Answer:
[tex]r = 2[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (0,3)[/tex]
[tex](x_2,y_2) = (5,96)[/tex]
Required
Determine the common ratio
An exponential function is of the form.
[tex]y(x) = ar^x[/tex]
For:
[tex](x_1,y_1) = (0,3)[/tex]
We have:
[tex]3 = a * r^0[/tex]
[tex]3 = a * 1[/tex]
[tex]a= 3[/tex]
For
[tex](x_2,y_2) = (5,96)[/tex]
We have:
[tex]96 = ar^5[/tex]
Substitute 3 for a
[tex]96 = 3 * r^5[/tex]
Divide both sides by 3
[tex]\frac{96}{3} = \frac{3 * r^5}{3}[/tex]
[tex]32 = r^5[/tex]
Express 32 as an exponent of 2
[tex]2^5 = r^5[/tex]
By comparison
[tex]2 = r[/tex]
[tex]r = 2[/tex]
Which statement best describes the association between variable X and variable Y?
a.) moderate positive association
b.) perfect negative association
c.) moderate negative association
d.) perfect positive association
Answer:
C.) moderate negative asdocation
this is because its going down (which means negative) and its not in a perfect line
statement best describes the association between variable X and variable Y is c.) moderate negative association
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
We take two points lying on the line representing the best relationship between variables X and Y.
Points are (1, 9) and (2, 8), so the slope will be (y₂ - y₁)/(x₂ -x₁)
Slope = (9- 8)/(1-2) = -1
Since the slope is negative, the Slope of (-1) shows the negative relationship between X and Y which may be represented by Y = (- X), the equation of a line.
thus It is a negative Association for sure.
A perfect negative correlation has a value of -1.0 and indicates that when X increases by z units, Y decreases by exactly z; and vice-versa. In general, -1.0 to -0.70 suggests a strong negative correlation, -0.50 a moderate negative relationship, and -0.30 a weak correlation.
Therefore, the association between variables X and Y can be best described as Option c.) moderate negative association
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You need a 40% alcohol solution. On hand, you have a 350 mL of a 15% alcohol mixture. You also have 90%
alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?
You will need
mL of the 90% solution
Submit Question
Let x be the amount of 90% solution you will use.
You have 350 mL of a 15% alcohol solution, so it contains 0.15 • 350 mL = 52.5 mL.
For each mL of the 90% solution that you use, you would add 0.9 mL of alcohol. So in the new mixture, the volume would be (350 + x) mL, and its concentration needs to be 40% so that
((52.5 + 0.9x) mL) / ((350 + x) mL) = 0.4
Solve for x :
(52.5 + 0.9x) / (350 + x) = 0.4
(52.5 + 0.9x) / 0.4 = 350 + x
131.25 + 2.25x = 350 + x
1.25x = 218.75
x = 175
so you will need to use 175 mL of the 90% solution.
Consider versus A random sample of 35 observations taken from this population produced a sample mean of 40.27. The population is normally distributed with Calculate the p-value. Round your answer to four decimal places.
Complete Question
Consider H0: μ=38 versus H1: μ>38. A random sample of 35 observations taken from this population produced a sample mean of 40.27. The population is normally distributed with σ=7.2.
Calculate the p-value. Round your answer to four decimal places.
Answer:
The [tex]p-value = 0.030742[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 38[/tex]
The sample size is n = 35
The sample mean is [tex]\= x = 40.27[/tex]
The standard deviation is [tex]\sigma = 7.2[/tex]
The null hypothesis is [tex]H_o[/tex]: μ=38
The alternative hypothesis is H1: μ>38
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x -\mu }{\frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 40.27 - 38 }{\frac{ 7.2 }{ \sqrt{ 35} } }[/tex]
=> [tex]t =1.87[/tex]
Generally from the z table the p-value of [tex](Z > 1.87 )[/tex] is
[tex]p-value = P(Z > 1.87) = 0.030742[/tex]
How do you do this question?
Answer:
(-½, ½)
Step-by-step explanation:
r = -2x. The geometric series converges when -1 < r < 1.
