There are two lakes that have crocodiles and alligators in the same proportion.The two lakes are Lake Winnipeg and Lake Champlain.
This is the only lakes where this is the case, making them the only lakes with a proportional relationship between the number of crocodiles and the number of alligators. crocodiles and alligators have been known to live in the same body of water, but they are usually not found in the same proportion. In these two lakes, however, they are found in equal numbers.
Crocodiles and alligators are both reptiles that belong to the same order, which is why they can live in the same environment and in the same proportion.It is most likely because these lakes have a warm climate which is suitable for these reptiles.
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a polling organization took a random sample of 1600 high school students to determine how many high school students have a part-time job. suppose 43% of all high school students have a part itme job. if the total population of high shool students is 15 million, is the 10% condition met? justify your answer
Based on this if we find the 10% of the population we have:
15000000 × 0.1 = 1500000 And we see that our sample 1600 & lt;
1500000 and we satisfy the 10% condition.
For this case we have the following data given:
n = 1600 represent the sample size select.
dp = 0.43, which, represent the estimated proportion of high school students that have a part time job
N= 15000000 represent the total population size
And we want to check if the 10% condition is satisfied. So we can use the following definitions for the 10% condition: “We need to have Bernoulli trials must be independent.
If that assumption is not satisfied, it is still okay to proceed if we have that the sample is smaller than 10% of the population.”"One of the conditions to be checked before using the normal model for sample proportions is, “The sample size, n, must be no larger than 10% of the population.
”So based on this if we find the 10% of the population we have:
15000000 × 0.1 = 1500000
And we see that our sample 1600 & lt;
1500000 and we satisfy the 10% condition.
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Solve x² + 5x - 14 = 0
By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
Given,
In the question:
To solve the equation:
x² + 5x - 14 = 0
Now, According to the question:
x² + 5x - 14 = 0
Split the middle term into two terms :
x² - 2x + 7x - 14 = 0
Factor the first two terms and the last two terms separately
x(x - 2) + 7 (x -2) = 0
Factor out
(x - 2) (x + 7) = 0
Apply Zero Product Property
x - 2 = 0 or x + 7 = 0
x = 2 or x = -7
Hence, By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
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Which of the following equations have infinitely many solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-6x+35=-6x-35−6x+35=−6x−35minus, 6, x, plus, 35, equals, minus, 6, x, minus, 35
(Choice B)
B
-6x+35=-6x+35−6x+35=−6x+35minus, 6, x, plus, 35, equals, minus, 6, x, plus, 35
(Choice C)
C
6x+35=-6x+356x+35=−6x+356, x, plus, 35, equals, minus, 6, x, plus, 35
(Choice D)
D
6x+35=-6x-356x+35=−6x−356, x, plus, 35, equals, minus, 6, x, minus, 35
The equation which has infinitely many solutions include the following: B. -6x + 35 = -6x + 35
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal.
This ultimately implies that, an equation would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and intercept for the two lines are the same.
In this scenario, we can reasonably and logically deduce that the following equations satisfy the condition for an equation which has infinitely many solutions:
-6x + 35 = -6x - 35 (False).
-6x + 35 = -6x + 35 (True).
6x + 35 = -6x + 35 (False).
6x + 35 = -6x - 35 (False).
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Complete Question:
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A. -6x + 35 = -6x - 35
B. -6x + 35 = -6x + 35
C. 6x + 35 = -6x + 35
D. 6x + 35 = -6x - 35
If x²y - 3x = y³ – 3, then at the point (-1,2), dy/dx=
now, the assumption in this implicit differentiation is that "y" is really a function in x-terms, whilst "x" is just a simple variable
[tex]x^2y-3x=y^3-3\implies \stackrel{product~rule}{\left( 2xy + x^2\cdot \cfrac{dy}{dx} \right)}-3=\stackrel{chain~rule}{3y^2\cdot \cfrac{dy}{dx}} \\\\\\ 2xy-3=3y^2\cdot \cfrac{dy}{dx}-x^2\cdot \cfrac{dy}{dx}\implies 2xy-3=\cfrac{dy}{dx}(3y^2-x^2) \\\\\\ \left. \cfrac{2xy-3}{3y^2-x^2}=\cfrac{dy}{dx} \right|_{(-1,2)}\implies \cfrac{2(-1)(2)-3}{3(2)^2-(-1)^2}\implies -\cfrac{7}{11}[/tex]
The sum of the ages of pam,dion, and their three children, in years, is 5x - 99. where x is dion's age. pam is five years younger than dion. what is the usm of the ages of their children?
The sum of the ages of the children would be 3x - 94 years.
We have the total sum of the ages of pam ,dion and their children
as 5x - 99
here , x is the age of Dion .
we see , pam is five years younger than Dion , so
age of Pam = x - 5
Now as the sum of all the ages = 5x - 99
therefore ,
Age of Dion + Age of Pan + Age of children = 5x - 99
x + x - 5 + Age of children = 5x - 99
2x - 5 + Age of children = 5x - 99
therefore ,
Age of children = 3x - 94
So the age of their children would be 3x - 94 years
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Find the value of X. Find the m
Answer:
Step-by-step explanation:
all angles of a triangle add up to 180 degrees, so:
3x-40+x+60 = 180
4x = 180 - 60 + 40
4x = 160
x = 40
Check:
LS: RS:
3(40)-40+40+60 180
= 180
because LS = RS,
x = 40
Hope this helps and you understand!!
after collecting the historical data from a process of filling coca-cola bottles, it was found that the variance in the filling process is constant. however, clogs in the machine often affect the average volume. the historical standard deviation is 5 ml. in filling 250 ml bottles, a sample of 20 bottles found an average of volume of 246 ml. create a 95% confidence interval for the average volume of coca-cola in a bottle. can you conclude from your results that the manufacturer needs to adjust the equipment to meet the standard?
The manufacturer needs to adjust the equipment to meet the standard with the margin of error of 2.34.
Define the term margin of error?The calculated number known as the margin of error is added to and removed from the mean value to get the resulting confidence interval. The confidence interval expands as the margin of error does.
Alpha value = 0.05Standard deviation = 5Sample size = 20Sample average = 246Calculate the 95% confidence interval's margin of error based on the aforementioned data.
α = 0.05
n = 20
s = 5
The following is the formula to determine the margin of error:
E = T(n-1) ×s/√n
The t-distribution table is used to determine the value of tn-1 at 19 degrees of freedom.
Replace the values in the formula above.
E = 2.093 ×5/√20
Thus, its margin of error is 2.34 as a result.
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sam rolls 3 standard fair dice. that probability that the three numbers rolled on the dice are the sides of a triangle is , where are relatively prime positive integers. what is the value of ?
The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.
Here,
When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).
Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.
As a result, 186 outcomes or triplets are possible and satisfy this property.
Hence, the required probability is 186/216=31/36.
The required probability is 31/36 for three dice rolls to produce triangle sides.
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Solve for X:
1/2x + 1/3x = 10
Answer:
Step-by-step explanation:
weknr f not sure
Answer:
12
Step-by-step explanation:
1/2x+1/3x=10
We simplify by making common denominator and adding them (if you don’t know how to do that please tell me)
3/6x+2/6x=10
5/6x=10
Now divide 5/6 on both sides
5/6x=10
/5/6. /5/6
x=10*6/5
x=60/5
x=12
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Sandy bought an outboard motor for a total selling price of $420 in Maine, which has a 7% sales tax rate. Calculate the sales tax.
Answer
you do 420x0.7= 29.40
Answer:
The sales tax is 29.4
Step-by-step explanation:
Just divide in half until you reach 5 and then calculate the other 2 percent of it and add the 2 percent back onto it.
the american management association is studying the income of store managers in the retail industry. a random sample of 49 managers reveals a sample mean of $45,420. the standard deviation of the population is $2,050. using a 95% level of confidence, what is the confidence interval for the population mean?
Answer:
burgers
Step-by-step explanation:
ahhhhhhhhhhhhhhhhhh
Simplify the expression:
2(2f+5) =
Answer:
4f+10
Step-by-step explanation:
multiply the 2 to both the numbers in the parenthesis. 2 times 2f is 4f and 2 times 5 is 10
The sum of two numbers is 12. The difference of the same two numbers is -4. Wht is the smaller number?
Answer:
The smaller number is 4.
