Answer:
x=7 and 1/6
Step-by-step explanation:
LOOK AT THE PICTURE! Because the transversal (line that goes through A and B) is straight, then:
(Angle C)+(20x+10)=180 deg
Angle C=(180 deg)-20x+10 deg
Angle C=170-20x
We know that 4x+2 is equal to angle C (marked in the picture) because of alternate interior angles are congruent theorem. So:
170-20x=4x+2
172=24x
x=7 and 1/6
As an experiment, a charity decides to use SMART to determine a shortlist from the seven applicants who have
applied for the post of Regional Officer for the Western Region. The main criteria which will be used to
compare candidates are: salary they would expect (SALARY), their experience of charity work (CHARITY EXP),
their managerial experience (MANAGEMENT EXP), their educational qualifications (EDUCATION), their
apparent commitment to the charity's work (COMMITMENT) and the quality of the ideas they put forward on
the form (IDEAS).
(a) Discuss if the weights of the attributes are appropriate. If so, why do you think so? If not, why do you
think the weights are not appropriate? (You don't need to discuss whether the attributes are
appropriate. Only focus on the "weights". This is your own opinion and subjective. You don't need
references for this.)
The personnel manager ranked all the criteria, except salary, in order of importance and then assigned weights
as follows:
COMMITMENT
MANAGEMENT EXP
IDEAS
CHARITY EXP
EDUCATION
Candidate A's aggregated score is 50.
(You don't need to worry about how 50 was calculated.)
The other candidates' aggregated scores are found below.
100
70
65
55
10
The weights assigned to attributes seem appropriate based on the personnel manager's ranking according to of importance. The weights reflect the relative importance of each attribute in the decision-making.
Why is commitment given the highest weight?For example, COMMITMENT is given the highest weight, indicating that the charity places a lot of value on a candidate's commitment to their work. MANAGEMENT EXP and IDEAS are given the next highest weights, indicating that the charity values a candidate's ability to manage and come up with innovative ideas.
On the other hand, EDUCATION is given the lowest weight, indicating that the charity places less emphasis on formal qualifications than on other attributes such as experience and commitment.
The aggregated score for Candidate A is 50, but we don't have any information about the scale or method used to calculate the scores. Therefore, we cannot comment on whether the score is good or bad or whether Candidate A is the best choice for the job.
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You have 9 apples and 7 oranges in a basket. You take randomly 3
items from the basket. What is the probability that you selected 1 apple and 2 oranges?
Please write your answer as a decimal. Round your answer to three decimal places.
Answer:
0.337 or about 33.7%
Step-by-step explanation:
The number of ways to choose 1 apple out of 9 is:
C(9, 1) = 9! / (1! * (9 - 1)!) = 9
The number of ways to choose 2 oranges out of 7 is:
C(7, 2) = 7! / (2! * (7 - 2)!) = 21
So the total number of ways to choose 1 apple and 2 oranges is:
9 * 21 = 189
The total number of ways to choose 3 fruits out of 16 is:
C(16, 3) = 560
Therefore, the probability of selecting 1 apple and 2 oranges is:
189 / 560 ≈ 0.337 or about 33.7%
Tests show that the lives of light bulbs are
normally distributed with a mean of 750 hours
and a standard deviation of 75 hours. Find
the probability that a randomly selected light
bulb will last between 675 and 825 hours.
675 750 825 900 975
P = [? ]%
Hint: use the 68-95 99.7 rule.
525 600
Enter
the probability that a randomly selected light bulb will last between 675 and 825 hours is 68.26%, or 0.6826.
Define probabilityProbability is a measure of the likelihood of an event occurring. It is a numerical value that ranges from 0 to 1, where 0 represents an impossible event and 1 represents a certain event. A probability of 0.5 (or 50%) means that the event is equally likely to occur as not occur.
To solve this problem, we can use the standard normal distribution with a mean of 0 and a standard deviation of 1, and then convert the given values to z-scores using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
For the lower value of x (675 hours), the z-score is:
z = (675 - 750) / 75 = -1
For the upper value of x (825 hours), the z-score is:
z = (825 - 750) / 75 = 1
We can then use a standard normal distribution table or calculator to find the probabilities associated with these z-scores:
P(z < -1) ≈ 0.1587
P(z < 1) ≈ 0.8413
The probability of a randomly selected light bulb lasting between 675 and 825 hours is then:
P(-1 < z < 1) = P(z < 1) - P(z < -1) ≈ 0.8413 - 0.1587 ≈ 0.6826
Therefore, the probability that a randomly selected light bulb will last between 675 and 825 hours is approximately 68.26%, or 0.6826 as a decimal.
