The interest accrued after one month at a rate of 15.5% on a principal amount of $1,000 is $12.92.
To use the formula I=Prt to calculate the interest accrued after one month at a rate of 15.5%, we need to know the principal amount (P) and the time period (t) in years.
Assuming that the principal amount is $1,000, and the time period is one month, which is equivalent to 1/12 of a year, we can calculate the interest as follows:
[tex]I = Prt[/tex]
[tex]I[/tex] [tex]= 1000 x 0.155 x (1/12)[/tex]
[tex]I = $12.92[/tex]
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A community organization wishes to know the proportion of subjects who feel financially comfortable in a certain town.
Based on last year's census, 64% of the residents in this town felt financially comfortable. In this year's survey 56 out of 115 randomly chosen subjects felt financially comfortable. Comfortable.
If indeed the residents' economic opinions have NOT changed from last year, what's the probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable?
a. 0. 0006
b. 0. 0003
c. 0. 3245
d. 0. 0927
e. 0. 9997
The probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable is 0.0003. Therefore, the correct option is B.
To find the probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable if the residents' economic opinions have not changed from last year, we can use the normal distribution as an approximation to the binomial distribution.
1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the proportion from the census (64%) and the sample size (n = 115).
Mean (μ) = n * p = 115 * 0.64 = 73.6
Standard deviation (σ) = √(n * p * (1-p)) = √(115 * 0.64 * 0.36) ≈ 6.45
2. Convert the observed value (56) to a z-score:
z = (x - μ) / σ = (56 - 73.6) / 6.45 ≈ -2.73
3. Find the probability of getting a z-score less than or equal to -2.73 using a z-table or an online calculator.
P(Z ≤ -2.73) ≈ 0.0032
The closest answer choice to this probability is 0.0003, so the correct answer is (b) 0.0003.
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A scale model of a statue has a height of 10 cm. The real statue has a height of 2 m. The model and statue are both made of the same stone which has a density of 2 g/cm(3). The mass of the real statue is 1632 kg. Find the volume of the model in cm(3)
Answer:
102 cm³
Step-by-step explanation:
density = m/v
1 g = 0.001 kg
Volume of real statue = v = m/d = 1632 kg / 0.002 kg/cm³ = 816,000 cm³
scale factor for height: 200 cm : 10 cm = 20 : 1
scale factor for volume: 20³ : 1³ = 8,000 : 1
Volume of model = 816,000 cm³ / 8,000 = 102 cm³
Which numbers are solutions to the inequality *> 145 ? check all that apply. fraction is larger than 14 1/2 be decimals larger than 14 1/2 while numbers larger than 14 1/2 the number 14 1/2
fractions smaller than 14 1/2, decimal smaller than 14 1/2, whole number smaller than 14 1/2
For the solutions to the inequality *> 145, you can consider the given terms: 1. Fractions larger than 14 1/2: These are solutions since 14 1/2 is equivalent to 145/2, which is smaller than 145. 2.
Decimals larger than 14 1/2: These are also solutions as any decimal larger than 14.5 (14 1/2 as a decimal) will be greater than 145/2 and thus smaller than 145. 3. Whole numbers larger than 14 1/2: These are solutions as well, since any whole number greater than 14 is greater than 14 1/2 and therefore greater than 145/2. The numbers that are not solutions to the inequality are: 1. Fractions smaller than 14 1/2 2. Decimals smaller than 14 1/2 3. Whole numbers smaller than 14 1/2 These values are all less than 145/2 and therefore do not satisfy the inequality *> 145.
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Hallar la altura de una asta bandera, si un estudiante la observa desde un punto a, con un ángulo de 30° y entre el estudiante y la asta hay una distancia de 10m.
Answer:
The height of the flagpole is approximately 5.774 meters.
Step-by-step explanation:
Let's call the height of the flagpole h. We can use trigonometry to set up the following equation:
tan(30°) = h/10
Simplifying this equation, we get:
h = 10 tan(30°)
Using a calculator, we find that tan(30°) ≈ 0.5774, so:
h ≈ 5.774 meters
Therefore, the height of the flagpole is approximately 5.774 meters.
