Answer:
The slope is -4/5
The y intercept is (0,7)
Step-by-step explanation:
f(x) = 7 -4/5x
Rewriting
y = -4/5x +7
This is in slope intercept form
y = mx+b where m is the slope and x is the y intercept
The slope is -4/5
The y intercept is (0,7)
The population of City A in 2000 was 40 thousand people and the population increased by 13% each year. The function f determines the population of this city (in thousands of people) in terms of x . Write a function formula for f .
Answer:
f(x) = 40(1 + 0.13)^x
Step-by-step explanation:
The general formula for an exponential growth function is;
f(x) = a(1 + r)^x
Where;
a= initial population of the city
r= population growth rate
x = number of years
Given that;
a= 40,000
r= 0.13
The population of the city in thousands of people in terms of x is;
f(x) = 40(1 + 0.13)^x
Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.
9514 1404 393
Answer:
(x +5)² +(y -3)² = 25x² +y² +10x -6y +9 = 0Step-by-step explanation:
The "center-radius" form is ...
(x -h)² +(y -k)² = r² . . . . . . . circle with center (h, k) and radius r
The graphed circle has its center at (-5, 3) and a radius of 5. Putting these numbers into the above form gives the equation ...
(x +5)² +(y -3)² = 25 . . . . center-radius form
Expanding the parentheses, we get ...
x² +10x +25 +y² -6y +9 = 25
Subtracting 25, and putting in general form, the equation becomes ...
x² +y² +10x -6y +9 = 0 . . . . general form
_____
Additional comment
General form is f(x, y) = 0, where the terms of f(x, y) are lexicographical order and decreasing degree.
find out the area of the following composite figures
For the function f(x) = x^2 + 4x -5 solve the following f(x)=0
That's a question about quadratic function.
Any quadratic function can be represented by the following form:
[tex]\boxed{f(x)=ax^2+bx+c}[/tex]
Example:
[tex]f(x)= -3x^2-9x+57[/tex] is a function where [tex]a=-3[/tex], [tex]b=-9[/tex] and [tex]c=57[/tex].
Okay, in our problem, we need to find the value of x when [tex]f(x)=0[/tex]. That's mean that the result of our function is equal to zero. Therefore, we have the quadratic equation below:
[tex]x^2+4x-5=0[/tex]
To solve a quadratic equation, we use the Bhaskara's formula. Do you remember the value of a, b and c? They going to be important right now. This is the Bhaskara's formula:
[tex]\boxed{x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} }[/tex]
So, let's see the values of a, b and c in our equation and apply them in the Bhaskara's formula:
In [tex]x^2+4x-5=0[/tex] equation, [tex]a=1[/tex], [tex]b=4[/tex] and [tex]c=-5[/tex]. Let's replace those values:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-4\pm \sqrt{4^2-4\times1\times(-5)} }{2\cdot1}[/tex]
[tex]x=\frac{-4\pm \sqrt{16-(-20)} }{2}[/tex]
[tex]x=\frac{-4\pm \sqrt{16 + 20)} }{2}[/tex]
[tex]x=\frac{-4\pm \sqrt{36} }{2}[/tex]
[tex]x=\frac{-4\pm 6 }{2}[/tex]
From now, we have two possibilities:
To add:
[tex]x_1 = \frac{-4+6}{2} \\x_1=\frac{2}{2} \\x_1=1[/tex]
To subtract:
[tex]x_2=\frac{-4-6}{2} \\x_2=\frac{-10}{2} \\x_2=-5[/tex]
Therefore, the result of our problem is: [tex]x_1 = 1[/tex] and [tex]x_2=-5[/tex].
I hope I've helped. ^^
Enjoy your studies. \o/
Determine the degree of the term 2^3x2yz4
Answer:
7
Step-by-step explanation:
It looks like the term is [tex]2^3}x^2}yz^4[/tex]
First simplify
[tex]8x^2}yz^4[/tex]
[y has an exponent of 1 btw]
Then to find the degree of a term, just add up the values of all the exponents
2+1+4=7
I hope this helps!
Find a homogeneous second-order Cauchy-Euler equation with real coefficients if the given number is a root of its auxiliary equation.
mi= i
C1cos(ln(x)) + C2sin(ln(x))
I'm going to assume that you mean to say that i = √(-1) is a root of the auxiliary equation. That is, if the Cauchy-Euler DE is
x ²y'' + axy' + by = 0
then the auxiliary equation obtained by substituting y = xᵐ is
x ² (m (m - 1) xᵐ ⁻ ²) + ax (m xᵐ ⁻ ¹) + bxᵐ = 0
which reduces to
m (m - 1) + am + b = 0
or
m ² + (a - 1) m + b = 0
By the fundamental theorem of algebra, we can write the quadratic in terms of its roots r₁ and r₂,
(m - r₁) (m - r₂) = 0
Given that one root is the imaginary unit i, and the coefficients of the aux. equation are real, it follows that the other root is -i, because complex roots must occur with their conjugates. So we have as our aux. equation,
(m - i ) (m + i ) = 0
or
m ² + 1 = 0
Then a - 1 = 0 and b = 1, so that the given root and general solution correspond to the DE,
x ²y'' + xy' + y = 0
7. A machine produces memory sticks of varying lengths, distributed uniformly between 3mm and 13 mm. Memory sticks longer than 10 mm do not meet the design criteria and must be scrapped. Calculate the proportion of memory sticks that will be scrapped, which is the probability that memory stickers longer than 10 mm will be scrapped.
Answer:
The proportion of memory sticks that will be scrapped is 0.3 = 30%.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Distributed uniformly between 3mm and 13 mm.
This means that [tex]a = 3, b = 13[/tex]
Calculate the proportion of memory sticks that will be scrapped:
[tex]P(X > 10) = \frac{13 - 10}{13 - 3} = \frac{3}{10} = 0.3[/tex]
The proportion of memory sticks that will be scrapped is 0.3 = 30%.
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 5 hours of burning, a candle has a height of 21.5 centimeters. After 24 hours of burning, its height is 19.6 centimeters. What is the height of the candle after 11 hours?
YEsStep-by-step explanation:
The LARGEST angle has a measure of ______degrees
Answer:
90 i think
Step-by-step explanation:
In a random sample of 7 residents of the state of Maine, the mean waste recycled per person per day was 1.4 pounds with a standard deviation of 0.23 pounds.
a. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Maine. Assume the population is approximately normal.
b. Find the critical value that should be used in constructing the confidence interval.
Answer:
a) The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.
b) [tex]T_c = 2.4469[/tex]
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 7 - 1 = 6
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469, and the answer to question b is [tex]T_c = 2.4469[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{0.23}{\sqrt{7}} = 0.21[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1.4 - 0.21 = 1.19 pounds.
The upper end of the interval is the sample mean added to M. So it is 1.4 + 0.21 = 1.61 pounds.
The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.
bionomial probabilities
Answer:
Binomial probability refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment).
Hope this will help you :)the two roots a minus the square root of b and a plus the square root of b are called
Answer:
The two roots a+√b and a-√b are called Conjugate radicals
Step-by-step explanation:
I'd really appreciate a brainleast:)
equation of a line with slope -1 and y intercept 0,-2
Answer:
y = - x - 2
Step-by-step explanation:
y=mx+b
m refers to slope
b refers to y intercept
y = (-1)x + (-2)
y = - x - 2
Answer:
y=-1x-2
Step-by-step explanation:
plug in the slop and y intercept to the equation y=mx+b
A 40-foot tree casts a shadow 60 feet long. How long would the shadow of a 6-foot man be at that time?
Answer:
26 ft
Step-by-step explanation:
I'm guessing this is how it's done
60-40= 20
there for at this time any shadow would be 20x it's original height/length
so 6+20=26 ft
lmk if I'm correct
Taking ratios
Let the shadow length=x ft
[tex]\\ \sf\longmapsto 40:60=6:x[/tex]
[tex]\\ \sf\longmapsto \dfrac{40}{60}=\dfrac{6}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{4}{6}=\dfrac{6}{x}[/tex]
[tex]\\ \sf\longmapsto 4x=6(6)[/tex]
[tex]\\ \sf\longmapsto 4x=36[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto x=9[/tex]
a person who take 40 paces to cover 20m finds that a square field has a side that is 520 paces long .calculate the length of the side and the area of the field
The area of the square field is 67600 m² and the side is 260 m long.
What is square?A quadrilateral with all sides equal and all angles are right angles.
Given that, a person takes 40 paces to cover 20 m of a square field according to him the field has a side that is 520 paces long, we need to find the measure of the side and the area,
Since,
40 paces = 20 m
1 pace = 1/2 m
Therefore,
520 paces = 0.5 x 520 m
= 260 m
Therefore, the square field is 260 m long,
Area of the square field = side² = 260²
= 67600 m²
Hence, the area of the square field is 67600 m² and the side is 260 m long.
Learn more about squares, click;
https://brainly.com/question/14198272
#SPJ2
Four- sevenths of the children in class earned A's on the last math test. 18 children did not earn an A. How many earned A's? SHOW ALL WORK!!!
Answer: 24 people earnt As
Step-by-step explanation:
1. We know that 18 people are the other 3/7 of the class
2. We first find out 1/7, which is calculated by dividing 3/7 by 3, which is 18 / 3 so 6
3. We can then find 4/7 by multiplying the amount of 1/7 by 4, so 6 x 4 = 24
There are 9 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommitteeses are possible?
Answer:
126
Step-by-step explanation:
9 choose 4 (Order does not matter)
9 nCr 4 = 126
Grams in this equation
30 .650 pounds of gramsin vegetables
If the mean age of the managers in company is 52 years with a standard deviation of 2.5 years, what is the probability that a randomly chosen manager will be between 54.5 and 57 years old
Answer:
13.5 %
Step-by-step explanation:
For a normal distribution, the Empirical Rule states that 68% of values lie between 1 standard deviation of the mean, 95% of values lie between 2 standard deviations of the mean, and 99.7% of values lie between 3 standard deviations of the mean. Here, we can see that 54.5 is 1 standard deviation away from the mean and 57 is 2 standard deviations away. This means that we want to find the difference between 1 and 2 standard deviations from the mean (in the positive direction)
To find the difference, we can simply find (percent of values 2 standard deviations of the mean) - (percent of values 1 standard deviation from the mean) = percent of values between 1 and 2 standard deviations from the mean
= 95-68 = 27 %
Finally, this gives us the percent of values between 1 and 2 standard deviations from the mean on both sides. We want to only find the positive aspect of this, as we don't care how many values are between 49.5 and 47 years old. Because normal distributions are symmetric, or equal on both sides of the mean, we can simply divide by 2 to eliminate the half we don't want, resulting in 27/2 = 13.5
The probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.
Given that, average age managers = 52 years standard deviation = 2.5 years.
What is standard deviation?Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Considering the equation Z = (X−μ)/σ
Where, X is the lower or higher value, as the case may be μ is the average σ is standard deviation
Now, z1= (54.5 - 52)/2.5
= 1
z2= (57 - 52)/2.5
= 2
Now, z2-z1= 2-1
= 1
P(54.5>Z<57)= 0.8413
Therefore, the probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.
Learn more about the standard deviation visit:
brainly.com/question/13905583.
#SPJ2
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.01. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
Answer:
1.) scatter plot is attached below.
There is no sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals.
Step-by-step explanation:
Given the data :
Overhead width : 7.2 7.5 9.7 9.3 8.7 8.2
Weight : 119 156 243 200 199 188
The linear correlation Coefficient, R = 0.946
Using the Pvalue calculator for R score ;
Pvalue = 0.0149
Since, Pvalue > Α ; WE fail to reject the Null and conclude that there is no sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals.
use the elimination method to slove the system of equations.choose the correct ordered pair.6x+2y=8 12x+y=22
Answer: use photo. math
Step-by-step explanation:
boom
A teacher finishes explaining a new concept to the class and wants to check that all the students have grasped the concept. The teacher asks those who do not understand to raise their hands. This process leads to which of the following bias(es)?
a) Response bias
b) Measurement bias
c) Both response bias and measurement bias
d) neither response bias nor measurement bias
Answer:
response bias
Step-by-step explanation:
because whan you are asked a question you expect response in return
1) Seven less than twice a number, n, is 32.
A. 7 - 2n = 32
B. 2n - 7 = 32
C. 7-n=2.32
D. (n - 7). 2 = 32
1) Seven less than twice a number, n, is 32.
ANS) B. 2n - 7 = 32
Answer:
1.
B. 2n - 7 = 32 is the right answer
A route up a mountain is 20 Km long. john followed this route at an average speed of xkm/h. write down an expression in terms of x,for the number of hours he took to walk up the mountain.
Answer:
20/x
Step-by-step explanation:
speed = distance /time
x km/h is speed
20 km is distance
x= 20/t
t= 20/x
Find the measure of the missing angles.
Answer:
Step-by-step explanation:
e = 61°, f = 119°, and d = 90°
We know that vertically opposite angles are equal.
So, e = 61° [Vertically opposite angles]
We know that linear pair of angles are supplementary (180°).
So, f + 61° = 180° [Linear pair of angles]
=> f = 180° - 61°
=> f = 119°
and d + 90° = 180° [Linear pair of angles]
=> d = 180° - 90°
=> d = 90°
Terry got 27 out of 50 for his Maths test. What is his mark as a percentage?
Answer:
54%
Step-by-step explanation:
Concepts:
A percent is a value indicating hundredth parts of any number. 1%/one percent would be equal to a hundredth part, and 100% would be the entire quantity.Solving:
Let's solve this problem by going through the steps to find the percentage.
1. Find out the entire amount
Since Terry got 27/50 on his math test, we can assume he got 27 questions right out of 50 questions. This means, in total, there was 50 questions.2. Divide the number you want expressed as a percent by the total quantity
The number we want in this question to be expressed as a percent is 27, and the total quantity is 50.27 ÷ 50 = 0.543. Multiply the resulting value by 100
The result we got when we divided 27 by 50 is 0.540.54 · 100 = 544. Add the percent symbol (%) at the end of the value
The value we got was the number 5454%Therefore, Terry's marks as a percentage is 54%.
Find the unit price of each of the following items Round your answer to the nearest tenth
frozen orange juice
16.0% at $2.01
12 oz at $1.69
Answer:
12.56 cents
14.08 cent
Step-by-step explanation:
The unit price for each of the following items could be obtained thus :
The unit price = price of one item
Therefore, given that x numbers of a certain item cost y ;
The unit price will be : y / x
frozen orange juice
16.0 oz at $2.01
12 oz at $1.69
If 16 oz cost $2.01
1 oz = $2.01 / 16 = $0.125625 * 100 = 12.56 cents
If 12 oz = $1.69
1 oz = $1.69 / 12 = $0.1408333 * 100 = 14.08 cent
Shortern this expression pls
Answer:
[tex]c =\frac{8}{3}[/tex]
Step-by-step explanation:
Given
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]
Required
Shorten
We have:
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]
Rationalize
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}[/tex]
Expand
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} + \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}[/tex]
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} + \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}[/tex]
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} + \sqrt{\frac{(4 - \sqrt 7)^2}{9}[/tex]
Take positive square roots
[tex]c =\frac{4 + \sqrt 7}{3} + \frac{4 - \sqrt 7}{3}[/tex]
Take LCM
[tex]c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}[/tex]
Collect like terms
[tex]c =\frac{4 + 4+ \sqrt 7 - \sqrt 7}{3}[/tex]
[tex]c =\frac{8}{3}[/tex]
1. Choose the correct decimal for "three tenths."
3
0.03
0.003
0.3
Please hurry, if you do reply thank u, it means alot! <3 :)
Answer:
3 tenths means 3 over ten represented as as 3/10 and 10 has one zero I.e tenth different from hundredths which has 2 zeros so our decimal shld also have one zero which is 0.3...so 0.3 is the answe hope it helps❤
can anybody help me with this?
Answer:
Option (a)
Step-by-step explanation:
[tex]\sqrt[6]{1000m^{3} n^{12} } = \sqrt[6]{10^{3} } \sqrt[6]{m^{3} } \sqrt[6]{n^{12} } =\\\sqrt{10} \sqrt{m} n^{2} = n^{2} \sqrt{10m}[/tex]
