Answer:
Step-by-step explanation:
Overtime Rate = [tex]17.70 \times 1\frac{1}{2}[/tex]
[tex]= 17.70 \times \frac{3}{2}[/tex]
[tex]=\frac{53.10}{2}[/tex]
[tex]=\pounds26.55[/tex]
Pay [tex]=11*26.55=\pounds 292.05[/tex] (I assume you can use a calculator for this)
Solution: [tex]\pounds 292[/tex]
An assignment of probabilities to events in a sample space must obey which of the following? They must obey the addition rule for disjoint events. They must sum to 1 when adding over all events in the sample space. The probability of any event must be a number between 0 and 1, inclusive. All of the above
An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.
What is probability?Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.
The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.
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what do you mean by arithmetic series?
Answer:
The sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ). It is called the arithmetic series formula.
Step-by-step explanation:
An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms. Following is a simple formula for finding the sum: Formula 1: If S nrepresents the sum of an arithmetic sequence with terms , then. This formula requires the values of the first and last terms and the number of terms.
Please mark me as Brainliest if possible! Thank you :)
true or false: when multiplying and dividing measurements, to determine the correct level of uncertainty of the solution i use measurement that is uncertain in the largest decimal place.
Answer:
Step-by-step explanation:
The answer is true
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches.
(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
(b) If a random sample of eight 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the mean is larger for the x distribution.
The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
The probability in part (b) is much higher because the mean is smaller for the x distribution.
The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
The probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793 and the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057 and the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
What do you mean by normally distributed data?
In statistics, a normal distribution is a probability distribution of a continuous random variable. It is also known as a Gaussian distribution, named after the mathematician Carl Friedrich Gauss. The normal distribution is a symmetric, bell-shaped curve that is defined by its mean and standard deviation.
Data that is normally distributed follows the pattern of the normal distribution curve. In a normal distribution, the majority of the data is clustered around the mean, with progressively fewer data points further away from the mean. The mean, median, and mode are all the same in a perfectly normal distribution.
Calculating the given probabilities :
(a) The probability that an 18-year-old man selected at random is between 70 and 72 inches tall can be found by standardizing the values and using the standard normal distribution table. First, we find the z-scores for 70 and 72 inches:
[tex]z-1 = (70 - 71) / 5 = -0.2[/tex]
[tex]z-2 = (72 - 71) / 5 = 0.2[/tex]
Then, we use the table to find the area between these two z-scores:
[tex]P(-0.2 < Z < 0.2) = 0.0793[/tex]
So the probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793.
(b) The mean height of a sample of eight 18-year-old men can be considered a random variable with a normal distribution. The mean of this distribution will still be 71 inches, but the standard deviation will be smaller, equal to the population standard deviation divided by the square root of the sample size:
[tex]\sigma_x = \sigma / \sqrt{n} = 5 / \sqrt{8} \approx 1.7678[/tex]
To find the probability that the sample mean height is between 70 and 72 inches, we standardize the values using the sample standard deviation:
[tex]z_1 = (70 - 71) / (5 / \sqrt{8}) \approx -1.7889[/tex]
[tex]z_2 = (72 - 71) / (5 / \sqrt{8}) \approx 1.7889[/tex]
Then, we use the standard normal distribution table to find the area between these two z-scores:
[tex]P(-1.7889 < Z < 1.7889) \approx 0.9057[/tex]
So the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057.
(c) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. When we take a sample of eight individuals, the variability in their heights is reduced compared to the variability in the population as a whole. This reduction in variability results in a narrower distribution of sample means, with less probability in the tails and more probability around the mean. As a result, it becomes more likely that the sample mean falls within a given interval, such as between 70 and 72 inches.
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use the formula for the sum of a geometric series to find the sum or state that the series diverges. (use symbolic notation and fractions where needed. enter dne if the series diverges.) (4^3 / 5^3) + (4^4 / 5^4) + (4^5 / 5^5) = ________--
The sum of the geometric series is 3904/3125.
By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.
Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;
The first term, a = 4³/5³
Common ratio, r = 4/5
The number of terms, n = 3
We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;
S_n = a(1 - rⁿ) / (1 - r)
S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]
S₃ = {(64/125) [1 - (64/125)]} / [1/5]
S₃ = (64/125) [(125-64)/125] [5/1]
S₃ = (64/125) (61/125) (5)
Therefore, S₃ = 3904/3125.
Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.
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150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons
The total value of both bonds is $704,367,500.
Coupon payment = [tex]\frac{Coupon rate * Par value}{2}[/tex]
Coupon payment = [tex]\frac{11 * $1,000}{2}[/tex]
Coupon payment = $55
PV = [tex]55 * [1 - (1 + 0.04)^{^-40} ] / 0.04 + $1,000 / (1 + 0.04)^40[/tex]
[tex]PV = $1,026.45[/tex]
[tex]Total value = PV * Number of bonds * Par value\\Total value = $1,026.45 * 150,000 * $1,000\\Total value = $153,967,500[/tex]
[tex]PV = \frac{Price}{(1 + r)^n}[/tex]
[tex]PV = \frac{16}{(1 +0.03)^60}\\PV = $1.72[/tex]
[tex]Total value = PV * Number of bonds * Par value\\Total value = $1.72 * 320,000 * $1,000\\Total value = $550,400,000[/tex]
Therefore, the total value of both bonds is:
[tex]Total value = Value of coupon bonds + Value of zero coupon bonds\\Total value = $153,967,500 + $550,400,000\\Total value = $704,367,500[/tex]
A coupon rate is the annual interest rate paid by a bond or other fixed-income security to its bondholders or investors. It is typically expressed as a percentage of the bond's face value, also known as its par value. For example, if a bond has a face value of $1,000 and a coupon rate of 5%, the bond will pay $50 in interest each year to its bondholders. The coupon payments are usually made semi-annually or annually, depending on the terms of the bond.
The coupon rate is set when the bond is issued and remains fixed throughout the life of the bond unless the bond issuer chooses to call the bond or the bond defaults. Coupon rates are determined by a variety of factors, including market conditions, the creditworthiness of the issuer, and the length of the bond's maturity.
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Complete Question: -
The IPO Investment Bank has the following financing outstanding,
Debt: 150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons.
Preferred stock: 240,000 shares of 9 percent preferred stock with a current price of $67, and a par value of $100.
Common stock: 3,500,000 shares of common stock; the current price is $53, and the beta of the stock is.9.
Market: The corporate tax rate is 24 percent, the market risk premium is 8 percent, and the risk-free rate is 5 percent.
What is the WACC for the company? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
[LAST QUESTION, OFFERING BRAINLIEST]
??? PTS
Answer:
Step-by-step explanation:
Let h be the height of the trapezoid.
The area of a trapezoid is given by the formula:
Area = (1/2) × (sum of parallel sides) × (height)
In this case, we know that the area is 21 cm², one base length is 5 cm, and the other base length is 9 cm. So we can write:
21 = (1/2) × (5 + 9) × h
Simplifying this equation, we get:
21 = 7h
Dividing both sides by 7, we get:
h = 3
Therefore, the height of the trapezoid is 3 cm.
Answer:
Height of Trapezium is 3 cm.Step-by-step explanation:
Area of Trapezium is 21 cm². Parallel sides are 5 cm and 9 cm .
Shorter parallel side is 5 cm and the Longer Side is 9 cm.
As we know that formula of area of Trapezium is,
Area of Trapezium = ½ (a + b) hWhere,
a and b are Parallel sides and h is the height.On substituting the values of area and the two parallel sides in the above formula we will get the required Height.
Substituting the values,
21 = ½ (5 + 9)h
21 = ½ × 14 × h
21 = 7 × h
h = 21/7
h = 3 cm
Therefore, Height of the Trapezium will be 3 cm respectively.