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A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.4 inch and a height of 2.2 inches. How many total square inches of gift wrap will the makeup artist need to wrap 3 lipsticks? Leave the answer in terms of π.
2.08π square inches
6.24π square inches
8.32π square inches
19.59π square inches
The makeup artist will need approximately 7.296π square inches of gift wrap to wrap 3 lipsticks. Rounded to two decimal places, the answer is 19.59π square inches.
How to calculate how many total square inches of gift wrap will the makeup artist need to wrap 3 lipsticksThe formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder.
For one lipstick, the surface area is:
SA = 2π(0.4)² + 2π(0.4)(2.2)
SA = 1.024π + 1.408π
SA = 2.432π square inches
To wrap 3 lipsticks, the total surface area would be:
SA = 3(2.432π)
SA = 7.296π square inches
Therefore, the makeup artist will need approximately 7.296π square inches of gift wrap to wrap 3 lipsticks. Rounded to two decimal places, the answer is 19.59π square inches.
So the correct option is: 19.59π square inches.
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Aabc is dilated by a factor of to produce aa'b'c!
28°
34
30
62
b
16
what is a'b, the length of ab after the dilation? what is the measure of a?
To find the length of a'b', we first need to know the scale factor of the dilation. The scale factor is given by the ratio of the corresponding side lengths in the original and diluted figures.
In this case, we are given that the original figure Aabc has been diluted by a factor of √2. So the length of each side in the dilated figure aa'b'c is √2 times the length of the corresponding side in Aabc.
To find the length of a'b, we can use the Pythagorean theorem in the right triangle aa'b'. Since we know that ab is one of the legs of this triangle, we can find its length as follows:
ab = (a'b' / √2) * sin(28°)
We are not given the length of ab or a in the original figure, so we cannot find their exact values. However, we can find the measure of angle A using the Law of Sines in triangle Aab:
sin(A) / ab = sin(62°) / b
where b is the length of side bc in Aabc. Solving for sin(A) and substituting the expression for ab that we found earlier, we get:
sin(A) = (sin(62°) / b) * [(a'b' / √2) * sin(28°)]
Since we know the values of sin(62°) and sin(28°), we can simplify this expression and use a value for b (if it is given in the problem) to find sin(A) and then A.
Use this scenario on this and the next problem.
Tobias received an inheritance from his grandfather of $20,000. When he gets out of
college in 4 years he wants to use it as a down payment on a piece of lakeside property.
If he puts all the money in a savings account paying 6. 5% interest compounded daily,
how much money will be in the account at the end of the four years to use as the down
payment on the property?
The amount of money that will be in the account at the end of the four years to use as the down payment on the property is $26,102.47.
What is the compound interest?In the above question, we need to use the formula for compound interest and it is:
A = P(1 + r/n)^(nt)
Note that:
A = the amount of money at the end of the investment
P = the principal amount
r = the annual interest rate
n = the number of times the interest is compounded per year
t = the number of years of the investment
Since:
P = $20,000
r = 6.5% = 0.065
n = 365 (note the interest is compounded everyday)
t = 4
We shall put the values into the formula:
A = $20,000(1 + 0.065/365)^(365*4)
A = $20,000(1.0178)¹⁴⁶⁰
A = $20,000 x 1.305124
A = $26,102.47
Therefore, at the end of the four years, there will be $26,102.47.
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Jaoan reads that themass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. How many kilograms is an average elephant's brain?
Answer:
Step-by-step explanation:
Let's call the mass of an average man's brain "m."
According to the problem, the mass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. We can write this as:
mass of elephant's brain = m + 3 4/10
To find out how many kilograms an average elephant's brain weighs, we need to know the value of "m." However, this information is not given in the problem.
Therefore, we cannot determine the exact mass of an average elephant's brain.
Scott has a rectangular garage that has a length of 234 inches. The width is 1. 5 times shorter than the length. What is the area of his garage?
The area of garage is 36,504 square inches.
The width of Scott's garage is 156 inches (since it is 1.5 times shorter than the length of 234 inches).
so width = 234/1.5
=> 156
To find the area, we multiply the length by the width:
=> 234 inches x 156 inches
=> 36,504 square inches.
