Find slope between 2 points (4,9) and (1,6)
Answers
Answer:
Step-by-step explanation:
Related Questions
Which term is −20,155,392 for the following sequence, assuming that the pattern continues?
2, −12, 72, −432, ...
a
a9
b
a10
c
a11
d
a12
Answers
The term that is the −20,155,392 in the sequence is a₁₀.
What is sequence?A sequence is defined as an arrangement of numbers in a particular order.
The given sequence is 2, -12, 72, -432
a = first term
n = number of terms
r = common ratio
r = -12 / 2 = 72 / -12 = -432 / 72 = -6
a = 2
Therefore, nth term = arⁿ⁻¹
−20,155,392 = 2 × -6ⁿ⁻¹
−20,155,392 / 2 = -6ⁿ⁻¹
- 10077696 = -6ⁿ⁻¹
6ⁿ⁻¹ = 10077696
6ⁿ⁻¹ = 6⁹
n - 1 = 9
n = 9 + 1
n = 10
Hence, it's the 10th term.
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When you calculate In (10), you would be finding the value of which of the following expressions?
O log (10)
O log₁0(e)
O log(10)
O 10 In(e)
Answers
Answer: Given the log function ln(100), this can therefore be written as loge(100)
Step-by-step explanation: Logarithmic functions
Logarithmic functions are inverse of exponential functions. There are different ways to write log function;
Some are written as a exponent base
Some to the base of 10
Loga is also written as log10(a)
lna is written as loge(a)
Given the log function ln(100), this can therefore be written as loge(100)
Answer: C log(10).
Step-by-step explanation: When you calculate In (10), you would be finding the value of log(10).
In mathematics, the logarithm function is used to express the exponent to which a base must be raised in order to produce a given number. The base of the logarithm is usually denoted by "b" and the number whose logarithm is being taken is denoted by "x". The logarithm of x to base b is denoted as logb(x).
For example, the logarithm of 10 to base 10 is denoted as log10(10), which is equal to 1. The logarithm of 100 to base 10 is denoted as log10(100), which is equal to 2.
In general, the logarithm of x to base b can be calculated as follows:
logb(x) = y
This equation states that b raised to the power of y is equal to x.
The natural logarithm, denoted as In, is a special case of the logarithm function where the base is the mathematical constant e (approximately 2.718). The natural logarithm of x, denoted as In(x), is equal to the logarithm of x to base e.
Therefore, when you calculate In (10), you are finding the value of the natural logarithm of 10, which is the logarithm of 10 to base e.
Option A log (10) is incorrect because it is missing the base of the logarithm (e).
Option B log₁0(e) is incorrect because it is the logarithm of e to base 10, which is not the same as the natural logarithm of 10.
Option D 10 In(e) is incorrect because it is the value of 10 raised to the power of the natural logarithm of e, which is not the same as the natural logarithm of 10.
Option C log(10) is correct because it is the natural logarithm of 10, which is the value we are trying to find. Therefore, the correct answer is C log(10).
Find x and y -- if your answer is not a whole number, round to the tenths!
x =
y =
Answers
Answer: x = 10.57 and y = 15 degree
Step-by-step explanation:
Answer: x= 10 degrees
y= 15 degrees
Step-by-step explanation:
In the diagram below, UV is parallel to RS. If UV is 12 less than UT, RT = 42,
and RS = 21, find the length of UT. Figures are not necessarily drawn to scale.
State your answer in simplest radical form, if necessary.
Answers
The length of UT if, The line UV || RS, UV is 12 less than UT, RT = 42, and RS = 21 is,24.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
Given:
The line UV || RS,
UV is 12 less than UT,
RT = 42, and RS = 21,
Write the equation for the UV and UT,
UV = UT - 12
Calculate the value of UT as shown below,
UT / RT = UV / RS (For parallel lines, the ratio should be the same)
UT / 42 = (UT - 12) / 21
21 × UT / 42 = (UT - 12)
UT / 2 = (UT - 12)
UT = 2UT - 24
2UT - UT = 24
UT = 24
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an anova procedure is used for data that were obtained from five sample groups each comprised of six observations. the degrees of freedom for the critical value of f are . a. 5 and 26 b. 4 and 29 c. 4 and 25 d. 4 and 30
Answers
The correct option 4 and 25; the degrees of freedom for the critical value of f.
Explain the term degrees of freedom?The number of separate bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. It is determined by subtracting the number of constraints from the sample size. The greatest number of logical manner independent variables is, values with the freedom to change—in the data sample is referred to as the degree of freedom.The essential value F's degrees of freedom are (k-1,n-k).
Four sample groups are provided to us, so,
k = 5.
Additionally, we know that each of the five groups has six observations, therefore
n = 5*6
n = 30
The crucial factor F can vary in freedom.
(k-1,n-k)
(5-1, 30 - 5)
(4,25).
Its degrees of freedom again for critical F value are as a result (4,25).
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( (-2)³)²
help me solve please
Answers
The answer is 64
If you need a breakdown I don't know how to help.
So, the order of operations requires you do the inside parentheses first. -2^3 is -8. Then, (-8)^2 means -8 • -8 = 64. (negative times negative is positive). Peace.
|-10-2| • 3(2x+7) -25+2y
x=2
y=3
Answers
Answer:
377 is answer
Step-by-step explanation:
12.33-25 +6
396-25+6
377
solve for x:ax=bx+c , a≠b
Answers
The solution for x in the equation ax = bx + c is x = c/(a - b)
How to determine the solution for x in the equationFrom the question, we have the following parameters that can be used in our computation:
ax=bx+c
Also, from the question, we have the following variable to solve
Variable = x
Rewrite the given equation as
ax = bx + c
Using the above as a guide, we have the following:
Subtract bx from both sides of the equation
So, we have the following representation
-bx + ax = bx + c - bx
Evaluate the like terms
ax - bx = c
So, we have
x(a - b) = c
Divide by a - b
x = c/(a - b)
Hence, the solution is x = c/(a - b)
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What is the difference in the things shown on the photo
Answers
option c) 4x⁴ -2x³ -2x² +3x -10
On subtracting we will get
(3x²₋ 2x + 4x⁴) - (5x²+2x³-5x+10)
= 3x²- 5x²- 2x -2x³+ 4x⁴+ 5x -10
= -2x² + 3x -2x³ + 4x⁴- 10
= 4x⁴ -2x³- 2x² + 3x - 10
The given sum belongs to quadratic equation
Quadratic equation definition:
When a, b, and c are real-world coefficients, a second-order equation is said to be quadratic if it is represented as ax²+ bx + c = 0.
The Characteristics of Quadratic Equations' Roots
The discriminant of the quadratic equation ax2+bx+c=0 is (b2-4ac), which determines whether or not the equation has real roots.
The quadratic equation ax2+ bx + c= 0 hence
If b2-4ac >0, two different real roots
If b2-4ac= 0, there are two equal real roots.
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You roll two fair 6-sided dice with sides labeled 1, 2, 3, 4, 5, 6. What is the probability of rolling a sum that is at most 7
Answers
The probability of rolling a sum that is at most 7 = 1/6
What is probability and example?
Probability = the number of ways of achieving success. the total number of possible outcomes.For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail).P(heads) = ½ .sample space (S) = 36
The probability of rolling a sum that is at most 7
No of sample space = { (1,6) ,(2,5) ,(3,4), (4,3),(5,2),(6,1)}
n(s)/ total sample space = 6/36
= 1/6
Therefore, he probability of rolling a sum that is at most 7 = 1/6
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A machine is designed to dispense 20 mg of d-desoxyephedrine into each capsule of a medicine. 13
pills are tested, and it's found that they have a mean drug content of 20.2 mg, with a standard
deviation of 2.4 mg. To a 1% level of significance, can it be asserted that the standard deviation of
the process (in general) is over 2 mg?
[Assume that the drug contents of all the pills are normally distributed.]
Answers
There is no enough evidence to assert that the standard deviation of the process (in general) is over 2 mg
How to determine if it can be asserted that the standard deviation of the process (in general) is over 2 mg?To determine whether the standard deviation of the process (in general) is over 2 mg to a 1% level of significance, you can perform a hypothesis test.
In this case, the null hypothesis is that the standard deviation of the process is equal to or less than 2 mg, and the alternative hypothesis is that the standard deviation of the process is greater than 2 mg.
To perform the hypothesis test, you can first calculate the test statistic. That is:
test statistic = (sample mean - hypothesized mean) / (standard error of the mean)
test statistic = (20.2 - 20) / (2.4 / √(13))
= 0.2 / 0.67
= 0.3
Next, you can look up the critical value for the test statistic in a table of critical values for a one-tailed test with a 1% level of significance and 12 degrees of freedom (df = 13 - 1).
The critical value for the test statistic is 2.6. Since the test statistic (0.3) is less than the critical value (2.6), you cannot reject the null hypothesis.
This means that you do not have enough evidence to assert that the standard deviation of the process (in general) is over 2 mg to a 1% level of significance.
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The maximum temperature is: ______________________
Answers
Answer:
56.7C
Step-by-step explanation:
The highest temperature on the was 56.7C and it is recorded in United States on 10 July 1913
A pilot flew a jet from City A to City B, a distance of 2400 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 5 h 30 min. What was the speed from City A to City B?
Answers
The speed from City A to City B is 873.33 mi/h.
What is the speed, distance and time?
That is speed = distance ÷ time. Or to put it another way, distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third.
Let's call the speed from City A to City B x. The speed on the return trip was 1.2x. The total distance traveled was 2400 + 2400 = 4800 mi. The total time taken was 330 minutes, which is 330/60 = 5.5 hours. The average speed is the total distance traveled divided by the total time taken, so:
4800 mi / 5.5 h = 873.33 mi/h
The total speed for both legs of the trip is 873.33 + 873.33 = 1746.66 mi/h
The speed for just one leg of the trip is half of the total speed, so the speed from City A to City B is 1746.66/2 = 873.33 mi/h.
Hence, the speed from City A to City B is 873.33 mi/h.
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y=3x-8- here is it’s the right answer
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Given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
What is the general equation of a Straight line?
The general equation of a straight line is -
y = mx + c[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have the equation of line as -
y = 3x - 8
The given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
Therefore, given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
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In 2012, the population of a city was 6.51 million. The exponential growth rate was 2.75% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 10 million? d) Find the doubling time.
Answers
The exponential growth function is P = 6.51 (1.0275)^t. The population of the city in 2018 will be 7.66 million. The population of the city will be 10 million in 15.82258467 years and the doubling time is 25.55035862 years
How to find the exponential growth function?The exponential growth function is of the form P = P₀(1+r)^t
where P₀ is the current population, r is the growth rate and t is the time
Given: P₀ = 6.51 million, r = 2.75% per year
a) The exponential growth function
P = 6.51 (1+0.0275)^t
P = 6.51 (1.0275)^t
b) The population of the city in 2018
t = 2018-2012 = 6 years
P = 6.51 (1.0275)^t
P = 6.51 (1.0275)⁶ = 7.66 million
c) When the population of the city will be 10 million
P = 6.51 (1.0275)^t
10 = 6.51 (1.0275)^t (Solve for t)
(1.0275)^t =10/6.51
log (1.0275)^t = log(10/6.51)
t × log (1.0275) = log(10/6.51)
t = [log(10/6.51)] / [log (1.0275)]
t = 15.82258467 years
d) The doubling time
P = 6.51 (1.0275)^t will become:
2 = 1 (1.0275)^t
1.0275^t = 2
log(1.0275)^t = log 2
t log(1.0275) = log 2
t = log 2 / log 1.0275
t = 25.55035862 years
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Drag each tile to the correct box.
Arrange the numbers as they appear from left to right on a horizontal number line.
Answers
The numbers as they appear from left to right on a horizontal number line is Horizontal number line.
This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.
What's the equation of a horizontal line?
Horizontal lines have a slope of 0. Thus, in the slope-intercept equation y = mx + b, m = 0. The equation becomes y = b, where b is the y-coordinate of the y-intercept.
-2.76
-2.57
-2.5
-1.85
-1.58
2.5
2.85
On a number line, we have this horizontal line, meaning it moves left and right, and zero is placed in the middle.