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The complete question is:
Image is attached below.
Find the quotient of 6x³-18x²-12x
-6x
-x²-3x - 2
x²-18x-12
-x²+18x-12
−x² + 3x + 2
Answer:
The answer is: −x² + 3x + 2
Step-by-step explanation:
divide the whole expression by -6x
then you get: −x² + 3x + 2
due today, ill mark brainliest!!!
Isla flipped a coin 30 times. The coin landed heads up 9 times and tails up 21 times.
Part A: Based on the results, what is the experimental probability of the coin landing heads up? Show your work. (5 points)
Part B: What is the theoretical probability of the coin landing heads up? Show your work. (5 points)
Answer:
Part A.) 0.3 or 30%
Part B.) 0.5 or 50%
She flipped the coin 30 times.
She flipped it 9 times for heads.
She flipped it 21 times for tails.
Part A.)
9/30
When you simplify that you get 3/10.
Which is 0.3 or 30%
Part B.)
So there are only 2 sides of a coin.
Heads or tails, So its a 50 - 50
For One side it is 50/100
Which simplifies to 1/2
Or 0.5 which is 50%
Step-by-step explanation:
If the store receives a new shipment of 20 car batteries, (we don't know this, but) 5 of them are faulty, and we selected 2 car batteries at random, then what is the probability that;
A. both of them are good batteries?
B. one battery is good while one battery is bad?
c. both batteries are bad?
a. The probability that both of them are good is 9/16
b. Probability that one battery is good while one 3/16
c. probability that both batteries are bad is 1/16
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.
Probability = sample space / total outcome
the sample space for bad batteries = 5
the sample space for good batteries = 15
Therefore
a. probability that both are good = 15/20 × 15/20 = 3/4 × 3/4 = 9/16
b. probability that a battery is good and the other is bad = 15/20 × 5/20
= 3/4 × 1/4 = 3/16
c. The probability that both are bad
= 5/20 × 5/20 = 1/4 × 1/4 = 1/16
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81^3/4 / 81^1/2 =
A. (81/3)^ -1/2
B. 27
c. 9
d. 3
x^2 =−8x−7 solve by rewriting the square
I HOPE THIS HELPS
x=−7
x=−1
x
2
=−8x−7
Add 8x to both sides.
x
2
+8x=−7
Add 7 to both sides.
x
2
+8x+7=0
To solve the equation, factor x
2
+8x+7 using formula x
2
+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.
a+b=8
ab=7
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.
a=1
b=7
Rewrite factored expression (x+a)(x+b) using the obtained values.
(x+1)(x+7)
To find equation solutions, solve x+1=0 and x+7=0.
x=−1
x=−7
Please anyone explain
Find zα/2 for the 99% confidence interval.
Find zα/2 for the 94% confidence interval.
The 99% confidence interval, zα/2 ≈ 2.576 and for the 94% confidence interval, zα/2 ≈ 1.88.
Hi! To find the zα/2 value for both the 99% and 94% confidence intervals, we will use the standard normal distribution table or a calculator with a z-score function.
For a 99% confidence interval, the area between the two tails (α) is 1 - 0.99 = 0.01. We need to find the value that corresponds to an area of 0.01/2 = 0.005 in each tail. Looking up this value in a standard normal distribution table or using a calculator, we get zα/2 ≈ 2.576.
For a 94% confidence interval, the area between the two tails (α) is 1 - 0.94 = 0.06. We need to find the value that corresponds to an area of 0.06/2 = 0.03 in each tail. Looking up this value in a standard normal distribution table or using a calculator, we get zα/2 ≈ 1.88.
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The triangular prism has a volume of 252 yd³. What is the height, h, of the prism?
Answer:
The height of the prism is 9yd.
Step-by-step explanation:
The volume of the prism is
Vol
= BaseArea×height
The area of the base is the area of the triangle.
Area_triangle
= 1/2 b•h
= 1/2•8•7
= 28
28 is the BaseArea of the prism.
Again the volume of the prism is:
Vol = BaseArea•h
This h is the height of the prism. That is what we are looking for.
Fill in what we know or calculated already.
252 = 28•h
Divide by 28
9 = h
The height of the prism is 9yd.
