The National Junior Honor Society made $238at their cake sale. They sold circular Shaped cakes for $7 and heart shaped cakes for $5. If they Sold twice as many heart cakes as circular ones. how many heart cakes did they sell?​

There for the diameter is 2(4.8 )= 9.6 ft

Given: Volume of the cone is 83.7 m³

We know that:

\(\bigstar \ \ \boxed{\sf{\textsf{Volume of cone is given by} : \dfrac{\pi r^2h}{3}}}\)

where r is the radius of the cone and h is the height of the cone

Given: Height of the cone = 5m

Substituting the values in the formula, we get:

\(\sf{\implies \dfrac{\pi r^2(5)}{3} = 83.7}\)

\(\sf{\implies \pi r^2 = 83.7 \times \dfrac{3}{5}}\)

\(\sf{\implies \pi r^2 = 83.7 \times 0.6}\)

\(\sf{\implies \pi r^2 = 50.22}\)

\(\sf{\implies r^2 = \dfrac{50.22}{\pi}}\)

\(\sf{\implies r^2 = 16}\)

\(\sf{\implies r = 4}\)

We know that : Diameter is two times the radius

⇒  Diameter of the Cone is 8 meters

Answer:

Step-by-step explanation:

Answer:

\(y=\frac{2}{5}x-5\)

Step-by-step explanation:

\(y=\frac{2}{3}x+4\)

the line parallel  to this line is

\(y=\frac{2}{3}x+k\) ; k ∈ R

the line passes through the point (3,6)

so,

\(6=\frac{2}{3} (3)+k\\6=2 +k\\k=4\)

∴the line that passes through point (2, -1) and is parallel to the line described y = (2/3)x - 6 is

\(y=\frac{2}{3}x+4\)

Answer:

D.

Step-by-step explanation:

Answer:

2.3333333333333333333333333333333 sec

Answer:

∠f=34°

Step-by-step explanation:

Answer:

x = -4 and 2

Step-by-step explanation:

When x = -4 and 2, y = 0 so -4 and 2 are the roots

From the histogram,

The students securing 10-19 points are 14 and student securing 70-79 points are 16.

Thus there are more students securing 70-79 points thann student securing 10-19 points.

The answer is 70-79 points.

answer is C

He made an error in Step 3. He should have subtracted 2 from both sides.

Answer:

c

Step-by-step explanation:

Answer:

(-3, 7)

Step-by-step explanation:

ok so first take the square root of both sides, so you get (x-2)=5, since the square root gets rid of the power, and the square root of 25, is 5, and since we did a square root, we also have to do the - + thing, so the equation really is now x-2=(+-)5

subtract 2 from both sides, and you get x=(+-)5+2

Solving for x we get -5+2=-3

and also

5+2=7 since there was a positive, and a negative 5.

therefore x would equal (-3, 7)

hope this helps, please mark as brainliest.

Answer:

It will take 1.6 hours for the two trains to be 336 miles apart.

Step by step explanation:

Given that:

Speed of eastbound train = 95 miles per hour

Speed of westbound train = 115 miles per hour

Combined speed = 95+115 = 210 miles

Distance = 336 miles

\(Speed = \frac{Distance}{Time}\\\\210 = \frac{336}{Time}\\\\Time = \frac{336}{210}\\\\Time = 1.6\ hours\)

Hence,

It will take 1.6 hours for the two trains to be 336 miles apart.

Thus, total, we have 6 + 4 + 2 = 12 four-digit integers that  that are not multiples of 1111 do the digits form an arithmetic sequence.

Let's first understand the criteria for the four-digit integers:

1. They are not multiples of 1111.
2. Their digits form an arithmetic sequence.

Now, let's analyze the four-digit integers. We can represent them as ABCD, where A, B, C, and D are the individual digits. Since the digits form an arithmetic sequence, we can represent this sequence as A, A+d, A+2d, and A+3d. Here, "A" is the first digit, "d" is the common difference, and A ≠ 0.

Since A+3d is the last digit, it must be less than 10. So, A+3d < 10. Given that A ≥ 1, we can deduce that d can take the values 1, 2, or 3.

Now let's consider each value of "d":

1. If d = 1, A can range from 1 to 6. This results in 6 possible four-digit integers.
2. If d = 2, A can range from 1 to 4. This results in 4 possible four-digit integers.
3. If d = 3, A can range from 1 to 2. This results in 2 possible four-digit integers.

