5. Which value is closest to (7.5 x 10³)+(5.2 x 105) ?
A.
B.
C.
D.
11.7 x 105
11.7 x 104
5.275 x 105
5.275 x 104

PART A: Linda has $4.41 more than Enrique after one year.

PART B: Enrique has $12.10 more than Linda after the second year.

PART A: After one year, we can calculate the amount of money each person has in their respective accounts.

For Linda's account:

Principal amount = $610

Interest rate = 1.2%

\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)

\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)

For Enrique's account:

Principal amount = $590

Interest rate = 3.9%

\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)

Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91

Comparing the two amounts, after one year Linda has more money.

The difference in the amount is:

$617.32 - $612.91 = $4.41

Therefore, Linda has $4.41 more than Enrique after one year.

PART B: After a second year, we need to calculate the amounts again.

For Linda's account:

Principal amount = $617.32

Interest rate = 1.2%

\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)

Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73

For Enrique's account:

Principal amount = $612.91

Interest rate = 3.9%

\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)

Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83

Comparing the two amounts, after the second year Enrique has more money.

The difference in the amount is:

$636.83 - $624.73 = $12.10

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Answer:

It will take 26.4 years for investment to reach $2000

Step-by-step explanation:

2000=100(1+.12)^x

20=1.12^x

㏒_{20} 1.12=x

log 1.12/ log 20=x

x= 26.434

The number of years that should be taken for reaching $2,000 is 26.40 years.

Given that,

Based on the above information, the calculation is as follows:

\(2000=100(1+.12)^x\\\\20 = 1.12^x\)

Now apply log to both sides

\(\frac{log1.12}{log20} = x\)

x = 26.4 years

Therefore we can conclude that the number of years that should be taken for reaching $2,000 is 26.40 years.

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Answer:

D.

Step-by-step explanation:

It's the most miles.

After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

Herein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:

dy / dt = 3 · y · (1 - y / 14)

dy / [3 · y · (1 - y / 14)] = dt

dy / [- (3  / 14) · y · (y - 14)] = dt

By partial fractions we find the following expression:

- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt

- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.

y = 14 / [1 - C · tⁿ], where n = - 14² / 3.

If y(0) = 10, then the particular solution is:

y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

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Answer:

A

Step-by-step explanation:

YESYESYESYESYESx85

Answer:

a = 3/28

Step-by-step explanation:

To start solving for a variable, you need to isolate it.

-4/3b = 4a

-4/3 divided by 4 equals -4/12 or -1/3

a = -1/3b

To completely solve for a we need to plug it back in and solve for b.

b = (4(-1/3b)) - 3/4

b = -4/3b - 3/4

7/3b = -3/4

b = -9/28

Finally, we can plug b back in to the previous equation we got for a to solve for a.

a = -1/3(-9/28)

a = 3/28

Furthermore, we can check if this is correct by plugging in 3/28 for a into the original problem and see if we get what we got for b (-9/28)

Step-by-step explanation:

work he in a department store

Answer:

67 degrees

Step-by-step explanation:

Answer:

67 degrees

Step-by-step explanation:

You wanna sub. 75 from 142. Hope this helped.

Answer:

9

Step-by-step explanation:

This problem is represented below.

=3(4+2)-9

=3(6)-9

=18-9

=9

6:35 a.m.

1) To find out what time it is, then let's add them up:

hours minutes

3 15

3 20

--------------------------

6 35

2) Note that since the sum of the minutes does not pass 60 minutes, then we can end up right here.

3) Hence, the answer is 6:35 a.m.

The measure of angle x on the straight line is 130 degrees.

The sum of interior angles in a triangle equals 180 degrees.

To determine the value of x, we first determine its suplemetary angle x .

Hence:

40 + 90 + ( suplemetary angle of x ) = 180

Solve for the suplementary angle:

130 + ( suplemetary angle of x ) = 180

Suplementary angle of x = 180 - 130

Suplemetary angle of x = 50 degree

Now, we can find the measure of  angle x.

Note that, sum of angles on a straight line equals 180 degree.

Hence:

x + ( suplemetary angle of x )  = 180

x + 50 = 180

Solve for x

x = 180 - 50

x = 130 degrees.

Therefore, the value of x is 130 degrees.

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Answer:

A plane flying horizontally at an altitude of 1 mi. and a speed of 500 mi ./hr. passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing ex when it is 2 mi. away

Answer:

The following are the solution to the given points:

Step-by-step explanation:

Given value:

\(1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}\)

Solve point 1 that is \(\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\\):

when,

\(k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\\)

                  \(= \frac{1}{2} - \frac{1}{3}\\\\\)

\(k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\\)

                  \(= \frac{1}{3} - \frac{1}{4}\\\\\)

\(k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\\)

                  \(= \frac{1}{4} - \frac{1}{5}\\\\\)

\(k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\\)

Calculate the sum \((S=s_1+s_2+s_3+......+s_n)\)

\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\\)

   \(=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\\)

When \(s_n \ \ dt_{n \to 0}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\\)

\(\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}\)

In point 2: \(\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}\)

when,

\(k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\\)

                  \(= \frac{1}{7 \times 8}\\\\= \frac{1}{56}\)

\(k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\\)

                  \(= \frac{1}{8 \times 9}\\\\= \frac{1}{72}\)

\(k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\\)

                  \(= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\\)

\(k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\\)

calculate the sum:\(S= s_1+s_2+s_3+s_n\\\)

\(S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\\)

when \(s_n \ \ dt_{n \to 0}\)

\(S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066\)

\(\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}\)

The shaded region of the rectangle is 242.9 cm² and the shaded region of the sector is 7.1 square units.

Question 17) is a figure of a rectangle and two inscribed circles.

The area of a rectangle is expressed as: A = length × width

The area of a circle is expressed as: A = πr²

Where r is the radius.

To determine the area of the shaded region, we simply subtract the areas of the two circles from the area of the rectangle.

Area = ( Length × width ) - 2( πr² )

Area = ( 40 × 10 ) - 2( π × 5² )

Area = ( 400 ) - 2( 25π )

Area = 400- 50π

Area = 242.9 cm²

Area of the shaded region is 242.9 squared centimeters.

Question 18) is the a figure a sector of a circle and a right triangle.

The area of a sector is expressed as: A = (θ/360º) × πr²

The area of a triangle  is expressed as: A = 1/2 × base × height

To determine the area of the shaded region, we simply subtract the areas of the triangle from the area of the sector.

Hence:

Area = ( (θ/360º) × πr² ) - ( 1/2 × base × height )

Plug in the values:

Area = ( (90/360º) × π × 5² ) - ( 1/2 × 5 × 5 )

Area = 25π/4 - 12.5

Area = 7.1

Therefore, the area of the shaded region is 7.1 square units.

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Answer:

3053.63 cu. inches

Step-by-step explanation

Volume = 4/3 pi r^3

Answer:

\(v \: \: ≈

3053.62 {in}^{3}

\)

Step-by-step explanation:

\(v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times \pi \times {9}^{3} \\ ≈

3053.62806

\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

x = -2

Step-by-step explanation:

Given angles are,

→ 9x + 96°

→ 7x + 92°

Now we have to,

→ Find the required value of x.

We know that,

→ Vertically opposite angles are equal.

Forming the equation,

→ 9x + 96° = 7x + 92°

Then the value of x will be,

→ 9x + 96° = 7x + 92°

→ 9x - 7x = 92° - 96°

→ 2x = -4

→ x = -4/2

→ [ x = -2 ]

Hence, the value of x is -2.

When the given proportion is solved the value of w is calculated to be 6.

What is proportion?

A proportion can be commonly understood as two ratios that have been set equal to each other; a proportion is an equation that can be solved.

When it is said that proportion is two ratios that are equal to each other, it means in the sense of two fractions being equal to each other.

for example 5/10 = 1/2, 5:10 = 1: 2

7:42 = 1 : w

\(\frac{7}{42} = \frac{1}{w} \\\)

w = 1 x 6

w = 6

When the given proportion is solved the value of w is calculated to be 6

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A statement that describes the result of running the code segment is: the number 10 is displayed

The correct answer is an option (B)

In this question, we have been given the program code.

We need to select a correct statement that describes the result of running the code segment.

Consider the given code.

Start by setting n and sum to 0.

Add the value of n to sum. The first time, the value of n is 0, so sum remains 0.

Increment n by 1, so now the value of n is 1.

The Boolean condition (n = 5) is still false, so the loop will run again. Add 1 to sum (which is now 1), and then increment n (so n is now 2).

Repeat this three more times (while the value of n = 2, 3, and 4)

Increment n, so the value of n is now 5. Now the Boolean condition is true, so the loop stops.

Display sum is 10

Therefore, the result of running the code segment : the number 10 is displayed

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The complete question is:

Consider the following program code.

Which of the following best describes the result of running the program code?

A. The number 0 is displayed.

B. The number 10 is displayed.

C. The number 15 is displayed.

D. Nothing is displayed; the program results in an infinite loop

a) There are 2 x 2 = 4 sample points in the sample space

b) Tree Diagram

O D.\nH\nHe\nT\nH\nT\n

Sample space: D. HH, HT, TH, TT

c) P(no tails) = P(HH)

= 1/4

d) P(exactly one tail) = P(HT, TH)

= 2/4

= 1/2

e) P(2 tails) = P(TT)

= 1/4

f) P(at least one tail) = P(HT, TH, TT)

= 3/4

In mathematics, tree diagrams are often used in probability and statistics to show all the possible outcomes of an event. In computer science, they are used to represent the hierarchical structure of files and directories in a file system

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Answer: x³-9x²+13x-17

Step-by-step explanation:

I used Photomath with is an app that takes pictures of equations and figures them out for you, 100% percent recommend.

Answer:

$9.49

Step-by-step explanation:

you take the $56.94 and divide by 6 to get the unit price

The standard deviation of the response time is 1.53 minutes.

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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Answer:

250 and 250.1

Answer:

250.1

Step-by-step explanation:

5002 divided by 20 equals 250.1

Mathematics provides a framework for developing critical thinking, problem-solving, and analytical skills that are valuable in many aspects of life.

What is mathematics?

Mathematics is a fundamental discipline that plays a crucial role in our daily lives and in shaping our understanding of the world.

Mathematics is a field of study that deals with the properties and relationships of numbers, quantities, shapes, and patterns. It involves using logical reasoning, abstraction, and symbolic manipulation to understand and solve problems related to these concepts.

Mathematics is important for many reasons. First and foremost, it is a fundamental tool for understanding and describing the world around us. It plays a crucial role in science, technology, engineering, economics, finance, and many other fields by providing tools for modeling and analyzing complex phenomena.

Mathematics is also essential for making accurate predictions and decisions based on data and evidence, as well as for designing and optimizing systems and processes.

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To solve this problem, we need to convert all the measurements to a consistent unit. Let's convert the height to inches since the height of the bounce is given in inches.

64 ft = 64 * 12 inches = 768 inches

Now, we can set up an equation to represent the height of each bounce. Let's use "b" to represent the number of bounces, and "h" to represent the height of each bounce in inches.

The height of each bounce is three-fourths (3/4) the height of the previous bounce. So, we can write the equation as:

h = (3/4) * h_previous

where h_previous is the height of the previous bounce.

We know that the initial height of the ball is 768 inches, and we want to find the number of bounces when the height of the bounce is less than 9 inches. We can set up an inequality to represent this situation:

h < 9

Substituting the expression for h from the equation above, we get:

(3/4) * h_previous < 9

Now, we can start with the initial height of 768 inches and keep applying the equation for each bounce until the height of the bounce is less than 9 inches.

1st bounce:

h = (3/4) * 768 = 576 inches

2nd bounce:

h = (3/4) * 576 = 432 inches

3rd bounce:

h = (3/4) * 432 = 324 inches

4th bounce:

h = (3/4) * 324 = 243 inches

5th bounce:

h = (3/4) * 243 = 182.25 inches

6th bounce:

h = (3/4) * 182.25 = 136.6875 inches

7th bounce:

h = (3/4) * 136.6875 = 102.515625 inches

8th bounce:

h = (3/4) * 102.515625 = 76.88671875 inches

9th bounce:

h = (3/4) * 76.88671875 = 57.6650390625 inches

10th bounce:

h = (3/4) * 57.6650390625 = 43.248779296875 inches

So, the ball will bounce up to a height less than 9 inches after 10 bounces.

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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Hi,

Answer:

Tachycardia is a fast heart rate