Twice the difference of a number and 4 is 7
Answer:
Step-by-step explanation: Twice means x2
Difference means subtract
A number is a unknown value so you put a variable
(Z - 4) x 2= 7
3.5 x 2= 7
(7.5 - 4) x 2= 7
Question
The average daily balance of a credit card for the month of January was $800, and the unpaid balance at the end of the
month was $900. If the monthly interest rate is 2.0% of the average daily balance, what is the total balance on the next
billing date February 1? Round your answer to the nearest cent. Do not use commas to separate numbers or dollar signs.
For example, $5, 678.00 should be entered as 5678.00.
Answer:
Necesito puntos, lo siento, no puedo ayudarlo con la pregunta, solo informe esto y elimínelo o lo que sea
Step-by-step explanation:
A football player waiting to receive a kickoff stands at point B as the kicker, at point A, attempts to kick it 55 yd to him. The kicked ball travels a bit off course and travels 63 yd at an angle of 6 to the right of the receiver, as shown in the figure (point C). Find the distance the receiver must run to catch the ball to the nearest yard. Please show all work for full credit.
Answer:
Step-by-step explanation:
draw a number line and mark the points that represents all the numbers described if possible. Positive Numbers.
The cοrrect answer is x > 0 and x < (- 3) where x is any number οn the number line.
A number line is a οne dimensiοnal graph (rather an endless straight line) οn which οne can represent every pοssible real number. Usually we have zerο serving as the center οf the number line, with the right hand side serving as the pοsitive part οf the real line and the left hand side as the negative part οf the real line.
A number line is endless which implies there is nο bοund tο a number line.
Any number οn the real line is denοted by a dark spοt οn the real line. Fοr example if οne needs tο denοte 3 οn the real line he/she has tο mark 3 with a spοt.
There are three kind οf intervals that can be represented οn the number line namely clοsed [ ] , οpen ( ) and semi-clοsed οr semi- οpen [ ) οr ( ]. Intervals οn number line are being shοwn by thickening that part οf the real line that are under cοnsideratiοn.
Fοr example: (4 , 5) is representing by thickening the number line between 4 and 5 with οpen ends , i.e. circles οn digit 4 and 5.
[4 , 6] is represented by thickening the number line between 4 and 6 with clοsed οr black dοt ends.
Similarly semi οpen and semi clοsed intervals are represented by thickening the interval between thοse twο pοints with apprοpriate circles and dοts οn the endpοints.
Accοrding tο the given questiοn we need tο mark all described pοints that are pοsitive. Thus all pοints greater than zerο are tο be thickened (excluding zerο). This is dοne by having an οpen end οn pοint zerο and thickening the whοle οf the right hand side οr the pοsitive side οf the number line.
Similarly tο represent all described pοints οn the number line less than ( -3) (excluding ( - 3)) can be dοne by having an οpen end οn pοint ( - 3) and thickening the whοle οf the negative side tο the left οf ( - 3).
Thus to represent all the required points we can write them in a set A as:
A = { x : x > 0; x < ( - 3) }.
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Mary works in an office and her current salary is £28,500.
Mary has been successful in applying for a new role in the company and will receive a pay increase of 2/9.
What will Mary's new salary be after the pay increase? Give your answer correct to 2 decimal places.
Answer:
34833,33 £
Step-by-step explanation:
First, we need to find how much will her sallary increase:
[tex] \frac{28500 \times 2}{9}≈ 6333.33[/tex]
And now we add this number to her old salary:
28500 + 6333,33 = 34833,33 £
Todd is traveling to Mexico and needs to exchange $360 into Mexican pesos. If each dollar is worth 12.29 pesos, how many pesos will he get for his trip?
Answer: 4424.4 pesos
Step-by-step explanation:
To convert dollars to pesos, we need to multiply the number of dollars by the exchange rate:
360 dollars x 12.29 pesos/dollar = 4424.4 pesos
Therefore, Todd will get 4424.4 pesos for his trip to Mexico.
34.59 + ? = 136.926 i need whyyy
[tex] \: \: \: \: \: \texttt{34.59 + \boxed{\texttt\red{102.336}}} \\ \texttt{ = 136.926}[/tex]
[tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps:)
The circumference of a circle is 18 inches. What is the radius?
C=18 in
Answer: 2.86 (2 d.p.)
Step-by-step explanation:
The formula for the circumference of a circle is C = πd = 2πr
Substitute 18 for C in the equation
18 = 2πr
Rarrange for r
r = 18 / 2π = 2.86 (2 d.p.)
