9) If the area of the base of a square pyramid is 28 square centimeters and the total surface area is 64 square
entimeters, explain how to and find the area of one triangular face.
Answers
The area of one triangular face in the square pyramid given the total surface area is 12 square centimeters
How to find the area of one triangular face.Let's denote the side length of the square base of the pyramid as s, and the height of the pyramid as h.
Then we know that:
The area of the square base, s² = 28 square centimeters.The total surface area of the pyramid is the sum of the area of the square base and the areas of the three triangular faces, which gives:3 * (area of a triangular face) + s² = 64 square centimeters
To find the area of one triangular face, we can rearrange this equation
area of a triangular face = (64 - s²) / 3
Now we can substitute the given value of s² = 28
area of a triangular face = (64 - 28) /3
area of a triangular face = 12
Therefore, the area of one triangular face of the square pyramid is 12 square centimeters
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Related Questions
How much will it take to do a work of 190J with 15w power
Answers
Answer:
\(\Huge \boxed{\mathrm{12.67 \ s}}\)
Step-by-step explanation:
\(\displaystyle power \ (W) = \frac{work \ done \ (J)}{time \ (s)}\)
\(\displaystyle P= \frac{W}{t}\)
\(\displaystyle 15= \frac{190}{t}\)
Solve for t.
Multiply both sides by t.
\(15t =190\)
Divide both sides by 15.
\(\displaystyle t= \frac{190}{15}\)
\(t \approx 12.67\)
\( \bf \underline{ \underline{given : }}\)
Work = 190 JPower = 15 W\(\bf \underline{ \underline{To \: be \: calculated : }}\)
Calculate the time ?
\(\bf \underline{ \underline{
Formula \: applied :}}\)
\( \boxed{ \bf{Power = \frac{Work \: done}{Time} }}\)
\(\bf \underline{ \underline{Solution : }}\)
We know,
\(\sf {Power = \dfrac{Work \: done}{Time}}\)
\( \sf{ Time = \dfrac{Work \: done}{Power } }\)
Substituting the values of work and power, we get:
\( \sf \implies{Time = \dfrac{190}{15} }\)
\( \sf\implies{Time = 12.66 \: s}\)
Thus,the time taken by a body is 12.66 seconds.
Suppose you borrowed $45,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year? Select the correct answer. a. $7,594.46 b. $7,600.46 c. $7,618.46 d. $7,612.46 e. $7,606.46
Answers
The correct answer is option a. $7,594.46.
To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:
Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate
In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.
Let's calculate the amount you would reduce the amount you owe in the first year:
Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825
Installment = $12,825
Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.
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Marco is starting a savings account. He begins his account with $25. Each month he plans to add an additional $25. Marcos aunt wants to know how many months it will take for his account to reach a given amount. His aunt decides to write a function to describe her way of thinking about the money in Marco's function. Write the function that the aunt would create. Let T = total amount of money in the account, and let m = number of months. m1 =
Answers
Answer:
T=m(25)
Step-by-step explanation:
I think maybe its been awhile since functions
The total amount in the account is :
T = 25 +25m.
Here, we have to calculate the total amount of money in Marco's account after a given number of months (m), the aunt's function would take into account the initial amount ($25) and the additional amount Marco plans to add each month ($25).
The function can be written as follows:
T = 25 + 25m
Where:
T is the total amount of money in the account after m months.
m is the number of months.
The initial amount of $25 is added to the additional amount of $25 multiplied by the number of months (m).
This function represents the total savings in Marco's account over time as he adds $25 each month.
Hence, The total amount in the account is :
T = 25 +25m.
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Please help on number 7.
Answers
Answer:
Pyramid
Step-by-step explanation:
Answer:
A pyramid
Step-by-step explanation:
square root of 342354456
Answers
Answer:
18502.8229198
Answer:
18502.82292
Step-by-step explanation:
calculator
pleaseee answer this question quickly.. I will give brainliest MAKE SURE ITS RIGHT
Answers
Answer:
JKM is acute and MKL is obtuse
Step-by-step explanation:
because an acute triangle's interior angles are always 180° and an obtuse triangle's sum is greater than 90°
If b = 9, what is
\( \sqrt{4b} \)
Answers
Answer:
= 6
Step-by-step explanation:
\(\sqrt{4b}\\ b = 9\\then:\)
= √(4*9)
= √36
= 6
the starting sales price of a new car on monticello car lot is normally distributed with a mean of $40,000 and a standard deviation of $5,000. what is the probability that a randomly selected individual will buy a car that costs at least $30,000?
