Answers
Answer:
The rate of change, or slope, is 1/2.
To find the slope of a line, first, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!
Related Questions
the bacteria count in a certain culture was 200 after 10 days and 1200 after 20 days. assume the bacteria are growing exponentially
Answers
The initial size of the bacteria culture is 33
The count of the bacteria after 10 days = 200
The count of bacteria after 20 days = 1200
The difference in time = 20 - 10
= 10 days
Then the exponential growth equation will be
1200 = 200×[tex]e^{10k}[/tex]
[tex]e^{10k}[/tex] = 1200 / 200
Divide the terms
[tex]e^{10k}[/tex] = 6
10k = ln(6)
10k = 1.79
k = 1.79 / 10
Divide the terms
k = 0.179
Use the same equation to find the initial size of the bacteria culture
200 = x × [tex]e^{10(0.179)}[/tex]
x = 200 / [tex]e^{10(0.179)}[/tex]
x = 200 / 5.99
Divide the terms
x = 33.38
x ≈ 33
Hence, the initial size of the bacteria culture is 33
The complete question is:
The bacteria count in a certain culture was 200 after 10 days and 1200 after 20 days. assume the bacteria are growing exponentially. Find the initial size of the bacteria culture
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Solve the following equations. Will give brainliest.
Answers
Answer:
[tex]x=10^{\frac{4}{3}}=\sqrt[3]{10000}[/tex]
Step-by-step explanation:
Given equation:
[tex]9^{\log_3 (\log x)}= \log x-2\log^2x+4[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^{\log_3 (\log x)}= \log x-2\log^2x+4[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2\log_3 (\log x)}= \log x-2\log^2x+4[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies 3^{\log_3 (\log x)^2}= \log x-2\log^2x+4[/tex]
[tex]\textsf{Apply log law}: \quad a^{\log_ab}=b[/tex]
[tex]\implies (\log x)^2= \log x-2\log^2x+4[/tex]
Simplify:
[tex]\implies\log ^2 x= \log x-2\log^2x+4[/tex]
[tex]\implies 3\log ^2 x- \log x-4=0[/tex]
Let log(x) = u:
[tex]\implies 3u^2-u-4=0[/tex]
Factor:
[tex]\implies 3u^2+3u-4u-4=0[/tex]
[tex]\implies 3u(u+1)-4(u+1)=0[/tex]
[tex]\implies (3u-4)(u+1)=0[/tex]
Apply the zero-product property:
[tex]\implies 3u-4=0 \implies u=\dfrac{4}{3}[/tex]
[tex]\implies u+1=0 \implies u=-1[/tex]
Substitute u=log(x) back in:
[tex]\implies \log x = -1[/tex]
[tex]\implies \log x= \dfrac{4}{3}[/tex]
On the left side of the original equation, we have log₃ (log x).
As logs of negative numbers cannot be taken, log(x)=-1 is not a valid solution since this would give log₃(-1) which is undefined.
Therefore, the only valid solution is:
[tex]\implies \log x= \dfrac{4}{3}[/tex]
[tex]\implies x=10^{\frac{4}{3}}[/tex]
[tex]\implies x=\left(10^4\right)^{\frac{1}{3}}[/tex]
[tex]\implies x=10000^{\frac{1}{3}}[/tex]
[tex]\implies x=\sqrt[3]{10000}[/tex]
Note: If a log has no base, assume that the base is 10.
Grace is going to invest $650 and leave it in an account for 15 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Grace to end up with $1,490?
Answers
Answer:
5.5%
Step-by-step explanation:
You want the interest rate that can be compounded continuously to give $1490 from an investment of $650 after 15 years.
ValueThe formula for account value with continuously compounded interest is ...
A = Pe^(rt) . . . . P=principal, r=interest rate, t=years
Interest rateSolving for r, we find ...
ln(A/P)/t = r
ln(1490/650)/15 = 0.0553...
The interest rate is about 5.5%.
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7/2x + 1/2x = 7 + 9/2x
Answers
Answer: x=-14
Step-by-step explanation:
74 - 21 x 6 + 329 / 2
Answers
74-126+329/2
-52+329/2
277/2
138.5
Explanation:PEMDAS
21x6=126
126/2=63
63+329=392
392-11=381
Review for Features of Functions Assessment
Suppose that the function f(x) = 20 + 5.5x represents the cost of making x t-shirts.
a. What is f(12)?
b. What does your answer to part a mean in context?
Answers
It costs $86 dollars to make 12 T-shirts.
f(12)=86
It costs 86$ to make 12 shirts
Which equation illustrates the identity property of multiplication? (x yi) × z = (xz yzi) (x yi) × 0 = 0 (x yi) × (z wi) = (z wi) × (x yi) (x yi) × 1 = (x yi)
Answers
The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .
In the question ,
Four equations are given , we need to find the equation that represents the identity property of multiplication .
we know that the identity property of multiplication states that the product of any number and 1 is the same given number .
For Example : the product of a number 'a' and 1 is = a , that is a×1 = a .
So , by the applying the definition of Identity property of multiplication we get that the equation that models the identity property is
(a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi)
Therefore , The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .
The given question is incomplete , the complete question is
Which equation illustrates the identity property of multiplication?
(a) (a + bi) × c = (ac + bci)
(b) (a + bi) × 0 = 0
(c) (a + bi) × (c + di) = (c + di) × (a + bi)
(d) (a + bi) × 1 = (a + bi)
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Determine whether the expression is a monomial. 1/2(c^3)(d^6)
A. Monomial
B. Not a monomial
Answers
Answer:
not a monomial
Step-by-step explanation:
monomial
Prefix mono- means 1 so, monomial means one term
This has more than one term so it’s not a monomial
Hopes this helps please mark brainliest
In 2015, sarah spent $800 buying lunches. In 2017, she spent $550 buying lunches. What was the rate of change from 2015 to 2017?.
Answers
As per the Sarah buying pattern, the rate of change from 2015 to 2017 is $250
Rate of change
Rate of change refers the speed at which a variable changes over a specific period of time.
Given,
In 2015, sarah spent $800 buying lunches. In 2017, she spent $550 buying lunches.
Here we need to find the rate of change from 2015 to 2017.
While we looking into the given question, we have identified that,
Buying lunch cost for 2015 = $800
Buying lunch cost for 2017 = $550
Now, the rate of change from 2015 to 2017 is calculated by finding the difference between them,
So, rate of change is,
=> 800 - 550
=> 250
Therefore, the rate of change from 2015 to 2017 is $250
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What is the slope of a line perpendicular to the line whose equation is x-2y=-8 Fully simplify your answer.
Answers
Answer:
[tex]-2[/tex]
Step-by-step explanation:
The perpendicular slope is the opposite of the reciprocal of the original slope. So, let's find the slope of this line! I will put it in slope-intercept form (y = )
[tex]x-2y=-8\\-2y=-8-x\\y=4+\frac{1}{2} x\\y=\frac{1}{2} x+4[/tex]
Here, I see that the slope of the line is [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2. The opposite of 2 is [tex]-2[/tex]. The slope of the perpendicular line is [tex]-2[/tex]!
Evaluate 4y - 5x + 10m
y=2 x=3 m=5
Answers
Answer:
43
Step-by-step explanation:
4(2)-5(3)+10(5)
8-15+50
-7+50
43
hopes this helps please mark brainliest
Answer:
17/54,x=3 m=5
Step-by-step explanation:
You jog 2 kilometers in 12 minutes. Your friend jogs
3 kilometers in 16.5 minutes. Who jogs faster? How much sooner will the faster
jogger finish a five-kilometer race?
Answers
Answer:
Person 2 jogs faster as compared to person 1.
The time taken by the faster jogger finish a five-kilometer race will be, 27.5 minutes.
Step-by-step explanation:
speed = distance/time
i need help with this
Answers
Answer:
[tex](f+g)(x)=7x^2-3x-5[/tex]
Step-by-step explanation:
Step 1: What you are given & need to find
[tex]f(x)=\sqrt{16x^4}[/tex][tex]g(x)=3x^2-3x-5[/tex][tex](f+g)(x) = ?[/tex]Step 2: Set up the problem
[tex](f+g)(x) = f(x)+g(x)[/tex][tex](f+g)(x)=(\sqrt{16x^4} )+(3x^2-3x-5)[/tex]Step 3: Simplify
[tex](f+g)(x)=\sqrt{16x^4} +3x^2-3x-5[/tex][tex](f+g)(x)=4x^2+3x^2-3x-5[/tex][tex](f+g)(x)=7x^2-3x-5[/tex]what is 100x100x200x1x2000x10000,000x40000x1000002x0000003xxxxxxxxxxxx000000
Answers
Answer:16.e+6.18
Step-by-step explanation:
Find the absolute value of the complex number.
2+i
Answers
Under any circumstances, the imaginary number i = √-1. We use i to represent the square root of a negative number because negative numbers cannot have square roots (ex: 2^2 = 4, -2^2 = 4).
So, we have a complex number 2 + i. The absolue value? Simple.
[tex]|2 + i|\\2 + |\sqrt{-1} |\\2 + \sqrt{1} \\2 + 1\\3[/tex]
If you need an explanation, look at it this way. The number cannot exist. Yet let's assume it did exist for a moment. What would be the absolute value of a negative square root if they could exist? Well, it would be the same as the square root of that number's opposite, it's positive counterpart!
So, what is the positive counterpart of -1? That would be 1. What's the square root of 1? 1! So, why don't we eliminate these steps? Instead of assuming √-1 can exist and then finding the absolute value of that, just skip those steps and instead take √1, or just 1.
So finally: |√-1| = 1
Nina has some nickels and 9 pennies in her pocket. Her friend, Maurice, has twice as many nickels as Nina. Together, these coins are worth 84¢. How many nickels does Nina have? Show all of your work and label your answers
Answers
Answer:
x = 5
Step-by-step explanation:
Let's say
x = #s of nickels Nina has (we are going to try to get X)
y = # of nickels Maurice has
5x + 9 < The amount Nina has
y = 2x < Amount that Maurice has
Add them both to the total, 84
5x + 9 + 5y = 84
Transfer the 9 to the other side
5x + 5y = 75
Substitute y with it's value
5x + 5(2x) = 75
5x + 10x = 75
15x = 75
Divide
x = 5
During the past five months, Elle
spent $3.25 on candy, $12.09 on
cupcakes, and $9.88 on chips. ABOUT
how much did Elle spend?
Answers
forty percent of students at sbcc have brought their own personal computers to campus. a random sample of 120 entering freshmen was taken. what is the standard error of the sample proportion bringing their own personal computers to campus? round your answer to 3 decimal places.
Answers
The standard error of the sample proportion bringing their own personal computers to campus is 0.045
The standard error of a sample proportion is calculated as:
[tex]SE=\sqrt{\frac{p(1-p)}{n} }[/tex]
with p=0.4 and n=120:
[tex]SE=\sqrt{\frac{0.4(1-0.4)} {120}}[/tex]
[tex]SE=\sqrt{0.002}[/tex]
[tex]SE=0.045[/tex]
The standard error of the sample proportion of students bringing their own computer is 0.045.
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a random sample of 362 california residents responded to a municipal water district poll about how often they water the garden or lawn. the response choices were: daily, every other day, 2-3 times per week, once per week, less than once. the municipal water district wants to know if there is a difference between watering habits in northern california and southern california. a municipal water district employee conducted a chi-square test of independence. in this results table, the observed count appears above the expected count in each cell. daily every other day 2-3 times per week once per week less than once per week totals northern 17 19.2 24 33.1 62 160.0 48 37.6 11 12.1 162 southern 26 23.8 50 40.9 72 74.0 36 46.4 16 14.9 200 totals 43 55 153 84 27 362 which hypothesis is appropriate for a test of independence? check all that apply. group of answer choices : living in northern or southern california is not associated with watering habits. : living in northern or southern california is associated with watering habits. : the proportion of northern california residents watering daily is equal to the proportion of southern california residents watering daily. : the proportion of northern california residents watering daily is less than the proportion of southern california residents watering daily.
Answers
The correct answer is H0 : Living in Northern or southern California is not associated with watering habits and Ha : Living Northern or southern California is associated with watering habits.
Given that,
H0 : Living in Northern or southern California is not associated with watering habits.
Ha : Living Northern or southern California is associated with watering habits.
In independent test in that test we Check the two variables are independent or not. The chi square can be used for any variable. Both the group (independent) and test variable(dependent) can be nominal, ordinal, or grouped interval.
Therefore, The difference between living in Northern or Southern California and the difference between living in Northern or Southern California is that the former is related to watering practices.
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123.05 to the nearest cent
Answers
Answer:
123.00
Step-by-step explanation:
Determine the relationship between the X and Y values write an equation
1 -2
2 -4
3 -6
Answers
The equation is, y = x-2
The table showing the values of x and y is:
x 1 2 3 4
y -1 0 1 2
From the question, we have
y increases by 1 unit with 1 unit increase in x.
The equation is, y = x-2
Subtraction:
Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.
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Becky ha 5 candy bar. She want to hare with 3 friend. How much will each friend get
Answers
Answer:
The number of candy bars each friend will receive is 1.66.
Step-by-step explanation:
Given that Becky has 5 candy bars
She wants to share them with 3 friends.
To determine the number of candy bars each friend will receive
We need to determine the number of candy bars each friend will receive
So, the number of candy bars would be
5/3 which would = to 1.66
and that's how much she will give each friend
find the sum. [1 4 [0 0
0 3] 0 0]
Answers
Answer:
1st
Step-by-step explanation:
Explanation in the picture.
w+5r use w=4 and r=6
Answers
4 + 5(6)
4 + 30
answer = 34
hope this helps!
A bike path is 12.5 miles. Dominic is 70% of the way to the end. How far is Dominic on the path? HELPPP PLEASE :
Answers
Answer:
The percentage of the distance Dominic is on the path is his distance
travelled as a fraction of the total distance when equivalent to 100.
The distance he has travelled on the path is 8.75 miles.
Reasons:
The given parameter are;
Length of Dominic's path = 12.5 miles
The length of the way Dominic is to
Step-by-step explanation:
Use the quadratic formula to solve for x.
8x²-8x-1=0
Answers
Answer:
in the picture
Step-by-step explanation:
Hope this helped! Solve your problem: Use the quadratic formula to solve for x.
8x²-8x-1=0
help please and thankyou
Answers
The length of the side x on the right triangle is 41.06
What is a right triangle?A right triangle is a triangle that has one interior angle of 90°
The parameters in the right triangle are;
Acute angle = 47°
Leg length of side adjacent to 47° = 28
Length of the hypotenuse = x
From trigonometric ratios, we have;
[tex]cos(\theta) =\mathbf{ \dfrac{Length \, of \, adjacent \, side}{Length \, of \, Hypotenuse}}[/tex]
The cosine of the 47° angle is therefore;
[tex]cos(47^{\circ}) = \dfrac{28}{x}[/tex]
From which we have;
[tex]x= \dfrac{28}{cos(47^{\circ}) } \approx 41.06[/tex]
The length of the side, x ≈ 41.06
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1
Based on the triangle shown, what is the approximate value of COS(20)?
Use exact fractions. To receive credit for this question, you must show your work.
SHOW WORKKK
Answers
Answer:
?
Step-by-step explanation:
its a litter hard too see can you get it closer??
QUICK!! EMERGENCY!! PLEASE HELP ME!!
As shown in the graph, Jane has a car payment of $200 a month. Her loan amount is $3,000. Assume there is no interest.
A. What is the slope of the line?
What does this slope in this situation mean?
B. What is the y-intercept of the line?
What does the y-intercept mean in this situation?
C. How many months will it take Jane to pay off the loan?
Show your work.
Answers
Answer:
A ) What is the slope of the line? What does this slope in this situation mean?
The equation of the line is y = -200x +3000 so the slope of the line would be -200x.
This means that as x ( Month ) increases, y ( Loan ) decreases.
B ) What is the y-intercept of the line? What does the y-intercept mean in this situation?
As stated above the equation of the line is y = -200x +3000 so the y-intercept would be +3000.
In this case the y-intercept represents the cost of the loan before Jane's first payment.
C ) How many months will it take Jane to pay off the loan? Show your work.
It will take 15 months to pay off Jane's car loan.
On the graph we can see when x ( month ) equals fifteen, y ( loan ) equals zero. This means that it will take fifteen months for Jane to pay off the loan.
We can check this by putting it into our equation...
y = -200( 15 ) +3000 = 0
Hope this helps! :)
Which expression has the value of 7?
(3)+4
(3+4)
Answers
Answer:
both
Step-by-step explanation:
because the first one, since the number 4 isn’t next to the parentheses then we are not multiplying so it’s actually adding so it still equals 7