Given that LMN is a triangle and LM=7, NL=10 and MN=9. We need to find out the angles of the triangle LMN listed in order from largest to smallest. So, option C is correct.
To find the angles of triangle, we can use the cosine rule which states that: $c² = a² + b² - 2ab\cos(C) $ where c is the side opposite to angle C in triangle ABC. We can use this rule to find out each angle of triangle LMN:
Let us find cos L: MN² = LM² + NL² - 2(LM)(NL) cos(L)9²
= 7² + 10² - 2(7)(10) cos(L)81
= 149 - 140 cos(L) 140cos(L)
= 68 cos(L)
= 68/140cos(L)
= 0.4857
Similarly, we can find cos M and cos N as follows:
cos M = 0.3214
cos N = -0.027
Now, we can use the inverse cosine function on the calculator to find the value of each angle:
∠L = cos⁻¹(0.4857) = 61.45°
∠M = cos⁻¹(0.3214) = 70.76°
∠N = cos⁻¹(-0.027) = 90.79°
The angles of LMN in order from largest to smallest are:∠N, ∠M, ∠L
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A scientist is trying to use a PCR reaction to amplify a gene with a high GC (guanine:cytosine) content. The scientist will need to use a _________________ denaturation temperature to separate the newly synthesized DNA strand from the template for subsequent PCR cycles.
The scientist will need to use a high denaturation temperature to separate the newly synthesized DNA strand from the template for subsequent PCR cycles.
The PCR (Polymerase Chain Reaction) method is a common laboratory technique used to amplify and produce multiple copies of a specific segment of DNA. The PCR method allows researchers to isolate and amplify DNA in vitro, which is then used for various research applications.A gene with a high GC content has a stronger bond than a gene with a low GC content, which can make it difficult to separate the newly synthesized DNA strand from the template. This high temperature causes the hydrogen bonds between the complementary strands of DNA to break, resulting in the separation of the double-stranded DNA into single strands. A high denaturation temperature is used to ensure that the newly synthesized DNA strand is separated from the template for subsequent PCR cycles, and it is usually around 94°C to 98°C.
During Polymerase Chain Reaction (PCR), researchers often need to isolate and amplify DNA, allowing for multiple copies of a specific DNA segment. A gene with a high GC (guanine:cytosine) content has a stronger bond than a gene with a low GC content, which can make it difficult to separate the newly synthesized DNA strand from the template.During PCR, DNA is heated to a high temperature to separate its strands, and then primers are annealed to the single-stranded DNA, allowing DNA polymerase to synthesize new strands. This high temperature causes the hydrogen bonds between the complementary strands of DNA to break, resulting in the separation of the double-stranded DNA into single strands. A high denaturation temperature is used to ensure that the newly synthesized DNA strand is separated from the template for subsequent PCR cycles. A low denaturation temperature could result in incomplete separation of the DNA strands, which could lead to failed amplification reactions. Therefore, the scientist needs to use a high denaturation temperature to separate the newly synthesized DNA strand from the template for subsequent PCR cycles.
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Shawna's sister drank gallon of water after running a marathon. If she ran four races and drank the same amount of water after each race, how many gallons of water would she drink?
If Shawna's sister drinks a gallon of water after each of the four races she runs, she would consume a total of four gallons of water.
Given that Shawna's sister drinks a gallon of water after running each race, we can multiply the amount of water consumed per race (1 gallon) by the number of races (4) to determine the total amount of water consumed.
1 gallon of water per race x 4 races = 4 gallons of water
Therefore, Shawna's sister would drink a total of four gallons of water after running the four races. Each race contributes 1 gallon to the total, resulting in a cumulative consumption of four gallons.
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How to divide 134880 by 240 using the long division method
134880 divided by 240 using the long division method is 562.
In order to divide 134880 by 240 using the long division method, follow the given steps below:
Step 1: Set up the division with dividend inside the bracket and divisor outside it.
Step 2: Determine how many times the divisor goes into the first digit(s) of the dividend. Here, 240 goes into 1348 five times. Write 5 above the first digit of the dividend, to the right of the bracket.
Step 3: Multiply the divisor by the quotient. 5 x 240 = 1200. Write this product beneath the first digits of the dividend.
