Let m s the slope of the given equation 2y+3x-1. So m=-3/2.
What is meant by slope?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
m =Δy/Δx = change in y/change in x
where "m" represents a line's slope.
Write alternative way to write slope.Slope can also be written as
tanθ = Δy/Δx
The given equation is:
2y+3x-1=0
Separate y
2y= -3x+1
y= -3/2x +1/2
Comparing it with equation of line y=mx+c where m is the slope we conclude that slope of the given equation is m=-3/2.
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The clearing house has resistors that sell for $3.50 each and circuit boards that sell for $2.25 each. Write an inequality that represents how many of each type of electronic equipment can be bought with at most $7.
Answer:
3.50x + 2.25y smaller than or equal 7
Step-by-step explanation:
Let x represent the resistor and y represent the circuit board
Resistor: $3.50
Circuit board: $2.25
We know it can be bought at most for $7, so it will be smaller than or equal to $ 7. So, we have equation
3.50x + 2.25y smaller than or equal 7
list the data in the following stem-and-leaf plot. the leaf represents the tenths digit.
As per the given stem and leaf plot, the range of the stem and leaf plot is 4.
The term stem and leaf plot in math is referred as a type of table where the stem (or first column) represents the first place values of numbers and the leaves (or second column) represent the final place value of the numbers.
Here we given the following stem and leaf plot data.
Now we have to find the range of the stem and plot.
As we all know that range is defined as the maximum and minimum number in the data set.
While we looking into the given data, we have identified the the minimum number is 14 and the maximum number is 18.
Then the range is calculated as,
=> 18 - 14 = 4.
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Predict the next three numbers in the pattern 25,5,1,1/5,1/25
The next three number is 1/125, 1/625, 1/3125.
What is pattern?
A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Given pattern is 25, 5, 1, 1/5, 1/25.
Assume first term is a₁ = 25
The second term is a₂ = 5
The third term is a₃ = 1
The fourth term is a₄ = 1/5
The fifth term is a₅ = 1/25
The ratio of each consecutive term is
a₂/a₁= a₃/a₂ = a₄/a₃ = a₅/a₄ = 1/5.
The 6th term is a₆ = (1/25)× (1/5) = 1/125
The 7th term is a₇ = (1/125) × (1/5) = 1/625
The 8th term is a₈ = (1/625) × (1/5) = 1/3125
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Is asymptote the same as discontinuity?
An asymptote is not the same as discontinuity.
What is asymptote and discontinuity?An asymptote is a line or curve to which a function's graph draws closer without touching it. A vertical asymptote is a line that a function approaches but never quite touches. A vertical asymptote isn't always a discontinuity. It only matters if there's something "on the other side" since then how are you supposed to get across that gap without picking up your pencil? For instance ln(x) has a vertical asymptote at x=0 but it's no big thIng. But ln(|x|) (which is just ln(x) together with its "mirror image" on the negative side) is discontinuous.
An asymptote is not the same as discontinuity.
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algebra 1-
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2,200 people enter the fair and $5,050 is collected. Determine how many children and adults attended?
Lily finds some dimes and quarters in her piggy bank. How much money (in dollars) does she have if she has 5 dimes and 12 quarters? How much money (in dollars) does she have if she has x dimes and y quarters?
Answer: 7 dollars
Step-by-step explanation:
i think
Answer: A dollar is 100 cents, so you would add the 5 dimes and 12 quarters together. A dime is 10 cents so 10x5 is 50, so you would have 50 cents in dimes. A quarter is 25 cents, so you would multiply 12x25 and you would get 300 and you add those both together to get 350 cents. A dollar is 100 cents so you would have 3 dollars and the remaining 50 cents would stay 50 cents! <33
Step-by-step explanation:
Please help me solve
I will mark as brainliest
Answer:
3. B
4. C
Tell me if you need an explanation, I can add it for you :D
The figure(Figure 1) is a graph of Ex. The potential at the origin is -140 V . What is the potential at x=3.0m? Expert Answer. Who are the experts?
As per the given origin, the potential at x = 3.0m is 143.0V
The term origin in math is referred as the initial point or the starting point from where we begin our calculations or measurements.
Here we have given that the potential at the origin is -140 V.
And we need to find the potential at x = 3.0m.
While we looking into the given question, we have identified that the region of space has a non-uniform electric field that points in the +x-direction and has magnitude and as the reference point, it take the potential at the origin to be -140 V .
Then the electric potential at x=3.0m is calculated as,
=> V(3) - 140 = 3.0
=> V(3) = 143.0
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The acceleration y, in meters per second squared, of an object after x seconds is given by y =. During the first 10 seconds, over which intervals is the acceleration increasing?.
During the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.
The acceleration is: y = 7*sin( x*pi/4).
Sin(θ) increases between -pi/2 and pi/2
Sin(θ) decreases between pi/2 and (3/2)*pi.
And so on.
Here we have:
θ = x*(pi/2)
When x = 0, θ = 0.
And sin(θ) is increasing in θ = 0.
Then we must choose one of the options that start with x = 0.
now it will stop increasing when:
θ = pi/2 = x*(pi/4)
x = 2.
So the acceleration is increasing in the segment (0,2)
And it will start increasing again when:
θ = (3/2)*pi = x*(pi/4)
(3/2)*pi*(4/pi) = 6 = x.
So at x= 6 the acceleration starts increasing again, and the acceleration is only defined until x = 10, then
the correct option is: (0, 2) and (6, 10)
Thus, during the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.
Complete question:
The acceleration y, in meters per second squared, of an object after x seconds is given by y = 7 sin (pi/4 x). During the first 10 seconds, over which intervals is the acceleration increasing?
(2, 6)
(4, 8)
(0, 2) and (6, 10)
(0, 4) and (8, 10)
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The acceleration is: y = 7*sin( x*pi/4).
Sin(θ) increases between -pi/2 and pi/2
Sin(θ) decreases between pi/2 and (3/2)*pi.
And so on.
Here we have:
θ = x*(pi/2)
When x = 0, θ = 0.
And sin(θ) is increasing in θ = 0.
θ = pi/2 = x*(pi/4)
x = 2.
θ = (3/2)*pi = x*(pi/4)
(3/2)*pi*(4/pi) = 6 = x.
So at x= 6 the acceleration starts increasing again, and the acceleration is only defined until x = 10, then
Thus, during the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.
(2, 6)
(4, 8)
(0, 2) and (6, 10)
(0, 4) and (8, 10)
Congruent triangles. What does x equal?
The value of x for the congruent triangles will be equal to 10.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
Given that the angles are ∠E = 95, ∠F = 32 and ∠R=4x +13. The value of x will be calculated as,
Calculate the value of angle ∠G,
∠G = 180 - 32 - 95
∠G = 53
The value of x will be,
4x + 13 = 53
4x = 40
x = 10
Therefore, the value of x for the congruent triangles will be equal to 10.
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What is the median if there are 11 numbers?
The Median for n = 11 numbers will be 6th term of the Observation set.
One measure of central tendency is the median. The median is the number that lies in the middle of the specified range of integers. It separates the higher half from the lower half of a particular data sample. At least half of the observations are above or equal to the median, and at least half of the observations are below the median.
The median can be calculated as follows when there are odd numbers of observations in a data collection:
Step 1: Arrange the sample of data in ascending or descending order.
Step 2: If the number of observations (let's say n) is odd, the middle observation is the median of the given data.
Median = [tex](\frac{n+1}{2} )^{th}[/tex] term.
Here n = 11, So median will be 6th term of Observation set.
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Make Sense and Persevere Neil and Yuki run a data entry service. Neil starts at 9:00 A.M can type 45 words per minute. Yuki arrives at 10:30 A.M. and can type 60 words per minute. Write and solve an inequality to find at what time Yuki will have typed more words than Neil. Let x represent the time in minutes. MP.1 . and
Yuki would have typed more than Neil at 10:30 AM and the inequality is 45×90+45 × x < 90 × x
We know that Neil started 90 minutes earlier than Yuki by subtracting the time difference So that tells us that
at 10:30 AM Neil would have typed 45 times 90. After x minutes he would have typed 45*90+45*x and Yuki would have typed 60*x.
Words typed by Yuki will be greater than those that will be Words typed by Neil
45×90+45 × x < 90 × x
When we will try in Solving the above inequality would give us
x >90
it means that 90 minutes after 10:30 AM
Yuki would type more than Neil.
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The height of a triangle is 8 centimeters greater than three times its base. The area of the triangle is 128 square centimeters. What is the base of the triangle?
(Hint: area of triangle=12⋅base⋅height)
40 cm
8 cm
5 1/3 cm
16 cm
Answer:
To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:
A = 1/2bh
128 = 1/2bh
We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:
h = 3b + 8
We can substitute the second equation into the first equation to get the following:
128 = 1/2bh
128 = 1/2(3b + 8)b
128 = 3/2b^2 + 4b
We can then use the quadratic formula to solve for b, the base of the triangle:
b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))
b = (-4 +/- sqrt(64 - 192))/3
b = (-4 +/- sqrt(-128))/3
Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.
Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.
To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:
A = 1/2bh
128 = 1/2bh
We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:
h = 3b + 8
We can substitute the second equation into the first equation to get the following:
128 = 1/2bh
128 = 1/2(3b + 8)b
128 = 3/2b^2 + 4b
We can then use the quadratic formula to solve for b, the base of the triangle:
b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))
b = (-4 +/- sqrt(64 - 192))/3
b = (-4 +/- sqrt(-128))/3
Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.
Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.
Sharonda uses a blend of dark chocolate and milk chocolate to make the ice cream topping at her restaurant. She needs to buy 120\,\text{kg}120kg120, start text, k, g, end text of chocolate in total for her next order, and her recipe calls for twice the amount of dark chocolate as milk chocolate. Let ddd be the number of kilograms of dark chocolate she buys and mmm be the number of kilograms of milk chocolate she buys. Which system of equations represents this situation?.
The equations m = 2d and m+d = 120 represent this situation.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
d = kilograms of dark chocolate
m =kilograms of milk chocolate
So, her recipe calls for twice the amount of dark chocolate as milk chocolate.
Mathematically speaking:
m = 2d
She needs to buy 120 kg, of chocolate in total. So;
m + d = 120
The following system of equations represents the situation:
m = 2d
m+d = 120
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The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
So, her recipe calls for twice the amount of dark chocolate as milk chocolate.
m = 2d
She needs to buy 120 kg, of chocolate in total. So;
m + d = 120
The following system of equations represents the situation:
m = 2d
m+d = 120
P(x)= 1/2x^2+3x-4x^3x+6x^4-1 write in standard form, is it polynomial, what degree, type, and leading coefficient is it?
Answer is 1. Polynomial Function is a quadratic, cubic, and of any degree function. It involves only a non - negative powers of x.
Find the solution ?Things to Remember: Leading coefficient is the numerical coefficient of the term with the highest degree.To write a polynomial function in standard form, simply arrange the terms according to the degree of the variable. The number of turning points/solutions of the polynomial function is based on the highest degree of the polynomial function.Polynomial Function is a quadratic, cubic, and of any degree function. It involves only a non - negative powers of x. The roots of the function are the values that when substituted equates the polynomial to 0.These are also the values that intercepts the x-axis with the graph. involves only non-negative integer powers or only positive integer exponents of a variable in a equation like the quadratic equation, cubic equation, and others.To learn more about Polynomial Function refer
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Tan 32 deg + tan 88 deg / 1 - tan32 tan88 = -√3
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{tan32^0+tan88^0}{1-tan32^0tan88^0} \ \ \ \ (1)\\\\Let\ \alpha =32^0\ and\ \beta =88^0\\\\Hence,\ expression\ (1)\ will \ look\ like\ this:\\\\\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }\\[/tex]
The trigonometric formula for adding angles for a tangent is as follows:
[tex]\displaystyle\\\\\boxed {tan(\alpha +\beta )=\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }}[/tex]
Thus,
[tex]\displaystyle\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }=tan(32^0+88^0)\\\\\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }=tan120^0[/tex]
Calculate the value of tan120°:
[tex]tan120^0=tan(90^0+30^0)\\\\tan120^0=-cot30&^0\\\\tan120^0=-\sqrt{3}[/tex]
So,
[tex]\displaystyle\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }\equiv-\sqrt{3}[/tex]
A student was attempting to write an inequality that she could use to find how many more hours she had to work at her job to buy a bicycle. The student had already
saved $55 and earns $9 per hour at their job. The student will need at least $199 to buy the bicycle.
Look at the student's inequality below. Find and explain the student's error in writing her inequality.
h = the amount of hours worked
55+9h ≤ 199
The correct Inequality that shows the above situation is 55 + 9h ≥ 199, the error in the given expression is taking less than or equal to.
What is Inequality:Inequality simply means that two things aren't equal. One of the items might be lower too, greater than, or equivalent to the others.
Mathematical expressions with inequalities are those in which the two sides are not equal.
the signs we use in Inequalities are
≠ means not equal to
< means less than
> means greater than
≤ means less than or equal to
≥ means greater than or equal to
Here we have
The student already saved $ 55
She earns $ 9 per hour
The money that she needs to buy the bicycle is at least $ 199
Let's assume that she worked for h hours to earn at least $ 199
The amount that she earned after h hours = 9h
As we know she already saved $ 55
Finally the amount that she had = 55 + 9h
She wants at least $ 199 but not less than that, so the amount 55 + 9h must be greater than $ 199
=> 55 + 9h ≥ 199
The expression that the student used is 55 + 9h ≤ 199, here error is taking less than or equal to.
Therefore,
The correct Inequality that shows the above situation is 55 + 9h ≥ 199, the error in the given expression is taking less than or equal to.
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If x = 6, y = 4 and z = 1, evaluate x(y to the power of 2 - z)
The solution to the evaluation of the expression x(y² - z) x = 6, y = 4 and z = 1 is 90
How to solve equationEvaluate:
x(y² - z)
When
x = 6, y = 4 and z = 1
x(y² - z)
substitute the value of x, y and z
= 6(4² - 1)
Applying PEMDAS:
P = parenthesis
E = Exponential
M = Multiplication
D = Division
A = Addition
S = Subtraction
= 6(16 - 1)
= 96 - 6
= 90
In conclusion, the expression x(y² - z) when evaluated gives 90.
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Determine the Domain and Range
Answer:
Step-by-step explanation:
domain
all real numbers, because the graph keeps going to the left and to the right
range
y ≥ 1 because the function starts in y = 1 and then keeps going up
a physicist examines 28 sedimentary samples for potassium chloride concentration. the mean potassium chloride concentration for the sample data is 0.158 cc/cubic meter with a standard deviation of 0.0171. determine the 98% confidence interval for the population mean potassium chloride concentration. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
The critical value that should be used in constructing the confidence interval is (0.150 , 0.166).
The given parameter is as follows,
t\alpha /2,df = 2.473
Margin of error = E = t\alpha/2,df * (s sqrt n)
= 2.473 * (0.0171 / \sqrt28)
Margin of error = E = 0.008
If the populace preferred deviation (σ) is known, a speculation take a look at carried out for one populace imply is known as one-imply z-take a look at or definitely z-take a look at. A z-take a look at is a speculation take a look at for trying out a populace imply, μ, in opposition to a intended populace imply, μ0.
The 98% confidence interval estimate of the population mean is,
\bar x - E < \mu < \bar x + E
0.158 - 0.008 < \mu < 0.158 + 0.008
0.150 < \mu < 0.166
(0.150 , 0.166)
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, if "y varies directly as x", find the constant of variation and write an equation of direct variation that
relates the two variables.
y = 12 when x = 1/4
Answer:
k = 48 , y = 48x
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 12 when x = [tex]\frac{1}{4}[/tex] , then
12 = [tex]\frac{1}{4}[/tex] k ( multiply both sides by 4 to clear the fraction )
48 = k
constant of variation is then k = 48 , so
y = 48x ← equation of variation
Type the correct answer in the box. Use numerals instead of words. What percentage of a radioactive substance remains after two half-lives?.
Answer:
25%
Step-by-step explanation:
[tex](1/2)^2=1/4 \\ \\ \frac{1}{4} \times 100=25\%[/tex]
A zookeeper predicted the weight of a new baby elephant to be 232 pounds when it was born. The elephant actually weighed 264 pounds at birth. What was the percent error of the zookeeper's prediction?
The percent error in zookeeper's prediction on baby elephant's weight is 13.79%.
What is percentage error?
Percentage error is the difference between the estimated value and the actual value compared to the actual value, expressed as a percentage. So the percent error is the relative error multiplied by 100.
Uses of percentage error:
The main purpose of calculating percent error is to analyze how close the measured value is to the actual value. This is part of a comprehensive error analysis.
Solution:
Percent error = (Actual weight - Predicted weight/Predicted weight)x100
Percent error = (264 - 232/232) x 100
Percent error = ( 32/232) x 100
Percent error = 0.1379 x 100
Percent error = 13.79%
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What is parallel to the line y 3x 1?
Equation y = 3x is parallel to the line y = 3x - 1.
Describe parallel lines.Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees. If two lines have different y-intercepts and equal slopes, they are said to be parallel. In other words, the reciprocals of perpendicular slopes are negative. Pairs of parallel lines cross one another. If they went on, they'd never run into each other. The separation between parallel lines is always the same.
Given
A line that passes through (0,0) has the equation Y=mX, where m is the slope of the line.
Now that this line is perpendicular to the line Y=3X-1, m is equal to 3.
As a result, the line's equation is Y=3X.
Equation y = 3x is parallel to the line y = 3x - 1.
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This year, a small business had a total revenue of $16,500. If this is 34% less than their total revenue the previous year, what was their total revenue the previous year?
Answer:
$25000
Step-by-step explanation:
100% - 34% = 66%
We know that
66% = $16,500
We have to find 1%
16500 divided by 66 = $250
Then we have to find the 34%
250 times 34 = $8500
Then we add both numbers to find their previous year's revenue
$16500 + $8500 = $25000
So, their previous year's revenue is $25000
How do you describe the relationship of a square root?
Therefore , the relationship of square root can be illustrated as [tex]y^{2}[/tex] = x.
What is square root ?A number's square root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as [tex]3^{2}[/tex] or as 3 x 3.
Here,
In math, the square root of a number x is a number y such that y2 = x, or a number y whose square
(the result of multiplication by itself, or y), is x.
As an illustration, 4 and 4 are the square roots of 16, since 42 = (4)2 = 16.
Therefore , the relationship of square root can be illustrated as [tex]y^{2}[/tex] = x
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need help on these questions. Help anyone, please!
Step-by-step explanation:
a linear function is defined as
y = ax + b
the variable x is only occurring with the exponent of 1.
this represents a straight line in a graphic representation (hence the name "linear").
if the exponent of the variable x is not 1, then it is not a linear function
P : y = 3/x + 2³
it is not linear.
the exponent of x = -1, as 1/x = x^-1. -1 is different to 1, which would be needed as exponent of x to make it linear.
Q : y = (1/3)x² + 3
it is not linear.
the exponent of x = 2. and 2 is different to 1, which would be needed as exponent of x to make it linear.
What is the factorization of the polynomial below 3x² 36x 81?
The factorized form of the formula is (3x+9)(x+9) of [tex]3x^{2}[/tex]+ 36x + 81 = 0 . Quadratics can be defined using a polynomial equation of the second degree.
what is a quadratic equation ?The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.
here ,
= [tex]3x^{2}[/tex] + 36x + 81 = 0
= 3x² + 27x + 9x + 81
= 3x(x+9) + 9(x+9)
= (3x+9)(x+9)
= 3(x+3)(x+9)
The factorized form of the formula is (3x+9)(x+9) of [tex]3x^{2}[/tex]+ 36x + 81 = 0 .
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Indefinite Integrals
f"(x)=6x, f'(-3)=20. f(-3) = -5
f(x)= ?
The function f(x) = x³ - 7x + 1 for the given f''(x) = 6x, f'(-3) = 20 and f(-3) = -5. By using the antiderivative formula, the required function is evaluated.
What is the antiderivative formula?The antiderivative formula for indefinite integrals is
[tex]\int f'(x)dx = f(x) + c[/tex]
or we can also write this as
[tex]\int f^n(x)dx = f^{n-1} + c[/tex]
Calculation:It is given that,
f''(x) = 6x, f'(-3) = 20, f(-3) = -5
Then, by the antiderivative formula, we can write
[tex]\int f''(x)dx = f'(x) + c[/tex] ...(1)
On substituting, we get
[tex]\int f''(x)dx = \int 6x dx = 6\int xdx[/tex]
Since we have the formula for the indefinite integral, [tex]\int x^n dx = \frac{x^{n+1}}{n+1}+c[/tex], we get
[tex]\int f''(x)dx = 6(\frac{x^{1+1}}{1+1})+c[/tex]
⇒ [tex]\int f''(x)dx = 6(\frac{x^2}{2})+c=3x^2+c[/tex]
So, from (1), we get f'(x) = 3x² + c
But we have f'(-3) = 20. So, on substituting x = -3 in the above function f'(x), we get
f'(x) = 3x² + c
⇒ f'(-3) = 3(-3)² + c
⇒ 20 = 3(9) + c
⇒ 20 - 27 = c
∴ c = -7
So, the second derivative function is f'(x) = 3x² - 7.
From the antiderivative expression, we can write
[tex]\int f'(x)dx = f(x) + c[/tex] ...(2)
On substituting f'(x) in the above integral we get
[tex]\int f'(x) dx = \int (3x^2 +-7)dx[/tex]
⇒ [tex]\int f'(x)dx = 3\int x^2dx -7\int dx + c[/tex]
⇒ [tex]\int f'(x) dx = 3(\frac{x^3}{3})-7x+c[/tex]
⇒ [tex]\int f'(x) dx = x^3 - 7x + c[/tex]
From (2), we can write
f(x) = x³ - 7x + c
But we have f(-3) = -5;
Then,
f(-3) = (-3)^3 - 7(-3) + c
⇒ -5 = -27 + 21 + c
⇒ -5 = -6 + c
∴ c = -5 + 6 = 1
Thus, the function f(x) = x³ - 7x + 1.
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a person goes to store to buy clothes. the probability of the events are independent. the probability of buying a hat is 0.25. the probability of buying a pair of gloves is 0.72. what is the probability of both events occurring?
The probability of both events occurring is 0.18.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
Since the person goes to store to buy clothes. the probability of the events are independent. the probability of buying a hat is 0.25. the probability of buying a pair of gloves is 0.72.
The probability of both events occurring will be:
= P(hat) × P(glove)
= 0.25 × 0.72
= 0.18
The probability is 0.18.
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