A: (a) The 98% confidence interval would be wider than the 95% interval. As the confidence level increases, the margin of error increases, thus making the interval wider.
(b) The width of the confidence interval would decrease as the sample size increases. This is because a larger sample size will result in a more accurate representation of the population, thus allowing for a narrower confidence interval.
(c) The manufacturer cannot adjust the confidence interval to take this nonresponse into account, as the nonresponse does not affect the accuracy of the sample. The confidence interval is based on the sample itself and not the population from which it was drawn.
What is mean by random sample?Random sampling is a method of selecting a sample of individuals from a population such that each member of the population has an equal chance of being selected.
Random sampling is often used in research studies to ensure that the sample is representative of the population as a whole.
Random sampling is also used to minimize bias and ensure that the sample is not influenced by any particular group or individual.
Random sampling is important because it helps ensure that the results of the study are accurate and valid.
Random sampling helps to ensure that the sample is representative of the population and that the results are not influenced by any particular group or individual.
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Jacob has 6. 15 meters of rope. He is going to use 1. 2 meters of rope to tie up his boat. How many centimeters of rope does he have left?
The remaining rope he left is 495cm
Now, According to the question:
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Jacob has 6. 15 meters of rope.
He is going to use 1. 2 meters of rope to tie up his boat.
When you do the subtraction, whatever is left (the decimal part) is the length in cm when multiplied by 100.
Remaining rope = starting length - what was used.
Remaining rope = 6.15 - 1.2
Remaining rope = 4.95 meters
Hence, The remaining rope he left = 4.95 × 100 = 495 cm
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The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number, the number of bacteria in the culture after 8 hours. The exponential function is b(t)=. After 8 hours, there are about bacteria in the culture
If the growth rate of bacterial culture is 150% each hour , then the correct exponential function is b(t) = 10(2.5)^t instead of b(t) = 10(1.5)^t , and after 8 hours there are about 15259 bacteria in culture .
The percent growth in the bacterial culture is = 150% = 1.5 ;
the initial amount of bacteria present is = 10 ;
the exponential function used to denote this situation is written as :
⇒ b(t) = 10(1 + 1.5)^t
⇒ b(t) = 10(2.5)^t
to find number of bacteria after 8 hours ,
we substitute t = 8 in b(t) ;
we get ;
⇒ b(8) = 10(2.5)⁸ ;
⇒ b(8) = 15258.789 ≈ 15259
Therefore , there will be 15259 bacteria present after 8 hours .
The given question is incomplete , the complete question is
The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in the data below, in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number,
"The number of bacteria in the culture after 8 hours. The exponential function is b(t) = 10(1.5)^t , b(8) = 10(1.5)⁸ . After 8 hours, there are about 256 bacteria in the culture ."
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The function f(x) is shown on the graph.
f(x)
O Logarithmic
B 7
O Polynomial
654
-10-9-8-7-6-5-4-3-2-10
3
2
-1
-2
-3
47999
-7
-10
Which type of function describes f(x)?
O Exponential
X
2 3 4 5 6 7 8 9 10
An exponential function is represented by taking into account the fact that the graph has an asymptote and does not cross it.
What is exponential function?A function with the formula f(x)=ax is an exponential function. Here, x is the input and an is a positive, real integer (referred to as the base) (independent variable). The independent variable is always in the exponent for exponential functions, which is important to keep in mind.
It is based on:
where a represents the y-intercept.
The rate of change is b.
The asymptote, which the function does not cross, is y = c.
Consequently, the graph in this issue models an exponential function with an asymptote at y = 0.
An exponential function is represented by taking into account the fact that the graph has an asymptote and does not cross it.
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Which of the following graphs represents the function g(x) = 3∛x – 1?
A graph which represent the function g(x) = 3∛x – 1 is: graph A.
How to graph the given function?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis and y-axis respectively.
Based on the information about this graph, it represents the following function:
Function, g(x) = 3∛x – 1
By rewriting the cube root in the above function, we have the following:
Function, g(x) = 3∛x – 1
Function, g(x) = 3(x^{1/3}) – 1.
Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
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Need Help ASAP!!!! 15 POINTS
Using Quadratic formula, the roots of the equation are -11 + √217/6, -11 - √217/6 .
