Final answer:
To find the annual inflation rate when prices increase at a monthly rate of 1.1%, you use the formula for compounding interest, resulting in an approximate annual rate of 13.97%.
Explanation:
If prices increase at a monthly rate of 1.1%, to calculate the annual inflation rate, you should consider the compounding effect over the year. The general formula for finding the total percentage increase over multiple periods when compounded at each period is:
(1 + rate)^number of periods - 1.
In this case, the monthly rate is 1.1%, or 0.011 when expressed as a decimal. The number of periods (months) in a year is 12. Plugging these values into the formula gives:
(1 + 0.011)^12 - 1,
which calculates to:
1.011^12 - 1 = 0.1397 or 13.97%.
So, the annual inflation rate when prices increase at a monthly rate of 1.1% is approximately 13.97%.
A new fence is constructed on three sides of a housing block with area 240 m2. the fourth side facing the road is left open. if 52 m of fencing is used, what are the dimensions of the block?
To find the housing block dimensions, we set up a system of equations based on the total fencing and area given, and then solve for the length and width.
Explanation:The student has asked about finding the dimensions of a housing block where a new fence is constructed on three sides and the total area of the block is 240 m2. Given that 52 m of fencing is used, to determine the dimensions, we need to solve a system of equations derived from the perimeter and area provided.
Let's assume the length of the block is L meters, and the width is W meters. The area of the block (A) can thus be defined as A = L × W. Given that A = 240 m2, we have L × W = 240. Since the fence covers three sides, the total length of fencing used would be L + 2W, which is equal to 52 meters. Therefore, we have L + 2W = 52 meters.
To solve for L and W, we set up the system of equations:
L × W = 240L + 2W = 52From the second equation, we can express L as L = 52 - 2W and then substitute into the first equation to find W. Finally, we can determine the value for L using the found value of W.
A class has 24 boys and 16 girls. on a test the class mean was 75. the mean of the girls' score was 72. what was the mean of the boys' scores?
The mean of the boys' scores was 77.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.
We have been given that the class has 24 boys and 16 girls.
And the class mean was 75
The total number of students in the class was:
24 + 16 = 40
Total scored by 40 students = 40 × 75 = 3000
Number of girls = 16 and their mean = 72
Total scored by girls = 16 × 72 = 1152
The difference between the scores will give the total score of boys:
⇒ 3000 - 1152 = 1848
Number of boys = 24
Their mean will be 1848 / 24
So the mean of the boys' scores = 77
Therefore, the mean of the boys' scores was 77.
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How to find amplitude and period from equation?
Final answer:
The amplitude of a wave is the coefficient A in the equation y(x, t) = A sin(kx - ωt + φ), and the period T can be calculated using T = 2π/ω, where ω is the angular frequency. Additional properties like wavelength and speed can be found using related equations involving the wave number and frequency.
Explanation:
To find the amplitude and period from the equation of a wave, look at the standard form of a sinusoidal wave function, which is generally y(x, t) = A sin(kx - ωt + φ). Here, the amplitude can be directly read from the equation as the coefficient A, which represents the maximum displacement from the rest position. As for the period, it can be derived from the angular frequency using the formula T = 2π/ω, where T is the period and ω is the angular frequency.
The wavelength (λ) and speed (v) of the wave can also be determined from the properties of the wave. The wavelength is related to the wave number by the equation λ = 2π/k, and the speed can be calculated if the frequency (f) is known, using the equation v = λf.
For example, if the amplitude is provided as 30 V/m and the frequency is given as 2.0 MHz, the period (T) would then be 5.0 × 10-7 s based on the relationship between frequency and period, T = 1/f.
For this tangent line approximation question, my answer is D. 4. Is my work correct?
f(x) = f(a) + (x - a)f'(a)
a = -0.5
x = 0
f(0) = 2 + 0.5(4) = 4
Ariel has a standard deck of 52 cards. She draws one card from the deck and then replaces it. She then draws a second card from the deck. What is the probability that both cards are clubs? B) Alisa has a bag of 10 red and 6 green marbles. She takes one marble out of the bag and does not replace it. She then takes a second marble out of the bag. What is the probability that both marbles are green? C) In a bag of apples there are 4 green apples and 2 red apples. Bethany takes a green apple out of the bag and does not replace it. She then takes another apple out of the bag. What is the probability that the second apple is red? D) In Mrs. Brown's Geometry class there are 15 boys and 10 girls. The students are presenting projects to th
Answer:
A)
Step-by-step explanation:
What is the volume of the cone to the nearest tenth?
