The loan have a higher monthly payment Because the lease is riskier to the financing company.
To Determine the costs of buying versus leasing a motor vehicle, we need to consider the total costs associated with each option. For buying, the total cost is the sum of the down payment, loan payments, and the estimated value at the end of the loan, minus the resale value of the car.
On the other hand, for leasing, the total cost can be calculated as the sum of the security deposit, lease payments, and end-of-lease charges. We also need to consider the opportunity cost of investing the down payment and the security deposit.
We know that Melisha can pay for her vehicle with a 4-year loan or with a lease with the same down payment and same interest rate.
Therefore, the loan have a higher monthly payment Because the lease is riskier to the financing company.
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Researchers are analyzing the total annual cost for the top ranked universities. They need to display the data in a way that is helpful
for relaying information regarding the data.
Identify the advantage of using a dotplot (choose one) :
A- Easily identify outliers
B- Easily determine the total number of data points for larger data sets
C- Cannot determine the minimum or maximum
D-Cannot identify the exact median
One advantage of using a dot plot is that it makes it easy to identify outliers. Option A is correct.
An outlier is a data point that is significantly different from the others in the data set, either in terms of its value or its position within the range of values. In a dot plot, outliers are represented by individual dots that are far away from the other dots, either above or below them.
By looking at the dot plot, researchers can quickly identify any outliers and investigate them further to determine why they are different and whether they should be included or excluded from the analysis.
Hence, A. is the correct option.
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In IXL I need help im bad :(
Answer:
Wilma will pay $23.44 total.
Step-by-step explanation:
Cost of sweater = (+) $24.49
Discount = (-) $5
Shipping cost = (+) $3.95
Solve:
24.49 - 5 = 19.49
19.49 + 3.95 = 23.44
Wilma will pay $23.44 total.
A business manufactures and sell laptops.Each laptop is sold for R14000.the fixed monthly cost is R32000 and it cost R9000 to manufacture each laptop.let L be number of laptops manufactured and sold per monthly
The total cost equation can be written as:
Total Cost = 32000 + 9000L
What is total cost?
Total cost refers to the complete amount of money or resources that are required to produce or obtain a particular good or service. It includes all of the expenses associated with production, such as labor costs, materials costs, overhead costs, and any other costs necessary to manufacture or acquire the product.
The total cost equation can be expressed as:
Total Cost = Fixed Cost + Variable Cost
where Fixed Cost is the cost that does not vary with the number of laptops manufactured and sold, and Variable Cost is the cost that depends on the number of laptops manufactured and sold.
In this case, the fixed monthly cost is $32,000 and it does not depend on the number of laptops manufactured and sold. The variable cost is the cost of manufacturing each laptop, which is $9,000 per laptop.
If L is the number of laptops manufactured and sold per month, then the variable cost can be expressed as 9000L. Therefore, the total cost equation can be written as:
Total Cost = 32000 + 9000L
This equation represents the total cost of manufacturing and selling L laptops per month. The fixed cost of $32,000 is added to the variable cost of $9,000 per laptop multiplied by the number of laptops sold, L, to obtain the total cost.
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Complete question: A business manufactures and sell laptops. Each laptop is sold for 14000.the fixed monthly cost is 32000 and it cost 9000 to manufacture each laptop. let L be number of laptops manufactured and sold per monthly. What is the total cost equation?
The volume of a rectangular prism is 5,890.625cm3 . if the height is 14.5 cm and the length is 25 cm, with is the value of the width ?
A. 16.25 cm B. 16.5 cm C. 16.75cm D. 16.97cm
Answer:
Step-by-step explanation:
The answer is A. 16.25cm.
Explanation:-
We know,
The Volume of Prism =height*width*length;
Here, In the question Height and length is given.
So We have to do a simple calculation to find,width=
(Vol of Prism)/Heigth*length;=> 5890.625/(14.5*25)
=>16.25 cm .
We don't need to worry about dimensions because all are in the same cm dimensions.
