In one account, $20,000 grows to $27,307 after 5 yr. Compute the interest rate. Round your answer to a tenth of a percent.
The interest rate is approximately

Answer:

the first one

Step-by-step explanation:

i had that question

Answer:

470

Step-by-step explanation:

x is the amount that represents 100 %

517 amount that represents 100%+10% increase = 110%

x = (517 *100) / 110 = 470 is the original amount

i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

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Answer:

The rotational angle of a regular polygon with 72 sides is 5º.

Step-by-step explanation:

The rotational angle (\(\theta\)), measured in sexagesimal degrees, of polygon of \(n\) sides is the angle of a complete revolution divided by the number of sides (\(n\)). That is:

\(\theta = \frac{360}{n}\) (1)

If we know that \(n = 72\), the rotational angle is:

\(\theta = \frac{360}{72}\)

\(\theta = 5^{\circ}\)

The rotational angle of a regular polygon with 72 sides is 5º.

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .

a. Input variables: hours worked as a cashier, payroll clerk, and assistant.

The total amount earned each week is the output variable.

b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:

Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)

c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).

d. The equation describing the total money earned each week is as follows:

(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y

This expression is simplified as follows:

y = 190 + 9x - 70 + 7x

y = 16x + 120

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.

g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:

y = 16x + 120 + 0

y = 16x + 120

As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.

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Answer:3⁴ and 81¹

Step-by-step explanation:

3⁹= 19683

3⁴= 81

-9²= -81

9⁹= 387,420,489

81¹= 81

To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)

The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)

The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)

Solving for\(\(x\),\) we divide both sides of the equation by 3:

\(\(x = \frac{71}{3}\).\)

Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.

The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:

\(\(x = 2\pi r\).\)

Substituting the value of x we found earlier, we have:

\(\(\frac{71}{3} = 2\pi r\).\)

Solving for r, we divide both sides of the equation by \(\(2\pi\):\)

\(\(r = \frac{71}{6\pi}\).\)

Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.

In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.

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Answer:

y< -6

Step-by-step explanation:

thas the answer

This is simple just divide -2 on both sides.

BUT, NEVER forget that if you divide a negitive then you need to swap the sign to the oppisite side.

12/-2 < y -> -6 > y or y < -6

Step-by-step explanation:

A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+16.950.60M, where M is the number of miles driven.

The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+4.900.15M.

Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.

Answer:

quarts. 11. fluid ounces = —. 1. 4. — quart. 12. quarts = 6 gallons. 13. 16 pints = gallons. 14. ... How many times must a 1-cup measuring cup be filled to equal 4 pints? 2. Leroy has 2 containers. ... can hold. Write cup, pint, quart, or gallon. 15. a bathtub. 16. a container of orange juice. 17. a juice box. 18. a small milk carton. 1

Step-by-step explanation:

Answer:

(5,5)

Step-by-step explanation:

left 5 is -5 and right 8 is +8.

-5+8=3

2+3=5

When talking about left and right, you change the x-coordinate, when up and down, y-coordinate.

Overall, (5,5)

Answer:

5,5

Step-by-step explanation:

since we are not changing the height of the point and just moving side to side, the y intercept does not change. Once you move 5 units to the left, your new point is -3,5 but then when you move 8 to the right it switches to positive again and the new point is 5,5

Step-by-step explanation:

17)

sec(x) = 1/cos(x)

cot(x) = cos(x)/sin(x)

so,

cos(x)/sin(x) × 1/cos(x) = 1/sin(x) = csc(x)

18)

2×sin(x) + 1 = 0

2×sin(x) = -1

sin(x) = -1/2 = -0.5

x = 210° or x = 330°

why ? sin(30°) = 0.5

so, sin(x) = -0.5 means the angles in the 3rd and 4th quadrant (where sine points "down" and is therefore negative). and x is then either 30° more than 180° (210°) or 30° less than 360° (330°).

draw a circle with the coordinate axis through the center. and then try and see.

19)

again the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides (a, b, c) are always opposite to the correlated angles (A, B, C).

so, in our case we have

8/sin(A) = 10/sin(58)

sin(A) = 8×sin(58)/10 = 0.678438477...

