Roger is a 38 year old man who lives with his father. He wants to move out but needs to figure out how much he needs to save a month to be able to move in. He has found the apartment he wants but needs to come up with the Deposit which is first and last month’s rent. Currently he makes $2000 a month at his job. His current expenditures living with his father is $800 a month. He figures he can comfortably afford this apartment which costs $1200 a month. How long in his current situation will it take Roger to save for his Deposit and finally move out?

Answer:

............ .. .......

Answer:

14.1 mm

Given:

∠BAC = 90° (angle A should be 90°)

AB = 4.4mm

BC = 14.8mm

See the diagram given below.

Solving using Pythagoras Theorem: a² + b² = c²

x² + 4.4² = 14.8²

x = 14.8² -  4.4²

x = 219.04 - 19.36

x = 199.68

x = √199.68

x = 14.13 ≈ 14.1 mm (rounded to 1 decimal place)

120Rs is spend in 6 days on these things and distributive property is used

Properties of whole numbers are defined to operate basic arithmetic operations such as addition and multiplication, in an easy way. Applying these properties helps us to solve such math problems quickly, without even using calculators. These properties are almost similar to the properties of integers, although the definition for whole numbers and integers are different.

Total cost of a single day= 15 + 5 = 20Rs

∴ In 6 days total cost = 20 x 6 = 120Rs

Thus 120Rs is spend in 6 days on these things and distributive property is used.

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a) A function that expresses f(x) is f(x) = 1.5x.

b) A graph of the function is shown in the image below.

c) The domain and range of the function are all real numbers or [-∞, ∞].

Assuming the variable x represent the amount of a transaction and the variable f(x) represent the amount Isabel is charged for the transaction, a linear function charges on each sale by the credit card company can be written as follows;

f(x) = 1.5x

Part b.

In this exercise, we would use an online graphing tool to plot the function f(x) = 1.5x as shown in the graph attached below.

Part c.

By critically observing the graph shown below, we can logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-∞, ∞] or all real numbers.

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Complete Question:

A transaction is positive if there is a sale and negative when there is a return. Each time a customer uses a credit card for a transaction, the credit company charges Isabel. The credit company charges 1.5% of each sale and a fee of 0.5% for returns.

a) Let x represent the amount of a transaction and let f(x) represent the amount Isabel is charged for the transaction. Write a function that expresses f(x).

b) Graph the function.

c) What are the domain and range of the function?

The positive square root of 0.1445 by division method is approximately 0.38 (correct to two decimal places).

To find the positive square root of 0.1445 by division method, we can follow these steps:

Step 1: Add a decimal point after the first digit to make it 0.14. Step 2: Pair the digits from the decimal point in pairs starting from the decimal point and moving left. If there is an odd number of digits, pair the leftmost digit with a zero. So, we have: 0. 14 45 Step 3: Find the largest number whose square is less than or equal to 14. Write this number on top of the paired digits and subtract its square from 14. The largest number whose square is less than or equal to 14 is 3. 3 | 0.14 45 9

5 14 4 89

255

Step 4: Bring down the next pair of digits (45) and double the quotient (3) to get the dividend for the next step. So, we have: 3 | 0.14 45 9

5 14 4 89

255

249

---

  66

Step 5: Find the largest digit d such that 6d multiplied by d is less than or equal to 66. Write this digit on top of the remainder (66) to get the next digit of the square root.

The largest digit d such that 6d multiplied by d is less than or equal to 66 is 7.

So, we have:

3 | 0.14 45

9  4

5 14 66 4 89

255

249

---

  66

  63

  --

   3

Step 6: Repeat steps 4 and 5 until you have found the desired number of decimal places. In this case, we stop here since we only need to find the square root correct to two decimal places.

Therefore, the positive square root of 0.1445 by division method is approximately 0.38 (correct to two decimal places).

