The required inverse of the given function is expressed as [tex]y=\sqrt{\frac{x+10}{7} }[/tex]
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.
Replacing y with x
x = 7y² – 10
Making y the subject of the formula:
7y² = x+ 10
Dividing both sides by 7
7y²/7 = (x+10)/ 7
y² = (x+10)/ 7
Taking the square root of both sides
[tex]\sqrt{y^{2} } =\sqrt{\frac{x+10}{7} }[/tex]
[tex]y=\sqrt{\frac{x+10}{7} }[/tex]
Hence the required inverse of the given function is expressed as [tex]y=\sqrt{\frac{x+10}{7} }[/tex]
Complete question:
Which equation is the inverse of y = 7x² – 10
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dr. yung tests a new anti-malaria drug in an asian population and concludes that he cannot reject the null hypothesis, and must conclude he does not have sufficient evidence to conclude that the drug works. in reality, the drug does work. dr. yung has committed a error. group of answer choices logical type i (false positive) type ii (false negative) statistical
Dr. Yung has committed a type l ( false positive) error.
What is a type I error?Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually false in the population results in a type II error (false-negative).
A type I error occurs when a null hypothesis that is actually true is mistakenly rejected during statistical hypothesis testing (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"),
Therefore, the error is a type 1 error.
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What are binomials give five examples?
"A binomial is an algebraic expression which has exactly two terms." The examples of binomials are x² + 3, x + y, x³ + 2x, 9 + 7y, xy² + xy, etc.
A polynomial is of various types like monomial, binomial, trinomial, etc.
Monomial contains only single term.
Trinomial contains exactly three terms. All the three are dissimilar.
A binomial is said to have only positive exponents and no negative exponents.
In x³ + 2x, x³ and 2x are two different terms. The variable is only x. The exponent of x³ is 1, the exponent of x is 1. The coefficient of x³ is 1, the coefficient of x is 2.
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Ridgid motions to prove
Answer:
Sequence:
1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex]
. . . . . . . . . . ⭐ please take a ruler and measure the distance from AA', . . . . . . . . BB', CC', DD', and EE', and then write that distance (it should . . . . . . . . be the same for each measurement) in place of 5 in -5. I just . . . . . . . . wrote -5 because it was my best approximation for looking at . . . . . . . . a laptop screen. ⭐
2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex]
3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex]
Step-by-step explanation:
1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex] means that when you move figure ABCDE down by 5 units, it will map onto the image of A'B'C'D'E.
2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex] means that when you rotate figure A'B'C'D'E' 180 degrees counterclockwise about point B', said figure will map onto the image of A''B''C''D''E''.
3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex] means that when you reflect figure A''B''C''D''E'' across segment D''E'', said figure will map onto the image A'''B'''C'''D'''E'''.
Which is a discontinuous process?
The function of the graph which is not connected with each other is known as a discontinuous function. A function f(x) is said to have a discontinuity of the first kind at x = a, if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.
The function is an expression or law that defines a relationship between one variable and the independent variable and another variable the dependent variable
The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes because of this control
Some examples of a discontinuous function
f(x) = 1 / (x - 2)
f(x) = tan x
f(x) = x2 - 1
For x < 1 and f(x) = x3 - 5 for 1 < x < 2
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A relationship between one variable, the independent variable, and another variable, the dependent variable, is defined by an expression or law known as the function.
The variable being controlled in the problem is the independent variable, and the variable that changes as a result of this control is the dependent variable.
f(x) = 1 / (x - 2)
f(x) = tan x
f(x) = x2 - 1
For x < 1 and f(x) = x3 - 5 for 1 < x < 2
Solve for x: 7x-22=3x+18
Answer:
x = 10
Step-by-step explanation:
7x-22=3x+18
4x -22 = 18
4x = 40
x = 10
I need help on this please someone answer me!
So basically for the first one do 14.0%x 4.6
How do you solve the mean error?
ME adds up the variances and divides the result by n. In this context, an error is defined as an uncertainty in a measurement or the difference between the measured value and the true/correct value.
What is mean?In mathematics and statistics, the mean is the average of a set of variables. The simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean are all ways for calculating the mean. The mean (average) of a data set is computed by adding all of the numbers in the set and dividing by the number of values in the set. When arranging data from smallest to greatest, the median is the value in the middle. The mode is the most commonly occurring number in a data set.
Here,
Subtract each measurement from another.
Find the absolute value of each difference from Step 1.
Add up all of the values from Step 2.
Divide Step 3 by the number of measurements.
Mean Error (ME) is calculated by adding the variances and dividing the result by n. An error in this sense is an uncertainty in a measurement, or the discrepancy between the measured value and the true/correct value.
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Can a 7th grader take algebra?
Yes, a 7th grader may be taken algebra. Depending on the school district, and capacity some 7th graders may be able to take algebra as an elective or as part of their regular curriculum.
Algebra is the branch of mathematics that helps in the rendering of problems or situations in the form of mathematical expressions.
It includes variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Some of the branches of mathematics such as trigonometry, calculus, coordinate geometry, involve the use of algebra. One example is in algebra is 2x + 4 = 8.
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Find the missing measures in the parallelogram given below. Also, state the property used.
Answer:
see explanation
Step-by-step explanation:
AD = BC = 8 ( opposite sides of a parallelogram are congruent )
DC = AB = 15 ( opposite sides of a parallelogram are congruent )
Consecutive angles in a parallelogram are supplementary , sum to 180° , so
∠ A + ∠ D = 180° , that is
∠ A + 68° = 180° ( subtract 68° from both sides )
∠ A = 112°
the opposite angles of a parallelogram are congruent , then
∠ B = ∠ D = 68° , and
∠ C = ∠ A = 112°
Harry's soccer team is trying to raise $2,520 to travel to a tournament in florida, so they decided to host a pancake breakfast. Each person must pay $15 for the breakfast. How many people need to attend their breakfast in order to raise $2520?.
Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.
To find the number of people that need to attend the pancake breakfast, we can set up the following equation:
Number of People x Cost per Person = Total Cost
We know that the total cost is $2,520 and the cost per person is $15, so we can substitute those values into the equation:
Number of People x $15 = $2,520
We can solve for the number of people by dividing both sides of the equation by $15:
Number of People = $2,520 / $15
This gives us the number of people that need to attend the pancake breakfast in order to raise the desired amount of money. In this case, the number of people is 168.
Therefore, Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.
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is an integer.
Given that the value of lies between between 29 and 39 Write down the value of .
The values of the integers lie between 29 and 39 and is 30,31,32,33,34,35,36,37,38.
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
Given that the integers lie between the numbers 29 and 39. The numbers will be,
29, { 30,31,32,33,34,35,36,37,38 }, 39
Therefore, the values of the integers lie between 29 and 39 and are 30,31,32,33,34,35,36,37,38.
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True or false math. Make sure you are correct though. Thank you!
Answer:
True
Step-by-step explanation:
Most of the function f(x) has the domain is (- infinity, positive infinity), So I think this is true!
How do you solve for x and y values?
Solving for two variables (normally denoted as "x" and "y") requires two sets of equations.
Assuming you have two equations, the best way for solving for both variables is to use the substitution method, which involves solving for one variable as far as possible, then plugging it back in to the other equation. Knowing how to solve a system of equations with two variables is important for several areas, including trying to find the coordinate for points on a graph.
Write out the two equations that have the two variables you want to solve. For this example, we will find the value for "x" and "y" in the two equations "3x + y = 2" and "x + 5y = 20"
Solve for one of the variables in on one of the equations. For this example, let's solve for "y" in the first equation. Subtract 3x from each side to get "y = 2 - 3x"
Plug in the y value found from the first equation in to the second equation in order to find the x value. In the previous example, this means the second equation becomes "x + 5(2- 3x) = 20"
Solve for x. The example equation becomes "x + 10 - 15x = 20," which is then "-14 x + 10 = 20." Subtract 10 from each side, divide by 14 and you have end up with x = -10/14, which simplifies to x = -5/7.
Plug in the x value in to the first equation to find out the y value. y = 2 - 3(-5/7) becomes 2 + 15/7, which is 29/7.
Check your work by plugging in the x and y values in to both of the equations.
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Calculate the approximate degree measure of the angle, given the following expression: cos(y°) = -0.10 Round your answer to the nearest tenth.
Answer:
y ≈ 95.7°
Step-by-step explanation:
To solve for the angle a trigonometric function is being used on, we have to use the inverse of the trigonometric function.
Inverse of tan(y°) = 4.12:
[tex]tan^{-1}(-0.10) = y[/tex]
Next, I used a scientific calculator to find the angle measure of y. I recommend using the Desmos Scientific Calculator.
[tex]95.7 = y[/tex]
In a survey of 118 randomly selected gun owners, it was found that 81 of them said they owned a gun primarily for protection.
Find the margin of error and 95% confidence interval for the percentage of all gun owners who would say that they own a gun primarily for protection. Report answers to at least 2 decimal places.
Margin of Error (as a percentage)
The margin of error is 0.086 and its C.I is (0.575 , 0.785).
What is margin of error?
Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.n = 117 , x =87
Point estimate for the proportion:
P = x/n
= 81/118
= 0.68644
Confidence = 95%, α = 0.05
From z-table area 0.975 close to z=1.96
Margin of error, E = 1.96 √((0.68*0.55)/130)
= 1.96 * 0.05363
= 0.105
= 0.086
Confidence = P ± E
= 0.68 ± 0.105
=(0.68-0.105 , 0.68+0.105)
= (0.575 , 0.785)
Hence, the margin of error is 0.086 and its C.I is (0.575 , 0.785).
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How do you solve for the mean variance and standard deviation of the sampling distribution of sample means?
From the provided sample, The mean variance and standard deviation of the sample is given by [tex]\bar x = \frac{\sum x}{n} , variance = {standard deviation }^2[/tex] and
[tex]\sqrt \frac{\sum {(x-\bar x)^2}}{n-1}[/tex] .
What do you mean by sample?Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.
What is mean and standard deviation?The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
sample size =n .
[tex]\sum x[/tex] = sum of sample data.
[tex]\bar x = \frac {\sum x}{n}[/tex] (sample mean)
sample standard deviation(s) = [tex]\sqrt \frac{\sum {(x-\bar x)^2}}{n-1}[/tex]
[tex]variance = standard deviation ^2[/tex]
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What is a real value of x?
Answer:
X is a variable, the value depends on the equation
The sophomore class needs a combined total of 216 medium and large t-shirts for field day. The number of medium t-shirts needed is three times the number of large t-shirts needed. Based on this information, would it be reasonable for the sophomore class to order 72 large t-shirts and 144 medium t-shirts?.
No it is not reasonable , because the number of medium T-shirts is not 3 times the number of large T-shirts .
Given :
Let say that the class need x medium and y large t - shirts .
so ,
x + y = 216
x = 3y
substitute
3y + y = 216
4y = 216
divide by 4 on both sides
4y / 4 = 216 / 4
y = 216/4
y = 54
x = 54 * 3
= 162
so here we need 162 medium t - shirts and 54 large t - shirts
given 72 large and 144 medium t - shirts so it not reasonable .
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what distance has a cheats gone if it travels 25 m/s in 3 seconds
Answer:
75 m
Step-by-step explanation:
three seconds of 25 m/s and 3 x 25 = 75
Use the quadratic formula to solve x^2+3x-28=0
The solutions to the quadratic equation x² + 3x - 28 = 0 are 4 and -7.
What are the solutions to the quadratic equation?The quadratic formula is expressed as;
x = (-b±√(b² - 4ac)) / (2a)
Given the equation;
x² + 3x - 28 = 0
a = 1b = 3c = -28Substitute the values of a, b, and c into the formula and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -3 ±√( 3² - ( 4 × 1 × -28) )) / (2×1)
x = ( -3 ±√( 9 - ( -112) )) / (2)
x = ( -3 ±√( 9 + 112 )) / (2)
x = ( -3 ±√( 121 )) / 2
x = ( -3 ± 11 ) / 2
x = ( -3 - 11 ) / 2, x = ( -3 + 11 ) / 2
x = -14/2, x = 8/2
x = -7, x = 4.
Therefore, -7 and 4 are the solutions to the equation.
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Write the number 1. 8 in the form , using integers, to show that it is a rational number.
The number 1. 8 in the form a / b, using integers, to show that it is a rational number is 9 / 5 .
Note that the number 1.8 consists of two parts 1 and 0.8.
The decimal 0.8 can be written as the fraction is 8 / 10
Add these two numbers :
= 1 + 8 / 10
multiply and divide by 10
= 10 / 10 + 8 / 10
= 10 + 8 / 10
= 18 / 10
simplify the number
= 2 * 3 * 3 / 2 * 5
= 1 * 3 * 3 / 1 * 5
= 9 / 5
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How many points lie on a line?
How do you describe the relationship of the volume between the volume of a sphere and the volume of a cylinder?
The relationship between the volume of a sphere and the volume of a cylinder is: the volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.
In this question we need to describe the relationship of the volume between the volume of a sphere and the volume of a cylinder.
Consider a cylinder with radius r and height h.
we know that the formula for the volume of cylinder is,
V1 = π * r² * h
Consider a sphere with radius r1.
We know that the formula for the volume of sphere is,
V2 = 4/3 * π * r1³
If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r1 = r and h = 2r
V2 = 4/3 * π * r³
And V1 = π * r² * (2r)
V1 = 2 * π * r³
V1 = 2 * 3/4 * V2
V1 = 3/2 * V2
volume of cylinder = 3/2 * volume of sphere
Therefore, the volume of a sphere = 2/3 * the volume of a cylinder
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Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.
Complete each of the 2 activities for this Task.
Activity 1 of 2
Find the value of c(7).
In the equation c(n) = 50+4n, the value of c(7) is equal to 78.
What is a function?Absolutely one element of Y is assigned to every element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively.
Al-Biruni and Sharaf al-Din al-Tusi were two Persian mathematicians who developed the earliest known approach to function and its concept. The basic conception of functions was the relationship between fluctuating quantities and other variables. An illustration of this is how time affects a planet's position. In the past, the idea was developed with the infinitesimal calculus around the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable.
This is how the function is defined:
The equation c(n) = 50+4n defines function c, and n is the number of visits.
The function displays the cost in USD per month.
Thus, the following formula can be used to get the value of c(7):
c(7) = 50+4n
c(7) = 50+4(7)
= 50+28
=78
Therefore, c(7)=78
So, the value of c(7)=78.
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8. The speed of an object can be found by taking the distance it travels and dividing it by the
time it takes to travel that distance. An object travels 100 feet in 2.5 seconds Let the speed, be
measured in fleet per second. Write an equation to represent the relationship between the three
quantities (speed, distance, and time).
Speed of object = 40 feet per second
What is speed and its formula?Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s).Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar number.Based on the distance travelled in a certain amount of time. These automobiles can travel at speeds of more than 150 kilometres per hour (km/h). Meters per second (m/s) is the fundamental unit of speed in the metric system.Given data :
Distance cover by object = 100 feetTime taken by object = 2.5 secondsEquation represent speed is s = d/t
Assume;
Speed = S
Time taken = T
Distance cover = D
So,
Speed = Distance / Time
S = D / T
Speed of object = 100 / 2.5
Speed of object = 40 feet per second
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What are the 3 lengths of a right triangle?
What is the relation between area height and volume?
The relation between area, height and volume is: volume = area * height
In this question we need to find the relation between area height and volume.
the formula for area and volume are based on height:
volume = base area * height
Let v represents the volume, A represents area and h represents the height.
V = A * h
As we know the volume of rectangular prism is:
volume = length * width * height
i.e., V = l * w * h
and the base area is:
area = length * width
i.e., A = l * w
Substitute A = l * w in V = l * w * h
Then we get, V = A * h
Therefore, the relation between area, height and volume is: V = A * h i.e., volume = area * height
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How do you store 3 values in one variable in Python?
My_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .
Now, According to the question:
Create a list containing your 3 variables : my_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .
How do I store multiple values in one variable Python?
append()
We use the append() method for this. You can use this to append single values to the list – value, list, tuple.
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5 dogs had long hair out of the 8 dogs at the park. What percent of the dogs had long hair? Round your answer to the nearest whole percent.
Answer:
62.5%
Step-by-step explanation:
5/8 × 100
should give you 62.6%
I really need help on this page, could anyone help me?
F=9/5C+32 is the required equation and Greg statement is true
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that Greg is expressing temperature in farenheit and Josh expressing it in the celsius.
C=5/9(F-32)
We need to rewrite the formula so that Josh can quicly convert the temperature that Greg describes F.
F=9/5C+32
The temperature where John leaves has 77 F.
Let us convert to celsius.
C=5/9(77-32)
C=5/9(45)
C=5(5)
C=25 degrees.
25 degress< 30 degrees.
Hence, F=9/5C+32 is the required equation and Greg statement is true.
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