The angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.
what is the rate of change in calculus?
The rate of change defines the relationship between two changing variables. Consider a moving object that moves twice as much in the vertical direction (y) as it does in the horizontal direction (x). This can be expressed mathematically as y = 2x.
Let 'θ' represent the angle between the minute and hour hand.
Let θ1 be the angle between the minute hand and 12.
[tex]\frac{d\theta_2}{dt}=\frac{1}{60*12}\times2\pi\\\\\frac{d\theta_2}{dt}=\frac{\pi}{360}[/tex](Between hour hand and 12)
[tex]\theta=\pm(\theta_1-\theta_2)\\\\\frac{d\theta}{dt}=\pm(\frac{d\theta_1}{dt}-\frac{d\theta_2}{dt})\\\\\frac{d\theta}{dt}=\pm(\frac{\pi}{30}-\frac{\pi}{360})\\\\\frac{d\theta}{dt}=\pm5.5$ degree$[/tex]
Hence the angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.
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at a particular pressure and temperature, it takes 4.55 min for a 1.5-l sample of he to effuse through a porous membrane. how long does it take for 1.5 l of f2 to effuse under the same conditions?
Time required to diffuse the F2 gas under the same conditions pressure and temperature with same volume is equal to 14 mins( approximately).
As given in the question,
Time taken by 1.5L sample of He gas to diffuse = 4.55 min.
Molar mass of He gas = 4g
Volume of He gas = 1.5L
Volume of F2 gas = 1.5L
Molar mass of F2 = 38gm
Formula of Rate of diffusion is given by :
Rate of diffusion of He / Rate of diffusion of F2
= √Molar mass of F2 / √Molar mass of He
Now,
Rate of He = Volume of He / time taken
= 1.5 / 4.55
Rate of F2 = [ ( Rate of He ) ×√ Molar mass of He ] / √ Molar mass of F2
= ( 1.5 / 4.55 ) × ( √4 / √38)
= 3 / 28.028
= 0.107 L / min
Time of F2 = Volume of F2 / Rate of F2
= 1.5 / 0.107
= 14.02 minutes
≈ 14 minutes.
Therefore, the time taken by F2 to diffuse under the same condition of He is equal to 14 minutes.
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. make up three data sets with 5 numbers each that have: a. the same mean but different standard deviations. b. the same mean but different medians. c. the same median but different means
The following data sets represents the required properties:
a. . Same mean but different standard deviation :
3 3 3 3 3
1 2 3 4 5
2 2 3 4 4
b. Same mean but different medians
1 2 3 4 5
1 1 4 4 5
1 2 2 5 5
c. Same median but different median:
1 2 3 5 5
1 2 3 4 5
2 2 3 5 5
As given in the question,
Three data sets with 5 numbers representing :
a. Same mean but different standard deviation :
Mean Standard deviation
3 3 3 3 3 15/5 = 3 0
1 2 3 4 5 15/5 = 3 2.5
2 2 3 4 4 15/5 = 3 1
Mean of the data set = 3
Standard deviation = [tex]\frac{\sum (x - \bar{x} )^{2} }{n -1}[/tex]
b. Same mean but different medians :
Mean Median
1 2 3 4 5 3 3
1 1 4 4 5 3 4
1 2 2 5 5 3 2
c. Same median but different median:
Mean Median
1 2 3 5 5 3.2 3
1 2 3 4 5 3 3
2 2 3 5 5 3.4 3
Therefore, above are the following data set to represent same mean different standard deviation, same mean different median and same median different mean.
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1)A confidence interval is used for estimating a population parameter. TRUE/FALSE
2)A confidence interval always captures the sample statistic.TRUE/FALSE
3) A confidence interval always captures the population parameteTRUE/FALSE
4)When constructing a confidence intervals we should always use Z-critical values.TRUE/FALSE
5) The margin of error determines the center location of the confidence interval.TRUE/FALSE
6)In general, we would like to have a precise confidence interval while having a high level of confidence.TRUE/FALSE
7)When constructing a confidence interval for a proportion we need a large sample size. Read answers carefully.
