2185 people make up the sample size.
What is proportion?
An equation in which two ratios are made equal is called a proportion. For instance, you could write the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.
The formula used to determine sample size (n) is as follows:
n = p(1 - p) (z²/ e² )
Where z = 1.96 with a 95% confidence interval (), p is the proportion, and e is the margin of error.
z = 1.96, p = 0.35, e = 0.02
n = 0.35(1 - 0.35) (1.96²/ 0.02²)
n = (0.2275)(9604)
= 2184.91
n ≈ 2185
2185 people make up the sample size.
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f(x)=-3x+5 find f(-2)
Answer:
f(-2) = 11
Step-by-step explanation:
f(-2) = -3 ( -2 ) + 5
f(-2) = 6 + 5
f(-2) = 11
What happens to the area when you dilate?
When we dilate the area , it is multiplied by the square of dilation factor .
In the question ,
it is given that ,
the area of the figure ,
we have to explain what will happen to the area when we dilate the figure .
let the figure be a square ;
let the unit square's length be x ,
and let the dilation factor be "k" ;and
So ,the comparison square's length be kx .
the area of the original square is = x² and
the area of the new square is = (kx)²
So , the ratio of the areas will be = (kx)²/x²
simplifying further ,
we get ,
= k² .
Therefore , the area gets multiplied by k² .
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What is the probability that a person chosen at random from this group has brown or green eyes?.
For the given table of different eyed colour people , the probability that a person chosen at random from this group has brown or green eyes is 0.6036..
We have given a table lists eye colour for a random sample of people as seen above.
Total number of people or possible outcomes
= 222
Total number of people have blue eye colour
= 38
Total number of people have green eye colour
= 13
total number of people have Amber eye colour
= 22
Total number of people have Hazel eye colour
= 28
Total number of people have Brown eye colour
= 121
A person chosen at random from this group.
Probability that the selected person has brown eye Colour , P(B)
= total brown eyed persons /total persons
=> P(B) = 121/222
Probability that the selected person has gren eye Colour , P(G) = total green eyed person/total persons
=> P(G) = 13/222
Now, probability that a person chosen at random from this group has brown or green eyes ,
P(G or B ) = P(G) + P(B)
= 13/222 + 121/222
= 134/222 = 0.6036
Hence, the required probability is 0.6036..
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Complete question:
The above-mentioned table lists the eye colors of a random sample of people. If a person is chosen at random, What is the probability that a person chosen at random from this group has brown or green eyes?
In a sale, the price of a computer is reduced by $124. The sale price is $1,394. Find the marked price (original price) and the rate of the discount. Round the discount rate to the nearest tenth of a percent if necessary. A. $1,270; 8. 9% c. $1,518; 8. 9% b. $1,270; 9. 79% d. $1,518; 8. 2%.
The marked price is $1518 and the rate of the discount is 8.9%.
What is meant by marked price?The marked price or list price is the amount that appears on a product's label. This is the price that the product will be sold for. But this price might be discounted in some way, and the product's real selling price might be less than the advertised price. Typically, MP is used to indicate it.
This was the initial selling price, but $194 was deducted, making the final price $1394.
Use the following formula to determine percent markdown:
(Markdown amount/Selling price)×100 is the percent markdown.
To locate Markdown
Original Selling Price – Markdown Price
Connect what you have now.
Markdown=$1518-$1394
M=124
The Markdown, as we already know, is 124.
At this point, Percent Markdown equals (124/1394)×100 PM=0.088952654×100
PM=8.9 (rounded)
As a result, the growth rate is 8.9%.
And $1394+$124=$1518.
Hence, The marked price is $1518 and the rate of the discount is 8.9%.
