the product of the first ten prime numbers must be divisible by...
E. 16
F. 18
G. 20
H. 22
Answers
Related Questions
Barbara and $400 one week she then spent $283 the next week she earned $120 the next week she had to pay a bill that cost $253 will she have enough to pay the bill can you represent how much money she will owe or have left after paying the bill as an integer select all that I apply
A. yes she will have enough to pay the bill
B. no she will not have enough to pay the bill
C. +16 which means she will have $16 left
D.+16 which means she will owe $16
Answers
Cheryl is creating a rectangular garden in her backyard. The length of the garden is 11 feet. The perimeter of the garden must be at least 36 feet and no more than 38 feet. Use a compound inequality to find the range of values for the width w of the garden.
Answers
Answer:
The range of values for the width is within 7 to 8 feet i.e 7 feet, 7.5 feet, 8 feet.
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2( L + W)
Perimeter = P ≥ 36 and P ≤ 38
hence, the perimeter is within the range of 36 and 38 feet ( i.e 36, 37, 38).
L = 11 feet
When Perimeter is 36 feet
36 = 2L + 2 W
36 = 2(11)+ 2 W
36 = 22 + 2W
36 - 22 = 2W
14 = 2W
W = 14/2
W = 7 feet
When Perimeter is 37 feet
37 = 2L + 2 W
37 = 2(11)+ 2 W
37 = 22 + 2W
37 - 22 = 2W
15 = 2W
W = 14/2
W = 7.5 feet
When Perimeter is 38 feet
38 = 2L + 2 W
38 = 2(11)+ 2 W
38 = 22 + 2W
38 - 22 = 2W
16 = 2W
W = 16/2
W = 8 feet
The range of values for the width is within 7 to 8 feet i.e 7 feet, 7.5 feet, 8 feet.
What is the minimum acceptable rate of 1 sigma of quality production? O a) 95.4 b) 99.7 c) 99.9 d) 68
Answers
The minimum acceptable rate of 1 sigma of quality production is d) 68.
This corresponds to a 68% acceptance level, which is equivalent to 1 standard deviation in a normal distribution.
A 1 sigma level corresponds to a standard deviation that captures approximately 68% of the data within a normal distribution. This means that if a process is operating at a 1 sigma level, it has a 68% acceptance rate, and the remaining 32% of the data falls outside the acceptable range
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What's the answer to this question
Answers
Step-by-step explanation:
there are several things to be considered to solve this.
the strategy is to caucuses the volume of the full "box", and then to deduct the 3-dimensional triangle that is "cut off" from the oil.
then we know the volume of the pool.
next step is to calculate the volume of a "box" with the same layout but is only 20 cm deep.
then we know how much volume can be pumped out in 30 minutes.
and then we divide the whole volume by that small volume to see how many 30-minues units are needed to empty the whole pool.
and then we transform the 30- minutes units into actual minutes or hours.
so, let's begin :
the whole box's volume is
2×1×1.4 = 2.8 m³
the volume of the 3-D triangle we need to subtract is the area of the triangle × width of the pool (this pool width is the height of the 3-D triangle).
2×(1.4 - 0.6) × 1 / 2 = 2×0.8 × 1 / 2 = 1.6/2 = 0.8 m³
so, the volume of the pool is
2.8 - 0.8 = 2 m³
now, how much volume can the pump eliminate in 30 minutes ?
the content of a box
1×2×0.2 = 0.4 m³
as 20 cm = 0.2 m
so, the pump pumps out 0.4 m³ in 30 minutes.
and we need to empty 2 m³.
that means we need
2 / 0.4 = 5
30-minues units = 5×30 = 150 minutes = 2.5 hours.
Colin has to wait 2.5 hours (150 minutes) to empty the complete pool.
MATH EXPERTS OUT THERE I NEED YOUR ASSITANCE!!!!PLEASE SHOW YOUR WORK ITS DUE RIGHT NOW!!!
1. The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
(c) Explain your answer to Part 1b.
.
.A line goes through the points, (8,9) and (-2,4).
What is the slope of the line? Show your work.
Write the equation of the line in point-slope form. Show your work.
Write the equation of the line in slope-intercept form. Show your work.
.
.
Line A is represented by the equation, y=1/4 x+5.
Write in slope-intercept form the equation of a line that is parallel to Line A and passes through the point, (8,-2). Show your work.
Write in slope-intercept form the equation of a line that is perpendicular to Line A and passes through the point, (4," 1"). Show your work.
Answer:
Answers
a) x = 25 tickets
y = 43.75 - Total cost
a = admission cost
b/c) 1.25(25)+a=43.75
31.25+a=43.75
43.75-31.25=12.50 cost of admission
12.50+31.25=43.75 total cost at the country fair.
(8,9) and (-2,4)
equation would be y = 1/2x+5
(do the work its a lot there can be videos found online)
nfadkjnbvjkn I'm busy i hope this helped
Determine whether the matrix is in row-echelon form. if it is, determine whether it is also in reduced row-echelon form. (select all that apply.) 2 0 0 0 0 1 1 6 0 0 0 0
Answers
The given matrix is in row-echelon form, but it is not in reduced row-echelon form. The given matrix is:
2 0 0 0
0 1 1 6
0 0 0 0
To determine if it is in row-echelon form, we need to check the following conditions:
1. All rows consisting entirely of zeros are at the bottom: In the given matrix, the third row consists entirely of zeros and is located at the bottom, so this condition is satisfied.
2. The first nonzero entry in each row, called a leading entry, is always strictly to the right of the leading entry in the row above it: In the given matrix, the leading entry in the second row is 1, which is to the right of the leading entry in the first row (which is 2). So this condition is satisfied.
3. Any rows of all zeros are at the bottom: Again, in the given matrix, the third row consists entirely of zeros and is located at the bottom, satisfying this condition.
Therefore, the given matrix is in row-echelon form.
To determine if it is also in reduced row-echelon form, we need to check one additional condition:
4. Each leading entry is 1, and each leading 1 is the only nonzero entry in its column: In the given matrix, the leading entries are 2 and 1, which are not equal to 1. Therefore, the matrix is not in reduced row-echelon form.
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A man left savings of 250000 to his wife 2 daughters 1 son find the value of shares
Answers
To find the value of each share, you need to divide the total savings left by the man by the total number of shares that are to be divided among his wife, two daughters, and one son. The value of each share will be the quotient of the division.
The total amount of savings left by the man is 250000.The total number of shares to be distributed is 4 (wife, two daughters, and one son).Therefore, the value of each share will be:Value of each share = Total savings left / Total number of shares. Value of each share = 250000 / 4Value of each share = 62,500.
In this question, we are given that a man left savings of 250000 to his wife, 2 daughters, and 1 son. We are required to find the value of shares distributed among them.To find the value of each share, we need to divide the total savings left by the man by the total number of shares that are to be divided among his wife, two daughters, and one son.Let's calculate the total number of shares to be distributed. As there are four members who will receive the shares, so the total number of shares will be 4. Now, let's substitute the values in the formula to get the value of each share.Value of each share = Total savings left / Total number of sharesValue of each share = 250000 / 4Value of each share = 62,500.The value of each share will be 62,500. Therefore, each of the man's wife, two daughters, and one son will get a share of 62,500 from the total savings left by the man.
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Lydia was out at a restaurant for dinner when the bill came. Her dinner came to $30. After adding in a tip, before tax, she paid $34.50. Find the percent tip.
Answers
Answer:
is 16.75
Step-by-step explanation:
Answer:
15%
Step-by-step explanation:
The Malelane gate into the Kruger National Park is 392km away from the nut farm. The Toyota Fortuner that was rented uses 7.9l of diesel for every 100km.
2.1.1) How many litres of fuel will the car use to get to the gate? round off to the nearest whole number.
2.1.2) The journey took 5 hours and 14 minutes. Calculate the average speed in km/h.
Answers
Fuel used = 392 km * 7.9 liters/100 km = 31.068 liters, average speed = 74.4 km/h.
What do you mean by Speed?It is defined as the distance traveled by an object in a certain amount of time. The unit of speed is usually meters per second (m/s) or kilometers per hour (km/h). Speed is a fundamental concept in physics, as it is a measure of the motion of objects. It is also an important concept in engineering, transportation, and many other fields. The speed of an object can be determined by dividing the distance traveled by the time taken to travel that distance. The magnitude of speed represents the rate of change of position, and the direction indicates the direction of the change.
