Hence, by multiplying the number of airports in California by a factor of three-quarters, we may get the number of airports in Georgia.
How to find how many airports Georgia has?To find how many airports Georgia has, we need to use division. We can divide the total number of airports in California by 3 to find the number of airports in Georgia.
The key math word in the problem is "three times."
Let's say the number of airports in California is "C". Then, we can represent the number of airports in Georgia as "G," and we know that:
C = 3G
To solve for G, we can divide both sides of the equation by 3:
C/3 = G
Therefore, the number of airports in Georgia is equal to one-third of the number of airports in California.
The key math word in the problem is "three times."
We need to divide in order to determine the number of airports in Georgia. The number of airports in Georgia can be calculated by dividing the total number of airports in California by 3.
Let's say the number of airports in California is "C". Then, we can represent the number of airports in Georgia as "G," and we know that:
C = 3G
To solve for G, we can divide both sides of the equation by 3:
C/3 = G
Therefore, the number of airports in Georgia is equal to one-third of the number of airports in California.
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A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 73° and AB = 8.6.
Calculate the length of BC rounded to 3 SF
Answer:
using the trigonometry identities
Cos ∅ = Adj/Hyp
where ∅ = 73°
Cos 73 = 8.6/x
X × Cos 73 = 8.6
x = 8.6/0.2923
x = 29.421 ≈ 29.4
• A recipe uses 5/8 cup of vegetable oil and 2 cups of water. Write the ratio the ratio of vegetable oil to water, then find the value of the ratio.
The ratio of vegetable oil to water is [tex]\frac{5}{8}[/tex] : 2 and the value of the ratio is 0.3125.
What is ratio?
By dividing two amounts of the same unit, it is possible to determine how much of one quantity is in the other. This is referred to as ratio in mathematics.
We are given that a particular recipe uses [tex]\frac{5}{8}[/tex] cup of vegetable oil and 2 cups of water.
So, from this, we get the ratio of vegetable oil to water as [tex]\frac{5}{8}[/tex] : 2.
Now, the value of the obtained ratio is
⇒ 0.625 : 2
⇒ 0.3125
Hence, the required solution has been obtained.
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If h=7 units and r= 2 then what is the approximate volume of the cone shown above
Answer:
[tex]v = \frac{28\pi}{3} [/tex]
Step-by-step explanation:
First, we can find the area of the cone's base:
[tex]a(base) = \pi \times {r}^{2} = 4\pi[/tex]
Now, let's find the volume:
[tex]v = \frac{1}{3} \times a(base)\times h[/tex]
[tex]v = \frac{1}{3} \times 4\pi \times 7 = \frac{28\pi}{3} [/tex]
3. Compare 1/2 with ¾ using ( <, >, =).
A. 1/2= 3/4
B. 1/2<3/4
C. 1/2>3/4
D.None of the above
The function f(x) = 3x + 13 x + 4 1 is a transformation of the function g(x) = r(x) To make the transformation visible, rewrite the rule for f in the form f(x) = q (x) + d (r) where q, r, and d are polynomials.
The rule for f in the desired form is: f(x) = (3x^2 + 12x + 13r(x) + 52) / (x + 4)
How to rewrite the rule for f in the formTo rewrite the rule for f in the form f(x) = q(x) + d(r), we need to first write g(x) in terms of r(x).
We know that g(x) = r(x) / (x + 4) + 1, so we can rewrite it as:
g(x) = r(x) / (x + 4) + (x + 4) / (x + 4)
g(x) = (r(x) + x + 4) / (x + 4)
Now, we can see that f(x) is a transformation of g(x) with q(x) = 3x and d(r) = 13. So, we can write:
f(x) = q(x) + d(r)
f(x) = 3x + 13(r(x) + x + 4) / (x + 4)
f(x) = (3x(x + 4) + 13r(x) + 52) / (x + 4)
Therefore, the rule for f in the desired form is: f(x) = (3x^2 + 12x + 13r(x) + 52) / (x + 4)
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In politics, marketing, etc. we often want to estimate a percentage or proportion p . One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2% . Describe the conclusion about p using an absolute value inequality. Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).
The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
What is absolute value inequality?
An expression using absolute functions and inequality signs is known as an absolute value inequality.
We know that the absolute value inequality about p using an absolute value inequality is written as,
[tex]|p-\hat{p}|\leq E[/tex]
where E is the margin of error and is the sample proportion.
Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,
[tex]|p-0.72|\leq 0.04\\(0.72-0.04)\leq p\leq (0.72+0.04)\\\\0.68 \leq p \leq 0.76[/tex]
Thus, the p is most likely to be between the range of 68% to 76%.
Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,
[tex]|p-0.32| \leq 0.022\\\\0.248 \leq p \leq 0.342[/tex]
Thus, the p is most likely to be between the range of 29.8% to 34.2%.
Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
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A dealer selling an automobile for $18,340 offers a $500 rebate. What is the percent markdown (to the nearest tenth of a percent)?
Answer:
The selling price of the automobile after the $500 rebate is:
$18,340 - $500 = $17,840
The markdown is the difference between the original selling price and the selling price after the rebate, expressed as a percentage of the original selling price. The markdown can be calculated as follows:
Markdown = [(Original Price - Discounted Price) / Original Price] × 100%
Markdown = [(18,340 - 17,840) / 18,340] × 100%
Markdown = (500 / 18,340) × 100%
Markdown ≈ 2.72%
Rounding to the nearest tenth of a percent, the percent markdown is approximately 2.7%.
help pleaseeee
question
What are reasonable constraints for the context?
A) 0 <= x <= 9 and 16 <= y <= 40
2)- 9 <= x <= 9 and - 1.798 <= y <= 17.798;
C) 0 <= x <= 12 and 16 <= y <= 48
D)0 < x < 12 and 16 < y < 48
The correct option is- C) 0 <= x <= 12 and 16 <= y <= 48, is the reasonable constraints for the give graph of total number of patients showed up to nurse Jackie.
Explain about the reasonable constraints:When variables are employed in equations to simulate real-world scenarios, constraints must be applied to set limits and bounds on those variables.
It's possible that some answers, while theoretically proving an equation correct, may not make sense within the setting of a real-world word problem. In order for the mathematical formula to accurately depict the situation, constraints are then required.An equation's related x-values (its independent variable) or y-values (the dependent variable) may be subject to restrictions.From the given graph
x-axis shows the time duration between 9 AM to 9 PM.
y-axis shows the number of patients visited.
Value shown on the graph;
Thus, 0 <= x <= 12 and 16 <= y <= 48, is the reasonable constraints for the give graph of total number of patients showed up to nurse Jackie.
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An employee at a department store is stocking cell phone cases. He has a box of 80 cases. Among the 80 cases, 40 are black, 10 are white, and 30 are pink.
If he reaches into the bag randomly and removes one at a time, what is the probability that the first three cases are all pink?
2Points
The probability that the first three cases are all pink is 0.015. In most cases, the probability is given as a ratio between the total number of outcomes in the sample space and the number of positive outcomes.
What exactly is probability in mathematics?Probability is the potential for something to occur. The value is expressed in the range of 0 to 1 .In light of this, whenever we are unsure of how an event will turn out, we can talk about the probabilities of various outcomes, or how likely they are.
Statistics is a term that refers to the study of probability-based phenomena. Hence, the probability that an event will occur depends on both the quantity of favorable outcomes and the total number of outcomes.
Probability = no. of favorable cases/total number of cases
Given
Total No. of cases = 80
Black = 40
White = 40
Pink = 30
Probability = no. of favorable cases/total number of cases
For first draw
Pink cases = 10
Total cases = 80
P1 = 10/80
For second draw
Pink cases left = 9
Total cases = 79
P2 = 9/79
For second draw
Pink cases left = 8
Total cases = 78
P2 = 8/78
Now Total Probability is
P = P1× P2 × P3
P = 10/80 × 9/79 × 8/78 = 720/492,960
P = 3/2054 ≈ 0.015
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One function, f(x), is defined as f(x) = (x + 4)2 - 3. A second function, g(x), is a parabola that passes through the points shown in the table below. What is the absolute value of the difference between the y-intercepts of f(x) and g(x)? 17 15 9 6
According to the given information, the absolute value of the difference between the y-intercepts of f(x) and g(x) is 0.
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
To find the y-intercept of a function, we set x=0 and evaluate the function at that value.
For the function f(x) = (x + 4)2 - 3, we have:
f(0) = (0 + 4)2 - 3 = 13.
To find the y-intercept of the function g(x), we can use the given points and try to write it in the form y = ax² + bx + c, where a, b, and c are constants.
Using the given points, we can write three equations:
When x = -2, y = 17: 17 = 4a - 2b + c
When x = -1, y = 15: 15 = a - b + c
When x = 1, y = 9: 9 = a + b + c
Solving this system of equations, we get a = -1, b = 1, and c = 13. Therefore, the equation of the function g(x) is:
g(x) = -x² + x + 13.
To find the absolute value of the difference between the y-intercepts of f(x) and g(x), we can subtract the two y-intercepts and take the absolute value:
|f(0) - g(0)| = |13 - 13| = 0.
Therefore, the absolute value of the difference between the y-intercepts of f(x) and g(x) is 0.
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100 Points! Use the given key features to sketch a nonlinear graph. Photo attached. Thank you!
A). The function is symmetric about the line x = 1 and continuous.
For 0 x 2, the function is positive. The highest value for the function is
(1, 1). The value of f(x) increases as x approaches positive infinity.
Describe function?Each input value is given a distinct output value by a rule known as a function.
Functions can be shown using graphs, tables, mathematical notation, and other techniques.
The function is positive in the range 0 x 2, therefore we can limit the curve to that region. As a result, the curve may increase quickly as x moves away from 2. The produced graph might look like this:
B). The function is continuous and symmetrical about the line x = 2. For the function, the bare minimum is (2, 3). As x approaches positive or negative infinity, f(x) approaches infinity.
Similar to how we can design a symmetric curve with a minimum point at x = 2 because the function is symmetric around that value. (2, 3). When x gets close to positive or negative infinity, the function moves towards infinity.
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If OS is a radius perpendicular to chord WV and intercepts it at point M. Find MW.
Answer:
o find MW, we need to use the fact that OS is perpendicular to WV, which means that OS is also perpendicular to MW since it bisects WV.
Let's label the midpoint of WV as point N. Then we can use the Pythagorean theorem to find MW.
First, we need to find the length of ON. Since OS is a radius of the circle, it is equal to the radius of the circle, which we can call r. Then, using the Pythagorean theorem, we have:
ON^2 = OS^2 - SN^2
ON^2 = r^2 - (WV/2)^2
ON^2 = r^2 - (MW/2)^2 (since NW = MV)
Next, we need to find the length of MN. We know that OM is half of WV, so OM = WV/2. Then, using the Pythagorean theorem again, we have:
MN^2 = ON^2 + OM^2
MN^2 = r^2 - (MW/2)^2 + (WV/2)^2
MN^2 = r^2 - (MW/2)^2 + (2MW/2)^2 (since WV = 2MW)
MN^2 = r^2 - (MW/2)^2 + MW^2
Finally, we can solve for MW by using the Pythagorean theorem one more time:
MW^2 = MN^2 + NW^2
MW^2 = (r^2 - (MW/2)^2 + MW^2) + (MW/2)^2
MW^2 = r^2 - (MW/2)^2 + MW^2/4 + MW^2/4
MW^2 = r^2 - (MW/2)^2 + MW^2/2
Multiplying both sides by 4 gives:
4MW^2 = 4r^2 - MW^2 + 2MW^2
3MW^2 = 4r^2
MW^2 = 4r^2/3
MW = 2r/sqrt(3)
Therefore, the length of MW is 2r/sqrt(3).
The following estimates were provided; MPL 20-0.4L; and APL= 20-0,2L-320/L i. Over what range of l (variable inputs) should production take place? ii. What is the range of output over the range of labour in (i)
Answer: To determine the range of input (L) over which production should take place, we need to find the point at which the marginal product of labor (MPL) is zero:
MPL = 20 - 0.4L
0 = 20 - 0.4L
0.4L = 20
L = 50
So production should take place for values of L less than or equal to 50.
To find the range of output over this range of labor, we can use the average product of labor (APL) equation:
APL = 20 - 0.2L - 320/L
Substituting L = 50, we get:
APL = 20 - 0.2(50) - 320/50
APL = 20 - 10 - 6.4
APL = 3.6
So the range of output over the range of labor from 0 to 50 is approximately 0 to 3.6 units of output.
Step-by-step explanation:
explain why the radical expression is or is not in simplified form.
√12n/n
Hence, (2/n)* is the radical expression's abbreviated form (3n) as 12 and n have a common factor of 4.
what is expression ?In maths, an expressions is a set of digits, parameters, and operators that denotes a quantity or relationship. Aside from basic arithmetic operations like addition, reduction, multiplication, and division, expressions can also include more intricate operations like exponents, number theory, and trigonometric functions. Expressions might be basic, including a single variable and one operation, like 3x or 5 + 7, or complex, requiring several variables and actions, like (x + y)2 - 2x. Expressions can represent arithmetic, inequalities, and other scientific connections.
given
Due to the fact that 12 and n have a common factor of 4, the radical statement 12n/n can be further reduced.
We can rewrite 12 as 4 * 3 to simplify the expression, and then we can take the square root of 4 to get 2:
√12n/n = √(4 * 3 * n)/n = √(4/n) * √(3n) = (2/√n) * √(3n) (3n)
Hence, (2/n)* is the radical expression's abbreviated form (3n) as 12 and n have a common factor of 4.
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please help me im failing her class i need atlest an 80 im at 77
Answer:
Step-by-step explanation:
For question 3,
Simplified brackets -> (8+11)2-8+11
Open brackets -> 19*2-8+11
Multiply -> 38-8+11
Calculate -> 41
Solution = 41
For question 4,
Remove Brackets -> m+11+m+44
Put common numbers together -> m+n+44+11
Calculate -> m+55+n
Solution = m+55+n
-Your smart 6th grader
Part Two!
Angela worked on a straight 11%
commission. Her friend worked on a salary of $950
plus a 7%
commission. In a particular month, they both sold $23,800
worth of merchandise.
Step 2 of 2 : How much did her friend earn for the same month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
Angela's friend earned a salary of $950 plus a commission of $1,599.50 for a total earnings of $2,549.50 in the month they both sold $23,800 worth of merchandise.
To find out how much Angela's friend earned in the same month, we need to first calculate their commission earnings.
Angela's commission earnings can be found by multiplying the total sales by her commission rate of 11%:
Commission earnings = $23,800 x 0.11 = $2,618
Now, let's calculate her friend's commission earnings. First, we need to subtract the salary from the total sales:
Total sales - Salary = Commissionable sales
$23,800 - $950 = $22,850
Next, we can calculate the commission earnings by multiplying the commissionable sales by the commission rate of 7%:
Commission earnings = $22,850 x 0.07 = $1,599.50
Adding the commission earnings to the salary gives us the total earnings for the month:
Total earnings = $950 + $1,599.50 = $2,549.50
Therefore, Angela's friend earned $2,549.50 for the same month.
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A flag-shaped like an equilateral triangular has a perimeter of 45 inches. What is the length of each side of the flag?
Answer: 15 inches
Step-by-step explanation:
An equilateral triangle has three equal sides, so if the perimeter of the triangle is 45 inches, then each side must be 45 inches divided by 3, which gives us:
45 in ÷ 3 = 15 in
Therefore, the length of each side of the flag is 15 inches.
I’m trying to do old homework for fun but now I’m stuck
Answer: The length is 8 yards
Step-by-step explanation: First, take the volume of the prism (115 cubic yards), divide it by the width (2 1/2), the divide that by the height (5 3/4) getting you the length: 8 yards
The life of Sunshine CD players is normally distributed with mean of 4.3
years and a standard deviation of 1.1
years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts.
Find the 90th percentile of the distribution for the time a CD player lasts.
The 90th percentile of the distribution for the time a CD player lasts is approximately 4.674 years.
Percentile of the distribution:In statistics, a percentile is a measure used to indicate the value below which a given percentage of observations falls in a dataset or distribution.
For example, the 90th percentile is the value below which 90% of the observations fall, and above which only 10% of the observations fall.
Similarly, the 50th percentile (also known as the median) is the value below which 50% of the observations fall, and above which 50% of the observations fall.
Here we have
The life of Sunshine CD players is normally distributed with a mean of 4.3 years and a standard deviation of 1.1 years.
To find the 90th percentile of the distribution for the time a CD player lasts, find the value of x such that 90% of the CD players last less than x and 10% last more than x.
First, standardize the distribution by converting it to a standard normal distribution with a mean of 0 and a standard deviation of 1.
This can be done by subtracting the mean and dividing by the standard deviation:
Z = (x - μ) / σ
To find the Z-score corresponding to the 90th percentile,
We can use a standard normal distribution table or a calculator.
The Z-score corresponding to the 90th percentile is approximately 1.28.
Now we can solve for x by rearranging the standardization equation above:
=> Z = (x - μ) / σ
=> 1.28 = (x - 4.3) / 1.1
=> 1.28 * 1.1 = x - 4.3
=> x = 4.674
Therefore,
The 90th percentile of the distribution for the time a CD player lasts is approximately 4.674 years.
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1. Find the equation of the line parallel to the line shown in the graph passing through the
point (-2, 3).
A) y = 2/3 x + 13/3
B) y = 3/2 x - 13/3
C) y = 3/2 x + 13/3
D) y = 2/3 x - 13/3
-
2. Find the equation of the line perpendicular to the line shown in the graph passing through the point (-2, 3).
-
A) y = - 3/2x + 3
B) y = 3/2x
C) y = -3/2x
D) y = 3/2x - 3
The equation of the line perpendicular to the given line passing through the point [tex](-2, 3)[/tex] is [tex]y = -3/2 x + 15/2[/tex] , which is not one of the options provided.
What is the perpendicular to the line?To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of [tex]2/3,[/tex]so the parallel line we're looking for will also have a slope of [tex]2/3[/tex]. Using the point-slope form of a line, we can write:
[tex]y - y_{1} = m(x - x_{1} )[/tex]
where m is the slope and [tex](x_{1} , y_{1} )[/tex] is the given point. Substituting the values we have:
[tex]y - 3 = (2/3)(x - (-2))[/tex]
[tex]y - 3 = 2/3 x + 4/3[/tex]
[tex]y = 2/3 x + 13/3[/tex]
So the equation of the line parallel to the given line passing through the point [tex]t (-2, 3) is y = 2/3 x + 13/3[/tex], which is option A.
To find the equation of a line perpendicular to a given line, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The given line has a slope of 2/3, so the perpendicular line we're looking for will have a slope of -3/2. Using the point-slope form of a line again, we can write:
[tex]y - y_{1} = m(x - x_{1} )[/tex]
where m is the slope and [tex](x_{1} , y_{1} )[/tex] is the given point. Substituting the values we have:
[tex]y - 3 = (-3/2)(x - (-2))[/tex]
[tex]y - 3 = -3/2 x - 9/2[/tex]
[tex]y = -3/2 x + 15/2[/tex]
Therefore, the equation of the line perpendicular to the given line passing through the point [tex](-2, 3) is y = -3/2 x + 15/2,[/tex] which is not one of the options provided.
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What is 27500.00 minus .025
Answer:27499.975
Step-by-step explanation:
HELP ASAP 20 POINTS PLS
will mark branliest!
which equation is represented by the graph?
The graph represents the equation with option C, tan x/2.
What is graph?A graph is a structure that resembles a collection of objects in discrete mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each set of connected vertices is referred to as an edge.
Here,
The graph of the function tan(x/2) represents the tangent of half of the angle x in radians.
The tangent function has vertical asymptotes at odd multiples of π/2, which means that the function is undefined at those points. Therefore, the graph has vertical asymptotes at x = π/2, 3π/2, 5π/2, ....
The function also has zeros at even multiples of π, which occur when tan(x/2) = 0. This happens when x/2 = kπ where k is an integer, so x = 2kπ.