In total, we have 6 + 4 + 2 = 12 four-digit integers that meet the given criteria.

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The simple interest rate that will ensure that Bob's investment of R6,500 equals Alice's 3% compound interest per year investment is 3.2%.

The difference between simple interest and compound interest is that simple interest computes interest on the principal only for each period.

Compound interest computes interest on both the principal and accumulated interest for each period.

Alice:

Principal investment = R6,500

Compound interest rate per year = 3%

Investment period = 5years

Future value = R7,535.28 (R6,500 x 1.03⁵)

Total Interest R1,035.28 (R7,535.28 - R6,500)

Bob:

Principal invested = R6,500

The simple interest rate = r

Investment period = 5years

The future value of the simple interest investment, A = P(1+rt)

7,535.28 = 6,500(1 + 5r)

Dividing each side b 6,500:

1.15927 = (1 + 5r)

5r = 0.15927

r = 0.031854

r - 0.032

r = 3.2% (0.32 x 100)

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Calculate r, giving your answer correct to 1 decimal place.

Answer:

C: 5%

Step-by-step explanation:

175 out of 3500 = 175/3500

175/3500 = 1/20

1/20 = 0.05

0.05 = 5%

Answer:

C 5%

Step-by-step explanation:

I am smart so trust me

Answer:

1200 cm^2

Step-by-step explanation:

There are four 10 cm by 25 cm sides; the total area of these sides is

4 (10 cm) (25 cm) = 1000 cm^2.

There are two ends; the total area of these is 2 (10 cm) (10 cm) = 200 cm^2.

Thus, the total surface area is 1000 cm^2 + 200 cm^2, or 1200 cm^2 (Answer A).

Answer:

The truck is on pace.

Step-by-step explanation:

To find which truck will arrive first, you need to find each vehicle's mph. To get the mph of each vehicle you just need to divide the distance by time.

Bus: 110 (miles) ÷ 2 (hours) = 55 (miles per hour)

Truck: 180 (miles) ÷ 3 (hours) = 60 (miles per hour)

When you do this you can see the mph of the bus is < the mph of the truck.

If you have any questions please leave them in the comments.

To solve the initial value problem  \(dy/dx = 2x\) with the initial condition y(0)=2 in Python, we can use an appropriate numerical method, such as Euler's method or the built-in function odeint from the scipy.integrate module.

Here's an example code snippet in Python that solves the given initial value problem using Euler's method:

import numpy as np

import matplotlib.pyplot as plt

def f(x, y):

   return 2*x

def euler_method(f, x0, y0, h, num_steps):

   x = np.zeros(num_steps+1)

   y = np.zeros(num_steps+1)

   x[0] = x0

   y[0] = y0

   for i in range(num_steps):

       y[i+1] = y[i] + h * f(x[i], y[i])

       x[i+1] = x[i] + h

   return x, y

x0 = 0

y0 = 2

h = 0.1

num_steps = 10

x, y = euler_method(f, x0, y0, h, num_steps)

plt.plot(x, y)

plt.xlabel('x')

plt.ylabel('y')

plt.title('Solution of dy/dx = 2x')

plt.show()

In this code, we define the function f(x, y) that represents the right-hand side of the differential equation. Then, we implement the Euler's method in the euler_method function, which takes the function f, the initial values x0 and y0, the step size h, and the number of steps num_steps as inputs. The method iteratively calculates the values of x and y using the Euler's method formula. Finally, we plot the solution using matplotlib.pyplot. Running the code will generate a plot showing the solution of the initial value problem dy/dx = 2x with y(0)=2 over the specified range of x-values.

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The probability of getting 5 consecutive "Heads" in 5 coin tosses is approximately 0.03.

To find the probability of getting 5 consecutive "Heads" in 5 coin tosses, follow these steps:

Step 1: Determine the probability of a single coin toss resulting in "Heads".
- Since a coin has 2 sides (Heads and Tails), the probability of getting "Heads" in one toss is 1/2 or 0.5.

Step 2: Calculate the probability of getting "Heads" in all 5 tosses.
- Since each toss is an independent event, multiply the probabilities for each toss together: (1/2) x (1/2) x (1/2) x (1/2) x (1/2).