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The probability of obtaining tails and the number 5 is 1/12

the probability of obtaining an even number is 1/2

P(heads and prime number)  1/4

Since the events are independent, the probability of obtaining tails and the number 5 is:

P(tails and 5) = P(tails) * P(5) = (1/2) * (1/6) = 1/12

The coin toss outcome is irrelevant, so the probability of obtaining an even number is:

P(even number) = 1/2

The probability of obtaining heads and a prime number is:

P(heads and prime number) = P(heads) * P(prime number) = (1/2) * (1/2) = 1/4

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Answer:

(r + 20)t = r

Step-by-step explanation:

Distance is constant in the scenario above, distance from home to wedding and wedding back home is the same.

From wedding back home. :

Recall : Distance = speed * time

Distance = r * 1 hour

From home to wedding :

Speed = 20 mph more ; r + 20

Time = t

Distance = (r + 20)* t = (r +20)t

Since the distance are the same, we can equate both :

(r + 20)t = r * 1

= (r + 20)t = r

To find the maximum profit, we can look for the vertex of the parabolic function representing the profit.

The given profit function is:

\(Z = -3x^2 + 12x + 25\)

We can see that the coefficient of the \(x^2\) term is negative, which means the parabola opens downwards. This indicates that the vertex of the parabola represents the maximum point.

The x-coordinate of the vertex can be found using the formula:

\(x = \frac{-b}{2a}\)

In our case, a = -3 and b = 12. Plugging these values into the formula, we get:

\(x = \frac{-12}{2 \cdot (-3)}\\\\x = \frac{-12}{-6}\\\\x = 2\)

To find the maximum profit, we substitute the x-coordinate of the vertex into the profit function:

\(Z = -3(2)^2 + 12(2) + 25\\\\Z = -12 + 24 + 25\\\\Z = 37\)

Therefore, the maximum profit is 37.

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The approximate arc length rounded to the nearest hundredth, between each spoke is 54.9 mm.

Diameter = 559 mm, r = d/2 = 279.5 mm

Number of spokes = 32

π = 3.14

To solve this question, we have to use the formula of the length of an arc which is given as

L = θ/360 × 2πr

To calculate the angle between each spoke, let's divide 360 by 32

θ = 360/32

θ = 11.25°

Now we have the value of the angle, substitute it and solve for the length of the arc.

\(L_{arc}\) = θ/360 × 2πr

= 11.25/360 × 2 × 3.14 × 279.5

= 54. 9 mm

Therefore the length of the arc is approximately 54.9 mm.

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Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

Answer:

A and C are parallel

Step-by-step explanation:

They both are 70 degrees

Answer and Step-by-step explanation:

Lines A and C MUST be parallel.

This is because they both have the same vertical angles, that being 70 degrees. The other lines have different angle measures, so those can't be parallel.

So, the answer is:

D. A and C

#teamtrees #PAW (Plant And Water)

The first one I'll do is Physics because you know the amount of girls and total amount of students. Use the equation x+19=33. Note that x is the amount of boys we are trying to find. All you need to do is simply subtract 19 from both sides to get x alone.

                                             x + 19 = 33

                                                  -19   -19

                                             x         = 14

For the total that's going up and down, you can do this same process again, but just using x for girls instead of boys. Your equation should look like 47+x=80. Once again, subtract 47 from both sides.

                                             47 + x = 80

                                             -47        -47

                                             x         =  33

Now you can find whole row for boys. This equation will be a little longer, but it's still pretty easy. 18+x+14=47 is what we will be using. We first will need to combine like terms (the 18 and 14), then subtract it off from both sides to get x alone.

                                             18 + x + 14 = 47

                                                    x + 32 = 47

                                                        -32   -32

                                                     x         = 15

Moving onto the biology column, we'll be using the equation 15+x=21

                                             15 + x = 21

                                            -15        -15

                                             x         = 6

Now we can find out the girls column with this equation: x+6+19=33

                                           x + 6 + 19 = 33

                                           x + 25      = 33      

                                               -25         -25

                                                     x      = 8

Lastly, we can find the chemistry column by just adding 18+8 to get 26.

