9514 1404 393
Answer:
r = -8
Step-by-step explanation:
The terms of a geometric sequence have a common ratio, so we have ...
[tex]\dfrac{r+4}{r}=\dfrac{r+6}{r+4}\\\\1+\dfrac{4}{r}=1+\dfrac{2}{r+4}\\\\4(r+4)=2(r)\qquad\text{subtract 1, cross multiply}\\\\2r=-16\qquad\text{subtract $2r+16$}\\\\\boxed{r=-8}\qquad\text{divide by $2$}[/tex]
_____
Then the terms of the sequence are ...
-8, -4, -2, ...
and the common ratio is 1/2.
Answer: r = -8
Step-by-step explanation:
Suppose that a population of bacteria triples every hour and starts with 700 bacteria.
(a) Find an expression for the number n of bacteria after t hours.
(b) Estimate the rate of growth of the bacteria population after 1.5 hours.
Answer:
(a) An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
(b) The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
Step-by-step explanation:
An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)=aˣ
being a real positive.
When 0 <a <1, then the exponential function is a decreasing function and when a> 1, it is an increasing function.
An exponential function allows us to refer to phenomena that grow faster and faster, such as population growth.
In that case, the formula used to model the growth of a population is given by:
P(t)=P0*[tex]a^{t}[/tex]
where the function P (t) grows exponentially and represents the quantity of the population at time t; a represents the constant of growth or decrease and P0 represents the initial population at time zero.
In this case:
P0=700a=3Replacing, you get:
P(t)=700*[tex]3^{t}[/tex]
An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
The derivative of this function P (t) is:
n'(t)=700*ln(3)*[tex]3^{t}[/tex]
and reflects the growth rate of the bacteria population.
So, the rate of growth of the bacteria population after 1.5 hours is:
n(1.5)=700*ln(3)*[tex]3^{1.5}[/tex]
Solving, you get:
n(1.5)≅ 3,996
The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
An equation is shown. What factor is missing from the equation? 32 + 20= (8+5)*
Answer:
4
Step-by-step explanation:
32+20=52
8+5=13
52/13=4
A tree that is 10 feet tall casts a 20 foot shadow. What is the length of the shadow of a nearby 30 foot tall tree
Answer:
It should be 60 feet following the pattern!
It would cast a 60 foot shadow following the pattern but depending on how far the trees are apart the 30 foot tree could also cast a 40 foot shadow:)
HURRY PLEASE
The quadratic function f(x) crosses the x-axis at -3 and 1.
What are the solutions of f(x) = 0?
A) -3 and -1
B) -3 and 1
C) -1 and 3
D) 1 and 3
Answer:
B
Step-by-step explanation:
The solutions to a quadratic equation is whenever the graph crosses the x-axis. The solutions are also known as the roots or zeros of the quadratic.
Our quadratic crosses the x-axis at -3 and 1. So, at those two points, f(x) is 0. Namely, we have the two points (-3, 0) and (1, 0).
So, our two solutions are -3 and 1.
Hence, our answer is B.
Answer:
I think it would be B
Step-by-step explanation:
If f(x) is 0, that means the value of x would not change at all. and since its only on the x-axis and neither numbers are used for the y-axis, the solutions would most likely be -3 and 1.
a line has the equation 3x-4y=1 choose the equation of a line that is parallel to the given line
Step-by-step explanation:
The equation of the given line is 3x - 4y = 1
A line parallel to the given line will have slope that is the same as this one.
The equation of a straight line is expressed as;
y = mx + c
y and x are the coordinates
m is the slope
c is the y-intercept
Now, we write the given line in the slope - intercept form;
3x - 4y = 1
-4y = -3x + 1
Divide through by -4
[tex]\frac{-4y}{-4}[/tex] = [tex]\frac{-3x}{-4}[/tex] + [tex]\frac{1}{-4}[/tex]
y = [tex]\frac{3}{4} x[/tex] - [tex]\frac{1}{4}[/tex]
The slope of this line is [tex]\frac{3}{4}[/tex]
Any line with the slope [tex]\frac{3}{4}[/tex] will be parallel to the given line.
what dose 3, 3 in the table indicate??? plzzz helppppp
Step-by-step explanation:
it indicates f(x) and g(x)
Answer:
3,3 is a placment in a graph
Step-by-step explanation:
A line passes through the point (2, -7) and has a slope of
21
Please help!!!!
(Show work if possible)
Constant rate of 2/6, 4/12, 5/15, 6/8, 10/30
Answer:
ysME
Step-by-step explanation:
Find the measure of each angle
Answer:
All the work and answer is on the screenshot I have attached.
Step-by-step explanation:
What is the constant of proportionality in the equation y = 5/9x
Answer: 5/9
This is assuming the equation is y = (5/9)x
Note it is in the form y = kx with k = 5/9 as the constant of proportionality.
A fair 66-sided die is rolled 77 times and the resulting sequence of 77 numbers is recorded. A) How many different sequences are possible?B) How many different sequences consist entirely of even numbers? C) How many different sequences are possible if the first, third, and fourth numbers must be the same? D) How many sequences are there where every number is different? E) How many sequences are there where there are at least two numbers that are the same?
Answer: A. 279936 sequences.
B. 2187 sequence.
C. 7776 sequence.
D. 46656 sequence
E. 64 sequence.
Step-by-step explanation:
Given data:
A 6 sided fair die
No of time rolled = 7
Resulting sequence recorded = 7.
Solution.
A.) No of different possible sequence
= 6^7
= 279936 sequences.
B.) Sequence consisting of only even number
= there are 3 even numbers between 1 and 7 ( 2,4,6).
= 3^7
= 2187 sequence.
C.) possible sequences are when the first, third, and fourth numbers must be the same.
= 6* 6 ^n
where n = 4
= 6*6^4
= 7776 sequence.
D.) sequence when every number is different.
There are 6 sides of a die, so when every number is different it is.
= 6^6
= 46656 sequence
E.) sequence when atleast there are two numbers that are the same.
= 2^6
= 64 sequence.
can some help me???????
Given: BD is perpendicular to AC, measure DBA = 7x+6. Find x
Answer:
x = 12
Step-by-step explanation:
[tex] \because BD \perp AC... (given) \\\\
\therefore m\angle DBA =90\degree... (1)\\\\
\because m\angle DBA=(7x + 6)\degree... (2)\\[/tex]
From equations (1) & (2)
[tex](7x + 6)\degree= 90\degree \\\\
7x + 6 =90\\\\
7x = 90 - 6\\\\
7x = 84\\\\
x = \frac{84}{7}\\\\
\huge \orange {\boxed {x = 12}} [/tex]
If f(x) =(1/7)(7x)what is (3)?
?
Answer:
f(3) = 3
Step-by-step explanation:
f(x) = (1/7)(7x)
f(3) = (1/7)(7×3)
f(3) = (1/7)(21)
f(3) = 3
I really need help
Answer:
A and D
Step-by-step explanation:
Hope this helps!
I NEED HELP WITH THIS MATH PROBLEM!!
Answer:
x equal 20 Step-by-step explanation:
H equal 58 I equal 71 J equal 51 we will just simply the equation you wrote
The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion.Fill in the blanks: We are ________ confident that the population mean is between _______ and _______.a) 1%, 0, 0.583120b) 99%, 0, 0.583120c) 99%, 0.385631, 0.780609d) 1%, 0.385631, 0.780609
Answer:
The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion.Fill in the blanks:
We are ____99%____ confident that the population mean is between ___0.385631____ and ___0.780609____.
c) 99%, 0.385631, 0.780609
Step-by-step explanation:
This is the only correct option, given the relevant population mean range. Option B is not correct as the population mean cannot range between 0 and 0.583120 as given by the option. Options 'a' and 'd' are not relevant to the question because they have 1% confidence level, instead of the stated 99% confidence level.
Researchers are interested in assessing if there is an association between dietary cholesterol intake and high blood pressure. The following data was summarized:
Blood Pressure
Dietary Cholesterol High Low Total
High 159 91 250
Low 78 172 250
Total 237 263 500
Required:
a. Estimate the conditional probabilities of high and low blood pressures given the level of dietary cholesterol.
b. Compute an estimate of the odds ratio of high blood pressure for the two groups
c. Interpret the odds ratio and determine if high blood pressure is related to dietary cholesterol.
Answer:
A) Conditional probability for a high BP given that dietary cholesterol is high as well
P = 159 / 250
Conditional probability for a high BP given that dietary cholesterol is low
P = 78 / 250
Conditional probability for a low BP given that Dietary cholesterol is high
P = 91 / 250
Conditional probability for a low BP given that Dietary cholesterol is low
P = 172 / 250
B) High BP for High dietary cholesterol
= 159 / 237
High BP for low dietary cholesterol
= 78 / 237
C) The odds ratio shows that BP is directly proportional to Dietary cholesterol
Step-by-step explanation:
A) estimate the conditional probabilities of high and low blood pressures given the level of dietary cholesterol
Conditional probability for a high BP given that dietary cholesterol is high as well
P = 159 / 250
Conditional probability for a high BP given that dietary cholesterol is low
P = 78 / 250
Conditional probability for a low BP given that Dietary cholesterol is high
P = 91 / 250
Conditional probability for a low BP given that Dietary cholesterol is low
P = 172 / 250
B) Compute an estimate of the odds ratio of high blood pressure for the two groups
High BP for High dietary cholesterol
= 159 / 237
High BP for low dietary cholesterol
= 78 / 237
C) Interpret the odds ratio and determine if high blood pressure is related to dietary cholesterol.
The odds ratio shows that BP is directly proportional to Dietary cholesterol as seen in the the odds ratio that ratio between High BP and High Dietary cholesterol is higher than other odds ratios
1. Using powers of 10, which would be the best choice for the first number to subtract in the division problem 956 ÷ 87?
Answer:
not sure i it is one of these answers but if so , it d
Step-by-step explanation:
When performing division by repeated subtraction method, an equal
amount is subtracted from the dividend several times.
The best choice for the first number to subtract is the the option; 870
Reasons:
Dividing 956 by 87 and subtracting 10 each time, by subtracting 10 87 times gives;
956 - 87 × 10¹ = 86
From which we get;
[tex]\hspace {15} 10\\87| \overline{956}\\\hspace{15in.....} \overline{870}\\\hspace {120in......} 86[/tex]The 870 which is the part product is subtracted first to get a remainder of
86 which is less than 87.
Therefore; using powers of 10, the best choice for the first number to
subtract in the division problem 956 ÷ 87 is 87 × 10 = 870.
Learn more here:
https://brainly.com/question/146837
What value of x makes the equation -0.2(3x – 25) = -0.1x + 7 true?
Answer:
x = -4
Step-by-step explanation:
Ok first let's put the equation.
-0.2(3x – 25) = -0.1x + 7 (first distribute the -.2 to 3x and -25)
-0.6x + 5 = -0.1x + 7 (subtract 5 on both sides)
-0.6x = -0.1x + 2 (add -0.1x on both sides)
-0.5x = 2 (divide by -0.5 on both sides)
x = -4
Hope this helps!!
Find the probability of selecting an heartt out of a
standard deck of cards.
Answer:
4/9
Step-by-step explanation:
Write a minimum 100-word essay on how you can currently use and may use your knowledge and skills of rotations and it's use in digital technology. (WILL MARK BRAINLIEST!! NO SILLY ANSWERS PLS)
What type of transformation has occurred?
A Translation
B Dilation
C Reflection
D Rotation
Answer:
B dilation
Step-by-step explanation:
the shape didnt move but it got bigger
What are the steps in solving the equation 4(2x + 3) = 10x?
Answer:
Step-by-step explanation:
Distributive property, subtraction, division
4(2x + 3) = 10x
8x + 12 = 10x
12 = 2x
6 = x
What is the total amount, including interest, that the shoe store must pay on the loan? (2 points)
Answer:
2550
Step-by-step explanation:
Hope This Helps
Answer:
2550
Step-by-step explanation:
please help me with the question.
Answer:
Step-by-step explanation:
∠a is corresponding to ∠f
∠b is alternate interior angle to ∠e
∠g is alternate exterior to ∠d
∠f is vertical to ∠h
∠b is consecutive( same side) interior with ∠f
Find the missing angle. solve for ?
PLZ HELP =<
Answer:
70 degrees
Step-by-step explanation:
180-120=60
180-(60+50)=70
Muller Farms uses at least 800 lb of special feed daily. The special feed is a mixture of corn and soybean meal with the following compositions:
lb per lb of feedstuff
Feedstuff Protein Fiber Cost ($/lb)
Corn .09 .02 .30
Soybean meal .60 .06 .90
The dietary requirements of the special feed are at least 30% protein and at most 5% fiber. The goal is to determine the daily minimum-cost feed mix.
(a) Formulate a linear programming (LP) problem to model the situation (minimizing cost and satisfying constraints). (Hint: let x1 be the lb of corn in the daily mix, and x2 represent the lb of soybean meal in the daily mix. Formulate objective function and constraints (3 constraints and non-negativity) according to the information given above)
(b) Set up an Excel sheet with the information of this LP problem.
(c) Use Excel Solver to compute the solution to this diet problem.
(d) Include in your report a screenshot of the Excel sheet you used to and a solution.
Answer:
470.59x₁ + 329,41x₂ = $437.65
Step-by-step explanation:
minimize: 0.30x₁ + 0.90x₂
where:
x₁ = pounds of corn
x₂ = pounds of soybean
constraints:
x₁ + x₂ ≥ 800
0.09x₁ + 0.60x₂ ≥ 0.30(800) ⇒ 0.09x₁ + 0.60x₂ ≥ 240
0.02x₁ + 0.06x₂ ≤ 0.05(800) ⇒ 0.02x₁ + 0.06x₂ ≤ 40
x₁ ≥ 0
x₂ ≥ 0
the optimal solution is: 470.59x₁ + 329,41x₂ = $437.65
Gisele trains 7 days per week for a biathlon. She covers a total of 20 miles cycling and running each day. Gisele cycles a total of 105 miles each week, and runs a certain number of miles per week. If she cycles the same number of miles each day and runs the same number of miles each day, the equation StartFraction 1 over 7 EndFraction (105 + r) = 20 represents the situation. Which describes the solution, r, to this equation?
The solution is 5, which represents the number of miles she runs each day.
The solution is 5, which represents the number of miles she runs each week.
The solution is 35, which represents the number of miles she runs each day.
The solution is 35, which represents the number of miles she runs each week.
Answer:D :)
Step-by-step explanation:
TRUST ME
Answer:
D
Step-by-step explanation:
I just did the quiz on edge 2020-2021