The required minimum sample size is 2875
Given that,
A government organization wanted to determine how many drivers between the ages of 16 and 24 had recently engaged in an accident. The agency wanted to make the estimate with a 90% confidence level and within one percentage point.
From the standard normal table, the z-critical value at 90% confidence is 1.65.
The information represent E = 0.01, p = 0.12 and z. =1.65 for finding sample size.
n = (Zc / E )² x P(1-P)
= (1.65 2x0.12(1 - 0.12)0.01
= 2874.96 ~ 2875
Hence, 2875 is the necessary number of samples, minimum.
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30 point reward if you help ! find the volume of each shape and then compare. do not reduce your fractions.
The volume of the cuboid is [tex]\frac{6}{125}[/tex] and The volume of the cube is [tex]\frac{8}{27}[/tex]
The comparison of both a cube and a cuboid have six faces,a cube has six faces which are all squares and on the other hand, the cuboid is but a cuboid has rectangular faces.
What is a Cube?
A cube is a symmetrical three-dimensional shape which has all six sides equal.
To find the volume of cube is addition of all seen sides or the given sides all squared.
i.e volume of a cube= [tex]a^{3}[/tex]
volume of the cube=([tex]\frac{2}{3}[/tex])^3
Volume= [tex]\frac{8}{27}[/tex] cubic inches
How to dertermine the volume of a cuboid
Whar is a Cuboid?
A Cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges which the volume can be measured by multiplying the length by the breadth by the height .
Volume of a cuboid = L×B×H
Volume of a cuboid=[tex]\frac{2}{3}[/tex]×[tex]\frac{1}{5}[/tex]×[tex]\frac{3}{5}[/tex]
Volume of a cuboid=[tex]\frac{6}{125}[/tex] cubic inches.
To compare,
A cube has shapes of equal sides six faces and a cuboid faces are non-equal with six faces, 8 vertices and 12 edges.
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Find two consecutive positive odd integers such that three times the sum of the largest number plus 22 is equal to the product of both numbers.
Answer:
Step-by-step explanation:
Let's say your consecutive numbers are A and B with A+2=B. Using the information we have been given, we can get the linear equation; AB=3B+22. A=B-2, so we can replace A with B-2 to get (B-2)(B)=3(B+22). Multiplying this out, we get B^2-2B=3B+66. Simplifying, we get B^2-5B-66=0. This is a quadratic equation. Using the quadratic formula, we get B=11,-6. B has to be positive, so B=11. A+2=11, so A=9
helen buys two pineapples she pays with a £5 note and gets £3.60 change work out the cost of one pineapple
Answer:
Each pineapple costs £0.70.
Step-by-step explanation:
Let P be the number of pineapples Helen purchased and C the cost per pineapple, in £.
Helen's total cost would be: P*C = total cost.
The total cost is the difference between £5 and £3.60, which is £1.40.
We are given P (the number of pineapples, 2) and the total cost (£1.40) , so enter those numbers in the equation:
P*C = total cost
2*C = £1.40
C = £0.70
What do you need to multiply the subtotal by in order to get the total?
Given: Subtotal: 42.00
Total: 45.99
Tax rate: 9.5%
Sales tax: $3.99
the two-way relative frequency table given shows the results from the lunch orders from an upperclassman picnic. 11th grade 12th grade total salad 12% 6% 18% sandwich 20% 24% 44% soup 8% 30% 38% total 40% 60% 100% a segmented bar chart was created showing the lunch preference by grade. what percentage would the bar for 11th graders show for preferring salad? 67% 40% 30%
The bar for 11th graders show 30% for preferring Salad.
Given, that the lunch orders from an upperclassman picnic.
11th Grade 12th Grade Total
Salad 12% 6% 18%
Sandwich 20% 24% 44%
Soup 8% 30% 38%
Total 40% 60% 100%
To find the relative frequency we divide the frequency by the total.
hence, to find the relative frequency for 11th graders preferring Salad
12/40 = 0.3 = 30%
Hence, the bar for 11th graders show 30% for preferring Salad.
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the recursive formula for the height above the ground on the nth step of the stairs show is an=an-1+4 with a1=7 what explicit formula finds the height above the ground of the nth step?
The explicit formula is a_n = 3+4n
From the question, we have
a1 = 7
We know that,
a_n = a_1 +(n-1)d
a_n = 7 +(n-1)4
a_n = 7+4n-4
a_n = 3+4n
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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750 people go on a coach trip
each coach can hold 55 people
How many coaches are needed
Step-by-step explanation:
750 people go on a coach trip each coach can hold 55 people How many coaches are needed?
750/55 = 13.636 coaches are needed.
Because you cannot have a partial coach, you round up to needing 14 coaches.
J is the midpoint of segment CT.
CJ = 9x + 1
JT = 2x + 15
Find CT.
The length CT of the line segment is 38 units
How to determine the length of CT?From the question, we have the following parameters
CJ = 9x + 1
JT = 2x + 15
Also, we understand that:
Point J is the midpoint of segment CT.
This means that
CJ = CT
So, we have
9x + 1 = 2x + 15
Evaluate the like terms
7x = 14
So, we have
x = 2
Length CT is calculated as
CT = 9x + 1 + 2x + 15
So, we have
CT = 9 x 2 + 1 + 2 x 2 + 15
Evaluate
CT = 38
Hence, the length is 38 units
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7. What number multiplied by 2/3 has a product
of 1? (Example 2) it's saying 4/6 is wrong what do i do
Answer:
3/2
Step-by-step explanation:
To multiply fraction×fraction, you multiply top×top and bottom×bottom.
2/3 × 3/2
= 6/6
= 1
The 3/2 is called the reciprocal. Take the number in the problem and flip it over to find the reciprocal.
Write the equation of the line that is parallel to the line 14x - 2y = 51 and goes through the point(3, -11)
Find the perimeter of a rectangle with a diagonal of 20 inches that make angle measure 30 and 60 using trigonometric function (sine, cosine, tangent)
The perimeter of the rectangle is 20 + 20√3 inches.
How to find the perimeter of a rectangle?The perimeter of a rectangle is sum of the whole side of the rectangle. The side bounded by the rectangle is the perimeter of the rectangle.
Therefore, the diagonal of the rectangle is given as 20 inches.
Using trigonometric ratios, let's find the sides of the rectangle.
sin 30 = opposite / hypotenuse
sin 30 = x / 20
x = 20 sin 30
x = 20 × 0.5
x = 10 inches
Therefore, using Pythagoras theorem,
20² - 10² = b²
b² = 400 - 100
b = √300
b = √100 × 3
b = 10√3
Hence,
perimeter of the rectangle = 2(l + w)
perimeter of the rectangle = 2(10 + 10√3)
perimeter of the rectangle = 20 + 20√3
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Solve the equation for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
3.5(x +2) = 17
Answer:2.86
Step-by-step explanation:
3.5(x +2) = 17
3.5x + 7 = 17
3.5x =17 - 7
3.5x =10
x = 10/3.5
x = 2.86
Find the slope of the line passing through the points (4, -2) and (9, -2).
slope:
Find the slope of the line passing through the points (2, 9) and (2, - 7).
slope:
Answer:
x1 y1 x2 y2
1. 0 - explanation - (4, -2) (9, -2) -2 - -2
4 - 9 (put a fraction bar when you put the y2 and y1 together and put the x2 and y2 in the denominator spot) basically -2 subtract -2 equals 0
2. it would be defined or 0
how many ways can 7 students be assigned a seat in a classroom if there are 10 seats in a row? a) 70 b) 604,800 c) 120 d) 3,628,800 e) 17 f) none of the above.
The correct option c) 120; for the assignment of 7 students to 10 seats in a row.
What is referred as the combination?Combinations are mathematical techniques that count the number of potential arrangements for a set of elements only when order of the selections is irrelevant. You can choose the constituents of combos in any order.The procedure for determining how many arrangements are feasible when only a few items are selected from a set of items that are unique is as follows:The formula for finding the combination is-
ⁿCₓ = n!/ x!(n - x)!
Where,
n = total value.x = selected valueFor the given question.
Total students to be assigned a seat = 7.
Total seats in a classroom = 10.
Thus, Applying combination;
¹⁰C₇ = 10!/7!(10 - 7)!
¹⁰C₇ = 120
Thus, if there are 10 seats in a row, there are 120 different ways that 7 students could be seated in a classroom.
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Which inequality has like variable terms on each side of the inequality symbol?
Inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
As given in the question,
Inequality which have like variables term on each side of the given inequality symbol is :
a. 15c + 25 ≤ 115
In the given inequality, on left hand side we have variable c and constant term while on the right hand side of the inequality only constant.
Not correct option.
b. 0.75r - 6.25 > 10
In the given inequality, on left hand side we have variable r and constant term while on the right hand side of the inequality only constant.
Not correct option.
c. 16 - 2x > x + 16
In the given inequality, on left hand side we have variable x and constant term while on the right hand side of the inequality also variable x and constant term.
Correct option.
d. 12.25h -175 < 5,000
In the given inequality, on left hand side we have variable h and constant term while on the right hand side of the inequality only constant.
Not correct option.
Therefore, inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
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what is the best point estimate for the population's standard deviation if the sample variance is 49.7? round your answer to one decimal place, if necessary.
Using the relation between standard deviation and variance it is concluded that the standard deviation for the population for the given variance is 7.1
What is the relation between standard deviation and sample variance?In statistics, the two most crucial metrics are variance and standard deviation. While the variance is a measurement of how data points vary from the mean, standard deviation is a measure of the distribution of statistical data.