Step 4: Subtract the product obtained in step 3 from the first digits of the dividend. Write the result under the line. 1348 - 1200 = 148.
Step 5: Bring down the next digit of the dividend (in this case, 8) next to the remainder. Now, you have 1488.
Step 6: Determine how many times the divisor goes into the first digit(s) of the new dividend, i.e., 1488. Here, 240 goes into 1488 six times. Write 6 above the second digit of the dividend, to the right of the previous quotient digit (5).
Step 7: Multiply the divisor by the new quotient. 6 x 240 = 1440. Write this product beneath the first two digits of the dividend.
Step 8: Subtract the product obtained in step 7 from the first two digits of the dividend. Write the result under the line. 1488 - 1440 = 48.
Step 9: Bring down the next digit of the dividend (in this case, 0) next to the remainder. Now, you have 480.
Step 10: Determine how many times the divisor goes into the first digit(s) of the new dividend, i.e., 480. Here, 240 goes into 480 two times. Write 2 above the third digit of the dividend, to the right of the previous quotient digit (6).
Step 11: Multiply the divisor by the new quotient. 2 x 240 = 480. Write this product beneath the first three digits of the dividend.
Step 12: Subtract the product obtained in step 11 from the first three digits of the dividend. Write the result under the line. 480 - 480 = 0.
Therefore, 134880 divided by 240 using the long division method is 562.
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A large toy top is a cone with a slant height of
10
cm
and radius of
6
cm. The handle of the toy top is a cylinder with a diameter of
2
cm
and height
2
cm. Determine the approximate volume of the top. Use
π
≈
3. 14
Given that slant height of 10 cm and a radius of 6 cm for the cone, and a diameter of 2 cm and a height of 2 cm for the handle. Therefore, the approximate volume of the large toy top is approximately 295.16 cm³.
The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius and h is the height. Given that the slant height is 10 cm, we can use the Pythagorean theorem to find the height of the cone, which is √(10² - 6²) = √(100 - 36) = √64 = 8 cm. Substituting these values into the volume formula, we get V_cone = (1/3) × 3.14 × 6² × 8 ≈ 301.44 cm³.
The volume of the handle, which is a cylinder, can be calculated using the formula V = πr²h, where r is the radius and h is the height. The radius is half the diameter, so r = 1 cm. Substituting these values into the volume formula, we get V_handle = 3.14 × 1² × 2 = 6.28 cm³.
To find the approximate volume of the toy top, we subtract the volume of the handle from the volume of the cone: V_top = V_cone - V_handle ≈ 301.44 cm³ - 6.28 cm³ ≈ 295.16 cm³. Therefore, the approximate volume of the large toy top is approximately 295.16 cm³.
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Find the value of x. Enter your answer in the box.Granola Bars1242Box2xx =
To find the value of x in the equation "Granola Bars / 1242 = Box / 2x", we can set up a proportion and solve for x.
The proportion can be written as:
Granola Bars / 1242 = Box / (2x)
To solve for x, we can cross-multiply and solve the resulting equation:
Granola Bars * 2x = 1242 * Box
2 * Granola Bars * x = 1242 * Box
Dividing both sides by 2 * Granola Bars:
x = (1242 * Box) / (2 * Granola Bars)
Therefore, the value of x is given by (1242 * Box) / (2 * Granola Bars).
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1. You are a skateboarder. You go to a skateboard park that has a merry-go-round. You hold on to the railing while the merry-go-round spins rapidly, so you are moving in a circular path while on your skateboard. Suddenly, you let go of the railing. What is the path of your motion? Assume your skateboard has perfect ball bearings and that the ground has an ideal surface so that there is no friction to slow you down2. Now think about the Ferris wheel.You are holding onto a railing on the circumference of a Ferris wheel that is turning rapidly. Suddenly, you let go. Sketch the path of your fall for at least one position in each quadrant.
When you let go of the railing on the merry-go-round at the skateboard park, your path of motion will be tangential to the circular path. For the Ferris wheel, your path will be parabolic due to the influence of gravity.
When you let go of the railing on the merry-go-round at the skateboard park, your motion will follow the principle of inertia. Since there is no friction to slow you down, your path of motion will be tangential to the circular path at the moment you let go. This means you will continue moving in a straight line tangent to the circular path.
In the case of a Ferris wheel, when you let go of the railing, gravity comes into play. Your path of motion will follow a parabolic trajectory due to the influence of gravity. As you fall, your path will curve downward, creating a parabolic shape.
The exact shape and position of the parabolic path will depend on factors such as your initial position, speed, and the size of the Ferris wheel. To sketch the path of your fall for at least one position in each quadrant, you would need specific information about the Ferris wheel's dimensions and your initial position.
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A scatter plot was made to show the record for the 100-meter dash over several years at Meander High School. The equation of the scatter plot’s trend line is y = -. 14x 12. 5 where y is the record i seconds, and x is the number of years since the year 2000. Use the trend line equation to predict the year that the record for the 100-meter dash was 11. 8 seconds
The trend line equation, y = -0.14x + 12.5, can be used to predict the year when the record for the 100-meter dash was 11.8 seconds at Meander High School.
In the trend line equation y = -0.14x + 12.5, "y" represents the record time in seconds, and "x" represents the number of years since the year 2000. To predict the year when the record was 11.8 seconds, we can substitute this value for "y" in the equation and solve for "x."
11.8 = -0.14x + 12.5
Rearranging the equation, we get:
-0.14x = 11.8 - 12.5
-0.14x = -0.7
Dividing both sides by -0.14, we find:
x = -0.7 / -0.14
x = 5
The value of "x" represents the number of years since the year 2000. Therefore, to determine the year, we add "x" to the year 2000:
2000 + 5 = 2005
According to the trend line equation, the record for the 100-meter dash was predicted to be 11.8 seconds in the year 2005 at Meander High School.
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The cost of 6 cans of dog food is $3.90 Find the rate, include the units of measure Write 1 equation that represents the proportional relationship use (cost and (d) for cans of dog food..
Given the cost of 6 cans of dog food is $3.90Rate = Cost/ No. of cans of dog food
Rate = 3.9/6= 0.65$ per can of dog food
Hence, the rate is $0.65 per can of dog food and the unit of measure is dollars per can of dog food.
Proportional relationship can be written as;
Cost of dog food ∝ No. of cans of dog food
We know, for a proportional relationship; Cost of dog food = k × No. of cans of dog food
Where k is the constant of proportionality.
By substituting the given values in the above equation;
3.9 = k × 6
k = 3.9/6
k = 0.65
Given the cost of 6 cans of dog food is $3.90, we can calculate the rate by dividing the cost by the number of cans of dog food. Therefore, the rate of the dog food cans is $0.65 per can. The units of measure are dollars per can of dog food.We can also represent the proportional relationship between the cost and the number of cans of dog food using the formula; Cost of dog food ∝ No. of cans of dog food.
In this formula, the constant of proportionality is represented as k. We can find the value of k by substituting the given values in the equation and solving for k. Hence, the required equation that represents the proportional relationship is Cost of dog food = 0.65 × No. of cans of dog food.
We found that the rate of the dog food cans is $0.65 per can. We also found that the proportional relationship between the cost and the number of cans of dog food can be represented using the equation
Cost of dog food = 0.65 × No. of cans of dog food, where the constant of proportionality is 0.65.
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Leticia has two bouquets of flowers. Each bouquet contains 13 daisies. • Bouquet S contains 30 flowers. • Bouquet T contains 13 flowers. Which statement is true?.
Bouquet T contains 13 flowers, which matches the number of daisies in each bouquet. Therefore, the statement "Each bouquet contains 13 daisies" is true.
According to the information given, Bouquet S contains 30 flowers. However, the number of daisies in Bouquet S is not specified. On the other hand, Bouquet T is explicitly stated to contain 13 flowers. It is also mentioned that each bouquet contains 13 daisies. Since the number of flowers in Bouquet T matches the number of daisies in each bouquet, it can be inferred that Bouquet T consists entirely of daisies. Bouquet S, on the other hand, could have a different number of daisies, as the information does not specify the composition of the flowers within it. Therefore, the statement "Each bouquet contains 13 daisies" is true, with Bouquet T serving as an example of a bouquet that matches this description.
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d, to advance. d equals T minus a minus b minus c all over 2 d equals T over 2 minus a minus b minus c d equals T plus a plus b plus c all over 2 d = 2(T − a − b − c)
These equations provide different ways to calculate the value of 'd' based on the values of 'T,' 'a,' 'b,' and 'c.'
It seems like you have provided four equations involving the variable "d." I will break down each equation and explain them separately:
d = (T - a - b - c) / 2
This equation states that "d" is equal to the difference between "T," "a," "b," and "c," divided by 2.
d = T/2 - a - b - c
This equation expresses that "d" is equal to half of "T" minus the sum of "a," "b," and "c."
d = (T + a + b + c) / 2
This equation states that "d" is equal to the sum of "T," "a," "b," and "c," divided by 2.
d = 2(T - a - b - c)
This equation indicates that "d" is equal to twice the difference between "T," "a," "b," and "c."
These equations provide different ways to calculate the value of "d" based on the given variables "T," "a," "b," and "c." Each equation can be used depending on the context and requirements of the problem at hand.
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At a local college,72 of the male students are smokers and528 are non-smokers. Of the female students,118 are smokers and472 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers?Do not round your answer
The probability that both the male and female students selected are smokers is 0.024.
How to find the probability that both are smokersLet's calculate the probability of selecting a male smoker first. Out of the total number of male students, 72 are smokers and 528 are non-smokers. So the probability of selecting a male smoker is:
P(male smoker) = Number of male smokers / Total number of male students
= 72 / (72 + 528)
= 72 / 600
= 0.12
Next, let's calculate the probability of selecting a female smoker. Out of the total number of female students, 118 are smokers and 472 are non-smokers. So the probability of selecting a female smoker is:
P(female smoker) = Number of female smokers / Total number of female students
= 118 / (118 + 472)
= 118 / 590
= 0.2
To find the probability that both are smokers, we multiply the probabilities of each event:
P(both are smokers) = P(male smoker) * P(female smoker)
= 0.12 * 0.2
= 0.024
Therefore, the probability that both the male and female students selected are smokers is 0.024.
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Find the area of this polygon. Answer choices: A 41 square units B 44 square units C 52 square units D 56 square units
Let's consider a regular hexagon with a side length of 4 units. To find the area of this polygon, we can divide it into six equilateral triangles.
The formula to calculate the area of an equilateral triangle is:
Area = (side length^2 * sqrt(3)) / 4
In this case, the side length is 4 units. Substituting the values into the formula, we get:
[tex]Area = (4^2 * sqrt(3)) / 4\\\\\\\\ea = (16 * sqrt(3)) \\\\\\ 4Area = 4 * sqrt(3)[/tex]
Approximating the value of sqrt(3) to 1.732, we have:
Area ≈ 4 * 1.732
Area ≈ 6.928 square units
Therefore, the approximate area of the regular hexagon is 6.928 square units.
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Given below are the approximate runs scored by 5 batsman in Country cricketRepresent the data using bar graphThis is the table shown belowBatsman/. A / B /. C. / D. /. ERuns /10,000/15,000/7000/8000/11,000
To represent the data using a bar graph, you can use the following information:
Batsman A: 10,000 runs
Batsman B: 15,000 runs
Batsman C: 7,000 runs
Batsman D: 8,000 runs
Batsman E: 11,000 runs
Here is a visual representation of the data using a bar graph:
```
Runs
---------
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| A |
| B |
| C |
| D |
| E |
| |
---------
```
Each bar represents the number of runs scored by a batsman. The length of each bar corresponds to the number of runs.
The longest bar represents the batsman with the highest number of runs (Batsman B), and the shortest bar represents the batsman with the lowest number of runs (Batsman C).
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If P = $49,236. 45 , R = 10,5% , and T = 2 years , estimate I
Answer:60118.93636
Step-by-step explanation: Based on the given conditions, formulate:: 49236.45 x (10.5%+1)² Evaluate the equation/expression:: 60118.93636
The Top 15 How high must a 2019 vehicle's gas mile age be to fall in the top 15% of all vehicles?
The gas mileage of a 2019 vehicle must be higher than approximately 35 miles per gallon (mpg) to fall in the top 15% of all vehicles.
To explain further, if we consider the gas mileage of all 2019 vehicles, we can arrange them in ascending order. The top 15% would represent the highest gas mileage values. By finding the value at which 15% of the vehicles have a lower gas mileage, we can determine that it is around 35 mpg. Any vehicle with a gas mileage higher than this would fall in the top 15% in terms of fuel efficiency.
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What is the overlap of Data Set 1 and Data Set 2? high moderate low none.
Data sets overlap is an essential aspect of data analysis, particularly in determining the data's relationship with one another. In this case, determining the overlap of data set 1 and data set 2 will help provide insights on how they relate to one another, making it easier to analyze the data in question.
Overlap occurs when there is at least one shared element between two data sets. Data set 1 and data set 2 can be compared using a Venn diagram, a tool that is ideal for visualizing overlap in data sets. A Venn diagram has two circles, each representing a data set, with the overlapping portion representing the overlap of data set 1 and data set 2.A high overlap indicates that the two data sets have significant shared information. In contrast, a low overlap indicates that the two data sets have a minimal shared connection.
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The vertices of square ABCD are the midpoints of the sides of a larger square. Find the perimeter and the area of square ABCD. Round to the
nearest hundredth
The perimeter of the square ABCD, can be found to be 14.14 cm and the area would be 12.52 cm².
How to find the perimeter and area of a square?If the side of the larger square is 5 cm, then the diagonal of the smaller square ABCD is 5 cm because the diagonal connects two midpoints on adjacent sides of the larger square.
The sides of the smaller square can be found by applying the Pythagorean theorem, which in this case is a 45-45-90 right triangle theorem.
Given that in a 45-45-90 triangle, the sides are in the ratio of 1:1:√2, the sides of the smaller square (a) can be calculated as follows:
a = 5 / √2
= 5 x √2/2
= 3.54 cm
The perimeter of the square is:
= 4 x 3. 54
= 14. 14 cm
The area is:
= 3. 54 x 3. 54
= 12. 53 cm²
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Tay used 52 pieces of fruit alotogatherthey worte these equations to represent the situationthere xis the number of apples and y is the number of strwberriesy=3x52=x+yhow many apples and strawberries did tay use
y = 3x, represents the number of strawberries (y) in terms of the number of apples (x). 52 = x + y, represents the total number of fruit used. Therefore, Tay used 13 apples and 39 strawberries in total.
Let's solve the equations to find the number of apples (x) and strawberries (y) Tay used.
From the first equation, y = 3x, we can substitute this expression for y in the second equation:
52 = x + 3x
Combining like terms, we have:
52 = 4x
Dividing both sides of the equation by 4:
13 = x
Now, substituting this value of x back into the first equation:
y = 3(13)
y = 39
Therefore, Tay used 13 apples and 39 strawberries in total.
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what is the retook for the volumes of two similar pyramids given that the ratio of their edge lengths are 5:7
The ratio of the volumes of the two similar pyramids with edges of ratio 5:7 is 125:343.
The volumes of two similar pyramids can be found using the ratio of their corresponding edge length.
Let's assume that the ratio of the edge length of the two similar pyramids is 5:7. This means that the base edge of the larger pyramid is 7x, and the base edge of the smaller pyramid is 5x.
The ratio of their corresponding volumes is equal to the cube of the ratio of their edges. This means that the volume of the larger pyramid is [tex](7x)^3[/tex] and the volume of the smaller pyramid is (5x)^3.
So, the ratio of their volumes is:
The Volume ratio is: [tex](7x)^3 / (5x)^3 = (343/125) \times x^3 = 2.744 \times x^3[/tex]
This means that the larger pyramid has a volume 2.744 times larger than the smaller pyramid.
In general, for two similar pyramids with corresponding edges of ratio a:b, the ratio of their volumes is ([tex]a^3 : b^3[/tex]).
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What is the empirical formula for 1. 645 g N and 0. 355 g
H?
The empirical formula for the given amounts of N and H is NH3.
To determine the empirical formula, we need to find the ratio of the number of atoms of each element present in the given masses.
First, we convert the given masses of N and H to moles using their molar masses. The molar mass of N is approximately 14 g/mol, and the molar mass of H is approximately 1 g/mol.
For N: 1.645 g N / 14 g/mol ≈ 0.1175 mol N
For H: 0.355 g H / 1 g/mol ≈ 0.355 mol H
Next, we divide the moles of each element by the smallest number of moles to get the simplest whole-number ratio. In this case, the smallest number of moles is 0.1175 mol N.
N: 0.1175 mol N / 0.1175 mol N = 1
H: 0.355 mol H / 0.1175 mol N ≈ 3
The ratio of N to H is approximately 1:3, leading to the empirical formula NH3, which represents one nitrogen atom bonded to three hydrogen atoms.
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If 1 pot of flowers holds
2
3
cup of dirt, how many cups are needed for 14 pots?
Write an expression to represent this problem.
14
×
2
3
Great job!
The expression 14 × 23 represents the total number of cups of dirt needed for 14 pots of flowers. By multiplying the number of pots (14) by the amount of dirt needed per pot (23), we find that a total of 322 cups of dirt are required to fill all 14 pots.
To calculate the total number of cups of dirt needed for 14 pots of flowers, we can use the expression 14 × 23.
Let's break down the problem and explain the steps involved.
Given information:
Each pot of flowers requires 23 cups of dirt.
We want to find the total number of cups of dirt needed for 14 pots.
To solve this, we can multiply the number of pots (14) by the number of cups of dirt required for each pot (23).
Expression: 14 × 23
When we multiply 14 by 23, we perform the following calculation:
14 × 3 = 42 (multiplying the units digit)
14 × 20 = 280 (multiplying the tens digit)
Summing the results: 280 + 42 = 322
Therefore, the total number of cups of dirt needed for 14 pots is 322 cups.
Let's analyze this further.
When we say that 1 pot of flowers requires 23 cups of dirt, it means that each individual pot needs a specific amount of dirt to be properly filled. Multiplying this amount by the number of pots (14) gives us the cumulative requirement for all the pots.
Using the expression 14 × 23, we are essentially multiplying the number of pots (14) by the amount of dirt needed per pot (23). This expression allows us to find the total quantity of dirt required to fill all 14 pots.
The multiplication process involves multiplying the units digit (4) of 14 by 3, which gives us 12. The result has a carry-over of 1, which we then multiply by the tens digit (2) of 14, resulting in 20. Finally, we add these two products (12 and 20) to obtain the final result of 322.
In conclusion, the expression 14 × 23 represents the total number of cups of dirt needed for 14 pots of flowers. By multiplying the number of pots (14) by the amount of dirt needed per pot (23), we find that a total of 322 cups of dirt are required to fill all 14 pots.
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Anthony is going to invest in an account paying an interest rate of 4. 6% compounded
monthly. How much would Anthony need to invest, to the nearest ten dollars, for the
value of the account to reach $240,000 in 20 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 240000\\ P=\textit{original amount deposited}\\ r=rate\to 4.6\%\to \frac{4.6}{100}\dotfill &0.046\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]
[tex]240000 = P\left(1+\frac{0.046}{12}\right)^{12\cdot 20} \implies 240000=P\left( \cfrac{6023}{6000} \right)^{240} \\\\\\ \cfrac{240000}{ ~~ \left( \frac{6023}{6000} \right)^{240} ~~ }=P\implies 95810\approx P[/tex]
Suppose that 25% of all new cars sold last year had at least 1 manufacturer recall. If a survey is done and the standard error of the sampling proportion is found to be 0. 05, what is the sample size?
A) 25
B) 50
C) 75
D) 100
E) 200
Given that the standard error of the sampling proportion is 0.05. We have to find the sample size.Suppose that 25% of all new cars sold last year had at least 1 manufacturer recall.
We know that at least 25% of new cars had at least one manufacturer recall. This means that the probability that a new car sold last year had a recall was greater than 0.25. We are given that more than 250 new cars were sold last year.Therefore, the sample size can be found as follows:N = p(1 - p) / SE² wherep is the proportion of cars that had at least one manufacturer recall, which is 25% or 0.25.SE is the standard error of the sampling proportion, which is 0.05.N = (0.25)(1 - 0.25) / (0.05)²N = (0.25)(0.75) / (0.0025)N = 0.1875 / 0.0025N = 75Hence, the sample size is 75, which is option (C).
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In AVWX, w = 6 cm, ZX=126° and ZV=51º. Find the length of v, to the nearest 10th
of a centimeter.
