Angelica is paid $40,440 annually. What would be her semimonthly pay?

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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Answer:

Step-by-step explanation:

Factors of 12 are 1, 2, 3, 4, 6 and 12 ... ... because 2 × 6 = 12, or 4 × 3 = 12, or 1 × 12 = 12.

Answer:

  20 hours

Step-by-step explanation:

The volume of water when the pool is 80% full can be found using the proportion ...

  2250/75% = v/80%

  v = (80/75)(2250) = 2400 . . . cubic meters

Emptying at the rate of 120 m³/h will take ...

  time = volume/rate

  time = (2400 m³)/(120 m³/h) = 20 h

It will take 20 hours to empty the pool from 80% full.

To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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Answer:

7.

5/12

8.

12/39

Step-by-step explanation:

7.

5/6*1/2=5/12

8.

3/4*4/9=12/39

Answer:

Max made a mistake in step 5.

He should have used division instead of multiplication.

Step-by-step explanation:

In step #5, he made the mistake of multiply 5/6 by 5/6. The reason why this doesn't work is because y is not a full y. When there isn't a number beside a variable, it is implied that it is 1y. To solve for y, you need 1y or else results or inaccurate.

In reality, 5/6 * 5/6 is equal to 25/36. If you divided 5/6 by 5/6, it is equal to 1, which makes y a full y.

Answer:

he made a lot of mistakes, but i'd say he used division instead of multiplication in step 5

(but the biggest mistake was adding 1/6 to both sides instead of multiplying by it)

Step-by-step explanation:

Answer:

A triangular prism has base edges 4 cm, 5 cm, and 6 cm long. Its lateral area is

300 cm2.

What is the height of the prism?

Answer:

C. 88.8

Step-by-step explanation:

calculator.net/triangle-calculator.html

Answer:

1. C = 10π, A = 25π

2. 9 cm³

Step-by-step explanation:

Formula for circumference = πd

Formula for area of a circle = πr²

1. Set up the equation for circumference

10π

2. Set up the equation for area (radius = 1/2diameter) and solve

π(5²) = 25π

Formula for volume of a square pyramid = 1/3s² · h

The volume of a square pyramid is equal to 1/3 of the volume of a cube. The formula for a volume of a cube is s³ which is equal to s² · h because a cube has the same side length for all sides. Therefore, the volume of a square pyramid that perfectly fits within a given cube would equal 1/3 the volume of the cube.

1. Set up the equation and solve

27 ÷ 3 = 9

Answer:

Step-by-step explanation:

3.

diameter is equal two radiuses

D = 10 = 2R   ⇒  R = 5

circumference:  C = 2πR = 2R•π = 10π

area:                    A = πR² = π•5² = 25π

4.

If square pyramid fit perfectly inside cube then its base is the same as a face of cube, and the height (H) of pyramid is equal to the edge (S) of its base.

\(A_p=\frac13S^2\cdot H =\frac13S^2\cdot S=\frac13S^3=\frac13A_c=\frac13\cdot27\,cm^3=9\,cm^3\)

Two angles with a sum of 90° are called complementary angles, and when the sum is 180° they are called supplementary angles.

Complementary angles are two angles whose sum is 90°. In other words, the two angles are complementary if they combine to form a right angle (a 90-degree angle).

Example: ∠A and ∠B are complementary angles because ∠A + ∠B = 90°

Two angles are said to be supplementary angles if their sum is 180°. In other words, two angles are supplementary if they combine to form a straight angle.

Example: ∠P and ∠Q are supplementary angles because ∠P + ∠Q = 180°

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Complementary angles.

Supplementary angles.

What are the names for angles with a sum of 90° and 180°?

Two angles with a sum of 90° are called complementary angles, while angles with a sum of 180° are known as supplementary angles. Complementary angles are pairs of angles that, when combined, form a right angle of 90°. For example, if one angle measures 30°, its complementary angle would measure 60°. Supplementary angles, on the other hand, are pairs of angles that add up to a straight angle of 180°. For instance, if one angle measures 100°, its supplementary angle would measure 80°. These concepts are fundamental in geometry and provide a basis for understanding the relationships between angles in various geometric shapes and constructions.

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Complementary angles are often encountered in right triangles, where one angle is 90°. They play a crucial role in trigonometry and are used to determine the values of trigonometric functions. Understanding complementary angles is essential when solving equations involving right triangles and trigonometric identities. Supplementary angles are frequently encountered when dealing with parallel lines intersected by a transversal, forming various pairs of angles. They are used to prove geometric theorems and solve problems related to angles in polygons and other geometric figures.

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The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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Answer:

Agree with Luke!

Step-by-step explanation:

The Chess Club has 8 members

Total number of outcomes = 8

A new captain will be chosen by randomly selecting the name of one of the members

Number of favorable outcome (captain) = 1

Probability  = Number of Favorable outcome / Total number of outcomes

Probability = 1 / 8

Agree with Luke!

I don't agree with Leah.

I agree with Luke because.... The Chess Club has 8 members

Total number of outcomes = 8

A new captain will be chosen by randomly selecting the name of one of the members

Number of captains that will be chosen = 1

Probability  = Number of Favorable outcome / Total number of outcomes

Probability = 1 / 8

Answer:

-8 and then 6 maybe

Step-by-step explanation:

Answer:

The maximum number of text messages you can send per month would be 41.

Step-by-step explanation:

1. First, you want to create an inequality from the word problem.  You know that $24.99 is a constant, so we won't put any variables next to it.  You also know that each text message is $0.12, so that would need a variable since it can change each month.  You also know that you can spend $30 maximum each month, so that goes on the other side of the inequality.  Your inequality will look like this:  0.12x+24.99≤30 (x is the number of text messages).

2. Second, you want to solve for x.  To do this, subtract 24.99 from each side.  After this, the equation is 0.12x≤5.01

3. Now, divide each side by 0.12.  Now your inequality is x≤41.75.  This represents how many text messages you can send per month without going over 30.

4. Finally, you have to realize that is impossible to send exactly 41.75 text messages.  So, you have to round down to 41 to get an even number of text messages, and that's your answer!

Hope this helps!  Feel free to ask any questions :)

Answer:

41 text messages

Step-by-step explanation:

Eddie walks 60.03 yards in 1 minute using proportion.

What is proportion?

The term proportionality refers to any relationship that has the same ratio every time. The proportional relationship between the two supplied ratios is defined by an equation. In other terms, the proportion declares that the two fractions or ratios are equal. For instance, the average number of apples per tree determines the proportionality between the quantity of apples in a crop and the number of trees in the orchard.

Here let us take time and distance as proportional values,

=> \(\frac{distance}{Time}\)

=> 450.25/2.5 = x/1

=> x = 180.1 feet.

To convert feet to yards divide the length by 3. then

=> 180.1/3=60.03 yards,

Therefore Eddie Walks 60.03 yards in 1 minute.

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Answer:

Player B.

Step-by-step explanation:

Player A has a mean score of 25.

Let's calculate Player B's mean score and compare it to Player A's.

23 + 27 + 28 + 22 + 25 / 5 = 125 / 5 = 25.

So, Player A and Player B have the same mean score.

This doesn't tell the scout which player is "better", so let's look at the variance.

The other statistic given for Player A is the standard deviation for their points. The given number is 4. Let’s calculate the standard deviation for Player B, and compare it to player A.

Recall that we add up the squares of the difference between each score and the mean, divide it by the total number of data, and square root that. So, the standard deviation for player B is sqrt(2^2 + 2^2 + 3^2 + 3^2 + 0^2 / 5) = sqrt (26/5) = sqrt (5.2) = 2.3.

Excellent. We have player A’s standard deviation, as well as player B’s standard of deviation. Since player B’s standard deviation is less than player A’s, it can be inferred that player B has more consistent results than player A, and the scout should get Player B.

Hope this helps!

Answer:

1,044

Step-by-step explanation:

14 x 46 = 644

16 x 25 = 400

644 + 400 = 1,044

Answer:

Area for a rectangle-

l x b

(x + 5)+ (2x) =110

3x=110-5

x=105/3

x=35

Thus the answers are-

2 x 35

=70

35 + 5

=40

7.5

According to the law in the city, the maximum grade of stairs is about 33.3%.

This is because the law requires minimum treads of 10 in.

and maximum risers of 7.5 in. (illustration to the right).

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Step 2 : Define parameters

Step 3: Substitute the parameters into the equation

The terminal side of θ lies in the third quadrant if sin θ < 0 and  tan θ > 0

From the question, we have the following parameters that can be used in our computation:

sin θ < 0 and  tan θ > 0

There are four quadrants in a coordinate plane

And the quadrant where tangent is positive and sine is negative is the third quadrant

This means that the terminal side of θ lies in the third quadrant

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Question

Determine the quadrant in which the terminal side of θ lies.

sin θ < 0 and  tan θ > 0

The equation that will tell him what the width of the rectangle can be is w = 50m² / length.

A rectangle is a 2-dimensional quadrilateral with four equal right angles. A rectangle has two diagonals that are equal in length and bisect each other.

Area of a rectangle = length x width

Width = area / length

width = 50m² / length.

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Answer:

f(0) what ? i cant read the formulla of it

Answer:  x=12-3y

Step-by-step explanation:

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10)

11)

12)

13)

14)

15)

16)

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Solution (9):

Solution (10):

Solution (11):

Solution (12):

Solution (13):

Solution (14):

Solution (15):

Solution (16):

Solution (17):

Hoped this helped!

Answer:

sum of two function

Step-by-step explanation:

Answer:

first one is y= -2/3x-16

second one is 1/2x-5.5

Answer:

1) y = -2/3x - 16

2) y = 1/2x - 11/2

Step-by-step explanation:

I hope this helps!

The car is going the same speed as its average speed over the interval 0 to 10 seconds at t = 5 seconds.

To find the time when the car is going the same speed as its average speed over the interval 0 to 10 seconds, we need to compare the instantaneous velocity of the car at a given time with its average velocity over the interval [0, 10].

The position equation is given by:

\(\mathrm{s(t) = \frac{1}{4} t^2 + 1}\)

To find the instantaneous velocity, we need to take the derivative of the position equation with respect to time:

\(\mathrm{v(t) = ds/dt = d/dt [\frac{1}{4} t^2 + 1]}\)

\(\mathrm{v(t) = \frac{1}{2} t}\)

The average velocity over the interval [0, 10] is the change in position divided by the change in time:

Average velocity = \(\mathrm{\frac{s(10) - s(0)}{(10 - 0)}}\)

\(= \frac{1/4 (10^2) + 1 - (1/4)(0^2) - 1}{10} \\\\ = \frac{(25 + 1 - 0 - 1)} {10}\\\\= 25 / 10\\\\= 2.5\)

Now we need to find the time when the instantaneous velocity (v(t)) is equal to the average velocity (2.5):

(1/2)t = 2.5

Solving for t:

t = 2.5 x 2

t = 5

Therefore, the car is going the same speed as its average speed over the interval 0 to 10 seconds at t = 5 seconds.

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The company will need 6π cubic inches of wax to make a single candle.

Given that the company makes wax candles in the shape of a cylinder, each candle has a diameter of 2 inches and a height of 6 inches.

Now, we need to find out how much wax will the company need to make candles.

The formula to find out the volume of a cylinder is given byπr²h,

where r is the radius of the circular base, h is the height of the cylinder and π is the mathematical constant (approx. 3.14159).

Here, Diameter of the cylindrical candle = 2 inchesTherefore, radius (r) of the candle = diameter / 2= 2 / 2= 1 inch

Height (h) of the candle = 6 inchesSubstitute the values of r and h in the formula for the volume of a cylinder and simplify to get,

Volume of the cylindrical candle = πr²h= π(1)²(6)= π(1)(1)(6)= 6π cubic inches

Therefore, the company will need 6π cubic inches of wax to make a single candle.

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