An automated car wash serves customers with the following serial process: pretreat, wash, rinse, wax, hand dry. Each of these steps is performed by a dedicated machine except for the hand-dry step, which is performed manually on each car by one of three workers. The steps of the process have the following processing times:
Pretreat: 2 minute per car
Wash: 7 minutes per car
Rinse: 1 minutes per car
Wax: 4 minutes per car
Hand dry: 6 minutes per car
Which resource is the bottleneck of this process? Round your answer to 2 decimal places. If the car wash has a demand of 14 cars per hour, what is the flow rate of the process? cut. customers per hour Round your answer to 2 decimal places. If the car wash has a demand of 14 cars per hour, what is the utilization of the machine that
The utilization of the machines is the processing time for the machines divided by the cycle time: 14 / 20 = 0.7 or 70%.
The bottleneck resource in this process is the hand-dry step, as it is the only step that is performed manually and thus has limited capacity. The processing time for the hand-dry step is 6 minutes per car, which is longer than any of the other steps.
To calculate the flow rate of the process, we need to determine the cycle time, which is the time it takes to process one car through all the steps. The cycle time is the sum of the processing times for all the steps, which is 2 + 7 + 1 + 4 + 6 = 20 minutes per car.
To convert this to customers per hour, we divide the number of minutes per hour (60) by the cycle time: 60 / 20 = 3 customers per hour.
Therefore, the flow rate of the process is 14 cars per hour x 3 customers per hour = 42 customers per hour.
To calculate the utilization of the machines, we need to calculate the total time that the machines are processing cars. Since all the steps except for the hand-dry step are performed by dedicated machines, the total processing time for the machines is 2 + 7 + 1 + 4 = 14 minutes per car.
Therefore, the utilization of the machines is the processing time for the machines divided by the cycle time: 14 / 20 = 0.7 or 70%.
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What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y= 4?
Answer:
Point-Slope Form: y - 1 = -1/2(x - 4) or Standard Form: y = -1/2x + 3
Step-by-step explanation:
For a line to be perpendicular, you take the negative inverse of the slope of 2x - y = 4. To do this, rearrange the y to one side and you get y = 2x - 4. The slope of the line is 2. So, taking the negative inverse would be -1/m (with m being slope of the the equation given in the problem. This would give you -1/2.
Using point slope formula, y - y1 = m(x - x1), you can plug in the point given, (4,1) and the slope you found to get y - 1 = -1/2(x - 4). For standard form, isolating the y gets you y = -1/2x + 3.
You can check your answer by using Desmos by putting in the line 2x - y = 4, the point (4,1), and the equation you got as your answer. You will see that the equation is perpendicular to 2x - y = 4 and passes through point (4,1). Your equation of the line is y - 1 = -1/2(x - 4) or y = -1/2x + 3
moore's law says that the number of transistors that can be placed inexpensively on a silicon chip doubles every two years. in $1990$, a typical cpu contained about $1,\!000,\!000$ transistors. according to moore's law, how many transistors did a typical cpu contain in the year $2000$?
According to Moore's Law, the number of transistors that can be placed inexpensively on a silicon chip doubles every two years, a typical CPU contained about 1,000,000 transistors in 1990.
What is the number of transistors in a typical CPU in the year 2000?Let’s first calculate the number of doublings from 1990 to 2000. Number of years from 1990 to 2000 = 2000 - 1990 = 10 yearsDoublings from 1990 to 2000 = [tex]$\dfrac{10 \text{ years}}{2 \text{ years per doubling}} = 5$[/tex] doublingsNow, we can calculate the number of transistors in a typical CPU in the year 2000:
[tex]$$\begin{aligned} \text{Number of transistors in 2000} &= \text{Number of transistors in 1990} \times 2^{\text{number of doublings}} \\ &= 1,\!000,\!000 \times 2^5 \\ &= 32,\!000,\!000 \end{aligned}$$[/tex]
Therefore, a typical CPU contained about 32,000,000 transistors in the year 2000.
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Abdul flips a weighted coin 64 times and gets 16 tails. Based on experimental probability how many of the next 40 flips should Abdul expect to come up tails?
