Answer:
An exponential function can be used to model this situation.
In this case, we know that each hour following the initial dose, 80% of the concentration remains in the body from the preceding hour. This means that the amount of penicillin remaining in the body is decreasing exponentially.
We can use the formula for exponential decay, which is:
A = A0 * e^(-kt)
where A is the amount of penicillin remaining in the body at time t, A0 is the initial amount of penicillin (in this case, 500 milligrams), k is the decay constant, and e is the mathematical constant approximately equal to 2.718.
The decay constant, k, can be calculated using the following formula:
k = ln(0.8)
where ln is the natural logarithm.
So the exponential function that can be used to model this situation is:
A = 500 * e^(-0.2231t)
where t is the time in hours since the initial dose was administered.
This function will give us the amount of penicillin remaining in the body at any time t, based on the initial dose and the rate of decay.
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What is a formula for the nth term of the given sequence? 13, 15, 17...
Answer: The nth term of the sequence is given by the formula 2n + 11
Step-by-step explanation:
The given sequence is an arithmetic sequence because the difference between each pair of consecutive terms is the same. In this case, the common difference is 2, because:
15 - 13 = 2
17 - 15 = 2
and so on
The formula for the nth term of an arithmetic sequence is:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
For this sequence, the first term (a1) is 13 and the common difference (d) is 2. Therefore, the formula for the nth term is:
an = 13 + (n-1)2
Simplifying this expression, we get:
an = 2n + 11
Please help me I don't understand
1. (5, 12, 13) is a Pythagorean triple.
2. (20, 21, 27) is not a Pythagorean triple.
3. Fake triples are (7, 2, 25), (280, 450, 533), and (110, 60, 651)
4. A Pythagorean triple that I know is (3, 4, 5).
5. a.Thus, (6, 8, 10) is also a Pythagorean triple.
b. Thus, (30, 40, 50) is also a Pythagorean triple.
c. Thus, (1.5, 2, 2.5) is still a Pythagorean triple.
d. Yes, a Pythagorean triple consisting of three even numbers is (6, 8,
10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).
Define Pythagorean theorem?The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right-angled triangle.
1. To prove that (5, 12, 13) is a Pythagorean triple, we need to show that
⇒ 5² + 12² = 13²
⇒ 5² + 12² = 169 (5² = 25 and 12² = 144 and 13² = 169)
Therefore, 5² + 12² = 13², which means that (5, 12, 13) is a Pythagorean triple.
2. To prove that (20, 21, 27) is not a Pythagorean triple.
Assuming that (20, 21, 27) is a Pythagorean triple, we would have:
⇒ 20² + 21² = 27²
⇒ 400 + 441 ≠ 729
Therefore, (20, 21, 27) is not a Pythagorean triple.
3. To find the fakes among the following list of triples, we need to check if there is a whole number solution for the sides of a right-angled triangle with these measurements.
Therefore, the fakes are (7, 2, 25), (280, 450, 533), and (110, 60, 651).
4. A Pythagorean triple that I know is (3, 4, 5).
Scaling up each side by the same amount should still result in a Pythagorean triple, as the relationship between the sides will remain proportional.
5. a) Multiplying each side by 2, we get (6, 8, 10). Verifying Pythagoras' theorem, we have:
6^2 + 8^2 = 36 + 64 = 100
10^2 = 100
Thus, (6, 8, 10) is also a Pythagorean triple.
b) Multiplying each side by 10, we get (30, 40, 50). Verifying Pythagoras' theorem, we have:
30^2 + 40^2 = 900 + 1600 = 2500
50^2 = 2500
Thus, (30, 40, 50) is also a Pythagorean triple.
c) Halving each side of (3, 4, 5), we get (1.5, 2, 2.5). Verifying Pythagoras' theorem, we have:
1.5^2 + 2^2 = 2.25 + 4 = 6.25
2.5^2 = 6.25
Thus, (1.5, 2, 2.5) is still a Pythagorean triple.
d) The observation is that scaling up or down a Pythagorean triple by the same amount results in another Pythagorean triple. This is because the sides of a Pythagorean triple are related by the Pythagorean theorem, which is a quadratic equation. Multiplying each side by the same amount simply scales the sides up or down proportionally, while preserving the quadratic relationship.
Yes, a Pythagorean triple consisting of three even numbers is (6, 8, 10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).
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1. (5, 12, 13) is a Pythagorean triple.
