an architect has an annual income of $85,750. the income rax the professional has to pay is 6%. What is the amount of income tax that the architect has to pay?

Answer:

Step-by-step explanation:

Therefore, you would need 3 cakes to feed a class of 70 and staff of 3.

If a cake provides 24 servings, and you need to feed a class of 70 and staff of 3, you would need to calculate the total number of people you need to serve, then divide by the number of servings per cake to determine how many cakes you need.Let the number of cakes needed be x.So, we can represent the problem as follows:Number of servings needed = class size + staff size = 70 + 3 = 73 servings per cake = 24x cakes requiredWe can use the formula below to solve for x:x = (number of servings needed) ÷ (servings per cake)x = 73 ÷ 24x = 3 (rounded up to the nearest whole number)Therefore, you would need 3 cakes to feed a class of 70 and staff of 3. Note that this answer assumes that each person is having only one serving of cake.

Answer:

23 friends

Step-by-step explanation:

100 - 8= 92

92/4 = 23

HEATHER IS SO POPULAR!!

Answer:

Answers are from left to right of each row;

2d^3 , 11d^2 , -4d

-18d^2 , -99d , 36

Step-by-step explanation:

Okay, here we are to multiply each of the row heading by the column heading.

For the d part;

The answers are;

d(2d^2) d(11d) d(-4)

= 2d^3 , 11d^2 , -4d

For the -9 part, we have;

-9(2d^2) -9(11d) -9(-4)

= -18d^2 , -99d , 36

Step-by-step explanation:

The figure above is a cube since all it's sides are equal

Volume of a cube = l³

where l is the length of one side

From the question

l = 3yd

So the volume of the cube is

Volume = 3³

Volume = 3yd³

Surface area of a cube = l²

Surface area = 3²

= 9yd²

Hope this helps you

The trigonometric expression \(\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}\) is equivalent to the trigonometric expression \(\sec \alpha \cdot \csc \alpha + 1\).

In this problem we must prove that one side of the equality is equal to the expression of the other side, requiring the use of algebraic and trigonometric properties. Now we proceed to present the corresponding procedure:

\(\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}\)

\(\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }\)

\(\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}\)

\(\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}\)

\(\frac{\tan^{3}\alpha - 1}{\tan \alpha \cdot (\tan \alpha - 1)}\)

\(\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}\)

\(\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}\)

\(\tan \alpha + 1 + \cot \alpha\)

\(\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1\)

\(\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1\)

\(\frac{1}{\cos \alpha \cdot \sin \alpha} + 1\)

\(\sec \alpha \cdot \csc \alpha + 1\)

The trigonometric expression \(\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}\) is equivalent to the trigonometric expression \(\sec \alpha \cdot \csc \alpha + 1\).

To learn more on trigonometric expressions: https://brainly.com/question/10083069

#SPJ1

The mode is the value that appears most frequently in a dataset. In this case, the mode is 4, as it has the highest frequency of occurrence.

The median is the middle value when the data is arranged in ascending or descending order. Since there are an odd number of families (21 in total), the median will be the value of the 11th observation when the data is sorted. Arranging the data in ascending order, we find that the median is also 4, as it is the middle value.

The mean is the average value and is calculated by summing up all the values and dividing by the total number of observations. In this case, we can calculate the mean by multiplying each number of pets by its corresponding frequency, summing up these products, and dividing by the total number of families (21). Using this approach, the mean can be calculated as:

Mean = (0*2 + 1*1 + 2*8 + 3*1 + 4*9 + 5*0) / 21 ≈ 2.76

Therefore, based on the provided data, the mode, median, and mean number of pets owned by the families are all approximately 4.

Learn more about Median here

https://brainly.com/question/300591

#SPJ11

Answer:

x=48 and y is 132 my guy u welcome

Answer:

48 + y = 180

y= 132

5x - 17 = 132

x=29.8

P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Explanation:

1 hat = 45 dollars

6 hats = 6*45 = 270 dollars

1 phone = 40 dollars

4 phones = 4*40 = 160 dollars

total = $270 + $160 = $430

Felicia spent a total of $430. Since this amount of money leaves her account, this means we write a negative sign out front to end up with the final answer of -430

In other words, her account balance went down by $430 which is why we use a negative. If someone gave her $430, then the answer would be positive.

Answer:

gcf is 4

Step-by-step explanation:

Answer:

4(3+20)

Step-by-step explanation:

the 4 is the greatest common factor so i pulled it out and divided 12 and 80 to simplify

Answer:78.5

Step-by-step explanation:

The total surface area of the rectangular prism shown is 78.5 feet².

Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.

The surface area of a rectangular prism can be calculated as,

Surface area = 2 (lw + wh + lh)

Here l is the length, w is the width and h is the height of the rectangle.

From the figure,

l = 4.5 feet

w = 4 feet

h = 2.5 feet

Surface area = 2 [ (4.5 × 4) + (4 × 2.5) + (4.5 × 2.5)]

                     = 2 [18 + 10 + 11.25]

                     = 2 × 39.25

                     = 78.5 feet²

Hence the surface area is 78.5 feet².

Learn more about Rectangular Prism here :

https://brainly.com/question/21308574

#SPJ3

Answer:

Step-by-step explanation:

Q1

Q2

Q3

Q4

Answer:

(9×3)+(4×2)

Step-by-step explanation:

Let a represent the price of books

Let b represent the price of magazines

Alicia purchase 3 books for $9

She also purchased 2 magazines for $4

(9×a) +(4×b)

= (9 ×3) + (4×2)

= 27+8

= 35

Answer:

x = 155º

Step-by-step explanation:

y = 25°    {Vertically opposite angles}

x + y = 180    {Co-interior angles are supplementary}

x + 25 = 180

Subtract 25 from both sides

x = 180 - 25

x = 155°

answer:

p=2(l+w)

150=2.5+w

150=10w

150/10=w

15=w

Answer:

7y=14x+3 is your answer

The angle ∠LON is congruent to the angle ∠LMN. Then the measure of the angle ∠LON will be 162.66°.

It is a polygon with four sides. The total interior angle is 360 degrees. A Rhombus's opposite sides and angles are parallel, and each side is congruent to the other sides. Its diagonals intersect at the right angle at the center.

In Rhombus LMNO angle LMN measures 162.66 degrees.

We know that the angle ∠LON is the opposite angle ∠LMN. Then ∠LON is congruent to the angle ∠LMN. Then we have

∠LON = ∠LMN

∠LON = 162.66°

The measure of the angle ∠LON will be 162.66°.

More about the Rhombus link is given below.

https://brainly.com/question/27870968

#SPJ1

Answer:

See explanation

Step-by-step explanation:

Here is the complete question:

Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs $3.25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30 before tax. The restaurant only sells pancakes in stacks of 4 pancakes for $5.50 . Let S represent the number of stacks of pancakes that Benjamin buys. What is the largest number of pancakes that Benjamin can afford?

Given:

Cost of chocolate milk = $3.25

Maximum bill that Benjamin wants before tax = $30

Cost of stack of 4 pancakes = $5.50

Let S be the number of stacks of pancakes that Benjamin buys

Solution:

Cost per stack of pancakes = $5.50  

Cost of S number of stacks of pancakes = S*5.50  = 5.50 S

So benjamin will spend money on 1 chocolate milk and S number of stacks of pancakes

Compute the total money spent by Benjamin:

Cost of chocolate milk + cost per stack of pancakes = 3.25 + 5.50 S

Maximum bill that Benjamin wants is $30 So,

The total money should be less than equal to the maximum bill that benjamin wants i.e. less than or equal to 30. So it is represented as:

3.25 + 5.50S ≤ 30  ----- (1)

Now using (1) we can find the largest number of pancakes that  Benjamin can afford :

3.25 + 5.50S ≤ 30

5.50S ≤ 30 - 3.25    

subtract 3.25 from 30

5.50S ≤ 26.75

Divide by 5.50

S ≤ 4.863636

S ≤ 4.86

S≤ 4 approx

Since the restaurant only sells pancakes in stacks of 4 pancakes so,

4 stacks = 4 *4 =  16

So the largest number of pancakes that Benjamin can afford are 16.

If we do not round off the the value stacks then we get:

4.86 stacks = 4.86 *4 =  19.44 pancakes

So the largest number of pancakes that Benjamin can afford are 19

We determined the properties of openness, path-connectedness, compactness, and closedness of each set and marked the appropriate boxes. Set 3a is compact, set 3b is closed, and set 3c is open, closed, and compact.