To find the amount of fuel used to get to the gate, we need to multiply the distance traveled by the fuel consumption per kilometer.
1. Fuel used = 392 km * 7.9 liters/100 km = 31.068 liters. Rounding to the nearest whole number, the answer is 31 liters.
2. To find the average speed, we need to divide the distance traveled by the time taken.
Average speed = 392 km / (5 hours + 14 minutes/60) = 74.4 km/h.
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The harbor at Green Top Lake has a lot of green algae at the end of the summer. However, as the weather gets colder, the algae begins to die. At the beginning of the fall, the harbor has 150,000 square feet of algae. Half of the algae dies per month.
Answers
Answer:
Step-by-step explanation:
5)))
NEED HELP ASAP ! Questions are in the pic
Answers
Answer:
(2,1)
Step-by-step explanation
4x+5y=7
y=3x+9
4x+5(3x+9)=7 4x+5y=7
4x+15x+45=7 4(2)+5y=7
19x+45=7 8+5y=7
-7 -7 -7 -7
19x = 38 5y=1
19 19 5 5
x=2 y= 1.1
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Write the equation of the ellipse in standard form that has vertices (3, 2) and (3, -6) and endpoints of the minor axis (0, -2) and (6, -2). Show all work.
Answers
The parts of the ellipse are:
In this case, we have:
• Vertices,: (3, 2) and (3, -6) → the vertices lie over the vertical line x = 3 → , the ellipse has the form of the ellipse at the ,right, in the graph,,
,• Endpoints of minor axis,: (0, -2) and (6, -2).
In this case, the general equation of the ellipse is:
\(\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1.\)Where:
• (h, k) are the coordinates of the center of the ellipse,
,• a and b are the legs.
From the graph at the right, we see that the equations for:
• the vertex are:
\(\begin{cases}\mleft(h,k+a\mright)=\mleft(3,2\mright), \\ (h,k-a)=(3,-6)\text{.}\end{cases}\)We see that h = 3. Summing the equations and solving for k and a, we get:
\(\begin{gathered} k+a=2,k-a=-6, \\ 2k=2-6=-4\Rightarrow k=-2, \\ -2+a=2\Rightarrow a=4. \end{gathered}\)So we have a = 4 and k = -2.
• the endpoints of the minor axis are:
\(\begin{gathered} (h+b,k)=(0,-2), \\ (h-b,k)=(-6,-2)\text{.} \end{gathered}\)Solving for b and replacing the value h = -3, we get:
\(h+b=0\Rightarrow b=-h\Rightarrow b=-(-3)=3.\)So we have b = 3.
The four parameters of the ellipse are:
• (h, k) = (3, -2),
,• a = 4
,• b = 3.
Replacing these values in the general equation of the ellipse, we get:
\(\begin{gathered} \frac{(x-3)^2}{3^2}+\frac{(y+2)^2}{4^2}=1, \\ \frac{(x-3)^2}{9^{}}+\frac{(y+2)^2}{16^{}}=1. \end{gathered}\)Answer
\(\frac{(x-3)^2}{9^{}}+\frac{(y+2)^2}{16^{}}=1\)
HELLLLPPPP?!!ASAP
Coordinates are (-4,-6) (9,7)
Answers
The coordinate of point 3 / 10 away from A in the direction of AB is (6, 4).
What is section formula?Section formula is used in Coordinate geometry to find the ratio between two points on a line given one another point on the line.
Given that,
AB is a line segment.
The coordinate of A is (-4, -6) and that of B is (9, 7).
The distance of the point C 3 / 10 from A is 7 / 10 from B.
Suppose the point is C and its coordinate is (x, y).
Thus, the point c divides AB in the ratio AC : CB = 3 : 10.
Now, use section formula to get the coordinate of the given point as,
x = (mx₁ + nx₂) / (m + n) and y = (my₁ + ny₂) / (m + n)
Substitute the respective values to get the coordinates of C as,
x = (3 × -4 + 10 × 9) / (3 + 10) and y = (3 × -6 + 10 × 7) / (3 + 10)
⇒ x = 6 and y = 4
Hence, the coordinate of the given point is (6, 4).
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During the first week of her vacation, Madison practices playing her flute 5.75 hours. In the following week, she spends 4.2 hours practicing the flute. What is the difference in the amount of time she spends practicing the flute during these weeks?
Answers
Answer:
1.55 hours
Step-by-step explanation:
5.74-4.20=1.55
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anyone know how to do #14 and #15?????
Answers
Answer:
He Melanie , use SOH CAH TOA to remember the trig functions
Step-by-step explanation:
for 14 they hyp = 22 and we know one angle of 45°, we also know that the triangle has a right angle or 90° and by inspection we can tell that the other angle is also going to be 45° so we know X and Y will be the same length, is why this is a good observation.
Use one of the trig functions with H in it b/c you know Hyp is 22, so,
SOH = Sin(Θ)= Opp / Hyp
Sin(45) = Opp / 22
Sin(45) * 22 = Opp
\(\sqrt{2}\) / 2 * 22 = opp
11*\(\sqrt{2}\) = opp is the exact answer, if you would like some decimal places, it's 7.7781 units, both X and Y
for 15 we can use SOH again for the bigger triangle. we know the Hyp is 24 and the angle is 30°
Sin(30) = Opp / 24
Sin(30) *24 = Opp
12 = Opp ( Because I know Sin(30) = 1/2 )
Opp is the upright between the two triangles
Use CAH Cos(Θ) = Adj / Hyp
Cos(30) = Adj / 24
Cos(30) * 24 = Adj
\(\sqrt{3}\) /2 *24 =Adj
12\(\sqrt{3}\) = Adj
Z = 12\(\sqrt{3}\) or if you want some decimals 20.7846
Becasue the smaller triangle is also a 45° right triangle we know that the upright and side Y are the same lengths
then
Y = 12
You could use SOH or CAH to find the Hyp but, lets just resort to Pythagoras, and use his formula to find Hyp
Hyp = \(\sqrt{12^{2} +12^{2} }\)
Hyp = \(\sqrt{288}\)
hyp = 16.97
X = 16.97
:)
Which phase of inferential statistics is sometimes considered to be the most crucial because errors in this phase are the most difficult to correct?
Answers
The phase of inferential statistics which is sometimes considered to be the most crucial because errors in this phase are the most difficult to correct is "data gathering".
What is inferential statistics?Inferential statistics are frequently employed to compare treatment group differences.
Some characteristics of inferential statistics are-
Inferential statistics compare treatments groups and make conclusions about the greater population of participants using measures from the experiment's sample of subjects.Inferential statistics aids in the development of explanations for a condition or phenomenon. It enables you to draw conclusions on extrapolations, which distinguishes it from descriptive statistics, which simply summarize the information that has been measured.There are numerous varieties of inferential statistics, each with its own set of research design & sample characteristics. To select the correct statistical test of their experiment, researchers should reference the numerous texts about experimental design and statistics.To know more about the inferential statistics, here
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Natalie i working two ummer job, making $11 per hour babyitting and $10 per hour landcaping. Lat week Natalie earned a total of $86 and worked 3 time a many hour babyitting a he worked hour landcaping. Determine the number of hour Natalie worked babyitting lat week and the number of hour he worked landcaping lat week
Answers
The number of hours Natalie worked babysitting last week is 6hrs and the number of hours she worked landscaping last week is 2 hrs.
Let x be the number of hours Natalie worked babysitting and y be the number of hours she worked landscaping. Then, the total earnings were 11x + 10y = $86.
Also, x = 3y, because she worked 3 times as many hours babysitting as she did landscaping.
Substitute x = 3y into the first equation:
11(3y) + 10y = $86
Expanding the first term we get,
33y + 10y = $86
Combining terms,
43y = $86
Dividing both sides by 43 we get,
y = $2
So, Natalie worked y = 2 hours of landscaping.
To find the number of hours she worked babysitting, substitute y = 2 into x = 3y as follows -
x = 3(2) = 6
So Natalie worked x = 6 hours babysitting.
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How much do you need to subtract from 43/10 to make 4?
Answers
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\( \frac{43}{10} - x = 4 \\ \)
\( \frac{43}{10} - x = \frac{40}{10} \\ \)
Subtract sides 43 / 10
\( - \frac{43}{10} + \frac{43}{10} - x = - \frac{43}{10} + \frac{40}{10} \\ \)
\( - x = \frac{ - 43 + 40}{10} \\ \)
\( - x = - \frac{3}{10} \\ \)
Negatives simplifies
\(x = \frac{3}{10} \\ \)
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Thus we need to subtract
\( \frac{3}{10} \\ \)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
83/10
Step-by-step explanation:
let x represent the number:
43/10 - x = 4
x = 4 + 43/10
simplifying the answer:
x = (4(10) + 43)/10
x = (40 + 43)/10
x = 83/10
Which numbers are solutions to the inequality 2x – 1 > x + 2? Check all of the boxes that apply
Answers
Answer:
x>3
Step-by-step explanation:
2x – 1 > x + 2
2x-x-1>2
x-1 >2
x>3
Answer:
4,5
Step-by-step explanation:
Please help, having a lot of trouble with this
Answers
Answer:
d. -1
Step-by-step explanation:
the slope is the rise over the run from one point to another.
i hope this helps :)
Each line is 1 unit.
Use the dots A and B
A is located at (-3,3)
B is located at (3,-3)
Slope is the change in y over the change in x
Slope = (-3 -3) / (3 - -3)
Slope = -6/6
Slope = -1
The answer is D -1
Assume that a professor gives an exam to a class of 50 students. The high score is 98 points and the low score is 48 points. The professor wants to create a frequency distribution that is divided into five classes for the exam scores. The class width for the data is approximately _____________ points.
Answers
Answer:
98-48=50 so the answer is 50
Which of the following would be classified as categoricalâdata?
Choose the correct answer below.
Hair color
Number of suitcases on a plane
Tree height
Amount of rainfall
Answers
Categorical data is data that can be divided into different categories. Examples of categorical data include hair color, number of suitcases on a plane, tree height, and amount of rainfall.
Hair color would be classified as categorical data because it can be divided into categories such as black, brown, blonde, and red. Number of suitcases on a plane would also be classified as categorical data because the amount of suitcases can be divided into categories such as 0, 1, 2, 3, etc. Tree height would be classified as categorical data as it can be divided into categories such as small, medium, and large. Amount of rainfall would also be classified as categorical data as it can be divided into categories such as light rainfall, moderate rainfall, and heavy rainfall.
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Six cousins inherited a total of 5/8 of their great aunt’s assets, which they divided evenly. What fraction of their great aunt’s assets did each cousin inherit?
Answers
============================================
Work Shown:
We'll divide the total 5/8 evenly among the 6 cousins.
(5/8) ÷ 6 = (5/8) ÷ (6/1)
(5/8) ÷ 6 = (5/8) * (1/6)
(5/8) ÷ 6 = (5*1)/(8*6)
(5/8) ÷ 6 = 5/48
Each cousin gets 5/48 of the aunt's assets.
So for instance, if the aunt had $48,000 in assets, then each cousin gets (5/48)*(48,000) = 5000 dollars.
------------------
An alternative approach:
Draw 6 rectangles side by side that represent the 6 cousins. Then divide each rectangle into 8 pieces, with 5 pieces shaded. The yellow pieces represent the amount given to the cousins. For any given rectangle, 5/8 of it is shaded yellow. Refer to the diagram below.
Overall we have 6*8 = 48 pieces.
The first cousin gets 5 yellow pieces out of 48 total. The same applies to the other five cousins. So this is a visual way to arrive at the answer 5/48.
put you answers in correct form
f-3/7=2/3
Answers
Answer:
f=23/21
Step-by-step explanation:
Answer:
f=23/21
Step-by-step explanation:
The fundamental question addressed by the correlational method is
a. "Does variable A cause variable B?"
b. "How is a control group influenced by the absence of an independent variable?"
c. "What impact does random assignment have on psychological behavior?"
d. "Are two or more variables related in some systematic way?"
Answers
The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.
Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.
For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.
It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.
Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.
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Linda made $228 for 12 hours of work. At the same rate, how many hours would she have to work to make $133?
Answers
Step-by-step explanation:
228 ÷12 =19
So 19 dollars per hour
Now 133÷19= 7 hours
t/f if f '(x) = g'(x) for 0 < x < 6, then f(x) = g(x) for 0 < x < 6.
Answers
The statement "if f'(x) = g'(x) for 0 < x < 6, then f(x) = g(x) for 0 < x < 6" is false. This statement is False. If f'(x) = g'(x) for 0 < x < 6, it means that the derivatives of both functions are equal on the interval (0, 6).
However, this does not necessarily mean that the functions themselves are equal on that interval.
In other words, there could be a constant difference between f(x) and g(x), which would not affect their derivatives.
To illustrate this, consider the functions f(x) = x^2 and g(x) = x^2 + 1. The derivative of both functions is 2x, which is equal for all values of x.
However, f(x) and g(x) are not equal on the interval (0, 6), as g(x) is always greater than f(x) by 1.
Therefore, the statement "if f'(x) = g'(x) for 0 < x < 6, then f(x) = g(x) for 0 < x < 6" is false.
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Aschool playground is rectangular and has a length of50 m and
a width of 30 m as shown. A safety eone of uniform width surrounds
the playground. lfthe area ofthe safety zone equals the area ofthe
playground, what is the width of the safety zone, to 2 decimal places?
Answers
The most appropriate choice for quadratic equation will be given by
Width of safety zone is 7.84 m
What is equation and Quadratic equation?
A statement that shows the equality between two mathematical expressions by connecting the two mathematical expression with an equal to (=) sign is called equation.
A two degree equation is known as quadratic equation.
Let \(ax^2+bx +c\) be a quadratic equation (a ≠ 0)
Then
\(x = \frac{-b \pm \sqrt{b^2 -4 \times a \times c}}{2\times a}\)
Here,
Let the width of the safety zone be x metre
Length of rectangular park = 50m
Breadth of rectangular park = 30m
Area of rectangular park = \(50 \times 30\)
= \(1500\) \(m^2\)
Length of rectangular park with safety zone = (x + x + 50) m
= (2x + 50) m
Breadth of rectangular park with safety zone = (x + x + 50) m
= (2x + 30) m
Area of rectangular park with safety zone = (2x + 50)(2x + 30) \(m^2\)
= \(4x^2 +60x + 100x + 1500\)
= \((4x^2 + 160x +1500) m^2\)
Area of safety zone = \(4x^2 +160x+1500-1500\)
= \(4x^2 +160x\)
By the problem,
\(4x^2 +160x=1500\)
\(4x^2 +160x-1500=0\)
\(4(x^2 +40x-375)=0\)
\((x^2 +40x-375)=0\)
\(x = \frac{-40 \pm \sqrt{40^2 -4 \times 1 \times (-375)}}{2\times 1}\)
\(x = \frac{-40 \pm \sqrt{1600 +1500}}{2\times 1}\)
\(x = \frac{-40 \pm \sqrt{3100}}{2}\)
\(x = \frac{-40 \pm 55.68}{2}\)
\(x = \frac{-40 + 55.68}{2}\) or \(x = \frac{-40 - 55.68}{2}\)
\(x =7.84\) or \(x = -47.84\)
\(x = -47.84\) is not possible as width cannot be negative
so \(x = 7.84\) m
Width of safety zone is 7.84 m
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8=4(q-2)+4
Please help
Answers
Answer:q=3
Step-by-step explanation:
Answer:
so, q=3
Step-by-step explanation:
8=4 (q-2)+4
8=4q-8+4
collect like terms
8=4q-4
8+4=4q
12=4q
divide by 4 both sides
12/4=4q/4
3=q
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A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is ___. a. 0.450 b. 0.9505 c. 0.0495 d. 0
Answers
The probability that the sample mean will be greater than 57.95 is 0.0495.
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.
To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.
Normal probability distributionProblems of normally distributed samples can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z=\dfrac{X-\mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit TheoremThe Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).
In this problem, we have that:
\(\mu=53,\sigma=21,\text{n}=49,\text{s}=\frac{21}{\sqrt{49} }=3\)The probability that the sample mean will be greater than 57.95
This is 1 subtracted by the p-value of Z when X = 57.95. So
\(Z=\dfrac{X-\mu}{\sigma}\)
By the Central Limit Theorem
\(Z=\dfrac{X-\mu}{\text{s}}\)
\(Z=\dfrac{57.95-53}{3}\)
\(Z=1.65\)
\(Z=1.65\) has a p-value of 0.9505.
Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495
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