2. (20, 21, 27) is not a Pythagorean triple.
3. Fake triples are (7, 2, 25), (280, 450, 533), and (110, 60, 651)
4. A Pythagorean triple that I know is (3, 4, 5).
5. a.Thus, (6, 8, 10) is also a Pythagorean triple.
b. Thus, (30, 40, 50) is also a Pythagorean triple.
c. Thus, (1.5, 2, 2.5) is still a Pythagorean triple.
d. Yes, a Pythagorean triple consisting of three even numbers is (6, 8,
10. A Pythagorean triple consisting of three odd numbers is (5, 12, 13).
Define Pythagorean theorem?The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right-angled triangle.
1. To prove that (5, 12, 13) is a Pythagorean triple, we need to show that
⇒ 5² + 12² = 13²
⇒ 5² + 12² = 169 (5² = 25 and 12² = 144 and 13² = 169)
Therefore, 5² + 12² = 13², which means that (5, 12, 13) is a Pythagorean triple.
2. To prove that (20, 21, 27) is not a Pythagorean triple
Assuming that (20, 21, 27) is a Pythagorean triple, we would have:
⇒ 20² + 21² = 27²
⇒ 400 + 441 ≠ 729
Therefore, (20, 21, 27) is not a Pythagorean triple.
3. To find the fakes among the following list of triples, we need to check if there is a whole number solution for the sides of a right-angled triangle with these measurements.
Therefore, the fakes are (7, 2, 25), (280, 450, 533), and (110, 60, 651).
4. A Pythagorean triple that I know is (3, 4, 5).
Scaling up each side by the same amount should still result in a Pythagorean triple, as the relationship between the sides will remain proportional.
5. a) Multiplying each side by 2, we get (6, 8, 10). Verifying Pythagoras' theorem, we have:
6² + 8² = 36 + 64 = 100
10² = 100
Thus, (6, 8, 10) is also a Pythagorean triple.
b) Multiplying each side by 10, we get (30, 40, 50). Verifying Pythagoras' theorem, we have:
30² + 40² = 900 + 1600 = 2500
50² = 2500
Thus, (30, 40, 50) is also a Pythagorean triple.
c) Halving each side of (3, 4, 5), we get (1.5, 2, 2.5). Verifying Pythagoras' theorem, we have:
1.5² + 2² = 2.25 + 4 = 6.25
2.5² = 6.25
Thus, (1.5, 2, 2.5) is still a Pythagorean triple.
d) The observation is that scaling up or down a Pythagorean triple by the same amount results in another Pythagorean triple. This is because the sides of a Pythagorean triple are related by the Pythagorean theorem, which is a quadratic equation. Multiplying each side by the same amount simply scales the sides up or down proportionally, while preserving the quadratic relationship.
Yes, a Pythagorean triple consisting of three even numbers is (6, 8, 10). A Pythagorean triple consisting of three odd numbers is (5, 12, 13).
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3
What is the measure of arc JR?
J
?
mJR
R
37°
K
L
degrees
The measure of angle subtended by the arc JR is determined as 74 ⁰.
What is the measure of arc JR?
The measure of arc JR is calculated by applying the following principle of circle geometry for a cyclic quadrilateral as shown below.
The measure of the angle tangent to the circle opposite the arc JR is given as 37 ⁰.
The measure of angle subtended by the arc JR is calculated as
m∠ JR = 2 x 37 ⁰ ( angle at the tangent is half of the angle subtended by the arc.
m∠ JR =74 ⁰
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Y=3/2x+4
which point lines on the line defined by the following equation?
The point (2, 7) lies on the line defined by the equation Y=3/2x+4
The given equation is [tex]Y = 3/2x + 4[/tex]
To find the point that lines on the line defined by this equation, we need to solve for x. Start by subtracting 4 from both sides of the equation:
[tex]Y - 4 = 3/2x[/tex]
Next, multiplying both sides by 2:
[tex]2Y - 8 = 3x[/tex]
Finally, divide both sides by 3:
[tex]x = (2Y - 8) /3[/tex]
Now, given a value, we can calculate the corresponding x value. For example, if Y = 7, then:
[tex]x = (2 * 7 - 8) / 3x = (14 - 8) / 3x = 6 / 3x = 2[/tex]
Therefore, the point (2, 7) lies on the line defined by this equation.
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Complete question :
What is the value of x for the point (x,7) that lies on the line defined by the equation Y = 3/2x + 4?
A. 1
B. 2
C. 3
D. 4
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.
(−3,−7) and (−7,−1)
The length of the hypotenuse is the line connecting the two points (-3,-7) and (-7,-1), which has length 2√13, as calculated above.
What precisely is a triangle?A triangle is a clοsed, dοuble-symmetrical shape cοmpοsed οf three line segments knοwn as sides that intersect at three places knοwn as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factiοns equal), isοsceles, οr scalene based οn their sides.
Next, we can find the length of the hypotenuse by using the distance formula, which is:
d = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, in this case, we have:
d = √((-7 - (-3))² + (-1 - (-7))²)
= √((-4)² + (-6)²)
= √(16 + 36)
= √52
= 2√13
Therefore, the distance between the two points in simplest radical form is 2√13.
The length of the hypotenuse is the line connecting the two points (-3,-7) and (-7,-1), which has length 2√13, as calculated above.
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What is the result when the number 64 is increased by 50%?
Answer:
96
Step-by-step explanation:
Because you're increasing the number, you'll add the percentage to 100%. After that, use ratio to solve.
Therefore,
100% : 64
100% + 50%(150%) : ?
= 150/100 × 64
= 15/10 × 64
= 3/2 × 64
= 3/1 × 32
= 3 × 32
= 96
HELPPP URGENT!! Will give brainiest if it’s right !
If each of the numbers in the following data set were multiplied by 22, what would be the new median of the data set?
14, 20, 18, 58, 71, 36, 28
A. 792
B. 484
C. 616
D. 440
The new median of the data set is 616
Multiply all the numbers by 22
308, 396, 440, 792, 1276, 1562looking at this number they both are in the middle. So you add both numbers and divide by two.
440 + 792 = 1232
1232 / 2 = 616a student just took two different mid-term exams. their score on the sociology test was a 92 and their score on the human sexualty test was 88. which test did they do better on.
Answer:
Step-by-step explanation:
I have two questions; One, are you the student? Two, is this a trick question because if it is it's freaking hilarious
Determine if each of the following points would fall inside the parallelogram.
The points or coordinates that will fall inside the parallelogram are 0,4 and 4,7.
How to know which points will fall inside or outside the parallelogram?Start by creating a graph that shows the limits of the parallelogram as the one attached below.Once you have created the parallelogram check if each of the coordinates given would fit inside or outside the parallelogram.Categorize each pair of coordinates according to this principle.Based on the above, the coordinates that would fit inside the parallelogram are:
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NO RANDOM ANSWERS
A bee colony produced 8 pounds of honey, but bears ate 0.32 pounds of it. How much honey remains?
7.68 pounds of honey remains after the bears ate 0.32 pounds.
What is a initial amount mean?
When referring to any Capital Appreciation Bond, Original Amount refers to the Bond's Accrued Value as of the date of issuance.
To find how much honey remains, we need to subtract the amount eaten by the bears from the initial amount produced:
Remaining honey = Initial honey - Honey eaten by bears
Remaining honey = 8 pounds - 0.32 pounds
Remaining honey = 7.68 pounds
Therefore, 7.68 pounds of honey remains after the bears ate 0.32 pounds.
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What is the measure of ∠r in △pqr? round to the nearest degree. 26° 42° 45° 64°
The measure of ∠R in ΔPQR is option (a) 26⁰
Since angle P is a right angle (90 degrees), triangle PQR is a right triangle.
Using the Pythagorean theorem, we can find the length of the remaining side PQ
PQ^2 = PR^2 - QR^2
PQ^2 = 12.7^2 - 14.1^2
PQ^2 = 161.29 - 198.81
PQ^2 = 37.52
PQ ≈ 6.12
Now we can use the sine function to find the measure of angle R
sin(R) = opposite/hypotenuse = PQ/PR
sin(R) = 6.12/12.7
sin(R) ≈ 0.482
Taking the inverse sine (sin^-1) of both sides, we get:
R ≈ sin^-1(0.482)
R ≈ 26 degrees
Therefore, the correct option is (a) 26⁰
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The given question is incomplete, the complete question is
What is the measure of angle R in triangle PQR?
a) 26°
b) 42°
c) 45°
d) 64°
Penny has at least $4.50 plus 2/5 of the amount of money that Susie has. Write an expression for the amount Penny has (p) in terms of how much Susie has (s). If Susie has $11.50, use your expression to calculate how much Penny has.
We can begin by defining Penny's total wealth as a mix of a set sum and a portion of Susie's wealth to develop an expression of how much money she has. We are informed that Penny has at least $4.50 and an additional 2/5 of Susie's wealth. Hence, we can write:
p = $4.50 + (2/5)s
where p is Penny's wealth, s is Susie's wealth, and s is represented by the letters.
If Susie has $11.50, we may enter s = $11.50 into the formula for p to see how much Penny has:
p = $4.50 + (2/5)($11.50)
p = $4.50 + $4.60
p = $9.10
As a result, Penny has $9.10 and Susie has $11.50.
In conclusion, the equation for Penny's wealth in terms of Susie's wealth is p = $4.50 + (2/5)s. When we enter s = $11.50 into the formula, we obtain p = $9.10, which is how much money Penny has while Susie has $11.50.
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a rectangular bird sanctuary with one side along a straight river is to be constructed so that it contains 72 km2 of area. find the dimensions of the rectangle to minimize the amount of fence necessary to enclose the remaining three sides. (give your answer as a whole or exact number.)
The rectangular bird sanctuary has dimensions of 12 km by 6 km in size to reduce the amount of fencing required to enclose the other three sides.
The given rectangular bird sanctuary has a side along a straight river. To minimize the amount of fence necessary to enclose the remaining three sides, we need to find the dimensions of the rectangle.
Therefore, let us consider that the width of the rectangular bird sanctuary is x and the length is y.
The area of the given bird sanctuary is given as,
A = xy= 72 km²
The amount of fence required for the bird sanctuary can be written as,
F = 2x + since we are looking to minimize the amount of fence necessary to enclose the remaining three sides, we need to differentiate the expression for a fence with respect to x and equate it to zero to obtain the value of x that will minimize the fence.
dF/dx = 2 - 0 (since dy/dx = 0)
Therefore, dF/dx = 2 Let us consider this to be equation (1) Differentiating the expression for a fence with respect to y and equating it to zero to obtain the value of y that will minimize the fence.
dF/dy = 0 + 1 (since dx/dy = 0)
Therefore, dF/dy = 1
Let us consider this to be equation (2)
Now, we can solve equations (1) and (2) to obtain the values of x and y that will minimize the fence.
dF/dx = 2 ⇒ 2x + y
= 0dF/dy
= 1 ⇒ 2y + x
= 0
Solving the above two equations for x and y, we get x = 12 km and y = 6 km
Therefore, the dimensions of the rectangular bird sanctuary are 12 km and 6 km to minimize the amount of fence necessary to enclose the remaining three sides.
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A restaurant claims to have 455 different combinations when you buy a 3-course meal.
The restaurant serves 5 different starters.
What is the total number of mains and desserts that the restaurant serves?
tripling the sample size will reduce the standard error of the sample proportion by one-third. group of answer choices true false
After tripling the sample size will reduce the standard error of the sample proportion by one-third we have:
a. Trueb. truec. falsed. falsee. falseThe sample size in statistics is a measurement of the total number of samples utilised in an experiment. The sample size is 50, for instance, if we are evaluating 50 samples of city dwellers who watch TV. It is sometimes referred to as sample statistics.
One of the mathematical techniques used in statistics to calculate variability is the standard error. It is referred to as SE. The standard deviation of a sample distribution serves as the standard error of a statistic or estimate of a parameter. It may be characterised as a projection of that standard deviation.
a. true
population = 25% = 0.25
sample = n= 12
n x p
= 12 x o. 25 = 3 and 3 is less than 10
12(1 - p)
= 12 x 0.75
= 9 and is less than 10
b. True
the sample distribution of the population is normal when
sample size x population > or equal to 10
40 x 0.75
= 30 and 30 is greater than 10
c. false
50 x 0.25 = 12.5
50 x 0.20 = 10
[tex]z = 10 - \frac{12.5}{\sqrt{12.5} }[/tex]
= -2.5/3.54
= -0.70
H0: Young American family who delayed
H1: young American family who did not delay
p(z = -0.70)
0.2420>0.005
therefore we accept the null hypothesis.
d. false
150 x 0.20 = 30
150 x 0.75 = 37.5
[tex]z = 30 - \frac{37.5}{\sqrt{37.5} }[/tex]
= -7.5/6.12
= -1.22
p(z = -1.22) = 0.1112 > 0.05
therefore we do not reject the null hypothesis.
e. false
[tex]se1 = \sqrt{(p(1-p)/n}\\se2 = \sqrt{(p(1-p)/3n}\\se2 = 1/\sqrt{(3)se2}[/tex]
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Complete question:
About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.a. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.b. In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximatly normal, we need random samples where the sample size is at least 40.c. A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.d. A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.e. Tripling the sample size will reduce the standard error of the sample proportion by one-third.
how fast are nfl players? prior to 2012, the average forty yard dash time for running backs and wide receivers was 4.53. on average, were nfl players between 2012-2014 significantly faster than in previous years?
The average speed of NFL players varies by position and other factors, and while the forty-yard dash is a common measure of speed, it's important to consider other factors and potential biases when comparing average times between different years.
The average speed of NFL players can vary depending on their position and other factors such as age, height, and weight. The forty-yard dash is a common measure of speed and agility for NFL players.
Regarding the question about whether NFL players were significantly faster between 2012-2014 compared to previous years, we would need to compare the average forty-yard dash times for running backs and wide receivers from 2012-2014 to the average times from prior years to determine if there was a significant difference.
However, it's worth noting that the average forty-yard dash time can be influenced by a variety of factors, including changes in the testing conditions, differences in the player population being tested, and changes in training and coaching techniques. Therefore, we cannot make any definitive conclusions about changes in player speed based solely on this one measure.
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a pilot approaching a 10,000 ft runway finds that the angles of depression of the ends of the runway are 17.0 and 12.5 degrees. how high is his plane and how far is it from the nearer end of the runway?
The height of the plane is about 3855 feet and the distance from the nearer end of the runway is about 13580 feet.
To find out the height of the plane and the distance of it from the nearer end of the runway, we have to use trigonometry.
Let's start by finding the height of the plane, h.
Using the angle of depression of 12.5 degrees, we can write this equation:
tan 12.5 = h/d
Where d is the distance from the nearer end of the runway. If we cross-multiply, we get:
d = h/tan 12.5
We can use the equation from the other angle of depression to eliminate the distance,
d.tan 17.0 = h/(d + 10,000)
By substituting the previous equation in for d, we get:
tan 17.0 = h/(h/tan 12.5 + 10,000)
Simplifying: tan 17.0 = h(tan 12.5)/(h/tan 12.5 + 10,000)
Multiplying both sides by h/tan 12.5 + 10,000:
tan 17.0 (h/tan 12.5 + 10,000) = h tan 12.5
Expanding the left side: distributed = h + 10,000 tan 17.0 tan 12.5
Simplifying and isolating h: h = 10,000 tan 17.0 tan 12.5/(tan 12.5 - tan 17.0) ≈ 3855 ft
Therefore, the height of the plane is about 3855 feet. To find the distance from the nearer end of the runway, we use the previous equation:d = h/tan 12.5 ≈ 13580 ft
Therefore, the distance from the nearer end of the runway is about 13580 feet.
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What is the area of this trangle?
Answer:
Step-by-step explanation:
1/2*base*height
!!PLEASE HELP ASAP!!
The function g(x) is the height of a football x seconds after it is thrown in the air. The
football reaches its maximum height of 28 feet in 6 seconds, and hits the ground at
12 seconds.
What is the practical domain for the function f(x)?
Type your answer in interval notation.
Answer:
[0,12]
Step-by-step explanation:
The unit of the domain is seconds
x is greater than or equal to zero because time can't be negative
Time stops at 12 seconds since the ball hits the ground.
Brackets are used to include both 0 and 12 as values
AE and CD intersect at point B. Find m
AE and CD intersect at point B then angle ABD = 152°
A straight angle in mathematics is one with a degree value of 180. Because it resembles a straight line, it is called straight. Essentially, two rays linked end to end create an angle according to the definition of angles in mathematics. As a result, where the rays are linked at endpoints, the two 180-degree angle rays are subtended in the opposite direction.
AE and CD intersect at point B,
angle DBE = 48,
and AE is a straight line,
So the sum of angles on a straight line is 180,
We have to find the angle ABD,
∠DBE+∠ABD=180
∠ABD=180-48
∠ABD=152°
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if x>3, which of the following is equivalent to 1/(1/x+2)+(1/x+3)
Answer:Option B is correct.
Step-by-step explanation: Given:
x+2
1
+
x+3
1
1 =
(x+3)(x+2)
x+3+x+2
1 =
2
+5x+6
2x+5
1
=
2x+5
x
2
+5x+6
The expression 1/(1/x+2) + (1/x+3) is equivalent to (x² + 4x + 44)/x(x + 11) when x > 3.
We have,
To simplify the expression 1/(1/x+2) + (1/x+3), we can apply the concept of finding a common denominator and combining fractions.
Let's start by finding the common denominator for the two fractions.
The denominators are (1/x + 2) and (1/x + 3).
To find the common denominator, we multiply the denominators together:
Common denominator = (1/x + 2) x (1/x + 3)
Expanding the expression:
Common denominator = (1/x * 1/x) + (1/x * 3) + (2 * 1/x) + (2 * 3)
Simplifying further:
Common denominator = 1/x^2 + 3/x + 2/x + 6
Combining the fractions with the common denominator:
1/(1/x+2) + (1/x+3) = (1/x) / (1/x^2 + 3/x + 2/x + 6) + (1/x+3)
To simplify the expression further, we can multiply the first fraction by x/x to clear the fraction in the numerator:
(1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3) = (x/x) * (1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3)
Simplifying:
= 1 / (x/x * 1/x) / (1/x² + 3/x + 2/x + 6) + (1/x+3)
= 1 / (1/x²) / (1/x² + 3/x + 2/x + 6) + (1/x+3)
= 1 / (1/x²) / (1/x² + (3 + 2)/x + 6) + (1/x+3)
= 1 / (1/x²) / (1/x² + 5/x + 6) + (1/x+3)
= 1 / (1/x²) / (1/x² + 5/x + 6) + (x/x) * (1/x+3)
Simplifying further:
= 1 / 1 / (1 + 5/x + 6x/x²) + (x/x² + 3x/x)
= 1 / (1 + 5/x + 6x/x²) + (x + 3x)/x²
= 1 / (1 + 5/x + 6/x) + (4x)/x²
= 1 / (1 + (5 + 6)/x) + (4x)/x²
= 1 / (1 + 11/x) + (4x)/x²
= 1 / (x + 11)/x + (4x)/x²
= x / (x + 11) + (4x)/x²
= (x² + 4(x + 11))/x(x + 11)
= (x² + 4x + 44)/x(x + 11)
Therefore,
The expression 1/(1/x+2) + (1/x+3) is equivalent to (x² + 4x + 44)/x(x + 11) when x > 3.
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you want to estimate the average time college students spend studying per week. you know that the population standard deviation for studying time per week for college students is 3.5 hours. you want a 99% confidence interval with a margin of error of 30 minutes (0.50 hours). how many students do you need in your study?
You need a sample size of approximately 82 students to estimate the average time college students spend studying per week with a 99% confidence interval and a margin of error of 30 minutes (0.50 hours).
To determine the sample size, we will use the formula given below;
Where, n = sample size
Zα/2 = the z-score associated with the level of confidence
α = level of significance
σ = population standard deviation
d = margin of error of the estimation.
Substituting the given values, we have; n = [(Zα/2 * σ)/d]^2
We are given the population standard deviation, σ = 3.5 hours.
We are also given the margin of error, d = 0.5 hours.
We need to find the value of Zα/2 at 99% confidence level.
Since the sample size is large enough, we can use the z-distribution to find the z-value.
The area under the standard normal distribution curve for a 99% confidence level is as shown below;
Using the z-tables, the value of Zα/2 for a 99% confidence level is 2.576.
Substituting the values into the formula; n = [(Zα/2 * σ)/d]^2n = [(2.576 * 3.5)/0.5]^2= (9.006)^2= 81.12
Since we need a whole number for the sample size, we round up the value to get 82.
However, since the standard deviation of the population is known, we can use the z-distribution to construct a confidence interval for the population mean. This will give us an accurate interval estimate of the population mean.
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A triangle has angles that measure 70°, 55°, and u. What is u?
Answer: 55 degrees
Step-by-step explanation: 180-70-55=u
This answer is because the sum of all the angles is 180 degrees.