-1 < -2x < 1
½ > x > -½
The interval of convergence is (-½, ½).
A grocery store clerk can scan 1 product every
1
2
of a second. At what rate can she scan products?
Answer:
2 products a second.
Step-by-step explanation:
Look at this table, X W 11 1 10 3 13 -17 17 Is this relation a function? yes or no
Kevin feeds his dog 3/4
pounds of dog food for each meal. Kevin has just bought 24 pounds of dog food. For how many meals will the food last?
Answer:
18 meals
Step-by-step explanation:
3/4 of 24 is 18. That means his food will last for 18 meals.
Which answer choice shows the numbers in correct order from least to greatest?
(3)
A 1-3.5], -3.65, 37, 3.85
B 3.85, 3, 1-3.51, -3.65
C -3.65, 1-3.51, 32, 3.85
D 33,1-3.5), 3.65, 3.85
please answer this asap
What’s the slope please be sure
Answer:
no slope
Step-by-step explanation:
when it goes straight down it has no slope. just did this question. good luck!
What is the distributive property 3(50.15)
Using the distributive property, 3(50.15) can be simplified to 150.45 by multiplying 3 with each term inside the parentheses.
The distributive property is a fundamental concept in mathematics, explains how multiplication distributes over addition or subtraction. It says that you can distribute or apply the multiplication to each term inside the parentheses separately when you multiply a number by a sum or difference enclosed in parentheses.
expression: 3(50.15)
apply the distributive property, which states that a number outside parentheses can be multiplied by each term inside the parentheses.
Multiply 3 by 50.15.
3 × 50.15 = 150.45
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In a small city, approximately 15% of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year. (a) What is the probability that a particular eligible person in this city is selected in both of the next 2 years
Answer:
0.0225
Step-by-step explanation:
Probability that an eligible individual is called for jury duty in any one calendar year = 15/100 = 0.15
a) What is the probability that a particular eligible person in this city is selected in both of the next 2 years
Probability that an eligible person is chosen in each of the next 2years:
P(being chosen in first year) * P(being chosen in second year)
Since the probability of being chosen is the same in any one year with a probability of 0.15
Hence,
P(being chosen in first year) * P(being chosen in second year)
0.15 * 0.15 = 0.0225
a. the probability that a particular eligible person in this city is selected in both of the next 2 years is 0.0225
Calculation of the probability:Since In a small city, approximately 15% of those eligible are called for jury duty in any one calendar year and there is two years.
So, the probability is
= 0.15 (0.15)
= 0.0225
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Which of the following numbers can be expressed as repeating decimals 4/7, 2/5, 7/8, 4/9. I will mark brainliest
Answer:
4/9
Step-by-step explanation:
Put it in a calculator and you get .4 but there's a lot of 4's. That's the repeating decimal.
Answer:4/9 and 4/7
Step-by-step explanation: Trust
A bag contains 5 blue 3 red 6 green 9 orange and 20 black marbles. What is the ratio of the number of blue marbles to the number of marbles that are orange or green
Answer: 5 to 9
Step-by-step explanation:
you just add them all together! (:
Two number cubes are rolled. What is the probability that the sum is 5?
Answer:
2.2
Step-by-step explanation:
In a survey of 2,100 people who owned a certain type of car, 420 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
a box has a square base of side x and height h find the dimensions x, h for which the volume is 14 and the surface area is as small as possible
Volume of cuboid :
[tex]14 = x^2h\\\\h = \dfrac{14}{x^2}[/tex]
Surface area of this cuboid :
[tex]A = 2( x^2 + xh + xh )\\\\A = 2( x^2 + 2xh)[/tex]
Putting [tex]h = \dfrac{14}{x^2}[/tex] in above equation, we get :
[tex]A=2(x^2 + 2x\times \dfrac{14}{x^2})\\\\A = 2( x^2 + \dfrac{28}{x} )[/tex]
For minimum area, [tex]\dfrac{dA}{dx}=0[/tex] :
[tex]\dfrac{dA}{dx}=2( 2x -\dfrac{28}{x^2})\\\\\dfrac{dA}{dx }= 4(x - \dfrac{14}{x^2})\\\\x - \dfrac{14}{x^2}=0\\\\x=\sqrt[3] {14} = 2.41[/tex]
Therefore, value of x is 2.14 .