A woman leaves at 7 AM and drive to New York City 200 miles away. If she averages 50 mph what time will she arrive at the city?
The woman will arrive in New York City at 11 AM.
Plane takeoff angle.
Angel
During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 10 km. The distance the plane flies during take off should be in the range 57 km to 62 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d. p.
Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:
tan(θ) = 10/x
We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.
Plugging this into the equation above, we get:
tan(θ) = 10/62
θ = arctan(10/62) ≈ 8.8°
Therefore, the smallest possible angle that the path of the plane could make with the ground is approximately 8.8 degrees.
Angel
Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.
Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary
Let's assume that the distance from Xochitl to point A is d1 and the distance from Xochitl to point B is d2. We want to find the distance the plane traveled from point A to point B, which is the difference between d1 and d2.
From the given information, we can set up the following two equations:
tan(19°) = 7425/d1
tan(37°) = 7425/d2
Solving for d1 and d2, we get:
d1 = 7425/tan(19°) ≈ 22977.6 feet
d2 = 7425/tan(37°) ≈ 13060.2 feet
Therefore, the distance the plane traveled from point A to point B is:
d1 - d2 ≈ 9917.4 feet ≈ 3021 meters
Rounding to the nearest foot, we get that the distance the plane traveled from point A to point B is approximately 9917 feet.
Angel
Plane B is flying 75mph 75 mph faster than Plane A. Find the time it takes for Plane A to travel 2300 2300 miles if it takes Plane B the same amount of time to travel 2600 2600 miles.
Let's start by using the formula for distance, rate, and time:
distance = rate x time
Let's assume that Plane A's speed is r mph. Then we know that Plane B's speed is r + 75 mph.
We also know that Plane A travels 2300 miles and Plane B travels 2600 miles. Since they take the same amount of time to travel their respective distances, we can set up the following equation:
2300/r = 2600/(r + 75)
To solve for r, we can cross-multiply and simplify:
2300(r + 75) = 2600r
2300r + 172500 = 2600r
300r = 172500
r = 575 mph
Now that we know Plane A's speed, we can use the formula for distance, rate, and time to find the time it takes for Plane A to travel 2300 miles:
distance = rate x time
2300 = 575 x time
time = 4 hours
Therefore, it takes Plane A 4 hours to travel 2300 miles.
Angel
A woman leaves at 7 AM and drive to New York City 200 miles away. If she averages 50 mph what time will she arrive at the city?
To determine the arrival time of the woman in New York City, we need to use the formula for time:
time = distance / rate
In this case, the distance is 200 miles and the rate (or speed) is 50 mph. Plugging these values into the formula, we get:
time = 200 miles / 50 mph = 4 hours
Since the woman left at 7 AM, we can simply add the travel time of 4 hours to the departure time to get the arrival time:
7 AM + 4 hours = 11 AM
Therefore, the woman will arrive in New York City at 11 AM.
what is 3x10x30÷5
[tex].4[/tex]
Answer:
180
Step-by-step explanation:
3x10= 30
30/5 = 6
30 x 6 = 180
square root of 98 / simplify
Answer:
[tex] \sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \sqrt{2} = 7 \sqrt{2} [/tex]
What’s the answer to this question and how to do it? Please answer quick as I’m studying for my geometry eoc in May
Answer:
5cm because you have to round off to the nearest 1000
HELPPP PLEASEEEE
The circle has center P.
A
P
E
16
C
(4x + 7)° B
D
(5x − 5)°
Solve for X
X=
Find CD
CD=
SHOW WORK PLEASEEEEEEEE
Rectangle ABCD has diagonals AC and BD that converge at point O and
OA = 5x-7, OD = 4x-5.
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X
Hence, Rectangle ABCD has diagonals AC and BD that converge at point O and
OA = 5x-7, OD = 4x-5.
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pythagorean theorem
find the value of x
Answer:
x = 35.8
Step-by-step explanation:
[tex]x = 2 \sqrt{ {14}^{2} - {11.2}^{2} } + 19 [/tex]
[tex]x = 2(8.4) + 19 [/tex]
[tex]x = 16.8 + 19 = 35.8[/tex]
Janelle;s art project requires her to use exactly 4 different colors of paint. How many ways
can she choose the 4 colors from 10 available colors?
There are 210 ways that Janelle can choose 4 colors from 10 available colors for her art project.