The square root of the variance yields the standard deviation, i.e.
Standard deviation = [tex]\sqrt{variance[/tex]
Given that sample, the variance is 49.7 and we have to calculate the standard deviation.
Standard deviation (σ) = [tex]\sqrt{variance[/tex]
= [tex]\sqrt{49.7}[/tex]
= 7.0498
=7.1
Hence, the standard deviation for the population for the given variance is 7.1
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Sutton takes 48 minutes to walk to work. after getting a new job, sutton takes 30.72 minutes to walk to work. what was the percent decrease in the travel time?
The percent decrease in the travel time after getting a new job is 36%.
Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".
First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.
decrease in time = 48 - 30.72
decrease in time = 17.28
Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.
percent decrease = (17.28 / 48) x 100
percent decrease = 36%
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What is the value of y in the equation 2(2y − 16) = 0? (5 points)
a 4
b 6
c 8
d 9
Answer:
the options are wrong
Step-by-step explanation:
open the bracket2(2y)2(-16)=04y-32=0make y the subject of formulary=-32÷4y=-8Answer:
C. 8
Step-by-step explanation:
2 x 8 = 16
16 - 16 = 0
2 x 0 = 0
if the probability of pulling a four of hearts from a randomly shuffled deck is 1 / 52, and the probability of pulling a spade from a randomly shuffled deck are 1 / 4, then the probability of pulling a spade or a four of hearts from a randomly shuffled deck is:
The probability of pulling a spade or a four of hearts is 0.264 .
we have , from a deck of cards
probability of pulling a spade = 1/4 = 13/52
probability of not pulling a spade 3/4 = 39/52
probability of pulling a 4 of hearts = 1/52
probability of not pulling a spade = 51/52
we have to find the probability of pulling a spade or a four of hearts from a random shuffled deck
So we can get three cases :
case A :
getting a spade and not getting four of hearts
∴ P (A) = [tex](\frac{13}{52} ) (\frac{51}{52} )[/tex] = 663/2704
case B :
not getting a spade and getting four of hearts
P(B) = [tex](\frac{39}{52}) (\frac{1}{52} )[/tex] = 39/2704
case C :
getting a spade and getting four of hearts
P(C) = [tex](\frac{13}{52})(\frac{1}{52} )[/tex] = 13/2704
therefore , the required probability will become
P = P(A) +P(B) + P(C)
P = 715/ 2704
P = 0.264
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Which ordered pair is NOT a solution to the equation y = 2x? Four points plotted on a coordinate plane. Point A has coordinates 1 comma 2. Point B has coordinates 2 comma 4. Point C has coordinates 3 comma 8. Point D has coordinates 5 comma 10. point A point B point C point D
Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.
Given that,
To determine which ordered pair is NOT a solution to the equation y = 2x.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given relation y = 2x
Now substitute every value of x from the ordered pair and match the output with the corresponding value of the ordered pair.
put x = 1, 2, 3, 5
Y = 2(1)
y = 2
Similarly the outcome of the values,
x = 2, 3, 5
y = 4, 6, 10
Thus, Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.
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An investor invested a total of $2,900 in two mutual funds. One fund eamed a 7% profit while the other eamed a 3% profit. If the investor's total profit was $143, how much was invested in each mutual fund?
Answer:
one is 203
two is 87
Step-by-step explanation:
y=4x^2-8x+3
find the vertex form
The vertex of the quadratic equations is at (1, -1), then the vertex form will be:
y = 4*(x - 1)^2 - 1
How to find the vertex form?For a quadratic equation with leading coefficient a and a vertex (h, k), the vertex form is:
y = a*(x - h)^2 + k
And for a equation: y = a*x^2 + b*x + c
The x-value of the vertex is at:
h = -b/2a
In this case, we have:
y = 4x^2 - 8x + 3
So the x-value of the vertex is at:
h = -(-8)/2*4 = 1
To get the y-value we evaluate in x = 1
y = 4*1^2 - 8*1 + 3
y = 4 - 8 + 3 = -1
The vertex is at (1, -1) and the leading coefficient is 4, then the vertex form is:
y = 4*(x - 1)^2 - 1
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a box has a width of 15 inches and a length of 16 inches. the volume of the box is increasing at a rate of 569 cubic inches per second, with the width and length being held constant. what is the rate of change, in inches per second, of the height when the height is 6 inches?
The rate of change in height when height is 6 inches is 2.37 inches per second approximately.
We know that the volume of cube with length L, width W and height H is given by,
V = L*B*H
So given that the length is 15 inches
the width is 16 inches
Let the height be h inches.
So now the volume is given by,
V = 15*16*h
Differentiating the volume with respect to time 't' we get,
dV/dt = 15*16 dh/dt
Now given that the rate of change in volume per second is 569 cubic inches.
So, dV/dt = 569
So, 15*16 dh/dt = 569
dh/dt = 569/(15*16) = 569/240 = 2.37 (approx)
So the rate of change in height is 2.37 inches approximately.
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In a circle, the length of an arc intercepted by a central angle is 12 mm, and the radius of the circle
8 is 8 mm. What is the measure, in radians, of the angle?
Answer:
1.5
Step-by-step explanation:
we calculate the circumference of this circle.
circumference of a circle=2πr
data:
r=8 mm
circumference=2(8 mm)π=16π mm
2)we calculate the measure, in radians of the angle.
We know that:
circumference of a circle=2π radians
therefore:
16π mm=2π radians.
16 π mm--------------------------2π radians
12 mm----------------------------- x
x=(12 mm * 2π radians) / 16π mm=1.5 radians.
Type the correct answer in the box. use numerals instead of words. the weight of a bag of golf balls varies directly as the number of golf balls in the bag. if a bag of 69 golf balls weighs 2,553 grams, how many golf balls are in a bag that weighs 1,110 grams? number of golf balls:
A total of 30 golf balls are there in the bag that weighs 1110 grams.
A total of 69 golf balls weights 2553 grams in a bag.
It is asked that how much golf balls does make 1110 grams of weight.
Let us say that the weight of one ball is X.
So, Using unitary method,
We can write,
69 times mass of one golf ball = 2553 grams.
69X = 2553
X = 2553/69
X = 37 grams.
Hence, the weight of one ball is 37 grams.
Now, let us say that Y balls weights 1110 grams,
So, we can write,
Y time weight of one ball = 1110
37Y = 1110
Y = 1110/37
Y = 30.
Hence, 30 golf balls will weight 1110 grams.
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Answer:
30
Step-by-step explanation:
a news poll which estimated that 82% of all voters believe global warming exists had a margin of error of /- 3%. suppose an environmental group planning a follow-up survey on this issue wants to determine a 95% confidence interval with a margin of error of no more than 2%. how large a sample do they need? (for estimate of p use 0.82)
The needed sample size is 1419. Sample Size is defined as the number of observations in the study.
In the question we have ,
estimate value of all voters who believe global warming ( p) = 82% = 0.82
margin of error (M.E) = 2% = 0.02
confidence of interval is calculated by estimate point value and add or subtract margin of error .
here,we have the value of confidence of interval is 95% = 0.95
Margin of error formula is
M.E = Z × √(p(1-p)/n)
where, p --> is estimated value
n---> sample size , which we required
Z ----> is z-value for observation
for the confidence of interval level 95% , the Z-value is 1.96 exist.
put all value in above formula we get,
0.02 = 1.96 × sqrt( ( 0.82)(1-0.82)/n)
=> 0.02 = 1.96× √(0.82×0.18/n)
= 0.02/1.96 = √0.1476/n => 0.000104= 0.1476/n
=> n = 1419
So, sample size is large and it is 1419.
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Ahmad decided to increase his homework time of 8 hours per week by 15%,
Calculate his new homework time.
Give your answer in hours and minutes.
Answer:
it's a answer done bro
Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked how much is Nick share of the money. Nick and Pam are paid ?
Nick got a total of $33.25 for his part of work.
What is the general equation of a Straight line? How it represents a proportional relationship?
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.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked.
Assume that Nick recieved $[x]. Then, Pam will get - (52.25 - x). For direct proportionality -
y₁/x₁ = y₂/x₂
We can write -
x/3.5 = (52.25 - x)/2
2x = 3.5(52.25 - x)
2x = 182.875 - 3.5x
x = 33.25
Therefore, Nick got a total of $33.25 for his part of work.
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I need help asap… Is this relation a function or no ?
Answer:
Step-by-step explanation:
yes, it is a function
Answer: no
Step-by-step explanation: you have -2,-5 and -2,0 you cant have 2 or more x values that are the same.
Mariyah wants to enlarge a triangle with sides of 3 inches, 6 inches, and 6 inches. If the shortest side of the new triangle is 13 inches, how long will the other two sides be?
The other sides of the new triangle are 13, 26 and 26 inches as calculated by the properties of similarity.
We know that when two triangles are similar then the ratio of the sides are also equal.
Let the original triangle be ΔABC and the new triangle be ΔXYZ
So from the property of similarity.
AB/XY = BC /YZ = CA/ ZX
Now it is given AB = 3 inches
XY = 13 inches
Hence AB/XY = 13/3
Hence YZ = 13 / 3 × 6 =26 inches
Again ZX = 26 inches
Similar triangles have parallel sides that are proportional to one another and parallel angles that are identical to one another.
Triangles can have different diameters despite having comparable exteriors. Triangles that are congruent and similar to each other usually don't match up.
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