Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)
What is mean value theorem ?
The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].
The property of derivative : r'(t) is the rate of change of water flow.
Justification :
r(s) - r(4) = r'(3) (5-4)
- 5 = r(3)
In (4,5) , r(t) decreasing , so there are value of 3 and r'(3) > 0 , r'(3) = -5.
r(6) - r(5) = r'(3) (6-5)
4 = r'(3)
In (5,6), r(t) increasing , so there are values of 3 and r'(3) > 0, r'(3) = 4.
∴ Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)
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The complete question is :
Water is flowing into a tank at a rate of r(t) where t is measured in seconds. Is there ever a time where the r'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem.
PLEASE HELP
C is the circumcenter of APQR.
PC=3x+7, RC=5x-15, & QC=51-x
S
Q
X=[ ? ]
Using circumcenter the value of x is 11.
What is circumcenter of triangle?
The center of a triangle's circumcircle is known as the circumcenter. It is located at the point where the perpendicular bisectors intersect. Let the circumcenter of ABC be O (x, y). Then, because there are no differences in the distances from the vertices to O, we have AO = BO = CO = Circumradius.
Here the given is PC=3x+7 , RC = 5x-15 and QC = 51-x
Now according to the circumcenter the distance of the vertices are same . Then,
=> PC = RC
=> 3x+7 = 5x-15
=> 5x-3x =15+7
=> 2x = 22
=> x = 11.
Hence the value of x is 11.
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Find the number that belongs in the green box.
14
15
170° [?]°
Round your answer to the nearest tenth.
Using Trigonometric ratios, the value of missing angle is 60.45°.
There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
If we draw an imaginary line dividing the given triangle in 2 equal parts,
we will get 2 right angled triangles.
So, using trigonometric ratios,
Sin θ = Perpendicular / hypotenuse
⇒ Sin 70 ° = perpendicular / 14
⇒ 0.94 = perpendicular / 14
⇒ perpendicular = 0.94 × 14
⇒ perpendicular = 13.16
Now the other right angled triangle is
Sin θ = Perpendicular / hypotenuse
⇒ Sin θ = perpendicular / 15
⇒ Sin θ = 13.16 / 15
⇒ θ = sin⁻¹(13.16 / 15)
⇒ θ = sin⁻¹(0.87)
⇒ θ = 60.45
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A study of existing records of 27,000 automobile accidents involving children in Michigan found that about 10 percent of children who were wearing a seatbelt (group SB) were injured and that about 15 percent of children who were not wearing a seatbelt (group NSB) were injured. Which of the following statements should NOT be included in a summary report about this study?
(A) Driver behavior may be a potential confounding factor.
(B) The child's location in the car may be a potential confounding factor.
(C) This study was not an experiment, and cause-and-effect inferences are not warranted.
(D) This study demonstrates clearly that seat belts save children from injury.
(E) Concluding that seatbelts save children from injury is risky, at least until the study is independently replicated.
The correct answer is This study demonstrates clearly that seat belts save children from injury.
Given that,
According to an analysis of the 27,000 child passenger vehicle incidents in Michigan with records currently available, around 10% of children who were wearing seatbelts (group SB) and 15% of children who were not (group NSB) sustained injuries. Which of the following statements is NOT appropriate for a report summarizing this study?
Options are :
(A)Driver conduct could be a complicating variable.
(B) The location of the youngster in the vehicle could be a complicating variable.
(C) Since this study was not an experiment, drawing conclusions about causes and effects is not appropriate.
(D) This study amply demonstrates how seat belts protect kids from harm.
(E) It is dangerous to draw the conclusion that seatbelts protect kids from harm, at least until the study is independently reproduced.
So,The correct answer is This study demonstrates clearly that seat belts save children from injury.
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Tell the percentage below:
Answer:
10%
Step-by-step explanation:
if the volume of the water increase by 10 when turns to
ice so it must be decrease by 10 if it changes to water again
Stefanie has 18 grams of 20% sugar syrup and John has 30 grams of 25% sugar syrup.
how many grams of sugar are in Stefanie's syrup?
how many grams of sugar are in John's syrup?