Janelle needs to choose 4 colors out of 10 available colors for her art project. The order in which she chooses the colors does not matter. We can use the combination formula to determine the number of ways she can choose 4 colors from 10 available colors:
nCr = n! / r!(n - r)!
where n is the total number of colors available, r is the number of colors Janelle needs to choose, and ! denotes the factorial operation.
In this case, we have:
n = 10 (total number of colors available)
r = 4 (number of colors Janelle needs to choose)
Substituting these values into the formula, we get:
10C4 = 10! / 4!(10 - 4)!
= 10! / 4!6!
= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)
= 210
Therefore, for her art assignment, Janelle can select 4 colors from a palette of 10 in 210 different ways.
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A cone has a radius of meters and a height of meters. What is the volume of the cone to the nearest cubic meter? Use for .
Therefore, the volume of the cone to the nearest cubic meter is approximately 333 cubic meters.
What's volume?Volume is a measure of the quantum of three- dimensional space enthralled by an object, substance, or region of space. It's frequently measured in boxy units similar as boxy measures, boxy bases, or liters. The volume of an object can be calculated using its confines similar as length, range, and height, or by relegation styles where the volume of the object is determined by the quantum of fluid it displaces when submerged in a liquid. The conception of volume is used in numerous areas of wisdom, engineering, and everyday life, similar as measuring the capacity of holders, determining the quantum of fluid in a force, or calculating the size of a room.
by the question.
To find the volume of a cone, we can use the formula:
[tex]V = (1/3) * π * r^2 * h[/tex]
where V is the volume, r is the radius, and h is the height.
Plugging in the given values, we get:
[tex]V = (1/3) * π * (meters)^2 * (meters)[/tex]
V ≈ 333.33 cubic meters (rounded to the nearest cubic meter)
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Rochelle deposits $4,000 in an IRA. What will be the value (in dollars) of her investment in 25 years if the investment is earning 8% per year and is compounded continuously? (Simplify your answer completely. Round your answer to the nearest cent.)
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 4000e^{0.08\cdot 25} \implies A=4000e^2\implies A \approx 29556.22[/tex]
Y=x-8 and 2x-2y = 16 EMERGENCY Substitution Method
Answer:
infinite number of solutions
Step-by-step explanation:
y = x - 8 → (1)
2x - 2y = 16 → (2)
substitute y = x - 8 into (2)
2x - 2(x - 8) = 16
2x - 2x + 16 = 16 ( subtract 16 from both sides )
0 = 0 ← true statement
this true statement indicates the system has an infinite number of solutions
Taxable income Tax on income
$0–$18 200 Nil
$18 201–$37 000 19c for each $1 over $18 200
she was paid a gross salary of $18 700. How much tax should she pay?
$
Answer: First, we need to calculate the taxable income, which is the gross salary minus the tax-free threshold of $18,200:
Taxable income = Gross salary - Tax-free threshold
Taxable income = $18,700 - $18,200
Taxable income = $500
Since the taxable income falls within the range of $18,201-$37,000, we can use the tax rate of 19c for each $1 over $18,200 to calculate the amount of tax payable:
Tax on income = (Taxable income - $18,200) × 0.19
Tax on income = ($500 - $18,200) × 0.19
Tax on income = -$3,382 × 0.19
Tax on income = -$642.58 (rounded to the nearest cent)
However, the calculated tax is negative, which means that the person is entitled to a tax refund as they have paid more tax than they are required to. This can happen if they have been working for only part of the financial year, or if they have had tax withheld at a higher rate than necessary.
Step-by-step explanation:
.
Find the first five terms of the geometric sequence
The first five terms of the sequence with a = 3 and r = -2 are: 3, -6, 12, -24, 48.
Finding the first five terms of the geometric sequenceThe general formula for a geometric sequence is given by:
an = a * r^(n-1)
where "a" is the first term, "r" is the common ratio, and "n" is the number of the term we want to find.
In this case, we have:
a = 3
r = -2
So the first term is 3, and the common ratio is -2. We can use the formula above to find the first five terms of the sequence:
a1 = 3
a2 = 3 * (-2)^(2-1) = -6
a3 = 3 * (-2)^(3-1) = 12
a4 = 3 * (-2)^(4-1) = -24
a5 = 3 * (-2)^(5-1) = 48
Therefore, the first five terms of the geometric sequence with a = 3 and r = -2 are: 3, -6, 12, -24, 48.
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