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Answer:
A. 16.25 cm
Step-by-step explanation:
To solve for the volume of a rectangular prism, we would use the formula V = l·w·h, where:
"l" is the base length
"w" is the base width
"h" is the height of the prism
In this problem, we are given the volume, height, and length of the rectangular prism. That means we need to find the value of w, the base width. To do this, we plug our known values into the equation and solve for w.
5,890.625 = (14.5)(25)w
To get w by itself, we first divide each side of the equation by 14.5. Remember that when you divide a number by itself, they cancel out.
(5,890.625)/(14.5) = (14.5)(25)w/(14.5)
406.25 = (25)w
Next, we can divide each side of the equation by 25 to get our answer.
406.25/25 = (25)w/25
w = 16.25 cm
Making an Informed Decision Using the Quantitative Reasoning Process
Step 1: Understand the Problem
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 190 miles per week to commute to work. With gas prices currently at $
2.9 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 18 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $
770 per year (as long as nothing serious goes wrong).
The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $
6,500 over a three-year loan process. This car gets 32 miles per gallon and would only require an average of $
10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
Step 2: Identify variables and assumptions
Manny has identified some key variables for his situation. Select the two variables that should be removed from his list because they do not apply to the current situation.
Manny’s graduation date from elementary school.
The cost of repairs on the old car.
The cost of gas.
The number of miles Manny drives each week.
Manny’s wages.
The loan cost of the used car.
The year Manny was born.
The cost of the used car.
Manny has also made a list of key assumptions he will be using to make his decision. Check the boxes for the three assumptions from his list that are not useful in this scenario.
Manny assumes that nothing will go seriously wrong with either car during this three year period.
Manny assumes the loan period will be 3 years.
Manny assumes gas costs will remain about the same over the three years.
Manny assumes he will continue to go running in the mornings every weekday for the next three years.
Manny assumes there are 52 weeks in a year.
Manny assumes his lunches will continue to cost about the same for the next three years.
Manny assumes he will continue to drive about the same number of miles each week over this three year period.
Manny assumes he will still like spinach at the end of three years no matter which choice he makes.
Step 3: Apply Quantitative Tools
Use computational and algebraic tools to quantify the total costs (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Scenario
Total Cost for Three Years
Keep the old car
$
Number
Buy the fuel-efficient used car
$
Number
Step 4: Make an Informed Decision
Based on the information presented what do think Manny should decide?
Option #1: Keep the old car
Option #2: Buy the fuel-efficient used car
Option #
1
Step 5: Evaluate Your Reasoning
Manny plans to start looking at cars and will evaluate his reasoning before he makes a purchase.
( need help on the assignment)
PLEASE HELP (1 point)
Let X be a continuous random variable with probability
distribution represented by the graph below.
Find P (X≤2).
f(x)
The probability P (X≤2). from the probability distribution is 1/3
Evaluating the probability from the probability distributionA continuous random variable is a type of random variable that can take on any value within a specific range, often an infinite range.
It has a probability distribution function that describes the probability of the variable taking on certain values within that range.
This means that
P (X≤2) = the f(x) value
From the graph, we have
P (X≤2) = 1/3
Hence, teh value is 1/3
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Given the circle below with secants GHI and KJI. If JI = 4, KJ = 10 and
HI = 5, find the length of GH. Round to the nearest tenth if necessary.
Answer:
GH = 6.2
Step-by-step explanation:
(PLEASE ANSWER BOTH)
1. What is the value of Angle X?
2. How do you know (What type of angle pairs are they)?
Answer:
angle x is 160
Step-by-step explanation:
180 - 20
Triangle GFH has vertices G(2, –3), F(4, –1), and H(1, 1). The triangle is rotated 270° clockwise using the origin as the center of rotation. Which graph shows the rotated image?
On a coordinate plane, triangle G prime H prime F prime has points (negative 3, negative 2), (1, negative 1), (negative 1, negative 4).
On a coordinate plane, triangle G prime H prime F prime has points (3, 2), (negative 1, 1), (1, 4).