Answers
The chance that a randomly selected individual will buy a car that charges at the least $30,000 is 0.9772, or approximately 97.72%.
To clear up this problem, we need to discover the probability that a randomly selected person will purchase a vehicle that prices as a minimum $30,000, given that the starting income rate of a new automobile on the Monticello vehicle lot is usually dispensed with a mean of $forty,000 and a preferred deviation of $5,000.
We can use the same Standard normal distribution to solve this problem with the aid of changing the beginning sales price of $30,000 to a z-score, and then using a standard normal distribution table or calculator to discover the corresponding opportunity.
The z-rating for a starting sales rate of $30,000 is:
z = (30,000 - 40,000) / 5,000 = -2
Using a standard normal distribution table or calculator, we will locate that the opportunity of a z-score less than or identical to -2 is approximately zero.0228.
But, we need to find the possibility that the starting sales price is at the least $30,000, so we want to subtract this chance from 1:
P(X ≥ 30,000) = 1 - P(X < 30,000)
P(X ≥ 30,000) = 1 - 0.0228
P(X ≥ 30,000) = 0.9772
Therefore, the chance that a randomly selected individual will buy a car that charges at the least $30,000 is 0.9772, or approximately 97.72%.
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a rectangle is transformed according to the rule r0 90 T/F
Answers
When the rectangle is transformed according to the rule r0 90 T/F, it first undergoes a reflection about the y-axis, followed by a rotation of 90 degrees counterclockwise about the origin, and finally a translation of a certain distance in either the x or y direction depending on whether the final image is a reflection or not.
The final image obtained will be a rectangle as well, but with different dimensions and position depending on the translation distance.Let's assume that the rectangle has width w and height h. When reflected about the y-axis, its width changes sign but its height remains the same, resulting in a new width of -w and height of h.
After that, the rectangle is rotated 90 degrees counterclockwise about the origin, which swaps its width and height but preserves their signs, resulting in a new width of -h and height of -w.
Finally, a translation of distance d is applied to either the x or y coordinate depending on whether the final image is a reflection or not. If the final image is a reflection, then the translation is applied in the y direction by a distance of d, resulting in a new position of (-h, d).
Otherwise, the translation is applied in the x direction by a distance of d, resulting in a new position of (d, -w).In summary, the rectangle is transformed according to the rule r0 90 T/F by undergoing a reflection, rotation, and translation, resulting in a new rectangle with dimensions and position depending on the original dimensions and the translation distance.
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A rectangle can be transformed according to the rule r0 90 T/F, which can have different results, depending on how the transformation is done.
The rule can be interpreted as follows:r0: No rotation90: Rotate the rectangle 90 degreesT/F: Flip the rectangle horizontally (T) or vertically (F)For example, if a rectangle with a width of 4 units and a height of 2 units is subjected to this transformation rule, the result will vary depending on the order of transformations.
Consider the following cases : Case 1: r0 90 F T (rotate by 0 degrees, then rotate by 90 degrees, then flip vertically, then flip horizontally) In this case, the rectangle is first rotated by 0 degrees, which means that its position and size are unchanged. Next, it is rotated by 90 degrees, which means that its width becomes its height and vice versa. After that, it is flipped vertically, which means that its top and bottom edges are swapped.
Finally, it is flipped horizontally, which means that its left and right edges are swapped. The resulting rectangle has a width of 2 units and a height of 4 units. It is also reflected across the line y = 0 (the x-axis).Case 2: F T r0 90 (flip vertically, then flip horizontally, then rotate by 0 degrees, then rotate by 90 degrees) In this case, the rectangle is first flipped vertically, which means that its top and bottom edges are swapped. Next, it is flipped horizontally, which means that its left and right edges are swapped.
