Answer:
No, you should not approximate using the normal distribution because your sample size is too small.
Step-by-step explanation:
You can use the normal distribution in the following cases:
Your sample size is larger than 25You know that the sample size comes from a normally distributed population.Based on the rule of thumb, I would collect at least 7 more answers before using the normal distribution.
Because the sample size is too tiny, one should not use the normal distribution for approximation.
Given that,
In a recent survey, 83% of the community favored building a police substation in their neighborhood. You randomly select 18 citizens and ask each if he or she thinks the community needs a police substation.
The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
The sample size should be greater than 25, and the sample size should originate from a regularly distributed population. As the sample size of the distribution is to small normal distribution cannot be used.
Thus, Because the sample size is too tiny, one should not use the normal distribution for approximation.
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An object is thrown off a 256-foot-tall building, and the distance of the object from the ground is measured every second. The function that models the height, h, of the object after t seconds is h(t) = –16t2 + 96t + 256. Determine the time when the object hits the ground.
After how many seconds does the object hit the ground?
2
4
8
16
Answer:
C. 8
At 8 seconds the object will hit the ground.
Answer: C. 8
Step-by-step explanation:
just did this
Sam subtracted 5 from the quotient of a number and 3. Write an algebraic expression to represent the operations that Sam preformed
Answer:
(x/3) - 5.
Step-by-step explanation:
Let the number be x.
The quotient of the number and 3 is x/3.
So the expression is:
(x/3) - 5.
The function y = 8.5(1.1)x models the population in thousands of a town where x is the number of years after 2000. What will be the town's population in 2007? Give the answer to two decimal places.
The population of the town in 2007, according to the exponential growth function y = 8.5(1.1)x, would be approximately 16,630 people.
Explanation:The function given is an exponential growth function, where y = 8.5(1.1)x. Here, the variable y represents the population in thousands and x represents the number of years after 2000. To find the town's population in 2007, we replace x with 7 (since 2007 is 7 years after 2000) and calculate y.
Using the formula, y = 8.5 * (1.1)7. When calculated, we find y to be approximately 16.63. This means that, according to the model, the town's population in 2007 would be approximately 16630 (because the model represents the population in thousands).
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Selena and Tracey play on a softball team.Selena has 8 hits out of 20 times at bat, andTracey has 6 hits out of 16 times at bat.Based on their past performance, what is theprobability that both girls will get a hit nexttime at bat?[A] 31 40[B] 48 320[C] 1 [D] 14 36
Answer:
The correct option is option [B].
The probability that both girls Selena and Tracey will a next at bat is [tex]\frac{48}{320}[/tex].
Step-by-step explanation:
Independent events:
If A and B are event. The occurrence of one of them does not affect the outcomes of other event. Then A and B are independent events.
P(A and B) =P(A)× P(B)
Dependent events:
If A and B are event. The outcomes of one of them affects the outcomes of other event. Then A and B are called dependent events.
P(A and B) =P(A)× P(B|A)= P(B)×P(A|B)
Given that,
Selena has 8 hits out of 20 times at bat.
The number of hits by Tracey out of 16 is 6 at bat.
A= Selena hits a softball.
B= Tracey hits a softball.
The probability that the Selena his a softball is
=P(A)
[tex]=\frac{8}{20}[/tex]
The probability that the Tracey his a softball is
=P(B)
[tex]=\frac{6}{16}[/tex]
Both event are independent. Sine the events do not affect the outcomes of other event.
The probability that both girls will a next at bat is
=P(A and B)
=P(A)×P(B)
[tex]=\frac{8}{20}\times \frac{6}{16}[/tex]
[tex]=\frac{48}{320}[/tex]
Rico wants to find the distance between the points (-2,-3) and (2,-5) his work is shown.|-3| + |-5| = 3+5 = 8the distance is 8 unitsis Riko correct explain why or why not?
