Which is the simplified form of the expression
3(7/5x+ 4) – 2( 3/2- 5/4)

Answer: 30 yards

Step-by-step explanation: To get the diameter, we double the radius.

So 15 doubles is 30 so we now that the diameter of the circle is 30 yards.

Answer:

The diameter would be 30 yards.

Step-by-step explanation:

Answer:

its b x=2

Step-by-step explanation:

hope it helps

Answer:

ja ksjslsj si wlsjsñw ja

Answer:

No, I don't think so.

Step-by-step explanation:

Answer: 3.375

Step-by-step explanation:

Multiply

1 1/2 × 2 1/4 = 27/8

Simplify

27/8 = 3  3/8

Answer:

Step-by-step explanation:

P: the principal, amount invested

A: the new balance

t: the time

r: the rate, (in decimal form)

n: the number of times it is compounded.

Ex2:Suppose that $5000 is deposited in a saving account at the rate of 6% per year. Find the total amount on deposit at the end of 4 years if the interest is:

P =$5000, r = 6% , t = 4 years

a) simple : A = P(1+rt)

A = 5000(1+(0.06)(4)) = 5000(1.24) = $6200

b) compounded annually, n = 1:

A = 5000(1 + 0.06/1)(1)(4) = 5000(1.06)(4) = $6312.38

c) compounded semiannually, n =2:

A = 5000(1 + 0.06/2)(2)(4) = 5000(1.03)(8) = $6333.85

d) compounded quarterly, n = 4:

A = 5000(1 + 0.06/4)(4)(4) = 5000(1.015)(16) = $6344.93

e) compounded monthly, n =12:

A = 5000(1 + 0.06/12)(12)(4) = 5000(1.005)(48) = $6352.44

f) compounded daily, n =365:

A = 5000(1 + 0.06/365)(365)(4) = 5000(1.00016)(1460) = $6356.12

Answer:

2552.60

Step-by-step explanation:

The binomial x - 12 is a factor of the trinomial [tex]4x^2 - 4x - 120.[/tex]

To determine which binomial is a factor of the trinomial [tex]4x^2 - 4x - 120,[/tex] we can use the factor theorem and test each binomial by dividing it into the trinomial.

The binomials given are:

A. x + 12

B. 2x + 5

C. 2x - 5

D. x - 12

To test each binomial, we perform polynomial division:

A. x + 12:

Dividing [tex]4x^2 - 4x - 120 by x + 12,[/tex] we find that there is a remainder, indicating that x + 12 is not a factor of the trinomial.

B. 2x + 5:

Dividing [tex]4x^2 - 4x - 120[/tex] by 2x + 5, we also find that there is a remainder, so 2x + 5 is not a factor.

C. 2x - 5:

Dividing [tex]4x^2 - 4x - 120[/tex]  by 2x - 5, we again find a remainder, indicating that 2x - 5 is not a factor.

D. x - 12:

Dividing [tex]4x^2 - 4x - 120[/tex]  by x - 12, we find that there is no remainder, indicating that x - 12 is a factor of the trinomial.

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Answer: A Quick silver

Step-by-step explanation:

he can run fast and is cool

Answer:

mystique

Step-by-step explanation:

shes just the perfect spy, with her no mission can go wrong

Answer:

[tex]\boxed {y = -\frac{1}{2}x + 3}[/tex]

Step-by-step explanation:

Convert the equation from Standard Form to Slope-Intercept Form:

[tex]Ax + By = C[/tex]  ⇒  [tex]y = mx + b[/tex]

-The following equation:

[tex]x - 2y = 6[/tex]

-Solve:

[tex]x - 2y = 6[/tex]

[tex]x - x - 2y = 6 - x[/tex]

[tex]2y = -x + 6[/tex]

[tex]\frac{2y}{2} = \frac{-x}{2} + \frac{6}{2}[/tex]

[tex]\boxed {y = -\frac{1}{2}x + 3}[/tex]

So, the equation in Slope-Intercept Form is [tex]y = -\frac{1}{2}x + 3[/tex].

Answer:

Line Symmetry: Yes

Point Symmetry: Yes

Rotational Symmetry: Yes

Step-by-step explanation:

The "Line of Symmetry"  is the imaginary line where you could fold the image and have both halves match exactly

Point Symmetry is when every part has a matching part: the same distance from the central point.