Answer:
10
Step-by-step explanation:
Based on the given conditions, formulate: 40x16 divided by 64
Cross out the common factor: 40/4
Cross out common factor: 10
Get the result
Answer: 10
In ΔJKL, the measure of ∠L=90°, JK = 7. 3 feet, and KL = 4. 7 feet. Find the measure of ∠J to the nearest tenth of a degree
The measure of ∠J in ΔJKL is approximately 57.5 degrees.
The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.
The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.
tan(∠J) = JK/KL
tan(∠J) = 7.3/4.7
∠J = arctan(7.3/4.7)
∠J = 57.5 degrees (rounded to the nearest tenth of a degree)
Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.
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HELP. I'm really struggling on this one. My calculus teacher claimed this to be the easiest math problem ever but I still can't understand. Is anyone smart enough to figure this one out. Whats 1 + 1?
Answer:
The answer to 1 + 1 is 2.
Very complicated problem, please mark brainliest!
Answer:
1+1 = 2
Or, 1=2-1
1=1
we know value of one is one
so,
1+1=11
What is the area of this figure?
6 mm
4 mm
3 mm
5 mm
3 mm
15 mm
3 mm
9 mm
Write your answer using decimals, if necessary. Square millimeters
Based on the given data, The shape's whole surface area is about 252 mm².
Based on the image, the shape appears to be a set of rectangles with different lengths and widths.
To find the area of this shape, we can break it down into smaller rectangles and add up their areas.
Starting from the bottom, we can see that the first rectangle has a length of 6 mm and a width of 4 mm. Its area is:
Area1
= 6 mm × 4 mm
= 24 mm²
Moving up to the second rectangle, we see that it has a length of 6 mm and a width of 3 mm. Its area is:
Area2
= 6 mm × 3 mm
= 18 mm²
The third rectangle has a length of 6 mm and a width of 5 mm. Its area is:
Area3
= 6 mm × 5 mm
= 30 mm²
The fourth rectangle has a length of 6 mm and a width of 3 mm. Its area is:
Area4
= 6 mm × 3 mm
= 18 mm²
The fifth rectangle has a length of 6 mm and a width of 15 mm. Its area is:
Area5
= 6 mm × 15 mm
= 90 mm²
The sixth rectangle has a length of 3 mm and a width of 9 mm. Its area is:
Area6
= 3 mm × 9 mm
= 27 mm²
Finally, the seventh rectangle has a length of 5 mm and a width of 9 mm. Its area is:
Area7
= 5 mm × 9 mm
= 45 mm²
To find the total area of the shape, we can add up the areas of all seven rectangles:
Total Area
= Area1 + Area2 + Area3 + Area4 + Area5 + Area6 + Area7
= 24 mm² + 18 mm² + 30 mm² + 18 mm² + 90 mm² + 27 mm² + 45 mm²
= 252 mm²
Therefore, the total area of the shape is approximately 252 mm².
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IN A BOX PLOT , IF THE MEDIAN IS TO THE LEFT OF THE CENTER OF THE BOX AND THE RIGHT WHISKER IS SUBSTANTIALLY LONGER THAN THE LET WHISKER, THE DISTRIBUTION IS SKEWED LEFT OR RIGHT?
The distribution is skewed to the right.
How to find distribution is skewed?If the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker in a box plot, then the distribution is skewed to the right.
This means that the majority of the data is clustered on the left side of the box plot and there are some extreme values on the right side that are causing the right whisker to be longer.
The median being to the left of the center of the box indicates that the data is not symmetric and is pulled to the left by the majority of the values.
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Let all of the numbers given below be correctly rounded to the number of digits shown. For each calculation, determine the smallest interval in which the result, using true instead of rounded values, must lie. (a) 1.1062+0.947 (b) 23.46 - 12.753 (c) (2.747) (6.83) (d) 8.473/0.064
An interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.