Equations involving quadratics The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0.
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).
Using Quadratic formula,
3x² + 11x - 8
(-b±√(b²-4ac))/(2a)
⇒ (-11 ± √11² - 4(3)(-8)/2(3))
⇒ -11 ± √217 / 6
⇒ -11 + √217/6, -11 - √217/6
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Find the mean, median, mode, and range for each data set given.
a. 7, 12, 1, 7, 6, 5, 11
b. 85, 105, 95, 90, 115
c.15, 11, 11, 16, 16, 9
Answer:
Answers are in bold
Data set A:
Mean: 7
Median: 7
Mode: 7
Range: 11
Data set B:
Mean: 78
Median: 95
Mode: No mode or all the numbers (85, 105, 95, 90, 115)
Range: 30
Data set C:
Mean: 13
Median: 13
Mode: 11 and 16
Range: 7
Step-by-step explanation:
You're welcome.
Please help will give brainliest
Write a letter to a student who will be taking this math class next year and give them some advice about this class
A letter to a student who will be taking this math class next year to give them some advice about this class has been written below.
(Sender's address)
20/01/2023
Dearest,
I was happy to see your letter, and I hope this letter finds you in the best of health. I have wanted to go on a trip with you for a long time but I guess that would happen later since you have to start attending classes soon.
I have a list of things to keep in mind when you start your classes. I was always too scared of mathematics, and I know you are too, but I have always wanted to tell you how fruitful it is to learn a subject that will help you in every field you want to go in. Let me know what you think about it after you finish reading this letter. I know it is no secret that maths is a difficult subject but you can master it if you keep what I am going to tell you in mind. Practice your concepts daily. Keep brushing up on whatever your teacher teaches you. Remember the formulas and you will know how to answer any question. I know for sure that it is going to be worth it too.
I will make sure that I meet you next weekend so that we can meet before you begin the classes. If you try hard, you can make this work. See you soon.
Love,
(Sender's name)
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What is the solution to StartFraction 5 over 6 EndFraction x minus one-third greater-than 1 and one-third?
x > StartFraction 25 over 18 EndFraction
x < StartFraction 25 over 18 EndFraction
x > 2
x < 2
The value of x is x > 2.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Any number can be expressed as fractions.
The given expression is [tex]\frac{5}{6}[/tex]x - [tex]\frac{1}{3}[/tex] > 1 [tex]\frac{1}{3}[/tex]
We have to rewrite the expression with x on one side.
[tex]\frac{5}{6}[/tex]x - [tex]\frac{1}{3}[/tex] > 1 [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > 1 [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > [tex]\frac{4}{3}[/tex] + [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > [tex]\frac{5}{3}[/tex]
x > [tex]\frac{5}{3}[/tex] × [tex]\frac{6}{5}[/tex]
x > 2
So the value of x is greater than 2.
Hence the correct option is x > 2.
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help me out pleaseeeeeeeeeeeeeeeeeee
Answer:
3 and 5
Step-by-step explanation:
One company estimates same-day delivery as more than three less than half the total number of miles which graph represents the overall equation represented by the scenario or points may not apply to the scenario note that the graphs have similar miles for the independent variable on the X axis and the Y axis is a unit of time dependent on the number of miles
A graph that represents the overall equation represented by this scenario is shown in the image attached below.
How to determine the graph?Based on the information provided about this company with respect to its same-day delivery and total number of miles to be covered, we would assign variables to the parameters as follows:
Let the variable x represent be the total number of miles.Let the variable y represent same-day delivery.Next, we would translate the word problem into an algebraic equation by using an inequality:
Half the total number of miles = x/2.
y > x/2 - 3
Furthermore, we would determine the x- and y-intercepts as follows:
When x = 0, we have;
y = 0/2 - 3
y = -3.
Therefore, y-intercept = (0, -3).
For the x-intercept (y = 0), we have:
0 = x/2 - 3
x/2 = 3
x = 6.
Therefore, x-intercept = (6, 0).
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The vertices of YEAR are Y(1,-4) E(3,0), A (-1,2) and R( -3,-2) . prove that YEAR is a Square
To prove that YEAR is a square, we need to show that all four sides have the same length and all four angles are right angles (90 degrees).
Side Lengths: To find the lengths of the sides, we can use the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
For example, to find the length of the side that connects Y and E, we can use the following calculation:
d = √((3 - 1)² + (0 - (-4))²) = √((2)² + (4)²) = √(4 + 16) = √20
We can use the same formula to calculate the lengths of the other sides. By doing so, we will find that the length of all four sides are the same, which is √20. This means that all four sides of YEAR are congruent, and therefore it is a square.
Assume that when adults with smartphones are randomly selected, 37% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 19 of them use their smartphones in meeting or classes the probability is (Round to four decimal places as needed.
The probability of adults using smartphones in meetings or classes as per the randomly selected adults is equal to 0.3375.
Percent of randomly selected adults use smartphones in meetings or classes represents the probability of success 'p' = 37%
= 0.37
1 - p = 1 - 0.37
= 0.63
Number of randomly selected adults use smartphone in meetings or classes represents sample size 'n' = 30
Exactly 19 adults use smartphone represented by x
x = 19
Using binomial distribution :
Required probability is :
P(x) = ⁿCₓ× pˣ × ( 1 - p )ⁿ⁻ˣ
⇒P(x) = [ n! / x! (n - x)! ] × pˣ × ( 1 - p )ⁿ⁻ˣ
Substitute the values
⇒P(19) = [ 30! / 19! (30 - 19)! ] × 0.37¹⁹× ( 0.63 )³⁰⁻¹⁹
⇒P(19) = ( 30!/19! ×11! ) × 0.37¹⁹× ( 0.63 )¹¹
⇒P(19 ) = 0.3375
Therefore, the required probability of selecting exactly 19 adults who use their smartphones in meetings or classes is equal to 0.3375.
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In the first week of July, a record 1,120 people went to the local swimming pool. In the second week, 110 fewer people went to the pool than in the first week. In the third week, 135 more people went to the pool than in the second week. In the fourth week, 137 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
If in the first week of July, a record 1,120 people went to the local swimming pool. the percent decrease in the number of people who went to the pool over these four weeks is 10%.
How to find the percentage decrease?First week:
Number of people went to the local swimming pool =1120
Second week:
Number of people went to the local swimming pool =1120-110
Number of people went to the local swimming pool =1010
Third week:
Number of people went to the local swimming pool =1010+135
Number of people went to the local swimming pool =1145
Fourth week:
Number of people went to the local swimming pool =1145-137
Number of people went to the local swimming pool =1008
Decrease in number of people over four week=1120 -1008
Decrease in number of people over four week = 112
Percentage decrease = 112 /1120 × 100
Percentage decrease = 10%
Therefore the percentage decrease is 10%.
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free bilirubin is transported by the blood to the liver. TRUE OR FALSE
True, free bilirubin is transported by the blood to the liver.
Macrophages begin the disposal of hemoglobin by separating the heme from the globin. They hydrolyze the globin into free amino acids, which can be used for energy-releasing catabolism or recycled for protein synthesis.
Bilirubin
Bilirubin is a red-orange compound that occurs in the normal catabolic pathway that breaks down heme in vertebrates. This catabolism is a necessary process in the body's clearance of waste products that arise from the destruction of aged or abnormal red blood cells.
Hemoglobin
Hemoglobin is a protein in your red blood cells that carries oxygen to your body's organs and tissues and transports carbon dioxide from your organs and tissues back to your lungs.
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Can someone help me please?
Answer:
Part A.) 153 Boxes
Part B.) 394 Boxes (395 if rounding up)
Step-by-step explanation:
The inequality used in this situation would be:
3.74x + 25 < 600
3.74 is the price of each box
x is the number of boxes
25 is that deposit
and < 600 is not making $600 in sales
What we need to do is get X alone. First we will subtract 25 from both sides since that's the opposite of +25.
Doing that will get you
3.74x = 575
Next step is to divide 3.74 on both sides since 3.74 is being multiplied by x and division is the opposite.
That will give you X = 153.74. We round down to stay under and we end up with 153.
For part B, we would do the same process, but instead of < 600, we would do >= 1500. Just typing the same steps out.
3.74x >= 1475 since we subtract 25 from both sides
x = 394.38 since we divide 3.74 on both sides. Rounding would get us 394
Tamisha works as an intern in an architect’s office. A designer drew a scale drawing of a kitchen without using grid paper. In the drawing, 1 inch represents 2 1/2 feet. Tamisha’s supervisor wants her to determine the skill factors for the length and the skill factors for the areas of.
a. Find the scales factor for the lengths
b. Find the scales factors for the areas
Answer:
length: 1:30, area: 1:900
Step-by-step explanation:
1ft = 12 inches, so 2.5' = 30". scale for length is 1:30, for area it's square - 1:900
The triangle below is equilateral. Find the length of side x to the nearest tenth.
x
12
Answer:
Step-by-step explanation:
I NEED HELP ON THIS ASAP!!!!
The volume of an ice cream cone is the measure of how much ice
cream fits inside the cone. An ice cream cone company wants to
make an ice cream cone with a greater height that still holds the
same amount of ice cream.
Write an equation to calculate the volume of a cone.
Then rewrite the equation to solve for the height.
Explain how your equation determines a linear measurement when the original equation determined a cubic measurement
The volume of a cone is V = πr²h/3
The equation rewritten to solve for the height is V = πr²h/3
How to determine the equationIt is important to note that the formula for volume of a cone is expressed as;
V = πr²h/3
The parameters are;
V is the volume of the coneπ takes the constant value, 22/7 or 3. 142h is the height of the coneSince the ice cream fits inside the cone and the height still holds the ice cream, let's make the height subject of formula.
Let's take the following steps;
V = πr²h/3
cross multiply the equation, we get;
V × 3 = πr²h × 1
Multiply the values
3V = πr²h
To make the variable 'h' stand alone, let's divide both sides of the equation by its coefficient
3V/πr² = πr²h/πr²
Divide the values
c
Hence, the equation determines a linear measurement since the value 3 multiply the volume and not divides it.
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Week 23-Practice 19: Surface Area (PA.GM.2.1 & PA.GM.2
A cylinder has a surface area of 48 cm² and a radius of 2 cm. What is the height of the cylinder?
O 8 cm
O 10 cm
O 12 cm
O 14 cm
The lateral surface area of the cylinder is 51.22 cm2.
What is surface area?
Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.
The cylinder shown below has a diameter of 5.2 cm on the base and a height of 7.1 cm. The diameter of the base is referred to as 'd' and the height of the cylinder is referred to as 'h'. The lateral surface area of the cylinder can be found by using the formula LSA = 2πrh, where 'r' is the radius of the base. The radius of the base of this cylinder is half of the diameter, or 2.6 cm. Therefore, the lateral surface area of the cylinder is: 2π x 2.6 x 7.1 = 51.22 cm2.
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What are the domain and range of f (x) = -5/6 (x + 2)^2 - 8?
Answer:
Option B
Domain: all real numbers
Range [tex]f(x) \le -8[/tex]
Step-by-step explanation:
Given function is:
[tex]f\left(x\right)=-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]
The domain is the set of all x values that result in a real and defined value for f(x).
The function has no undefined points and x is free to range from -∞ to +∞
So the domain is -∞ < x <∞ which is
All real numbers
The range is the set of all possible values for f(x) given a specific domain. In order to determine the range without too much hard work, let's first examine the function f(x)
The above function is the equation for a parabola.
Some things to note about a parabola equation:
The vertex form equation of a parabola is:Let us compare the general vertex form equation of the parabola with the specific f(x) equation given
General Equation: [tex]a (x - h)^2 + k[/tex]
This example: [tex]-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]
Comparing the similarity between the two equations we easily see that
[tex]\boxed{a = -\dfrac{5}{6}}[/tex]
This means the parabola opens downward and (h, k) represents a max point in the parabola
[tex]x - h = x + 2\\\\-h = 2\\\\h = -2\\[/tex]
[tex]k = -8[/tex]
So the vertex is at (-2, -8)
Since -8 is the maximum value for f(x), and the parabola extends to infinity on both sides, the range is :
[tex]\boxed{f(x) \le -8}[/tex]
The attached graph may help you understand better
The supermarket has 20 aisles. 10 of the aisles are empty. What percentage of the aisles are empty?
The percentage of the aisles that are empty, given the number of aisles in total in the supermarket, is 50 %
How to find the percentage of aisles ?To find the percentage of the aisles that are empty, you can use the formula :
= Number of aisles that are empty / Number of total aisles in the supermarket x 100 %
Number of aisles that are empty = 10 aisles
Number of total aisles in the supermarket = 20 aisles
The percentage of aisles empty is:
= 10 / 20 x 100 %
= 0. 5 x 100 %
= 50 %
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Evaluate the expression for the given value of the variables.
0.5c−2.3d
c=15, d=3
DUE IN 20 MIN
Answer:
I got 0.6
Step-by-step explanation:
plug in c and d
0.5(15) - 2.3(3)
multiply them
7.5 - 6.9 = 0.6
An airplane takes off from the airport. After 2 minutes the plane is at 500 ft. Assume the plane continues at the same rate. The plane’s height and minutes above the ground are related to each other.
A. Write an equation for the situation.
An equation for the situation described above is h = 2m + 500.
How to write an equation to model this situation?In order to write an algebraic equation that model this situation, we would assign a variable to the number of minutes after an airplane takes off from the airport and the plane’s height respectively, and then translate the word problem into algebraic equation as follows:
Let the variable m represent the number of minutes.Let the variable h represent the plane’s height.Next, we would translate the word problem into an algebraic equation based on the fact that after 2 minutes the plane is at 500 feet as follows;
h = 2m + 500.
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if 12% of a number is 75, find 4% of that number
Answer:
25.60
Step-by-step explanation:
first divide 12%of a number with 75 Ans will be 6.25 then multiply with 4 Ans will be 25.60
Answer: 25
Step-by-step explanation:
12 divided by 4 = 3
75 divided by 3 = 25
25 = 4%
Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 per job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.
30 + 15 x greater-than-or-equal-to 90
Which best describes the restrictions on the jobs Deepak will accept?
Answer:
He only accepts jobs that last 4 or more hours.
Step-by-step explanation:
He only accepts jobs that last 4 or more hours.
He only accepts jobs that last 5 or more hours.
He only accepts jobs that last 8 or more hours.
He only accepts jobs that last 9 or more hours.
30 + 15x ≥ 90
15x ≥ 60
x ≥ 4
Answer: He only accepts jobs that last 4 or more hours.
what is the axis of symmetry of this graph?
Answer:
The axis of symmetry is x = -3.
If you draw a line at x = -3, the graph is reflected over it.
6x−10y=-40 in slope intercept form
PLEASE HURRY I HAVE LIMITED TIME!
Question- Find the standard form equation of a circle given a center of (7, 14) and a point on the circle of (4, 15).
Answers-
A.(x-7)^2 + ( y-14)^2 = 10
B.(x-7)^2 + (y-14)^2 = 15
C.(x-7)^2 + (y-14)^2 = 25
D.(x+7)^2 + (y+14)^2 = 2
Answer:
A
Step-by-step explanation:
R = sqrt((7-4)^2+(14-15)^2)=sqrt(10)
The answer is A since that's the only answer with the proper radius, using the formula for a circle.
a factory (f) is producing smoke that causes damage of $80 per month to a local residents laundry (l). the damage can be eliminated in one of two ways:
The following two methods can be used for eliminating the damage to the laundry (l).
Factory (f) can install a scrubber at a cost of $500 to reduce the smoke, thereby eliminating the damage to the laundry (l).Local resident (l) can purchase and install a clothesline at a cost of $100, thereby eliminating the damage to their laundry.The factory and the local resident must decide whether to install the scrubber or the clothesline, depending on which option will result in the lowest cost. The best option for each party depends on their own willingness to pay for the damage reduction and their ability to pay for the solution.
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Solve pleaaase i really need help
The equation of the model is (b) 2x = 5
How to determine the equation of the model?From the question, we have the following parameters that can be used in our computation:
Left = x x
Right hand side = 1 1 1 1 1
The above parameters mean that
Left = 2x
Right = 5
When represented as an equation, we have
2x = 5
Hence, the equation is (b)
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