Rotational symmetry, also known as radial symmetry, is the property a shape has when it looks the same after some rotation by a partial turn.

Hope this helps!

Answer: 6+4i

Step-by-step explanation:

Answer: r=0

It’s very easy to do and make sure to simplify

Answer:

y=3x^2+6x−24

Step-by-step explanation:

Answer:

Step-by-step explanation:

Y=3(x-2)(x+4)

= 3(x2 -2x +4x -8)

=3(x2+2x-8)

= 3x2 + 6x - 24

Hey there!

Each person would mostly get approximately $10.35 because you simply DIVIDE 31.05 from 3 & 10.35 * 3 gives you $31.05

Here’s an equation you can set it up as

• 3p = number of people

• 31.05 could be the one the one we’re dividing with p

• So your equation will most likely look like:

3p = 31.05

“3p = 31.05”

• DIVIDE both of your sides by 3

3p/3 = 31.05/3

• Cancel out

3p/3 because that gives you 1

• Keep

31.05/ 3 because that helps us solve what we give to the number of people

p = 31.05 / 3

➡️ 31.05 / 3 = 10.35

Thus, each person will get: 10.35

So that further a do: your answer is “10.35”☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

We know that:

1 inch in the drawing, equals 3 feet in the real room.

Then if the scale is 6 in by 4 in, the actual room is:

6*3ft by 4*3ft

18ft by 12ft.

The total area of the room is:

18ft*12ft = 216ft^2.

Now we know that the price of the carpet is $5,50 per square ft,

The area of the room is 216 ft^2, then if we want to carpet the whole room, we need to pay 216 times $5.50.

Cost = 216*$5.50 = $1,188

Answer: x= -1

2x + 3(5 - x) - 12 = 4(x + 2)

1) pass: Delete the parentheses, making the multiplications.

2x + 15 - 3x - 12 = 4x + 8

2) pass: Put the numbers with incognito on the left and change the signal when changing sides if necessary, put the numbers without incognito on the right by changing the signal if necessary.

2x + 15 - 3x - 12 = 4x + 8

2x - 3x - 4x = - 15 + 12 + 8

3) pass: Solve the equations not forgetting the signal rules.

2x - 3x - 4x = - 15 + 12 + 8

- x - 4x = - 3 + 8

- 5x = 5 Simplify by (-1) Exchanging the signals

5x = -5

Answer:

C) 256

Step-by-step explanation:

√256 = 16

Answer:

Okay I mayyy be wrong on this but, is it 12?

Answer:

Hippo potamus

Step-by-step explanation:

Cause the hypotenuse said so.

1) The quantum that should be paid moment for the security is$ 5,634.34. 2) Alicia will have$ in her withdrawal account at age 65.

1) We're given that the security will pay$ 7,000 in 8 times and the interest rate is2.75 per time.

We've to calculate what should be paid moment for the security.

First, we will calculate the present value of the security by using the following formula

PV = FV/( 1 r) n

where, FV = unborn value = $ 7,000

r = periodic interest rate = 2.75

n = number of times = 8

Substituting the given values, we get

PV = $ 7,000/( 10.0275) 8PV = $ 5,634.34

Hence, the quantum that should be paid moment for the security is$ 5,634.34.

2) We're given that Alicia will save$ 6,000 at the end of each time until she's 65.

We need to calculate how important she'll have in her withdrawal account at age 65, given that the account earns6.5 per time.

To calculate the unborn value of her savings, we can use the following formula

FV = PMT *(( 1 r) n- 1)/ r

where, PMT = payment per period = $ 6,000

r = interest rate per period = 6.5 = 0.065

n = number of ages = 40( since she's saving until she's 65 and she's presently 25)

Substituting the given values, we get

FV = $ 6,000 *(( 10.065) 40- 1)/0.065 FV = $

Hence, Alicia will have$ in her withdrawal account at age 65.

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Answer:

x=.12

Step-by-step explanation:

The reason:

-11=14+3j

-14 -14

-25=3j

divide 3 =

-.12

Answer:

[tex]j=-\frac{25}{3}[/tex]

Step-by-step explanation:

[tex]-11=3j+14[/tex]

Simple numerical terms are commonly written last.

[tex]-11+(-14)=(3j+14)+(-14)[/tex]

To solve this linear equation, we need to group all the variable terms on one side, and all the constant terms on the other side of the equation.

In our example, [tex]14[/tex], will be moved to the left side.  Notice that a term changes sign when it 'moves' from one side of the equation to the other.

Answer:

45

Step-by-step explanation:

15x3=45

Answer:

8⋅(x−3)  2

Step-by-step explanation:

In question 1, the recursive formula for the balance of Mohamed's credit card debt each month can be written as Bₙ = 1.02Bₙ₋₁ - 300, where Bₙ represents the balance in the nth month.

In question 2, (i) The second term in the expansion of (y-2x)³ is option B: -8y³x.

(ii) Row 7 of Pascal's Triangle is option B: 1, 5, 10, 10, 5, 1.

(iii) Expanding (2x³ + 1)³ completely yields 8x⁹ + 12x⁶ + 6x³ + 1.

In question 3, To prove the statement that the sum of the first n odd numbers is equal to the nth square (1+3+5+7+...+(2n-1) = n²) by mathematical induction, the induction assumption is option A: The statement is true for n=k: 1 + 3 + 5 + 7 + ... + (2k-1) = k².

In question 4, the probability distribution for the random variable X, representing the work atmosphere scores, can be constructed using the given frequency distribution.

In question 1(i), the recursive formula Bₙ = 1.02Bₙ₋₁ - 300 represents the balance of Mohamed's credit card debt each month. The balance increases by 2% each month due to interest and decreases by the monthly payment of AED 300.

In question 1(ii), to find the first three iterates of the function f(x) = 5x + 4 starting with x₀ = 2, we substitute the value of x₀ into the function and then repeatedly apply the function to obtain x₁, x₂, and x₃.

In question 2, the answers are obtained as follows:

(i) To find the second term in the expansion of (y-2x)³, we use the binomial expansion formula (a-b)³ = a³ - 3a²b + 3ab² - b³. In this case, a = y and b = 2x. Using the formula, the second term is -3a²b = -3(y)²(2x) = -3y²(2x) = -6xy². However, in the given options, the term is in the form -8y³x. To match this form, we can rewrite -6xy² as -8y³x. Therefore, the second term is -8y³x, which corresponds to option B.

(ii) Pascal's Triangle is a triangular arrangement of numbers where each number is the sum of the two numbers above it. Row 7 of Pascal's Triangle is 1, 6, 15, 20, 15, 6, 1. However, none of the options matches this row. Thus, the given options are incorrect, and the correct row 7 of Pascal's Triangle is not provided.

(iii) To expand (2x³ + 1)³ completely, we use the binomial expansion formula (a + b)³ = a³ + 3a²b + 3ab² + b³. In this case, a = 2x³ and b = 1. Applying the formula, we obtain (2x³ + 1)³ = (2x³)³ + 3(2x³)²(1) + 3(2x³)(1)² + (1)³. Simplifying this expression gives 8x⁹ + 12x⁶ + 6x³ + 1.

Therefore, the second term in the expansion of (y-2x)³ is -8y³x, the correct row 7 of Pascal's Triangle is not provided, and the expansion of (2x³ + 1)³ is 8x⁹ + 12x⁶ + 6x³ + 1.

In question 3, To prove the given statement using mathematical induction, we need to follow the steps of induction: base case and induction step.

The base case is when n = 1. We need to show that the statement is true for n = 1. Evaluating the left-hand side (LHS) and right-hand side (RHS) of the equation, we have 1 = 1², which is true.

Next, we assume that the statement is true for some value k, which is the induction assumption. In this case, the assumption is that 1 + 3 + 5 + 7 + ... + (2k-1) = k².

Now, we need to prove that the statement holds for n = k+1. This is the induction step. We add (2k+1) to both sides of the assumption and evaluate the LHS and RHS. The LHS becomes 1 + 3 + 5 + 7 + ... + (2k-1) + (2k+1), and the RHS becomes (k+1)².

By applying the induction assumption and simplifying the LHS, we can show that it is equal to (k+1)², proving the statement for n = k+1.

Therefore, option A: The statement is true for n=k: 1 + 3 + 5 + 7 + ... + (2k-1) = k² is the correct induction assumption for proving the sum of the first n odd numbers is equal to the nth square.

Regarding the second part, to prove that 7ⁿ - 4ⁿ is divisible by 3, we can use mathematical induction. By verifying the base case (n = 1) and assuming the statement is true for n = k, we can prove that it holds for n = k+1.

In question 4, to construct the probability distribution for the random variable X, we use the frequency distribution to determine the probabilities associated with each score. The expected value of the distribution can be calculated by multiplying each score by its corresponding probability and summing the results.

By understanding the concepts and applying the appropriate formulas and techniques, the solutions to these questions can be obtained.

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The bearing of D from C is determined as 315 degrees clockwise from north of C.

A bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.

From the given diagram, the bearing of D from C is calculated by taking the angle measure of point D from North of C clockwise as follows;

D from C = 360⁰ - 45⁰ = 315⁰

Note; 45⁰ is the position of D from north of C anti clockwise, since we are interested in the clockwise measure of the bearing, we subtracted 45 degrees from 360 degrees; which is the sum of angle at a point.

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The equation of a line perpendicular to 2x-3y=6 and passes through the point (6,-1) is y=2/3x-5.

The given line 2x-3y=6 has a slope of m=2/3.

A line perpendicular to this line will have a slope that is the negative reciprocal of this slope. Therefore, the slope of the line perpendicular to 2x-3y=6 is -3/2.

Using the point-slope formula to find the equation of the line:y-y1 = m(x-x1).

Substituting in the point (6,-1) and the slope of -3/2:y-(-1) = -3/2(x-6)y+1 = -3/2x + 9y = -3/2x + 8.

The equation of a line perpendicular to 2x-3y=6 and passes through the point (6,-1) is y=2/3x-5.

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Answer:

C. 16

Step-by-step explanation:

First of all, these two angles are corresponding angles, which means that they equal each other. So, the equation here would be: 2x+18= 4x-14.

Step 1- Move the variables to one side.

2x+18= 4x-14

-2x       -2x

18= 2x-14

Step 2- Add 14 to both sides of the equation.

18= 2x-14

+14      +14

32= 2x

Step 3- Divide 2 to both sides of the equation to isolate the variable.

32= 2x

2     2

x= 16

Answer:

24.2

Step-by-step explanation:

37.45-13.25=24.2

24.2/2=12.1

each friend contributes $12.1

The Probability of all four boys being chosen is only 1.8%. This means that it would be highly unlikely to occur by chance alone.

In a classroom with some girls and some boys, four students are chosen at random to lead a class discussion. All of those chosen are boys. The probability of this happening would be highly unlikely to occur by chance alone.

In probability theory, the probability of an event is a measure of the possibility of the event occurring. It is expressed as a value between zero and one, with zero representing impossibility and one representing certainty.

The formula for calculating the probability of an event is the number of ways the event can occur divided by the total number of possible outcomes. In this case, the probability of four boys being chosen from a mixed group of boys and girls is calculated as follows:

The probability of the first boy being chosen is the number of boys divided by the total number of students. If there are 30 students in the class, 15 boys, and 15 girls, then the probability of the first boy being chosen is 15/30.

The probability of the second boy being chosen is the number of remaining boys divided by the total number of remaining students. After the first boy is chosen, there are 14 boys and 29 students left. Therefore, the probability of the second boy being chosen is 14/29.

The probability of the third boy being chosen is the number of remaining boys divided by the total number of remaining students. After the second boy is chosen, there are 13 boys and 28 students left. Therefore, the probability of the third boy being chosen is 13/28.

The probability of the fourth boy being chosen is the number of remaining boys divided by the total number of remaining students.

After the third boy is chosen, there are 12 boys and 27 students left.

Therefore, the probability of the fourth boy being chosen is 12/27.To find the probability of all four boys being chosen, we multiply the probabilities of each event together:15/30 * 14/29 * 13/28 * 12/27 = 0.018 or 1.8%

Therefore, the probability of all four boys being chosen is only 1.8%. This means that it would be highly unlikely to occur by chance alone.

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