A = 42.7217403...° ≈ 43°

20)

so, we have 2 sides and the enclosed angle.

the area of the triangle in this case is

1/2 × a×c×sin(B) = 1/2 × 12×8×sin(60) = 48×sin(60) =

= 41.56921938... ≈ 42

The equation of a circle is the equation that represents the circle on the coordinate plane

The equation of the circle is \((x +3)^2 + (y -6)^2 = 13\)'

From the attached figure, we have the following parameters:

Start by calculating the radius r using the following distance formula

\(d = \sqrt{(x -a)^2 +(y - b)^2}\)

So, we have:

\(r = \sqrt{(0 --3)^2 +(8 - 6)^2}\)

\(r = \sqrt{9 +4}\)

\(r = \sqrt{13}\)

Square both sides

\(r^2 = 13\)

The equation of the circle is then calculated as:

\((x - a)^2 + (y -b)^2 = r^2\)

Substitute values for a and b

\((x - -3)^2 + (y -6)^2 = r^2\)

This gives

\((x +3)^2 + (y -6)^2 = r^2\)

Substitute \(r^2 = 13\)

\((x +3)^2 + (y -6)^2 = 13\)

Hence, the equation of the circle is \((x +3)^2 + (y -6)^2 = 13\)'

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The odds that a carton of eggs will have at least one cracked egg is the same as the probability that a carton of eggs taken from the cooler at a store will have at least one cracked egg, which is 2.5%.

Probability is the odds, chance, or likelihood of an expected outcome happening amid many possible and likely outcomes.

Probability is stated as a fractional value when it hovers between zero and one.  Otherwise, when it is 100% sure, it is described as a certainty with the probability as 1.

On the other hand, when the event is unlikely with 100% uncertainty, its probability is described as zero.

Thus, the probability that one cracked egg exists among a carton of eggs is the same as its odds.

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Since AB is parallel to CD, we have alternate interior angles forming when transversal CE intersects the parallel lines. Therefore,

mZDCE = mZECB (Alternate Interior Angles)

(7x + 2) = (x + 8) (Substitute in the given angle measures)

Solving for x, we get:

7x + 2 = x + 8

6x = 6

x = 1

Now, we can use x to find the measure of angle ZDCE:

mZDCE = (7x + 2)

= (7*1 + 2)

= 9

Therefore, the measure of angle ZDCE is 9 degrees.

Answer:

$0.72 C

Step-by-step explanation:

ON E2020 THE ANSWER IS CCC

Freida's ffinance charge on credit card if the purchase of $60.99 and payment of $85.33 occured between September 7th and 20th is $0.72 C which is option C.

The interest on the credit amount for one year on the credit card.

                                    ⇒0.0115

APR for credit cards is charged on  purchased amount =$60.99

⇒Interest on $60.99 for 00ne month is= $60.99×0.0115  

                                                                   =$0.72

According to the given option:-

a. $0.13

b. $0.41

c. $0.72

d. $0.28

the answer will be option C $0.72.

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The coordinates of vertex D in the parallelogram are (-7, -10).

We have,

To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.

One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.

Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:

Find the vector representing one of the sides of the parallelogram.

We can use the vector AB.

Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)

= (6 - 8, -4 - 2)

= (-2, -6)

Add this vector to point C to find the coordinates of D.

Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)

= (-5 - 2, -4 - 6)

= (-7, -10)

Therefore,

The coordinates of vertex D are (-7, -10).

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Answer:

The expression that represents how much more Elena spent is $3.2 + p

Step-by-step explanation:

Answer:

68%

Step-by-step explanation:

Given that:

Mean speed (m) = 46

Standard deviation (s) = 13

Approximately what percentage of vehicle speeds were between 33 and 59 mph

Obtain the Zscore for P(Z < x) for both values and subtract :

For x = 33

Zscore :

Z = (x - m) / s

Z = (33 - 46) / 13 = - 1

p(Z < - 1) = 0.15866 ( Z probability calculator)

For x = 59

Zscore :

Z = (x - m) / s

Z = (59 - 46) / 13 = 1

p(Z < 1) = 0.84134 ( Z probability calculator)

Hence, 0.84134 - 0.15866 = 0.68268 = 0.68

0.68 * 100% = 68%

Given the following sample of three data points: 3, 6, 9, calculate the (estimated) standard error for the sample mean. Round to 3 decimal places.

s = √((3 - 8)² + (6 - 8)² + (9 - 8)²) / (3 - 1) = 4

2. Calculate the standard error of the sample mean:

SE = s / √n = 4 / √3 = 2.45

3. Round the standard error to three decimal places:

SE = 0.567

The standard error of the sample mean can be calculated by first finding the standard deviation of the sample (s). This is done by taking the sum of the squared differences between each data point and the mean, divided by the number of data points minus one. In this case, the standard deviation is 4. The standard error is then calculated by dividing the standard deviation by the square root of the number of data points, which is 3. The result is 2.45, which can be rounded to 0.567.

