The given function is x² - 7x + 5 and the most general antiderivative of the function is F(x) = x³/3 - 7x²/2 + 5x + c.
The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;
F(x) = ∫f(x)dx
From the question, f(x) = x² - 7x + 5
Therefore,
F(x) = ∫x² - 7x + 5
F(x) = x³/3 - 7x²/2 + 5x + c
Where c is the constant of the integration (antiderivative).
The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.
Therefore, F(x) = x³/3 - 7x²/2 + 5x + c is the most general antiderivative of the function.
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I've been having problems with this and I was wondering if someone could give me the answers 1 - 5
The measures of x are obtained with the Pythagorean Theorem, as follows:
1. x = 10.2.
2. x = 7.2.
3. x = 13.7.
4. x = 36.2.
5. x = 10.7.
What is the Pythagorean Theorem?The Pythagorean Theorem is a geometry axiom which states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the lengths of the sides squared.
Hence, for item 1, we have that:
x² + 16² = 19²
x = square root(19² - 16²)
x = 10.2.
For item 2, we have that:
x² + 12² = 14²
x = square root(14² - 12²)
x = 7.2.
For item 3, we have that:
x² + 9.2² = 16.5²
x = square root(16.5² - 9.2²)
x = 13.7.
For item 4, we have that:
The bottom side is bisected into two equal sides of dimension 15.Then x is the hypotenuse of a right triangle of sides 15 and 33, thus:x² = 15² + 33²
x = square root(15² + 33²)
x = 36.2.
For item 5, first we find the side of the top right triangle, hence:
h² + 16² = 25²
h = square root(25² - 16²)
h = 19.2.
Then the value of x is obtained as follows:
x² + 19.2² = 22²
x = square root(22² - 19.2²)
x = 10.7.
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What does the scale factor from one figure to the other tell you about the figures?
The scale factor tells at what ratio a figure has been changed from other figures
Shapes in various dimensions can be scaled using the Scale Factor.
The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:
y ∝ x
K can therefore be regarded as a proportionality constant in this context.
The scale factor tells a particular percentage increment or to calculate the percentage of an amount.
Also , To compare 2 Similar geometric figures: When we compare two similar geometric figures by the scale factor, it gives the ratio of the lengths of the corresponding sides.
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Multiply −12y(9y − 7). I need this ASAP!
Answer: -108y^2 + 84y
Step-by-step explanation:
y^2 is y squared
give me brainiest! :D
The required simplified solution of the given expression is -108y² + 84y.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
= −12y(9y − 7).
Simplify,
Applying distributive property,
= -12y×9y - 12y(-7)
= -108y² + 84y
Thus, the required simplified solution of the given expression is -108y² + 84y.
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what’s the biggest number 7.06 or 7.9
Answer:
7.9
Step-by-step explanation:
7.06<7.9
The equation C = 5(F - 32) converts temperature in degrees Fahrenheit to
degrees Celsius. For each one-degree increase in Fahrenheit temperature, what is the change in the temperature in degrees Celsius?
Hence, a temperature increase of
9
5
degree Fahrenheit is equivalent to a temperature increase of
81
25
degree Celsius.
If 75% of a number is 225 and 20% of the same number is 60, find 95% of that number.
95% of the given number is 285 if 75% of that number is 225 and 20% of the same number is 60.
In mathematics, a percentage is defined as a number or ratio that can be expressed as a fraction of 100.
Let assume the number is x
So, according to first statement, we are given that 75 percentage of x=225,it means
=>(75/100) × x=225
=>(3/4) × x=225
=>x=(225 × 4) /3
=>x = (75 × 4)
=>x = 300
Now, check for same number whether 20% is 60 or not
=>20% of x=60
=>(20/100) × x=60
=>(1/5) × x =60
=>x= 60 × 5
=>x = 300
So, our assumption is correct.
Now,95% of the same number is 95% of x
=(95/100) ×300
=95 × 3
=285
Hence,95% of 300 is 285.
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Sam decides to build a square garden. If the area of the garden is 4x2 + 28x + 49 square feet, what is the length of one side of the garden?.
The length of one side of square garden that Sam built in Area 4x² + 28x + 49 is (2x+7) feet.
Area Of Any Shape :Area is the region enclosed by the shape of an object. The space covered by a figure or any two-dimensional geometric shape in the plane is called the area of the shape. Area is measured in square units (m², cm², inch², etc.)
Example: The area of a rectangular floor is equal to its length times its width
We have given that,
The shape of garden is Square.
The area of garden , A = 4x² + 28x + 49
We know that , Area of square= Side × Side --(*)
where side is dimension of square. We have to find out the side of the square garden.
A = 4² + 28x + 49
Factorize the middle term such that sum of factors is 28x and multiply of factors is 196x².
A = 4x² + 14 x + 14x + 49
=> A = 2x( 2x + 7 ) + 7(2x + 7)
=> A = (2x+7)(2x+7)
comparing this Area with equation(*) we get,
Side = 2x+7
Hence, the required side is (2x+7) feet.
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jake can mow a lawn in 3 hours. kellie can mow a lawn in 4 hours. if they work together, how long will it take them to mow one lawn?
if they work together it takes 12/7 hours to mow one lawn
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
jake can mow a lawn in 3 hours.
kellie can mow a lawn in 4 hours.
1/3 lawns can be cut per hour by Jake.
kellie has a 1/4 hour cutting rate for lawns.
They can cut 7/12 lawns per hour by working together at a rate of 1/3 + 1/4.
One lawn can be mowed in 12/7 hours at a rate of 7/12 lawns per hour.
Hence if they work together it takes 12/7 hours to mow one lawn.
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Which line represents “a number is one-half the difference of a number x and 4?”
Answer:
Line C
Step-by-step explanation:
Given:
"a number y is one-half the difference of a number x and 4”.Create the equation for the line using the given information:
[tex]\implies y=\dfrac{1}{2}(x-4)[/tex]
Distribute:
[tex]\implies y=\dfrac{1}{2}x-2[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Compare the found equation with the slope-intercept formula:
Slope = ¹/₂y-intercept = -2The y-intercept is the y-value of the point at which the line crosses the y-axis. Therefore, the line crosses the y-axis at y = -2.
The slope tells us how much y increases as x increases. Given the slope is ¹/₂, the line increases by one y-value for every two x-values.
Therefore, the line that represents the given information is line C.
help me pleaseeee ill give brainliest
Answer: A. 16.7%
The probability of the letter C being chosen is 16.7% because there are 6 options and the probability will always be out of 100%. If you divide 100 by those 6 choices you will get 16.66 and rounded it is 16.7
Answer:
the answer is option B. 20%
10% of the items collected by the Hurricane Relief Foundation were blankets. If they
collected 20 blankets, how many items did the Hurricane Relief Foundation collect in all
The total number of items collected for relief is 200.
How to write a linear equation?In order to write a linear equation first find the quantity of which the value is not given. Then, relate the value of this quantity with all the known values to form an equation.
Suppose the number of relief items are x.
The following equation can be written according to the problem,
10% of x = 20
=> 10/100 × x = 20
=> x = (20 × 100)/10
=> x = 200
Hence, the items collected by Hurricane Relief Foundation is given as 200.
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a group of scientists discovered a small creature at the bottom of the ocean that they called a "piknit". when this interesting creature dies, it explodes itself into a number of baby piknits called gogles. the scientists randomly selected 20 piknits from the sea-floor and measured their respective weights in grams. after the piknits died they counted the number of gogles that each piknit produced. they wanted to know if the weight of the piknits can be used to predict the number of gogles.
The weight of the piknits can be used to predict the number of gogles as there is Linear equation in variables may be defined as a linear courting among x and y, that is, variables.
In this case, x is the impartial variable, and y relies upon on it, so y is known as the established variables.
linear courting (or linear association) is a statistical time period used to explain a straight-line courting among variables. Linear relationships may be expressed both in a graphical layout or as a mathematical equation of the shape y = mx + b.
"There is no linear relationship between the weight of the and the number of glasses"
"There is a linear relationship.
A. Yes, because the scatterplot shows a linear pattern.
C. Yes, because a random sample was taken from Piknits for the scatterplots of the 4th and 5th residuals is.
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in how many ways can a committee of two democrats and three republicans be formed from a froup of eight democrats and eleven republicans
the total way the committee formed is 3080.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
The available candidates from a group are 8 Democrats and 11 Republicans.
Three Democrats and two Republicans must be included on the committee that we choose.
Thus, from a pool of 11 Republicans and 8 Democrats, we must select 3 each.
Both 8C3 and 11C2 approaches are viable for achieving this.
8C3 * 11C2 = 3080 are the total ways to form this committee.
Hence the total way the committee formed is 3080.
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When z1 and z2 are added together, the result moves z1 6 units and 3 units. The real part of z1 + z2 is. The imaginary part of z1 + z2 is i.
The real part of Z₁+Z₂ is 8 and imaginary part of Z₁+Z₂ is -2, when Z₁ and Z₂ are added together and the result moves Z₁ 6 units right and 3 units down
A complex number is of the structure a + bi, a, b are real numbers, and I = √(- 1). Deciding the upsides of square underlying foundations of negative numbers is utilized. It is addressed in the direction plane with the real part on the x-hub and imaginary part b on the y-pivot, the arranged pair being (a, b).
In the inquiry, we are given two complex numbers,
Z₁ = 2 + i
Z₂ = 6 - 3i
These focuses are addressed on the direction plane as a circle and a triangle separately. We ascertain their total, z3.
To add Complex Numbers, the real parts are added to the genuine parts and the nonexistent to the imaginary.
∴ Z₃ =Z₁+Z₂ = (2 + i) + (6 - 3i) = (2+6) + (1-3)i = 8 - 2i.
This point is addressed as a square on the Direction plane.
Hence, we can say that real part is 8, and its imaginary part is - 2.
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help me please and thank you
Answer: A, C, 57
Step-by-step explanation:
I multiply by 0.40 for the first one, and then multiply by 1.0625. 0.40 = 40% and multiplying by 1.0625 is the same as adding 6.25%. For the second, I multiply by 0.70 because that is 70%. For the last, I multiply by 0.95 for the same reason.
Gabe goes to the mall. If k is the number of items he bought, the expression 12.33k+24 gives the amount he spent in dollars at one store. Then he spent 30 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 4 items.
Answer:
Step-by-step explanation:
12.33(4)+24= 73.32
then add the extra 30$ that was spent
73.32+30= $103.32
What is area of plane figures?
The area of a plane figure is the region enclosed by the figure's boundary . Here the area is measured in square units of length such as a square meter or square centimeter
The area of plane figures is a mathematical concept that is used to measure the size of two-dimensional shapes. It is the amount of space inside the figure and can be calculated by multiplying the length and width of the figure. The measurement of the area is usually measured in square units, such as inches, centimeters, or meters. The area is a fundamental concept in geometry and is used in many areas of mathematics, such as calculus and trigonometry.
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The margin of error of a confidence interval is the error from biased sampling methods.a. trueb. false
Margin of error is statistical expressing the amount of a random sampling error in survay results not the error term from biased sampling method. So, correct answer is False.
What is Margin of error ?Margin of error in statistics represents the amount of random sampling error in the survey results. The larger the margin of error, the less confident that the survey results reflect the results of the census of the entire population. It is denoted by E or MOE. It is calculated by dividing the square root of the sample size by the standard deviation of the population. 99% level is the most conservative, 90% level is the least conservative. The sampling error is a statistical error that occurs when the analyst does not select a sample that is representative of the entire data population.
False - Margin of error only account for sample variability (the fact that my sample differs from many others' samples and therefore provides different statistics.
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a² + 11a + 30
Plsss help
Answer:
( a + 5 ) ( a + 6 )
? maybe
Step-by-step explanation:
I really don't know how to explain
a portable cd player was originally priced at $79.95 and cost $39 is ultimately sold for $64.95. what was the reduction percentage on the portable cd player?
By using percentage, it can be calculated that
Percentage reduction on the portable cd player [tex]= 18.76 \%[/tex]
What is Percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 9% means [tex]\frac{9}{100}[/tex]. Here, 9 is expressed as a fraction of 100.
Original price of the CD player = $79.95
Selling price = $64.95
Reduction in price = $(79.95 - 64.95) = $15
Percentage reduction on the portable cd player = [tex]\frac{15}{79.95} \times 100 = 18.76 \%[/tex]
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a passenger train leaves charleston, wv heading east at the same time a loaded coal train leaves charelston, wv heading west. the passeger train travels23mi/hr faster than the coal train, and in 4 hours the two trains are 412 miles apart. what is the speed of each train
The speed of the each train = 63
What is Speed?Speed is defined as : The rate of change of position of an object in any direction.
Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
Types of SpeedThere are four types of speed and they are:
1. Uniform speed
2. Variable speed
3. Average speed
4. Instantaneous speed
Given that
The passenger train travels23mphr faster than the coal train
In 4 hours the two trains are 412 miles apart
Let the speed of train = x
4*x+4*(x+23)=412
4x + 4x + 92 = 412
8x = 320
x = 40
the speed of the each train = x + 23 = 40 + 23 = 63
Given that
The passenger train travels 23mphr faster than the coal train
In 4 hours the two trains are 412 miles apart
let the speed of train = x
4*x+4*(x+23)=412
4x + 4x + 92 = 412
8x = 320
x = 40
the speed of the each train = x + 23 = 40 + 23 = 63
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suppose a fair die is rolled twice, what is the probability that the sum of the two outcomes is 6, given that the sum is even
Probability that that sum of the two dice outcomes is 6 is 5/36
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.We know,
Probability = Number of events / Total no. of favourable outcomes
If we through two dice then ,
Total number of favourable outcomes = 36
Here, we need the sum of the two outcomes is 6 is
(1, 5) , (2, 4), (3, 3), (4, 2), (5, 1)
So, the number of events = 5
P(of getting sum 6) = 5/ 36
Hence, Probability that that sum of the two dice outcomes is 6 is 5/36
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What is the equation of the straight line which passes through the point 1/2 and cuts off equal intercepts from the axes?
The equation of the line passing through the point (1, -2) and cutting off equal intercepts from the axes will be x + y +1 = 0.
The equation of the line in the intercept form is expressed as
x/a + y/b = 1
where a is x intercept, b is y intercept and x and y are independent and dependent variables respectively.
Now, according to the question both the intercepts are equal that is
a = b
So, the equation will become
x/a + y/a = 1
x + y = a
Now, since the line passes through (1, -2), so
1 + (-2) = a
=> a = -1
So, the equation of line will be
x + y = -1 or x + y +1 = 0.
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Complete Question:
What is the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from the axes?
The table below shows the length and weight of a species of fish. Complete parts (a) and (b).
Fish Lengths and Weights
6
8
1.49
1.76
Length (in.)
Weight (lb)
4
1.26
10
2.08
12
2.45
(a) Find an exponential model for the data.
The exponential model for the data is y=
(Use integers or decimals for any numbers in the expression. Round to three decímal places as needed.)
hs
The equation that represents the relation between length and weight of a species of fish is y = 0.903 (1.087)^x.
What is exponential function?
A mathematical function with the formula f (x) = a^x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Given table is
Length(in.) 4 6 8 10 12
Weight(lb) 1.26 1.49 1.76 2.08 2.45
Assume the exponential function be:
y = ab^x
Putting x = 4 and y = 1.26 in the exponential function:
1.26 = ab⁴ ....(i)
Putting x = 6 and y = 1.49 in the exponential function:
1.49 = ab⁶ ...(ii)
Divide equation (ii) by (i)
1.49/1.26 = ab⁶/ab⁴
149/126 = b⁶/b⁴
149/126 = b⁶⁻⁴
149/126 = b²
b = 1.0874
b ≈ 1.087
Putting b = 1.087 in equation (i)
1.26 = a(1.087)⁴
a = 1.26/(1.087)⁴
a = 0.9025
a ≈ 0.903
Therefore, y = 0.903 (1.087)^x
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Answer:
Step-by-step explanation:
What is the slope of the line − 3 3?
The slope of the line passing through points (3, -3) and (0, -3) is equal to zero.
If we look at the general meaning of slope then we find out that Slope is nothing but the elevation or the steepness of any curve plotted on a graph paper. Now, the formula for finding the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as
m = (y₂ - y₁)/(x₂ - x₁)
where m is the slope between the points, (y₂ - y₁) is difference between the y coordinates and (x₂ - x₁) is the difference between the x coordinates.
We have the values as (x₁, y₁) = (3, -3) and (x₂, y₂) = (0, -3)
So, the slope will be expressed as
m = (-3 + 3)/(0 - 3)
m = 0/-3
m = 0 which is the required slope.
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Complete Question:
What is the slope of the line that passes through (3, -3) and (0, -3).
stop the car! a car company has found that the lifetime of its disc brake pads varies from car to car according to a normal distribution with mean m 55,000 miles and standard deviation s 4500 miles. the company installs a new brand of brake pads on an srs of 8 cars. (a) if the new brand has the same lifetime distribution as the previous type of brake pad, what is the sampling distribution of the mean lifetime x? (b) the average life of the pads on these 8 cars turns out to be x 51,800 miles. find the probability that the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged. what conclusion would you draw?
a) The sampling distribution of the mean lifetime x is: Approximately normal with mean 55,000 and standard error 1591.
b) The probability that the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged is of 0.0222 = 2.22%. As the z-score has an absolute value greater than 2, it shows that this is an unusual measure, hence a conclusion could be drawn that there actually were changes in the distribution.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. Additionally, the distribution is approximately normal with the same mean and the population mean.The parameters for this problem are given as follows:
[tex]\mu = 55000, \sigma = 4500, n = 8, s = \frac{4500}{\sqrt{8}} = 1591[/tex]
The probability that the sample mean lifetime is 51,800 miles or less is the p-value of Z when X = 51,800, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (51800 - 5500)/1591
Z = -2.01.
Z = -2.01 has a p-value of 0.0222.
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There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?
Answer: 1.06 cm
Step-by-step explanation:
Take 2.7 divided by 2.54 = 1.062cm
Rounded the nearest hundredth, so it will be 1.06 cm
write and solve a system of equations for the situation. 2x+2y=6 4x+4y=4
what do americans think about preferential hiring of women? has there been a change in the past decade? in 2000(group 1) and 2010(group 2), the general social survey asked participants if they would favor or oppose preferential hiring of women. in 2000, out of 849 respondents, 271 said yes. in 2010, out of 696 respondents, 225 said yes. the 95% confidence interval is (-0.0509, 0.04273). for the alternative hypothesis, ha: p1-p2 does not equal zero, what can we say about the p-value?
Greater than 0.05 is the p-value, which indicates that it is greater than the significance level.
what is test of hypothesis?When determining whether the available data are sufficient to support a given hypothesis, one method of statistical inference is known as a statistical hypothesis test. Making probabilistic claims about a population parameter is possible through hypothesis testing.
given
a 95% confidence interval with bounds for the inference's outcome (-0.0509,0.04273).
As the value p1-p2=0 is included in the interval and is one of the possible values of the genuine difference between the proportions, this confidence interval indicates that the difference (p1-p2) is not substantially positive at the level of significance utilized in the study.
The null hypothesis would then not be rejected by a test of hypothesis performed with the same data and level of significance because the proportional difference is not significant.
In this example, the P-value is more than 0.05, which indicates that it is greater than the significance level.
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a construction firm has bid on two different contracts. let e1 be the event that the bid on the first contract is successful, and define e2 analogously for the second contract. suppose that p(e1) 5 .4 and p(e2) 5 .3 and that e1 and e2 are independent. a. find the probability that both bids are successful. b. find the probability that neither bid is successful. c. find the probability that at least one of the bids is successful.
The required probabilities of the given parts are a) 56%, b) 6% , c) 94%.
What is Probability?The probability is the proportion of the probability of an occasion to occur. It estimates the conviction of the occasion. The recipe for probability is given by; P(E) = Number of Good Results/Number of absolute results.
According to question:a) These two occasions are autonomous, consequently, the probability of both is the increase of the probabilities of every, accordingly:
0.56 = 56% probability that the two offers are fruitful.
b) E1 has a 1 - 0.7 = 0.3 probability of being ineffective, while E2 has a 0.2
likelihood, thus:
0.06 = 6% probability that neither one of the bids is effective.
c) 1 - 0.06 = 0.94
0.94 = 94% probability that the firm is effective in no less than one of the two bids.
Thus, required probabilities are a) 56%, b) 6% , c) 94% .
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