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3. two sides of a triangle have lengths 12m and 15m. the angle between them is increasing at a rate of 0.35 radians/minute. a. how fast is the area of the triangle increasing when the angle between the given sides is /6
The area of the triangle will increase at a rate of 3.81 m² per second
Given,
The length of the sides of the triangle are base, 12 m and hypotenuse 15 m
Area of the triangle = 1/2 bh
We have to find h;
That is,
Sin ∅ = opposite side /hypotenuse = h/15
h = 15Sin ∅
d∅/dt = 0.06rad/s
Now,
A = bh/2 = 12 × 15sin∅/2
A = 90sin∅,
By differentiating this equation with respect to A, we have
d(A)/dt = 90cos∅d∅/dt
d(A)/dt = 90cos∅(0.06)
∅ = π/4, cosπ/4 = 0.7071
90×0.7071×0.06
= 3.81m²/s
That is,
The area of the triangle will increase at a rate of 3.81 m² per second
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in a valid syllogism, . group of answer choices the conclusion is true. all of the others. the conclusion follows from the premises. the premises are true.
In a valid syllogism, the conclusion follows logically from the two premises.
A syllogism contains information that is compatible with the facts, it is said to make truthful assertions. A syllogism can, however, be true without being valid or valid without being true. When a syllogism's conclusion flows naturally from its premises, it is considered legitimate or logical. When a syllogism contains information that is compatible with the facts, it is said to make truthful assertions.
Here is a good categorical syllogism illustration: The majority of mammals have warm-blooded systems. Minor: Black dogs are all animals. Consequently, all black dogs have heated blood.
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an international food festival charges for admission and for each sample of food admission and 4 samples cost $8.75 admission and 9 samples cost $13.75 write a linear function rule to model the cost t for any number of samples x
Answer:
t = x +4.75
Step-by-step explanation:
You want the linear function rule relating t to x, given (x, t) = (4, 8.75) and (9, 13.75).
SlopeThe slope of the function can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (13.75 -8.75)/(9 -4) = 5.00/5 = 1.00
InterceptThe y-intercept of the function can be found from ...
b = y -mx
b = 8.75 -(1.00)(4) = 4.75
Slope-intercept equationThe slope-intercept equation is of the form ...
y = mx +b
For m=1 and b=4.75, and using t instead of y, we have ...
t = x +4.75 . . . . linear function rule
Does a dilation affect the slope?
Answer: no
Step-by-step explanation: the slope stays the same because the image and pre- image are parallel which means their slope is equal
A car moves on a straight road. As the driver passes a point A on the road with a speed of 20 ms–1, he
notices an accident ahead at a point B. He immediately applies the brakes and the car moves with an
acceleration of ams–2, where a = – 6 and t s is the time after passing A. When t = 4, the car passes
the accident at B. The car then moves with a constant acceleration of 2 ms–2 until the original speed of
20 ms–1 is regained at a point C. Find
(i) the speed of the car at B, [4]
(ii) the distance AB, [3]
(iii) the time taken for the car to travel from B to C. [2]
Sketch the velocity-time graph for the journey from A to C.
Answer:
The answer to the problem is:
(i) The speed of the car at B is -4 ms$^{-1}$.
(ii) The distance AB is 32 meters.
(iii) The time taken for the car to travel from B to C is 10 seconds.
Step-by-step explanation:
To find the speed of the car at B, we can use the formula $v = v_0 + at$, where $v$ is the final speed, $v_0$ is the initial speed, $a$ is the acceleration, and $t$ is the time. In this case, $v_0 = 20$ ms$^{-1}$, $a = -6$ ms$^{-2}$, and $t = 4$ s. Plugging these values into the formula gives us:
$v = 20 + (-6)(4) = 20 - 24 = -4$ ms$^{-1}$
Thus, the speed of the car at B is -4 ms$^{-1}$.
To find the distance AB, we can use the formula $d = v_0t + \frac{1}{2}at^2$, where $d$ is the distance, $v_0$ is the initial speed, $a$ is the acceleration, and $t$ is the time. In this case, $v_0 = 20$ ms$^{-1}$, $a = -6$ ms$^{-2}$, and $t = 4$ s. Plugging these values into the formula gives us:
$d = (20)(4) + \frac{1}{2}(-6)(4^2) = 80 - 48 = 32$ meters
Thus, the distance AB is 32 meters.
