Answer:

7:55am

Step-by-step explanation:

The hour hand is not quite at the eight so it would be 7. The minute hand is directly on the 11, from each number is 5 minutes multiplying 11×5 would be 55. therefore it being 7:55am which is morning.

Answer:

-56

Step-by-step explanation:

f(x) = 7x + 7

x = -9

We meed to plug in x = -9 into the first equation:

f(-9) = 7(-9) + 7

We can open up the parentheses:

f(-9) = -63 + 7

And then simplify:

f(-9) = -56

Hope the above helps you......

Answer:

94.5 minutes or 1 hour and 34.5 minutes

Step-by-step explanation: If it takes you 7 minutes for 2 math problems then that means it takes you 3.5 minutes for one problem. Then you multiply it by 27 and you get 94.5 minutes you can convert it into 1 hour and 34.5 minutes if you want.

The procedure which is deemed to be the type of sample in discuss is; representative sample are free of bias.

Representative sampling and random sampling are two techniques used to help ensure data is free of bias. A representative sample on the other hand is a group or set chosen from a larger statistical population according to specified characteristics. A random sample is a group or set chosen in a random manner from a larger population.

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A. The angle that the second ball emerges after the collision can be written as sin' = cos v × (1 - cosθ).

B. The velocities of the balls after the collision are v₁ = u × cosθ - u × cos²θ - v₂ × cos(v) × (1 - cosθ)v₂ = u × sinθ + v₂ × sin(v) × (1 - cosθ)

(a) To determine the angle at which the second ball emerges after the collision, we can use the principle of conservation of momentum and conservation of kinetic energy.

Let's consider the collision in the x and y directions separately.

In the x-direction:

The initial velocity of the first ball (before collision) is given by:

u₁x = u × cosθ

The initial velocity of the second ball (before collision) is zero:

u₂x = 0

After the collision, let v₁x and v₂x be the final velocities of the first and second balls in the x-direction, respectively.

By applying the conservation of momentum in the x-direction, we have:

m × u₁x + m × u₂x = m × v₁x + m × v₂x

m × u × cosθ = m × v₁x + m × v₂x ----(1)

In the y-direction:

The initial velocity of both balls (before collision) is zero:

u₁y = 0

u₂y = 0

After the collision, let v₁y and v₂y be the final velocities of the first and second balls in the y-direction, respectively.

By applying the conservation of momentum in the y-direction, we have:

m × u₁y + m × u₂y = m × v₁y + m × v₂y

0 = m × v₁y + m × v₂y ----(2)

Since the masses of the balls are the same (m = m), equation (2) simplifies to:

v₁y + v₂y = 0 ----(3)

Now, let's consider the conservation of kinetic energy in the collision.

The initial kinetic energy of the system is given by:

KE_initial = (1/2) × m × u₁² + (1/2) × m × u₂²

= (1/2) × m × u² × (cos²θ + sin²θ)

= (1/2) × m × u²

The final kinetic energy of the system is given by:

KE_final = (1/2) × m × v₁² + (1/2) × m × v₂²

By applying the conservation of kinetic energy, we have:

KE_initial = KE_final

(1/2) × m × u² = (1/2) × m × v₁² + (1/2) × m × v₂²

u² = v₁² + v₂² ----(4)

Now, let's substitute v₁x = v₁ × cosθ and v₂x = v₂ × cosφ into equation (1):

m × u × cosθ = m × v₁ × cosθ + m × v₂ × cosφ

Dividing both sides by m × cosθ:

u = v₁ + v₂ × (cosφ / cosθ) ----(5)

Dividing equation (5) by u:

1 = v₁/u + v₂/u × (cosφ / cosθ)

Since sin' = v₂/u and cos v = v₁/u, we can rewrite equation (5) as:

1 = sin' × (cosφ / cosθ) + cos v

Multiply both sides by cosθ:

cosθ = sin' × cosφ + cos v × cosθ

Rearranging the equation, we have:

sin' × cosφ = cosθ - cos v × cosθ

sin' × cosφ = cosθ × (1 - cos v)

sin' = cosθ × (1 - cos v) / cosφ

Since sin' = sin(90° - φ)

and cosφ = cos(90° - φ), we can simplify the equation to:

sin(90° - φ) = cosθ × (1 - cos v) / cos(90° - φ)

sin(90° - φ) = cosθ × (1 - cos v) / sinφ

Using the trigonometric identity sin(90° - φ) = cos φ, we get:

cos φ = cosθ × (1 - cos v) / sinφ

Finally, since cos φ = cos(180° - φ), we can write:

cos φ = cosθ × (1 - cos v)

Hence, we have shown that the angle that the second ball emerges after the collision can be written as: sin' = cos v × (1 - cosθ).

(b) To find the velocities of the balls after the collision, use the equations derived in part (a) along with the conservation of momentum equation (1).

From equation (1), we have:

m × u × cosθ = m × v₁x + m × v₂x

u × cosθ = v₁ + v₂ × cosφ ----(6)

From equation (5), we have:

1 = v₁/u + v₂/u × (cosφ / cosθ)

Rearranging equation (6), we get:

v₁ = u × cosθ - v₂ × cosφ

Substituting this into equation (5), we have:

1 = (u × cosθ - v₂ × cosφ)/u + v₂/u × (cosφ / cosθ)

Multiplying through by u and simplifying, we get:

u = u × cosθ - v₂ × cosφ + v₂ × (cosφ / cosθ)

Dividing through by u and rearranging, we get:

1 = cosθ - v₂ × (cosφ / u) + v₂ × (cosφ / (u × cosθ))

Multiplying through by u × cosθ, we get:

u × cosθ = cosθ × u × cosθ - v₂ × (cosφ × cosθ) + v₂ × cosφ

Simplifying, we have:

0 = u × cos²θ - v₂ × (cosφ × cosθ) + v₂ × cosφ

Dividing through by u, we get:

0 = cos²θ - v₂ × (cosφ × cosθ) / u + v₂ × cosφ / u

Rearranging, we get:

v₂ × (cosφ × cosθ) / u = cos²θ + v₂ × cosφ / u

Multiplying through by u, we get:

v₂ × (cosφ × cosθ) = u × cos²θ + v₂ × cosφ

Substituting this into equation (6), we have:

u × cosθ = v₁ + (u × cos²θ + v₂ × cosφ)

Rearranging, we get:

v₁ = u × cosθ - u × cos²θ - v₂ × cosφ

Now, substituting the values of sin' and cos φ from part (a), we have:

v₁ = u × cosθ - u × cos²θ - v₂ × cos(v) × (1 - cosθ)

Therefore, the velocities of the balls after the collision are:

v₁ = u × cosθ - u × cos²θ - v₂ × cos(v) × (1 - cosθ)

v₂ = u × sinθ + v₂ × sin(v) × (1 - cosθ)

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The probability of randomly selecting the number 0.13 from a uniform distribution between 0 and 1 can be calculated by considering the range of values that satisfy the condition.

Since the distribution is uniform, all numbers within the range have an equal probability of being selected. The range between 0 and 1 is of unit length, and any specific number within that range represents a single point. Therefore, the probability of selecting any particular point, such as 0.13, is infinitesimally small since it represents a single value within an infinite set of possible values. The probability of randomly selecting the number 0.13 from a uniform distribution between 0 and 1 is extremely low, approaching zero. This is because the range of possible values within the distribution is continuous, and the probability of selecting any specific point is infinitesimal.

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Answer:

The answer would be 2133.3cm squared

The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral \(\( \int_{1}^{2} x \ln x \, dx \)\) is approximated using \(\( n = 4 \)\)subintervals. In part (b), the integral\(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) is given with incorrect limits, so it cannot be evaluated.

To approximate \(\( \int_{1}^{2} x \ln x \, dx \)\) using the Composite Trapezoidal rule, we divide the interval \(\([1, 2]\) into \( n = 4 \)\) subintervals. The step size, \(\( h \)\), is calculated as\(\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)\). Then, we evaluate the function \(\( x \ln x \)\)at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: \(\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\]\)

Using this formula, we can calculate the approximation for the given integral. The limits of the integral \(\( \int_{2}^{2} x^{3} e^{x} \, dx \)\) are given as \(\( 2 \)\) to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

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Answer:

26/35

Step-by-step explanation:

So we gotta add it together, so 1/7+0.6 or 1/7+3/5. Common denominator is 35, so the answer is 26/35

'One inch represents 2,000 feet' is a verbal type scale.

The link between a length unit on a map and its corresponding length on the ground is known as the map scale. It will be beneficial for you to carefully study this section because we will use map scale principles throughout the course.

We can use three distinct scales to relate a map to the ground:

'One inch represents 2,000 feet' is an example of a Verbal scale. The relationship between a map distance and a ground distance is expressed verbally using a verbal scale.

Here, it is inferred that one inch on the map corresponds to 2000 feet on the ground. Popular atlases and maps frequently use verbal scales.

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Answer:

the value of x= -90

is this the answer you need?

if yes then please make me brainliest

Answer:

24

Step-by-step explanation:

first subtract 0.1x from both sides and add 5 to both sides to get your variables together and constants together.

0.6x-0.1x=7+5

now simplify both sides

0.5x=12

Divide both sides by 0.5 to get the variable by itself

x=12/0.5

simplify

x=24

Answer:

Correct, 25.

Step-by-step explanation:

Answer:

17.25

Step-by-step explanation:

15+2.25=17.25

2.25 is 15 percent of 15

No, it is average  that Neymar and Luis would have the same tastes and rank a given set of bundles equally. Everyone has unique preferences and tastes that are shaped by their individual experiences.

It is unlikely that Neymar and Luis would have the same tastes and rank a given set of bundles equally. This is because everyone's preferences and tastes are shaped by their individual experiences. Even though Neymar and Luis may have similar backgrounds, they may have had different experiences that have shaped their tastes. For example, Neymar may have had a different upbringing than Luis, which may have resulted in different tastes and preferences. Additionally, Neymar and Luis may have had different life experiences that have shaped their individual tastes. Therefore, it is unlikely that Neymar and Luis would have the same tastes and rank a given set of bundles equally.

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Answer: C

Step-by-step explanation:

Answer: I think the answer is A.

Step-by-step explanation:

Answer:

The 95% confidence interval based on this sample is =

[6.41, 7.79]

Step-by-step explanation:

The formula for Confidence Interval =

Mean ± z × standard deviation/√n

Sample mean = 7.1 hours

Standard deviation = 5 hours

n = 200 students

z = 95% confidence interval z score

= 1.96

C.I = 7.1 ± 1.96 × 5/√200

C.I = 7.1 ± 0.693

Hence, Confidence Interval

= 7.1 - 0.693

= 6.407

Approximately = 6.41

= 7.1 + 0.693

= 7.793

Approximately = 7.79

Therefore, the 95% confidence interval based on this sample is

[6.41, 7.79]

The answer is B Your welcome!!!!

Answer:

78/12 or 6 1/2

Answer:

D.) 0

Step-by-step explanation: