For a bounded region, R between the curves y = 4x² and y = 4 and the volume of a solid has base R, and cross sections perpendicular to the y-axis is equals to the π square units.
We have a region R is bounded by the curves y = 4x² and y = 4. Solid has base R and cross sections perpendicular to the y-axis are semicircles with the diameter lying in region R. When solving the volume using slicing method we use the basic formula which is the area times the length V = A×l, where A is the area of the cross-section. Also, the formula for the area of cross section for semicircle
= (1/2)π(d/2)²
= (π/8)d², where d is the diameter
Based on the graph the volume of a single semicircle strip is, dV = (π/8)x²dy
=> dV = (π/8) (y/4) dy ( since, y = 4x² , x²
= y/4 )
=> dV = (π/32)4y dy
=> dV = (π/8)ydy --(1)
Now, the limits are, y = 0, 4
Integrating equation (1), with limits 0 to 4.
[tex]∫dV = \frac{π}{8} ∫_{0}^{4}y dy[/tex]
[tex]V= \frac{π}{8} [ \frac{y^{2} }{2} ]_{0}^{4} [/tex]
[tex]V = \frac{π}{8} [ \frac{16}{2} - 0] = 8(\frac{π}{8}) = π[/tex]
Hence, the required volume is π square units.
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math question please help
Answer:
Step-by-step explanation:
only the 1st and 5th statements are true
A triangle has area 100 square inches. It's dilated by a factor of k= 0.25.
Mai says, "The dilated triangle's area is 25 square inches."
Lin says, "The dilated triangle's area is 6.25 square inches."
1. For each student, decide whether you agree with their statement. If you
agree, explain why. If you disagree, explain what the student may have done to arrive at their answer.
2. Calculate the area of the image if the original triangle is dilated by each of these scale factors:
a. K = 9
b. K = 3/4
Lin's statement is correct. The incorrect answer is obtained due to inaccurate calculations of the new area of triangle.
What is dilation?A geometric modification called a dilation alters a figure's size. Each coordinate in the graphic is multiplied by a preset scale factor k to obtain it. The same element causes the figure to be stretched or contracted in all directions, creating a new figure that resembles the original but is smaller. Both two-dimensional (2D) and three-dimensional (3D) dilations are possible (3D). They are frequently employed in geometry to generate analogous figures and compute scale factors.
Mai's statement is incorrect. When a triangle is dilated by a factor of k, its area is multiplied by k².
When the given area of 100 square inches is dilated by a factor of 0.25 the new area is 6.25.
Hence, Lin's statement is correct. The incorrect answer is obtained due to inaccurate calculations of the new area.
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Most exposures and outcomes used in correlational studies are in the form of:
A. Individual data
B. Aggregate data
C. Average data
D. Relative data
Most correlational studies use d)relative data, which compares two variables.
This means that one variable is being measured against another, often in the form of ratios or percentages. For example, one might compare the number of people who smoke cigarettes with the number of people who develop lung cancer, in order to determine whether there is a correlation between the two.
Relative data allows researchers to examine the relationship between variables, allowing them to assess the strength of the relationship between them.
In order to compare variables, correlational studies rely on either primary or secondary data. Primary data is collected through direct observation and experimentation, while secondary data is obtained from existing sources.
In most cases, correlational studies use secondary data, such as survey results or statistics from public databases. This data is often in the form of relative data, such as percentages or ratios.
By using relative data, correlational studies can determine the strength of the relationship between two variables. This information can be used to better understand how the variables are related, as well as to draw conclusions about their relationship. For example, the relationship between smoking and lung cancer can be examined using relative data, allowing researchers to identify patterns and draw conclusions about the correlation between the two variables.
Hence Option D is correct.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer:
The perimeter of the shape is 53km.
Answer : 53km
Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!
Consider all four-digit numbers that can be created from the digits 0-9 where the first and last digits must be even and no digit can repeat. Assume that numbers can start with 0. What is the probability of choosing a random number that starts with 2 from this group? Enter a fraction or round your answer to 4 decimal places, if necessary
Answer:
Step-by-step explanation:
To find the probability of choosing a random number that starts with 2, we need to find two things:
1. The total number of valid four-digit numbers that can be created from the digits 0-9 where the first and last digits are even and no digit can repeat.