For each calculation, the smallest interval in which the result, using true instead of rounded values, must lie is as follows:
(a) 1.1062+0.947 = 2.0532 ≤ true result ≤ 2.053
(b) 23.46 - 12.753 = 10.707 ≤ true result ≤ 10.708
(c) (2.747) (6.83) = 18.6181 ≤ true result ≤ 18.6182
(d) 8.473/0.064 = 132.3906 ≤ true result ≤ 132.3907
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the expression when y=-6 y^2+8y-9
Answer:
-21
Step-by-step explanation:
y^2 + 8y - 9 y = -6
(-6)² + 8(-6) - 9
36 - 48 - 9
-21
So, the answer is -21
Answer:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}
Step-by-step explanation:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}
PLS ANSWER THIS ASAP
In two similar triangles, the ratio of the lengths of a pair of corresponding sides is 7:8. If the perimeter of the larger triangle is 32, find the perimeter of the smaller triangle.
The perimeter of the smaller triangle would be = 28.1
How to calculate the perimeter of the smaller triangle?A triangle can be defined as a three sided polygon that has a total internal angle of 180°.
To calculate the perimeter of the triangle is to find out the scale factor that exists between the two triangles.
The formula for scale factor = original object/new object
Scale factor= 8/7 = 1.14
The perimeter of the smaller triangle = 32/1.14
= 28.1.
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3
Each player on a softball team will get a uniform with a randomly selected
number between 1 and 30. No two players will have the same number.
The first player to get a uniform thinks the probability that she will
get a single-digit number is. Is the player correct? Explain
10
your reasoning.
30 percent chance
There are 30 possible numbers that a player can get on their uniform. Out of these, there are 9 single-digit numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) and 21 double-digit numbers (10, 11, 12, ..., 29, 30).
If no two players can have the same number, then the probability that the first player will get a single-digit number is simply the number of single-digit numbers divided by the total number of possible numbers:
P(single-digit number) = 9/30 = 0.3
So the player is correct that there is a 30% chance that she will get a single-digit number on her uniform.
please answer the question in the photo (will mark brainliest + 15p)
we have
13x+6y=−30------------- > 6y=-30-13x--------------- > y=(-30-13x)/6
x−2y=−4-- > 2y=x+4-------- > y=(x+4)/2
Using a graphing tool---------- > see attached figure
the solution of the system is the point (-2.625,0688)
the best estimate pair for the solution to the system is (−2.5, 0.75)
stive efforts in
Eamples (finding slope in tables and graphs)
termine the slope of each linear equation. You may want to use the slope formula.
X O
1
2
3
y
S5
7
9
11
b)
566
X
-7
-6
-5
-4
y
10
7
4
1
c)
X
-2
0
2
4
y
I
3
5
can't
7
9
The slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
What is equation?An equation is an expression that states the equality of two things. It typically consists of an equal sign (=) and two expressions on either side of the equal sign that represent the same thing. Equations are used to describe relationships between different variables and can be used to solve mathematical problems. They can also be used to show the relationships between different quantities in physics and chemistry.
a)The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 6, and the run is 2, so the slope is 3.
b) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 3, and the run is -7, so the slope is -3/7.
c) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 4, and the run is 6, so the slope is 2/3.
Finding slope in tables and graphs is a common mathematical skill that is used to identify the rate of change of a linear equation. This is determined by finding the change in the dependent variable (the y-axis) divided by the change in the independent variable (the x-axis). This is what is referred to as the slope of the equation. To find the slope in tables and graphs, you must look at the differences between the points on the x-axis and y-axis, and divide the change in the y-axis by the change in the x-axis. This will give you the slope of the equation. Finding the slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
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A+9 as a verbal expression
Answer:
"9 more than A" is a verbal expression.
Pls read ss
PLS HELPP
The slopes are,
1) 7/6
2)7/2
3) -1
4) -2
5) 10/9
What is slope?
Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.
