The rate of change of the area of a square is 12m^2/sec.
What do you mean by rate of change?
The term "rate of change" refers to the rate at which one quantity changes in respect to another. Consequently, if y value is the dependent variable and x value is the independent variable.
Rate of Change is equal to [tex]\frac{Change in y}{Change in x}[/tex].
Change rates may be positive or negative. This reflects a change in the y-value between the two data points, either up or down. Zero rate of change is the state where a quantity does not change over time.
Solution Explained:
Given,
S = 2m and ds/dt = 3m/s
So, we use
Area = s^2
dA/dt = 2s ds/dt
= 2 X 2 X 3
Therefore, the rate of change of the area is 12m^2/s.
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Question 10 of 10
What is the slope of a line that is parallel to y = 3x+ 5?
Answer:
[tex]\huge\boxed{\sf 3}[/tex]
Step-by-step explanation:
Given slope-intercept equation:y = 3x + 5
Comparing it with standard form of slope-intercept equation i.e. y = mx + b.
Where,
m = slope = 3
b = y-intercept = 5
A line that is parallel to this line will have the same slope as this line.
So, it will also have a slope of 3.
[tex]\rule[225]{225}{2}[/tex]
A group of friends wants to go to the amusement park. They have no more than $115 to spend on parking and admission. Parking is $15, and tickets cost $25 per person, including tax. Write and solve an inequality which can be used to determine xx, the number of people who can go to the amusement park
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $115 to spend on parking and admission. Parking is $15, and tickets cost $25 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.
115 ≥ 25p + 15
115 ≥ 25p + 15
subtract 15 from both sides:
115 - 15 ≥ 25p + 15 - 15
100 ≥ 25p
divide both sides by 25:
100/25 ≥ 25p/25
4 ≥ p
4 people
The number of people who can go to the amusement park is 4.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number lineby their size.
Given that, the money to be spend, is no more than $115 to spend on parking and admission.
Parking is $15, and tickets cost $25 per person, including tax.
we need to determine the maximum number of people that can go to the park,
115 ≥ 25p + 15
115 ≥ 25p + 15
subtract 15 from both sides:
115 - 15 ≥ 25p + 15 - 15
100 ≥ 25p
divide both sides by 25:
100/25 ≥ 25p/25
4 ≥ p
Hence, the number of people who can go to the amusement park is 4.
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unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression . multiple choice can be greater than 1 measures the percentage of variation explained by the regression line indicates whether the slope of the regression line is positive or negative is a proportion
the regression line indicates whether the slope of the regression line is positive or negative is a proportion will be between 0 to 1
Regression is a statistical method that links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether variations in the dependent variable are related to variations in one or more of the explanatory variables.
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1. Marcus is training for a bike race and has biked 25 miles this week. He needs to bike at least
80 miles this week to complete his training. How many miles should Marcus bike on each of the 5
remaining days this week?
Answer: 11 miles each day for the remaining 5 days
Step-by-step explanation:
First, you subtract the miles already done (25) from the total (80) to get 55 (miles left to do) then next divide 55 by 5 (days left), and then your left with 11. Finally, check the work and see how 11x5=55 then 55+25=80.
That's how to get the answer :)
16. if alexa's car can typically travel 300 miles on a full tank of gasoline, and if her car's tank can hold 18 gallons, then at this rate how far should the car be able to travel on 12 gallons of gasoline?
The distance covered by the car with 12 gallons of gasoline is 200 miles.
Given,
Distance travelled by a car with full tank gasoline = 300 miles
The capacity of the car's tank = 18 gallons
We have to find the distance covered by the car with 12 gallons of gasoline;
Here,
x be the distance covered by the car with 12 gallons of gasoline
Then,
300/18 = x/12
x = (300 x 12) / 18
x = (300 x 2) / 3
x = 100 x 2
x = 200 miles
That is,
The car will cover 200 miles with 12 gallons of gasoline.
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if olive construction company gets the job, what is the probability that base construction company did not bid?
If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.
The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
So, the probability that the base construction company did not bid:
[tex]\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}[/tex]
Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.
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3 Isosceles Trapezoid
128°
y is to the left of it
X is diagonal to it
What is x and y
Answer:
x = 52°y = 128°Step-by-step explanation:
Base angles are congruent.
[tex]\tt y=128^o[/tex]
Let's solve for x first:-
[tex]\tt x+y=180^o[/tex]
[tex]\tt x=180-y[/tex]
[tex]\tt x=180-128[/tex]
[tex]\tt x=52^o[/tex]
Therefore, x = 52° and y = 128°
_________________
Hope this helps you!
Have a nice day! :)
What is h, the height of the tree? use the law of sines to first find at. Then use that measure to find the value of h. 3. 0 yards 3. 2 yards 3. 8 yards 4. 4 yards.
The measured height of the tree is found as 3.2 yards.
Explain the term trigonometric relation?Trigonometric ratios are based on the measurement of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. These trigonometric ratios of a given acute angle are the ratios of the sides of such a right-angled triangle in respect to that angle.Let 'h' be the height of the three.
Let distance between student A and tree = x.
Using trigonometric relation;
tan 57 = h/x
x = h/tan 57 ......eq 1
tan 46 = h/(x + 1)
x + 1 = h/tan 46 ......eq 2
Equation eq 1 and eq 2.
h/tan 57 + 1 = h / tan 46
h / tan 46 - h / tan 57 = 1
Further solving,
h(tan 57 - tan 46) = tan 46.tan 57
h = tan 46 tan 57 / (tan 57 - tan 46)
h = 3.2 yards
Thus, the measured height of the tree is found as 3.2 yards.
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The complete question is-
Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.
What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.
A) 3.0 yards
B) 3.2 yards
C) 3.8 yards
D) 4.4 yards
Answer: 3.2 is correct
Step-by-step explanation:
edge 2023
At a clothing store, ted bought 4 shirts and 2 ties for a total price of $95. At the same time store, stephen bought 3 shirts and 3 ties for $84. Each shirt was the same price, and each tie was the same price. Which system of equations can be used to find s, the cost of each shirt in dollar, and t, the cost of each tie in dollars ?.
The required system of equation for the cost of shirt and tie are-
4s + 2t = 953s + 3t = 84 Explain the term system of equations?simultaneous equations, or a system of equations, In order for two or so more equations in algebra to be solved jointly, the system's equations must all be satisfied by the solution. The quantity of equations must match the number of unknowns for a system to have a singular solution.For the stated question-
Ted spent a total of $95 on 4 shirts and 2 ties from a clothes store. Stephen spent $84 on three shirts and three ties at the same time store. Each shirt and each tie cost the same amount.Let 's' be the cost of each shirt.
Let 't; be the cost of each tie.
Then, the equations become-
4s + 2t = 95
3s + 3t = 84 are the required system of equation.
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correlation will not show whether or not there is weight loss. which tool would be more appropriate?
The following ways of measuring weight loss are more appropriate than correlation, i.e.,Skin calipers, Impedance scales, DEXA scanning, Body measurements.
What is meant by weight loss?Calories factor into the equation while trying to maintain a healthy weight. The key to losing weight is to burn more calories than you consume. You may do this by consuming fewer calories than you need and increasing the number of calories you burn via physical exercise.
A realistic, efficient, and lasting weight loss plan might be difficult to follow even if it may appear straightforward.
You don't have to do it by yourself, though. Seek advice from your doctor, family, and friends. Consider whether this is the right time and whether you're prepared to make the essential changes. Plan wisely as well: Consider how you'll respond to circumstances that put your determination to the test and the inevitable slight setbacks.
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what is the statement of |×+1|+5=2
Step-by-step explanation:
|x+1|=2-5
|x+1|= -3
statement doesn't have solution
2(vh)/k=r Solve equation for v in terms of all other variables involved
The equation v in terms of other variables is v = kr/2h
What is the subject of an equation?It is a variable which is expressed in terms of other variables involved in the formula.
Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.
2(vh) / k = r
by cross multiplication
2(vh) = kr
divide both sides by 2h
v = kr/2h
In conclusion, v in terms of other variables is kr/2h
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two websites sell the same type of headphones. website a website b e47.68 16.95 cost of headphones cost of postage including the cost of postage which website is cheaper and by how much? e49.95 14.39
Website B is cheaper then website A.
What are headphones?
A user wears headphones, which are a pair of small loudspeaker drivers, on or near their head over their ears.
They function as electroacoustic transducers, converting an electrical signal into an associated sound.
People can listen to music and carry on conversations at any time and from any location thanks to headphones. It is impossible to overstate how simple it is to use headphones and how much mobility they provide.
There are two types of headphones, website A and website B.
First to find the cost for website A.
Cost of website A = Cost of headphone + cost of postage
= 47.68 + 16.96
Cost of website A = 64.63
Cost of website B = Cost of headphone + cost of postage
= 49.95 + 14.39
Cost of website B = 64.34
The cost of website B is less than the cost of website A.
Hence, website B is cheaper then website A.
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I need help fast please!!
Name the Property of Congruence that justifies the statement:
A. Symmetric Property
B. Transitive Property
C. Reflexive Property
D. none of the above
Answer:
A. Symmetric Property
Step-by-step explanation:
The Symmetric Propertry states that if x = y, then y = x.
Since XY = WX, and WX = XY, its the Symmetric Property.
You have blue ribbon and red ribbon in the ratio 1/2:1/5 . Your friend finds the value of the ratio. Is your friend correct? :
Answer:
No.
Step-by-step explanation:
Below I should you two ways to get the correct answer.
If x = 2, y = -5 and z = -7, then find the value of the following expression. (4x^3-10)/((〖3y〗^2+5)-(〖4x〗^3 (z^2-8))/((y^3+5)))
The value of the mentioned expression is -43.24.
To solve the expression, firstly rewriting the equation followed by keeping the values of x, y and z at their respective places.
Equation = (4x³ - 10)/(3y² + 5) - (4x³ (z² - 8))/(y³ + 5)
Now keeping the values of each variable in the equation
Equation = (4×2³ - 10)/(3×(-5)²) - (4×2³ ((-7)² - 8))/((-5)³ + 5)
Taking cube and square on Right Hand Side of the equation
Equation = (4×8 - 10/(3×15)) - (4×8 (49 - 8))/(25 + 5)
Solving the bracket first where we will perform multiplication on the Right Hand Side
Equation = (32 - 10/45) - ((32 × 41)/30)
Equation = 22/45 - 1312/30
Now performing division on Right Hand Side of the equation
Equation = 0.49 - 43.73
Performing subtraction on Right Hand Side of the equation
Equation = -43.24
Hence, the value is -43.24.
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a research firm determined that the equation y=2x+80 can be used to model the total amount of spending by tourist in florida,y, in billions of dollars, for the years 2013-2017 where x is the number of years since 2013.
determine the key features for the context
domain? range? as x values increase,y values ? slope? x intercept? y intercept? thank ya
The slope and intercept of the line will be 2 and 80 respectively.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that, the total amount of tourist spending in Florida from 2013 to 2017 can be predicted using the equation y=2x+80, where x is the number of years since 2013, to the tune of billions of dollars.
Compare the equation with the standard equation,
y=mx+ c
Where m is the slope and c is the intercept of the line.
Thus the slope and intercept of the line will be 2 and 80 respectively.
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twenty high school students took an examination and received the following scores: 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73 determine what percent of the students scored within ( ) one standard deviation of the mean
70% of students had scores that were within (±) one standard deviation of the mean.
Explain the term standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.For the stated question-
Total number of students = 20
Scores received; 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73.
Mean = Sum of all/ Total number
Mean x = 79.7
standard deviation = 8.7
Thus, (±) one standard deviation SD of the mean becomes;
-1 SD; 79.7 - 8.7 ≈ 70.994
+1 SD; 79.7 + 8.7 ≈ 88.406
Thus, 71 to 88
Percentage = scores between 71 to 88/ total scores
Percentage = 14/20 x 100 %
Percentage = 70%
Thus, 70% of students had scores that were within (±) one standard deviation of the mean.
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Subtract and choose the answer in simplest form.
1\frac {(3)} {(4)}-\frac {1} {3}
(4)
(3)
−
3
1
The required evaluation to the given expression is 5/12.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The expression is given in the question as:
1 3/4 - 1/3 (4)(3) - 1/3
We have to determine the evaluation to the given expression
As per the given question, we have
⇒ 1 3/4 - 1/3 (4)(3) - 1/3
⇒ 7/4 - 1/3 (12) - 1/3
Apply the subtraction operation,
⇒ 7/4 - 4 - 1/3
Take the LCM in the above fractions,
⇒ (21 - 12 - 4)/12
⇒ 5/12
Thus, the required evaluation to the given expression is 5/12.
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The length of a rectangle is two feet greater than twice its width. If the perimeter is 25 feet, find the width which of the following is correct 25=2L+2(2+2W)
Answer:
w=7/2=3.5
Step-by-step explanation:
width =w
length = l = 2w+2
25=2(l+w)= 2(2w+2+w) =2(3w+2)=6w+4
25=6w+4
6w=21
w= 21/6 = 7/2
a flipped coin can land in one of two states: heads or tails. write a vi that simulates simultaneously flipping four coins and determines how many of these coins land in the heads state.
The probability flipping of four coin that will give head is 0.93
Probability:
In statistics, Probability defines the possible way of occurring a particular event.
Given,
A flipped coin can land in one of two states: heads or tails.
Here we need to find the probability while flipping four coins then how many of these coins land in the heads state.
In order to calculate the probability of these event, we have to know the values of the sample space and the possible number of events,
Here the value of sample space is written as,
S = {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}
So, the value of n(S) = 16
The possible number of way to obtain the head state is,
E = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}
the value of n(E) = 15.
Therefore, the probability of getting head state is
=> P(E) = 15/16
=> P(E) = 0.93
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Explain how comparing the values of two signed numbers is different than comparing their absolute value?
The difference between the value of two signed numbers and the absolute value is that
signed numbers does not neglect the signs, they can be positive or negative while absolute value gives the positive valueIn a number line signed numbers have specific positions and directions while absolute values ranges from the zero to the positiveWhat are signed numbers?Positive and negative numbers are referred to as signed numbers. The number is automatically regarded as positive if no sign is present.
On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0
What are absolute values?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
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a rectangular lot measures 60 feet wide and has an area of 1,200 square yards. what is the depth of the lot?
The depth of the given rectangular lot is 60 yards.
Here, we are given that the area of a rectangular lot is 1,200 square yards.
Further the width of the lot is 60 feet
As the area and the width are given in different units, we first need to convert them into the same units.
Now, 1 foot = 0.33 yards
⇒ 60 feet = 0.33*60 yards
= 20 yards
Further, we know that the area of a rectangle is given by the formula-
area = length × breadth
Thus,
1,200 = 20 × breadth
1,200/20 = breadth
breadth = 60 yards
Thus, we find that the depth of the given rectangular lot is 60 yards.
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Calculate the social security and Medicare deductions for the following employee assume a tax rate of 6.2% on $128,400 for social security and 1.45% for Medicare. Logan has a cumulative earnings before this pay period was $128,300 , and pay amount this period was$3,000. What is the social security and what was the medicare
The social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots
Main body:
Cumulative Earnings before this pay period = $128,300
pay amount this period = $3000
tax rate of 6.2% on social security = 6.2%
effective earning = 128300 = 3000
= 125300
social security deduction = 6.2 % of 125300
⇒ 6.2 *125300 /100
⇒$7768
Medicare deductions = 1.45%
⇒ 1.45*125300/100
⇒$1816
Hence , the social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
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Three positive numbers are in the ratio 7:3:2. The sum of the least number and the greatest number exceeds twice the remaining number by 30. Find the three numbers.
The three numbers that are in the ratio 7:3:2 are 70, 30, and 20.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
So, let 7x, 3x, and 2x be the three numbers.
7x+2x = 9x is the product of the lowest and greatest number.
In accordance with:
9x-30=2(3x)
To make the equation easier:
9x-30=6x
30 extra on both sides:
9x=6x+30 or,9x-6x=30
3x=30, x=10,
So, the numbers will be:
7x=7(10) = 70
3x=3(10) = 30
2x=2(10) = 20
Therefore, the three numbers that are in the ratio 7:3:2 are 70, 30, and 20.
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Triangle ABC has vertices A(-6, 6), B(4, 2), and C(-4, 0).
Which statement about triangle ABC is true?
A. Since none of the sides are congruent, it is not a right triangle.
B. Since none of the sides have slopes that are negative reciprocals, it is not a right triangle.
C. Since two of the sides have slopes that are negative reciprocals, it is a right triangle.
D. Since two of the sides are congruent, it is a right triangle.
The statement that is true about the triangle ABC with vertices A(-6, 6), B(4, 2), and C(-4, 0) is C. Since two of the sides have slopes that are negative reciprocals, it is a right triangle.
How to check if the triangle is right triangleRight triangles are triangles with have perpendicular relationships
The lines will be checked for perpendicularity by calculating the slopes, if any two slopes are negative reciprocals then they are perpendicular and the triangle is a right triangle'
the points A(-6, 6), B(4, 2), and C(-4, 0)
Using point A(-6, 6) and B(4, 2)
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - 6) / (2 - -6)
m = -1/2
Using point B(4, 2), and C(-4, 0)
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - -4) / (2 - 0)
m = 2
Comparing the slopes shows that slopes calculated are negative reciprocals
2 and -1/2Therefore the triangle is a right triangle
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when transforming a shape twice, do you transform it from the pre image or image?
Which of the following techniques might be most useful in helping a restaurant determine how to position itself in the marketplace?
a. factor analysis
b. multiple regression analysis
c. conjoint analysis
d. perceptual mapping
what is the actual explanation of what happens when you subtract a negative number from another negative number
Ue the right triangle and the given information to olve the triangle. A = 3; b = 64\deg ; find b, c, and a
The value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.
Define the term trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.For the given question-
The length of the side are-
a = 3 units
Angle B = 64°.
Then,
Applying trigonometric properties-
Tan B = b/a
b = a tan B
b = 3 tan 64°
b = 12.47 units
Now,
Sin B = b/c
c = b sin B
c = 12.47 sin 64°
c = 11.21 units.
Thus, the value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.
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