On a coordinate plane, triangle G prime H prime F prime has points (2, negative 3), (1, 1), (4, negative 1).
On a coordinate plane, triangle G prime H prime F prime has points (2, 3), (4, 1), (1, negative 1).
Check the picture below.
Answer:
b
Step-by-step explanation:
edge 2023
I need help to get the residual plot from this data 13.8 1.42 16.7 3.21 0.7 1.11 18 4 16.7 3.21 20 4 18 3.8 19.5 3.78 21.9 3.69 0.7 1.11
Answer:
To create a residual plot, you need to first fit a model to the data. Without any information about the problem you are trying to solve or the model you are fitting, I will assume that you are trying to fit a linear regression model to these data points.
First, you would need to find the equation of the line that best fits the data using a regression analysis software or by hand. Let's assume that the equation of the line is:
y = 0.2x + 2.5
where y is the response variable (dependent variable) and x is the predictor variable (independent variable).
Next, you would calculate the predicted values of y (i.e., the values that the model predicts) for each value of x in your dataset, using the equation of the line. For example, for the first data point (13.8, 1.42), the predicted value of y would be:
y_predicted = 0.2 * 13.8 + 2.5 = 5.06
The residual for this data point would be the difference between the actual value of y and the predicted value of y:
residual = 1.42 - 5.06 = -3.64
You would repeat this process for each data point in your dataset, to get a list of residuals.
The Question Is Inside Of The Picture
The percentage of sugar price per pound less than 64 cents is 50%
What percentage of sugar price per pound are less than 64 centsFrom the question, we have the following parameters that can be used in our computation:
Mean = 64
Standard deviation = 2
For sugar price per pound that are less than 64 cents, we have
z = (64 - 64)/2
z = 0
This is then represented as
Probability = (z < 0)
Using a graphing calculator, we have
Probability = 0.5
Express as percentage
Probability = 50%
Hence, the probability is 50%
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Using the discriminant
Answer:
n = 20/3
Step-by-step explanation:
Theory about the discriminant, and how solutions are acquired via the quadratic formula
One variable quadratic equations in the form [tex]0=ax^2+bx+c[/tex] have exactly one solution when the discriminant [tex](b^2-4ac)=0[/tex].
This is because for quadratic equations of the original form, the two solutions are given by the quadratic formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
which is equivalent to [tex]x=\dfrac{-b}{2a}\pm \dfrac{\sqrt{b^2-4ac}}{2a}[/tex].
The [tex]x=\dfrac{-b}{2a}[/tex] is the axis of symmetry, and the [tex]\dfrac{\sqrt{b^2-4ac}}{2a}[/tex] part is how much the solutions deviate from the axis of symmetry. If the deviation is zero, then the two solutions are both ON the axis of symmetry, and are the same number, giving exactly one solution.
Addressing the given equation
Putting it into standard form
Given the given equation...
[tex](n-4)u^2+6=8u[/tex]
subtract 8u from both sides to obtain an equation that looks like the standard form equal to zero...
[tex](n-4)u^2-8u+6=0[/tex]
The variable here is "u" instead of "x", so the solutions to this equation would be [tex]u=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex], where [tex]a=n-4[/tex], [tex]b=-8[/tex], and [tex]c=6[/tex].
Identifying the discriminant
The discriminant then, with values of a, b, and c, substituted, becomes:
[tex]Discriminant=(-8)^2-4(6)(n-4)[/tex]
If we want the discriminant to equal zero (so that there is exactly one solution for "u"), substitute zero on the left side of the equation, and solve for n.
Solving for n
[tex]0=(-8)^2-4(6)(n-4)[/tex]
[tex]0=64-4(6)(n-4)[/tex]
[tex]0=64-24(n-4)[/tex]
Add -24(n-4) to both sides...
[tex]24(n-4)=64[/tex]
Divide both sides by 24...
[tex]n-4=\dfrac{64}{24}[/tex]
Reduce the right hand side...
[tex]n-4=\dfrac{8}{3}[/tex]
Add 4 to both sides...
[tex]n=\dfrac{8}{3}+4[/tex]
Find a common denominator...
[tex]n=\dfrac{8}{3}+\dfrac{12}{3}[/tex]
Find a common denominator...
[tex]n=\dfrac{20}{3}[/tex]
So, if [tex]n=\dfrac{20}{3}[/tex], then the equation [tex](n-4)u^2+6=8u[/tex] has exactly one solution. Furthermore, this is the only value of "n" for which the equation has exactly one solution, because it is the only value of "n" for which the discriminant is zero.
ASAP PLEASE
The histogram shows data collected about the number of passengers using city bus transportation at a specific time of day.
A histogram titled City Bus Transportation. The x-axis is labeled Number Of Passengers and has intervals of 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 9. There is a shaded bar for 1 to 10 that stops at 2, for 11 to 20 that stops at 4, for 21 to 30 that stops at 5, for 31 to 40 that stops at 6, and for 42 to 50 that stops at 3.
Which of the following data sets best represents what is displayed in the histogram?
1 (4, 5, 7, 8, 10, 12, 13, 15, 18, 21, 23, 28, 32, 34, 36, 40, 41, 41, 42, 42)
2 (4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)
3 (4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42)
4 (4, 6, 11, 12, 16, 18, 21, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 41, 41, 42)
Answer:
Step-by-step explanation:
After organizing the data, the researcher must present them so they can be understood by those who will benefit from reading the study. The most useful method of presenting the data is by constructing statistical charts and graphs. There are many different types of charts and graphs, and each one has a specific purpose.
This chapter explains how to organize data by constructing frequency distributions
and how to present the data by constructing charts and graphs. The charts and graphs
illustrated here are histograms, frequency polygons, ogives, pie graphs, Pareto charts,
and time series graphs. A graph that combines the characteristics of a frequency distribution and a histogram, called a stem and leaf plot, is also explained.
Section 2–2 Organizing Data 35
2–3
Objective
Organize data using
frequency
distributions.
1
2–2 Organizing Data
Suppose a researcher wished to do a study on the number of miles that the
employees of a large department store traveled to work each day. The researcher
first would have to collect the data by asking each employee the approximate distance the
store is from his or her home. When data are collected in original form, they are called
raw data. In this case, the data are
1 2 6 7 12 13 2 6 9 5
18 7 3 15 15 4 17 1 14 5
4 16 4 5 8 6 5 18 5 2
9 11 12 1 9 2 10 11 4 10
9 18 8 8 4 14 7 3 2 6
Since little information can be obtained from looking at raw data, the research
Answer:
c
Step-by-step explanation:
its ez
fill it in The value of a certain investment over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Years Since Investment Made, x
1
2
3
4
Value of Investment ($), f(x)
14,944.54
16,357.04
17,974.72
19,891.18
function would best fit the data because as x increases, the y values change
. The
of this function is approximately
.
An exponential function would be more appropriate than a linear function, as exponential growth
the best function for the dataTo determine which type of function best fits the data, we can analyze the difference in the y values (Value of Investment) as x increases.
Differences between consecutive y values:
16,357.04 - 14,944.54 = 1,412.50
17,974.72 - 16,357.04 = 1,617.68
19,891.18 - 17,974.72 = 1,916.46
The differences between consecutive y values are increasing as x increases. This suggests that an exponential function would be more appropriate than a linear function.
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what is the value for 43.7 x 0.25
Answer:
43.7 x 0.25 is 10.925
Step-by-step explanation:
To multiply decimals, we can use the following steps:
1. Multiply the numbers as if they were whole numbers, ignoring the decimal points.
2. Count the total number of decimal places in the factors being multiplied. This will be the number of decimal places in the product.
3. Place the decimal point in the product so that it has the same number of decimal places as the total counted in step 2.
Using these steps, we can find the product of 43.7 and 0.25 as follows:
1. 437 x 25 = 10925
2. There are two decimal places in 43.7 and two decimal places in 0.25, so there are a total of four decimal places in the factors being multiplied.
3. Place the decimal point in the product so that it has four decimal places: 10.925
Therefore, the value of 43.7 x 0.25 is 10.925.
The sales of a certain product after an initial release can be found by the equation s=12 sqrt (4t) + 10 , where s represents the total sales (in thousands) and t represents the time in weeks after release. Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release.
about $586,000
about $586
about $93
about $93,000
The sales 12 weeks after release is $586,000 . Option A is the correct answer.
To create a table of values, we can plug in different values of t and find the corresponding values of s:
t s
0 10
1 19.882
2 26.248
3 31.177
4 35.064
5 38.185
6 40.731
7 42.837
8 44.6
9 46.095
10 47.384
11 48.508
12 49.498
To graph the function, we can plot the values from the table on a coordinate plane. The horizontal axis represents time in weeks, and the vertical axis represents sales in thousands of units. The resulting graph is a curve that starts at (0,10) and increases as t increases.
To estimate the sales 12 weeks after release, we can look at the graph and see that the corresponding value of s is around 49.5 thousand units. Therefore, the answer is about $586,000 (49.5 x 1000 x 12). Option A is the correct answer.
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Write an inequality that matches the number line model. Then write
a situation that the inequality could represent.
-2.75 is greater than or equal to x
Answer:
x<=-2.75
Step-by-step explanation:
Which of the following statements about transportation in the United States is NOT true?
A. Most Americans commute to work in a personally owned vehicle.
B. Most Americans who commute to work in car's drive alone.
C. Americans spend more income on transportation than anything else except
housing.
D. The cost of gasoline is higher in the U.S. than anywhere else in the world.
Answer: D
Step-by-step explanation:
The answer is D. The cost of gasoline is higher in the U.S. than anywhere else in the world.
According to the U.S. Energy Information Administration, the average price of a gallon of regular unleaded gasoline in the United States was $3.53 on March 8, 2023. This is higher than the average price of gasoline in many other countries, including Canada ($1.56), Mexico ($1.97), and the United Kingdom ($1.73). However, the cost of gasoline in the United States is lower than the average price in some countries, such as Norway ($6.62), Sweden ($5.62), and Denmark ($5.51).
Here are the facts about the other statements:
A. Most Americans commute to work in a personally owned vehicle. According to the U.S. Census Bureau, in 2019, 77.4% of workers commuted to work by driving alone.
B. Most Americans who commute to work in car's drive alone. According to the U.S. Census Bureau, in 2019, 77.4% of workers who commuted to work by driving did so alone.
C. Americans spend more income on transportation than anything else except housing. According to the U.S. Bureau of Labor Statistics, in 2020, Americans spent an average of $10,564 on transportation, more than any other category except housing ($16,916).
Can yall help me with this pls
Answer:
x=6.4
Step-by-step explanation:
2/3.2 = 4/x
2x=4(3.2)
2x=12.8
x=6.4
9 belongs to the set N
Answer:
9 belongs to set N, natural, whole, integer, rational, and real number
Step-by-step explanation:
* Natural number: use for counting
* Whole number: includes natural number and zero
* Integer : are whole numbers and their opposite
*Rational number:come from fraction, and their results can be positive integer
*Real number: includes all numbers
[tex]y=2cos^{2}(x) , y=2e^{-x}+2x-2[/tex]
(a) Write an equation whose solutions are the points of intersection of the graphs.
(b) Use the intersect feature of the graphing utility to find the points of intersection (to four decimal places). (Enter the point of intersection whose x-coordinate is within the interval [0, 2). If there is no solution, enter NO SOLUTION.)
a. The equation whose solutions are the points of intersection of the graphs is y = -0.14x + 0.80.
b. The points of intersection are (-0.827, 0.918) and (0.951, 0.675).
The solution has been obtained using the slope - intercept form.
What is the slope - intercept form?
When you are aware of the slope of the line being investigated and the given point is also the y intercept, use the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is represented by the symbol b in the equation.
a. From the graph, we have two points of intersection.
Using this, we get the slope as;
m = -0.14
Now, using the slope intercept form, we get the intercept as
b = 0.80
So, the equation comes out to be
y = -0.14x + 0.80
b. The graph of the equations have been attached below.
From the graph, we get the points of intersection as (-0.827, 0.918) and (0.951, 0.675). Both the points have their x-coordinate within the interval [0, 2).
Hence, the required solutions have been obtained.
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- x²= +x +12=0 .....................................
Therefore, the solutions of the equation -x² + x + 12 = 0 are x = -3 and x = 6.
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.
Here,
The given equation is:
-x² + x + 12 = 0
To solve for x, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, we have:
a = -1, b = 1, and c = 12
Substituting these values into the quadratic formula, we get:
x= (-1 ± √(1² - 4(-1)(12))) / 2(-1)
x = (-1 ± √(1 + 48)) / (-2)
x = (-1 ± √(49)) / (-2)
x = (-1 ± 7) / (-2)
There are two solutions:
x = (-1 + 7) / (-2)
= -3
x = (-1 - 7) / (-2)
= 6
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Can someone help me please
here is the picture
The result of adding -4 (row 1) to row 3 is determined as (0 - 9 2)|12.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 2 1] | -5
To multiply row by -4, we will multiply each entity by 4 as shown below;
= -4(1 2 1) | -5
= (-4 -8 - 4) |20
To add the result to 3;
(-4 -8 - 4)|20 + (4 - 1 6) | -8
= (0 - 9 2)|12
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.
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The type-1 error (false positive) for a carbon monoxide detector installed in your house is 0.05 and its type-2
error (false negative) is 0.03. The probability that a gas heater malfunctions and releases carbon monoxide is
very low, only 0.000007.
What is the probability that the carbon monoxide detector will not go off?
O 0.9998642
O 0.9499936
O 0.0500064
O 0.0001358
The probability that the carbon monoxide detector will not go off is approximately 0.9998642 (rounded to 7 decimal places),
Option A is the correct answer.
We have,
The probability of the carbon monoxide detector not going off can occur in two ways: either there is no carbon monoxide present, or there is carbon monoxide present but the detector fails to detect it.
The probability of the detector failing to detect carbon monoxide when it is present (type-2 error) is 0.03, and the probability of the gas heater malfunctioning and releasing carbon monoxide is 0.000007.
So the probability of the detector failing to detect carbon monoxide when it is present is:
0.03 x 0.000007
= 0.00000021
The probability of there being no carbon monoxide present is 1 minus the probability that the gas heater malfunctions and releases carbon monoxide, which is:
1 - 0.000007
= 0.999993
Now,
So the overall probability of the detector not going off is the sum of the probabilities of these two events:
0.999993 + 0.00000021
= 0.99999321
Therefore,
The probability that the carbon monoxide detector will not go off is approximately 0.9998642 (rounded to 7 decimal places), which is option A.
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Triangle AABC, right angled at C, is given. Height and the median from point C form an angle y.
The measure of larger acute angle of AABC is:
A 45°-
B
C
D
60° +
90°
24
92
2
92
4
The measure of the larger acute angle of ΔABC is: α = 45° + φ/2. Option A.
How do you solve for the larger acute angle of ΔABC ?Let's denote the angles of triangle ΔABC as follows:
∠A = x
∠B = y
∠C = 90° (right-angled triangle)
Let D be the midpoint of AB, so CD is the median. Let E be the point on AB such that CE is the height from point C.
Since CD is the median, we know that angle ∠ECD = φ.
