Approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.
To find the percentage of times that are more than 91 seconds and more than 63 seconds, we can use the properties of a normal distribution and the standard normal distribution table (also known as the z-table).
Given:
Mean (μ) = 84 seconds
Standard deviation (σ) = 7 seconds
1. Probability of times more than 91 seconds:
First, we need to find the z-score for the value 91 seconds:
[tex]\(z = \frac{X - \mu}{\sigma} = \frac{91 - 84}{7} = \frac{7}{7} = 1\)[/tex]
Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = 1\)[/tex]. The z-table provides the percentage of values below a given z-score, so we need to find the complement (1 - percentage) to get the percentage of values above [tex]\(z = 1\).[/tex]
From the z-table, the area to the right of [tex]\(z = 1\)[/tex] is approximately 0.1587.
So, the percentage of times more than 91 seconds is [tex]\(1 - 0.1587 = 0.8413\)[/tex] or 84.13%.
2. Probability of times more than 63 seconds:
Similarly, we need to find the z-score for the value 63 seconds:
[tex]\(z = \frac{X - \mu}{\sigma} = \frac{63 - 84}{7} = \frac{-21}{7} = -3\)[/tex]
Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = -3\)[/tex]. Again, we need to find the complement to get the percentage of values above [tex]\(z = -3\).[/tex]
From the z-table, the area to the right of [tex]\(z = -3\)[/tex] is approximately 0.9987.
So, the percentage of times more than 63 seconds is [tex]\(1 - 0.9987 = 0.0013\)[/tex] or 0.13%.
Therefore, approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.
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Jill Hartman earns $750 per week plus 3% of sales in excess of $6,500. If Jill sells $25,000 in the first week, her earnings are:
The earnings of Jill Hartman for the week is A = $1,305
Given data ,
To calculate Jill's earnings for the first week, we need to determine the amount of sales in excess of $6,500 and then calculate her additional earnings based on that amount.
Sales in excess of $6,500 = Total sales - $6,500 = $25,000 - $6,500 = $18,500
Now we can calculate Jill's additional earnings based on the sales in excess of $6,500:
Additional earnings = 3% of sales in excess of $6,500 = 0.03 * $18,500
Additional earnings = $555
Finally, we can calculate Jill's total earnings for the first week by adding her base salary to her additional earnings:
Total earnings = Base salary + Additional earnings = $750 + $555
Total earnings = $1,305
Hence , Jill's earnings for the first week, with sales of $25,000, are $1,305
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Explain how to use the grid method for multiplying binomials
F 100 tires are randomly selected for shipment to an outlet what is the probability that they are all good?
Each pair of points lies on a line with the given slope. Find y. (2,2), (5,y); slope: 2
Which choices are equivalent to the quotient below? Check all that apply √75/√15 A. 5 B. √25/√5 C. 15/3 D. √5 E. √3 F. √15/√3
Answer:
sqrt15/3, sqrt 5, sqrt 25/5
Step-by-step explanation:
aye pex
Four hundred people were asked whether gun laws should be more stringent. three hundred said "yes," and 100 said "no." the point estimate of the proportion in the population who will respond "no" is
a. 75
b. 0.75
c. 0.5
d. 0.25
The proportion in the population who will respond "no" is 0.25
what is probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Given:
Total people surveyed= 400
people say 'yes'= 300
people say 'no' = 100
Now, proportion in the population who will respond "no" is
= 100/400
=1/40
= 0.25
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Which of the following are NOT sufficient to prove that a quadrilateral is a parallelogram? I. Two pairs of opposite angles congruent. II. A pair of adjacent angles are supplementary. III. Both pairs of opposite sides are congruent. IV. A pair of opposite angles congruent and a pair of opposite sides congruent. V. Both pairs of opposite sides are parallel. VI. A pair of opposite sides parallel and the other pair of opposite sides congruent. VII. One pair of opposite sides are both parallel and congruent. VIII. The diagonals bisect each other. A. IV and VII only B. II, VI, and VII only C. II and VI only D. II, IV, and VII only
A pair of adjacent angles being supplementary, a pair of opposite angles congruent and a pair of opposite sides congruent, and one pair of opposite sides being both parallel and congruent are not sufficient conditions on their own to prove that a quadrilateral is a parallelogram.
Among the given statements concerning the characteristics that are sufficient to prove a quadrilateral is a parallelogram, the following are NOT sufficient on their own:
A pair of adjacent angles are supplementary (statement II).
A pair of opposite angles congruent and a pair of opposite sides congruent (statement IV).
One pair of opposite sides are both parallel and congruent (statement VII).
While having a pair of adjacent angles that are supplementary is common in parallelograms, it alone does not guarantee that a quadrilateral is a parallelogram, as many quadrilateral types can have supplementary adjacent angles. Similarly, having just one pair of opposite angles and one pair of opposite sides congruent doesn't necessarily make a quadrilateral a parallelogram, as these characteristics could describe a kite or other quadrilaterals as well. The condition of one pair of opposite sides being both parallel and congruent, although a property of parallelograms, is not by itself a conclusive proof, as there may need to be additional information to rule out other shapes like rectangles.
Correct Answer: B. II, VI, and VII only
Find the greatest possible enclosed area of a rectangular corral given 400 feet of fencing
Answer:
Maximum area = 10000 square units.
Step-by-step explanation:
We are given the following information:
Rectangular perimeter of coral = 400 units.
Let length of the coral be x. Then,
Perimeter = 400 = 2(Length +Breadth)
[tex]400 = 2(x + Breadth)\\Breadth = 200 - x[/tex]
Thus, the area of rectangle is given by,
[tex]Area = Length\times Breadth = x\times (200-x) = 200x - x^2[/tex]
Thus, we have to maximize the function:
[tex]f(x) = 200x - x^2[/tex]
We will use double derivative test.
First we differentiate with respect to x.
[tex]\displaystyle\frac{d(f(x))}{dx} = \displaystyle\frac{d(200x - x^2)}{dx} = 200 - 2x[/tex]
Equating this to zero to obtain critical points,
[tex]200 - 2x = 0\\200 = 2x\\x = 100[/tex]
Now, again differentiating with respect to x.
[tex]\displaystyle\frac{d^2(f(x))}{dx^2} = -2 < 0[/tex]
Thus, by double derivative test, local maxima occurs for this function at x = 100
So, Length = x = 100 units
Breadth = 200 - x = 100 units
Maximum area = 10000 square units.
A cylindrical chemical storage tank mush have a height 4 meters greater than the radius of the top of the tank. determine the radius of the top and the height of the tank if the tank must have a volume of 15.71 cubic meters
Final answer:
To determine the radius and height of the cylindrical tank with a given volume of 15.71 cubic meters, where height is 4 meters greater than the radius, we use the volume formula for a cylinder, resulting in a cubic equation that must be solved.
Explanation:
The question asks for the radius of the top and the height of a cylindrical tank with a volume of 15.71 cubic meters, where the height is 4 meters greater than the radius. The formula for the volume of a cylinder is V = πr²h, where V is volume, r is radius, and h is height. Since h = r + 4, we can write the equation in terms of r as V = πr²(r + 4).
To find the radius, we substitute the given volume, 15.71 m³, into the equation:
15.71 = πr²(r + 4)
This results in a cubic equation which we need to solve to find the value of r. After solving (which may require numerical methods or approximations due to the complexity of cubic equations), we find the value of the radius and can then determine the height by adding 4 meters to the radius.
The total amount of money in a savings account after t years is given by the function A=1000(1.023)^t .
How could this function be rewritten to identify the monthly interest rate?
What is the approximate monthly interest rate?
Drag and drop the choices into the boxes to correctly complete the table. If a value does not match, do not drag it to the table.
Function Monthly interest rate
A = 1000(1 + 0.023)^12t
A = 1000(1.023^12)^t/12
A = 1000(1.023^t/12)^12t
0.23%
0.19%
0.31%
Answer:
[tex]A=1000(1+\frac{0.023}{12})^{12t}[/tex]
Rate of interest (r) = 0.19% monthly
Step-by-step explanation:
Given: The total amount of money in a saving account after t years.
[tex]A=1000(1.023)^t[/tex]
Formula:
[tex]A=P(1+r)^t[/tex]
Now we compare this formula with with given model.
P=1000
Rate of interest annually (r) = 0.023
Time = t
We need to change into monthly interest
New rate will divide by 12
New time will multiply by 12
[tex]r=\frac{0.023}{12}=0.0019[/tex]
[tex]t=12\times t =12t[/tex]
Function for monthly rate
[tex]A=1000(1+\frac{0.023}{12})^{12t}[/tex]
Rate of interest (r) = 0.19% monthly
[tex]\text{Thus, Function Monthly interest rate: }A=1000(1+\frac{0.023}{12})^{12t}\text{ and Monthly Interest rate }= 0.19\%[/tex]
PLEASE HELP ASAP WILL GIVE 30 POINT FOR WHOEVER ANSWER IT AND WILL MARK BRAINIEST
Look at the cups shown below (images are not drawn to scale):
A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.
Determine the correct equation for the following verbal sentence: The total distance traveled, d, at a constant speed of 45 miles per hour is the product of the speed and the number of hours traveled, h. a. d = h + 45 c. 4072-01-01-03-00_files/i0210000.jpg b. d = 45h d. d = 45 - h Please select the best answer from the choices provided A B C D
Your answer is B..........
If the balance is $1020, the payment is $100, and the interest is 1.5% per month, how much is the unpaid balance?
A) $920.00
B) $933.80
C) $13.80
D) $1,020.00
Quadrilateral ABCD is shown on the grid. Jonah finds the length of the sides of the quadrilateral before finding the perimeter. Which statement is true about the length of the sides of quadrilateral ABCD? Side CD has a length of units. Side BC has a length of units. Side DA has a length of 5 units. Side AB has a length of 6 units.
The correct option is B. Side BC has a length of √10 units.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that Quadrilateral, ABCD is shown on the grid. Jonah finds the length of the sides of the quadrilateral before finding the perimeter.
The length of side BC will be calculated by using the distance formula:-
D = √ [ ( 3 - 2 )² + 4 - 1 )² ]
D = √ ( 1 + 9 )
D = √10
Therefore, the correct option is B. Side BC has a length of √10 units.
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The population for a city is 39194 and grows continuously at the rate of 6.9% each year. What is the approximate population in 17 years?
Answer:
121,854
Step-by-step explanation:
Initial population of the town A= 39194
rate growth of population R= 6.9%= 0.069
we need to find the population after n = 17 years
we can find that easily using growth rate formula
A= P(1+R/100)^n
A= 39194(1+0.069)^17
= 121,854
therefore population at the end of 17 years= 121,854
Which equations represent hyperbolas?
A) 2x2 + 16x + 2y2 + 14y − 9 = 0
B) 2x2 + 4x − 5y2 − 10y + 57 = 0
C) -x2 + 5x − 7y2 + 2y − 81 = 0 d) x − 2y2 + 4y + 15 = 0
E ) -x2 + 12x + 3y2 + 7y + 11 = 0
Answer:
D
Step-by-step explanation:
Let g(x) = 2x and h(x) = x2 + 4. Evaluate (g ∘ h)(3).
A. 16
B. 40
C. 26
D. 36
The value of (goh)(3) is 26.
What is composition of function?The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).
given:
g(x) = 2x , h(x) = x²+4
Now,
(goh)(3)
=g(h(3))
=g(9+4)
=g(13)
=2*13
=26
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The letters A, B, C, D, E, F, G, H, I, and J are written on slips of paper and placed in a hat. Two letters are then drawn from the hat. What is the probability that the letters chosen would be only B, C, D, or F?
The price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $5.00
In 1994, it will the price reach $5.00.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We are given with the equation as,
⇒ [tex]p(t) = 1.1 e^{0.047t}[/tex]
where p represents the price, t represents the time in years. price varies exponentially with time.
Now, If p is 5 dollars in the future,
Then, We can formulate;
5 = [tex]1.1 e^{0.047t}[/tex]
ln 4.54 = 0.047 t
0.657 = 0.047 t
t = 13.97
t = 14 years
t = 14 years or year 1994.