1) The given points , [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (6,8)[/tex] then,
=> slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{8-1}{6-0} = \frac{7}{6}[/tex]
2) The given points [tex](x_1,y_1) =(-1,10)[/tex] and [tex](x_2,y_2) = (-5,-4)[/tex] then,
=> Slope = [tex]\frac{-4-10}{-5+1} = \frac{-14}{-4}=\frac{7}{2}[/tex]
3) The given points [tex](x_1,y_1) =(-10,2)[/tex] and [tex](x_2,y_2) = (-3,-5)[/tex] then,
=> slope = [tex]\frac{-5-2}{-3+10} = \frac{-7}{7}=-1[/tex]
4) The given points [tex](x_1,y_1) =(-3,-4)[/tex] and [tex](x_2,y_2) = (-1,-8)[/tex] then,
=> slope = [tex]\frac{-8+4}{-1+3} = \frac{-4}{2}=-2[/tex]
5)The given points [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (-9,-9)[/tex] then,
=> slope = [tex]\frac{-9-1}{-9+0} = \frac{-10}{-9}=\frac{10}{9}[/tex]
Hence the slopes are,
1) 7/6
2)7/2
3) -1
4) -2
5) 10/9
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a rectangular swimming pool 50 ft long, 30 ft wide, and 8 ft deep is filled with water to a depth of 6 ft. use an integral to find the work required to pump all the water out over the top. (take as the density of water lb/ft. )
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
We have,
To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.
First, let's calculate the weight of the water in the pool.
The weight of an object is given by the formula:
Weight = mass x gravitational acceleration
Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.
The volume of the pool is given by the formula:
Volume = length x width x depth
Volume = 50 ft x 30 ft x 6 ft = 9000 ft³
Now, let's calculate the weight of the water:
Weight = density x volume x gravitational acceleration
Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb
To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.
The work required to pump the water out is given by the formula:
Work = weight x height
Work = 290,400 lb x 8 ft = 2,323,200 ft-lb
Therefore,
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
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Let A denote the balance at the end of Month n for each month where the balance is positive. To find a formula for An, we can do the following. For Month 1, note that A1 = 4000(1.015) - 100 For Month 2, note that A2 =[4000(1.015 ) – 100] (1.015) – 100
= 4000(1.015)^2 – 100 - 100(1.015) For Month 3, note that A3 = [4000(1.015)^2 - 100 - 100(1.015)] (1.015) - 100 = [4000(1.015)^3 - 100 - 100(1.015)] - 100(1.015)^2
B. (6 pts) (Formulas for An) i. Give a recursive formula for An. Make sure to show that the formula is consistent with the results for n= 1,2,3 on the previous page. ii. Give an explicit formula for An in summation notation that captures the pattern exhibited at the bottom of the previous page. Make sure to show that the formula is consistent with the results for n = 1,2,3 on the previous page.
(a) The recursive formula for An is: An = (1.015)An-1 - 100.
(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].
(a) This formula says that to find the balance for month n, we take the balance for month n-1, multiply it by 1.015 (to account for the interest rate), and subtract 100 (to account for the withdrawal). This formula is consistent with the results for n=1,2,3 on the previous page.
(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].
This formula says that to find the balance for month n, we take the starting balance of 4000 multiplied by the interest rate raised to the power of n, and then subtract the sum of 100 multiplied by the geometric series (1 + r + r^2 + ... + r^(n-1)), where r = 1.015. This formula is consistent with the results for n=1,2,3 on the previous page.
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Tamarisk company began operations on january 2, 2019. It employs 9 individuals who work 8-hour days and are paid hourly. Each employee earns 9 paid vacation days and 7 paid sick days annually. Vacation days may be taken after january 15 of the year following the year in which they are earned. Sick days may be taken as soon as they are earned; unused sick days accumulate. Additional information is as follows. Actual hourly wage rate vacation days used by each employee sick days used by each employee 2019 2020 2019 2020 2019 2020 $6 $7 0 8 5 6 tamarisk company has chosen to accrue the cost of compensated absences at rates of pay in effect during the period when earned and to accrue sick pay when earned
The total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
To calculate the cost of compensated absences for Tamarisk Company, we need to calculate the number of vacation days and sick days earned by the employees in 2019 and 2020, and then calculate the cost of the days earned but not taken.
Each employee earns 9 vacation days per year. As they can be taken after January 15th of the year following the year in which they are earned, the vacation days earned by the employees in 2019 can be taken in 2020. Therefore, in 2019, no vacation days were taken by any employee.
In 2020, the employees took a total of 8 vacation days. As there are 9 employees, the total vacation days taken in 2020 were 9 x 8 = 72.
Sick Days:
Each employee earns 7 sick days per year, and unused sick days accumulate. In 2019, the employees used a total of 5 sick days. Therefore, the unused sick days at the end of 2019 were 9 x 7 - 5 = 58.
In 2020, the employees used a total of 6 sick days, and the unused sick days at the end of 2020 were 58 + 9 x 7 - 6 = 109.
To find the cost of compensated absences. The unused sick days and vacation days must be multiplied to get the hourly wage rate in effect in a year.
In 2019, the cost of compensated absences was 58 x $6 = $348.
In 2020, the cost of compensated absences was (72 + 109) x $7 = $1,399.
Therefore, the total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
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Which of the following steps were applied to ABC obtain AA'B'C'?
A. Shifted 4 units left and 4 units up
B. Shifted 4 units left and 2 units up
C. Shifted 2 units left and 4 units up
D. Shifted 2 units left and 2 units up
Correct Option is Shifted 2 units left and 4 units up
Define triangleA triangle is a geometric shape that is formed by three straight line segments that connect three non-collinear points. The three points where the segments intersect are called the vertices of the triangle, while the segments themselves are called the sides. The area enclosed by the sides of the triangle is called its interior, while the space outside the triangle is called its exterior.
Given are two trianglesThe vertices of ABC are (4, 6), (7, 6), and (5,9)
The transformed image A'B'C' has vertices as
(2,10) (5,10) (3,13)
We see a pattern when we compare the matching vertices.
The y coordinate is raised by 4, while the x coordinate is shrunk by 2.
This implies the transformation is
Shifted 2 units left and 4 units up
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Answer:
Shifted 2 units left and 4 units up
Step-by-step explanation:
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In square $ABCD$ with sides of length 4 cm, $N$ is the midpoint of side $BC$ and $M$ is the midpoint of side $CD$. What is the area of triangle $AMN$,
Consequently, the area of triangle $AMN$ is equal to $A = \frac{1}{2}bh = \frac{1}{2}(4)(2) = 4$ cm2.
The area of triangle $AMN$ in square $ABCD$ can be calculated using the formula for area of a triangle, $A = \frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the height of the triangle.
Since side $BC$ has a length of 4 cm, we can determine that $N$ is located 2 cm away from point $B$ and 2 cm away from point $C$.
Similarly, we can conclude that $M$ is located 2 cm away from point $C$ and 2 cm away from point $D$.
Therefore, the base of triangle $AMN$ is equal to 4 cm, and the height of triangle $AMN$ is equal to 2 cm.
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Operación de vectores
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Step-by-step explanation:
When calculating a confidence interval for the difference between two means proportions How do you determine whether or not the results indicate a significant difference?
The interval does not include the null hypothesis value, then the results are significant.
When calculating a confidence interval for the difference between two means or proportions, the significance level must be considered to determine whether the results suggest a significant difference.What is a confidence interval?A confidence interval (CI) is an interval estimate that quantifies the uncertainty associated with the unknown population parameter. Confidence intervals are used to express how confident we are about the accuracy of an estimated population parameter.The significance level is the level at which the results of a statistical test are considered statistically significant. The significance level is frequently represented as alpha, and its value is usually set to 0.05 (5%) in most statistical analyses. This implies that there is a 5% chance that the statistical test findings will indicate a significant difference when, in fact, there is no such difference. The significance level is the probability of rejecting a true null hypothesis.Therefore, in order to determine whether or not the results of a confidence interval for the difference between two means or proportions indicate a significant difference, we must compare the interval with the significance level (alpha) that was established before the test. If the interval contains the null hypothesis value (usually 0), then the results are not significant. If the interval does not include the null hypothesis value, then the results are significant.
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