After that, it is rotated by 0 degrees, which means that its position and size are unchanged. Finally, it is rotated by 90 degrees, which means that its width becomes its height and vice versa. The resulting rectangle has a width of 2 units and a height of 4 units.
It is also reflected across the line y = -x (the line that goes through the origin with a slope of -1).In conclusion, a rectangle can be transformed in various ways, and the order of transformations matters. The rule r0 90 T/F can produce different results depending on the sequence of operations.
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Help plz test !! Four more than the product of a number and 10 is at most the opposite of 12.
Answers
Answer:
-1.6
Step-by-step explanation:
4 + 10x = -12
10x = -12 -4
x= -1.6
Please help me I don’t know how to do this and it is due at 10:00 please help
Answers
Answer:
number 12 is
\( \frac{3}{125} \)
Answer:
9. 1/2÷1/4
=1/2×4
=2
10. 1/12÷5/6
=1/12×6/5
=1/10
11. 5/6÷5/9
=5/6×9/5
=3/2
12.2 2/3%
=8/3%
=8/300
=2/75
=0.02666667
Anybody know ? I need help
Answers
Answer:
b
Step-by-step explanation:
Answer:
i believe it is b)alternate exterior
Step-by-step explanation:
have a nice day
btw it will help a lot if you can mark me brainliest
The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 varieties of Kellogg's cereal.Sugar (grams) -6 15 12 11 8 6 7 3 8 14 20 3 13Calories- 140 200 140 110 140 80 210 100 120 190 190 110 120The predictive regression equation of the number of calories on the amount of sugar is y^=94.639+4.918x, where x is amount of sugar (in grams) and y is calories. Calculate the predicted calorie count for a cereal with 14 grams of sugar per serving.Round your answer to the nearest integer._________calories
Answers
Rounding to the nearest integer, the predicted calorie count for a cereal with 14 grams of sugar per serving is approximately 163 calories.
An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics,
To calculate the predicted calorie count for a cereal with 14 grams of sugar per serving using the predictive regression equation y^ = 94.639 + 4.918x, we substitute x = 14 into the equation.
y^ = 94.639 + 4.918(14)
y^ = 94.639 + 68.852
y^ ≈ 163.491
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the operation manager at a tire manufacturing company believes that the mean mileage of a tire is 37,014 miles, with a standard deviation of 4617 miles. what is the probability that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires if the manager is correct? round your answer to four decimal places.
Answers
Probability or p-vale that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires is equals to zero if the manager is correct.
We have data of an operation manager at a tire manufacturing company.
Mean mileage of a tire, \( \mu\)
= 37,014 miles
standard deviation, \( \sigma\)
= 4617 miles.
Sample size, n = 56
We have to determine the probability that the sample mean would differ from the population mean by less than 221 miles. Using Z-score formula in normal distribution, \(\small z= \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}},\)
Plugging all known values in above formula, \(z = \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}\)
= 59.634
\(P( \bar x < 221) = P ( \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}} < \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}) \\ \)
=> P ( z < 59.63) = P( \bar x < 221)
Using the Z-distribution table, probability value is equals to 0. Hence, required probability is zero.
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PLEASE HELP
40 Points
Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australia. While booking her family's plane tickets, she notices on the itinerary that the airline is offering a sixteen hour straight flight from Los Angeles to Melbourne on a Boeing 747-8 Intercontinental Jet. In an effort to learn more about the capabilities of the Jet, Sheleah does a little research and stumbles upon the following graph and facts about the Jet's fuel consumption.
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.
Use a linear model to predict the amount of jet fuel that is present on the Jet after it has been in flight for 18 hours without stopping to refuel. In two or more complete sentences, explain your answer.
{the other question}
Create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours. Show all of your work.
Answers
Answer:
To create a linear model that represents the amount of fuel on the plane as a function of flight time, we can use the given information that the jet can travel 14,430 kilometers before needing to refuel. We also know that the flight from Los Angeles to Melbourne is 16 hours long. Therefore, we can use the ratio of the distances traveled in 18 hours and 16 hours to estimate the amount of fuel that would be left on the plane after 18 hours of flight.
The ratio of the distances traveled is:
18 hours / 16 hours = 1.125
This means that the jet would have traveled 1.125 times the distance it travels in 16 hours by the time 18 hours has passed. So, the distance traveled in 18 hours would be:
14,430 km × 1.125 ≈ 16,241 km
Now, we can use a proportion to find the amount of fuel left on the plane after 18 hours:
63,500 gallons / 14,430 km = x gallons / 16,241 km
Solving for x, we get:
x ≈ 71,270 gallons
Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:
fuel (in gallons) = -265.6 × time (in hours) + 134,800
This equation was obtained by fitting a linear regression model to the given data, where the fuel is the dependent variable and the time is the independent variable. The negative slope of the line (-265.6) indicates that as the flight time increases, the amount of fuel on the plane decreases. The intercept of the line (134,800) represents the amount of fuel on the plane at the start of the flight.
20-foot extension ladder set base six feet from house How far up will ladder reach?
Answers
The top of the 20-foot ladder used for painting will be 19 feet up from the base of the house
How to determine how high up the house the ladder will goinformation given in the question
Brian borrowed a 20-foot extension ladder: hypotenuse = 20-foot ladder
he sets the base of the ladder six feet from the house
adjacent = 6 feet from the house
opposite = how far up will the top of the ladder reach = ?
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = adjacent² + opposite²
substituting the values into the equation
let x be thow far up will the top of the ladder reach
20² = 6² + x²
400 = 36 + x²
400 - 36 = x²
x² = 364
x = √364
x = 19.08
The ladder Brain borrowed will go 19 feet high
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complete question
Brian borrowed a 20-foot extension ladder to use to paint his house. If he sets the base of the ladder six feet from the house how far up will the top of the ladder reach?
Please actually help me! I've asked this question twice and the first time, nobody answered and the second time, some idiot just said "use photomath" and i reported it and it hasn't gotten deleted. So I'm asking again! I'll give tons of points + Brainliest if correct! Please answer ASAP
Answers
Answer:
AC = 46BD = 50Step-by-step explanation:
The property of diagonals of a parallelogram:
diagonals bisect each otherDiagonal ACAC = 2(3y - 1)AC = 2(y + 15)Compare and solve for y:
3y - 1 = y + 153y - y = 15 + 12y = 16y = 8AC = 2(3*8 - 1) = 46Diagonal BDBD = 2(5x)BD = 2(3x + 10)Compare and solve for x:
5x = 3x + 102x = 10x = 5BD = 2*5*5 = 50The answer is:
AC = 46BD = 50Correct choice is A
Simplify the ratio of
35 : 14
Answers
Answer:
5:2
Step-by-step explanation:
divide both numbers by 7
hope this helps...
Answer:
Simplify the ratio of
35 : 14 = 5:2 divide both by 7
the formula for finding the surface area of a cylinder is sa = πr2 πrh . truefalse unlimited attempts remain
Answers
The statement ''the formula for finding the surface area of a cylinder is sa = πr2 πrh.'' is false because the formula for finding the surface area of a cylinder is given by: SA = 2πrh + 2πr^2 , where SA represents the surface area, r is the radius of the base, and h is the height of the cylinder.
The first term, 2πrh, represents the area of the curved surface of the cylinder (the lateral surface area), which is a rectangle that wraps around the cylinder. It is calculated by multiplying the height of the cylinder by the circumference of the base.
The second term, 2πr^2, represents the areas of the two circular bases of the cylinder.
By adding these two terms together, we obtain the total surface area of the cylinder.
Therefore, the correct formula for finding the surface area of a cylinder is SA = 2πrh + 2πr^2.
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Write an equation of the line in slope intercept form
Answers
Answer:
y = 2x - 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, 2)
m = \(\frac{2+2}{2-0}\) = \(\frac{4}{2}\) = 2
The line crosses the y- axis at (0, - 2) ⇒ c = - 2
y = 2x - 2 ← equation of line
Review Questions
1. Cindy is a baker and runs a large cupcake shop. She has already
a. How many workers will the firm hire if the market wage rate is
hired 11 employees and is thinking of hiring a 12th. Cindy esti- $27.95 ? \$19.95? Explain why the firm will not hire a larger or mates that a 12 th worker would cost her $100 per day in wages $ smaller number of units of labor at each of these wage rates. and benefits while increasing her total revenue from $2,600per. day to $2,750 per day. Should Cindy hire a 12 th worker? b. Show this firm Explain. L016.2 c. Now again determine the firm's demand curve for labor. Complete the following labor demand table for a firm that is assuming that it is selling in an imperfectly competitive marhiring labor competitively and selling its product in a competiket and that, although it can sell 17 units at $2.20 per unit, it tive market. L016.2 ginal product of each successive labor unit. Compare this demand curve with that derived in part b. Which curve is more elastic? Explain. 3. Alice runs a shoemaking factory that uses both labor and capital to make shoes. Which of the following would shift the factory's demand for capital? You can select one or more correct answers from the choices shown. LO16.3 a. Many consumers decide to walk barefoot all the time. b. New shoemaking machines are twice as efficient as older machines. c. The wages that the factory has to pay its workers rise due to an economywide labor shortage.
Answers
Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.
a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.
b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.
c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.
Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.
The events that would shift the factory's demand for capital are:
a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.
b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.
The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.
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Brie earns $3,000 a month. She spends $1,400 on rent and bills, $700 or
groceries, $200 on a car payment, and $100 on gas each month. She say
the rest of her money. How much money does Brie save? Show your work
Answers
Brie saves $600 each month.
What is equation?
An equation is a statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division
To determine how much money Brie saves each month, we need to subtract her expenses from her income.
Income = $3,000
Expenses = $1,400 + $700 + $200 + $100 = $2,400
Savings = Income - Expenses
Savings = $3,000 - $2,400
Savings = $600
Therefore, Brie saves $600 each month.
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The area of a rectangle is 108 m2 and its diagonal is 15 m. Find
the perimeter of the rectangle.
Please help
Answers
Answer:
42m
Step-by-step explanation:
Let's call the rectangle ABCD. Since this is a rectangle, the triangles inside this rectangle (ΔACD and ΔABD) are both right triangles because of the definition of a rectangle. In addition, AB = CD and AC = BD because of the definition of a rectangle. Since AD = 15 (The Diagonal), you can say that because of Pythagorean Triples that AC = 9 and CD = 12 (3 : 4 : 5 = 9 : 12 : 15). Since we stated that AB = CD and AC = BD, we can say that the perimeter of ABCD is equal to 9 + 9 + 12 + 12. 9 + 9 + 12 + 12 is equal to 42.
Therefore: Perimeter of ABCD = 42
Solve using any method(FOIL, Box, Distributive)
(2y+8)2
Answers
Answer:
4y^2 + 32y + 64
Step-by-step explanation:
To solve the expression (2y+8)^2, we can use the distributive property or the FOIL method. Let's use the distributive property to expand the expression:
(2y + 8) * (2y + 8)
Using the distributive property, we multiply each term in the first expression by each term in the second expression:
2y * 2y + 2y * 8 + 8 * 2y + 8 * 8
Simplifying each term, we get:
4y^2 + 16y + 16y + 64
Combining like terms, we have:
4y^2 + 32y + 64
So, the expanded form of (2y+8)^2 is 4y^2 + 32y + 64.
Match each product to the equivalent expression written as a sum.
21+ 15
27 +21
35 +21
35 + 15
3(9+7)
3(7+5)
5(7+3)
7(5+3)
Answers
28
56
50
48
36
50
56
Use calculators
Answer:
21 + 15 can be written as 3(7+5)
27 + 21 can be written as 3(9+7)
35 + 21 can be written as 7(5+3)
35 + 15 can be written as 5(7+3)
3(9+7) stays as is
3(7+5) stays as is
5(7+3) stays as is
7(5+3) stays as is
Find m, so that (-3) m+1 × (-3)5 = (-3)7
Answers
The equivalent value of m is given by the expression m = 1
Given data ,
We can use the properties of exponents to solve this problem. Specifically, when we multiply two powers with the same base, we add their exponents.
So, we have:
(-3)^(m+1) × (-3)⁵ = (-3)⁷
Using the property of exponents, we can add the exponents on the left-hand side:
(-3)^(m+1+5) = (-3)⁷
Simplifying the exponents on the left-hand side:
(-3)^(m+6) = (-3)⁷
We know that two powers with the same base are equal if and only if their exponents are equal. So, we can set the exponents equal to each other:
m + 6 = 7
Subtracting 6 from both sides:
m = 1
Hence , m = 1 is the value that satisfies the equation
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What value of n in the expression below would make it a
perfect square trinomial?
x² −14x + n
Answers
Answer:
n = 49
Step-by-step explanation:
49 has a factor of -7 which can also add up to -14
Eg : -7(-7) = 49, -7 + (-7) = -14
49
x²-14x+49=(x-7)²
An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial.
It is of the form (ax2 + bx + c).
Real numbers a, b, and c are present here, and a ≠0.
The given equation is x2 + 14x + c
To find the value of c
We can take half of the linear coefficient and square it
14/2 = 7
72 = 49
Therefore, the value of c is 49.
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Waiting period. Jamal is waiting to be a millionaire. He wants to know how long he must wait if a. he invests $22,108.44 at 21% today? b. he invests $45,104.11 at 16% today? c. he invests $152,814.56 at 8% today? d. he invests $276,434.51 at 6% today? a. How long will Jamal have to wait to become a millionaire if he invests $22,108.44 at 21% today? years (Round to the nearest whole number.)
Answers
If Jamal wants to become a millionaire, then Jamal must wait for 19 years if he invests $22,108.44 at 21% today, Jamal must wait for 18 years if he invests $45,104.11 at 16% today, Jamal must wait for 22 years if he invests $152,814.56 at 8% today, and Jamal must wait for 24 years if he invests $276,434.51 at 6% today
To calculate the waiting period for Jamal, follow these steps:
The formula for compound interest is given as: \(\[A=P{{\left( 1+\frac{r}{n} \right)}^{nt}}\]\) where P is the principal amount, r is the annual interest rate, t is the time the money is invested for, n is the number of times that interest is compounded per year and A is the amount of money accumulated after n years. The time required for $22,108.44 to grow to $1,000,000 at 21% can be calculated as \(\[1000000=22108.44{{\left( 1+\frac{21}{100} \right)}^{t}}\] \\ t=\frac{\ln (1000000/22108.44)}{\ln (1.21)}\). Therefore, t=19.25 years ≈19 years The time required for $45,104.11 to grow to $1,000,000 at 16% can be calculated as\(\[1000000=45104.11{{\left( 1+\frac{16}{100} \right)}^{t}}\] \\t=\frac{\ln (1000000/45104.11)}{\ln (1.16)}\). Therefore, t = 18.79 ≈18 yearsThe time required for $152,814.56 to grow to $1,000,000 at 8% can be calculated as \(\[1000000=152814.56{{\left( 1+\frac{8}{100} \right)}^{t}}\] \\t=\frac{\ln (1000000/152814.56)}{\ln (1.08)}\). Therefore, t = 22.18 years≈ 22 yearsThe time required for $276,434.51 to grow to $1,000,000 at 6% can be calculated as \(\[1000000=276434.51{{\left( 1+\frac{6}{100} \right)}^{t}}\] \\t=\frac{\ln (1000000/276434.51)}{\ln (1.06)}\). Therefore, t = 24.64 years ≈ 24years.Therefore, Jamal has to wait approximately 19, 18, 22, and 24 years respectively to become a millionaire by investing $22,108.44, $45,104.11, $152,814.56, and $276,434.51 respectively at 21%, 16%, 8%, and 6% interest rates.
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Factor out -2 out of -16m -12
-2(_m + _ )
please help me...
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Step-by-step explanation:
-2(8m+6)
this expands to -16m-12
Please help me, really need help
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The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.
What is vertical opposite angle ?
When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.
Main body:
1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.
2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.
Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.
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