Thang decided to borrow $7000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 5%. How much interest will Thang pay

We can conclude that -

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the regular price on a pair of jeans is $54. The store advertises a back-to-school sale at 40% off the regular price of the jeans. Two weeks later, the store advertises a sale at an additional off the sale price of these jeans at 5%.

Original price -

$54

Cost after 40% discount -

54 - {40% of 54}

54 - {40/100 x 54}

54 - {2/5 x 54}

54 - 21.6

$32.4

Cost after 5% discount -

32.4 - {5% of 32.4}

32.4 - {5/100 x 32.4}

32.4 - 1.62

$30.78

{ 3 } -

Calculating 60% of new price -

60% of 30.78

(60/100) x 30.78

18.5

Calculating 40% of new price -

40% of 30.78

(40/100) x 30.78

12.4

So, 60% of new price is greater than calculating 40%.

So, Manny is correct.

Therefore, we can conclude that -

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The total expenses of Marco's account are $174. The ending balance is $81. So, the starting balance will be $255.

Option A is correct for starting balance.

Further Explanation on Starting and Ending Balance

Given that Marco’s bank statement says that he has an ending balance of $81. The expenses $ of Marco is given as,

The total expenses can be calculated as given below.

Total Expenses = Sum of all Expenses

Total Expenses = 20+22+13+39+34+15+31

Total Expenses = $174

The starting balance can be calculated as given below.

Starting Balance = \(\$174 +\$81\)

Starting Balance = $ 255.

Hence we can conclude that the starting balance of Marco's account is $255. Option A is correct.

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Answer:

A

Step-by-step explanation:

The three angles opposite the three equal sides are equal in size because the three sides are equal.

Given,

An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. It is also known as an equiangular triangle since each angle is 60 degrees.

A right-angled triangle has one angle that is 90 degrees, thus if we define an equilateral triangle as having all angles that are 90 degrees, their sum would be 270 degrees, which is not conceivable because the sum of all the angles in a triangle is 180 degrees.

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Answer: 14

Step-by-step explanation:

Given the sequence : 55 176 539 1628

Each number after the first is derived by multiplying by x and then adding y;

If x and y are > 0 and they are integers.

Taking 55 and 176:

176 = 55*x + y

539 = 176*x + y

55x + y = 176 - - - (1)

176x + y = 539 - - (2)

From (1) y = 176 - 55x

Substitute y = 176 - 55x into (2)

176x + 176 - 55x = 539

121x = 539 - 176

121x = 363

x = 363 / 121

x = 3

Put x = 3 in y = 176 - 55x

y = 176 - 55(3)

y = 176 - 165

y = 11

x = 3, y = 11

x + y = 3 + 11 = 14

Answer:

a) 167 cups

b) 4 packages

Step-by-step explanation:

Given:

Diameter, d = 8cm

Height, h = 11 cm

10 gallon container

Since 1 gallon = 3085cm, 10 gallons will be:

= 10 * 3085 = 30850 cm

a) Consider that the shape of the cup is a cone. To determine how many paper cups are needed to empty the entire 10 gallon cooler, let's first find the volume of the cone.

Formula for volume of a cone:

\( V = \frac{1}{3} \pi r^2 h\)

We know radius, r = d/2 = 8/2 = 4cm

Substituting figures in the formula, we have:

\( V = \frac{1}{3} \pi 4^2*11\)

V = 184.31 cm³

The number of paper cups are needed to empty the entire 10 gallon cooler would be:

\( = \frac{30850}{184.31} = 167.38 cups \)

Approximately 167 cups

b) if the cups are sold in packages of 50, the number of packages to be bought will be:

\( = \frac{167}{50} = 3.34 \)

Which is approximately 4 packages

Answer:

  $0.04

Step-by-step explanation:

The cost per ounce is found by dividing the cost by the number of ounces.

In 2 gallons, there are 2×128 fl.oz. = 256 fl.oz. Then the cost per ounce is ...

  cost/ounces = $10.24/(256 fl.oz) = $0.04 /fl.oz.

The cost of the laundry detergent is $0.04 per fluid ounce.

__

Additional comment

Keeping the units with the numbers in a calculation can give you confidence that the calculated result has the units you want it to have.

Answer:

60.89 lbs.

Step-by-step explanation:

(362) x (4/9)

= 1448/9

= 160 8/9 = 60.89 lbs of canned goods

Answer:

it's going to be d.

Answer: c

Step-by-step explanation:

2*6=12

12+3=15

15 is not less than 10

2*4=8

8+3=11

11 is not less than 10

2*2=4

4+3=7

7 is less than 10

10*2=20

20+3=23

23 is not less than 10

The probability of the teacher selecting one green popsicle can be calculated by dividing the number of green popsicles in the box (4) by the total number of popsicles in the box (24). The probability of selecting one green popsicle is: P(green) = 4/24 = \(1/6 ≈ 0.1667\)

This means that there is a 16.67% chance of the teacher selecting a green popsicle from the box. To describe this simple event, we can say that the teacher will randomly select one popsicle from the box and the probability of that selected popsicle being green is 1/6.

If the teacher repeated this experiment many times (selecting one popsicle at a time), we would expect to see a green popsicle selected approximately once in every six trials.

It's important to note that this probability assumes that all the popsicles in the box are equally likely to be selected and that the teacher is selecting the popsicle at random without any bias or preference towards any specific color.

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Answer: x = 0

Step-by-step explanation:

Cross multiply 4 to (x+1)

4x + 4 = 3x + 4

Move all terms of X to one side of the equations, and non variable integers to the other side

4x (-3x) = 4 (-4)

x = 0

The answer is:

Work/explanation:

To solve this, I will distribute 4 on the left side:

\(\sf{4(x+1)=3x+4}\)

\(\sf{4x+4=3x+4}\)

Next, I subtract 3x from each side:

\(\sf{x+4=4}\)

Then, I subtract 4 from each side:

\(\sf{x=0}\)

According to the Statement The correct option is D.

The cause of Mozart’s demise is a long-standing medical mystery:

Wolfgang Amadeus Mozart, an Austrian composer, passed away at the age of 35 on 5 December 1791. Many studies and rumors have been produced regarding the circumstances of his passing.

Nevertheless, Mozart passed away from uremia and chronic kidney disease. Even a slight increase in stress can cause kidney failure if kidney damage reaches a critical stage.

Numerous sonatas and symphonies were also written by Mozart. The Jupiter Symphony, which was composed last, is arguably his most well-known work. In 1788, just three years before his passing, Mozart finished the Jupiter Symphony.

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Answer:

b-13=41

Step-by-step explanation:

Let b stand for the total number of minutes he practiced for. Subtracting 13 from it gets us Ashley's 41, so the equation can be b-13=41.

The solution to the system of equation y = 5x + 4 and y = 6x + 1 is (3,19).

Given the system of equation in the question;

y = 5x + 4

y = 6x + 1

To solve the system of equation, first plug equation one into equation two and solve for x.

y = 6x + 1

Plug in y = 5x + 4

5x + 4 = 6x + 1

Solve for x

6x - 5x = 4 - 1

x = 3

Now, plug x = 3 into equation one and solve for y.

y = 5x + 4

Plug in x = 3

y = 5( 3 ) + 4

y = 15 + 4

y = 19

Therefore, the value of x is 3 and y is 19.

Option A) (3,19) is the correct answer.

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If the line is sloping upward from left to right, so the slope is positive (+). If the line is sloping downward from left to right, so the slope is negative (-).

Answer:

|x|=-4 is immposible, absolute value is the distance of any number away from zero hence is it imposible for it to be a negative number

Hope this helps! :)

The triangle inequality is not satisfied. It is not possible for the third side of the reflective sticker to be 2 cm long.

(a) To determine if the third side of the reflective sticker could be 12 cm long, we can apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if the triangle inequality holds for the given side lengths:

6 cm + 8 cm > 12 cm

14 cm > 12 cm

Since the sum of the two given side lengths (6 cm and 8 cm) is greater than the potential third side length (12 cm), the triangle inequality is satisfied. Therefore, it is possible for the third side of the reflective sticker to be 12 cm long.

To draw the triangle, start by drawing a line segment of length 6 cm. From one endpoint of the 6 cm segment, draw another line segment of length 8 cm. Finally, connect the other endpoints of the two line segments with a line segment of length 12 cm. This will form the triangle with side lengths of 6 cm, 8 cm, and 12 cm.

(b) To determine if the third side of the reflective sticker could be 2 cm long, we again apply the triangle inequality theorem.