Height: 14 cm
Radius: 5 cm
A. 549.8 cm3
B. 73.3 cm3
C. 366.5 cm3
D. 1,026.3 cm3
True or False? A triangle with two congruent angles can never be scalene. A. True B. False
The depth of a lake, d, varies directly with r, the amount of rainfall last month. if k is the constant of variation, write an equation to represent the situation.
Acapulco, Mexico and Hyderabad, India both lie at 17° north latitude, and lie very nearly halfway around the world from each other in an east-west direction. The radius of Earth at a latitude of 17° is about 3790 miles. Suppose that you could fly from Acapulco directly west to Hyderabad or fly directly north to Hyderabad. Which way would be shorter, and by how much? Use 3960 miles for Earth’s radius. (Hint: To fly directly north, you would go from 17° north latitude to 90° north latitude, and then back down to 17° north latitude.)
For groups of students are doing a probability experiment with a standard number cube to see how many times they roll of four. The theoretical probability of rolling in for is one out of six or approximately 0.17 and one group came close to this possibility with an experimental probability of 0.175. This most likely came from which group
it took Otis 6 hours to travel to the Grand Canyon. along the way he took 18 minutes to get gasoline and 53 minutes to eat. how much time did Otis spend driving?
Choose as many answers as apply.
An employee can legitimately claim the following as exemptions:
A. family pet
B. self
C. dependents
D. neighbor's cousin Al
Answer:
An employee can legitimately claim the following as exemptions:
B. Self
C. Dependents
Step-by-step explanation:
We know that an employee can claim the health and medical insurance ( which is also known as Medicare and Social security deductions) for himself or for himself, his/ her spouse and his family members or dependents.
Hence,
An employee can legitimately claim the following as exemptions:
B. Self
C. dependents.
Hence, option B and C are the correct options.
What are the trigonometric ratios of a right triangle ABC that has its right angle at C? AC=12 and BC=5
Which set of numbers includes only whole numbers?
How is the graph of log x + 6 translated from the graph of log x
Find the exact value of each expression . Do not use a calculator .
8. cos^{-1} (0)
9.sin^{-1} 1
10.tan^{-1} (\frac{\sqrt{3}}{3} )
I need help !!
The exact values of the given expressions are 90 degrees or π/2 radians, 90 degrees or π/2 radians, and 60 degrees or π/3 radians respectively.
Explanation:Question 8:
The inverse cosine (cos^{-1}) of 0 is the angle whose cosine is 0. In other words, cos^{-1}(0) will give you the angle whose cosine is 0. The only angle that satisfies this condition is 90 degrees or π/2 radians.
Question 9:
The inverse sine (sin^{-1}) of 1 is the angle whose sine is 1. In other words, sin^{-1}(1) will give you the angle whose sine is 1. The only angle that satisfies this condition is 90 degrees or π/2 radians.
Question 10:
The inverse tangent (tan^{-1}) of (√3/3) is the angle whose tangent is (√3/3). In other words, tan^{-1}(√3/3) will give you the angle whose tangent is (√3/3). The angle that satisfies this condition is 60 degrees or π/3 radians.
If kaitlyn goes to the store, the probability that she buys blueberries is 90%. the probability of her going to the store is 30%. what is the probability of her going to the store and buying blueberries?
Final answer:
The answer explains the calculation of the probability of an event occurring using provided probabilities and the intersection formula.
Explanation:
The probability of Kaitlyn going to the store and buying blueberries can be calculated using the formula for the intersection of two events.
We know that P(going to the store) = 0.3, P(buying blueberries) = 0.9, and we are looking for P(going to the store and buying blueberries).
Therefore, the probability of Kaitlyn going to the store and buying blueberries is 0.3 × 0.9 = 0.27 or 27%.
Given: rectangle ABCD is similar to rectangle ZBXY.
If BA=8, BC=12 and the perimeter of rectangle BXYZ is 20, find BX.
a.) 3
b.) 4
c.) 5
d.) 6
Answer:
The answer is D. 6
Step-by-step explanation:
A.70
B.40
C.140
D.20
On a history test, Rasha scored 40 points on the essay portion. In addition to the essay, there were multiple-choice questions worth three points each. Which expression represents Rasha’s total points if she answered p multiple-choice questions correctly?
A. 3 + 40p
B. 3 + p + 40
C. 40-3p
D. 40 + 3p
The expression that represents the situation is 40 + 3p.
The correct option is D.
What is a linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
The essay is worth 40 points and each correctly answered multiple-choice question is worth 3 points.
If Rasha answered p multiple-choice questions correctly, she would earn a total of 40 + 3p points.
Therefore, the correct expression is D.
40 + 3p.
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You and a friend go to a mexican restaurant. you order 2 tacos and 3 enchiladas and your friend orders 3 tacos and 5 enchiladas. one bill was $7.80 plus tax and the other bill was $12.70 plus tax. how much was each taco and each enchilada?
To find the cost of each taco and enchilada, set up a system of equations based on the given bills and solve for the variables T (taco) and E (enchilada). The solution reveals that each taco costs $0.90 and each enchilada costs $2.00.
To solve the problem of determining the individual cost of a taco and an enchilada based on the two given bills, we can set up a system of linear equations. Let's denote the price of a taco as 'T' and the price of an enchilada as 'E'.
The first equation represents your order: 2T + 3E = $7.80.
The second equation represents your friend's order: 3T + 5E = $12.70.
To solve the system, you can use either the substitution or elimination method. For this example, we'll use the elimination method:
Multiply the first equation by 3 and the second by 2, which gives us:So, each taco cost $0.90 and each enchilada cost $2.00.
The circle is inscribed in the triangle. Find the perimeter of the triangle.
A. 20 cm
B. 24 cm
C. 35 cm
D. 48 cm
The perimeter of the triangle will be 48 cm. The correct option is D.
What is a perimeter?A perimeter is the total length of the boundary or outer edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
For example, the perimeter of a rectangle is the sum of the lengths of all four sides, while the perimeter of a circle is the distance around its circumference. The perimeter is usually measured in units such as meters, centimeters, inches, or feet, depending on the context of the problem.
Whenever we have two tangents outside the circle and they are in contact with each other, it means their lengths are the same
The perimeter of the triangle will be calculated as,
Perimeter = sum of all the sides
Perimeter = ( 11 + 11 + 7 + 7 + 6 + 6 )
Perimeter = 48 cm
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If each person takes up 2.5 square feet of space, how many people can fit in an elevator that is 8 feet by 6 feet? Round to the nearest person.
2.5
19
38
48
A truck whose bed is 2.5 m long, 1.5 m wide and 1.0 m high is delivering sand for a sand-sculpture competition. About how many trips must the truck make to deliver 7 m3 of sand?
A wedsite charges a fixed amount for each song download.If you can download six songs for $4.68,then how much would it cost to download ten song?
By determining the cost per song, which is $0.78, we can calculate that downloading ten songs from the website would cost $7.80.
Explanation:To determine the cost to download ten songs, we first need to calculate the cost per song. We are given that six song downloads cost $4.68. By dividing this total cost by the number of songs, we find the cost per song:
Cost per song = Total cost for six songs / Number of songs
= $4.68 / 6
= $0.78 per song
Now, to find the cost of ten songs, we multiply the cost per song by ten:
Total cost for ten songs = Cost per song * Number of songs
= $0.78 * 10
= $7.80
Therefore, it would cost $7.80 to download ten songs from the website.
Simplify 72x6 y7 z .
Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80 degrees. Approximately how tall is the tree? Enter the value rounded to the nearest tenth. Do not include the units of measure.
Assume that the original claim is true, and follow the directions given. what is the truth value of the claim you wind up with? all people who win lotteries are people who get lots of mail. (find the contrapositive, then convert.)
Using radicals, write an equivalent expression for 2 1/3
The equivalent expression of [tex]2^{\frac{1}{3} }[/tex] in radical forms is ∛2
What are radicals?Radical are expression that uses a root, such as square root, cube root . They are numbers represented in radical symbols.
Therefore,
[tex]2^{\frac{1}{3} }[/tex] in radical form can be represented as follows:
Using indices rule
[tex]a^{\frac{1}{b} } = \sqrt[b]{a}[/tex]
Therefore,
[tex]2^{\frac{1}{3} } = \sqrt[3]{2}[/tex]
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Evaluate 8 x 6 + (12- 4) divided by 2
Therefore, the solution of given equation is [tex]28.[/tex]
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Here given equation is
[tex]8[/tex] x [tex]6 + (12- 4)[/tex] which is divisible by [tex]2[/tex].
So,
[tex]\frac{8(6)+(12-4)}{2}\\\\=\frac{48+8}{2}\\\\=\frac{56}{2}\\\\=28[/tex]
Hence, the solution of given equation is [tex]28.[/tex]
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