To prove that all positive integers less than 4 are prime numbers, we will use the method of exhaustive proof.
Proof by contradiction is a method that establishes the the validity of a proposition, by assuming the proposition to be false leads to a contradiction.
Trivial Proof implies that if q is true then p → q is true regardless of the
truth value of p.
Proof by Induction is a method for proving that a statement P(n) is true for every natural number n
Finally, Proof by exhaustion, also known as proof by cases, is a method of proof in which the statement to be proved is split into a finite number of cases, and each type is then checked to see if the proposition in question holds.
Here, as we can see, by definition, exhaustive proof will be most appropriate as we can easily split the statement into 3 cases, taking the integers 1, 2 and 3 in each.
Thus, we will use Exhaustive Proof.
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g how many times would you expect a person selected at random to have to take the test until (s)he passes it? (if necessary, round your answer to 2 decimal places.)
The probability that a person selected at random to have the test until (s)he passes the test is, 0.03125
Given, a test occurred 5 times in a class.
we have to find that how many times a person selected at random to have the test until (s)he passes it.
the probability of getting pass in the exam be, 1/2
and similarly the probability of getting fail in the exam also be, 1/2
so, the probability that a person selected at random to have the test until (s)he passes the test is,
(1/2)^5
= 1/32
= 0.03125
Hence, the probability that a person selected at random to have the test until (s)he passes the test is, 0.03125
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During 1 week, an overnight delivery company found that the weights of its parcels were normally distributed, with a mean of 24 oz and a standard deviation of 6 oz. What percent of the parcels weighed between 12 oz and 24 oz?.
The percent of the parcels weighed between 14 ounces and 35 ounces will be 0.818. (b) The percentage of the parcels weighing more than 49 ounces will be 0.14 %.
(a)The percent of the parcels weighed between 14 ounces and 35 ounces will be 0.818.
The given data in the problem is;
The probability of parcels weighng 35 ounces or less, P₁=0.841
The probability of parcels weighing 14 ounces or less, P₂=0.023
The probability of parcels weighing between 14 and 35 ounces is found as;
P=P₁-P₂
P=0.841-01.023
P=0.818
The probability in the percentage will be 0.818 x 100 = 81.8
(b) The percent of the parcels weighing more than 49 ounces will be 0.14 %.
The probability of parcels weighing more than 49 ounces will be;
P₃ = 1 - 0.99835
P₃ = 0.00135
The probability in the percentage will be 0.00135 x 100 = 0.135% = 0.14%
Hence the percentage of the parcels weighed between 14 ounces and 35 ounces will be 0.818.
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Disclaimer
The question given by you is incomplete, a similar question has been solved above
The question is
Use the Empirical Rule to answer each question.
During 1 week an overnight delivery company found that the weights of its parcels were normally distributed, with a mean of 28 ounces and a standard deviation of 7 ounces.
(a) What percent of the parcels weighed between 14 ounces and 35 ounces? (Round your answer to one decimal place.)
(b) What percent of the parcels weighed more than 49 ounces? (Round your answer to two decimal places.)
The table shows some values of a function of the form y = ax2 + bx + c. The value of c, the constant of the function, is.
c is a constant of the function y = ax² + bx + c is -3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
y = ax² + bx + c
At point (5, 32)
32 = a(5²) + 5b + c (1)
At point (6,45)
45 = a(6²) + 6b + c (2)
At point (4, 21)
21 = a(4²) + 4b + c (3)
Hence:
a = 1, b = 2 and c = -3
The value of c which is a constant of the function y = ax² + bx + c, is -3.
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Select all irrational numbers. responses 14√ square root of fraction 1 over 4 end fraction end root 24√ square root of fraction 2 over 4 end fraction end root 34√ square root of fraction 3 over 4 end fraction end root 44√ square root of fraction 4 over 4 end fraction end root 54√
√(3/4) and √(5/4) are the irrational numbers
How to identify a rational answer?Irrational numbers are numbers that cannot be expressed in the form a/b. They are mostly in the form of square roots when evaluated e.g √7, 2/√5, 3√11, etc.
The opposite of irrational numbers is rational numbers. Rational numbers are numbers that can be written in the form of a/b, where a and b are integers, and b is not equal to 0. e.g 1/3, 2/3, √4 = 4/1, √(1/9) = 1/3, etc.
Given: √(1/4), √(2/4), √(3/4), √(4/4), and √(5/4)
For √(1/4):
√(1/4) = 1/2
This is a rational number
For √(2/4):
√(2/4) = (√2) / 2
This is an irrational number
For √(3/4):
√(3/4) = (√3) / 2
This is an irrational number
For √(4/4):
√(4/4) = 2/2 = 1
This is a rational number
For √(5/4):
√(5/4) = (√5) / 2
This is an irrational number
Therefore, the irrational numbers are √(3/4) and √(5/4). So select them
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When a pre-image is dilated is the resulting image congruent to the original?.
The statement of pre-image is dilated is the resulting image congruent to the origina is false.
Explain dilation.A dilation is a change that creates a picture that is a similar shape as the first, however is an alternate size. • An expansion that makes a bigger picture is called a development. • An expansion that makes a more modest picture is known as a decrease.
According to question:As we all know that dilation is used to resize the object. It make the objects larger or smaller.
It produces an image that is the same shape as the original, but is a different size.
This means, the original figure and the transformed figure would not be congruent.
Therefore, the statement 'When an object is dilated, the resulting image is congruent to the pre-image.' is False
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A six-sided die with sides labeled through will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number greater than ?.
The probability of rolling a number greater than 2 is 2/3
Given that a six sided die with sides labelled with numbers 1,2,3,4,5 and 6 is rolled once.
Since die is said to be equally likely for each number, die is unbiased
P(1) = P(2)=...=P(6) = 1/6
For a number greater than 2, we must not include 2 and hence numbers can be 3 or 4 or 5 or 6
Probability of rolling a number >2 = Probability of rolling 3 or 4 or 5 or 6
= P(3)+P(4)+P(5)+P(6)
= 1/6+1/6+1/6+1/6
=4/6
=2/3
Therefore, the probability of rolling a number greater than 2 is 2/3
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How many strings can be formed by ordering the letters salespersons if no two s’s are consecutive?.
There are 2,540,160 strings of SALESPERSONS with no consecutive S's.
Explanation:
The number of r-combinations of a set of n distinct objects is C(n,r) = [tex]\frac{n!}{r!(n-r)!}[/tex]
Multiplication principle : If one event can occur in m ways AND a second event can occur in n ways, then the number of ways that the two events can occur in sequence is then mn.
We want to place the 4S's in the string of the other letters such that there are not consecutive. Since there are 9 positions including spaces between two consecutive letters in the 8-letter string and two positions on either side of the string, we need to place 4 of the 9 positions to contain a single S each.
By the definition of combination, there are ⁹C₄ ways to select 4 of the 9 positions to place the S's (as the order of the positions is not important since a different order of the S's leads to the same string).
By the multiplication principle, there are then ⁹C₄. [tex]\frac{8!}{2}[/tex] (divided by 2 since , in remaining 8 characters 2E are identical) possible strings of SALESPERSONS with no consecutive S's.
⁹C₄ . [tex]\frac{8!}{2}[/tex] = [tex]\frac{9!}{4!(9-4)!}[/tex] [tex]\frac{8!}{2}[/tex]
= [tex]\frac{9!}{4!.5!} . 20,160[/tex]
= 126.20,160
= 2,540,160
Thus, there are 2,540,160 strings of SALESPERSONS with no consecutive S's.
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which expression is equivalent to 5x-2
Answer:B
Step-by-step explanation: Reducing 2x-2+3x results in 5x-2 because 2x+3x is 5x
Answer:
B)
Step-by-step explanation:
The answer is option B)
2x - 2 + 3x = 5x - 2
failing to reject a false null hypothesis is classified as a a) type i error b) type ii error c) power
The answer to the given question is Type II Error.
What is Type II Error?Type II Error is a statistical term which used in the context of hypothesis testing which defines the error that happens when one fails to reject a null hypothesis which is actually false. A Type II Error constructs a false negative, and also known as an error of omission.
Type II Error is mostly caused by the statistical power of a test being low. A Type II Error will happen if the statistical test is not powerful enough. The size of the sample may also lead to a Type I Error because the outcome of the test will be afflicted.
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Tranlate the entence into an inequality. A number c divided by 8 i greater than or equal to 26
A number c divided by 8 is greater than or equal to 26:
c/8 ≥ 26
The population
decreasing
of a country town is
at a rate of 4% p.a.
How many years will it take for the town's
population of 15000 to fall below 10000?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$10000\\ P=\textit{initial amount}\dotfill &15000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\\ \end{cases}[/tex]
[tex]10000=15000(1 - 0.04)^{t} \implies \cfrac{10000}{15000}=(1 - 0.04)^{t}\implies \cfrac{2}{3}=0.96^t \\\\\\ \log\left( \cfrac{2}{3} \right)=\log(0.96^t)\implies \log\left( \cfrac{2}{3} \right)=t\log(0.96) \\\\\\ \cfrac{\log\left( \frac{2}{3} \right)}{\log(0.96)}=t\implies 9.93\approx t\qquad \textit{about 9 years and 11 months}[/tex]
Find the minimum of x−y among all ordered pairs of real numbers (x,y), x and y between 0 and 1, where there exists a real number a≠1 such that logxa+logya=4logxya.
0 is the minimum (and maximum) of x−y for x, y ∈ (0, 1).
What is real numbers?
A real number in mathematics is a number that can be used to represent a continuous one-dimensional quantity, such as a length of time, temperature, or distance. In this context, continuous denotes that values may vary by arbitrary little amounts. An endless decimal expansion allows for a nearly universal representation of every real number.
The given equation is,
[tex]log_xa+log_ya=4log_x_ya[/tex]
Using the log rule: [tex]log_ab = \frac{ln b}{lna}[/tex]
⇒ [tex]\frac{lna}{lnx}+\frac{lna}{lny} = \frac{4lna}{lnxy}[/tex]
Multiply both sides by, [tex]\frac{lnxy}{lna}[/tex]
⇒ [tex]\frac{lnxy}{lnx}+\frac{lnxy}{lny} = 4[/tex], a ≠ e
Using log rule: [tex]ln(ab) = lna + lnb[/tex]
⇒
[tex]\frac{lnx+lny}{lnx} +\frac{lnx+lny}{lny} = 4\\ \frac{lnx}{lnx}+\frac{lny}{lnx}+ \frac{lnx}{lny}+\frac{lny}{lny} = 4\\1+\frac{lny}{lnx}+ \frac{lnx}{lny} +1=4\\\frac{lny}{lnx}+\frac{lnx}{lny}=2[/tex]
[tex]\frac{(lnx)^2+(lny)^2}{lnx(lny)} =2\\(lnx)^2+(lny)^2 = 2 lnx ln y\\(lnx)^2 - 2lnxlny+(lny)^2=0\\(lnx - lny)^2 = 0\\lnx - ln y = 0\\x = y[/tex]
Hence, 0 is the minimum (and maximum) of x−y for x, y ∈ (0, 1).
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Lucky's Market wanted to see if they could increase the number of sales per day before they close their locations nation wide. To test this, they randomly chose half of their 80 locations and send 50% off coupons to their customers only at those locations, while the other half of locations did not receive the 50% off coupons. They also collected information the amount of money spend on these extra customers. Which of these answers would be the best way to randomization in this study? allow location managers to volunteer O have an unbiased person just pick half of the locations for the coupons. use a computer program to select the locations who get coupons and those that don't
Correct option is:
Use a computer program to select the locations who get coupons and those who don't.
What is Volunteer role?
Volunteer work involves people giving freely of their time, labour, and skill; they frequently complete tasks that organizations would otherwise have to pay for. Governors are one example of a voluntary position in education, Trustees.
Given: Lucky's Market wanted to see if they could increase the number of sales per day before they close their locations nation wide.
To test this, they randomly chose half of their 80 locations and send 50% off coupons to their customers only at those locations, while the other half of locations did not receive the 50% off coupons.
They also collected information the amount of money spend on these extra customers.
So, the correct option is, use a computer program to select the locations who get coupons and those that don't.
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What are the examples of ASA congruence?.
The examples of ASA congruence in its only form, ASA is calculated via way of means of: ASA = Total Wait Time for Answered Calls/Total # of Answered Calls.
The concept at the back of ASA is to get a top level view of trendy performance.any angles and the aspect covered among the angles of 1 triangle are equal to the corresponding angles and aspect covered among the angles of the second one triangle, then the 2 triangles are stated to be congruent via way of means of ASA rule.
Examples on ASA Congruence RuleExample 1: For Δ ABC, display that AB = AC and Δ ABC is isosceles if the bisector AD of ∠ A is perpendicular to aspect BC. Also, this situation satisfies the homes of the isosceles triangles, thus, Δ ABC is an isosceles triangle. Example 2: Prove that △ACF≅△AEB, if ∠C=∠E and AC=AE.
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in multiple regression, a large value of the test statistic f indicates that most of the variation in the response is unexplained by the regression equation. a small value of f indicates that most of the variation in the response is explained by the regression equation.
In multiple regression, a large value of the test statistic f indicates that most of the variation in the response is unexplained by the regression equation and a small value of f indicates that most of the variation in the response is explained by the regression equation. False.
Multiple regression refers to a statistical technique utilized to evaluate the relationship between a single dependent variable and several independent variables. The main goal of the analysis is to use the independent variables with known values to predict the value of the single dependent value. Test statistic f refers to a statistical measure used to test the significance of regression coefficients in linear regression models. In testing the validity of a multiple regression model, a large value of the F-test statistic indicates that most of the variation in y is explained by the regression equation, hence most of the variation in the response is explained by the regression equation.
Note: The question is incomplete as it is missing options which are a) True. b) False.
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A six-foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight... (more down below)When the person is 12 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow.(a) Draw a right triangle that gives a visual representation of the problem. Show the known quantities and use a variable to indicate the height of the streetlight. (b) Use a trigonometric function to write an equation involving the unknown quantity.
h =(c) What is the height of the streetlight?
______ ft
b) h = [tex]tan \theta[/tex] x 17 is the required equation.
c) The height of the streetlight is 20.4 ft.
The height of the person is 6 ft.
The distance at which the person is standing from the streetlight = 12 ft.
The distance at which the person's shadow appears = 5ft.
a) Hence, we can make the following diagram.
The right triangle below gives a visual representation of the problem. It shows the known quantities and a variable 'h' to indicate the height of the streetlight.
b) Let's now find an equation trigonometric function involving the unknown quantity 'h'.
from the below diagram, we can say that,
[tex]tan \theta[/tex] = h/base
base= 12+5=17
hence we have, [tex]tan \theta[/tex] = h/17
h = [tex]tan \theta[/tex] x 17 is the required equation.
c) Now we have to find the height of the streetlight.
firstly let's find the value of [tex]\theta[/tex],
[tex]\theta[/tex] = tan 6/5.
[tex]tan^{-1}[/tex](6/5) = 50.2°
hence, tan 50.2 = h/17
1.20 = h/17
h= 1.20 x 17
h= 20.4 ft.
Hence, the height of the streetlight is 20.4 ft.
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the actual voltages of power packs labeled as 12 volts for a sample are as follows: 11.17, 11.32, 11.97, 11.54, 11.77, 11.29, 11.45, 11.64. determine a point estimate of the population mean. (round your answer to 2 decimal places.)
The point estimate of the population mean is 11.51.
Explain the term population mean?A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait.
A population is the group of people of whom a statistical sample is taken in statistics.The average calculated from the entire community, range, or population is known as the population mean. It is calculated by dividing the sum of all population variables by both the total population of variables. The population mean is shown here as. The population's observations are summed together to form ∑X.For the data given ;
11.17, 11.32, 11.97, 11.54, 11.77, 11.29, 11.45, 11.64
Let X0 be the population mean.
Then,
X0 = ∑X / n
∑X = summation of all data
n = total number of observations.
X0 = 11.17 + 11.32 + 11.97 + 11.54 + 11.77 + 11.29 + 11.45 + 11.64 / 8
X0 = 92.15/8
X0 = 11.51
Thus, a point estimate of the population mean is 11.51.
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HELP QUICKLYYYYY PLEASEEEEEE
Answer:
slope =- [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = (5, - 4 )
m = [tex]\frac{-4-(-3)}{5-2}[/tex] = [tex]\frac{-4+3}{3}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]
Answer:
points are ;
(2,-3).......X1,Y(5,-4).......X2, Y2
now
slope(m)=y2 -Y1 / X2-X1
= -4+3 / 5-2
-1 / 3
Is 30% of a number is 12. 6 find the number?.
What is HCF and LCM of 14 and 28?.
The HCF and LCM of 14 and 28 are 14 and 28 respectively.
Highest Common Factor:
The full form of HCF in maths is the Highest Common Factor. HCF of two or more numbers is the greatest factor that divides the numbers. For example, 2 is the HCF of 4 and 6.
Lowest common multiple:
LCM stands for least common multiple. The least common multiple of two numbers is the smallest number which is a multiple of both of them.
Here we have to find the HCF and LCM of 14 and 28.
The two numbers are 14 and 28.
We can write the number as:
14 = 2 × 7
28 = 2² × 7
The HCF is the common number in both the number, which is 2 and 7.
So HCF of two number = is 2 × 7
= 14
The LCM is the largest common multiple of the given numbers.
So LCM of two number = is 2² × 7
= 28
Therefore the HCF and LCM are 14 and 28 respectively.
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Think of 5 positive integers that have a
mode of 3 and 4, a median of 4 and a
mean of 6.
The required set of 5 positive integers is 3, 3, 4, 4, 16.
What is the mean?The mean is the mathematical average of a group of integers.
Given, to find a set of 5 positive integers such that their mode is 3 and 4, the median is 4, and the mean is 6.
Since the median is 4, the middle number or the number at the 3rd position will be 4.
Since the mode of the data set is 3 and 4, the frequency of 3 and 4 must be 2.
Now, the numbers found so far are 3,3,4,4.
Let the fifth number be x.
The mean of the data set is given by:
mean = (3 + 3 + 4 + 4 + x)/5
Given that mean is 6, therefore,
(3 + 3 + 4 + 4 + x)/5 = 6
14 + x = 30
x = 30 -14
x = 16
Hence, the required set of 5 positive integers is 3, 3, 4, 4, 16.
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Is every linear equation a quadratic equation?.
No, every linear equation is not a quadratic equation.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Any equation of the form ax²+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
Every linear equation is also a quadratic equation. A polynomial equation is a linear equation or a quadratic equation.
Thus, not every linear equation is not a quadratic equation.
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Find the value of "k" that makes this a true statement:
5x+1
x-2
4x²+kx+9
x2_5+6
1
x+6
x-3
=
Answer:
there fore kx = -13x^2-73x+5
then k = -13x^2-73x+5/x
Step-by-step explanation:
given that
5x+1x-2+4x^2+kx+9x^2-5+61x+6x-3 =
= you can write it as
4x^2+9x^2+kx+6x+61x+6x-5
= 13x^2+kx+73x-5
then find kx
-kx = 13x^2+73x-5
there fore
kx = -13x^2-73x+5
then k = -13x^2-73x+5/x
each marble bag sold by alonzo's marble company contains orange marbles for every blue marbles. if a bag has orange marbles, how many blue marbles does it contain?
Using the cross-multiplication method we know that the bag will contain 75 blue marbles if there will be 45 orange marbles.
What is the cross-multiplication method?When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term and vice versa.
We multiply the denominator of one side by the numerator of the other side, starting with the numerator of the first side.
So, a number of blue marbles when there are 45 orange marbles:
We know that there are 5 blue marbles when there are 3 orange marbles.
Now, we have 45 orange marbles, so the number of blue marbles will be:
The equation will be:
3/5 = 45/x
Solve the equation using the cross-multiplication method as follows:
3/5 = 45/x
3x = 5(45)
3x = 225
x = 225/3
x = 75
Therefore, using the cross-multiplication method we know that the bag will contain 75 blue marbles if there will be 45 orange marbles.
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Complete question:
Each marble bag sold by Alonzo's marble company contains 3 orange marbles for every 5 blue marble. if a bag has 45 orange marbles, how many blue marbles does it contain?
how many ways are there to distribute eight different toys among four children if the first child gets at least two toys?
there are 41479 to distribute eight different toys among four children if the first child gets at least two toys.
It is given that,
Total number of toys: 8
Total number of children: 4
The total number of ways to distribute eight different toys among four children is 4⁸.
If the first child gets no toys then the total number of ways to distribute eight different toys among the four children is 3⁸, and if the first child gets one toy then the total number of ways to distribute eight different toys among the four children is,
⁸C1 * 3⁷
The number of ways there to distribute eight different toys among four children if the first child gets at least two toys is calculated as follows.
Number of ways
=4⁸−3⁸−(⁸C1 ∗ 3⁷)
=65536 − 6561 −17496
=41479
Therefore, the required number of ways is 41479
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Find an equation of the tangent line to the curve xey + yex = 5 at the point (0, 5).
Equation of the tangent line to the curve [tex]xe^{y} + ye^{x} = 5[/tex] at5 the point (0,5) is y = - ([tex]e^{5}[/tex] + 5)x + 5.
Given curve is,
[tex]xe^{y} + ye^{x} = 5[/tex]
We will differentiate both sides with respect to x,
[tex]\frac{d}{dx}[/tex][tex][xe^{y} + ye^{x} ][/tex] = [tex]e^{y} + xe^{y}\frac{dy}{dx} + e^{x}\frac{dy}{dx} + ye^{x}[/tex] = 0
⇒ [tex]\frac{dy}{dx}[/tex] [tex][xe^{y} + e^{x} ] = - [e^{y} + ye^{x} ][/tex]
⇒ [tex]\frac{dy}{dx}[/tex] = [tex]- \frac{e^{y}+ye^{x} }{xe^{y}+e^{x} }[/tex]
We have to find the equation at point (0,5).
Therefore substituting values of x and y,
that is x = 0 and y = 5.
[tex]\frac{dy}{dx} = - \frac{e^{5}+(5)e^{0} }{(0)e^{5} + e^{0} }[/tex]
= [tex]- \frac{e^{5} + 5}{1}[/tex]
[tex]\frac{dy}{dx}[/tex] = - [[tex]e^{5}[/tex] + 5] = gradient
Therefore the equation of tangent line is
(y - y1) = [m(x - x1)]
where m is the gradient
⇒ y - 5 = - [([tex]e^{5}[/tex]+5)(x - 0)]
⇒ y = - ([tex]e^{5}[/tex] + 5)x + 5
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What is the ratio 1 to 3 mean?.
for every one (1) you have, you have 3 times the first
Ok,
for example for every 1 penny you have, you have 3dollars,
you counted and you have 4 pennies, in order to find out how many dollars you have, you have to times 4 by 3 to get 12
altogether you would have 4 pennies: 12 dollars.
a recent harris poll survey of u.s. adults selected at random showed that consider the occupation of firefighter to have very great prestige. estimate the probability (to the nearest hundredth) that a u.s. adult selected at random thinks the occupation of firefighter has very great prestige.
The estimated probability of the occupation of firefighters is 0.62
A recent Harris Poll survey of 1010 U.S. adults selected at random showed that 627 consider the occupation of firefighter to have very great prestige. i.e. The sample size of U.S. adults : n= 1010
The number of U.S. adults consider the occupation of firefighter to have very great prestige: x= 627
Now we see, the probability that a U.S adult selected at random thinks the occupation of firefighters has very great prestige will be:
p = x/n
= 627/ 1010 = 0.62 [ To the nearest hundredth]
Therefore, the estimated probability that a U.S adult selected at random thinks the occupation of firefighters has very great prestige = 0.62
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Write an equation uing ""x"" and olve the equation. The rate changed for a tandard room $250 dollar. A couple tayed in the tandard room for x night and their total room change $750
The equation which describes the problem statement would be 250x = 750.
What is the equation in one variable?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable.
The rent for staying one night is $250.
and if a couple stays in the standard room for x night and their total rent was $750 then this can be expressed as
250x = 750
Hence, the equation which describes the problem statement would be 250x = 750.
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How do you find the equation of a line that is perpendicular and passing through a point?.
The equation of a line that is perpendicular and passing through a point is y = -1/m + (y1 + x1/m).
Let y = mx + b be the perpendicular line and (x1,y1) be the point.
slope of y = mx + b is:
= m
we know that,
perpendicular slope = -1/m
substitute m and (x1,y1)
y1 = -1/m(x1) + b
y1 + x1/m = b
substitute b value in y = -1/m + b.
y = -1/m + (y1+x1/m)
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