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don't deposited $7,000 in an account earning 10% interest compounded annually to the nearest cent how much interest will he earn in 4 years
Answers
Interest in $2800 when deposited $7,000 in an account earning 10% interest compounded annually.
Define simple interest.Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows $5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Given
Principal = $7000
Rate = 10%
Time = 4 years
Using simple interest formula,
PRT
7000 × 0.1× 4
2800
Interest in $2800 when deposited $7,000 in an account earning 10% interest compounded annually.
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Answer: 3,248.70
Step-by-step explanation: You can use this formula when working with compound interest:
B=p(1+r)t
In this formula, B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
The interest is the balance minus the principal.
solve
Write the rate as a decimal.
10%=0.10
Calculate the balance.
B
= p(1+r)t
= $7,000(1+0.10)4
= $7,000(1.10)4
= $7,000(1.4641)
= $10,248.70
Now use this to find the interest, which is the balance minus the principal.
$10,248.70–$7,000=$3,248.70
The interest will be $3,248.70.
Solve the following and find Q R
Answers
Answer:
QR = 49
Step-by-step explanation:
QR = QP
3x + 22 = 10x - 41
x = 9
10(9) - 41
= 49
What is the perimeter of WXYZ?
I need the answer please help me
Answers
Answer: 48
Step-by-step explanation:
Using isosceles triangle [tex]XWZ[/tex], we know that [tex]WZ=11[/tex].
Using equilateral triangle [tex]XYZ[/tex], we know that [tex]YZ=XY=11[/tex].
So, the perimeter is [tex]WX+WZ+ZY+XY=11+11+11+15=48[/tex].
Mike has $90,000 to invest and can invest in two different funds. He invests some of the money at 5% per year and the rest at 8% per year. How much should mike invest in each fund in order to earn $5220 from both funds per year?
Answers
Using a system of equations, Mike should invest $66,000 in investment A and $24,000 in investment B to earn $5,220 from both funds per year.
How are the amounts determined?We can solve a system of equations to determine the amounts that should be invested in each fund to earn the stated amount yearly.
A system of equations is also called simultaneous equations because they can be solved together.
The total investible funds = $90,000
The expected annual earnings = $5,220
The earnings from investment A = 5% or 0.05
The earnings from investment B = 8% or 0.08
Equations:A + B = 90,000 ... Equation 1
0.05A + 0.08B = 5,220 ... Equation 2
Multiply equation 1 by 0.05:
0.05A + 0.05B = 4,500 ... Equation 3
Subtract Equation 3 from Equation 2:
0.05A + 0.08B = 5,220
-0.05A + 0.05B = 4,500
=0.03B = 720
= 24,000 (720/0.03)
B = $24,000
From Equation 1, substitute B = 24,000 to get A:
A + B = 90,000
A + 24,000 = 90,000
= 66,000
A = $66,000
Thus, we can conclude that Mike with $90,000 should invest $66,000 in Investment A earning 5% per year, and $24,000 in Investment B earning 8% annually to earn a total of $5,220 from both funds.
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The point (2, 90) represents the value that after 2 weeks, Paul's math average is a 90. The point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to a 50 because he doesn't do homework and doesn't know how to log into Quizlet. What equation represents the line of Paul's grade downfall?
Answers
The equation that represents the line of Paul's grade downfall is y = -20x + 130.
How to find the equation represents the line of Paul's grade downfall?To find the equation of the line that represents Paul's grade downfall, we need to use the two points given: (2, 90) and (4, 50).
We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula: slope (m) = (y2 - y1)/(x2 - x1).
Plugging in the values from the two points we have:
m = (50 - 90)/(4 - 2) = -40/2 = -20.
y = mx+b [Using (x= 2, y = 90)]
90 =-20(2) + b
90 = -40
b = 130
Plugging these values into the slope-intercept form, we get:
y = -20x + 130.
Thus, the equation is y = -20x + 130
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the dimension of an eigenspace of a symmetric matrix is sometimes less than the multiplicity of the corresponding eigenvalue.
a. true
b. false
Answers
True, The dimension of the eigenspace for each eigenvalue equals the multiplicity.