(3a) R237 B223(0)  □ open □ path-connected □ closed  ✔ compact
The set R237 B223(0) is compact because it is bounded and closed. It is not open or path-connected.

(3b) S= {(x, y, z) ER³ : x² + y² + z² ≤ 4 and |x|≥ 1)  □ open □ path-connected □ compact  ✔ closed
The set S is closed because its complement is the union of two open sets. It is not open or path-connected, but it is compact because it is closed and bounded.

(3c) S = {(xyz²,4x² sin²(yz), x³): x, y, z = [0, 1]}  ✔ open □ path-connected  ✔ compact  □ closed
The set S is open, closed, and compact because it is a closed and bounded subset of R³. It is not path-connected.

To know more about sets, visit:
brainly.com/question/30705181
#SPJ11

Answer:

Median: 20

first quartile: 9.75

third quartile: 28.75

interquartile range: 19

Explanation:

First we arrange the data from least to greatest

Answer:

f(2) = 22

Step-by-step explanation:

To find f(#), plug the number into each x of the equation.

f(x) = 10x + 2

f(2) = 10(2) + 2

Simplify the parentheses by multiplying.

f(2) = 20 + 2

Add.

f(2) = 22

Hope this helps!

The rate of the slower car is 152 km/hr.

Given:

two cars leave towns 340 kilometers apart at the same time and travel toward each other. one car's rate is 18 kilometers per hour less than the other's. if they meet in 2 hours.

Let x be the rate of slower car.

We have two cars heading towards each other. They start 340 km apart and meet up 2 hours later. This means that they are traveling:

340 / 2 = 170 km/hr towards each other.

If the two cars were traveling the same speed, they'd both be going:

170 / 2 = 85 km/hr

We know that one car is traveling 18 km/hr faster than the other car. One way we can account for this is to  ± 9 km/hr to the average speed:

85 ± 9 = 94 , 76 km/hr

rate of slower car x = 84 - 9 * 2

x = 76 * 2 km/hr

= 152 km/hr

Therefore The rate of the slower car is 152 km/hr.

Learn more about the kilometers here:

https://brainly.com/question/13987481

#SPJ4

Full question:

two cars leave towns 340 kilometers apart at the same time and travel toward each other. one car's rate is 18 kilometers per hour less than the other's. if they meet in 2 hours, what is the rate of the slower car?

Answer:

28

Step-by-step explanation:

each question is worth 2 points and he missed 6,6 times 2 is 12.therefore you subtract 40 by 12 and get 28 :)

In conclusion, the set {0} ∪ {1/n | n∈ℤ} is not an open set.

Explanation:

You are asking whether the set {0} ∪ {1/n | n∈ℤ} is an open set.

Step 1: Define the set
First, let's define the set in question. The set can be written as {0} ∪ {1/n | n∈ℤ, n≠0}, which means the union of two sets: {0} and {1/n | n∈ℤ, n≠0}. The second set contains all the elements of the form 1/n, where n is an integer, and n is not equal to 0.

Step 2: Determine if the set is open
An open set is a set in which for every point x, there exists some ε > 0 such that the open interval (x-ε, x+ε) is entirely contained within the set. Now, let's see if our set meets this criterion.

For any non-zero integer n, the point 1/n is in the set. However, there is no ε > 0 such that the open interval (1/n - ε, 1/n + ε) is entirely contained within the set, since the interval will contain points that are not of the form 1/n. This means that the set is not open, as there is no suitable ε for these points.

Since {0} is a singleton set and singleton sets are always closed, and {1/n | n∈ℤ} is a set of real numbers, the union "{0} u {1/n | n∈ℤ}" is not an open set. This is because it contains points on the boundary (0) as well as points that are not interior points (such as 1 and -1) due to the nature of the set {1/n | n belongs to z}.

In conclusion, the set {0} ∪ {1/n | n∈ℤ} is not an open set.

Know more about the open set click here:

https://brainly.com/question/31480826

#SPJ11

Answer:

Step-by-step explanation:

a₁ = 4 = 2² = (1 + 1)²

a₂ = 9 = 3² = (2 + 1)²

a₃ = 16 = 4² = (3 + 1)²

a₄ = 25 = 5² = (4 + 1)²

a₅ = 36 = 6² = (5 + 1)²

Therefore:

               aₙ = (n + 1)² = n² + 2n + 1

Answer:

88°?

Step-by-step explanation: