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The square root of 144 using the prime factorization method is 12.

When a number is multiplied by itself, the square of the number can be obtained.

The square root of 144 can be determined by the prime factorization method:

The prime factors of 144 are:

[tex]144 = 2 \times 2\times2 \times2 \times3 \times 3[/tex]

Since the square root can be obtained by forming the pair of the given number.

It can be written as:

144 = [tex]2^2 \times 3[/tex]

     =[tex]4 \times 3[/tex]

     = 12

Thus, the square root of 144 is 12.

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Answer:

60 km

455 km

23 km

60 km

82.5 km

Step-by-step explanation:

Time = t

Speed = s

Distance is given by

[tex]d=s\times t[/tex]

t = 2 hours

s = 30 km/h

[tex]d=30\times 2=60\ \text{km}[/tex]

Distance driven is 60 km.

t = 7 hours

s = 65 km/h

[tex]d=65\times 7=455\ \text{km}[/tex]

Distance driven is 455 km

t = [tex]\dfrac{1}{2}\ \text{hours}=0.5\ \text{hours}[/tex]

s = 46 km/h

[tex]d=46\times 0.5=23\ \text{km}[/tex]

Distance driven is 23 km

t = 45 minutes = [tex]\dfrac{45}{60}=0.75\ \text{hours}[/tex]

s = 80 km/h

[tex]d=80\times 0.75=60\ \text{km}[/tex]

Distance driven is 60 km

t = [tex]1\dfrac{1}{2}\ \text{hours}=1.5\ \text{hours}[/tex]

s = 55 km/h

[tex]d=55\times 1.5=82.5\ \text{km}[/tex]

The distance driven is 82.5 km

Answer:

i) a) 4 lines

b) 1 line

c) 3 line

d) 2 line

ii) don't know

To determine the percentage of the segment that should participate in the baseball camp in order to make a $1500 profit, we need to calculate the breakeven point and then find the corresponding percentage.

The breakeven point is the point where the revenue equals the total cost, resulting in zero profit. In this case, the breakeven point can be calculated by adding the fixed cost (TFC) to the variable cost per person multiplied by the number of participants.

Given that the price per participant is $80 and the variable cost per person is $5, we can set up the equation:

80x - (5x + 9000) = 0

Simplifying the equation, we have:

75x - 9000 = 0

75x = 9000

x ≈ 120

So, the breakeven point is approximately 120 participants.

To calculate the percentage, we need to divide the breakeven point (120) by the segment size (10000) and multiply by 100:

(120/10000) * 100 ≈ 1.2%

Therefore, the percentage of the segment that should participate in the baseball camp to make a $1500 profit is not exactly 1.2%, but it is closest to option D) about 1.4%.

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Answer:

Q:12) 9m-1.7m =7.3m

Q:13) 1.5m-0.8m=0.7

Q:14) 60cm-30cm= 30cm

Answer:

3 hours 5 minutes

Step-by-step explanation:

1 hour + 1 hour = 2hrs

15 minutes + 50 minutes = 65 minutes

65 minutes to 1 hr = 1 hr 5 minutes

2 hours + 1 hr 5 minutes = 3 hours 5 minutes

Answer:

3 hours and 5 minutes

Step-by-step explanation:

1 hour=60 minutes

1 hour +1 hour =2 hours

50 minutes +15 minutes = 1 hour and 5 minutes

1 hour and 5 minutes +2 hours=

3 hours and 5 minutes

Answer:

2 dollars donated.

Step-by-step explanation:

Answer:

18.18

Step-by-step explanation:

Answer:

-3/5 is the slope of the line.

Answer:

Parallelogram Theorem #1 Converse

Step-by-step explanation: : If each of the diagonals of a quadrilateral divide the quadrilateral into two congruent triangles, then the quadrilateral is a parallelogram. Parallelogram Theorem #2 Converse: If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Parallelogram opposite sides converse. Therefore, option A is the correct answer.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Let the diagonals AC and BC intersect at O.

Consider, triangle BOC and triangle AOD

OA=OC (Shown in the figure)

∠AOD=∠BOC (Vertically opposite angles are equal)

BO=DO (Shown in the figure)

By SAS congruence theorem

triangle BOC and triangle AOD are congruent

So, by CPCT AD=BC

Similarly,

From, triangle AOB and triangle DOC

AB=DC

Therefore, option A is the correct answer.

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Answer: 1. A 2. 1/5 3. 5/12 4. Not sure

Step-by-step explanation:

-30 is your answer.

Step by Step pictured below.

Answer:

1.32

Step-by-step explanation:

total area = 33

33/5 1/2 = 6 .         X=6

5 1/2 x 1/2 = 2.75 .       6 x 1/2 = 3

2.75 x 3 = 8.25

new area = 8.25

8.25 x .13 = 1.32

Answer:

calm down rosie....  it's okay to not be too good at math... take Justin Timberlake.  in the show   "Friends with Benefits"  he's horrible at math but good at life.  so don't worry too much. You are still a good person.. even if you're bad at math :P

Step-by-step explanation:

now for the math part

as below

Answer:

Cost of each cord = $7.5

Step-by-step explanation:

Given:

Discount rate = 30% = 0.30

Amount save by Lisa = $9

Number of charger = 4

Find:

Cost of each cord

Computation:

Total cost of 4 charger =  Amount save by Lisa[1/Discount rate]

Total cost of 4 charger =  9[1/0.30]

Total cost of 4 charger =  $30

Cost of each cord = Total cost of 4 charger / Number of charger

Cost of each cord = $30 / 4

Cost of each cord = $7.5

The NPV of the investment opportunity at a 6% interest rate is approximately $6,374. Taking into account the timing and value of the cash flows, it is advisable to take the opportunity.