I know this was a little hard to follow along, so here's a picture of it finished:  

Answer:

To find the mpg all we have to do is divide the numbers in the ratio.

119 miles / 3.5 gallons = 34 mpg

77 mi / 2.2 gal = 35 mpg

153 mi / 4.25 gal = 36 mpg

Answer:

y = 4

Step-by-step explanation:

First, distribute 8 through the parentheses

8y - 8 - 3y = 6(2y - 6)

Then, distribute 6 through the parentheses

8y - 8 - 3y = 12y - 36

Collect like terms (8y - 3y)

5y - 8 = 12y - 36

Move the variable (12y) to the left hand side and change its sign

5y - 12y - 8 = -36

Move the constant (-8) to the right hand side and change its sign

5y - 12y = -36 + 8

Collect like terms

-7y = -36 + 8

Calculate the sum

-7y = -28

Divide both sides of the equation by -7

y = 4

Answer:

x = 0, 2

Step-by-step explanation:

Step 1: Factor out GCF

2x(x - 2) = 0

Step 2: Divide both sides by 2

x(x - 2) = 0

Step 3: Solve for roots

x = 0

x - 2 = 0

x = 2

Answer:

A right triangle is equal to 180 degrees so we would subtrat 90 and 42 to find the missing angle

90+42

=132

180-132

=48 degrees

Answer is A

\( \color{plum}\bold{(C)} \) Diameter of circle P is the same length as the radius of circle Q.

Given :

Diameter of circle P = 26 cm

Radius of circle P :

\( =\tt \frac{diameter}{2} \)

\( = \tt \frac{26}{2} \)

\(\color{plum} = \tt13 \: cm\)

Thus, radius of circle P = 13 cm

Diameter of circle Q = 52 cm

Radius of circle Q :

\( = \tt \frac{diameter}{2} \)

\( =\tt \frac{52}{2} \)

\( \color{plum}= \tt26 \: cm\)

Thus, radius of circle Q = 26 cm

Radius of circle R = 52 cm

Diameter of circle R :

\( =\tt radius \times 2\)

\( =\tt 52 \times 2\)

\(\color{plum} = \tt104 \: cm\)

Thus, the diameter of circle R = 104 cm

☆ Conclusion :

▪︎Diameter of circle P is the same length as the radius of circle Q.

Therefore, the correct option is (C) Diameter of circle P is the same length as the radius of circle Q.

Answer:

2/3 hours or 40 mins.

Step-by-step explanation:

No. of trees planted by David = 11

No. of hours worked by David to plant 11 trees = 7 1/3 hours = (7*3 + 1) /3 = 22/3

It takes him about the same amount of time to plant each tree

let time taken to plan 1 tree be x

then  time taken to plan 1*11 tree = 11*x

But, given that total time taken is 22/3 hours

thus,

11x = 22/3 hours

x = 22/(3 *11) = 2/3

Thus, it took 2/3 hours to plant each tree.

As 1 hour has 60 minutes

Time taken in minutes to plant 1 tree = 2/3 *60 mins = 40 mins

It takes David 2/3 hours to plant each tree.

Since it takes David 7 1/3 hours today to plant 11 trees.

Therefore time taken to plant 11 trees = 7 1/3 hours = 22/3 hours

The time taken to plant each tree = 22/3 hours ÷ 11 trees = 2/3 hours per tree

Therefore it takes David 2/3 hours to plant each tree.

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Probability that the person randomly chosen from the town's population is under 18 or employed part time is the probability of a randomly chosen person is under 18 plus the probability of a randomly chosen person is  employed part-time subtracting the probability that they are both under 18 and employed part-time.