Between each pair of vertical asymptotes, the function oscillates between positive and negative infinity. The function is positive in the intervals (2kπ, (2k+1)π) and negative in the intervals ((2k-1)π, 2kπ) for all integers k.
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Solve for ∠B
. Round your answer to the nearest tenth.
∠B
= degrees
(50 points)
Answer:
m∠B = 36.9 °
Step-by-step explanation:
SOH - CAH - TOA
Sine → Opposite/Hypotenuse
sin(θ) = 3/5
[tex]\theta = sin^-^1(3/5)\\[/tex]
θ = 36.86 degrees
Round to nearest tenth, so m∠B = 36.9 °
Samantha sells tomatoes at a farmer's market. She uses 15 to 60 gallons of water each week to water her tomato plants. She measured the number of tomatoes produced each week and noticed that the amount of water given to the plants impacts the amount of tomatoes they produce.
What are the domain, independent and dependent variables in this situation?
a.) 15 to 60 gallons of water
b.) gallons of water used
c.) number of tomato plants
d.) number of tomatoes produced
e.) 0 to 60 gallons of water
f.) price per tomato sold
Domain: ?
Independent variable: ?
Dependent variable: ?
Samantha waters her tomato plants once a week with between 15 and 60 gallons of water.
15 to 60 gallons of water are the domain.Gallons of utilized water is an independent variable.The number of tomatoes produced is a dependent variable.Domain refers to the set of possible values that the independent variable can take. In this case, the domain is the range of possible amounts of water that Samantha can use to water her tomato plants, which is 15 to 60 gallons.
The independent variable is the variable that is being manipulated or controlled by Samantha, which in this case is the amount of water used to water the tomato plants. So, the independent variable is "gallons of water used".
The dependent variable is the variable that is being measured or observed, which in this case is the number of tomatoes produced each week. So, the dependent variable is the "number of tomatoes produced".
Therefore, the answer is:
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In 2018 Gallup poll, it was reported that about 5% of Americans identify themselves as vegetarians. You think that percent is higher in the age group 18 to 35 years. Test your hypothesis at 5% level of significance.
At a 5% level of significance, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the percentage of vegetarians in age group 18 to 35 years is higher than 5%.
To test the hypothesis that the percentage of vegetarians is higher in the age group 18 to 35 years at a 5% level of significance, we can use a hypothesis test with the following null and alternative hypotheses:
Null hypothesis (H0): The percentage of vegetarians in the age group 18 to 35 years is equal to 5%.
Alternative hypothesis (Ha): The percentage of vegetarians in the age group 18 to 35 years is greater than 5%.
We can conduct a one-tailed z-test to test this hypothesis, using the following formula:
z = (p - P0) / sqrt(P0 * (1 - P0) / n)
where:
p is the sample proportion of vegetarians in the age group 18 to 35 years
P0 is the hypothesized proportion (5%)
n is the sample size
We will reject the null hypothesis if the calculated z-value is greater than the critical z-value corresponding to a 5% level of significance (one-tailed test).
Assuming a sample of size n = 100, if we find that 10 people in the sample identify themselves as vegetarians, then the sample proportion is:
p = 10/100 = 0.1
Using the formula above, we can calculate the z-value:
z = (0.1 - 0.05) / sqrt(0.05 * 0.95 / 100) = 1.96
The critical z-value for a one-tailed test at a 5% level of significance is 1.645 .
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BRAINEST IF CORRECT 50 POINTS! Look at picture
Answer:
C) decreasing then increasing.
Step-by-step explanation:
A function is said to be increasing if the y-values increase as the x-values increase.
A function is said to be decreasing if the y-values decrease as the x-values increase.
From inspection of the given graph of y = x², we can see that for the first half of the graph, the y-values are decreasing as the x-values increase. Therefore, the function is decreasing for this part of the graph.
Similarly, for the second half of the graph, we can see that the y-values are increasing as the x-values increase. Therefore, the function is increasing for this part of the graph.
So the description of the graph of the function is:
C) decreasing then increasing.The three circles are arranged so that they touch each other, as shown in the
figure. Use the given radii for the circles with centers A, B, and C, respectively,
to solve triangle.
5.4, 4.4, 3.4
***
A=
□°
(Do not round until the final answer. Then round to the nearest degree as needed.).
B = 0°
(Do not round until the final answer. Then round to the nearest degree as needed.)
c=
(Do not round until the final answer. Then round to the nearest degree as needed.)
B
Answer:
Step-by-step explanation:
In the given figure, we have three circles arranged such that they touch each other. Let the centers of these circles be A, B, and C, with radii 5.4, 4.4, and 3.4, respectively.
We can see that triangle ABC is an equilateral triangle, since all sides are of equal length (the radii of the circles).
To find the angle A, we can use the law of cosines, which states that:
c^2 = a^2 + b^2 - 2ab cos(C)
where a, b, and c are the lengths of the sides of a triangle, and C is the angle opposite the side of length c.
Since triangle ABC is equilateral, we have a = b = c, and C = 60°. Therefore, we can rewrite the above equation as:
c^2 = 2a^2 - 2a^2 cos(60°)
Simplifying and solving for a, we get:
a = c / sqrt(3)
Substituting the given values, we have:
a = 4.4 / sqrt(3) ≈ 2.54
Therefore, angle A is:
A = 180° - 60° - 60° = 60°
And angle B is:
B = 180° - A = 120°
Finally, we can use the law of sines to find the length of side c:
sin(A) / a = sin(B) / b = sin(C) / c
Substituting the values we have found, we get:
sin(60°) / 2.54 = sin(120°) / c
Simplifying and solving for c, we get:
c = 2.54 / sqrt(3) / sin(120°) ≈ 3.71
Therefore, the length of side c is approximately 3.71, and angle B is 120°.
Help with math problems
Answer:
1) option A
2) p > 34
Step-by-step explanation:
1) Inequality: 7 ≤ n + 5
Subtract 5 from both sides,
7 - 5 ≤ n +5 - 5
2 ≤ n
The value of n is all values greater than or equal to 2.
So, the answer is option A.
2) Inequality: 16 + p > 50
Solution:
Subtract 16 from both sides,
16 - 16 + p > 50 - 16
p > 34
Find the
-coordinates at which the tangent line to =(x−6/x)^8
is horizontal.
The coordinates at which the tangent line to f(x) = (x-6/x)^8 is horizontal are (√6, f(√6)) and (-√6, f(-√6)), where f(x) is the given function.
Coordinates calculation.
To find the coordinates at which the tangent line to the function f(x) = (x-6/x)^8 is horizontal, we need to find the critical points of the function where the derivative is zero or undefined.
First, let's find the derivative of the function:
f(x) = (x-6/x)^8
f'(x) = 8(x-6/x)^7 * (1 - (-6/x^2))
Simplifying the second term, we get:
f'(x) = 8(x-6/x)^7 * (x^2+6)/x^2
Now we need to set the derivative equal to zero and solve for x:
8(x-6/x)^7 * (x^2+6)/x^2 = 0
(x^2+6) cannot be zero, so we can ignore that factor.
8(x-6/x)^7 = 0
(x-6/x) = 0
x^2 - 6 = 0
x = ±√6
So we have two critical points at x = √6 and x = -√6.
Now we need to determine whether these critical points correspond to a maximum, minimum, or inflection point. To do this, we can use the second derivative test.
Taking the derivative of the first derivative, we get:
f''(x) = 8(x-6/x)^6 * (56/x^3 + 7)
Evaluating the second derivative at x = √6, we get:
f''(√6) = 8(√6-6/√6)^6 * (56/√6^3 + 7)
f''(√6) > 0, so the function has a local minimum at x = √6.
Evaluating the second derivative at x = -√6, we get:
f''(-√6) = 8(-√6-6/-√6)^6 * (56/-√6^3 + 7)
f''(-√6) < 0, so the function has a local maximum at x = -√6.
Therefore, the coordinates at which the tangent line to f(x) = (x-6/x)^8 is horizontal are (√6, f(√6)) and (-√6, f(-√6)), where f(x) is the given function.
Learn more about coordinates below.
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