A equals (x+3) and b equals (x-3) the statement that is true for the two division problems is that a equals factor (x+3) and b equals (x-3).
For the first division problem, [tex](x^2-3x-18)[/tex]÷(x-6), the quotient is (x+3). To solve for the quotient, you first need to factor the numerator, which is (x-6)(x+3). Then, you need to divide the numerator by the denominator, which is (x-6). The quotient is (x+3). For the second division problem, [tex](x^3-x^2-5x-3)/(x^2+2x+1)[/tex], the quotient is (x-3). To solve for the quotient, you first need to factor the numerator, which is (x+1)(x-3). Then, you need to divide the numerator by the denominator, which is [tex](x^2+2x+1)[/tex]. The quotient is (x-3). Therefore, the statement that is true for the two division problems is that a equals (x+3) and b equals (x-3).
Learn more about factor here
https://brainly.com/question/29128446
#SPJ1
What is the slope of a line that is perpendicular to the line represented by the equation x – y = 8? 1 −1 8
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]x-y=8\implies -y=-x+8\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-8\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 1 \implies \cfrac{1}{\underline{1}}} ~\hfill \stackrel{reciprocal}{\cfrac{\underline{1}}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1} \implies \text{\LARGE -1}}}[/tex]
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)
To learn more about dimensional:
https://brainly.com/question/27271392
#SPJ1
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:
A1=4,an+1=3an+12. Find the first five terms of the given sequence
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:
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.)
20) Jamie has 1.04 meters of wire to make bracelets. If each bracelet requires 13 cm, how
many bracelets can she make?
Therefore, Jamie can make 8 bracelets with 1.04 meters of wire.
What is perimeter?Perimeter is a measure of the distance around the edge of a two-dimensional object, such as a polygon, a circle, or a rectangle. It is the total length of all the sides or edges that make up the shape. In simple terms, perimeter is the length of the boundary of a flat object, such as the circumference of a circle, or the sum of the lengths of the sides of a polygon. It is usually measured in units such as meters (m), centimeters (cm), feet (ft), or inches (in).
Here,
Jamie has 1.04 meters of wire, which is equivalent to 104 cm (since 1 meter = 100 cm).
Each bracelet requires 13 cm of wire, so the number of bracelets she can make is:
Number of bracelets = Total length of wire ÷ Length of wire per bracelet
Number of bracelets = 104 cm ÷ 13 cm/bracelet
Number of bracelets = 8
To know more about perimeter,
https://brainly.com/question/30458422
#SPJ1
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
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]
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
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.
To know more about MANAGEMENT, visit:
https://brainly.com/question/29023210
#SPJ1
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:
.
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.
Read more about sequence at
https://brainly.com/question/30499691
#SPJ1
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.
To learn more about : confidence
https://brainly.com/question/29576113
#SPJ11
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
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.
To learn more about art project please click on below link.
https://brainly.com/question/901624
#SPJ1
a dilation of P centered at A maps P onto B. What dilation constant is needed?
The dilation is an enlargement, then k > 1. If the dilation is a reduction, then 0 < k < 1.
What is dilation constant?The dilation constant, also known as the scale factor, represents the amount by which the original figure is enlarged or reduced in the dilation.
Equation:We can find the dilation constant by using the distance formula. Let the coordinates of point P be (x,y) and the coordinates of point A be (a,b). Let the coordinates of point B be (u,v), where u and v are unknown.
The distance from A to P is:
d(AP) = √[(x-a)² + (y-b)²]
The distance from A to B is:
d(AB) = √[(u-a)² + (v-b)²]
Since the dilation is centered at A and maps P onto B, we know that the ratio of the distances is the dilation constant:
d(AP)/d(AB) = k
Substituting the expressions for the distances and simplifying, we get:
√[(x-a)² + (y-b)²] / √[(u-a)² + (v-b)²] = k
Squaring both sides, we get:
[(x-a)² + (y-b)²] / [(u-a)² + (v-b)²] = k²
Since we know the coordinates of P and A, we can substitute these values into the equation and solve for k. Once we have k, we can use it to find the coordinates of B.
Note that if the dilation is an enlargement, then k > 1. If the dilation is a reduction, then 0 < k < 1.
To know more about dilation, click here
https://brainly.com/question/30240790
#SPJ1
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:
PLEASE HELP!!
Dalia buys 20 collectible gems per month. Grace sells 10 gems from her collection of 120 each month. When will Dalia have more gems than Grace? Show your work.
After 4 months, Dalia will have the same number of gems as Grace, and after that, she will have more.
To determine when Dalia will have more gems than GraceWe need to find out when the number of gems Dalia has will exceed the number of gems Grace has.
Let's represent the number of months by "t".
After t months, Dalia will have 20t gems.
After t months, Grace will have 120 - 10t gems.
To find when Dalia will have more gems than Grace, we can set up an inequality:
20t > 120 - 10t
Simplifying the inequality, we get:
30t > 120
Dividing both sides by 30, we get:
t > 4
This means that Dalia will have more gems than Grace after 4 months.
To check our answer, we can substitute t = 4 into the expressions we found earlier:
After 4 months, Dalia will have 20t = 20(4) = 80 gems.
After 4 months, Grace will have 120 - 10t = 120 - 10(4) = 80 gems.
So, we can see that after 4 months, Dalia will have the same number of gems as Grace, and after that, she will have more.
Learn more about inequality here : brainly.com/question/11613554
#SPJ1
what is 3x10x30÷5
[tex].4[/tex]
Answer:
180
Step-by-step explanation:
3x10= 30
30/5 = 6
30 x 6 = 180
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
learn more about probability from
https://brainly.com/question/24756209
#SPJ1
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.
Learn more about function here:
brainly.com/question/2253924
#SPJ1
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]
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%
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.
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.
To know more about event, visit:
https://brainly.com/question/12961938
#SPJ1
The complete question is:
Image is attached below.
102m 25cm+15m 75cm=
help me
Answer:
118m
Step-by-step explanation:
102.25m+15.75m=118m
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
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:)
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) }.
To know more about number line visit,
https://brainly.com/question/24644930
#SPJ1