In right-angled triangle ΔCEB, we have:
∠CEB = 90° - y
Now, let's examine triangle ΔCED. We know that the sum of the angles in a triangle is 180°. Therefore:
∠CED + ∠CEB + ∠ECD = 180°
Substitute the known values:
∠CED + (90° - β) + φ = 180°
Since ∠CED and ∠A are supplementary angles, we can also write:
∠CED = 180° - x
Now substitute this value into the previous equation:
(180° - x) + (90° - y) + φ = 180°
Simplify the equation:
270° - x - y + φ = 180°
Subtract 90° from both sides:
180° - x - y + φ = 90°
From this equation, we get:
x + y = 90°
Substitute this value back into the equation involving φ:
180° - (90°) + φ = 90°
Simplify:
90° + φ = 90°
Therefore, the measure of the larger acute angle of ΔABC is:
x = 45° + φ/2 (option a)
the above answer is in response to the full question below;
Triangle ΔABC, right angled at C, is given. Height and the median from point C form an angle φ. The measure of larger acute angle of Δ ABC is:
a. 45⁰ + φ/2
b. 60⁰ + φ/2
c. 90⁰ - φ/2
d. 2φ
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Raman is watching the movie 4 times and he fislokw s the value wirh
Answer:learn how to spell :)
Step-by-step explanation:
Select the correct answer.
Which set of coordinates satisfies the equations x − 2y = -1 and 2x + 3y = 12?
A.
(1, 2)
B.
(3, 1)
C.
(3, 2)
D.
(-3, -2)
E.
(3, -2)
The set of coordinates that satisfy the equation are as follows:
(2, 3)
How to solve equation?The equation given is as follows:
x - 2y = -1
2x + 3y = 12
Therefore, let's find the set of coordinates that satisfies the equation. Hence,
x - 2y = -1
2x + 3y = 12
multiply equation(i) by 2
Hence,
2x - 4y = -2
2x + 3y = 12
Therefore, subtract the equations
7y = 14
divide both sides of the equation by 7
y = 14 / 7
y = 2
Let's find x as follows
x - 2y = -1
x = -1 + 2(2)
x = -1 + 4
x = 3
Therefore, the solution is (2, 3)
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Can someone help me in here please
The addition of the two matrix is [34 -12 -36 -18 58]
[-42 -8 16 30 8 ]
[ 24 34 4 34 23]
[-12 -32 -12 -42 -52]
What is the matrix addition?The addition of the matrix is calculated as follows;
The result to 4 multiplied by G is calculated as;
4[G] = [32 -20 -32 -8 40]
[-24 -28 4 36 8 ]
[ 16 24 12 28 20]
[-16 -12 0 -40 -36]
2[F] = [2 8 -4 -10 18]
[-18 20 12 -6 0 ]
[ 8 10 -8 6 3 ]
[4 -20 -12 -2 -16]
The addition of the two matrix is calculated as follows;
4[G] + 2[F] = [34 -12 -36 -18 58]
[-42 -8 16 30 8 ]
[ 24 34 4 34 23]
[-12 -32 -12 -42 -52]
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Let S be a collection of subset of {2000, 2001, 2002, …, 2020} such that intersection of any two sets in S is nonempty. What is the maximum cardinality of S?
The maximum cardinality of S is 20.
How to find the maximum cardinality ?To increase the number of subsets within S, our goal must be to find as many non-empty subset intersections as possible. This is achieved by constructing subsets that possess only one shared element. In this particular case, any two sets contained in the collection will include the element 2000 in their intersection causing it to become a valid subset.
Now, we shall investigate whether an additional subset can be added to S. If an extension exists without including 2000, its intersection with the previous 20 subsets would negligibly have no common elements and would hence not be regarded as a valid subset for addition into S.
As a result, a total of 20 subsets represent maximum cardinality for set S per these conditions.
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if a clock shows it is 3 o'clock, how could you describe the smaller angle made my the two hands of the clock? solve this problem any way you choose
The smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
What is an angle?A figure known as an angle is created by two rays or line segments that meet at a place known as the vertex of the angle. The sides or legs of the angle are other names for the rays or line segments.
According to question:To determine the smaller angle made by the two hands of a clock when it is 3 o'clock, we can use the following formula:
angle = |(11/2) * m - 30h|
where:
m is the number of minutes past the hour (in this case, since it is 3 o'clock, m = 0)
h is the hour (in this case, h = 3)
By using this formula, we get:
angle = |(11/2) * 0 - 30(3)| = |0 - 90| = 90
Therefore, the smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
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