What is eigen value?Eigenvalues are a unique set of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar factor.
What is an Eigenspace?When a linear transformation is done to an eigenvector, a set of eigenvectors called an eigenspace is created for each eigenvalue. In many cases, the linear transformation uses a square matrix (a matrix that has the same number of columns as it does rows).
yes, it is true that the dimension of an eigenspace of a symmetric matrix is sometimes less than the multiplicity of the corresponding eigenvalue.
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Thirty students in a chemistry class each completed a particular lab assignment. Gerald and Sharon each collected data from the students to estimate the mean time it took for the class to complete the assignment.
Gerald asked 4 of the students now long eacn one ortem took to complete the assionment and correcuy carculated d fie an time of 38 minutes. Sharon asked 10 different students in the class the same question, and correctly calculated a mean time of 32 minutes
Both Gerald and Sharon claim their calculated mean time for completing the assignment is the better estimate of the actual mean time for the whole class. Which of the following statements best explains who is correct?
Answers
Answer:
Step-by-step explanation:
It is likely that Sharon's calculated mean time is the better estimate of the actual mean time for the whole class. This is because she collected data from a larger sample of the class (10 students) than Gerald (4 students). A larger sample size generally results in a more accurate estimate of the population mean.
It is more likely for the mean time calculated by Sharon to be better estimate than that of Gerald.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Given,
Mean time to complete the assignment taken from 4 students by Gerald = 38 minutes.
Mean time to complete the assignment taken from 10 students by Sharon = 32 minutes
Population size = 30 students
When the sample size is more closer to the population size, the sample mean would be more closer to the actual mean.
So Sharon's estimate is a better option.
Hence the estimate value of mean calculated by Sharon is more likely to be closer to the actual mean.
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solve this on graph paper
Answers
The graphs of the equations are drawn ad attached here.
What is the slope-intercept form of a line?The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.
The given equations are (i) y = x-4, (ii) y = 2x-4, (iii) y = 3x-4.
The equations are given in the slope-intercept form.
(i) The given equation is y = x-4.
the y-intercept of the equation is (0,-4).
Now, substitute y = 0 into the given equation:
0 = x - 4
x = 4
Hence, the line y = x-4 passes through points (0,-4) and (4,0).
Now, draw a line passing through the points (0,-4) and (4,0).
Using the same procedure, the graphs of the other two equations are also drawn.
Hence, the graphs of the equations are drawn ad attached here.
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Simplify and state the restrictions on the domain:
Answers
Answer:
its the first option explanation is up top
Given the function h(x)= 2x+3/4x-5 find h⁻¹(x)
Answers
The inverse of the rational function h(x) = (2 · x + 3) / (4 · x - 5) is the rational function h⁻¹(x) = (5 · x + 3) / (4 · x - 2).
How to find the inverse of a rational function
In this problem we have the definition of a rational function:
h(x) = (2 · x + 3) / (4 · x - 5)
Of which we must determine the inverse of the rational function by using algebraic properties:
h⁻¹(x) = f(x)
First, use the following substitution on h(x):
x = h(x)
h⁻¹(x) = x
Second, substitute in the rational equation:
x = [2 · h⁻¹(x) + 3] / [4 · h⁻¹(x) - 5]
Third, clear h⁻¹(x) in the expression by algebraic properties:
x · [4 · h⁻¹(x) - 5] = 2 · h⁻¹(x) + 3
(4 · x - 2) · h⁻¹(x) = 5 · x + 3
h⁻¹(x) = (5 · x + 3) / (4 · x - 2)
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The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies. Note C D E F G A B Frequency(Hz) 261.6 293.7 329.6 349.2 392.0 440.0 493.9 Determine the ratio of the note B to middle C
Answers
Answer:
Step-by-step explanation:
To determine the ratio of the note B to middle C, we can divide the frequency of B by the frequency of C. Using the information provided, the frequency of B is 493.9 Hz and the frequency of C is 261.6 Hz. The ratio of B to C is therefore 493.9 / 261.6, which is approximately equal to 1.89. This means that the note B is approximately 1.89 times higher in pitch than the note C.
Below is a graph showing the speed in meters/second of a cheetah s seconds after it starts running.
What interpretation can be made from the y-intercept? ____________.
How can the point (3.0, 12) on the graph above be interpreted? ___________.
What is the output value of this graph when the input value is 5.0? _________.
Does the graph above have a constant rate of change? ____________.
Answers
The graph in the problem is interpreted as follows
What interpretation can be made from the y-intercept?
the y-intercept shows start the timing started when the cheetah is not running
How can the point (3.0, 12) on the graph above be interpreted? At 3.0 s the cheetah was running at 12 m/s
What is the output value of this graph when the input value is 5.0?
the output is 30
Does the graph above have a constant rate of change?
No, the rate of change varies
What is rate of change?The term "rate of change" describes the rate at which something changes over time.
Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).
When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant.
The slope is another name for the constant rate of change. The rate of change for linear functions will be constant.
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The height of a model rocket, H(t), is a function of the time since it was
launched, t.
Height (feet)
450-
400-
350-
300-
250-
200-
150-
100
50-
0
0
H(t)
10
30
20
Time (seconds)
What is the domain of H(t)?
40
Answers
Step-by-step explanation:
the domain is the interval or set of all valid x- (or input-)values. in our case here t-values.
the graph shows us
0 <= t <= 35
For the given condition on the graph, the domain of the function is
0 ≤ t ≤ 36.
What is function?A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical connections in the sciences. A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output.
Here,
The correct answer is option B. 0 ≤ t ≤ 36
To do this question, the main thing is to look at picture.
We know from the graph that this is a quadratic function, So t has to be less than some positive number.
{ if t → -∞, H(t) → -∞, not in the line with the actual situation}
and look at the graph, the point where H(t) equals zero, one is 0 and one is 36.
The domain for the function is 0 ≤ t ≤ 36 for given condition in the graph.
For more information on function,
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A company produces shotgun shells in batches of 350. A sample of 5 is tested from each batch, and if more than one defect is found, the entire batch is tested. (Round your answers to five decimal places.) (a) If 1% of the shells are actually defective and we assume independence, what is the probability of 0 defective shells in the sample?
(b) If 1% of the shells are actually defective and we assume independence, what is the probability of 1 defective shell in the sample?
(c) If 1% of the shells are actually defective and we assume independence, what is the probability of more than 1 defective shell in the sample?
Answers
a. The probability of defective shells from the given samples are:
a. Probability of zero defective shells of samples is equal to 0.9510.
b. Probability of one defective shells of samples is equal to 0.04803
c. Probability of more than 1 defective shells of samples is equal to 0.00107.
As given in the question,
Total number of batches = 350
Sample size used to test for each batch 'n' = 5
Actual defective shells (success) 'p' = 1%
= 0.01
Actual non-defective shells ' 1 - p ' = 1 - 0.01
= 0.99
a. Probability of zero defective shells from the given samples is
= ⁵C₀ × ( 0.01 )⁰ × (0.99)⁵⁻⁰
= [ (5!)/(5-0)!0! ] × 1 × ( 0.99)⁵
= 0.9510
b. Probability of 1 defective shells from the given samples is
= ⁵C₁ × ( 0.01 )¹ × (0.99)⁵⁻¹
= [ (5!)/(5-1)!1! ] × 0.01 × ( 0.99)⁴
= 5 × 0.01 × 0.9606
=0.04803
c. Probability of more than 1 defective shells from the given samples is
= P(2) + P(3) + P(4) + P(5)
= ⁵C₂ × ( 0.01 )²× (0.99)⁵⁻² + ⁵C₃ × ( 0.01 )³ × (0.99)⁵⁻³ + ⁵C₄× ( 0.01 )⁴ × (0.99)⁵⁻⁴+ ⁵C₅× ( 0.01 )⁵× (0.99)⁵⁻⁵
= 0.00097 + 0.000098 +0.000000044 +0.0000000001
=0.00107
Therefore, the probability of following conditions are as follow:
a. Probability of zero defective shells of samples is equal to 0.9510.
b. Probability of one defective shells of samples is equal to 0.04803
c. Probability of more than 1 defective shells of samples is equal to 0.00107.
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