Thus, In 1994, it will the price reach $5.00.
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Which table represents a linear function?
Answer:
C: 1 -2
2 -10
3 -18
4 -26
Step-by-step explanation:
how because its me i'm always right
Factor the expression completely over the complex numbers.
y4−16
Solve for n: 21k − 3n + 9p > 3p + 12
Answer: n<7k+2p-4
Step-by-step explanation:
The final balance in an account that has a monthly fee and automatic monthly deposits is given by the expression. The initial account balance is $1200.
150x−4.99x+1200
What does the expression 150x−4.99x represent?
a.the final balance
b.the monthly balance change
c.the initial balance
d.the monthly fee total
i got b
Above answer is correct, I took the test.
answer: the monthly balance change
Expand
2y (2y + 8 )
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\boxed{\mathsf{2y(2y + 8)}}\\\\\large\text{DISTRIBUTE \boxed{\text{2y}} WITHIN the PARENTHESES}\\\\\large\boxed{\mathsf{= 2y(2y) + 2y(8)}}\\\\\large\boxed{\mathsf{= 4y^2+ 16y}}\\\\\large\text{You DON'T have any like terms so we cannot do anything to this}\\\large\text{equation.}\\\\\\\huge\boxed{\rm{Therefore, your\ answer \ is: \mathsf{4y^2 +16y}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the value of x?
A. 56
B. 78
C. 12
D. 24
Use this graph of g to find g(7)
When the mean, median, and mode are not in the same place, the distribution is:?
When the mean, median, and mode are not located at the same point, the distribution is skewed, either to the left (negatively skewed) or to the right (positively skewed).
Explanation:When the mean, median, and mode are not in the same place, the distribution is known to be skewed. If the mean is less than the median, which is often less than the mode, the distribution is skewed to the left (or negatively skewed). Conversely, if the mode is less than the median, which is less than the mean, the distribution is skewed to the right (or positively skewed). Skewness indicates that the data is not symmetrically distributed and reflects the direction of the tail where the values trail off more.
In symmetrical distributions, the mean, median, and mode are all located at the same point, typically at the center of the distribution. However, when the values are not symmetrical, it indicates a skew. For example, in a data set with the values 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, the distribution is not symmetrical since it is skewed to the left, with a higher frequency of higher values.
Thus, understanding the relationship among the mean, median, and mode helps in recognizing the type of distribution and in making inferences about the data set.
Simplify sec(arcsec 1/2).
A. undefined
B. -1/2
C. 1/2
D. 2
Using a six-sided die, what is the probability of rolling either a 5 or a 6?
The probability of rolling either a 5 or a 6 using a six-sided die is 1/3.
What is probability?Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases.
Now it is given that a six-sided die is rolled.
Total Number of outcomes = 6
To get either a 5 or a 6
So, Possible number of outcomes = 2
Since ,
Probability = Possible number of outcomes / Total Number of outcomes
⇒ Probability of rolling either a 5 or a 6 = 2/6
or, Probability of rolling either a 5 or a 6 = 1/3
Thus, the probability of rolling either a 5 or a 6 using a six-sided die is 1/3.
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HELP PLEASE SOMEONE ASAP
Some steps to construct an angle MNT congruent to angle PQR are listed below. Step 3 is not listed: Step 1: Use a compass to draw an arc from point Q which intersects the side PQ at point A and the side QR at point B. Step 2: Draw a segment NT and use the same width of the compass to draw an arc from point N which intersects the segment NT at a point X. Step 3: Step 4: Join points N and Y using a straightedge. Which statement describes step 3 correctly?
A.  Maintaining the same width of the compass as BQ, draw an arc from point X such that it intersects the arc drawn from N in a point Y. 
B. Use the same width of the compass as the width of NX, and draw an arc from point X such that it intersects the arc drawn from N in a point Y.
C.  Use the same width of the compass as AQ, and draw an arc from point X which intersects the arc drawn from N in a point Y. 
D. Maintaining the same width of the compass as AB, draw an arc from point X such that it