The Net Present Value (NPV) of an investment opportunity calculates the present value of future cash flows discounted at a specific interest rate. Let's calculate the NPV at a 6% interest rate:

Year 1: Receive $500.

Year 2: Receive $1,500.

Year 10: Receive $10,000.

To find the NPV, we need to discount each cash flow back to its present value and sum them up:

NPV = (Cash flow at Year 1 / (1 + Interest rate)^1) + (Cash flow at Year 2 / (1 + Interest rate)^2) + (Cash flow at Year 10 / (1 + Interest rate)^10) - Initial investment

Plugging in the values, we get:

NPV = (500 / (1 + 0.06)^1) + (1500 / (1 + 0.06)^2) + (10000 / (1 + 0.06)^10) - 10000

≈ $6,374

Therefore, at a 6% interest rate, the NPV of the investment opportunity is approximately $6,374. Since the NPV is positive, it indicates that the investment is expected to generate a return greater than the cost of capital. Hence, it is advisable to take the opportunity.

(Note: The calculation for the NPV at 0% interest rate requires all future cash flows to be treated at their face value. Therefore, the NPV at a 0% interest rate would be equal to the sum of all future cash flows, which is $11,000 in this case.)

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Answer:

[tex]\boxed {\boxed {\sf 53}}[/tex]

Step-by-step explanation:

This is a stem and leaf plot, so the stem represents the first digit, while the leaf is the last digit.

The first stem is 0, with a leaf of 4. Therefore,

The last stem is 5, with 2 leaves: 6 and 7. We want to find the largest number, so we will use 7.

The range is the difference between the largest and smallest number. The largest number is 57 and the smallest is 4.

The range is 53.

The test statistic is approximately 0.45.

To calculate the test statistic for testing the null hypothesis H₀:p = 0.55 against the alternative hypothesis H₁:p ≠ 0.55, you can use the formula for the z-test statistic:

z = (p' - p) / √(p(1-p)/n)

where:

p' = sample proportion

p = hypothesized proportion under the null hypothesis

n = sample size

In this case, the sample proportion is p' = 55/96 = 0.5729 (rounded to 4 decimal places), p = 0.55, and n = 96.

Now let's calculate the test statistic:

z = (0.5729 - 0.55) / √(0.55 × (1-0.55) / 96)

z = (0.0229) / √(0.55 × 0.45 / 96)

z = (0.0229) / √(0.2475 / 96)

z = (0.0229) / √0.002578125

z = (0.0229) / 0.050773383

z ≈ 0.4502 (rounded to 4 decimal places)

Therefore, the test statistic is approximately 0.45.

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Answer:    F  2^4+2^3 .3^2

Step-by-step explanation:

16+2*36

2^4+72

2^4+2^3 .3^2

here 2^3=8

    and 3^2=9

so 8*9=72

Answer:

the correct answer is d

hope it help

Answer:

d or c more likey d

Step-by-step explanation:

Answer:a

Step-by-step explanation:

Answer:

A. Side a is 7 inches long and side b is 6 inches long.

Step-by-step explanation:

a = 21/3 = 7

b = 18/3 = 6

The Laplace transform of f(t) = et-³h(t – 3) is F(s) = 1/3 * 1/(s + 3) - 1/3 * 1/s, or F(s) = (s - 1)/(3s(s + 3)).

To find the Laplace transform F(s) = L{f(t)} of the function f(t) = et-³h(t – 3), we can use the properties and formulas of Laplace transforms. Let's break down the function and compute its transform step by step.

et-³: This term represents the exponential function with a power of t-³. The Laplace transform of et is given by 1/(s - a), where a is the exponent in the exponential function. Therefore, the Laplace transform of et-³ is 1/(s + 3).

h(t - 3): This term represents the Heaviside step function, h(t), shifted by 3 units to the right. The Laplace transform of the Heaviside step function h(t) is 1/s. When the function is shifted by a constant, the Laplace transform remains the same.

Combining these results, we have F(s) = L{f(t)} = 1/(s + 3) * 1/s.

To simplify the expression, we can use partial fraction decomposition:

1/(s + 3) * 1/s = A/(s + 3) + B/s.

Solving for A and B by equating numerators, we find A = 1/3 and B = -1/3.

Therefore, the Laplace transform of f(t) = et-³h(t – 3) is F(s) = 1/3 * 1/(s + 3) - 1/3 * 1/s, or F(s) = (s - 1)/(3s(s + 3)).

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Answer:

8851.86

Step-by-step explanation:

100-4.3= 95.7%

15000(.957)^12

A composite figure consists of two smaller figures - a rectangle and a Triangle. Therefore, the answer is 4 cm² (option a).

A composite figure that consists of two smaller figures - a rectangle and a triangle.

To find the area of the composite figure, we need to find the area of each smaller figure and add them up .Areaof rectangle to find the area of the rectangle, we need to multiply its length and width :Area of rectangle = 2 cm × 4 cm = 8 cm²Areaof triangle too find the area of the triangle, we need to use the formula :

Area of triangle = 1/2 × base ×heightT

he base of the triangle is 4 cm and the height is 2 cm, so:

Area of triangle = 1/2 × 4 cm × 2 cm = 4 cm²Area of composite figure To find the area of the composite figure, we need to add up the area of the rectangle and the area of the triangle: Area of composite figure = 8 cm² + 4 cm² = 12 cm². Therefore, the answer is 4 cm² (option a).

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Answer:

7

Step-by-step explanation:

just add them

them you get answer