The grams of sugar that is in Stefanie's syrup = 3.60g
The grams of sugar that is in John's syrup = 7.50g
How to calculate the quantity of sugar?The quantity of sugar syrup that Stefanie has = 18grams
The percentage of sugar syrup that is sugar = 20%
That is, 20/100 × 18
= 360/100
= 3.60g
The quantity of sugar syrup that John has = 30 g
The percentage of sugar syrup that is sugar = 25%
That is;
= 25/100 × 30
= 750/100
= 7.50g
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According to Moore’s Law, the doubling time for the number of transistors that can be put on a computer chip is approximately two years. Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account with starting quantity A[0]. Enter the exact answer: f(t) =
The new function that takes that longer doubling time into account with starting quantity will be Aₙ = A₁ (1)ⁿ.
What is an exponent?Consider the function:
y = a (1 ± r)ˣ
Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.
As per Moore's Regulation, the multiplying time for the number of semiconductors that can be placed on a microprocessor is roughly two years. That's what ongoing information proposes, starting around 2013, the pace of development anticipated by Moore's Regulation does not hold anymore.
The rate is 0%, then the equation is given as,
Aₙ = A₁ (1 + 0)ⁿ
Aₙ = A₁ (1)ⁿ
The new function that takes that longer doubling time into account with starting quantity will be Aₙ = A₁ (1)ⁿ.
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A physical therapist claims that 75% of people lose their balance if they close their eyes while standing on one foot. A gymnast feels that the rate is less than 75%. To test this, she randomly selects 100 people and finds that 80 of them lose their balance while standing on one foot. To determine if these data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%, 150 trials of a simulation are conducted. The gymnast is testing the hypotheses: H0: p = 75% and Ha: p < 75%, where p = the true proportion of people who will lose their balance while standing on one foot and closing their eyes. Based on the results of the simulation, what is the estimate of the P-value of the test?
The P-value of the test is the probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true.
This can be calculated using the formula P(X <= x) = Σ (n x) p^(x) q^(n-x), where n = 100, x = 80, p = 0.75 and q = 1-0.75. Following this formula, the P-value of the test is calculated to be 0.0009. This means that there is a 0.0009 probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true. Therefore, the data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%.The P-value of the test is the probability of observing a sample proportion of 80/100 or less, given that the null hypothesis is true.
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A certain blend of coffee sells for $15 per pound. Part 3 If a container has 31-x lb of coffee, write an expression that represents the cost.
The expression that represents the cost of coffee per container is (blank)
T = si is an expression that can be used to represent the party's projected cost.
How should the information be illustrated?T = si is an expression that can be used to represent the party's projected cost.
It should be remembered that expressions depict how variables relate to one another.
We can use the following phrase to obtain an estimated party cost:
T = s×i
where:
T is the ice cream party's overall budget.
s is the number of ninth-graders.
I = the ice cream unit price.
discover more on expressions;
All ninth graders are invited to an ice cream celebration as a prize for accomplishing their goals.
1) Write an expression that could represent an estimated cost for the party. Use at least one letter. State what each part of the expression represents.
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A rectangular landing strip for an airplane has a perimeter of 8876 feet. If the length is 10 feet longer than 35 times the width, what is the length of the air strip?
The length of the air strip is 451feet
What is perimeter?Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).
Given;
Perimeter= 8876feet
Let the length be x
and the width be y
Then, length will be x= 10+35y
Perimeter of rectangle= 2l+2b
8876=2(10+35y)+y
8876=20+700y+y
y=12.6
x=10+35y
x=451
Therefore, the length by the given perimeter will be 451feet
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The patient is insured by an insurance plan that reimburses on a 75-25 basis. The
charge total for the office visit is $340.00.
What is the dollar amount billed to the insurance plan?Make
sure to have 2 decimal places.
What is the amount the patient must pay?
To calculate the dollar amount billed to the insurance plan:
What's the math rate?
A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.
$340.00 (total charge for office visit) x 75% (insurance reimbursement rate) = $255.00
To calculate the amount the patient must pay:
$340.00 (total charge for office visit) x 25% (patient responsibility rate) = $85.00
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The occupations of registered nurse, food service employee, and customer service representative are among the 5 with the largest growth from 2012 to 2022. The number of registered nurses is
predicted to grow 748 thousand less than three times the number of food service jobs. The number of customer service jobs is predicted to grow 71 thousand more than half the number of food
service jobs. If the total growth of these three jobs is predicted to be 1222 thousand, find the predicted growth of each job.
The predicted growth of registered nurse jobs is?
The predicted growth of job of registered nurse, food service employee, and customer service representative are 518 thousand, 282 thousand, and 422 thousand respectively.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For instance, 2x - 5 = 13.
Let us suppose the number of registered nurses = x
Let us suppose the number of food service jobs = y
Let us suppose the number of customer service jobs = z
The number of registered nurses is predicted to grow 748 thousand less than three times the number of food service jobs. This is represented as:
x = 3y - 748,000 (equation 1)
The number of customer service jobs is predicted to grow 71 thousand more than half the number of food service jobs. This is represented as:
z = (1/2) y + 71,000 (equation 2)
The total growth of these three jobs is predicted to be 1222 thousand. This is represented as:
x + y + z = 1222000 (equation 3)
Isolate the value of y in the first equation:
x = 3y - 748,000
y = (x + 748000) / 3
Substitute the value of y in the second equation:
z = (1/2) ((x + 748000) / 3) + 71,000
z = (x + 748000) / 6 + 71000
z = x/6 + 124666.66 + 71000
z = x/6 + 195666.66
Substitute the value of y and z in third equation:
x + (x + 748000) / 3 + x/6 + 195666.66 = 1222000
x + x/3 + 249333.33 + x/6 + 195666.66 = 1222000
x + x/3 +x/6 = 1222000 - 249333.33 - 195666.66
6x + 2x + x = 6 (777000.01)
9x= 4662000.06
x = 518000
Substitute the value of x in the equation of z:
z = x/6 + 195666.66
z = 518000/6 + 195666.66
z= 282000
Substitute the value of x in the equation of y:
y = (x + 748000) / 3
y = (518000 + 748000)/3
y = 422000
Hence, the predicted growth of job of registered nurse, food service employee, and customer service representative are 518 thousand, 282 thousand, and 422 thousand respectively.
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In the science club at school, 22 of the students have pets and 25 do not. In a sample of 10 students from the club, only one of them had a pet. The students want to do a simulation to determine if such a sample is unusual. Which of the following statements describes how the students could use a table of random digits to carry out this simulation?
Label the students with pets 01–22 and the students without pets 23–47. Go along the random number table, selecting digits two at a time until 10 numbers have been selected.
Label the students with pets 01–22 and the students without pets 23–47. Ignoring repeated values, go along the random number table, selecting digits two at a time until 10 students’ numbers have been selected.
Label the students with pets 01–22 and the students without pets 23–47. Ignoring numbers 48–99 and 00, go along the random number table, selecting digits two at a time until 10 students’ numbers have been selected.
Label the students with pets 01–22 and the students without pets 23–47. Ignoring repeated values and numbers 48–99 and 00, go along the random number table, selecting digits two at a time until 10 students’ numbers have been selected.
Label the students with pets 01–22 and the students without pets the rest of the two-digit numbers, 23–99 and 00. Ignoring repeated values, go along the random number table, selecting digits two at a time until 10 students’ numbers have been selected.
Indicate probability the students with pets (01–22) and those without (23–47).Go along the random number table, selecting digits two at a time and ignoring any repeated values, until 10 students’ numbers have been selected.
1.Indicate the students with pets (01–22) and those without (23–47).
2. Go along the random number table and select two digits at a time.
3. Check if the two digits are repeated.
4. If they are repeated, select the next two digits.
5. If they are not repeated, add them to the list of 10 students.
6. Repeat steps 2-5 until 10 students’ numbers have been selected.
The students in the science club can use a table of random digits to simulate if the sample of 10 students with only one of them having a pet is unusual. First, they need to label the students with pets 01–22 and the students without pets 23–47. Then, they can go along the random number table, selecting digits two at a time and ignoring any repeated values until 10 students’ numbers have been selected. This will help to see if the sample of 10 students is unusual or not. By doing this simulation, they can check if the sample they have is significantly different from what the expected results would be if they had a random sample of 10 students. This will help them to determine if the sample they have is unusual or not.
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Energy is generated from solar and wind power. Solar power must be at most 6units/day or the panels will burn out. Wind must be strong enough to power 1 unit/ day or else the turbines won’t turn. The wind power must be less than twice the solar power less one, or the batteries wont charge properly. Find the optimal production of wind and solar that will maximize overall power output
Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.
What is more efficient wind or solar energy?Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.This proves that a single home wind turbine can generate more electricity than a number of solar panels.By the movement of air in relation to the Earth's surface, wind energy, a type of solar energy, is created.When the Earth's surface is heated unevenly by the Sun, this type of energy is created. The Earth's rotation and surface topography then alter this energy.Photovoltaic (PV) panels or solar radiation-concentrating mirrors are two ways that solar technologies turn sunlight into electrical energy.Electricity can be produced from this energy, which can also be used to store energy thermally or in batteries.To learn more about solar energy refer
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students will read word problems and decide if they are one or two steps. then students will work to solve. great for a formative assessment or math centers.
When working with word problems, students should first read the problem and decide if it is a one-step or two-step problem.
A one-step problem involves solving for a single unknown quantity, such as finding the total cost of 10 pencils at $0.50 each. The formula for this would be C = Pn, where C is the cost, P is the price, and n is the number of items. To solve this problem, the student would multiply the price and number of items, so C = 0.50 x 10 = $5.00. A two-step problem involves solving for two unknowns, such as finding the total cost of 10 pencils at a 10% discount. The formula for this would be C = Pn (1 - r), where r is the discount rate. To solve this problem, the student would first calculate the discount by multiplying the price and number of items by the discount rate, so C = 0.50 x 10 x 0.10 = $0.50. Then the student would subtract the discount from the total cost, so C = 0.50 x 10 - 0.50 = $4.50.
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Write an expression that is equivalent to 5 - 2(3x + 4).
Show you work please.
An expression which is equivalent to 5 - 2(3x + 4) is,
⇒ - 3 - 6x
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.
We have to given that;
The expression is,
⇒ 5 - 2 (3x + 4)
Now, We can solve the expression as;
⇒ 5 - 2 (3x + 4)
⇒ 5 - 2 × 3x - 2 × 4
⇒ 5 - 6x - 8
⇒ - 3 - 6x
Thus, The equivalent expression is,
⇒ - 3 - 6x
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Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the volume of this segment is (∏h2(3r-h))/3
The volume of the segment formed when a sphere of radius r is cut by a plane is equal to (πh2(3r-h))/3. This can be found by using the formula for the volume of a spherical segment, where h is the height of the segment and r is the radius of the sphere.
Step 1: Calculate the volume of a sphere using the formula V = (4/3)πr3
Step 2: Calculate the volume of a cone using the formula V = (1/3)πr2h
Step 3: Calculate the difference between the two volumes to find the volume of the segment.
Step 4: The volume of the segment is (πh2(3r-h))/3.
To calculate the volume of the segment formed when a sphere of radius r is cut by a plane, we use the formula for the volume of a spherical segment. First, we calculate the volume of the sphere using the formula V = (4/3)πr3, then the volume of the cone using the formula V = (1/3)πr2h. By subtracting the two volumes, we find the volume of the segment, which is (πh2(3r-h))/3. This formula is useful in finding the volume of any segment formed when a sphere is cut by a plane.
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find the volume of the solid with semi-circular cross sections whose bases lie in the xy-plane on [0,9] and diameters run from y
The volume of the solid is equal to the integral of the area of the semi-circular cross sections multiplied by the length of the interval. The area of the semi-circular cross sections is equal to πr²/2, where r is the diameter running from y. Therefore, the volume is equal to π/2∫0,9r²dy.
Step 1: Substitute the expression for the area of the semi-circular cross section into the equation for the volume of the solid:
V = π/2∫0,9r²dy
Step 2: Integrate the equation to find the volume of the solid:
V = π/2[y³/3]|0,9
Step 3: Evaluate the integral:
V = π/2(9³/3 - 0³/3)
step 4: Solve for the volume of the solid:
V = 7π/2
The volume of the solid is equal to the integral of the area of the semi-circular cross sections multiplied by the length of the interval. The area of the semi-circular cross sections is equal to πr²/2, where r is the diameter running from y. Therefore, the volume is equal to π/2∫0,9r²dy. To calculate the volume, we must first substitute the expression for the area of the semi-circular cross sections into the equation for the volume of the solid: V = π/2∫0,9r²dy. Then, we must integrate the equation to find the volume of the solid: V = π/2[y³/3]|0,9. After that, we must evaluate the integral: V = π/2(9³/3 - 0³/3). Finally, we must solve for the volume of the solid: V = 7π/2. The answer is the volume of the solid is 7π/2.
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a gallup poll utilizing a random sample of adults ages or older was conducted in april . the survey indicated a majority of americans () say driverless cars will be common in the next years (gallup,
A Gallup poll conducted in April found that 55% of Americans believe driverless cars will be common in the next 10 years, as presented in a histogram showing the percentage of responses in different time intervals.
A Gallup Poll was conducted in April that surveyed adults aged 18 or older to gauge their perceptions on when fully automated "driverless cars" will be commonly used in the United States.
The question asked was "how soon do you think driverless cars will be commonly used in the United States?" The survey indicated that 55% of Americans believe that driverless cars will be common in the next 10 years.
The results of the survey were presented in a histogram, showing the percentage of responses in different time intervals, which means it shows how many people responded within a certain time frame (e.g. within 5 years, within 10 years, etc.) when they think driverless cars will be commonly used.
This poll gives an insight into how people perceive the future of driverless cars and how soon they think it will become a common sight on the roads.
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The question is -
A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.
find the area of this figure. round your answer to the nearest hundredth. use 3.14 to approximate pi A= ? m^2
The area of the given figure is 51.63 m².
What is an Area ?
Area in geometry refers to the volume occupied by a flat shape on a plane, such as a polygon, circle, or ellipse. A shape's area is always expressed in square units.
The area of the given figure = area of given triangle + area of given rectangle + area of given semi circle.
(I) area of given triangle
= 1/2 × base × height
= 1/2 × 3 × 5
= 7.5m².
(II) area of given rectangle
= length × breadth
= 6 × 5 = 30m².
(III) area of given semi circle
= πr²/2
here, r = 3 m ( 6m/2)
So, πr²/2 = (3.14 × 3² )/2
= 28.26/2
= 14.13 m².
Hence, The area of the given figure = 7.5 + 30 + 14.13
= 51.63 m².
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In June 2008, 88%88% of automobile drivers filled their vehicles with regular gasoline, 2%2% purchased midgrade gas, and 10%10% bought premium gas. Of those who bought regular gas, 28%28% paid with a credit card. Of customers who bought midgrade and premium gas, 34%34% and 42%42%, respectively, paid with a credit card. Suppose we select a customer at random. (a) Construct a tree diagram to represent this situation. (b) Find the probability that the customer paid with a credit card. Show your work. (c) Given that the customer paid with a credit card, find the probability that she or he bought premium gas.
The probability that the customer paid with a credit card is 25% and the customer bought premium gas given that she or he paid with a credit card is 16.8%.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
To find the probability that the customer paid with a credit card, we can use the law of total probability.
