The 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.
To construct the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list, we can use the following formula:
[tex]\hat{p} \pm z^* \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}[/tex]
where [tex]$\hat{p}$[/tex] is the sample proportion, [tex]$n$[/tex] is the sample size, and [tex]$z^*$[/tex] is the z-score corresponding to the desired level of confidence. Since we are looking for an 85% confidence interval, the z-score is 1.440.
First, we can calculate the sample proportion:
[tex]\hat{p} = \frac{109}{455} = 0.240[/tex]
Next, we can plug in the values into the formula:
[tex]$$ 0.240 \pm 1.440 \sqrt{\frac{0.240 (1 - 0.240)}{455}} $$[/tex]
Simplifying this expression, we get:
[tex]$$ 0.240 \pm 0.046 $$[/tex]
Therefore, the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is [tex]$(0.194, 0.286)$[/tex].
We can interpret this interval as follows: if we were to draw many samples of size 455 from the population of people who appear on the 10 Most Wanted list, and construct a 85% confidence interval for the proportion of people who are captured based on each sample, about 85% of these intervals would contain the true population proportion.
Furthermore, we are 85% confident that the true population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.
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find scale factor of the dilation
Answer:
Step-by-step explanation:
The original image is the the black one. The dilated image is blue. It got bigger. So it is an enlargment.
Each side got bigger by times 2
So the dilation is 2
Use the quadratic formula to determine the exact solutions to the equation.
2x2−9x+1=0
I feel like it's either b or d. I keep getting the same answer when I solve it but the thing is, it's not on the answer choices. My answer was (9 ± √ - 89 )/ 4
but it's not thereeeee :((
The exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.
To solve the quadratic equation 2x² - 9x + 1 = 0 using the quadratic formula, we first need to identify the values of a, b, and c. From the given equation, we can see that a = 2, b = -9, and c = 1.
The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a, b, and c, we get:
x = (-(-9) ± √((-9)² - 4(2)(1))) / 2(2)
x = (9 ± √(81 - 8)) / 4
x = (9 ± √73) / 4
So, the exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.
As for the answer choices, it's possible that the answer key has simplified the solution further. However, your answer is correct and provides the exact solutions to the equation.
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A group of students collected old newspapers for a recycling project. The data shows the mass, in kilograms, of old newspapers collected by each student.
23, 35, 87, 64, 101, 90, 45, 76, 105, 60, 55
98, 122, 49, 15, 57, 75, 120, 56, 88, 45, 100.
What percent of students collected between 49 kilograms and 98 kilograms of newspapers? Explain how you got to your solution
Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.
Total number of students is 22.
To find the percentage of students who collected between 49 and 98 kilograms of newspapers, we first need to count the number of students who collected within this range. From the given data, we can see that the following students collected between 49 and 98 kilograms of newspapers
87, 64, 90, 76, 60, 55, 57, 75, 56, 88
Percentage of students = (number of students in range / total number of students) x 100
= (10 / 22) x 100
= 45.45%
Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.
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(c) Give a specific example of a rule for the function f such that the series Σα) f(n)/n^2does not converge. You must justify your answer.
One specific example of a rule for the function f such that the series Σα) f(n)/n^2 does not converge is the function f(n) = (-1)^n.
To justify this, we can use the alternating series test, which states that if a series has alternating signs and the absolute values of its terms decrease monotonically to 0, then the series converges. However, if the absolute values of its terms do not decrease monotonically to 0, then the series diverges.
In this case, we have Σα) f(n)/n^2 = Σα) (-1)^n/n^2. The absolute value of each term is 1/n^2, which does decrease monotonically to 0. However, the signs of the terms alternate, meaning that the series does not converge. Therefore, this is a valid example of a rule for the function f such that the series Σα) f(n)/n^2 does not converge.
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Classify each angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles
Corresponding angles have the same position on the parallel lines, alternate interior angles are inside and opposite, alternate exterior angles are outside and opposite, and consecutive interior angles are on the same side.
When two parallel lines are intersected by a transversal, there are several types of angle pairs that are formed. Corresponding angles are pairs of angles that are located in the same position on the parallel lines relative to the transversal. They have the same measure and are congruent.
Alternate interior angles are pairs of angles that are located on opposite sides of the transversal and inside the parallel lines. They are congruent and have the same measure. Alternate exterior angles are pairs of angles that are located on opposite sides of the transversal and outside the parallel lines. They are congruent and have the same measure.
Consecutive interior angles are pairs of angles that are located on the same side of the transversal and inside the parallel lines. They add up to 180 degrees.