Step-by-step explanation:
X and Y are the two numbers
x+y=12
x-y=-4
Subtract these two equations
(x+y=12)
-(x-y=-4)
—————-
2y=16
y=8
Plug it in to any equation:
x+y=12
x+8=12
x=4
Solve for an angle in right triangles
I just need the answer :)
Answer:
19.47
Step-by-step explanation:
Answer:
[tex]m\angle A \approx 19.47 \textdegree[/tex]
Step-by-step explanation:
Utilize the trigonometric ratio sine.
[tex]\sin(m\angle A) = \dfrac{2}{6}[/tex]
[tex]\sin(m\angle A) = \dfrac{1}{3}[/tex]
[tex]m\angle A = \sin^{-1}\left( \dfrac{1}{3} \right)[/tex]
[tex]m\angle A \approx 19.47 \textdegree[/tex]
HELP ITS DUE IN A LITTLE BIT!!!
Answer:
Step-by-step explanation:
Yes it does
10 and 15
Answer:
A. the independent and dependent variables are the number of miles and total fee (y = 2.8 + 3.5x)
B. the domain is 0 <= x <= 20 and range is 2.8≤x≤20
Step-by-step explanation:
SOLVE FOR X Help please
Answer:
x = 20
Step-by-step explanation:
Comment
If you follow the angles down, you discover 2 things
There are only 2 answers
One is the supplement of the other.
In this case, both angles can be shown to be the same. The process is accomplished by two vertically opposite angles and 2 supplements. I can't show you how this is done because there are no letters on the lines.
It turns out that 3x + 10 = 4x - 10
Solution
3x + 10 = 4x - 10 Add 10 to both sides
3x + 10 + 10 = 4x - 10 + 10 Combine
3x + 20 = 4x Subtract 3x from both sides.
3x-3x + 20 = 4x-3x Combine
20 = x
Please help with slope question
choose any 2 points on the graph
To calculate the slope use the formula:
slope = y (point 2)-y (point 1)/x (point 2)-x (point1)
substitute the choses points in
calculate your awnser
Which is not true about a direct porprtion
The equation of the line in slope - intercept form will be -
y = (4/5)x + 5
Writ the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[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.
At [c] = 0 -
y = mx
We have a directly proportional relation.
The general equation of a straight line is -
[y] = [m]x + [c]
At [c] = 0, y = mx
m = y/x
where [m] acts as a constant of proportionality.
So -
y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.
Therefore, y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.
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Evaluate the expression (3 • 2)^2
Answer:
36
Step-by-step explanation:
(3*2)^2
3*2=6
6^2=36
Answer:
36
Step-by-step explanation:
(3x2)^2
6^2
36
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How do you find the x for both of these problems?
Considering the figure the required angle is solved using the vertical angle theorem. The values are
14. 42 degrees and 16. 20 degreesHow to determine the required angleThe problem is solved considering this theorems
vertical angle theorem
According to this theorem, when two straight lines cross, they create two sets of linear pairs and the vertical opposite angles are equal.
solution for the missing angle
x + 70 + 60 = 180 sum of angles of a triangle
x = 50
Using vertical angle theorem
? + 88 + 50 = 180 sum of angles of a triangle
? = 180 - 88 - 50
? = 42
solution for the missing angle
x + 75 + 30 = 180 sum of angles of a triangle
x = 75
Using vertical angle theorem
? + 88 + 75 = 180 sum of angles of a triangle
? = 180 - 85 - 75
? = 20
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A goat is tied by a rope 2.5 m to a peg
in some grass. The goat eats 1 m² of
grass in
28 min. How long does it take to eat all that
it can reach?
Time taken to eat all = 549.5 minutes.
What is unitary method?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
The goat can rototate in a circule the radius of the curcle is 2.5 mSo the area of circle is;A=(pi) (r^2)A=(3.14)(2.5)^2A=19.625 m^2As 28 minutes for 1 m^2 so;Time taken to eat all = (28)(19.625)=549.5 minutesHence,Time taken to eat all = 549.5 minutes.
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Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
It will take 25 minutes for the two containers to have the same amount of water .
In the question ,
it is given that ,
water present in container A = 200L
water present in container B = 500L
rate at which the water is filling in container A= 6 liter/minute
rate at which the water is draining in container B = 6 liter/minute
let the time taken = m minutes ,
So , According to the question ,
the equation representing the situation is
200 + 6m = 500 - 6m
Simplifying further , we get
6m + 6m = 500 - 200
12m = 300
m = 300/12
m = 25
Therefore , It will take 25 minutes for the two containers to have the same amount of water .
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f(x) = x + 2
g(x) = 3x
Work out the value of gf (4).
The value of gf(4) is 18
What is Function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given,
f(x) = x + 2
g(x) = 3x
Now we need Function of a function
i.e. g[f(x)]
Then on g(x) we have to replace the x with f(x)
Thus,
g[f(x)] = 3(x + 2)
= 3x + 6
Now by evaluating at
x = 4 i.e.
gf(4) = 3(4) + 6
gf(4) = 12 + 6
gf(4) = 18
Hence, The value of gf(4) = 18
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Given g(x)=-x-4g(x)=−x−4, solve for xx when g(x)=10g(x)=10.
The solution for x in the function when the function g(x) = 10 is 4
How to determine the solution for x in the function?From the question, we have the following equation that can be used in our computation:
g(x)=x-4
To make the equation legible, we need to rewrite it
So, we have the following representation
g(x) = x - 4
Also from the question, we have
g(x) = 10
This means that we calculate x when g(x) = 10
Substitute the known values in the above equation, so, we have the following representation
10 = x - 4
So, we have the following equation
x - 4 = 10
Add 4 to both sides of the equation
So, we have the following representation
x - 4 + 4 = 10 + 4
Evaluate the equation
x = 14
Hence, the solution is 14
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8 Write an equation of the line passing through the point (-7,-6) with slope m = 4
Can anyone write the equation of this graph?
The equation of the graph in the figure is f(x) = |x - 3| + 5
How to find the equation of the graph line?Given that the graph is an absolute value graph
We start by calculating the vertex of the graph
In this case, the graph has it minimum point located at the coordinate (3, 5)
This coordinate can then be interpreted as
(h, k) = (3, 5)
As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = |x - 3| + 5
Hence, the equation of the graph is f(x) = |x - 3| + 5
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the average flight time for the pilots is found to be 8.12 hours. the standard deviation reported by the faa is 0.72 hours, and there were 81 pilots in the sample. what is the t-statistic for this hypothesis test? report to two decimal places.
The t-statistic for this hypothesis test will be 1.50 as "the average flight time for the pilots is found to be 8.12 hours. the standard deviation reported by the faa is 0.72 hours, and there were 81 pilots in the sample."
What is test statistic?A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data match the distribution predicted by the statistical test's null hypothesis.
Here,
test statistic t is,
t = (x' - μ)/(σ/√n)
x'=8.12 hours
μ=8 hours
σ=0.72 hours
n=81 pilot
t=(8.12-8)/0.72/(√81)
=0.12/0.08
t=1.5
For this hypothesis test, the t-statistic will be 1.50 as "The pilots' average flight time was found to be 8.12 hours. There were 81 pilots in the sample, and the faa reported a standard deviation of 0.72 hours."
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help help help help help help
When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.
What are graph equations?Equations with graphs as unknowns are known as graph equations in graph theory. The concept of isomorphism is one of the key issues in graph theory.Different graph equations may be used to express the aforementioned graphs.So, the equations are graphs are:
Given equation: f(x) = 3x + 4Which is transform to equation: h(x) = f(x + 3)Now, graph both equations as follows:
Both equations are parallel to each other.(Refer to the graph attached below)Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.
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five people are to be seated around a circular table. two seatings are considered the same if one is a rotation of the other. how many different seatings are possible?
24 different seatings are possible when five people are to be seated around a circular table such that two seatings are considered the same if one is a rotation of the other.
What is fundamental counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting streamlines the method to choosing by taking into account all of the available options and their combinations in order to calculate the Probability.
Here,
Since there are 5 peoples,
let us fix the first person and remaining will be set according to that.
this can be arranged in,
(5-1)!=4!
=24 ways
When five persons are sitting around a circular table, 24 distinct seatings are available, with two seatings regarded the same if one is a rotation of the other.
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wilma can mow a lawn in 40 minutes. vanessa can mow the same lawn in 120 minutes. how long does it take for both wilma and vanessa to mow the lawn if they are working together?
It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.
A lawn can be mowed by Wilma in 40 minutes. In one hour, Vanessa can cut the same lawn in 120 minutes.
1/120 + 1/40 = 1/T
multiply by 40T;
3T = 40
T = 40/3
= 13 1/3 minutes
= 13 minutes 20 seconds
It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.
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