In AVWX,
w = 6 cm, ZX=126° and ZV=51º.
Find the length of v, to the nearest 10th of a centimeter.
Solution:
The given diagram is as follows:
[tex]\triangle AVX[/tex] is not a right-angled triangle.
So, we have to use sine rule here.
sine rule: [tex]\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}[/tex]
Consider [tex]\triangle AVX[/tex]
Therefore, [tex]\frac{AV}{\sin \angle XAV} = \frac{AX}{\sin \angle AVX}[/tex]
Given, w = 6 cm
Also, [tex]\angle AVX = 180 - \angle XAV = 180 - 126 = 54[/tex][tex]\sin 54 = \frac{AX}{\sin \angle AVX} \\\
Rightarrow AX = \frac{w \cdot \sin 54}{\sin (126 + 54)} = \frac{6 \cdot \sin 54}{\sin 180}[/tex][tex]\
Rightarrow AX = \frac{6 \cdot \sin 54}{0.1987} = 29.37 \approx 29.4[/tex]
Now, consider [tex]\triangle ZVX[/tex]
Clearly, [tex]\angle ZVX = 180 - (\angle ZVX + \angle VXZ) = 180 - (51 + 126) = 3[/tex][tex]\sin 3 = \frac{v}{AX}[/tex][tex]\
Rightarrow
[tex][tex]\triangle AVX[/tex] is not a right-angled triangle.
\\ [tex]\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}[/tex]\\
[tex]\triangle AVX[/tex]\\\
frac{AV}{\sin \angle XAV} = \frac{AX}{\sin \angle AVX}[/tex]\\
[tex]\angle AVX = 180 - \angle XAV = 180 - 126 = 54[/tex][tex]\sin 54 = \frac{AX}{\sin \angle AVX} \\
AX = \frac{w \cdot \sin 54}{\sin (126 + 54)} = \frac{6 \cdot \sin 54}{\sin 180}[/tex][tex]\\\
AX = \frac{6 \cdot \sin 54}{0.1987} = 29.37 \approx 29.4[/tex]\\\\
[/tex][/tex]
Hence, the length of v is approximately 1.5 cm. Thus, the length of v, to the nearest 10th of a centimeter, is 1.5 cm (approx).
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A 15 pound bag of dog food costs $27. 99. What is the cost per pound? Round your answer to the nearest penny
The cost per pound of the dog food is approximately $1.87.
A 15-pound bag of dog food costs $27.99. To find the cost per pound, we divide the total cost by the weight. The cost per pound is approximately $1.87.
To find the cost per pound, we divide the total cost by the weight. In this case, the total cost is $27.99 for a 15-pound bag of dog food. So, we divide $27.99 by 15 pounds:
Cost per pound = $27.99 / 15 pounds ≈ $1.87
Therefore, the cost per pound of the dog food is approximately $1.87.
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Compute square root of 9-4 times the square root of 5 divided by 2 minus the square root of 5
The expression involves finding the square root of a combination of numbers and expressions, including the square root of 5. It requires simplification and order of operations to obtain the result.
To compute the expression: square root of 9 minus 4 times the square root of 5, divided by 2 minus the square root of 5, we need to follow the order of operations (PEMDAS/BODMAS). Let's break down the calculation step by step:
First, we simplify the expression inside the square root: 9 - 4 times the square root of 5 becomes 9 - 4√5.
Next, we divide this expression by 2 minus the square root of 5: (9 - 4√5) / (2 - √5).
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is 2 + √5.
Expanding the expression: [(9 - 4√5) / (2 - √5)] * [(2 + √5) / (2 + √5)].
Simplifying the numerator and denominator: (18 + 9√5 - 8√5 - 20) / (4 - 5).
Combining like terms: (-2 - √5) / (-1).
Finally, simplifying the expression gives us the result: 2 + √5.
In conclusion, the square root of 9 - 4 times the square root of 5 divided by 2 minus the square root of 5 simplifies to 2 + √5.
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Zula spent part of her summer visiting relatives in Louisiana. She visited her aunt Mikki, whose home is located in New Orleans at an elevation of 7 feet below sea level.
It's worth noting that New Orleans is a vibrant and culturally rich city known for its unique history, music, and cuisine.