P(credit card) = P(credit card | regular gas) * P(regular gas) + P(credit card | midgrade gas) * P(midgrade gas) + P(credit card | premium gas) * P(premium gas)
P(credit card) = 0.28 * 0.88 + 0.34 * 0.02 + 0.42 * 0.1 = 0.25
So, the probability that the customer paid with a credit card is 25%.
Given that the customer paid with a credit card, we can find the probability that she or he bought premium gas using Bayes' theorem:
P(premium gas | credit card) = P(credit card | premium gas) * P(premium gas) / P(credit card)
P(premium gas | credit card) = 0.42 * 0.1 / 0.25 = 0.168 or 16.8%
So, the probability that the customer bought premium gas given that she or he paid with a credit card is 16.8%.
Hence, the probability that the customer paid with a credit card is 25% and the customer bought premium gas given that she or he paid with a credit card is 16.8%.
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Help please I think I’m not sure which one is the answer, confused!!!
the radius of the wheelsof car is 35cm the car take 1 hour to cover 66 km find the number of revolution that the wheel of the car makes in one minute
The wheel of the car makes 500.5 revolution per minute
What is frequency?frequency is defined as the number of oscillation or revolution made in one seconds. It measured in Hertz. frequency is denoted as F. And it is expressed as :
F = w/2π
Where w = angular velocity and
2π = 360 which is also a revolution
to calculate w ;
v = wr
r = 35cm = 0.35m
v = 66km/h = 66×1000/60
v= 1100m/mins
therefore from the relation, v = wr
w = v/r
w = 1100/0.35
w = 3142.9rad/mins
therefore F = w/2π
F = 3142.9/ 2×3.14
F = 500.5 revolution per minute
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HELP ME PLEASE. only need the answer pls and thanks
The value of the expression → p(q(-1)) will be → 5.
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.Any subset of the Cartesian product of two sets X and Y defines a binary relation R ⊆ X × Y between these two sets.A binary relation is univalent (also called right-unique) if -[tex]${\displaystyle \forall x\in X,\forall y\in Y,\forall z\in Y,\quad ((x,y)\in R\land (x,z)\in R)\implies y=z.}[/tex]
A binary relation is total if -[tex]${\displaystyle \forall x\in X,\exists y\in Y,\quad (x,y)\in R.}[/tex]
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the graphs of two function as shown in the image.
We have to find -
p(q(-1))
Now, we can see from the graph that -
q(-1) = -2
Then, p(q(-1)) will be -
p(-2) = 5
Therefore, the value of the expression → p(q(-1)) will be → 5.
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Three times a number minus 6 is equal to two times the sum of a number and 8.
Write as a equation
An amendment to the U.S. Constitution must be ratified by at least three fourths of the states to become law. Write this ratio as a percent.
The ratio of the stated that became law would be represented as = 75%
What is percentage?Percentage is defined as the representation of a part of a data as per 100.
The part of states that needs to be ratified = 3/4
To represent this portion in percentage, × by 100
That is,
= 3/4× 100
= 300/4
= 75%
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grass clippings are placed in a bin, where they decompose. for 0 30 t , the amount of grass clippings remaining in the bin is modeled by 6.687 0.931 t a t , where a t( ) is measured in pounds and t is measured in days. (a) find the average rate of change of a t over the interval 0 30 t . indicate units of measure
The average rate of change of a t over the interval 0 30 t is 0.03 pounds per day.
To find the average rate of change, we need to calculate the slope of the line representing the function a t( ) over the interval 0 to 30.
The slope is calculated by taking the change in a t over the change in t.
We can calculate the change in a t by subtracting the a t value at the start of the interval (0) from the a t value at the end of the interval (30):
a t (30) - a t (0) = 6.687 - 0 = 6.687
We can calculate the change in t by subtracting the t value at the start of the interval (0) from the t value at the end of the interval (30):
t (30) - t (0) = 30 - 0 = 30
We can now calculate the slope by dividing the change in a t by the change in t:
Slope = 6.687 / 30 = 0.03
The average rate of change of a t over the interval 0 30 t is 0.03 pounds per day.
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Determine the seating capacity of an auditorium with 35 rows of seats if there are 20 seats in the first row, 25 seats in the second row, 30 seats in the third row, 36 seats in the fourth row, and so on.
Total number of seats=_____.
The total number of seats in the auditorium is 3500.
What is the arithmetic series?
An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is always the same. It can also be defined as a sum of a finite number of terms of an arithmetic progression.
The seating capacity of the auditorium can be found by using the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is:
S = n/2 (2a + (n-1)d)
Where:
S is the sum of the series (total number of seats)
n is the number of terms in the series (number of rows of seats)
a is the first term in the series (number of seats in the first row)
d is the common difference between terms in the series (increase in number of seats per row)
In this case,
a = 20 (number of seats in the first row)
d = 25 - 20 = 5 (increase in number of seats per row)
n = 35 (number of rows of seats)
So,
S = 35/2 (2(20) + (35-1)(5))
S = 35/2 (40 + 160)
S = 35/2 (200)
S = 35*100
S = 3500
Hence, the total number of seats in the auditorium is 3500.
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Procedure: Pick a number. Add 5 to the number and multiply the sum by 3. Subtract 7 and then decrease this difference by the triple of the original number.
Answer:
(3n +8) -3n = 8
Step-by-step explanation:
You have the difference (3n+15) -7, and you want its value when it is decreased by the triple of the original number (n).
Triple the numberThe phrase "triple the original number" will be translated to 3n. This is the value you want to subtract.
(3n +15) -7 = 3n +8 . . . . . "the difference"
(3n +8) -3n = 8 . . . . . . . . "decreased by triple the original number"
This simplifies to 8, which is the point of the exercise: showing the sequence of steps always gives a value of 8.
Y interslope =
Slope=
Y-intercept is the point on the graph where the line crosses y-axis.
Slope of a line is the proportion of difference of y-coordinates to difference of x- coordinates.
What is a line?
A line is an object which has only one dimension i.e. it has only length and not width. A line is made up of several points that are endlessly stretched in the opposing directions.
Y-Intercept
It is a point on the graph where the line crosses y-axis. We know that any point on y-axis has its x-coordinate as 0. Therefore, for y-intercept, its x-coordinate is 0.
Slope
It is the proportion of difference of y-coordinates to difference of x- coordinates. The symbol 'm' denotes the slope.
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
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Question: Y-Intercept=
Slope=
run a regression analysis on the following data set, where y is the final grade in a math class and x is the average number of hours the student spent working on math each week. hours/week x grade y 5 52 5 44 11 67.4 13 89.2 13 75.2 14 92.6 15 87 16 84.4 17 86.8 17 88.8 State the regression equation y=m⋅x+by=m⋅x+b, with constants accurate to two decimal places.
What is the predicted value for the final grade when a student spends an average of 8 hours each week on math?
Grade = Round to 1 decimal place.
Expert Answer
The regression equation is y = 15.98x + 43.76. The predicted value for the final grade when a student spends an equation of 8 hours each week on math is 87.8.
The regression equation is found by using a linear regression analysis. First, the data points are plotted on a graph. Then, the best-fit line is determined. The equation of the line is then calculated by finding the slope (m) and y-intercept (b).
The slope (m) is calculated by taking the difference between the two y-values divided by the difference between the two x-values.
m = (y2 - y1) / (x2 - x1)
The y-intercept (b) is calculated by substituting the values of m and one of the data points into the equation of a line, and solving for b.
b = y - mx
Once the values of m and b are determined, the regression equation can be determined:
y = mx + b
For this data set, the regression equation is y = 15.98x + 43.76.
To find the predicted value for the final grade when a student spends an average of 8 hours each week on math, the value of x is substituted into the equation, and the result is rounded to one decimal place.
y = 15.98(8) + 43.76
y = 87.8
Therefore, the predicted value for the final grade when a student spends an average of 8 hours each week on math is 87.8.
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