To explain, the formula for finding the area of a rectangle is length x width. In this problem, we are given the length of the garage as 234 inches and are told that the width is 1.5 times shorter than the length.
To find the width, we can multiply the length by 1.5 to get 351 inches (which is longer than the length, so we know it must be incorrect). Instead, we need to divide the length by 1.5 to find the width, which gives us 156 inches. Then, we can multiply the length by the width to find the area of the garage, which is 36,504 square inches.
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In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
(2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept. Explain what each represents.
Use first two points and the slope equation to find the slope:
m = (4225 - 1990)/(5 - 2) = 745The slope is 745.
Use the first point and point-slope equation to find the y-intercept:
y - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the given pointy - 1990 = 745(x - 2)y - 1990 = 745x - 1490y = 745x - 1490 + 1990y = 745x + 500The y-intercept is 500.
The slope of 745 represents the profit per month and the y-intercept of 500 represents the initial profit.
Problem 1. (5 points): Evaluate the double integral by first identifying it as the volume of a solid. S SCH (4 - 2y) dA, R= [0, 1] x [0, 1] -
To evaluate the double integral, we first identify it as the volume of a solid. The integrand, S SCH (4 - 2y), represents the height of the solid at each point (x, y) in the region R=[0, 1] x [0, 1].
Therefore, the integral represents the volume of the solid over region R. We can evaluate the integral using Fubini's theorem or by changing the order of integration.
Using Fubini's theorem, we first integrate with respect to y from 0 to 1, then integrate with respect to x from 0 to 1:
∫[0,1]∫[0,1]S SCH (4-2y) dA = ∫[0,1]∫[0,1]S SCH (4-2y) dxdy
= ∫[0,1] [(4-2y)∫[0,1]S SCH dx]dy
= ∫[0,1] [(4-2y)(1-0)]dy
= ∫[0,1] (4-2y)dy
= 4y-y^2/2 | from 0 to 1
= 4-2-0
= 2
Therefore, the double integral is equal to 2, which represents the volume of the solid over the region R=[0, 1] x [0, 1].
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7. The table shows the linear relationship between the total amount Mrs. Jacobs will be
charged for a skating party and the number of children attending.
Which equation best represents y, the total amount in dollars Mrs. Jacobs will be
charged for
x number of children attending the skating party?
The equation that best represents the linear relationship between the total amount Mrs. Jacobs will be charged and the number of children attending the skating party is y = mx + b.
In this case, y represents the total amount in dollars that Mrs. Jacobs will be charged, x represents the number of children attending the party, m represents the slope of the line, and b represents the y-intercept.
To find the equation, we need to determine the slope and y-intercept from the table given. From the table, we can see that for every additional child attending the party, the total amount charged increases by $10. This means that the slope (m) of the line is 10.
To find the y-intercept (b), we can look at the table and see that when there are zero children attending the party, the total amount charged is $50. This means that the y-intercept is 50.
Putting it all together, the equation that best represents the linear relationship is y = 10x + 50.
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A 60 foot tall building casts a 20 foot. Shadow. Use the principles of similar triangles to determine the length of a shadow cast by a 5 foot 6 inch student
The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.
To solve this problem, we'll set up a proportion using the principles of similar triangles. The two triangles in this case are the building and its shadow, and the student and their shadow.
Convert the height of the student to feet. 5 feet 6 inches is equal to 5.5 feet.
Set up the proportion. Let x represent the length of the shadow cast by the student. We have the following proportion:
(height of building) / (length of building's shadow) = (height of student) / (length of student's shadow)
60 / 20 = 5.5 / x
Cross-multiply and solve for x:
60 * x = 20 * 5.5
60x = 110
x = 110 / 60
x = 1.83 (rounded to two decimal places)
The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.
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When calculating the price (p) of an item that has been marked down by 25%, Denise states that the expression
p - 0. 25p will calculate the
sale price. Kristal says that a shorter way to calculate the sale price would be to use the expression 0. 75p. Who is correct
A Denise is correct.
B Kristal is correct. .
C Both Denise and Kristal are correct.
D Neither Denise nor Kristal are correct.