Group of answer choices
False - The size of the sample is not important
True - n*(p-hat) OR n(q-hat) need to be at least 10
True - Both n*(p-hat) AND n(q-hat) need to be at least 10
The solutions for the given conditions are;
1. True
2. True
3. False
4. False
5. False
6. True
7. True
1) For estimating a population parameter, a confidence interval is used.
TRUE → CI is used for estimating a population parameter. But, it can also be used to estimate the sample statistic.
2) The sample statistic is always captured by a confidence interval.
TRUE → CI is calculated using the sample statistic.
3) The population parameter is always captured by a confidence interval.
FALSE → There is a type 1 error possibility.
4) Z-critical values should always be used when creating confidence intervals.
FALSE → Z stat is used only in a normal distribution with sizes>30. Else, it is recommended to use a t distribution.
5) The center of the confidence interval is determined by the margin of error.
FALSE → ME determines the maximum deviation from the center at a given confidence level
6) In general, we would like to have a high level of confidence and a precise confidence interval.
TRUE → This is attainable when we increase the sample size.
7) A large sample size is required to create a proportion's confidence interval.
TRUE → Along with the large sample, we also need to have np and nq at least 10.
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In the diagram, BCD is
BC=5 cm, AB = 12 cm,
AD= 13
straight line,
AC = 13 cm and ABC = 90°.
Find
(a) tan BAC
(b) cos ACD.
Give both answers as fractions.
Step-by-step explanation:
where is the diagram?
please
A guy wire runs from the top of a cell tower to a metal stake in the ground. Janelys places a 5-foot tall pole to support the guy wire. After placing the pole, Janelys measures the distance from the stake to the pole to be 14 ft. She then measures the distance from the pole to the tower to be 24 ft. Find the length of the guy wire, to the nearest foot.
The length of the guy wire will be equal to 27.78 feet.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that Janelys places a 5-foot tall pole to support the guy wire. After placing the pole, Janelys measures the distance from the stake to the pole to be 14 ft. She then measures the distance from the pole to the tower to be 24 ft.
The length of the wire will be calculated as,
L² = 24² + 14²
L² = 576 + 196
L² = 772
L = √772
L = 27.78 ft
Therefore, the length of the guy wire will be equal to 27.78 feet.
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Answer:
40ft
Step-by-step explanation:
ASAP WILL GIVE BRAINIEST
What are the solutions to the equation shown?
Answer:
Step-by-step explanation:
A B
The graph of y = f(x) is transformed to the graph of y = 2f(x - 1).
Describe fully the two single transformations which have been combined to give the resulting transformation.
Answer:
Stretches vertically by 2, shifts right by 1
Step-by-step explanation:
changes to y are direct, but you have to take the inverse for changes to x. This is because for a given value of y, with x-1, you would have to add one to x to make it the same value(to get the same point before the transformation)
If points A and B are both dilated using a center of C
and a scaling factor of 3, then which of the following
will be the distance between the images of A and B?
0
O24
18
12
9
5
A
10
C B
15
20
Answer:
1.8x101
Step-by-step explanation:
you order 3 strings of white led lights and 2 strings of colored led lightgs for 66$ In a second order you buy one string of each type for 27$ brainly math question braunlly
The cost of each white led lights and colored led lights is $12 and $15 respectively.
What is the cost of each led light?Let
White light = wColored light = cw + c = 27
3w + 2c = 66
From (1)
w = 27 - c
Substitute w = 27 - c into (2)
3w + 2c = 66
3(27 - c) + 2c = 66
81 - 3c + 2c = 66
- 3c + 2c = 66 - 81
- c = - 15
c = 15
Substitute c = 15
w + c = 27
w + 15 = 27
w = 27 - 15
w = 12
In conclusion, the task content can be solved using the concept of simultaneous equation.
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The sum of the measures of the angles of any triangle is 180 degrees . In a certain triangle, the largest angle measures 55degrees less than twice the medium angle, and the smallest angle measures 25 degrees less than the medium angle. Find the measures of each of the three angles.
Each of the three angles measures 75°, 65°, and 40°.
What is an angle measure?