Let's check if the triangle inequality holds for the given side lengths:

6 cm + 8 cm > 2 cm

14 cm > 2 cm

In this case, the sum of the two given side lengths (6 cm and 8 cm) is not greater than the potential third side length (2 cm).

Hence, we do not need to draw a triangle for the case where the third side is 2 cm long, as it does not form a valid triangle.

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Answer:

20%

Step-by-step explanation:

Answer:

time required = 26 min

Step-by-step explanation:

To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):

○ diameter of pipe = 64 mm ⇒ radius = 32 mm

○ water discharge rate = 2.05 mm/s

○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm

○ height of tank = 2.3 m = 2300 mm.

Now, let's calculate the cross-sectional area of the pipe:

Area = πr²

       ⇒ π × (32 mm)²

       ⇒ 1024π mm²

Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:

Volume transferred = 1024π mm² × 2.05 mm/s

                                ⇒ 6594.83 mm³/s

Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h

            ⇒ π × (38)² × 2300

            ⇒ 10433857 mm³

We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,

time required =  \(\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}\)  

                     ⇒ 1582.12 s

                     ⇒ 1582.13 ÷ 60

                     ≅ 26 min

Answer:

  26 minutes

Step-by-step explanation:

The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.

For some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...

  V = k·d²·h . . . . d = diameter; h = rate×time

  V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³

For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...

  V = k(0.76 dm)²(23 dm) = k·13.2848 dm³

Then the proportion involving (inverse) rates is ...

  time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)

  fill time = 13.2848/0.503808 min ≈ 26.369

__

Additional comments

1 dm = 100 mm = 10 cm = 0.1 m

1 dm³ = 1 liter, though we don't actually need to know that here.

We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).

__

The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.

The length of IKE is 2x - 12.

A condition on a variable that is true for just one value of the variable is called an equation.

Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:

KT + TI = d

KE + EI = d

Substituting in the given values, we get:

x + 6 + 2x = d

2x + IE = d

Solving for d in the first equation, we get:

3x + 6 = d

Substituting this into the second equation, we get:

2x + IE = 3x + 6

Solving for IE, we get:

IE = x + 6

Therefore, IKE is equal to:

IKE = IT - IE

IKE = (d - KT) - (x + 6)

IKE = (3x + 6 - x - 6) - (x + 6)

IKE = 2x - 12

So, the length of IKE is 2x - 12.

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Answer:

The measure of angle 7 is 47°

The value of x = 69

Step-by-step explanation:

(a) The measure of angle 7 is also 47° { therefore angle 5 angle 7 are vertically opposite angles so they are equal }

(b) if the angle 6 is represented by (2x-5) so the equation will be (2x-5) + angle 5 = 180° { linear pair}

(c)

=> 2x-5+47 = 180

=> 2x + 42 = 180

=> 2x = 180 -42

=> 2x = 138

=> x = 138/2

=> x = 69

Answer:

See below ↓↓↓

Step-by-step explanation:

(a) ∠7 = ∠5 (vertically opposite angles)

(b) ∠5 and ∠6 form a line, so their sum is equal to 180°, which is the angle of a straight line. Therefore, our equation :

(c) Solving for x :

Using a 92% learning curve rate, the estimated manual labor hours required to build the 5th house would be 1,034 hours, the 10th house would be 692 hours, and all 18 houses combined would require 3,046 hours. Additionally, if the learning curve rates are 70%, 75%, and 80%, the estimated manual labor hours for all 18 houses would be 5,177, 4,308, and 3,636 hours, respectively.

The learning curve formula is given by \(Y = a * X^b\), where Y represents the cumulative average time per unit, X represents the cumulative number of units produced, a is the time required to produce the first unit, and b is the learning curve exponent.

In this case, the learning curve rate is 92%, which means the learning curve exponent (b) is calculated as log(0.92) / log(2) ≈ -0.0833.

a. To estimate the time required to build the 5th house, we can use the learning curve formula:

\(Y = a * X^b\)

\(Y(5) = 3500 * 5 ^ (-0.0833)\)

Y(5) ≈ 1034 hours

b. Similarly, the time required to build the 10th house can be estimated:

\(Y(10) = 3500 * 10^(-0.0833)\)

Y(10) ≈ 692 hours

c. The cumulative time required to build all 18 houses can be estimated by summing the individual estimates for each house:

\(Y(18) = 3500 * 18^(-0.0833)\)

Y(18) ≈ 3046 hours

d. To calculate the manual labor estimates for all 18 houses using different learning curve rates, we can apply the respective learning curve exponents to the formula. The results are as follows:

- For a 70% learning curve rate: Y(18) ≈ 5177 hours

- For a 75% learning curve rate: Y(18) ≈ 4308 hours

- For an 80% learning curve rate: Y(18) ≈ 3636 hours

In conclusion, using the given learning curve rate of 92%, the estimated time required to build the 5th house is 1034 hours, the 10th house is 692 hours, and all 18 houses combined would require 3046 hours. Additionally, different learning curve rates yield different manual labor estimates for all 18 houses.

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A: divide annual salary by 12 months:

42,000 / 12 = $3,500 per month

B: multiply sales by the percentages:

First 40,000 x 2.5% = 40,000 x 0.025 = $1,000

Amount over 40,000 = 59,000 - 40,000 = 19,000 x 4% = 19,000 x 0.04 = $760

Total commission = 1,000 + 760 = $1,760

c. Add a and b:

3,500 + 1,760 = $5,260

In a sample of 50 children, the probability that none of them has a food allergy can be calculated using the binomial probability formula. Let X be the number of children in the sample with a food allergy, and X ~ Bin(50, 0.05).

The probability of none of the 50 children having a food allergy is given by P(X = 0), which can be calculated as follows:

P(X = 0) = (50 choose 0) * (0.05)^0 * (1 - 0.05)^(50 - 0)

Using the binomial coefficient (n choose k) formula, (50 choose 0) = 1, and simplifying the expression, we have:

P(X = 0) = 1 * 1 * (0.95)^50

Calculating this probability to three decimal places, we get:

P(X = 0) ≈ 0.076

Therefore, the probability that none of the 50 children in the sample has a food allergy is approximately 0.076 or 7.6%.

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A has 156 cards, B has 39 cards, and J has 312 cards.

To find out how many cards A, B, and J have, follow these steps:

Let the number of cards B has be represented by the variable 'b'.

A has four times as many cards as B, so the number of cards A has can be represented as '4b'.

J has twice as many cards as A, so the number of cards J has can be represented as '2(4b)' or '8b'.

Together, A and J have 468 cards. Therefore, the equation can be written as 4b + 8b = 468.

Combine the like terms: 12b = 468.

Divide both sides of the equation by 12 to find the value of 'b': b = 468 / 12, which results in b = 39.

Now that we have the value of 'b', we can find the number of cards A and J have:

- A has 4 times as many cards as B: A = 4 × 39 = 156 cards.

- J has twice as many cards as A: J = 2 × 156 = 312 cards.

So, A has 156 cards, B has 39 cards, and J has 312 cards.

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Answer:

Number of adult tickets  = 298

Number of child tickets = 140

Step-by-step explanation:

Number of adult tickets  = a

Number of child tickets = c

a + c = 438      -------------------(I)

14a + 6c = 5012  ----------------(II)

Multiply equation (I) by (-6) and then add, so c will be eliminated.

(I) * (-6)           -6a - 6c = -2628

(II)                  14a + 6c =  5012   {Add}

                      8a       =  2384

                           a    = 2384/8

a = 298

Plugin a  = 298 in equation (I)

298 + c = 438

         c = 438 - 298

         c = 140

The average rate of change of the function f( x ) = x² + 7x + 6 at the interval of −4 ≤ x ≤ −1 is 2

The average rate of change the function is simply the change in y-values of the two points divided by the change in x-values of the two points.

It is expressed as;

Given the data in the question;

Average rate of change = ( f(-1) - f(-4) ) / ( (-1) - (-4) )

Average rate of change = ( (-1)² + 7(-1) + 6 ) - ( (-4)² + 7(-4) + 6 ) ) / ( (-1) - (-4) )

Average rate of change = ( (1 + -7 + 6 ) - ( 16 - 28 + 6 ) ) / (-1 + 4 )

Average rate of change = ( ( 0 ) - ( -6 ) ) / (-1 + 4 )

Average rate of change = ( 0 + 6 ) / ( 3 )

Average rate of change = 6 / 3

Average rate of change = 2

Therefore, the average rate of change of the function is 2.

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