To classify each angle pair, we need to determine their positions relative to the parallel lines and the transversal. By knowing the classifications, we can identify each angle pair and their properties.
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Explain how you decided to divide your wholes into fractional parts and how you decided where your number scale should begin and end
The decision of how to divide a whole into fractional parts and where to begin and end a number scale depends on the context and purpose.
How do you decide on fractional division?when dividing a whole into fraction parts, the decision of how to divide it depends on the context and the specific problem being solved. For example, if a pizza needs to be divided among 4 people, it would make sense to divide it into 4 equal parts or fourths. If a recipe calls for 1/3 cup of flour, then the whole cup would be divided into 3 equal parts or thirds.
Regarding number scales, they can begin and end at different points depending on the context and purpose. For example, a temperature scale could start at 0 degrees and end at 100 degrees for Celsius, or start at 32 degrees and end at 212 degrees for Fahrenheit.
A financial scale could start at negative numbers for debts and end at positive numbers for assets. In general, number scales are designed to provide a clear and consistent way of measuring and comparing quantities in a particular context.
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Work out the size of an exterior angle of a regular hexagon
The size of an exterior angle of a regular hexagon is 60 degrees.
Working out the size of an exterior angleIn a regular hexagon, all the interior angles are equal and are given by the formula:
Interior angle = (n-2) x 180 / n
where n is the number of sides of the polygon.
For a hexagon, n = 6, so the interior angle is:
Interior angle = (6-2) x 180 / 6 = 120 degrees
An exterior angle is the supplement of an interior angle, which means it is the angle that when added to the interior angle, will equal 180 degrees.
So, exterior angle = 180 - interior angle = 180 - 120 = 60 degrees.
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π × 4 to the second power × 3 ( with steps !! )
The answer and what is the value of a
Answer:a=40
Step-by-step explanation:
angles on a straight line add to 180. This means that the missing angle that isn't a is 40. Angles in a triangle add to 180 so a=40
The harmonic series: 1+1/2+1/3+1/4+.
diverges, but when its terms are squared the resulting series converges. T or F
The statement "The harmonic series: 1+1/2+1/3+1/4+... diverges, but when its terms are squared the resulting series converges." is True.
The harmonic series is defined as the sum of the reciprocals of the natural numbers: Σ(1/n) for n = 1 to ∞. This series is known to diverge, meaning that its sum tends to infinity as more terms are added.
However, when the terms of the harmonic series are squared, we get a new series called the p-series, with p=2: Σ(1/n^2) for n = 1 to ∞. The p-series converges if p > 1, which is true for p=2. Thus, the series Σ(1/n^2) converges to a finite sum.
In conclusion, the given statement is true, as the harmonic series diverges, but its squared terms result in a convergent series.
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A business with two locations buys seven large delivery vans and five small del...
<
21 of 21
next >
x
a business with two locations buys different sized delivery
vans (small vans - x and large vans - y).
location a receives five small vans and two large vans for
a total cost of $72,500. location b receives two small
vans and six large vans for a total cost of $107,000.
what is the cost of each type of van?
cost of small vans (x)
cost of large vans (y)
After solving the cost function, the cost of each small van is $8,500 and the cost of each large van is $15,000.
Let's use the variables x and y to represent the cost of a small van and a large van, respectively.
From the information given, we can set up a system of two equations:
5x + 2y = 72500
2x + 6y = 107000
We can solve for x and y by using any method of linear equations, such as substitution or elimination. Here, we'll use elimination:
Multiplying the first equation by 3 and the second equation by -1, we get:
15x + 6y = 217500
-2x - 6y = -107000
Adding these two equations, we eliminate the y variable:
13x = 110500
Dividing both sides by 13, we get:
x = 8500
Now we can use this value to find y:
5x + 2y = 72500
5(8500) + 2y = 72500
42500 + 2y = 72500
2y = 30000
y = 15000
Therefore, the cost of each small van is $8,500 and the cost of each large van is $15,000.
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A person places $81200 in an investment account earning an annual rate of 3. 6%,
compounded continuously. Using the formula V = Pent, where Vis the value of the
account in tyears, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 13 years.
If a person places $81200 in an investment account earning an annual rate of 3. 6%, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.
To solve this problem using the formula V = Pent, we need to plug in the given values.
P = $81200 (the principal initially invested)
r = 0.036 (the annual interest rate, expressed as a decimal)
t = 13 years
Using the formula V = Pent, we get:
V = $81200e^(0.036*13)
Using a calculator, we can evaluate e^(0.036*13) to be approximately 1.5498.
So V = $81200*1.5498 = $125689.60
Therefore, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.
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Please help me with this question!
I need an explanation on how to get the answer!
Answer:
C - 136
Step-by-step explanation:
Something important to remember here is that whenever you replace a variable with something else, that something else needs to go in parentheses.
3(7)² - 2(7) + 3
Following PEMDAS, you need to take care of that exponent before anything else. While parentheses are included as coming first, that is referring to operations within parentheses, which we don't have here.
3(49) - 2(7) + 3
Multiplication is the next step...
147 - 14 + 3
And finally, addition and subtraction.
147 - 11
136
Answer:
136
Step-by-step explanation:
Since the question stated that x= 7 you simply substitute all x in the expression with 7 and it would look something like this
3 (7)^2 - 2 (7) +3
PLEASE BRAINLIEST
Calculate the interest and total value on a $6,300 deposit for 8 years at a compound interest rate of 4. 5%
The interest is $2,659.23 and the total value is $8,959.23.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Here the given principal P = $6300
Number of years = 8
Rate of interest = 4.5% = 4.5/100 = 0.045
Now using compound interest formula then,
=> Amount = [tex]P(1+r)^{t}[/tex]
=> Amount = 6300[tex](1+0.045)^8[/tex]
=> Amount = [tex]6300(1.045)^8[/tex]
=> Amount = $8,959.23
Then Interest = Amount - Principal
=> Interest = $8,959.23 - $6300 = $2,659.23.
Hence the interest is $2,659.23 and the total value is $8,959.23.
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a(a - b)+b(a - b) + (a - b)²
Answer:
a^4 - b^4
Step-by-step explanation:
a(a - b) + b(a - b) + (a - b)^2 --> Given
a^2 - ab + b(a - b) + (a - b)^2 --> Distributive Property
a^2 - ab + ba - b^2 + (a - b)^2 --> Distributive Property
a^2 - ab + ba - b^2 + a^2 - b^2 --> Distributive Property
a^4 - ab + ba - b^2 - b^2 --> Combine Like Terms
a^4 + 0 - b^2 - b^2 --> Combine Like Terms (a * b = b * a)
a^4 - b^4 --> Combine Like Terms
Which of the fraction, decimai, percent equivalencies are correct? Select THREE correct answers
The fractions, decimals, and percent equivalencies that are correct are:
b. 3/8 = 0.375 = 37.5%
c. 24% = 0.24 = 6/25
e. 24/30 = 80% = 0.8
What are fractions, decimals, and percentages?A fraction is a part of a whole.
The number is represented mathematically as a quotient, where the numerator and denominator are split.
In a simple fraction both the numerator and denominator are integers.
In a complex fraction, a fraction appears in the numerator or denominator.
In a proper fraction, the numerator is less than the denominator.
A decimal is a fraction that contains a decimal point.
A percentage is a value out of 100 parts.
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7x-1 is less than or equal to 62 answer
The value of the variable is 9
How to determine the valueIt is important to note that inequalities are described as non- equal comparison of numbers or expressions.
The signs of inequalities represents;
< represents less than> represents greater thanFrom the information given, we have that;
7x - 1 is less than or equal to 62
This is represented as;
7x - 1≤ 62
collect the like terms, we have;
7x ≤ 62 + 1
Add the values
7x ≤ 63
Divide both sides by the coefficient, we get;
x ≤ 63/7
x ≤ 9
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A charitable group will be shipping packages to an area of the country that has been devastated by tornadoes. they plan to ship two kinds of packages: food and clothing. they have donations of good and clothing and money. the money will be used to pay the shipping costs.
they collected $126. each package of food costs $18 to ship and each package of clothing costs $14 to ship.
write an inequality to represent this situation.
The charitable group has collected $126 to packages of food and clothing to the tornado-affected area
To represent the situation where a charitable group is shipping food and clothing packages to an area devastated by tornadoes, we can use the following inequality:
Let F be the number of food packages and C be the number of clothing packages. The shipping cost for food packages is $18 per package and for clothing packages is $14 per package.
They have collected $126 for shipping costs. The inequality representing this situation is:
18F + 14C ≤ 126
This inequality indicates that the total cost of shipping food packages (18F) plus the total cost of shipping clothing packages (14C) should be less than or equal to the available budget ($126).
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A cylinder has a base area of 64π m2. Its height is equal to twice the radius. Identify the volume of the cylinder to the nearest tenth
The volume of the cylinder is approximately 1024π cubic meters.
We are given the base area of the cylinder as 64π square meters, which means that the radius of the cylinder is 8 meters (since the area of a circle is given by πr^2). We are also given that the height of the cylinder is twice the radius, which means that the height is 16 meters.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Substituting the given values, we get V = π(8^2)(16) = 1024π cubic meters. Therefore, the volume of the cylinder is approximately 1024π cubic meters.
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Answer:
[tex]3217.0 m ^{3}[/tex]
Step-by-step explanation:
If f(x) = x - 7, then what is ƒ (8)?
Step-by-step explanation:
we use a function as a kind of recipe or template for an actual calculation (or actual "ingredients").
as long as we don't handle the actual food items or actual numbers, it all stays theoretical. variables have no actual value and represent every possible case with every possible value.
but as soon as we get an actual unit value (like 8 in our case), we can put it in place of the variables (that are really nothing else but placeholders for actual values) and simply caucuses the result.
so,
when the question asks what is f(8), it really means what is the result when x = 8.
therefore,
f(8) = 8 - 7 = 1
that's it. that is the whole thing. no mystery, magic or genius strikes necessary.
Answer:
[tex] \sf \: f(8) = 1[/tex]
Step-by-step explanation:
Given function,
→ f(x) = x - 7
Now we have to,
→ Find the required value of f(8).
We have to use,
→ x = 8
Then the value of f(8) will be,
→ f(x) = x - 7
→ f(8) = 8 - 7
→ [ f(8) = 1 ]
Hence, the value of f(8) is 1.
When a figure is translated on the coordinate plane you should add or subtract x and y? Is this statement true or false?
Answer: True
Step-by-step explanation:
You want to know the approximate height of a tall oak tree. You place a mirror on the ground and stand where you can see the top of the tree in the mirror. How tall is the tree? The mirror is 24 feet from the base of the tree. You are 36 inches from the mirror and your eyes are 5 feet above the ground. Round your answer to the nearest tenth
The approximate height of the tall oak tree is 60.0 feet.
To find the height of the tree, follow these steps:
1. Convert the distance between you and the mirror from inches to feet: 36 inches = 3 feet.
2. Create a proportion using similar triangles, where the height of the tree (h) divided by the distance from the tree to the mirror (24 feet) equals your eye height (5 feet) divided by the distance from your eyes to the mirror (3 feet).
3. Set up the proportion: h / 24 = 5 / 3.
4. Solve for h: h = (5 / 3) * 24.
5. Calculate h: h = 40 feet (height of tree above your eye level).
6. Add your eye height (5 feet) to the height of the tree above your eye level: 40 + 5 = 60 feet.
7. Round the answer to the nearest tenth: 60.0 feet.
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Review the equation used in writing a partial fraction decomposition.
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
Which system of equations can be used to determine the values of A and B?
The answer is B. 5A=-15 -2A+B=10
have a lovely day my darlings <3
To determine the values of A and B, we can use the following system of equations: 1. 5A = -15 2. -2A + B = 10 This system of equations can be used to find the values of A and B.
To review the equation used in writing a partial fraction decomposition, we start with a fraction that has a denominator that can be factored into linear or quadratic factors. The partial fraction decomposition separates the fraction into a sum of simpler fractions, each with a single linear or quadratic factor in the denominator.
The equation you provided for partial fraction decomposition is:
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
This equation shows that the original fraction can be decomposed into two simpler fractions, one with a linear factor of (5x - 2) in the denominator (A/(5x - 2)), and one with a quadratic factor of (5x - 2)² in the denominator (B/(5x - 2)²).
To determine the values of A and B, we need to solve for them using a system of equations. In this case, we can use the coefficients of x in the numerator of each fraction to create the following system of equations:
5A = -15
-2A + B = 10
We get the first equation by setting the numerator of the first fraction (A/(5x - 2)) equal to -15x + 10, and the second equation by setting the numerator of the second fraction (B/(5x - 2)²) equal to -15x + 10 and subtracting the first equation from it.
Solving this system of equations gives us:
A = -3
B = 5
Therefore, the partial fraction decomposition of the original fraction is:
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction -3 Over 5 x minus 2 EndFraction + StartFraction 5 Over (5 x minus 2) squared EndFraction
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Use the figure below to determine the value of the variable and the
lengths of the requested segments. Your answers may be exact or
rounded to the nearest hundredth. The figure may not be to scale.
Using tangents theorem, we can find the value of the missing length,
n = 18.7units.
Define a tangent?"To touch" is how the word "tangent" is defined. The same idea is conveyed by the Latin word "tangere". A tangent, in general, is a line that, while never entering the circle, precisely touches it at one point on its circumference. A circle has a number of tangents. They make a straight angle with the radius.