Answer:
Riko is wrong
Step-by-step explanation:
To find the distance of two point, we use the following formula:
A (x1, y1)
B (x1, y2)
AB = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
In this situation, we have:
A (-2,-3)
B (2,-5)
So the distance is: [tex]\sqrt{(2 - (-2))^{2} + (-5 - (-3))^{2} }[/tex] = [tex]\sqrt{4^{2} + 8^{2} }[/tex] = [tex]\sqrt{80} = 4\sqrt{5}[/tex]
Hope it will find you well.
Sample Response: No, Riko is not correct. The points do not have the same x-coordinates. If you connect the points, they do not form a horizontal or vertical line, so you cannot count spaces or use absolute value to find the distance.
-5-n/9=-8
-3/7=-2/3+x
3x-13=7(x+2)-4(x-7)
1/2x-9=15-5/6x
8(4x-3)=6(-7x-4)
2(a-24)=16-1/3(9a+27)
^^ solve the equations above and explain how you got the answer.
Answer:
ok
1) n=27
2) x=5/21
3) no solution
4) x=18
5) x=0
6) a=11
Step-by-step explanation:
hope this helps you..(:
Two number cubes each have sides that are labeled 1 to 6. Isis rolls the 2 number cubes. What is the probability that the sum of the numbers rolled will equal 4?
Answer:
The probability that the sum of the numbers rolled will equal 4 is [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Total possible outcome is 36
The sample space for the dice is shown below
[tex]\left[\begin{array}{cccccc}1,1&1,2&1,3&1,4&1, 5&1,6\\2,1&2,2&2,3&2,4&2, 5&2,6\\3,1&3,2&3,3&3,4&3, 5&3,6\\4,1&4,2&4,3&4,4&4, 5&4,6\\5,1&5,2&5,3&5,4&5, 5&5,6\\6,1&6,2&6,3&6,4&6, 5&6,6\end{array}\right][/tex]
From the above sample, the event of sum equals 4 is:
(1, 3)
(2, 2)
(3, 1)
Number of outcome with sum equals 4 is 3
[tex]Probability = \frac{number of possible outcome}{number of total outcome} \\Probability = \frac{3}{36} = \frac{1}{12}[/tex]
The probability that the sum of the numbers rolled will equal 4 is [tex]\frac{1}{12}[/tex]
Answer:
0.3333
Step-by-step explanation:
Out of 6x6 = 36 different scenarios that could happen when rolling the 2 cubes, there are 3 cases where the sum of the numbers rolled will equal 4:
(1,3) (3,1) and (2,2)
So the probability for these 3 cases to happen out of 36 is
[tex]\frac{3}{36} = \frac{1}{3}[/tex] or 0.3333
# 15. Tycho wants to prepare a schedule for his exercise over the next few months. Every
week, he wants to exercise on the same days of the week. He does not want to exercise on
two consecutive days. He wants to exercise three days per week. How many schedules can he
choose from?
(A) 6
(B) 7
(C) 9
(D) 10
(E) 35
There are a total of 9 possible schedules that Tycho can choose from.
Thus, option (C) is correct.
Let consider the days of the week as Monday (M), Tuesday (T), Wednesday (W), Thursday (Th), Friday (F), Saturday (Sa), and Sunday (Su).
To create a schedule for exercise, Tycho needs to choose three days of the week to exercise such that no two exercise days are consecutive.
So, the possibilities are:
1. Tycho chooses Monday, Wednesday, and Friday.
The schedule is MW FSu.
2. Tycho chooses Monday, Wednesday, and Saturday.
The schedule is MW SaSu.
3. Tycho chooses Monday, Thursday, and Saturday.
The schedule is MT F SaSu.
4. Tycho chooses Monday, Thursday, and Sunday.
The schedule is MT SaSu.
5. Tycho chooses Tuesday, Thursday, and Saturday.
The schedule is TThSaSu.
6. Tycho chooses Tuesday, Thursday, and Sunday.
The schedule is TTSaSu.
7. Tycho chooses Tuesday, Friday, and Sunday.
The schedule is TFSaSu.