Both Denise and Kristal are correct. The expression "p - 0.25p" is equivalent to "0.75p," which represents the sale price after a 25% markdown. Therefore, option C is the correct answer.
Denise's expression, "p - 0.25p," represents the original price (p) minus the 25% markdown (0.25p). This simplifies to 0.75p, which is indeed the sale price.
On the other hand, Kristal's expression, "0.75p," directly represents the sale price after applying a 25% discount. This expression skips the intermediate step of subtracting the markdown from the original price.
Both expressions, "p - 0.25p" and "0.75p," yield the same result, which is the sale price after a 25% markdown. Therefore, both Denise and Kristal are correct in their calculations.
The choice between the two expressions comes down to personal preference or convenience. Some individuals may find it easier to directly calculate the sale price using a percentage of the original price, while others may prefer subtracting the markdown amount from the original price.
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A coin is flipped, and a standard number cube is rolled. What is the probability for flipping tails and rolling an odd number.
Answer:
1/4
Step-by-step explanation:
The probability of flipping tails is 1/2, since there are two equally likely outcomes when flipping a coin (heads or tails).
The probability of rolling an odd number on a standard number cube is 3/6 or 1/2, since there are three odd numbers (1, 3, and 5) out of six possible outcomes (1, 2, 3, 4, 5, and 6).
To find the probability of both events happening (i.e., flipping tails and rolling an odd number), we multiply the probabilities of each event:
P(tails and odd number) = P(tails) * P(odd number)
P(tails and odd number) = 1/2 * 1/2
P(tails and odd number) = 1/4
Therefore, the probability of flipping tails and rolling an odd number is 1/4 or 0.25.
At the beginning of the summer, the water level in an underground well was -3 feet. During the hot summer months, the water level fell 4 feet. The expression -3 -4 gives the water level in feet at the end of the summer.
What was the water level at the end of the summer?
Answer:
-7 feet
Step-by-step explanation:
-3-4 = -7, so it is -7 feet
In a laboratory experiment, the population of bacteria in a petri dish started off at 380 and is growing exponentially at 3% per day. Write a function to represent the population of bacteria after tt days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent
The function is P(t) = 380 x [tex]1.0300^{t}[/tex], which is an exponential function, and the rate of change is 1.24% each hour.
The equation P(t) = 380 x [tex](1 + 0.03)^{t}[/tex] represents the population of bacteria after t days.
Rounding to four decimal digits and simplifying:
P(t) = 380 x [tex]0.0300^t[/tex]
We can use the following formula to determine the percentage rate of change each hour:
r = [tex]100 \times e^{(ln(1 + 0.03)/24) - 1)}[/tex]
where e is the Euler's number, ln is the natural logarithm, and r is the percentage rate of change per hour.
Rounding to the nearest tenth of a percent and simplifying:
r = 1.24%
This exponential function simulates the population of bacteria multiplying exponentially at a rate of 3% each day in a petri dish.
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Dr. Aghedo is saving money in an account with continuously compounded interest. How long will it take for the money she deposited to double if interest is compounded continuously at a rate of 3. 1%. Round your answer to the nearest tenth
The count of duration that is needed for Dr. Aghedo's money to be deposited is 22.3 years, under the condition that if interest is compounded continuously at a rate of 3. 1
The derived formula for doubling time with continuous compounding is applied to evaluate the length of time it takes to double the money in an account or investment that has continuous compounding. The formula is
Doubling time = ln 2 / r
Here,
r =annual interest rate as a decimal.
For the required case, the interest rate is 3.1% that can be written as 0.031 in the form of decimal. Then the doubling time will be
Doubling time = ln 2 / 0.031
≈ 22.3 years
Then, it should take approximately 22.3 years for Dr. Aghedo's money to double if interest is compounded continuously at a rate of 3.1%.
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The dean of students at a large college is interested in learning about their opinions regarding the percentage of
first-year students who should be given parking privileges in the main lot. he sends out an email survey to all
students about this issue. a large number of first-year students reply but very few sophomores, juniors, and seniors
reply. based on the responses he receives, he constructs a 90% confidence interval for the true proportion of
students who believe first-year students should be given parking privileges in the main lot to be (0.71, 0.79). which
of the following may have an impact on the confidence interval, but is not accounted for by the margin of error?
o response bias
o nonresponse bias
o sampling variation
o undercoverage bias
mark this and retum
save and exit
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The potential factor that may have an impact on the confidence interval, but is not accounted for by the margin of error, is nonresponse bias.
The dean of students received a large number of responses from first-year students but very few from sophomores, juniors, and seniors. Nonresponse bias occurs when some individuals chosen for a sample do not respond to a survey or study. In this case, the dean of students may not have received a representative sample of the opinions of all students, which could lead to an overestimation or underestimation of the true proportion of students who believe first-year students should be given parking privileges in the main lot.
The margin of error is the amount of random sampling error in a survey's results. It reflects the level of precision in the survey's results and decreases as the sample size increases. However, nonresponse bias is a systematic error that is not accounted for by the margin of error, as it may lead to a biased sample and inaccurate results. To minimize nonresponse bias, the dean of students could have used techniques such as follow-up emails or incentives to encourage a higher response rate from all student groups.
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Piscine is replacing the paving stones around her inground pool. Her pool is 10 m
by 5 m, and is surrounded by a 1. 5 m border of paving stones.
a) How many square metres of paving stones will she need in total?
b) If each paving stone is 25 cm by 40 cm, in theory, how many paving stones
will she need?
c) Will your answer in part b) actually be enough? Try fitting the stones in the
space to see whether Piscine can complete the border with exactly that
number of stones, or whether there will be waste, requiring some extras.
If Her pool is 10 m by 5 m and is surrounded by a 1. 5 m border of paving stones. Therefore, Piscine will need a total of 104 square meters of paving stones.
a) The area of the pool plus the surrounding border of paving stones can be calculated as follows:
Total area = (length + 2 x border width) x (width + 2 x border width)
Total area = (10 + 2 x 1.5) x (5 + 2 x 1.5)
Total area = 13 x 8
Total area = 104 square meters
Therefore, Piscine will need a total of 104 square meters of paving stones.
b) We need to convert the dimensions of each paving stone to meters:
25 cm = 0.25 m
40 cm = 0.4 m
The area of each paving stone is:
0.25 m x 0.4 m = 0.1 square metres
The number of paving stones required can be calculated by dividing the total area by the area of each paving stone:
Number of paving stones = Total area / Area of each paving stone
Number of paving stones = 104 / 0.1
Number of paving stones = 1040
In theory, Piscine will need 1040 paving stones.
c) To determine whether the answer in part b) will be enough, we need to see if we can fit the paving stones into the available space without any gaps. We can arrange the paving stones in rows, with each row containing 10 stones (since the width of the pool is 5 m and the width of each paving stone is 0.4 m).
There will be 26 rows of paving stones around the pool (since the length of the pool plus the two borders is 13 m and the length of each paving stone is 0.25 m). Therefore, the total number of paving stones required is: 26 rows x 10 stones per row = 260 stones
Since the number of paving stones required is less than the number calculated in part b), Piscine will have enough paving stones to complete the border around her pool without any waste.
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What is the volume of a right rectangular prism with a length of 4. 8 meters, a width of 2. 3 meters, and a height
of 0. 9 meters?
O4. 968 m3
O9. 936 m3
O 11. 94 m3
O 34. 86 m3
PLS ANSWER FAST I WILL GIVE BRAINIEST!!!!!
Answer:
Step-by-step explanation:
The volume of the given prism is 9.936 cubic meters, To calculate the volume of a right rectangular prism, we need to multiply its length, width, and height together.
Given that the length of the prism is 4.8 meters, the width is 2.3 meters, and the height is 0.9 meters, we can calculate the volume using the formula:
Volume = length x width x height
Volume = 4.8 m x 2.3 m x 0.9 m
Volume = 9.936 m^3
Therefore, the volume of the right rectangular prism is 9.936 cubic meters.
It is important to note that when we calculate volume, we are dealing with a three-dimensional space, and the units we use must be cubed (m^3 in this case). This is because we are measuring the amount of space occupied by the object in all three dimensions.
In summary, to find the volume of a right rectangular prism, we simply multiply its length, width, and height together. In this case, the volume of the given prism is 9.936 cubic meters.
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23. The function is defined by f:x → x + 2. Another function g is such that fg: x → 1/x-1 , x ≠ 1
Find g.
A school chess club needs to raise at least $750 to attend a state competition.
The inequality which can be used to determine amount the club needs to raise during remaining months is 400 + 4n ≥ 750.
The goal of the school chess club is to raise at least $750 in total so that they can attend a state competition. They have already raised $400, but they still need to raise more money. Let's call the amount they need to raise each month "n".
Since the club has 4 months remaining until the competition, they will need to raise a total of "4n" dollars during that time period.
To determine the minimum amount they need to raise each month, the inequality can be written as : 400 + 4n ≥ 750,
4n ≥ 350 ; n ≥ 87.5.
This means that the chess-club needs to raise at least $87.50 each month in order to reach their goal of $750 in 4 months.
Therefore, the required inequality is 400 + 4n ≥ 750.
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The given question is incomplete, the complete question is
A school chess club needs to raise at least $750 to attend a state competition. The club has already raised $400 and there are 4 months remaining until the competition. Write an inequality which can be used to determine the dollar amount the club will need to raise during the remaining months?
James and Padma are on opposite sides of a 100-ft-wide canyon. James sees a bear at an angle of depression of 45 degrees. Padma sees the same bear at an angle of depression of 65 degrees.
What is the approximate distance, in feet, between Padma and the bear?
A
21. 2ft
B
75. 2ft
C
96. 4ft
D
171. 6ft
The approximate distance between Padma and the bear is 21.2 ft, which corresponds to option A.
The approximate distance between Padma and the bear, we can use trigonometry. Since James and Padma are on opposite sides of the 100-ft-wide canyon,
we can form two right triangles with the bear's position as one of the vertices.
Step 1: Determine the horizontal distance from James to the bear.
Since the angle of depression from James to the bear is 45 degrees, the horizontal distance (x) and vertical distance (y) are equal due to the properties of a 45-45-90 right triangle. Therefore, x = y. Since the canyon is 100 ft wide, x + y = 100 ft. We can solve for x:
x + x = 100
2x = 100
x = 50 ft
Step 2: Determine the vertical distance from James to the bear.
Since x = y in the 45-45-90 right triangle, the vertical distance from James to the bear is also 50 ft.
Step 3: Determine the horizontal distance from Padma to the bear.
We can now use Padma's angle of depression, 65 degrees, to find the horizontal distance (p) from Padma to the bear. Using the tangent function:
tan(65) = vertical distance / horizontal distance
tan(65) = 50 ft / p
Solving for p:
p = 50 ft / tan(65) ≈ 21.2 ft
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Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale.
*
Captionless Image
1209 m^2
790 m^2
1125 m^2
898 m^2
The surface area of the regular pyramid is 1209 m².
How to find the surface area of the regular pyramid?A pyramid is a three-dimensional shape. It has a flat polygon base. All the other faces are triangles and are called lateral faces.
A pyramid is called by the shape of its base.
The surface area of the regular hexagonal pyramid is given by the formula:
SA = 3b(a + s)
Where a is the apothem, b is the base and s is the slant height of the pyramid.
In this case:
a = 8.5√3 m
b = 17 m
s = 9 m
SA = 3 * 17 * (8.5√3 + 9)
SA = 1209 m²
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The height of lava fountains spewed from volcanoes cannot be measured directly. Instead, their height in meters can be found using the equation
where y represents the height, g is 9.8, and t represents the falling time of the lava rocks. Find the height in meters of a lava rock that falls for 3 seconds.
A cistern in the form of an inverted circular cone is being filled with water at the rate of 65 liters per minute. if the cistern is 5 meters deep, and the radius of its opening is 2 meters, find the rate at which the water level is rising in the cistern 30 minutes after the filling process began.
Let's start by finding the volume of the cistern at any given time t. Since the cistern is in the form of an inverted circular cone, its volume can be expressed as:
V = (1/3)πr^2h
where r is the radius of the circular opening, h is the height of the cone (which is also the depth of the cistern), and π is the constant pi.
We are given that the cistern is 5 meters deep, and the radius of its opening is 2 meters. Therefore, we can plug these values into the equation above to get:
V = (1/3)π(2^2)(5)
V = 20/3 π
Now, we need to find the rate at which the water level is rising in the cistern after 30 minutes. Let's call this rate dh/dt (the change in height with respect to time).
We know that the water is being added to the cistern at a rate of 65 liters per minute. Since 1 liter is equal to 0.001 cubic meters, the volume of water being added per minute is:
(65 liters/minute) × (0.001 m^3/liter) = 0.065 m^3/minute
Therefore, the rate at which the height of the water in the cistern is changing is:
dh/dt = (0.065 m^3/minute) / (20/3 π m^3) = 3.87/π meters/minute
After 30 minutes, the height of the water in the cistern will have risen by:
h = (65 liters/minute) × (0.001 m^3/liter) × (30 minutes) / (20/3 π m^3) = 0.2925 meters
Therefore, the rate at which the water level is rising in the cistern 30 minutes after the filling process began is:
dh/dt = 3.87/π meters/minute
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Need HELP ASAP!! please
Answer :
D. XY = 5 , YZ = 2Step-by-step explanation :
As We Know that Opposite sides of the Parallelogram are equal.
SO,
(i) YZ = XW (opposite sides)
YZ = 2bXW = b + 1=> 2b = b + 1
=> 2b - b = 1
=> b = 1
Since, YZ = 2b
=> YZ = 2 × 1
=> YZ = 2.
Also,
(ii) XY = WZ (opposite sides)
XY = 3a - 4 WZ = a + 2=> 3a - 4 = a + 2
=> 3a - a = 2 + 4
=> 2a = 6
=> a = 6/2
=> a = 3 .
Since, XY = 3a - 4
putting the value of a = 3.
=> 3(3) - 4
=> 9 - 4
=> 5
XY = 5.
Therefore, Option D is the required answer.
Which ordered pair is a solution to the following system of inequalities?
y < –x2 + x
y > x2 – 4
(0, –1)
(1, 1)
(2, –3)
(3, –6)
(0, -1) is the solution to the given system of inequalities.
Option A is the correct answer.
We have,
To determine which ordered pair is a solution to the system of inequalities, we need to check if each ordered pair satisfies both inequalities simultaneously.
Let's evaluate each option:
(0, -1):
For this option, we have:
y < -x² + x
-1 < -(0)² + 0
-1 < 0
y > x² - 4
-1 > (0)² - 4
-1 > -4
Since both inequalities are satisfied simultaneously, (0, -1) is a solution to the system.
(1, 1):
For this option, we have:
y < -x² + x
1 < -(1)² + 1
1 < 0
y > x² - 4
1 > (1)² - 4
1 > -3
Since both inequalities are not satisfied simultaneously, (1, 1) is not a solution to the system.
(2, -3):
For this option, we have:
y < -x² + x
-3 < -(2)² + 2
-3 < -2
y > x² - 4
-3 > (2)² - 4
-3 > 0
Since both inequalities are not satisfied simultaneously, (2, -3) is not a solution to the system.
(3, -6):
For this option, we have:
y < -x² + x
-6 < -(3)² + 3
-6 < -6
y > x² - 4
-6 > (3)² - 4
-6 > 5
Since both inequalities are not satisfied simultaneously, (3, -6) is not a solution to the system.
Thus,
(0, -1) is the only solution to the given system of inequalities.
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40 points!!!
Peyton's photo album has 6 1/2 pages of family photos and f pages of
photos of friends. Write an expression that shows the total number
of pages in Peyton's album. Then evaluate the expression if there are
3 1/2 pages of photos of friends.
The expression that shows the total number of pages in Peyton's album is 6 1/2 + f.
We are given that;
Number of pages= 6 1/2
Now,
To write an expression that shows the total number of pages in Peyton’s album, you need to add the number of pages of family photos and the number of pages of friends photos. The expression is:
6 1/2 + f
To evaluate the expression if there are 3 1/2 pages of photos of friends, you need to substitute f with 3 1/2 and then add the fractions. The answer is
6 1/2 + 3 1/2 = 10
Therefore, by the expression the answer will be 6 1/2 + f.
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