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Answer:

-320000

Step-by-step explanation:

Given

Lost Land = 80,000 acres yearly

Duration 4 years

Required

The total change

Represent the total change with y;

y is calculated as thus;

\(y = Lost\ Land * Duration\)

\(y = -80,000 acres * 4\)

\(y = -320000\ acres\)

Hence, a total of 320000 acres were lost during the period

Answer:

Step-by-step explanation:

3t-9<6

3t<6+9

or 3t<15

or t<5

-3t<12

-t<4

or t>-4

or -4<t

combining

-4<t<5

The value of t for the inequalities are,

1)  t < 5

2) t > - 4

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality are,

⇒ 3t - 9 < 6

⇒ - 3t < 12

Now, Simplify the inequality for t as;

1) ⇒ 3t - 9 < 6

Add 9,

⇒ 3t - 9 + 9 < 6 + 9

⇒ 3t < 15

Divide by 3;

⇒ t < 5

2) - 3t < 12

⇒ - 3t < 12

Divide by 3;

⇒ - t < 12/3

⇒ - t < 4

Multiply by - 1,

⇒ t > - 4

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Answer: 20%

Step-by-step explanation: Annual depreciation = $2,600 * 12 = $31,200

Annual depreciation rate = Annual depreciation /Depreciable costs

= $31,200 / ($188,000 - $32,000)

= 20%

Answer:

2.5% of American women have shoe sizes that are greater than 11.47.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 8.47

Standard deviation = 1.5

The normal distribution is symmetric, which means that half the measures are below the mean, and half are above the mean.

What percentage of American women have shoe sizes that are greater than 11.47?

11.47 = 8.47 + 2*1.5

This means that 11.47 is two standard deviations above the mean.

Of those measures below the mean, none are greater than 11.47.

Of those measures above the mean, 95% are between the mean and 11.47, and 5% are above. So

0.5*0.05 = 0.025

2.5% of American women have shoe sizes that are greater than 11.47.

Answer:

Nate has 8 times more jelly beans than Walt.

Step-by-step explanation:

Nate's quantity:

8 x (12 x 34 x 56)

Walt's quantity:

(12 x 34 x 56)

To find the ratio, we can divide Nate's quantity by Walt's quantity:

Ratio = Nate's quantity / Walt's quantity

Ratio = (8 x (12 x 34 x 56)) / (12 x 34 x 56)

Simplifying the expression:

Ratio = 8

Therefore, Nate has 8 times more jelly beans than Walt.

Answer:

5 mm

Step-by-step explanation:

Given:

A rectangular pyramid

h (height) = 4 mm

l (side length) = 6 mm

Find: s (slant height) - ?

There is a right triangle in the middle

The bottom leg is 3 mm, because it's half the side length of the square

According to that, we can find x by using the Pythagorean theorem:

\( {x}^{2} = {3}^{2} + {4}^{2} = 9 + 16 = 25\)

\(x > 0\)

\(x = \sqrt{25} = 5\)

Answer: neither

Step-by-step explanation:

To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.

Answer:

-27e^(-2).

= -3.654 to 3 decimal places.

Step-by-step explanation:

d/dx((3x^2 + 3)e^-x)

Using the Product Rule:

Derivative =  (3x^2 + 3) d/dx(e^-x) + e^-x d/dx(3x^2 + 3)

                  =  -e^-x(3x^2 + 3) + e^-x(6x)

                  = e^-x(6x -1*(3x^2 + 3))

                  = e^-x(6x - 3x^2 - 3)

                  = 3e^-x(2x - x^2 - 1)

                  = -3e^-x(x^2 - 2x + 1)

                  = -3e^-x(x - 1)^2

When x = -2,

Derivative = -3e^(-2)(-2-1)^2

                 = -27e^(-2)