8. Tycho chooses Wednesday, Friday, and Sunday.
The schedule is W F SaSu.
9. Tycho chooses Wednesday, Thursday, and Saturday.
The schedule is W T FSaSu.
Thus, total of 9 possible schedules that Tycho can choose from.
Thus, option (C) is correct.
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One person can complete a task 8 hours sooner than another person. Working together, both people can perform the task in 3 hours. How many hours does it take each person to complete the tasking working alone?
Answer:
it takes 1st person 4 hour and second person is 8 hours
Step-by-step explanation:
Let t is the time (t >0)
We have:
1st person working rate per one task: 1/t-8 2nd person working rate per one task: 1/t Working rate per one task from 2 person: 1/3<=> 1/3 = 1/t + 1/t-8
<=> [tex]t^{2} -14t = -24[/tex]
<=> [tex](t-7)^{2} =25[/tex]
<=> t - 7 = 5
<=> t = 12
So it takes 1st person 4 hour and second person is 8 hours
Answer:
Person A complete the task in 1.125 hours
Person B complete the task in 9 hours
Step-by-step explanation:
Person A complete a task 8 hours sooner than person B
Working together they perform the task in 3 hours
Let call "x" hours person A need to do the task alone
Then person B will take 8*x hours to do the job
In 1 hour person A do 1/x part of the task
In 1 hour person B do 1/8*x part of the task
Then A + B in one hour of work will do
1/x + 1/8x = [ 8 + 1 ]/8*x ⇒ 9/8*x
And according to problem statement that time is 1/3 (one third of the time)
Then 3* (9/8*x) = 3
9 = 8*x
x = 9/8
x = 1.125 hours
And person B will take 8*1,125 = 9 hours
\text{Min}Minstart text, M, i, n, end text Q_1Q 1 Q, start subscript, 1, end subscript \text{Median}Medianstart text, M, e, d, i, a, n, end text Q_3Q 3 Q, start subscript, 3, end subscript \text{Max}Maxstart text, M, a, x, end text 121212 181818 232323 262626 292929 The five-number summary suggests that about 75\%75%75, percent of lakes in Minnesota have more than what number of house boats? Choose 1 answer:
Answer:
18 Houseboats
Step-by-step explanation:
Given the set of numbers
12 18 23 26 29
Minimum = 12
First Quartile, Q₁ = 18
Median, Q₂ = 23
Third Quartile, Q₃ = 26
Maximum = 29
The first 25% of lakes have less than or equal to 18 houseboats.
Therefore, the 5-Number Summary suggests that about 75% of lakes in Minessotta have more than 18 Houseboats.
Answer:
18
YEET
Step-by-step explanation:
Given a sector of a circle has an area of 40.8 square inches and a radius of 8 inches. What is the measure central angle of the circle round to the nearest degree?
Answer: The measure of the central angle of the circle is 73°
Step-by-step explanation: Please see the attachments below
Answer: 287 degree
Step-by-step explanation:
Area of a sector = θ/360 x pi r^2
Where pi = 22/7
Given that the
area = 40.8 square inches
radius = 8 inches
40.8 = θ/360 × 3.143 × 8 × 8
θ = (360 × 40.8)/201.06
θ = 73 degree
The measure of the central angle of the circle = 360 - θ
= 360 - 73
= 287 degree
Evaluate 6c + e2 when c = 6 and e = 2
[tex]c=6, e=2; so\\6\times6+2\times2=40[/tex]
Lucy invested $30,000 in an account paying an interest rate of 6.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 9 years?
Answer:
A≈54300
Step-by-step explanation:
To calculate the final amount in the bank account, we can use the formula A = P(e(rt)), where A is the final amount, P is the principal amount, e is the base of natural logarithms, r is the interest rate, and t is the time in years. In this case, Lucy invested $30,000 at an interest rate of 6.6% compounded continuously for 9 years. By substituting these values into the formula and evaluating the expression, the final amount in the account after 9 years is approximately $53,509.79.