New Orleans is a city in the state of Louisiana, located in the southeastern United States. What sets New Orleans apart from many other cities is its geographical situation below sea level.
The city is situated in a basin, with the Mississippi River flowing through it and the surrounding area consisting of marshlands and swamps.
Due to its unique geography, New Orleans faces challenges related to water management. The city is prone to flooding, especially during heavy rainfalls or hurricanes. To mitigate the risk of flooding, a system of levees, pumps, and canals has been implemented.
When we say that Zula's aunt Mikki's home is located at an elevation of 7 feet below sea level, it means that the ground level of her home is 7 feet lower than the average sea level. This implies that the land where the home is built is situated below the level of the nearby bodies of water, such as the Mississippi River or the Gulf of Mexico.
The elevation of land is typically measured in relation to mean sea level (MSL), which is an average level determined by tidal observations over a specific period. In this case, the elevation of 7 feet below sea level indicates that the ground level of Mikki's home is 7 feet lower than the average level of the nearby sea or ocean.
To protect against flooding, the city of New Orleans relies on an extensive network of levees, which are large embankments or walls built along the edges of water bodies. These levees act as barriers to prevent water from overflowing and flooding the city. In addition to levees, a complex system of pumps and canals helps to control water levels and drain excess water during heavy rainfall.
Living below sea level can present unique challenges and considerations for the residents of New Orleans. It requires careful water management, reliance on flood protection systems, and preparedness for potential weather events.
However, it's worth noting that New Orleans is a vibrant and culturally rich city known for its unique history, music, and cuisine.
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Zula spent part of her summer visiting relatives in Louisiana. She visited her aunt Mikki, whose home is located in New Orleans at an elevation of 7 feet below sea level?
3. The internal volume of Columbus, or the
space where the astronauts live and work,
is about 34. 7 cubic meters less than the
total volume. What is the internal volume
of Columbus?
The internal volume of Columbus is approximately 34.7 cubic meters. To find the internal volume of Columbus, we need to subtract 34.7 cubic meters from the total volume. Let's denote the total volume as V.
Therefore, the internal volume can be calculated as V - 34.7.
The question states that the internal volume of Columbus, which refers to the space where the astronauts live and work, is 34.7 cubic meters less than the total volume. This indicates that the internal volume is obtained by subtracting 34.7 cubic meters from the total volume.
By denoting the total volume as V, we can express the internal volume as V - 34.7. This represents the subtraction of the given amount from the total volume to obtain the specific volume occupied by the astronauts within Columbus. Hence, by subtracting 34.7 cubic meters from the total volume, we can determine the internal volume of Columbus, which is approximately 34.7 cubic meters.
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What is the seven in(7x0.001) in this number equivalent to
The seven in the number 7x0.001 is equivalent to 7 thousandths.
The given number is 7x0.001. This can be solved by multiplying 7 and 0.001, which is equal to 0.007. It is represented as 7 thousandths. In decimal form, the value of each place value is determined by the number of digits after the decimal point.
In the given number, 0.001 has 3 digits after the decimal point, so each place is one thousandth (0.001). Therefore, when we multiply it by 7, we get the answer in terms of thousandths, which is 7 thousandths. Hence, the answer is the seven in the number 7x0.001 is equivalent to 7 thousandths.
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Corey bought 16 pints of milk for the party. How many quarts is that equal to?
The 16 pints of milk is equal to 8 quarts.
To determine the number of quarts that 16 pints of milk is equal to, we need to understand the conversion between pints and quarts.
In the United States customary system of measurement, there are 2 pints in 1 quart. This means that 1 quart is equivalent to 2 pints.
Given that Corey bought 16 pints of milk, we can calculate the number of quarts by dividing the number of pints by the conversion factor:
16 pints / 2 pints/quart = 8 quarts
So, Corey's purchase of 16 pints of milk is equal to 8 quarts.
To understand why this conversion works, consider that both pints and quarts are units of volume. A pint is a smaller unit, and a quart is a larger unit. Since there are 2 pints in 1 quart, if we have 16 pints and we want to express it in quarts, we divide the number of pints by 2 to get the equivalent number of quarts. This conversion allows us to compare and measure volumes in different units.
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