Hence, this is the required solution.
The dimension for which the volume is 14 and the surface area is as small as possible are 2.41 by 2.41 by 2.41
The formula for calculating the volume of the square box is expressed as:
[tex]V = x^2h[/tex]
Given that the volume of the box is 14, on substituting the value we will have:
[tex]14 =x^2h\\h=\frac{14}{x^2}[/tex]
The surface area of the box is expressed as:
[tex]S = 2(x^2+xh+xh)\\S=2(x^2+2xh)\\S = 2(x^2+2x(\frac{14}{x^2} ))\\S = 2(x^2+\frac{28}{x} )\\S=2x^2+\frac{56}{x}[/tex]
To get the surface area is as small as possible, then dS/dx = 0
[tex]\frac{dS}{dx} = 4x-\frac{56}{x^2}\\0 = 4x-\frac{56}{x^2}\\4x = \frac{56}{x^2}\\4x^3 = 56\\ x^3=14\\x=\sqrt[3]{14}\\x= 2.41[/tex]
Get the height of the box. Recall that;
[tex]h=\frac{14}{x^2}\\h=\frac{14}{(2.41)^2}\\h=\frac{14}{5.8081}\\h= 2.41[/tex]
Hence the dimension for which the volume is 14 and the surface area is as small as possible are 2.41 by 2.41 by 2.41
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Mike drew p pictures. Rick drew 41 fewer pictures than Mike. Choose the expression that shows how many pictures Rick drew.
(A.) p
(B.) 41 + p
(C.) p - 41
(D.) 41 - p
Answer:
It's p - 41.
Step-by-step explanation:
We're trying to find how many pictures Rick drew, which is 41 less than how many Mike drew, p. To find the expression in situations like these, always take how many fewer was drawn from the amount the other person drew, which would be 41 - p. But this would most likely give us a negative answer, which isn't possible. Switch them around and you have p - 41.
identify the slope and Y intercept of the line for each equation
a) y=-5x-3/4
b) y=1/4x+5
Line d has a slope of -9/7. Line e is parallel to line d  what is the slope of line E
Answer: -9/7
Step-by-step explanation: The slope of parallel lines are the same/equal. Only the y intercept is different
6=a/4+2 one step equations
Answer:
[tex]a=16[/tex]
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write equation
[tex]6=\frac{a}{4} +2[/tex]
Step 2: Solve for a
Subtract 2 on both sides: [tex]4=\frac{a}{4}[/tex]Multiply 4 on both sides: [tex]16=a[/tex]Rewrite: [tex]a=16[/tex]Step 3: Check
Plug in a to verify it's a solution.
Substitute: [tex]6=\frac{16}{4} +2[/tex]Divide: [tex]6=4+2[/tex]Add: [tex]6=6[/tex]Please help ASAP
In the diagram, line a and b are parallel. Line is the transversal.
Given that the measure of angle POQ is 114° determine the measure of angle QON
In your explanation be sure to include the key terms corresponding angles ,supplementary Angles, parallel lines ,and transversal computational slep in complete sentences
Answer:
66 not parallel or transversal I believe its supplementary
Step-by-step explanation:
What is the degree of x5 - 4x + 2?
A. 5
B. 3
C. 4
D. 6
Answer:
c-5Step-by-step explanation:
.......
...................
The degree of the given polynomial x⁵ - 4x + 2 is 5. The correct answer is option A. 5.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The degree of a polynomial is the highest power of the variable with a non-zero coefficient.
As per the question,
Here, 5 is the highest power of x with a non-zero coefficient.
Therefore, the degree of x⁵ - 4x + 2 is 5.
Hence, the correct answer is option A. 5.
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What is the probability of spinning a C
The difference of F and 1/3 is 1/2
Answer:
f=5/6
Step-by-step explanation:
Answer: Are you giving us the answer?
Step-by-step explanation:
Are you giving us the answer.
Help me, pleeassee?
I'm dyyiinnnggg
Answer:
The function is an x exponential function.
The domain is infinite
The range is y<2
Find the distance from point A (-1/4,5) to the line -x+2y=14. Round your answer to the nearest tenth.
Answer:
1.7
Step-by-step explanation:
That was the correct answer trust me
Is the number a multiple of 3? Write yes or no.
11. 8
10 4
12. 24
13. 38
Answer:
10: No
11: No
12: Yes
13: No
Step-by-step explanation:
8 / 3 = 2.66
4 / 3 = 1.33
24 / 3 = 8
38 / 3 = 12.66
Hope this help and have a great day!
calculate the rate of change in your neighborhood population of squirrels based on the data from a june 2015
The question is incomplete. Here is the complete question.
Scenario: You are bored during quarantine. However, you have been observing a bird feeder in your backyard and wow... do there seem to be a lot of squirrels in your neighbourhood. You begin to wonder how many squirrels are actually in your neighbourhood and devise an experiment to track their population.
Part 1. Using the data below, estimate the population of squirrels in your neighbourhood as if you employed the Mark-and-Recapture method. Please be sure to include any units in your final answer.
#captured on 06/01/20 10
#captured on 06/30/20 6
#recaptured on 06/30 from 06/01 3
Part 2. Calculate the rate of change in your neighbourhood population of squirrels based on the data from a June 2015 report that indicated a population of 40 squirrels.
Part 3. Calculate the intrinsic growth rate (r) for this population of squirrels based on the data you have acquired so far.
Part 4. Interpretations: In 1-2 sentences, summarize what's happening here (e.g. is the population growing or shrinking or staying the same?) and propose one plausible explanation for this change.
Answer: Part 1: Population of 20 squirrels
Part 2: Rate of change 50%
Part 3: r = -0.1386 anos
Step-by-step explanation: The Mark-and-Recapture method is a method to estimate a population when counting each individual is impractical. The method consists in capture a small population of individuals, mark them and released them back to the population. After a while, you catch another group and record the ones with the mark.
The calculations are made following this formula:
[tex]N=\frac{M*C}{R}[/tex]
N is the estimated population
M is marked individuals
C is total number of captured individuals (with and without the mark) the second time
R is recaptured individuals with the mark.
Part 1: Population of squirrels will be:
[tex]N=\frac{10*6}{3}[/tex]
N = 20
Population of squirrels in 2020 is 20 squirrels.
Part 2: Rate of change is calculated by the change in the population divided by the original population:
rate = [tex]\frac{20-40}{40}[/tex]
rate = - 0.5 or 50%
Part 3: The model for a population growth is exponential:
[tex]N=N_{0}e^{rt}[/tex]
N is population at that moment
N₀ is initial population
r is growth rate
t is period of time
Growth rate will be:
[tex]N=N_{0}e^{rt}[/tex]
[tex]20=40e^{5r}[/tex]
[tex]e^{5r}=0.5[/tex]
[tex]5r=ln(0.5)[/tex]
[tex]r=\frac{ln0.5}{5}[/tex]
[tex]r=-0.1386[/tex]
Growth rate (r) for the population of squirrels after 5 years is [tex]r=-0.1386[/tex] years.
Part 4: The growth rate has a negative sign, which means population is decreasing along the 5 years, so population is shrinking.
One possible explanation is the environment the population are in is lacking the squirrels primary need, i.e., squirrels' food source is diminishing, causing the population to decrease.
The sum of three numbers is 1349 the greatest number is three times the least number the third number is 133 less than twice the least number what are the three numbers?
Answer:
1,216 131,784 130,435
Step-by-step explanation:
a manufacturer of college textbook is interested in estimating the strength of the binding produced by a particular binding mine strength can be measured by recording the force required to pull the page from the binding if this.force is measured in pounds how many book should be tested to estimate with 95% confidence to within 0.1 ib the average force required to break the binding assume that is known to be 0.6 lb