Explanation:To calculate the final amount in the bank account, we can use the formula: A = P(e(rt)), where A is the final amount, P is the principal amount, e is the base of natural logarithms, r is the interest rate, and t is the time in years. In this case, Lucy invested $30,000 at an interest rate of 6.6% compounded continuously for 9 years.
First, we need to convert the interest rate to a decimal by dividing it by 100: 6.6% = 0.066. Then, we can substitute the values into the formula: A = 30000(e0.066*9)). Using a calculator, we can evaluate this expression to get the final amount, which is approximately $53,509.79.
Mary was told that a line goes through the points (1, 3) and (6, -2) and has a slope of 3.
a. Explain why the information Mary was given cannot be correct.
b. If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the
coordinates of another point on the line
c. If the given points are correct for the line, what is the slope? Write an equation for the line
Answer:
a. The slope is incorrect
b. y = 3x, ( 0 , 0 )
c) y = 4 - x
Step-by-step explanation:
Given:-
The slope between two points (1, 3) and (6, -2) is 3.
a. Explain why the information Mary was given cannot be correct.
- The slope between two arbitrary points, ( x1 , y1 ) and (x2 , y2) is given by the following relationship:
slope = ( y2 - y1 ) / ( x2 - x1)
- Use the given points (1, 3) and (6, -2) and determine the slope:
slope = ( -2 - 3 ) / ( 6 - 1 )
slope = ( -5 ) / ( 5 )
slope = -1
- Yes, the given slope is incorrect it should be = -1
b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the coordinates of another point on the line
- We will assume the point (1,3) lies on line with a slope = 3.
- We will use the slope-intercept equation of line:
y = slope*x + c
Where, m : Slope
c : y-intercept
y = 3x + c
Using the given correct point to evaluate the y-intercept (c):
3 = 3*1 + c
c = 0
- The equation of line is,
y = 3x
- The origin (0,0) lies on the line y = 3x.
c. If the given points are correct for the line, what is the slope? Write an equation for the line
- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.
- We will use the slope-intercept equation of line:
y = slope*x + c
Where, m : Slope
c : y-intercept
y = -x + c
Using the given points to evaluate the y-intercept (c):
3 = -1 + c
c = 4
- The equation of line is,
y = -x + 4
Mary's information is incorrect because the slope of the line passing through the points (1, 3) and (6, -2) is -1, not 3. If the slope is actually 3, the line equation is y = 3x and an additional point on the line is (2, 6). If the given points are correct, the line equation is y = -x + 4.
Explanation:To understand these questions, it's important to know how the slope of a line is defined and how to write the equation of a line.
Given two points (x1, y1) and (x2, y2), the slope of the line is calculated as (y2 - y1) / (x2 - x1). For the points given, (1, 3) and (6, -2), the slope would be (-2 - 3) / (6 - 1) = -5/5 = -1. So, the slope of the line passing through these two points is not 3, which contradicts the information given. Therefore, the information Mary was given cannot be correct.
If the point (1, 3) and the slope 3 are correct, the equation of the line is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Substituting these values we get y - 3 = 3(x - 1). This simplifies to y = 3x. A point on this line can be (2, 6).
If the points (1, 3) and (6, -2) are correct, we've already calculated the slope as -1. To find the equation of the line we use the same formula, y - y1 = m(x - x1). Substituting these values we get y - 3 = -1(x - 1), simplifying to y = -x + 4.
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What problem led to playgrounds becoming more common in America cities
Answer: there were not a lot of safe places kids could play
Step-by-step explanation:
i got it right.
The problem led to playgrounds becoming more common in America cities is: Due to unsafe places.
What is playgrounds?Playgrounds is a safe place that is specifically set aside for children to play.
Playgrounds can tend to contribute to a child social growth when the child plays among is age group or peer group.
Playgrounds is common in America in order to prevent danger and injury because there were not safe places for children to play.
Therefore the problem led to playgrounds becoming more common in America cities is: Due to unsafe places.
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The length of a rectangle is nine inches more than its width. Its area is 850 square inches. Find the width and length of the rectangle.
Answer:
width= 25 inches
length= 34 inches
Step-by-step explanation:
width x length = 850 in²
w x (9+ w ) = 850 in²
9w+ w²=850 in²
9w + w²-850 =0
solve for w using quadratic formula
w= {-9 ±√(9)²-4(1)(-850)} ÷2(1)
w= 25; -34
The width is 25 because measurements can't be negative.
width= 25
length= 25+9=34
If a stone is thrown up at 10 m per second from a height of 100 meters above the surface of the moon, its height in meters after t seconds is given by s = 100+10t-0.8t^2 . What is its acceleration?
Answer:
-1.6 m/s
Step-by-step explanation:
According to the equations of motion, the height in meters (s) after t seconds is:
[tex]s(t) = s_0+v_0t+a\frac{t^2}{2}[/tex]
If the initial position is 10 m and the initial velocity is 10 m/s:
[tex]s(t) = 100+10+a\frac{t^2}{2}[/tex]
When comparing it with the given height equation, it is possible to obtain the acceleration as follows:
[tex]100+10+a\frac{t^2}{2} =100+10t-0.8t^2\\\frac{a}{2}=-0.8\\ a=-1.6\ m/s[/tex]
Acceleration is -1.6 m/s.
What is 75k industry into a percent?
Answer:
100%
Step-by-step explanation:
Amanda can word process 7 words in 6 seconds. At this rate, how many words can she word process in 3 minutes?
210
350
35
3.5
Answer:
He can process 210 words in 3 minutes
Angles PTQ and STR are vertical angles and congruent.
Which chords are congruent?
O QP and SR
O QR and PO
PR and RS
PR and PS
Answer: QP and SR on ed
Step-by-step explanation:
The chords in the circle that are congruent are PQ and SR.
CircleCircle is the locus of a point such that its distance from a fixed point known as the center is constant.
Given from the diagram that:
∠PTQ = ∠STR (Vertical opposite angles are congruent)
Hence:
PQ = SR
The chords in the circle that are congruent are PQ and SR.
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the diameter of a clock’s face is 6 inches. find the length of the minor arc formed my the hands of the clock at 4:00.
please help!
Answer:
4:30
:'?<>>{}_-(*>>>....,,::"{}}||\
15 POINTS PLZ HELP
It’s all in pic
Answer:
D
Step-by-step explanation:
it's In the picture
please like and Mark as brainliest
Answer:
Volume of the cylinder = D) 113.04 cubic cm
Step-by-step explanation:
[tex] \boxed{ \bold{formula = \pi \: {r}^{2} \: h }}[/tex]
= 3.14 × 2 × 2 × 9
= 3.14 × 36
= 113.04 cm³
A 3 cm * 3 cm rectangle sits inside a circle with radius of 4 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
44.24
Step-by-step explanation:
Khan academy
Answer:
Step-by-step explanation:
An oil storage tank is a cylinder with a height of 50 feet and a diameter of 20 feet.What is the volume of the tank?Use 3.14 for pi
Answer:
the anser is c
Step-by-step explanation:
just did the quiz and got 100 percent :)
Correct answer is C)
Step-by-step explanation:sorry this may not be helpful but the other answer is (A)
The label on Adriana's carton of juice has this information listed. One serving size equals 12 cup. Each serving has 30% of the recommended daily amount of vitamin C. Yesterday, Adriana drank 214cups of juice. What percent of the recommended daily amount of vitamin C was in the juice Adriana drank yesterday? 33.75% 67.5% 120% 135%
Answer:
135%
Step-by-step explanation:
we know that
One serving size equals 1/2 cup. Each serving has 30% of the recommended daily amount of vitamin C.
step 1
Using proportion
Find out the number of servings if Adriana drank 2 1/4 cups of juice
so
[tex]\frac{1}{\frac{1}{2}}=\frac{x}{2\frac{1}{4}}[/tex]
Convert mixed number to an improper fraction
[tex]2\frac{1}{4}=2+\frac{1}{4}=\frac{9}{4}[/tex]
substitute in the proportion
[tex]\frac{1}{\frac{1}{2}}=\frac{x}{\frac{9}{4}}\\\\x=\frac{(9/4)}{(1/2)}\\\\x=4.5\ servings[/tex]
step 2
we know that
Each serving has 30% of the recommended daily amount of vitamin C.
so
Multiply the number of servings by 30%
[tex]4.5(30\%)=135\%[/tex]
Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.