Step 3: Simplify the expression.
- (1/2)^5 = 1/32

Step 4: Express the answer as a proportion rounded to two decimals.
- 1/32 ≈ 0.03 (rounded to two decimals)

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Answer:

Red=17.1%

Green=54.3%

Purple=28.6%

All of these answers are rounded.

Step-by-step explanation:

To solve for all, all you have to do is divide the number of trials of the specific color by the total number of trials. To get a percentage you then multiply by 100%.

Red:

12/70=0.171*100%=17.1%

Green:

38/70=0.543*100%=54.3%

Purple:

20/70=0.286*100%=28.6%

To check if you've rounded correctly, add all your values and they should add up to 100 exactly. If it is slightly over or below you may need to go back and check for a rounding error.

The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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For a random variable X with an exponential distribution, it can be proven that (a) the expected value of X is equal to λ^-1, (b) the moment generating function of X is equal to λ/(λ-t), and (c) for t > 0, the probability that X is less than or equal to x+t given that X is greater than x is equal to the probability that X is less than or equal to t.

(a) To prove that E(X) = λ^-1, we need to calculate the expected value of X. The expected value is given by the integral of x times the probability density function f(x) over its range. Integrating λxe^(-λx) with respect to x from 0 to infinity yields λ/(λ^2) = λ^-1.

(b) The moment generating function (MGF) of X, denoted as M_X(t), is defined as the expected value of e^(tx). By substituting the exponential probability density function into the definition of the MGF and integrating, we obtain M_X(t) = λ/(λ-t).

(c) To prove that P(X ≤ x+t | X > x) = P(X ≤ t), we can use the memoryless property of the exponential distribution. The memoryless property states that the conditional probability of exceeding a given value does not depend on previous events. Therefore, P(X > x+t | X > x) = P(X > t). By rearranging the terms, we get P(X ≤ x+t | X > x) = 1 - P(X > x+t | X > x) = 1 - P(X > t). Simplifying further, we find that P(X ≤ x+t | X > x) = P(X ≤ t).

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Abby and her friends just dined at a restaurant and left a 20% tip, amounting to $25.35. We are to find the bill before tip in dollars. Rounding off the given tip to two decimal places, we have $25.35 ≈ $25.34.

We can now proceed with solving the problem using the formula that relates the bill before tip and the tip. The formula states that the bill before tip is equal to the sum of the tip and the bill after tip.Let x be the bill before tip in dollars.

Then, we can write the formula for the total bill as:x + 0.20x = x + 25.34. Simplifying the above equation, we have:0.20x = 25.34x = 25.34/0.20x = 126.7.

Rounding off to two decimal places, the bill before tip is approximately $126.70. In summary, if Abby and her friends left a 20% tip amounting to $25.35, then the bill before tip was approximately $126.70.

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The measure of the angle between Elm Street and Pine Avenue i.e. ∠FEH is 72°.

It is given that EFGH is a trapezium in which EF ≅ HG, side FG and EH are parallel.

∠G = 108°

since FG || EH

Then  ∠G = ∠H  = 108°  (corresponding angle are equal)

The measure of the angle between Elm Street and Pine Avenue would be equal to interior angles +  180°               (alternate angles are equal)

The measure of angle between Elm Street and Pine Avenue = 180° - 108°

The measure of angle between Elm Street and Pine Avenue = 72°

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The given question is incomplete, the complete question is :

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue? 54° 72° 108° 144°

Answer: 30%, look at the image for the explanation

Step-by-step explanation:

Answer:

Limited Liability partnership allows for a partnership structure where each partner's liabilities are limited to the amount they put into the business.

The kinds of businesses that limited liability partnerships would be a good option for jobs like:
-Law firms
-Accounting firms
-Doctor offices


Step-by-step explanation:

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We can rewrite the expression only using natural logarithms as:

logₐ(n)/logₙ(c) = (ln(n))^2/(ln(a)*ln(c))

First, you need to remember that:

logₐ(x) = ln(x)/ln(a).

Then the expression:

logₐ(n)/logₙ(c)

(I just changed the letter "b" for the letter "n" there, just because i don't have a "b" as a subscript).

Can be rewritten as:

logₐ(n)/logₙ(c) = (ln(n)/ln(a))*(ln(n)/ln(c)) = (ln(n))^2/(ln(a)*ln(c))

Then we have the simplification:

logₐ(n)/logₙ(c) = (ln(n))^2/(ln(a)*ln(c))

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