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Here, we have
Let the largest angle be x degrees, the median y, and the smallest z.
x = 2y - 55
z = y - 25
x + y + z = 180
Substituting for x in the last equation:
2y - 55 + y + z = 180
3y + z = 235
From the second equation:
- y + z = -25 Subtract this from the last equation:
4y = 260
y = 65 degrees
z = 65 - 25 = 40 degrees.
and x = 180 - 65 - 40 = 75 degrees.
Hence, each of the three angles measures 75°, 65°, and 40°.
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The measures of each of the three angles are 40,65 and 75 degrees.
What is angle ?
In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Give that:
Let us consider X,Y,Z re the largest ,medium and smallest angle in the triangle.
Sum of the measures of the angles of any triangle is 180 degrees .
X + Y + Z = 180 degree
The largest angle measures 55degrees less than twice the medium angle,
Z = 2Y - 55 degree
The smallest angle measures 25 degrees less than the medium angle,
X = Y - 25 degree
Now ,replace X by (Y - 25) and Z by (2Y - 55) in the first equation
Y - 25 +Y + 2Y - 55 = 180 degree
4Y = 180 + 25 + 55
4Y = 260
Y = 65 Degree of the medium angle
X = 65 - 25
X = 40 Degree of the smallest angle
Z = 2 * 65 -55
= 130-55
Z = 75 Degree of the largest angle.
40 + 65 + 75 = 180
180 = 180
Hence proved.
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Use point-slope form to write the equation of a line that passes through the point (1,-3)(1,−3) with slope -\frac{5}{3}−
3
5
.
Answer:
y + 3 = (-5/3) × (x - 1)
Step-by-step explanation:
5
(1, -3); m = - -------
x₁, y₁ 3
y - y₁ = m(x - x₁)
y - (-3) = (-5/3)(x - 1)
y + 3 = (-5/3)x + (5/3)
-3 -3
--------------------------------
y = (-5/3)x - (4/3) :Slope-intercept form
I hope this helps!
a manufacturer must test that his bolts are 5.00cm long when they come off the assembly line. he must calibrate his machines if the bolts are too long or too short. after sampling 49 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.88cm. he knows that the population standard deviation is 0.44cm. assuming a level of significance of 0.01, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.
Given that the test's p-value is 0.0562>0.05, there is enough data to conclude that the machines' manufacturer should perform a new calibration.
What is test statistic?A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.
Here,
x=4.88 cm
μ=5 cm
σ=0.44 cm
n=49
The test statistic,
=(4.88-5)/(0.44/7)
z=-1.909
The p-value of the test is the probability that the sample mean is different by at least 4.88 - 5 = 0.12 from the target value, which is P(|z| > -1.909), which is 2 multiplied by the p-value of z = -1.909
At z=-1.909, p-value=0.0281
2*0.0281=0.0562
The test's p-value is 0.0562>0.05, indicating that there is enough data to conclude that the machines' manufacturer should perform a recalibration.
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What is the surface of a rectangular prism with the length of 5 cm, width of 4 cm and height of 2 cm?
The surface area of the rectangular prism is 76cm^2
What are the basics of geometry?Geometry is the study of various mathematical or actual-world shapes, figures, and sizes. In geometry, we study various angles, transformations, and figure-to-figure similarities. The fundamental concepts of geometry primarily depend on point, line, angle, and plane.
What are the 3 types of geometry?The three most popular types of geometry are solid geometry (which deals with objects like the line, sphere, and polyhedron) and spherical geometry. Plane geometry deals with objects like the point, line, circle, triangle, and polygon.
According to the question:-
The surface area of the rectangular prism is:_
surface area= 2*(lb+bh+hl)
=2*(5*4+4*2+2*5)
=76 cm^2
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A stove is bought on hire purchase for $7500. A deposit of $1750 is paid in equal monthly payment of $ 250.
(I). Calculate the number of months required to complete the payments
The number of months required to complete the payments are 63 months.
How to calculate the number of months?We will make a equation, which represent total purchase amount in terms of number of months.
Let we consider number of months be t.
According to given information in the question:Total purchase amount = $17500, one time deposit = $1750
and monthly payment = $250
Then,
17500 = 1750 + 250t
250t = 17500-1750
250t = 15750
t = 15750/250
t = 63 months
Thus number of months required are 63.
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Water is rushing down the slide at a rate of 1 half gallon every 3 seconds .At this rate , how many gallons of water rush down the slide each seconds ?
1/2 gallons of water rush down the slide each seconds.
Explain the method of unitary?The unitary approach involves calculating the value of a specific unit, from which we can calculate the values of the necessary number of units.The unitary method's formula is to identify the value of a specific unit, then multiply that value by the number of units to obtain the required value.For the given question-
Rate of running water = 1 half gallon every 3 seconds.
Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.
It means-
In every 3 seconds ----> 3/2 gallons water flows.
Thus for 1 sec, divide both side by 3.
1 seconds ----> 1/2 gallons water flows.
Therefore, 1/2 gallons of water rush down the slide each seconds.
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the arithmetic progressions{2,5,8,11, . . .}and{3,10,17,24, . . .}have some common values. what is the largest value less than 500 that they have in common?
The largest value less than 500 that the arithmetic progressions have in common = 479
In this question, we have been the arithmetic progressions {2,5,8,11, . . .} and {3,10,17,24, . . .}
We need to find the largest value less than 500 that they have in common.
We know that the formula for the n-th term of arithmetic progression is: an = a + (n – 1)d
For arithmetic progression {2,5,8,11, . . .}
a_m = 2 + (m - 1)3
For arithmetic progression {3,10,17,24, . . .}
a_n = 3 + (n - 1)7
if we solve for m, n then m =160 and n =69
2 + (160 -1)*3 = 479 which is the 160th term in the arithmetic progression {2,5,8,11, . . .}
3 + (69 - 1)*7 =479 which is the 69th term in the arithmetic progression {3,10,17,24, . . .}
Therefore, the value which less than 500 that both the progressions have in common = 479
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explain how to identify the constant of proportionality from a graph of any proportional relationship
The constant of proportionality from a graph of any proportional relationship is find as below.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The constant of proportionality from a graph of any proportional relationship.
Now,
Let the solution of the graph = (2, 10)
Then, The constant of proportionality from a graph of any proportional relationship is find as;
⇒ Constant of proportionality = 10 / 2
= 5
Thus, The constant of proportionality from a graph of any proportional relationship is find as above.
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What percentage of diabetes patients have type 2? a. 5 - 10% b. 50 - 55% c. 75 - 80% d. 90 - 95% please select the best answer from the choices provided. A b c d.
The correct option d. 90 - 95%, is the percentage of diabetes patients having type 2.
Explain the term type 2 diabetes?A disorder in the body's ability to control and utilize sugar (glucose) as fuel is type 2 diabetes.
This chronic (long-term) disorder causes the bloodstream to circulate with an excessive amount of sugar. Over time, cardiovascular, neurological, and immune system issues might result from excessive blood sugar levels.Your body's cells cannot correctly absorb sugar (glucose) from of the meals you eat if you do have Type 2 diabetes. Diabetes type 2 can lead to heart disease, renal disease, and stroke if it is not addressed.The recipe for diabetes management is a healthy diet.
Thus, one in ten Americans, or more than 37 million people, have diabetes, and 90–95% of them suffer from type 2 diabetes.
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Answer:
D
Step-by-step explanation:
90-95
Cody has $1400 in a savings account that earns 4 % annually. How much will he have total after 3 years?
Answer: $4368
Step-by-step explanation:
Find 4% of 1400 by taking 1400 times 0.04 = $56
So a year he has 1456$
After 3 years just need to take 1456 times 3 = $4368
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HELP !! it’s due by midnight pleaseee help me
x =2173
Step-by-step explanation:
Determine which equation is linear
Answer:
A. No
B. No
C. Yes
D. Yes
Step-by-step explanation:
Confused please help Brainliest will be rewarded!!!!!!!
Answer:
56
Step-by-step explanation:
Take two points as far apart on the line (for maximum accuracy), preferably on grid points, and then calculate the vertical difference divided by the horizontal difference.
So (4, 224) and (0,0) are on the line, and (224-0)/(4-0) = 56
What is 1 plus 1?????????
Answer:
2
Step-by-step explanation:
you take 1 and add 1 to it... and bam... 2
Answer:
2
Step-by-step explanation:
1+1=2 because 2-1=1 :0
A field measures 40 by 80 yards. Larysa makes a scale drawing with a scale of 1 in. to 5 yd., and Prakash makes his own scale drawing with a scale of 1 in. to 8 yd. Whose drawing has a larger area? Explain your reasoning
Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
A field estimates 40 by 80 yards. Larysa makes a scale drawing with a size of 1 in. to 5 yd., and Prakash makes his own scale drawing with a size of 1 in. to 8 yd.
The dimension of the Larysa drawing is given as,
⇒ 40 x 1/5
⇒ 8 in
⇒ 80 x 1/5
⇒ 16 in
The dimension of the Prakash drawing is given as,
⇒ 40 x 1/8
⇒ 5 in
⇒ 80 x 1/8
⇒ 10 in
The dimension of the Prakash's drawing is less than the dimension of the Larysa's drawing. The Larysa's drawing has the larger area.
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trapezoid abcd has vertices at A(-4,-1) b(-2,3) c(4,3) and d(8,-1) what is the perimeter of abcd round to the nearest tenth
The perimeter of ABCD, given the vertices of the trapezoid, can be found to be 28.13 units
How to find the perimeter?To find the perimeter of this trapezoid, you need to find the distances between AB, BC, CD, and AD. To find these, you can use the formula for finding the distance between vertices.
That formula is:
= √( ( X₂ - X₁ ) + ( Y₂ - Y ₁))
Using this formula, the distance of AB is 4.47 units.
The distance between BC is 6 units.
The distance between CD is 5.66
The distance between AD is 12 units
The perimeter is the distance around the shape:
= 4.47 + 6 + 5.66 + 12
= 28.13 units
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Add.
(7v–4)+(–4v3–v2–8v–5)
Answer:
-4v³ - v² - v - 9
Step-by-step explanation:
1. Subtract the numbers
7v - 4 - 4v³ - v² - 8v - 5
7v - 9 - 4v³ - v² - 8v
2. Combine like terms
7v - 9 - 4v³ - v² - 8v
-v - 9 - 4v³ - v²
3. Rearrange Terms
-v - 9 - 4v³ - v²
-4v³ - v² - v - 9
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Determine if the following equation is linear or non-linear: y = x − 1
Answer:
Step-by-step explanation:
dan and sydney are getting high-speed internet access at the same time. dans provider charges $60 for installation and $42.95 per month. Syndey’s providee has a free installition and charges 57.95 per month after how many months will dan and gave paid the same amount for the internet
Answer:
after 4 months dan and sydney will have paid the same amount
Step-by-step explanation:
Answer:
Step-by-step explanation:
dan and sydney are getting high speed internet access at the same time.dans provider charges $60 for installation and $42.95 each month. sydney's provider has free installation and charges 57.95 per month. after how many months will dan and sydney have paid the same amount?
let 'm' represent the number of months they have subscribed
dan's total:
42.95m + 60
sydney's total:
57.95m
we want to calculate 'm' when the two totals are equal:
42.95m + 60 = 57.95m
60 =15m
m = 60/15 = 4
after 4 months dan and sydney will have paid the same amount
what is eguilvilt to -2 with the power of 4 over -2 with the power of 2
By using exponent properties we will find the equivalent expression:
(-2)⁴/(-2)² = (-2)² = 4
How to get an equivalent expression?Here we need to use the exponent property:
xⁿ/xᵇ = xⁿ⁻ᵇ
Here the expression we have is:
(-2)⁴/(-2)²
Using the above property we can rewrite the expression as:
(-2)⁴/(-2)² = (-2)⁴⁻² = (-2)²
Now we can solve this:
(-2)² = (-2)*(-2) = 4
Then the equivalent expression is 4.
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Davis can read 4/5 of a page in one minute. How many pages can he read in 4 1/2 minutes?
Simplify your answer completely.
Answer: I believe it is 18/5
or Decimal Form:
3.6
or Mixed Number Form:
3 3/5
Step-by-step explanation
4/5 x 4 1/2