2. The number of valid four-digit numbers that start with 2 and meet the other criteria.
Let's begin by calculating the total number of valid four-digit numbers.
There are 5 even digits (0, 2, 4, 6, 8) to choose from for the first and last digits. For the second digit, there are 9 digits to choose from (since 0 cannot be repeated), for the third digit there are 8 digits to choose from (since we used one digit already and neither the first nor last digit can be repeated), and for the last digit there are only 4 choices left (since we used 5 for the first digit, and one more can’t be repeated). Therefore, the total number of valid four-digit numbers is:
5 * 9 * 8 * 4 = 1,440
Now we need to calculate the number of valid four-digit numbers that start with 2.
We already determined that there are 5 even digits to choose from for the last digit, leaving 8 digits for the second and 7 for the third digit (since the first digit is fixed). So the number of valid four-digit numbers that start with 2 is:
5 * 8 * 7 * 1 = 280
Therefore, the probability of choosing a random number that starts with 2 is:
280 / 1,440 = 0.1944 rounded to 4 decimal places.
So the answer to the problem is 97/500, which simplifies to 0.1940 when rounded to 4 decimal places.
What would be the best first step in solving this system?
Answer:
D
Step-by-step explanation:
sub y into the 2nd equation and find x
A farmer has 20 boxes of eggs. There are 6 eggs in each box. Write, as a ratio, the number of eggs in two boxes to the total number of eggs. Give your answer in its simplest form.
Answer:
Step-by-step explanation:
number of eggs in 2 boxes = 12
Total number of eggs = 20 x 6 = 120
12:120
Simplify
2:20
Simplify
1:10
pls mark me brainiest
A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the height h of water in the tank in feet after t seconds is described by dh dt А. 2gh AW where A and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Awr An, and H. Use g = 32 ft/s2. (4„VH – 44,4) h(t) = osts 4A 4VĀ By hand, sketch the graph of h(t). h h H H/2 t h h H/2H H t (b) Suppose the tank is 11 ft high and has radius 2 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.) sec
The height of water in the tank in feet after t seconds can be expressed as h(t) = H - (Aw/Ah) 2gh t2, where Aw and Ah are the cross-sectional areas of the water and the hole in square feet respectively,
and g is the gravitational acceleration (32 ft/s2). The interval of definition for h(t) is 0 ≤ t ≤ H/2gh.
The graph of h(t) is a parabola with its vertex at (H/2gh, H) and is symmetric about the line t = H/2gh. It starts at (0, H) and gradually decreases to (H/2gh, 0).
Given the tank is 11 ft high, has radius 2 ft and the circular hole has radius in, and it is initially full, the time it will take to empty can be calculated as: t = √(2H/gAh) = √(22/(32 x π(0.52))) = 3.87 seconds. Therefore, it will take approximately 3.87 seconds to empty.
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Please help quick with this question.
Answer:
b = [tex]\frac{S-2la}{h+l}[/tex]
Step-by-step explanation:
S = bh + lb + 2la ( reversing the equation )
bh + lb + 2la = S ( subtract 2la from both sides )
bh + lb = S - 2la ← factor out b from each term on the left side
b(h + l) = S - 2la ← divide both sides by (h + l)
b = [tex]\frac{S-2la}{h+l}[/tex]
Water flows into a lake at a constant rate.
Grace recorded that 400 litres of water flowed into the lake in 1 minute.
She recorded the number of litres to the nearest 20 litres.
She recorded the time to the nearest
10 seconds.
Calculate the upper bound for the rate at which the water could have flowed into the lake.
Give your answer in litres per second to 2 d.p.
The upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.
What is an upper bound?An upper limit is a value that is larger than or equal to all the values in a set. In mathematics, it is used to specify a cap or a maximum value for a collection of data. For instance, an upper bound is frequently employed in optimization issues to place a cap on the highest value that a function or variable may take. Upper limits are used in statistics to specify a data set's maximum range which may be used to spot outliers or other abnormalities in the data. In calculus, upper bounds are used to specify a sequence's or series' limit, or the highest number that it may possibly approach.
Given that, 400 liters of water flowed into the lake in 1 minute.
The upper bound of water flow will be the maximum amount of water.
For the nearest measures taken by Grace the amount of water needs to ne more than 400, while the time must be less than 10 seconds from the recorded 1 min.
That is time must be 60 - 10 = 50 seconds.
Approximating the values we have:
410/50 = 8.2 liters per second.
Hence, the upper bound for the rate at which the water could have flowed into lake is 8.2 liters per second.
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A random sample of 100 freshman showed 9 had satisfed the university mathematics requirement and a second random sample of 50 sophomores showed that 10 had satisfied the university mathematics requirement.
A) The relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is: 2.222
b) The increased risk of having satisfied the university mathematics requirement for sophomores as compard to freshmen is:
a) The relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 2.222.
b) The increased risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 122.2%.
Relative Risk is defined as the ratio of the risk of an event in the exposed group and the risk of the event in the unexposed group. The formula for relative risk is
RR = [a / (a + b)] / [c / (c + d)].
where, a = the number of individuals in the exposed group with the event,
b = the number of individuals in the exposed group without the event,
c = the number of individuals in the unexposed group with the event, and
d = the number of individuals in the unexposed group without the event.
Now, in this question, we have to calculate the relative risk and the increased risk for sophomores as compared to freshmen.
Given that,
Sample size of freshman = 100
Number of freshman who have satisfied the mathematics requirement = 9
Sample size of sophomores = 50
Number of sophomores who have satisfied the mathematics requirement = 10
a = 10, b = 40, c = 9, and d = 91
Relative risk for sophomores as compared to freshmen = (10 / (10 + 40)) / (9 / (9 + 91)) = 2.222
Therefore, the relative risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 2.222.
Increased risk = (RR - 1) × 100% = (2.222 - 1) × 100% = 122.2%
Therefore, the increased risk of having satisfied the university mathematics requirement for sophomores as compared to freshmen is 122.2%.
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Christina’s car used 14 gallons of gas to travel 546 miles. How many miles did her car travel per gallon of gas.
Step-by-step explanation:
You are given miles ( 546) and gallons (14) and you
want miles / gal this is just 546 miles / 14 gallons = 39 mpg
Answer:
39
Step-by-step explanation:
14 is the main number here.
assuming 1 tank = 14gallons. / 546 miles
a = gallons
b = miles
b / a = mpg (miles per gallon)
so: 546 / 14 = 39
One of the legs of a right triangle measures 4 cm and its hypotenuse measures 11 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer: 10.2 cm
Step-by-step explanation:
We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's call the unknown length of the other leg "x". Then we can set up the following equation:
4^2 + x^2 = 11^2
Simplifying this equation, we get:
16 + x^2 = 121
Subtracting 16 from both sides, we get:
x^2 = 105
Taking the square root of both sides, we get:
x = sqrt(105)
x ≈ 10.2 cm (rounded to the nearest tenth)
Therefore, the measure of the other leg is approximately 10.2 cm.
In triangle ABC, AB = (x + 2) cm, AC = (x + 1) cm and BC = x cm.
Given that cos BAC=3/4 , find the value of x.
Answer:
the value of x is approximately 0.382 cm.
Step-by-step explanation:
Consider a hash table, a hash function of key % 10. Which of the following programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation? O c1 = 1 and 2 = 0 O c1 = 5 and c2 = 1 O c1 = 1 and c2 - 5 O c1 = 10 and 2
D: "[tex]c_{1} = 10[/tex] and [tex]c_{2} = 2[/tex]" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.
The quadratic probing equation is defined as:
h (k, i) = (h′(k) + [tex]c_{1}[/tex] * i + [tex]c_{2}[/tex] * i^2) mod m,
where h′(k) is the hash value of key
k and m is the size of the hash table.
The constants [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.
The given hash function is h(k) = k % 10.
Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:
Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.
Option B: [tex]c_1 = 5[/tex] and [tex]c_2 = 1[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.
Option C: [tex]c_1 = 1[/tex] and [tex]c_2 = 5[/tex] This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.
Option D: [tex]c_1 = 10[/tex] and [tex]c_2 = 2[/tex] This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.
Since [tex]c_{1}[/tex] is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `[tex]c_{1}[/tex]= 10` in the quadratic probing equation. Hence, the correct option is D.
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50 POINTS!! Scientists measure a bacteria population and find that it is 10,000. Five days later,
they find that the population has doubled. Which function f could describe the
bacteria population d days after the scientists first measured it, assuming it grows
exponentially?
According to the solving function f could describe the bacteria population d days after the scientists first measured it, assuming it grows exponentially F(d) = 10000 - a[tex]^\frac{d}{5}[/tex].
What is function, exactly?A mathematical expression, rule, or law known as a function defines the relationship between two independent variables and a dependent variable (the dependent variable). In mathematics, functions are often utilised, and they are essential for creating physical connections in the sciences.
According to the given information:Substituting d = 5 and f(d)
Solution: fid) = 10000⋅ ad
{substitute d=5 and fid)=20000 into fid=10000. ady
10000- a⁵ =20000
a⁵ =2[tex]^\frac{1}{5}[/tex]
a = 2
F(d) = 10000 - a[tex]^\frac{d}{5}[/tex]
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Aubrey used
4
7
liter
7
4
literstart fraction, 4, divided by, 7, end fraction, start text, space, l, i, t, e, r, end text of paint for a mural in her room and
2
10
liter
10
2
literstart fraction, 2, divided by, 10, end fraction, start text, space, l, i, t, e, r, end text for a wall in her bathroom.
The total amount of paint Aubrey used is more than 1/2 liter but less than 1 liter
Estimating the total amount of paint Aubrey usedTo estimate the total amount of paint that Aubrey used for both the mural and the wall, we can add the fractions of paint used
So, we have
Total = 4/7 + 2/10
Evaluate the sum in decimals
This gives
Total = 0.77 (approximated)
This value is between 0.5 liters and 1 liter
Hence, the estimate is between 0.5 liters and 1 liter
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Complete question
Aubrey used 4/7 liter of paint for a mural in her room and 2/10 for a wall in her bathroom.
Determine a reasonable estimate for the total amount of paint Aubrey used
Answer: B or the one that is more than 1/2 but it is less than 1
Step-by-step explanation: Took quiz on khan
9. Jess spins a pointer 25 times and finds an
experimental probability of the pointer landing
on 3 to be 25, or 16%. The theoretical probability
of the spinner landing on 3 is à, or 25%. Why
might there be a significant difference between
the theoretical and experimental probabilities?
The number of times the experiment is run affects the experimental probability.
What is Probability?Probability is the concept that describes the likelihood of an event occurring.
In real life, we frequently have to make predictions about how things will turn out.
We may be aware of the result of an occurrence or not.
When this occurs, we state that there is a possibility that the event will occur.
In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence
The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.
According to our question-
multiply that percentage by 25 to get the experimental probability percentage.
16%25
Hence, The number of times the experiment is run affects the experimental probability.
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PLEASE HELP I DONT HAVE TIME
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
The number of toy soldiers Leo has is 48.
How to calculate the number of toy soldiers Leo has?To solve this problem, we need to find a number that satisfies the three given conditions:
The number is between 27 and 54.
When the number is divided by 4, there is no remainder.
When the number is divided by 7, the remainder is 6.
When the number is divided by 5, the remainder is 3.
Let's start by finding a number that satisfies the first two conditions. We can do this by listing the multiples of 4 between 27 and 54:
28, 32, 36, 40, 44, 48, 52
Next, we need to find which of these numbers also satisfies the third condition, that is, leaves a remainder of 6 when divided by 7. We can go through each of these numbers and check:
28 divided by 7 leaves a remainder of 0.
32 divided by 7 leaves a remainder of 4.
36 divided by 7 leaves a remainder of 1.
40 divided by 7 leaves a remainder of 5.
44 divided by 7 leaves a remainder of 2.
48 divided by 7 leaves a remainder of 6.
52 divided by 7 leaves a remainder of 3.
So, the only number that satisfies the first three conditions is 48.
Finally, we need to check if 48 also satisfies the fourth condition, that is, leaves a remainder of 3 when divided by 5. Indeed, 48 divided by 5 leaves a remainder of 3.
Therefore, the number of toy soldiers Leo has is 48.
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Raj went to the theatre to watch a traditional Indian dance performance with his family. The theatre had 1050 seats. There were 50% fewer $50-seats than $30-seats. 90% of the $30-seats and some $50-seats were sold. A total of $34 650 was collected. How many seats were unsold?
Total number of seats that remain unsold are 168.
What is statistics?
The branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.
Let's start by defining some variables to represent the unknowns in the problem:
Let x be the number of $30-seats.Let y be the number of $50-seats.From the problem, we know that:
The total number of seats is 1050: x + y = 1050.There were 50% fewer $50-seats than $30-seats: y = 0.5x.90% of the $30-seats and some $50-seats were sold, which means that the revenue from the $30-seats is 0.9(30x) = 27x, and the revenue from the $50-seats is 0.9(50y) = 45y.We also know that the total revenue collected is $34,650:
27x + 45y = 34650
Now we can substitute y = 0.5x from the second equation into the third equation and simplify:
27x + 45(0.5x) = 34650
27x + 22.5x = 34650
49.5x = 34650
x = 700
So there were 700 $30-seats and 350 $50-seats.
The number of sold $30-seats is 0.9(30x) = 567, and the number of sold $50-seats is 0.9(50y) = 315.
Therefore, the total number of seats sold is 882, and the number of unsold seats is:
1050 - 882 = 168
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can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10
Answer:
can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10
Step-by-step explanation:
To solve sin y - cos (y + 20) = 0, we can rearrange it as sin y = cos (y + 20).
Then, we can use the identity sin (90 - x) = cos x to rewrite the right side as cos (y + 20) = sin (70 - y).
Substituting this into the equation, we get sin y = sin (70 - y).
Now, there are two possibilities:
y = 70 - y, which gives y = 35 degrees.
y = 180 - (70 - y), which gives y = 105 degrees.
To solve cos theta = sin theta - 10, we can rearrange it as cos theta - sin theta = -10 and then use the identity cos (x - 90) = sin x to rewrite it as -sin (theta - 90) = -10.
Taking the inverse sine of both
I need help! I need the graph drawn and the steps to how I got the answer but I don’t know it! Please help me!
Answer:
25 computers per hour
Step-by-step explanation:
look ate the point 2 hours corresponding to 50 computers
50/2 = 25/1 or 25 computers per hour
An amusement park opened at 10:00 a.m. In the first hour,
480 people purchased admission tickets. In the second hour,
40% more people purchased admission tickets than in the
first hour. Each admission ticket cost $24.50.
What was the total amount of money paid for all the tickets
purchased in the first two hours?
A) $16,464.00
B) $4,704.00
C) $18,816.00
D) $28,224.00
Answer:
D) $28,224.00
Step-by-step explanation:
1st hour: 480 ticket sales
2nd hour: 480 + 40% of 480 = 480 + 0.4 × 480 = 480 + 192 = 672
Total ticket sales in first 2 hours: 480 + 672 = 1152
Ticket price: $24.50
Total sales: 1152 × $24.50 = $28,224
kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
a. 1
b. x.x’
c. 1+ x.x’
d. (1+ x.x’)^2
e. exp (x+x’), for x.x’ ER
f. min (x.x’) for x.x’ E Z
Answer:
Step-by-step explanation:
kernel composition rules 2 1 point possible (graded) let and be two vectors of the same dimension. use the the definition of kernels and the kernel composition rules from the video above to decide which of the following are kernels. (note that you can use feature vectors that are not polynomial.) (choose all those apply. )
Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to
0.008.
0.02.
0.03.
0.04.
0.208.
The proportion of students who can roll their tongues will be estimated and the margin of error for a 95 percent confidence interval for the true proportion of tongue rollers among students will be determined. There were 317 tongue rollers out of a sample of 400 students.
As a result, the sample proportion is 317/400 = 0.7925.
We'll compute the margin of error next. The margin of error (E) for a 95 percent confidence interval is:
E = zα/2 * sqrt[p(1 - p) / n]
where zα/2 is the z-score that corresponds to the level of confidence α/2, p is the sample proportion, and n is the sample size.
E = 1.96 * sqrt[0.7925 * (1 - 0.7925) / 400]E
= 1.96 * sqrt[0.7925 * 0.2075 / 400]E
= 1.96 * sqrt(0.00040875)E
= 1.96 * 0.0202E
= 0.0395
The margin of error is approximately 0.04 or 4 percent. Hence, the correct option is 0.04.
The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to 0.04
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If a police officer wants to find out whether the average speed of motorists on a highway with a speed limit of 55 mph is greater than 55 mph, then the null hypothesis is 55.
True or False?
The null hypothesis is that the average speed of motorists on a highway with a speed limit of 55 mph is equal to 55 mph.Given statement is false.
What is hypothesis test?A statistical hypothesis test is a technique for determining whether the available data are adequate to support a specific hypothesis. We can make probabilistic claims about demographic parameters through hypothesis testing.
According to question:The null hypothesis should be a statement of no difference or no effect. In this case, the null hypothesis would be that the average speed of motorists on the highway is equal to 55 mph.
So the correct statement would be:
The null hypothesis is that the average speed of motorists on a highway with a speed limit of 55 mph is equal to 55 mph.
Thus, Given statement is false.
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The exponential 12 (3) 2x-12 has been converted to 12(k)*-6, what is the value of k?
Answer:
The solution set is (13,− 32). A quadratic equation of the form x 2= k can be solved by factoring with the following sequence of equivalent equations.
Step-by-step explanation:
There are 9 out of 25 students in science class who passed the test and 4 out of 16 in history. What is the percentages of students in each class that passed the test?
Answer: 36% passed the science test, while 25% passed the history test.
In order to find a percentage we divide our two know numbers
Science Class- 9/25 is a fraction with / standing for divided by. 9 divided by 25 is .36 This means 36% of the class passed the science test.
History Class- 4/16 is a fraction with / standing for divided by. 4 divided by 16 is .25 This means 25% of the class passed the science test.
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Complete the proof that △STU∼△WVU
So,To prove that △STU∼△WVU, we need to show that the two triangles are similar, which means that their corresponding angles are equal, and their corresponding sides are proportional.
What is triangle?A polygon with three sides and three angles is termed as triangle.
Triangles can be classified based on the length of their sides and the size of their angles, and they have a variety of properties and theorems associated with them in mathematics.
Angles: Since line VS is the bisecting line on line WT, angles VST and TSU are equal. Similarly, angles UVW and WVU are equal since U is the bisecting point on the line. Therefore, angle VUS is equal to angle WUV since they are vertically opposite angles.
Sides: We need to show that the corresponding sides are proportional.
Using the angle bisector theorem, we know that US/UT = VS/VT, which can be written as:
9/6 = VS/VT
Simplifying this, we get:
3/2 = VS/VT
Using the segment bisector theorem, we know that UW/WV = UT/TV, which can be written as:
6/4 = UT/TV
Simplifying this, we get:
3/2 = UT/TV
Since both ratios are equal to 3/2, we can say that:
VS/VT = UW/WV
Therefore, we can conclude that △STU∼△WVU by the angle-angle similarity theorem.
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The position vectors of points C and D are 2i + 37 and 7i + 5i respectively. Find the position vector of a point H which divides the line PQ in the ratio of 2: 3.
Answer:
Step-by-step explanation:
Let P be the point C with position vector 2i + 3j and Q be the point D with position vector 7i + 5j. We want to find the position vector of point H which divides PQ in the ratio 2:3.
Let the position vector of point H be r. Then we have:
PH/PQ = 2/3
(P - r)/(Q - r) = 2/3
Multiplying both sides by (Q - r), we get:
P - r = (2/3)(Q - r)
Expanding the brackets and rearranging, we get:
r = (2Q + 3P)/5
Substituting the position vectors of P and Q, we get:
r = (2(7i + 5j) + 3(2i + 3j))/5
= (14i + 10j + 6i + 9j)/5
= (20i + 19j)/5
= 4i + 3.8j
Therefore, the position vector of point H is 4i + 3.8j.