What do the x-intercepts represent in this real life situation in regards to the height of the soccer ball at that time?
What is the length of PR?
Answer:
[tex]8\sqrt{3}[/tex]
Step-by-step explanation:
2/3 pi radians = 2/3 * 180 = 2 * 60 = 120 degrees
split triangle in half:
30, 60, 90 triangle
1/2 PR= 4 root 3
Solve the equation.
- 2c + 6 = -8
Answer:
7
Step-by-step explanation:
We need to isolate the variable:
-2c + 6 = -8
-2c + 6 - 6 = -8 - 6
-2c = -14
-2c/-2 = -14/-2
c = 7
Thus, c = 7.
Hope this helps!
Method:
-2c+6=-8
-6 -6
-2c=-14
/-2 /-2
Answer:c=7
Please help me with the Square Root problems, Part 4. Please Show and Check the work.
[tex]13. x + 2 = 4\sqrt{x-2} \\\\14. \sqrt{2x-1} +\sqrt{3x-12} = 0\\\\15. x = 2\sqrt{x-4} + 4\\\\16. x-2= \sqrt{9x-36}[/tex]
Answers and Step-by-step explanations
13. Square both sides: x^2 + 4x + 4 = 16(x - 2) = 16x - 32
Move all the terms to one side: x^2 - 12x + 36 = 0
Factorize: (x - 6)^2 = 0 ⇒ x = 6
14. Move one of the roots to one side: [tex]-\sqrt{2x-1} =\sqrt{3x-12}[/tex]
Square both sides: 2x - 1 = 3x - 12
Solve for x: x = 11
15. Subtract 4 from both sides: x - 4 = [tex]2\sqrt{x-4}[/tex]
Square both sides: x^2 - 8x + 16 = 4(x - 4) = 4x - 16
Move all the terms to one side: x^2 - 12x + 32 = 0
Factorize: (x - 4)(x - 8) = 0 ⇒ x = 4 or x = 8
16. Square both sides: x^2 - 4x + 4 = 9x - 36
Move all the terms to one side: x^2 - 13x + 40 = 0
Factorize: (x - 5)(x - 8) = 0 ⇒ x = 5 or x = 8
Hope this helps!
Answer:
13. x = 6
14. No real solutions
15. x = 4, 8
16. x = 5, 8
Step-by-step explanation:
13. Square both sides
(x + 2)² = 4²(x - 2)
x² + 4x + 4 = 16x - 32
x² - 12x + 36 = 0
x² - 6x - 6x + 36 = 0
x(x - 6) - 6(x - 6) = 0
(x - 6)(x - 6) = 0
x = 6
14. sqrt(2x - 1) = -sqrt(3x - 12)
No real solutions because a positive square root can not be equal to a negative square root
15. x - 4 = 2sqrt(x - 4)
(x - 4)² = 4(x - 4)
(x - 4)² - 4(x - 4) = 0
(x - 4)(x - 4 - 4) = 0
(x - 4)(x - 8) = 0
x = 4, 8
16. x - 2 = sqrt(9x - 36)
(x - 2)² = (9x - 36)
x² - 4x + 4 - 9x + 36 = 0
x² - 13x + 40 = 0
x² - 5x - 8x + 40 = 0
x(x - 5) - 8(x - 5) = 0
(x - 8)(x - 5) = 0
x = 5, 8
what is the answer to the equation |n-6|+8=22
Answer:
n=20,−8
Step-by-step explanation: