The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.
We have been given parametric equations x = t^2 − 3t, y = √t
We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.
Consider x = 0
So, t^2 − 3t = 0
t(t - 3) = 0
t = 0 or t = 3
Let f(t) = t^2 − 3t and g(t) = t
Differentiate the curve f(t) with respect to t.
f'(t) = 2t - 3
NWe know that the formula to find the area under the curve.
A = ∫[a to b] g(t)f'(t) dt
here, a = 0 and b = 3
so, A = ∫[0 to 3] √t (2t - 3) dt
A = ∫[0 to 3] (2t√t - 3√t) dt
A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt
A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]
A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0
A = 4/5 3^(5/2) - 2 3^(3/2)
A = 6√3 /5
A = 2.08
Therefore, the area of the curve is 2.08 square units.
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The data on the table decribe the preferred type of muic a urveyed by 9th grader. Rock Pop Hip Hop Total Male 20% 17% 10% 47% Female 16% 28% 9% 53% Total 36% 45% 19% 100% Compare the conditional relative frequencie of a male preferring pop muic to a female preferring pop muic. Round your anwer to two decimal place. 0. 47 to 0. 53 0. 37 to 0. 62 0. 36 to 0. 53 0. 17 to 0. 28
The conditional relative frequencie of a male preferring pop music to a female preferring pop music is equals to 0.53/0.47 or 0.53 to 0.47. So, correct answer is option(A).
What is Two-way frequency table?Two-way frequency tables are powerful tools for examining relationships between categorical variables. The entries in the main part of the table are common frequencies. The entries in the "Total" row and "Total" column are limit frequencies. Relative frequencies are used when comparing different classes and classes to the entire data set. The relative frequencies in the body of the table is known as the conditional frequencies. We have a data on the table which decribe the preferred type of music (Rock, Pop and Hip Hop ) a surveyed by females and males as seen above table. We calculated the relative frequencies for each music type so that we should compare the data more reliably. Now, the relative frequency for males who prefer pop music = 10/19
= 0.53
the relative frequency for females who prefer pop music = 9/19 = 0.47
Based on the data collected, males are more likely to prefer pop music than females. The conditional relative frequencie of a male preferring pop music to a female preferring pop music is equals to 0.53/ 0.47 . So, required conditional relative frequency is 0.53/ 0.47 .
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Complete question:
The data on the table decribe the preferred type of muic a urveyed by 9th grader. Rock Pop Hip Hop Total Male 20 17 10 47 Female 16 28 9 53 Total 36 45 9 100 Compare the conditional relative frequencie of a male preferring pop muic to a female preferring pop muic. Round your anwer to two decimal place.
A) 0. 53 to 0. 47
B)0. 37 to 0. 62
C) 0. 36 to 0. 53
D) 0. 17 to 0. 28
The measures of the angles of △RST are given by the expressions in the table
In the given angles, the values of R=31⁰, x=34⁰, m<S= 38⁰, m<Y = 111⁰
How to find angles of a triangles?We know that a triangle is a polygon whose sum of angles is equal to 180 degress , with three sides and three vertices.
The given angles are
31⁰, (x+4)⁰, (3x+9)⁰
The sum of angles of the triangle
31+x+4+3x+9=180⁰
44+4x=180⁰
Collecting like terms
4x=136
Dividing by 4
x=34⁰
Substituting the value of x=34 in the given angles we have
R= 31⁰, given
(x+4)⁰ = 34+4=38⁰, (3*34+9)⁰=111⁰
In conclusion the values of R= 31⁰, x=34⁰ , m<S=38⁰, m<T=111⁰
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Aisha walked 3 days in a row. She walked the same distance each day. This model represents the situation. Each column represents one mile and the shaded parts of each column represent the fraction of a mile that Aisha walked each day. Which expression can be used to determine the total distance in miles Aisha walked over the 3 days?
An expression which can be used to determine the total distance in miles that Aisha walked over the 3 days is: C. 3 × 3/4.
What is distance?In Science, distance can be defined as the amount of ground that is covered (travelled) by a physical object over a particular period of time and speed, irrespective of its direction, starting point or ending point.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities.
From the information provided, we know that Aisha walked three (3) days in a row and three (3) miles out of four (4) miles. Therefore, a mathematical expression that represents the total distance in miles that she walked over the three (3) days is given by;
Total distance = 3/4 + 3/4 + 3/4
Total distance = 3 × 3/4
Total distance = 9/4 or 2.25 miles.
In conclusion, Aisha walked a total distance of 9/4 miles or 2.25 miles over the three (3) days.
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Find the lengths of the hypotenuses (x) of the triangle whose legs are given
1) 12cm,16cm
Answer:
Step-by-step explanation:
The hypotenuses(x) of the triangle whose legs are 12 cm and 16 cm is 20 cm.
As we know that in a right angled triangle there are base, perpendicular and hypotenuse. a hypotenuse is the longest side of a right triangle. In other words, the side opposite to the right angle is called the hypotenuse.
Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
By Pythagoras theorem, hypotenuse (x) = √(a² + b²)
= √(16² + 12²)
= 20 cm
Pls help I inserted a picture
The inequality is 7<x<31.
What is inequality ?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The third side of any triangle must be more than the difference between the other two sides.
x>19-12
x>7 (or) 7<x
The third side of any triangle must be less than the sum of the other two sides.
x<19+12
x<31 (or) 31>x
Put them together.
7<x<31 (or) 31>x>7
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adam has collected the birth rates, gender, age, and total population numbers for akron, ohio. what population statistic could adam calculate with this information?
By the age of four, Adam knows that changing one's exterior characteristics does not change one's gender. Adam has "acquired" or "learned" gender constancy.
Which of the three stages of gender constancy are you?
A child's developing sense of the permanency of being a boy or a girl, which happens in stages: gender identification, gender stability, and gender consistency. Gender constancy is similar to Piaget's concept of physical property conservation in that gender constancy relates to the awareness that gender is an invariant human property that is stable through time and superficial changes in appearance. It starts at the age of six or seven, when a youngster realizes that gender remains consistent across settings (e.g. if a man puts on a dress he is still a man).
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The polygons in each pair are similar. Find the
missing side length.
40
Type your answer...
20
?
4
Answer:
8
Step-by-step explanation:
40:20
x:4
20/4 = 5
40/5 = 8
A land developer is splitting up 1.31 hectares of land to form 5 identical properties. What size will each property be?
Answer:
0.262 hectares
Step-by-step explanation:
To find the size of each property, you need to divide the total area of the land by the number of properties. In this case, the total area of the land is 1.31 hectares, and it is being divided into 5 properties, so the size of each property is:
Property size = 1.31 hectares / 5 properties = 0.262 hectares/property
Therefore, each property will be 0.262 hectares in size.
Write the equation of the line in Standard Form
passing through the point (2,-5) with a slope of 4.
Step-by-step explanation:
[tex]y - y1 = m(x - x1[/tex]
[tex]y - - 5 = 4(x - 2)[/tex]
[tex]y + 5 = 4x - 8[/tex]
[tex]y= 4x - 8 - 5[/tex]
[tex]y = 4x - 13[/tex]
[tex]y = 2x - 13 \div 2[/tex]
- Which expression has the same meaning as p 11/5?
Answer:
[tex]5\sqrt{p} ^{11}[/tex]
answer the following questions
and get 20 points
Answer:
3/7 ; -7
Step-by-step explanation:
1)
(7-4)/(10-3)
3/7
2) -7 because is the number that multiplies x
Which problems can be solved by performing this multiplication? 2/3×18
Answer:
Matthew has 24 inches of green ribbon and 3/4 inch of yellow ribbon. How much ribbon does he have in all?
Kiki had 24 marbles. She put 3/4 of the marbles in a jar. How many marbles did she put in the jar?
There were 24 questions on a test. Three-fourths of the questions were science questions. How many questions were science questions?
Aisha baked 24 muffins. She gave 3/4 of the muffins to her friends. How many muffins does she have left?
Step-by-step explanation:
Answer:
Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes?
Min had 18 quarters. He used 2/3 of the quarters to play arcade games. How many quarters did Min use?
Step - by - step explanation
2/3 × 18
Checking all options
Sarah mixed 18 ounces of orange juice with 23 ounce of pineapple juice. How many ounces of juice did she have in all?
Ounces of orange juice = 18
Ounces of pineapple juice = 23
Total ounces of juice = 18 + 23
= 41 ounces
A container held 18 ounces of water. Two-thirds of the water leaked out of the container. How many ounces of water were left in the container?
Total water in the container = 18
Water leaked out = 2/3
Ounces of water left = 18 - 2/3(18)
= 18 - 36/3
= 18 - 12
= 6
Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes?
Total Number of coins = 18
Dimes = 2/3 of 18
Number of dimes = 2/3 × 18
= 36 / 3
= 12
Min had 18 quarters. He used 2/3 of the quarters to play arcade games. How many quarters did Min use?
Total quarters = 18
Quarters used for game = 2/3 × 18
= 2/3 × 18
= 36 / 3
= 12
Can anyone help me do this?
Answer:
yellow
Step-by-step explanation:
i can only see one line, and infinitely many points are on it
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A salesperson earns $1000 a month plus a commission of 20% of sales. Find the minimum
amount of sales needed to receive a total income of at least $5000 per month. (Write
an inequality and solve.)
Answer:
5000
Step-by-step explanation:
1000+0.8s < 5000
subtract 1000 from both sides of the inequality
0.8s < 4000
divide both sides by 0.8 to get the number of sales (s)
s <5000
Two payment options to rent a car: You can pay $25 a day plus 5¢ a mile (Option A) or pay $15 a day plus 30¢ a mile (Option B). For what amount of daily miles will option B be the cheaper plan?
Consider continuous functions f and g. then complete the statement. function g is the sum of 2 and the cube root of the sum of three times x and 1. select the correct answer from each drop-down. the x-intercept of function f is the x-intercept of function g.
The x-intercept of the function f is greater than the x-intercept of function g is the correct statement.
What is x-intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
How to find x-intercept?Setting y = 0 will provide the x-value at which the line crosses the x-axis, allowing us to find the x-intercept
Function g(x) is defined as:
g(x)=2+[tex]\sqrt[3]{3x+1}[/tex]
and f(x)=0
To find x-intercept let g(x)=0
So
2+[tex]\sqrt[3]{3x+1}[/tex]=0
[tex]\sqrt[3]{3x+1}[/tex]=-2
Taking cube on both sides we get
3x+1= -8
3x=-9
x=-3
The x-intercept of g(x) + -3, which is less than the x-intercept of function f(x), hence, the correct statement is:
The x-intercept of the function f is greater than the x-intercept of function g.
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Find three rational numbers such that their product is 210. The second number is 5 less than the first. The third number is 1 more than twice the first.
Answer:
7,2,15
Step-by-step explanation:
In general, to find rational numbers that satisfy a given set of conditions, it is often helpful to first write an equation that relates the numbers to each other.
The three rational numbers are 7, 2 and 15
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
First Number= x
Second Number= x- 5
Third Number = 2x+ 1
so, the product of the three number be 210
x(x-5 )(2x+ 1)= 210
(x² -5x )(2x+ 1)= 210
2x³ + x² - 10x² - 5x= 210
2x³ -9x² -5x -210=0
On solving the equation we get only one real value 7 and other values are imaginary.
Then, the number are
x= 7
2-x-5 = 2
2x+1 = 15
Hence, the three rational numbers are 7, 2 and 15.
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brine flows into a conical tank at a constant rate of 3 cubic feet per minute. the radius of the cone is 5 feet and its height is 12 feet. how fast is the radius increasing when the radius is 2 feet? group of answer choices
Using the values provided and a derivative of the cone's volume formula, the result is 0.059 feet per minute.
What does "derivative" mean to you?In mathematics, the rate at which a function changes in relation to a variable.
What is a cone and how does it calculate volume?A cone is a three-dimensional geometric structure that has a smooth transition from a flat base that is typically circular to the point at the top, which is also referred to as the apex or vertex.
The formula for cone volume is:
V=πr2h/3
yields the formula for cone volume:
dv/dt = 2r * h/3 * dr/dt dV/dt = 3 r=2 h=12
dr/dt = 0.059 feet per minute.
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Please help please! No fake answers pls
Answer:
x= 30
Step-by-step explanation:
Angle E
E + F + G = 180
E + 60 + 90 = 180
E + 150 = 180
E = 180-150
E = 30
Angle E is congruent to angle X so the measures must be the same
E = X = 30
X = 30
Answer:
[tex]E=30[/tex]
Step-by-step explanation:
[tex]E + F + G = 180\\E + 60 + 90 = 180\\E + 150 = 180 \\E= 180-150 = 30[/tex]
Hope this helps u :)
Please help solve this inequality question, with explanation.
x ≥ -26 / (6a - 15) where a >5/2.
What are inequalities?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.
Given a equation, (3ax + 2)/ 3 - (5x / 2) ≥ -8 where a > 5/2
solving for x in terms of a
ax + 2/3 - 5x/2 ≥ -8
x(6a - 15 ) ≥ -26
x ≥ -26 / (6a - 15)
since a is greater than 5/2 let a be 3 than the value of x ≥ -26/3.
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sets.
6. Which of the following BEST completes the
statement: "Net Income is a measure of..."
[A] the overall decrease in wealth over a period
and can be calculated by subtracting gross
income from expenses.
[B] the overall increase in expenses.
[C] the overall increase in liabilities over a period
and can be calculated by subtracting income
from expenses.
[D] the overall increase in wealth over a period
and can be calculated by subtracting expenses
from gross income.
[E] the overall decrease in expenses.
Net income is the overall increase in wealth over a period and can be calculated by subtracting expenses.
Option D is the correct answer.
What is net income?Net income is the amount remaining after deducting the expenses from the revenue collected.
We have,
Consider,
Amount collected after production of items = $400
Cost of production of the items = $250
Net income.
= Amount collected - Cost of production
= 400 - 250
= $150
Thus,
Net income is the overall increase in wealth over a period and can be calculated by subtracting expenses.
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Use the graph to write the factorization of x² + 4x - 5?
The quadratic function x² + 4x - 5 is factorized to give
(x + 5) (x - 1)
How to find the factorization of the quadratic expression from the graphThe given quadratic function is x² + 4x - 5
The graph is plotted and the roots of the equation which is the x intercepts that is the points where the graph cuts the x axis is found to be points 1 and -5
Using points 1 and -5 the equation is sort as follows
for 1
x = 1
x - 1 = 0
for -5
x = -5
x + 5 = 0
bringing the solutions together
(x + 5) (x - 1)
The solution is (x + 5) (x - 1)
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a boat moves 8 kilometers upstream in the same amount of time it moves 20 kilometers downstream. if the rate of the current is 5 kilometers per hour, find the rate of the boat in still water.
if the rate of the current is 5 kilometers per hour, The rate of the boat in still water is 15 km/h.
The rate of the boat in still water is the rate of the boat when the current is not affecting its motion, so we can calculate the rate of the boat in still water by subtracting the rate of the current from the rate of the boat while moving downstream and adding the rate of the current to the rate of the boat while moving upstream. In this case, the rate of the boat while moving upstream is 8 km/h, and the rate of the boat while moving downstream is 20 km/h. Since the rate of the current is 5 km/h, we can subtract 5 km/h from 20 km/h to get the rate of the boat in still water, which is 15 km/h.
Rate of boat in still water = Rate of boat while moving downstream - Rate of current + Rate of boat while moving upstream
= 20 km/h - 5 km/h + 8 km/h
= 15 km/h
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Which of the following is a polynomial function? c. f(x) = V2x3 + 5 A. y = x 3 + 2x2 + x - 1 B. y = - 2x3 + 5x – 4 - 4 D. f(x) = x3 +1.
A polynomial function is a mathematical function defined by an expression that is a sum of terms, each of which is a product of a constant and a non-negative integer power of a variable. The term "polynomial" comes from the Greek word "polys," which means "many," and "nomos," which means "terms." Polynomial functions are distinguished by the degree of their highest-degree term, which is the largest exponent of the variable. For example, the polynomial function f(x) = x3 + 2x2 + x - 1 has a degree of 3 because the highest-degree term is x3.
Out of the four given options, only the functions f(x) = x3 + 2x2 + x - 1 and f(x) = x3 +1 are polynomial functions. The other two options, y = -2x3 + 5x – 4 - 4 and f(x) = V2x3 + 5, are not polynomial functions because they contain terms that are not of the form "constant times a non-negative integer power of a variable." The function y = -2x3 + 5x – 4 - 4 contains the term -4, which is not a product of a constant and a non-negative integer power of a variable, and the function f(x) = V2x3 + 5 contains the term V2x3, which is not a product of a constant and a non-negative integer power of a variable. Therefore, the correct answer is A and D.
in 2010, husson had 2000 undergraduate students. in 2018, husson had 2800 undergraduate students. find the percent increase in enrollment, and round to the nearest percent.
the percent increase in enrollment, and round to the nearest percent is 40%
Given that number of students enrolled in 2010= 2000
Given that number of students enrolled in 2018 = 2800
2800is more than 2000 so that means number of students enrollment is increasing.
increase = 2800-2000= 800
Percent increase is given by formula:
% increase = 800/2000*100= 40
which is approx 40%.
Hence final answer is that enrollment increases by 40%
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Which must be true? point a is the center of the circle that passes through points e, f, and g but is not the center of the circle that passes through points x, y, and z. Point a is the center of the circle that passes through points x, y, and z but is not the center of the circle that passes through points e, f, and g. Point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z. Point a is not necessarily the center of the circle that passes through points e, f, and g or the center of the circle that passes through points x, y, and z.
The statements which must be true is statement 4 which is :-
Point a is not necessarily the center of the circle that passes through points e, f, and g or the center of the circle that passes through points x, y, and z.
3 points uniquely define a circle. so points e,f and g uniquely defines a circle C1 and point x,y and z uniquely defines a circle C2.
The below figure shows the condition that 2 different circle C1 and C2 can have same center , point a and this conditon occurs when they are concentric circle so statement 1,2 is false as in these statement it is told that point a can be center of only one circle but point a can be center of more than 1 circles.
and it is also possible that these 2 different cirlce C1 and C2 can have different center which is 2 different circle ,so statement 3 is also false.
so only statement which must be correct statement is 4 as in this case point a might be center of circle C3 which is neither C1 or C2.
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Answer: C
Step-by-step explanation: because I am amazing
the scatterplot below shows the performance of a thermocouple. which answer choice correctly indicates the explanatory variable and the response variable for the scatterplot?
The performance of a thermocouple is displayed in the scatterplot is
Explanatory variable: Temperature
Response variable: Voltage
Given that,
The performance of a thermocouple is displayed in the scatterplot below.
We have to find which of the following choices accurately identifies the explanatory and response variables for the scatterplot.
We know that,
Dots are used to indicate the values for two different numerical variables in a scatter plot (also known as a scatter chart or scatter graph). The positions of each dot on the horizontal and vertical axes represent the values of a single data point. To see how different variables relate to one another, utilize scatter plots.
Explanatory variable: Temperature
Response variable: Voltage
So, we can see the scatterplot in the picture.
Therefore, Explanatory variable: Temperature
Response variable: Voltage when the performance of a thermocouple is displayed in the scatterplot
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Answer:
Explanatory variable: Temperature
Response variable: Voltage
Step-by-step explanation:
Got it right on the test.
pls help almost done!
Answer:
Step-by-step explanation:
same as the last one, hope you are getting these better now.
minor angle (interior angle) J is the same as angle t, b/c of the red marks.
180 = 141 = ∠j
39 = ∠j
t = 39
then find s
180 = 2*t +s
180 = 2*39 +s
180 =78 +s
180-78 = s
102 = s
got it better now?
Jimm toed a die everal time. He got the number "3" on 8 of the toe. What i the bet etimate of the total number of time he toed the die?
The best estimate to get the total number of times to get a "3" will be 24 times.
This is an expression that simply refers to mathematical statements that have at least two terms which are related by an operator and contain either numbers, variables
In this case, Jimm tossed a die several times and he got the number "3" on 8 of the tosses.
Therefore, when there are 64 tosses, the estimate will be:
= 3/8 × 64
= 3 × 8
= 24
The number of times is 24.
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In the given figure, △ADE ∼ △ABC. Which triangle similarity theorem justifiesthis similarity? Show proof toyour answer.
5. a. Using the figure below, name the three similar triangles.
b. Write the proportions that exist among corresponding parts of similar
triangles.
Option a) The similar triangles are ⇒ ΔADE ≅ ΔABC
Option b) ∠ADE = ∠ABC
According to the figure given in the question,
We can observe that there are two right-angled triangles present and we have to derive the similarities between them
Let one triangle be = ΔADE
Another triangle be = ΔABC
Let us consider the angle arc at point A,
We can conclude that ⇒ ∠BAC = ∠DAE ( according to the property of similar angles )
⇒ ∠ADE = ∠ABC ( by the similar 90° angles )
and both angles are making a total of 180°
So, from the above expressions, we can say that,
⇒ ∠AED = 180° - ∠A - ∠ABC
⇒ ∠ACB = 180° - ∠A - ∠ABC
Hence, ∠AED = ACB ⇒ ΔADE ≅ ΔABC
Therefore,
Option a) The similar triangles are ⇒ ΔADE ≅ ΔABC
Option b) ∠ADE = ∠ABC
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