In order to find the probability that a person is under 18 or employed part-time, you would need to know the proportion of the population that is under 18 and the proportion of the population that is employed part-time. Then you can use the following formula:

P(under 18 or part-time) = P(under 18) + P(part-time) - P(under 18 and part-time)

Where P(under 18 and part-time) is the probability that a person is under 18 and employed part-time at the same time.

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To find the numbers that are solutions of the inequality x > -12, we need to identify the numbers that are greater than -12. Any number that is greater than -12 will satisfy the inequality.

All numbers greater than -12 are solutions of the inequality x > -12.

For example, x = -10 is a solution because -10 is greater than -12. Similarly, x = 0, x = 10, x = 100, and any other number greater than -12 are also solutions.

The numbers that are solutions of the inequality x > -12 include all numbers greater than -12.

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Any number greater than -12 is a solution to the inequality x > -12. So, we can choose any number greater than -12 as a solution.

The inequality x > -12 represents all numbers greater than -12. To find which numbers are solutions to this inequality, we need to consider numbers that are greater than -12.

Let's look at a number line to visualize this:
              -12 ----------------------------------> (positive numbers)

Any number to the right of -12 on the number line is greater than -12. Therefore, any number greater than -12 is a solution to the inequality x > -12.

Examples of numbers that satisfy this inequality are:

1. -10: Since -10 is to the right of -12 on the number line, it is greater than -12.
2. 0: Similarly, 0 is also greater than -12.
3. 100: 100 is much greater than -12 and therefore satisfies the inequality.

However, numbers that are equal to -12 or less are not solutions to the inequality. For example, -12 itself is not greater than -12, so it does not satisfy the inequality.

In conclusion, any number greater than -12 is a solution to the inequality x > -12. So, we can choose any number greater than -12 as a solution.

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The correct answer is "spines." Spines are the pointed edges of a droplet that radiate out from the spatter.

They can be useful in determining the direction of force applied to the droplet. When a droplet impacts a surface, it spreads out and creates elongated extensions or projections along its periphery, known as spines. By examining the shape and orientation of these spines, forensic analysts can infer the direction from which the force that caused the spatter originated.

The spines provide us with  valuable information about the trajectory and angle of impact, aiding in the investigation and analysis of the event.

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Answer:

f(4) = 13

Step-by-step explanation:

f(4) = 2(4)+5
f(4) = 13

Answer:

13

Step-by-step explanation:

f ( x ) = 2x + 5

To find : f ( 4 )

f ( 4 ) = f ( x )

Here,

x = 4

So,

f ( 4 ) = 2 ( 4 ) + 5

        = 2*4 + 5

        = 8 + 5

f ( 4 ) = 13

Answer:

24°

Step-by-step explanation:

π radians = 180°

180°/(π radians) = 1

2π/15 radians × 180°/(π radians) = 24°

Answer:

hope this help you

have a great day

Answer:

\( →\sqrt[3]{27000} \div \sqrt[3]{125} \\ → \frac{ \sqrt[3]{27000} }{ \sqrt[3]{125} } = \frac{ \sqrt[3]{ {(30)}^{3} } }{ \sqrt[3]{ {(5)}^{3} } } = \frac{30}{5} = \boxed{ 6}✓\)

Answer:

$14,362

Step-by-step explanation:

The computation of the minimum unit cost is shown below:

Given that

0.6x^2 - 108x + 19,222

And as we know that the quadratic equation form is

ax^2 + bx + c

where

a = 0.6

b = -108

c = 19,222

Now for determining the minimal cost we applied the following formula which is

\(= \frac{-b}{2a} \\\\ = \frac{-(-108)}{2\times 0.6} \\\\ = \frac{108}{1.2}\)

= 90

Now put these values to the above equation

\(= 0.6\times 90^{2} - 108 \times 90 + 19,222\)

= 14,362

Answer:

20

Step-by-step explanation:

Let Kayla's age be k.

Let Isaac's age be a.

Kayla is 6 years older than Raoul. This means that:

k = y + 6

lsaac is 4 years younger than Raoul. This means that:

a = y - 4

y = 12

=> k = 12 + 6 = 18

and

a = 12 - 4 = 8

The sun of Raoul's age and Isaac's age is:

12 + 8 = 20

a. Yes, there is a BST B and a query value X such that the search for X in B visits the following sequence of key values in the given order.

b. No, there is no BST B and a query value X such that the search for X in B visits the following sequence of key values in the given order.

c. Yes, there is a BST t and a query value x such that the search for x in t visits the following sequence of key values in the given order.

A binary search tree (BST) is a data structure used to store a set of elements in a way that allows efficient search, insertion, and deletion operations.

It is a binary tree in which each node has at most two children, called left and right children.

Here the values are 11, 41, 71, 101, 141 The given questions can be answered as follows

(a) Yes, it is possible to construct a BST where the search for x visits the sequence of key values 11, 41, 71, 101, 141.

(b) No, it is not possible to construct a BST where the search for x visits the sequence of key values 101, 141, 41, 11.

This is because in BST, the values to the left of a node are always smaller than the node's values, and the values to the right are always larger.

Therefore, if the search reaches a node with a value greater than the value of the query, it will never be reached

revisit nodes with smaller values.

(c) Yes, it is possible to construct a BST where the search for x visits the key value 1 sequence. The tree would consist of a single node with a key value of 1.

Therefore

a. Yes, there is a BST B and a query value X, so a search for X from B visits the next sequence of key values in the given order.

b. No, there is no BST B and a query value of X, so a lookup of X from B visits the next sequence of key values in the given order. c. Yes, there is a BST t and a query value x, so a search for x from t visits the next sequence of key values in the given order.

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May's total profit given the revenue, fixed cost and variable cost is $250.

Profit is when the difference between revenue and total cost is positive. A loss is earned when the difference between revenue and total cost is negative.

Total cost is the sum of fixed cost and variable cost. Fixed cost is the cost that remains constant regardless of the level of output. Variable cost changes based on the level of output.

Total cost = variable cost + fixed cost

$9,000 + $300 = $9,300

Profit = revenue - total cost

$9,950 - $9,300 = $250

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Answer: The price of the apartment lies in the range of $1300 to $1800

Step-by-step explanation: Because Carlos doesn't exactly know how much  he'll make at his new job but he knows the range will be between 3000$ and 4000$ we will use inequality to solve this problem.

Let the rent on the new apartment = r

let monthly pay of Carlos = x

Given, apartment related fees = 200$

Given he is willing to use half of his monthly pay for rent and apartment related fees combined.

∴rent + apartment related fees = Monthly pay / 2

⇒\(r + 200 = \frac{x}{2}\)

⇒\(x=2*(r+200)\)

⇒\(x=2r+400\)                                                (1)

Given Carlos' monthly pay is in the range of $3000 to $4000

∴\(3000\leq x\leq 4000\)

⇒\(3000\leq (2r+400)\leq 4000\)                             (from equation (1))

⇒\(3000-400\leq 2r+400-400\leq 4000-400\)     (subtracting 400)

⇒\(2600\leq 2r\leq 3600\)

⇒\(\frac{2600}{2}\leq \frac{2r}{2}\leq \frac{3600}{2}\)                                           (dividing by 2)

⇒\(1300\leq r\leq 1800\)                                           (2)

ANS: The apartment lies in the price range of $1300 to $1800 as given by equation (2)

here is a problem solved using inequality

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20 is the difference between the modal score of Class B and the modal score of Class A

The mode is defined as the value with the highest frequency that is the value that occur the most in a given data.

From the given data, you can see that the mode of the Class A is 70 since student that has 70 marks are the most while the modal score for class B is 90.

Determine the difference

Difference = 90 - 70

Difference = 20

Hence the difference between the modal score of Class B and the modal score of Class A is 20

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Answer:

xdb bsbdb

Step-by-step explanation:

sdfbdfbbs