Here in the diagram,
We can see that as per the central angle and tangent theorem,
AB/BC = ED/DC
⇒ 17/10 = n/11
Cross multiplying:
⇒ 17 × 11 = n × 10
⇒ 10n = 187
⇒ n = 187/10
⇒ n = 18.7
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What is the answer?
What is the gradient of the blue line?
Step-by-step explanation:
the gradient = the slope = the incline = ...
many different names for the same thing.
however you call it, it is the ratio
y coordinate change / x coordinate change
whet going from one point on the line to another.
for questions like this we should look for points with integer coordinates (going through a vertex of the coordinate grid squares).
I see for example right at the left beginning (0, 1).
the next one is then (4, 2).
when going from (0, 1) to (4, 2) :
x changes by +4 (from 0 to 4).
y changes by +1 (from 1 to 2).
so, the slope or gradient is
+1/+4 = 1/4
I would like to see the process steps of solving this as well please! Thank you!
You must begin to brake 234643.2 feet from the intersection.
What is stopping distance?In Mathematics and Science, stopping distance can be defined as a measure of the distance between the time when a brake is applied by a driver to stop a vehicle that is in motion and the time when the vehicle comes to a complete stop (halt).
Based on the information provided above, the speed of this car is represented by the following equation;
s = √(30fd)
Where:
f is the coefficient of friction.d is the stopping distance (in feet).By substituting the given parameters, we have:
20 = √(30(0.3)d)
400 = 9d
d = 400/9
d = 44.44
Conversion:
1 mile = 5,280 feet.
44.44 miles = 234643.2 feet.
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Lines lll, mmm, and nnn are parallel to each other and ppp is a transversal.
Also, 2\angle{x}=3\angle{y}2∠x=3∠y2, angle, x, equals, 3, angle, y
The measure of angle x is: x = (3/5)(180 - z) = (3/5)(180 - 90) = 36 degrees
And the measure of angle y is:y = (2/5)(180 - z) = (2/5)(180 - 90) = 24 degrees
Since lines lll, mmm, and nnn are parallel to each other and ppp is a transversal, we can use the angle properties of parallel lines to find the relationship between angle x and angle y.
From the given information, we have: 2x = 3y
Simplifying this equation, we get: x = (3/2)y
Now, we can use this relationship to find the measures of angles x and y in terms of a common variable. Let's use z as the common variable.
x + y + z = 180 (angles on a straight line)
Substituting x = (3/2)y, we get: (3/2)y + y + z = 180
Simplifying this equation, we get: (5/2)y + z = 180
Now, we can express y in terms of z:
(5/2)y = 180 - z
y = (2/5)(180 - z)
Similarly, we can express x in terms of z:
x = (3/2)y = (3/2)(2/5)(180 - z) = (3/5)(180 - z)
Now, we can use the relationship between angle x and angle y to find the measure of angle x in terms of z: 2x = 3y
2[(3/5)(180 - z)] = 3[(2/5)(180 - z)]
Simplifying this equation, we get: (6/5)z = 108
z = (5/6)(108) = 90
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Find the length of side x.
Give answer to 1dp.
Answer:
Set your calculator to degree mode.
Use the Law of Cosines.
x^2 = 18^2 + 15^2 - 2(18)(15)(cos 105°)
x^2 = 688.7623
x = 26.2 cm
A neighborhood watch association surveyed 40 neighbors about their feelings of safety in the neighborhood. They will survey an additional 80 neighbors. Based on the information, predict how many of the 80 neighbors will feel safe?
We can predict that around 50 of the additional 80 neighbors will feel safe in the neighborhood.
To make a prediction about the number of neighbors who will feel safe, we need to know the proportion of the initial 40 neighbors who felt safe. Let's say that 25 of the 40 neighbors surveyed felt safe.
Then, we can estimate the proportion of the larger group of 120 neighbors (the initial 40 plus the additional 80) who will feel safe as follows:
proportion feeling safe = number feeling safe / total number surveyed
proportion feeling safe = 25 / 40
proportion feeling safe = 0.625
We can use this proportion to estimate the number of the 80 additional neighbors who will feel safe:
number feeling safe = proportion feeling safe x total number surveyed
number feeling safe = 0.625 x 80
number feeling safe ≈ 50
So based on the information given, we can predict that around 50 of the additional 80 neighbors will feel safe in the neighborhood.
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Solve for the missing side. Formula: a^2+b^2=c^2
Answer:
[tex] \frac{7 \sqrt{39} }{5} [/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]( {11.2})^{2} - { {7} }^{2} = 76.44 > 0[/tex]
The missing side is equal to:
[tex] \sqrt{76.44} = \frac{7 \sqrt{39} }{5} [/tex]