Answer:
u = 55°
Step-by-step explanation:
The sum of the internal angles of a triangle = 180°
Then:
70 + 55 + u = 180
125 + u = 180
u = 180 - 125
u = 55°
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)? f(x) = –3x – 6 f(x) = –3x – 4 f(x) = –3x + 16 f(x) = –3x + 14
The linear function that represents the line is f(x) = -3x + 14
Calculating the linear relationWe can rewrite the point-slope equation y + 1 = -3(x - 5) in slope-intercept form, which has the general form of y = mx + b, where m is the slope and b is the y-intercept.
To do this, we first distribute the -3 on the right side of the equation:
y + 1 = -3x + 15
Then, we can isolate y by subtracting 1 from both sides:
y = -3x + 14
So the slope of the line is -3 and the y-intercept is 14. Therefore, the linear function that represents the line is:
f(x) = -3x + 14
Hence, the correct answer is f(x) = -3x + 14.
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Select the action you would use to solve x - 3 = 12. Then select the property that justifies this action select all that apply A. Action: add 3 to both sides B. Action: Multiple both sides by 3
Answer: A. Action: add 3 to both sides
Step-by-step explanation:
The property that justifies this action is the addition property of equality, which states that if you add the same number to both sides of an equation, the equation remains true.
I need help finding area
The area of the parallelogram is approximately 193.73 square meters.
How to find the area?
To find the area of a parallelogram, we need to multiply the length of one side of the parallelogram by the perpendicular distance between that side and the opposite side.
In this case, we know that one side of the parallelogram is 11.8 m and the other side is 18.5 m. Let's call these sides "a" and "b" respectively.
To find the perpendicular distance between these two sides, we need to draw a perpendicular line from one of the endpoints of side "a" to side "b". Let's call this perpendicular distance "h".
We can use the formula for the area of a parallelogram:
Area = base x height
where the base is side "a" and the height is "h".
To find "h", we can use the Pythagorean theorem:
h² = b² - (a/2)²
where "a/2" is half of side "a".
Plugging in the values we know, we get:
h² = 18.5² - (11.8/2)²
h² = 302.25 - 34.81
h² = 267.44
h ≈ 16.36
Now that we know the height of the parallelogram, we can calculate its area:
Area = 11.8 x 16.36
Area ≈ 193.73 m²
Therefore, the area of the parallelogram is approximately 193.73 square meters.
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The volume of a triangle
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{9\times 7}{63}\\ h=6 \end{cases}\implies V=\cfrac{(63)(6)}{3}\implies V=126~cm^3[/tex]
now, for the slanted cone, we can use Cavalieri's Principle for an slanted cylinder, thus we can say that the slanted cone will have the same volume of a non-slanted cone, now, since this one has a diameter of 6, that means is has a radius of 3.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3} \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3}\implies V=21\pi \implies V\approx 66~cm^3[/tex]
Answer:
64
Step-by-step explanation:
Need A B C and domain and the range.
Answer:
A=1 B=2 C=3 Domain: [2, infinity) Range: (neg. infinity, 3]
Step-by-step explanation:
a is rate B is Horitzontal shift C is vertical shift
hey guys whats expand 3(x + 4)
Answer:
3x + 12
Step-by-step explanation:
3(x + 4)
3x + 12
So, the expand is 3x + 12
Answer:
3x + 12
Step-by-step explanation:
You multiply the outside of the perentheses by everything inside, and 3(x) + 3(4) = 3x + 12
Anna's monthly Salary was $3000 in may. In June, she received a 20% rate. How much did she get in June? In July, she received a 20% pay cut from June. How much did she get in July? Show your work
Anna's monthly Salary in June was $3600 as she received a 20% rate and her monthly Salary in July was $2880 as she received a 20% pay cut from June.
It is given to us that: Ana's salary in May =3000$
in June she received 20% raise
the amount she received in June after 20% raise = 3000 x 20/100
= 30 x 20 = 600
we have to first find Ana's salary at the end of June month with 20% raise. and then her salary after the end of July month with the pay cut of 20%.
Ana's salary after June month when she got 20% raise in his salary after May:
= 3000 + (20% x 3000)
= 3000 + (20/100 x 3000)
= $3600
her new salary after June will be 3600$.
therefore, she received 3600 in June.
in July she received 20% pay cut.
To find Ana's monthly salary after the two changes in June and July.
Ana's salary after June month when she got 20% raise in his salary after May = $3600
now she got a pay cut of 20% on his new salary from July month,
= 3600 - (20% x 3600)
= 3600 + (20/100 x 3600)
= 3600 - 720
= $2880
so, her salary after that would be equal to $2880.
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