To find the time taken for the car to travel from B to C, we can use the formula $v^2 = v_0^2 + 2ad$, where $v$ is the final speed, $v_0$ is the initial speed, $a$ is the acceleration, and $d$ is the distance. In this case, $v_0 = -4$ ms$^{-1}$, $v = 20$ ms$^{-1}$, $a = 2$ ms$^{-2}$, and $d$ is the distance from B to C. We can find this distance by using the formula for distance and setting $t = 0$, since we're looking for the time it takes the car to travel from B to C, not from A to B:
$d = (20)(0) + \frac{1}{2}(-6)(0^2) = 0 - 0 = 0$ meters
Thus, the distance from B to C is 0 meters. Plugging these values into the formula gives us:
$20^2 = (-4)^2 + 2(2)(0) = 16 + 0 = 16$
We can solve this equation for $t$ to find the time it takes the car to travel from B to C:
$t = \sqrt{\frac{v^2 - v_0^2}{2a}} = \sqrt{\frac{20^2 - (-4)^2}{2(2)}} = \sqrt{\frac{400}{4}} = \sqrt{100} = 10$ seconds
Thus, the time taken for the car to travel from B to C is 10 seconds.
The velocity-time graph for the journey from A to C would have a positive slope from A to B, a negative slope from B to C, and a positive slope from C to the end of the journey.
Which of the correlation values represent a perfect linear relationship between x and y?
a. 0.5
b. 1
c. 100
d. -1
e. 0
The correlation values which represents a perfect linear relationship between x and y are:
b. 1 and d. -1
A perfect linear relationship is indicated by a correlation with a magnitude of 1. The sign of the correlation coefficient is the sign of the slope of the line describing the relationship. It may be positive or negative.
The appropriate choices are :
b. -1
d. 1
A perfect linear relationship (r=-1 or r=1) states that a linear function of one variable can perfectly describe the other.
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.
Hence we get the required answer.
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In which coordinate of the point which divides the join of 1/7 and 4/3 in the ratio 2 3?
The coordinates of the point dividing the join of given points will be equal to (1, 3).
If we need to find the coordinates of a point P(x, y) dividing the join of points (x₁, y₁) and (x₂, y₂) in the ratio m:n then the formula is expressed as
P(x, y) = [(mx₂ + nx₁/m + n), (my₂ + ny₁/m + n)]
We have the values as m:n = 2:3 and
(x₁, y₁) = (-1, 7) and (x₂, y₂) = (4, -3)
On using the above formula we get
P(x, y) = [2(4) + 3(-1)/2 + 3, 2(-3) + 3(7)/2 + 3]
P(x, y) = [(8 - 3)/5, (-6 + 21)/5]
P(x, y) = (1, 3) which is the required coordinate.
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Complete Question:
Find the coordinates of the point which divides the join of (-1, 7) and (4, - 3) in the ratio 2 : 3.
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 1- square root of 3 , and 6-i.
The polynomial function is P(x) = x⁴ - 14x³ + 59x² - 50x - 74
What is a polynomial?A polynomial is a function in which the least power of the unknown is 2.
What is the root of a polynomial?The root of a polynomial is the value of the unknown which makes the polynomial equal zero.
How to find the polynomial of least degree having real coefficients?Since we have that the given polynomial has roots 1 - √3 and 6 - i.
We also know that their conjugates 1 + √3 and 6 + i are also roots of the polynomial.
So, the factors of the polynomial are
x - (1 - √3) = (x - 1) + √3x - (1 + √3) = (x - 1) + √3x - (6 - i) = (x - 6) + i andx - (6 + i) = (x - 6) - iSo, the required polynomial is P(x) = [(x - 1) + √3][(x - 1) - √3][(x - 6) + i][(x - 6) - i]
= [(x - 1)² - (√3)²][(x - 6)² - i²] (Since a² - b² = (a - b)(a + b))
= [(x - 1)² - 3][(x - 6)² - (- 1)]
= [(x - 1)² - 3][(x - 6)² + 1]
Expanding the brackets, we have
= [x² - 2x + 1 - 3][(x² - 12x + 36 + 1]
= [x² - 2x - 2][(x² - 12x + 37]
= x⁴ - 12x³ + 37x² - 2x³ + 24x² - 74x - 2x² + 24x - 74
Collecting like terms, we have
= x⁴ - 14x³ + 59x² - 50x - 74
So, the polynomial is P(x) = x⁴ - 14x³ + 59x² - 50x - 74
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What number completes the prime factorization of 300?
2•2•3•5•___
Answer:
2 × 2 × 3 × 5 × 5 or 2² × 3 × 5²
Step-by-step explanation:
300
= 2 × 150
= 2 × 2 × 75
= 2 × 2 × 5 × 15
= 2 × 2 × 3 × 5 × 5
= 2² × 3 × 5²
Al’ garden i 18 feet long and 30 feet wide. He want to put fence pot the ame ditance apart along all ide of the garden. What i the greatet ditance apart that Alcan place the fence pot? (Show your work)
6 feet is the greatest distance apart by using the greatest common factor that Al can place the fence post.
What is the greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all of the numbers share.
Given:
The length of the garden is 18 feet.
The width of the garden is 30 feet.
We need to find the greatest common factor between 18 and 30. These numbers can be expressed as follows (using multiplication of prime numbers).
18 = 2*3*3
30 = 2*3*5
2*3 = 6 appears in both cases and is the greatest common factor.
Therefore, 6 feet is the greatest distance apart that Al can place the fence post
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pls help me this is due now and can you explain how to do it
Answer:
D) -5
Step-by-step explanation:
-5 x -5 x -5= -125
Cube root means u multiply a number three times. Since it is negative, you’ll have to multiply with a negative number because if you multiply with a negative number 3 times youll get a negative number. A and C are a result of addition or square root.
Hope that was clear. Ask me any other questions to clarify!
Answer:
D. -5
Step-by-step explanation:
∛-125
= [tex](-125)^{\frac{1}{3} }[/tex]
= [tex]((-5)^{3} )^{\frac{1}{3} }[/tex]
[tex](a^{b} )^{c} = a^{b*c}[/tex]
= -5
I need's da help I can get
Answer: c
Step-by-step explanation: 18/8=2.25
Which choice is an equation of the line written in point-slope form?
HINT: Use the answer to help you with the next two questions. You will be using the same graph.
A: y+1=12(x−1)
B: y−1=12(x+1)
C: y−1=2(x+1)
D: y+1=2(x−1)D:
Answer: The answer is C
Step-by-step explanation: If y plus 1 is 2 then y is one which is the difference between the second number of the dots on the graph
Answer:
[tex]y-1=\frac{1}{2} (x+1)[/tex]
Step-by-step explanation:
Point slope formula:
[tex]y-y_{1} = m(x-x_{1} )[/tex]
Find the slope using
[tex]m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\m = \frac{2-1}{1--1} \\m = \frac{1}{2}[/tex]
Plug the slope and points into the point slope formula
[tex]y+1=\frac{1}{2} (x-1)[/tex]
The management of the local zoo wants to know if all of their animal exhibits are equally popular. If there is significant
evidence that some of the exhibits are not being visited frequently enough, then changes may need to take place within the
zoo. A tally of visitors is taken for each of the following animals throughout the course of a week, and the results are
contained in the following table. At a = 0.10, determine whether there is sufficient evidence to conclude that some exhibit
are less popular than others.
Number
of
visitors
Animal Exhibits at the Zoo
Elephants Lions/Tigers Giraffes Zebras Monkeys Birds Reptiles
133
172
163
165
134
155
148
Copy Data
Step 2 of 4: Calculate the expected value for the number of visitors for the lions and tigers exhibit. Enter your answer as a
fraction or a decimal rounded to three decimal places.
There is not sufficient evidence to conclude that some exhibits are less popular than others.
How to test the hypothesis?We are going to test if all the animals are equally as likely to be seen, or if some are more likely than another, hence a goodness of fit test is made, using the chi-square distribution.
The test statistic for the chi-square distribution is given as follows:
Chi-squared = sum ((O - E)²/E)
In which:
O is the observed measure.E is the expected measure.The total number of measures in this problem is given as follows:
133 + 172 + 163 + 165 + 134 + 155 + 148 = 1070.
There are seven types of animals, hence the expected value is obtained as follows:
E = 1070/7 = 152.86.
The critical value is obtained with a chi-square calculator, for a two-tailed test, with 7 - 1 = 6 df and a significance level of 0.1, hence it is of:
Chi squared = 10.64.
Hence the conclusion will be reached as follows:
Chi-squared < 10.64 -> not enough evidence to conclude that some exhibits are less popular than others.Chi-squared > 10.64 -> enough evidence to conclude that some exhibits are less popular than others.The test statistic is calculated as follows:
Chi-squared = 1/152.86 x [(133 - 152.86)² + (172 - 152.86)² + (163 - 152.86)² + (165 - 152.86)² + (134 - 152.86)² + (155 - 152.86)² + (148 - 152.86)²]
Chi-squared = 9.13.
Less than the critical value, hence there is not sufficient evidence to conclude that some exhibits are less popular than others.
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solve 2(x+3)=x-4
solve 4(5x-2)=2(9x+3)
Answer:
2(x+3)=x-4 x = -10
4(5x-2)=2(9x+3) x = 7
Step-by-step explanation:
2x+6=x-4
Subtract 6 from both sides
2x=x-10
Subtract "x" from both sides
x=-10
20x-8=18x+6
You want to isolate the variable by dividing each side by factors that don't contain the variable
x=7
Answer: X=-10 and X=7
Step-by-step explanation: 2(x+3)=x-4 Distribute 2x+6=x-4 Subtract both sides by 6 SImplify x=-10
4(5x-2)=2(9x+3) Distribute 20x-8=2(9x+3) Add both sides by 8 x=7
A birdhoue and the pole that i in on cat a hadow 15 feet long, if a peron nearby cat a hadow 5 feet long, and the peron i 4 feet tall, how tall are the birdhoue and the pole
The pole and the birdhouse both stand 18.75 feet tall.
What is a word problem in math examples?Jack has two dogs and eight cats. Jill owns 4 dogs and 7 cats. In total, how many dogs are there? How many more cats does Jane have than I do if she has 23 and I have 2, and then Jane gives me 5 cats?
How do you solve word problems in mathematics?To answer a word issue with algebra:
Establish a variable.
Utilizing the variable, write an equation.
Make the equation work.
Use the variable to determine the answer if it is not the word problem's solution.
A person standing close by casts a shadow that is five feet long. The individual is 4 feet tall..
Assume that for the birdhouse and the pole are (x) ft tall.
The shadow is now 5 feet long for a person that is 4 feet tall.
Then, for one feet long person, the shadow would be (5/4) feet long.
Then, for 15 feet long -
[tex]\frac{x}{15}[/tex] = [tex]\frac{5}{4}[/tex]
x = (15 x 5)/4
x = 75/4
x = 18.75 feet tall
As a result, both the pole and the birdhouse are 18.75 feet tall.
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Helpppp
(5-√11) : 3 √7
Answer:
= 5√7 - 3√77: 63 or 5√7 - 3√77/63
What is the vertex of â ABC?
The vertex of angle ABC is equal to point B.
Step by Step explanation :
Given angle is represented by ∠ABC
Angle is representation of two rays meeting at the same point.Initial point of both the rays is same known as vertex of the angle.In the given angle ABC , two different rays are BA and ray BC.Initial point of ray BA is B and initial point of ray BC is B.Ray BA and BC meet at point B.Initial point of ray BA and BC is point B.Point 'B' is known as the vertex of angle ABC.Therefore, the vertex of the given angle ABC is given point B.
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Gabriella is deciding between two landscaping companies for her place of business. Company A charges $30 per hour and a $225 equipment fee. Company B charges $55 per hour and a $125 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t,t, and determine the number hours, t,t, that would make the cost of each company the same.
The number of hours that the cost will be the same is 4 hours.
How to illustrate the equation?From the information illustrated, Gabriella is deciding between two landscaping companies for her place of business.
Company A charges $30 per hour and a $225 equipment fee. Thus will be:
225 + 40h
Company B charges $55 per hour and a $125 equipment fee. This will be:
125 + 55h.
h = number of hours
Collate the equations
225 + 30h = 125 + 55h
Collect like terms
55h - 30h = 225 - 125
25h = 100
Divide
h = 100 / 25
h = 4
The number of hours is 4 hours
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what graph represents a liner function
Answer:
A linear function can be represented by a graph that is a straight line. The equation for a linear function is of the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). The slope of the line tells us how steep the line is, and whether it has a positive or negative slope. A positive slope means that the line is sloping upwards from left to right, while a negative slope means that the line is sloping downwards from left to right.
what kind of function can be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes
By using the concept of depreciation, it can be concluded that-
The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.
What is growth?
Growth is the exponential increase in the value of an asset or article or population at a certain rate over a certain period of time
EPA calculated that the air pollution should decrease by approximately 8% each year
The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.
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Complete Question
One function of the Environmental Protection Agency (EPA) is to reduce air pollution. After implementing several pollution reduction programs in a certain city, EPA calculated that the air pollution should decrease by approximately 8% each year. What kind of function could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes?
for what value of x is the equation true 10x-2 (x + 6) =52
A x=5
B =5 3/4
C x=7 1/9
D =8
Answer:
The answer should be D.8
what is the answer to 281+1
Answer: 282
Step-by-step explanation:
The first side of a triangle is twice as long as the second side. The third
side is 12 inches long. The perimeter of the triangle is 36 inches. What is
the measure of the first side of the triangle?
A. 8 inches
B. 10 inches
C. 12 inches
D. 16 inches
Answer:
The measure of the first side of the triangle is 10 inches. This can be determined by using the given information to set up and solve a system of equations. We are given that the first side is twice as long as the second side, and that the third side is 12 inches long. Let's call the length of the first side x and the length of the second side y. We can then set up the following system of equations:
x = 2y
12 = x + y
We can then solve this system of equations by substituting the first equation into the second equation, which gives us:
12 = 2y + y
We can then solve for y by subtracting 2y from both sides of the equation and dividing both sides by 2, which gives us:
y = 4
We can then substitute this value of y back into the first equation to solve for x, which gives us:
x = 2 * 4
x = 8
Therefore, the measure of the first side of the triangle is 10 inches. This can be verified by calculating the perimeter of the triangle, which should be equal to 36 inches. When we do this, we get:
x + y + 12 = 10 + 4 + 12 = 36
Which confirms that the measure of the first side of the triangle is 10 inches.
Step-by-step explanation:
The picture shows angles A and B. Explain why sin(B) = sin(A) and why cos(B) = -cos(A).
Answer:
Step-by-step explanation:
A = 45 degrees
B = 225 degrees
sin(225) = -√2/2
sin(45) = √2/2
-sin(45) = -√2/2
cos(225) = -√2/2
cos(45) = √2/2
-cos(45) = -√2/2
9w-10 help please i am so dum
Answer:
w=10/9
Step-by-step explanation: