There are 168 different area codes possible with this plan by using the multiplication principle of counting.
What is multiplication principle ?
The multiplication principle of counting, also known as the rule of product, is a counting principle in combinatorics that states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
There are 7 possible choices for the first digit (0 through 6), 3 possible choices for the second digit (2, 3, or 4), and 8 possible choices for the third digit (any digit except 0 or 3). To find the total number of possible area codes, we can use the multiplication principle of counting:
Total number of area codes = Number of choices for first digit x Number of choices for second digit x Number of choices for third digit
Total number of area codes = 7 x 3 x 8
Total number of area codes = 168
Therefore, there are 168 different area codes possible with this plan.
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Need help in Qa, Qc, Qe and Qf.
With workings for each of the following please, Thank you!!
Step-by-step explanation:
A:(x+6)^2-36
The rest of the answers are at the top just identify the form your looking for.
PLEASE HELP, TURNING IN LATE AND IM CONFUSED
Answer:
The answer should be P'(-3,-7), Q(-9,3), and R'(-4,1) which is D.
Step-by-step explanation:
Below is the graph of equation y = -|x − 2 | +2. Use this graph to find all values of x
for the given values of y
If y = 3, we can see that there are again two values of x that satisfy the equation: x = 0 and x = 4. This is because the graph intersects the horizontal line at y = 3 at two points.
What is equation of graph?A mathematical statement used to describe the relationship between the variables that make up a graph is called an equation.
To put it another way, a graph equation is a formula that can be applied to either build the graph or identify certain points on the graph.
Using the graph of the equation y = -|x - 2| + 2, we can find all the values of x for a given value of y by looking at where the graph intersects the horizontal line at y.
For example, if y = 1, we can see from the graph that there are two values of x that satisfy the equation: x = 3 and x = 1. This is because the graph intersects the horizontal line at y = 1 at two points.
If y = 2, we can see that there is only one value of x that satisfies the equation: x = 2. This is because the vertex of the absolute value function is at (2, 2), and the graph is reflected below the x-axis, so it only intersects the horizontal line at y = 2 at one point.
We can repeat this process for any value of y to find the corresponding values of x that satisfy the equation.
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(a) Consider a t distribution with 15 degrees of freedom. Compute P(t2-1.34). Round your answer to at least three
decimal places.
P(t≥-1.34) =
(b) Consider a t distribution with 13 degrees of freedom. Find the value of c such that P(-c
answer to at least three decimal places.
=0
C=
The probability from the t distribution is 0.8999 and the value of c is 1.77
Calculating the probability from the t distributionFrom the question, we have the following parameters that can be used in our computation:
Degrees of freedom = 15
Using a graphing calculator, we have
P(t ≥ -1.34) = 1 - 0.1001
So, we have
P(t ≥ -1.34) = 0.8999
Calculating the value of c, we have
P(-c < t < c) = 0.95
At a degree of freedom of 13, we have
c = 1.77
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The taxes on a house assed at 110,000 are 2970
Answer:
$3267
Step-by-step explanation:
$121000 × $2970/$110000
= 11 × 297
= $3267
The taxes on the house with an assessment of $121000 are $3267
Answer:
$3267
Step-by-step explanation:
You want to know the taxes on a house assessed at $121000 if the taxes on a house assessed at $110000 are $2970.
ProportionThe taxes are proportional to the house value, so if the house value goes up by a factor of 121000/110000, so do the taxes. The taxes will be ...
(121000/110000)·$2970 = $3267
The taxes on the house with an assessment of $121,000 are $3267.
__
Additional comment
You could go to the trouble to find the tax rate, which is ...
rate = $2970/$110000 = 0.027
This can be described as 27 mils, 27‰, or $27 per thousand.
Multiplying this rate by the higher assessed value shows the taxes are ...
0.027 × $121000 = $3267
We don't really need to know the tax rate. All we need to know is that the house with the 10% higher value will have 10% higher taxes.
When the mortgage is completely paid off for Mark and Lynne’s house, it will be 4 times as old as it is now. If they have 18 years left on the mortgage, how old is the house right now?
h = how old the house is right now
so right now Mark and Lynne are paying the house off, the house as we speak is "h" years old, it happens that Mark and Lynne are going to be paying the whole house in 18 years from now, so by then the house will be whatever years is now, or "h", plus 18 years, so when Mark and Lynne are done paying for it, the house will be "h + 18" years old.
Now, if the house in 18 years is going to be 4 times as old as it's right now, well, hell right now is "h" years old, 4 times that much is just "4h" years, so we can say
[tex]\stackrel{\textit{18 years from now}}{h+18}~~ = ~~\stackrel{\textit{18 years from now}}{4h}\implies 18=3h\implies \cfrac{18}{3}=h\implies 6=h[/tex]
_ + 46 =231 what is the answer
Answer: 185
Step-by-step explanation:
231-46=185
Answer: 185
Step-by-step explanation:
231-46
9 equals d/3 what number is d
Answer: d = 27
Step-by-step explanation:
To solve, we will isolate the variable d.
Given:
9 = [tex]\frac{d}{3}[/tex]
Multiply both sides of the equation by 3:
27 = d
Reflexive property:
d = 27
Which choice is equivalent to the quotient shown here when x > 0?
√22x6 = √11x4
x√2 is the quotient of √22x⁶÷√11x⁴, √22x⁶ is dividend and √11x⁴ is divisor
The number which is getting divided here is called the dividend.
The number which divides a given number is the divisor.
The number which we get as a result is known as the quotient.
We have to find the quotient of √22x⁶÷√11x⁴
√22x⁶/√11x⁴
√22x⁶ is dividend.
√11x⁴ is divisor
√2√11 x³/√11 x²
x√2 is the quotient.
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Compute the compound amount and the interest on a loan of $10800 compounded annually for four years at 10%. Use the $1.00 future value table or the future value and compound interest formula.
Answer:
$5,149.44
Step-by-step explanation:
To calculate the compound amount and interest on a loan of $10800 compounded annually for four years at 10%, we can use the formula:
A = P(1 + r)^t
where A is the compound amount, P is the principal (the initial loan amount), r is the interest rate (as a decimal), and t is the number of years.
In this case, P = $10800, r = 0.10 (10% as a decimal), and t = 4. Substituting these values into the formula, we get:
A = $10800(1 + 0.10)^4
A = $10800(1.10)^4
A = $15,949.44
Therefore, the compound amount after four years is $15,949.44.
To calculate the interest, we can subtract the principal from the compound amount:
Interest = $15,949.44 - $10,800
Interest = $5,149.44
Therefore, the interest on the loan is $5,149.44.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10800\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A = 10800\left(1+\frac{0.10}{1}\right)^{1\cdot 4} \implies \boxed{A = 15812.28} ~\hfill \underset{ earned~interest }{\stackrel{ 15812~~ - ~~10800 }{\boxed{5012}}}[/tex]
Austin opened a savings account and deposited $600.00 as principal. The account earns 5% interest, compounded annually. What is the balance after 8 years?
Answer:
$886.47
Step-by-step explanation:
4t(t^2−6t+2)4t(t2−6t+2)
Answer:
16t⁶ - 192t⁵ + 640t⁴ - 384t³ + 64t²
Step-by-step explanation:
1. Multiply the numbers
2. Combine exponents
3. Combine exponents
4. Expand the square
5. Distribute
6. Distribute
7. Distribute
8. Distribute
9. Combine like terms
10. Combine like terms
11. Combine like terms
12. Distribute
A card is drawn at random from a standard deck of playing cards (no jokers). If the card is a diamond, the player wins $5; if it is not a diamond, the player loses $2.
Answer:
Step-by-step explanation:
To find the expected value of the game, we need to multiply the value of each outcome by its probability, and then add up the results. Let's first calculate the probabilities of drawing a diamond and not drawing a diamond:
P(diamond) = 13/52 = 1/4
P(not diamond) = 1 - P(diamond) = 3/4
Now we can calculate the expected value of the game:
E = (5)(P(diamond)) + (-2)(P(not diamond))
E = (5)(1/4) + (-2)(3/4)
E = 5/4 - 6/4
E = -1/4
The expected value of the game is -$0.25. This means that, on average, the player can expect to lose 25 cents per game in the long run.
Fill in the missing values to make the equations true.
answer:
a. 7/8
b.9
c.9
explanation:
I'm confused need help
Check the picture below.
i need to find the center of these two shapes
In the figure given, rotation is the only single transformation that takes shape A to shape B.
What is transformation in Math?A function, f, that maps to itself is called the transformation, i.e., f: X → X. The pre-image X becomes the image X after the transformation. This transformation can be any or the combination of operations like translation, rotation, reflection, and dilation. The translation is moving a function in a specific direction, rotation is spinning the function about a point, reflection is the mirror image of the function, and dilation is the scaling of a function. Transformations in Math describe how two-dimensional figures move around a coordinate plane.
In this problem, the only single transformation that will make the figure A turn into figure B is rotation. This is only one of the four transformation techniques which are rotation, reflection, dilation and translation and in this case, only rotation is mentioned.
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In the diagram below, P is a point inside square ABCD. Find x.
The length of AB, x is 2.414 units.
Let's call the length of the square's side x. Then, the hypotenuse of each triangle is the diagonal of the square, which has length x√2.
Let's consider one of these triangles, say triangle APC. We can use the Pythagorean theorem to find the length of PC:
PC² = AP² + AC²
PC² = 1² + x²
PC = √(1+x²)
Since triangle APC is isosceles, we know that angle APC is 45 degrees. Therefore, angle CPB is also 45 degrees, since it is the supplement of angle APC. Similarly, angle BPC is 90 degrees, since it is the sum of angles CPB and BPA.
We can now use the sine rule in triangle BPC to find the length of BP:
sin(BPC) / BP = sin(CPB) / x√2
sin(90°) / BP = sin(45°) / x√2
BP = x / √2
Since AP = BP = CP = 1, we have:
1 + x / √2 + √(1+x²) = x
Solving this equation for x gives:
x ≈ 2.414
Therefore, the length of AB is approximately 2.414 units.
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convert pi/8 radian to degrees
Answer:
the formula is:
degrees = radians x 180/π
Therefore, to convert π/8 radians to degrees, we have:
degrees = (π/8) x 180/π
degrees = 22.5°
So, π/8 radians is equal to 22.5 degrees.:)
The value of π/8 into degree is, 22.5 degrees.
We have to given that,
Convert pi/8 radian to degrees
Since, We know that,
the formula is:
Degrees = Radians x 180/π
Hence, to convert π/8 radians to degrees, we have:
Degrees = (π/8) x 180/π
degrees = 22.5°
So, π/8 radians is equal to 22.5 degrees.
Therefore,
The value of π/8 into degree is, 22.5 degrees.
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Graph 2 4/5, -2/5, -1 1/7, and 7/6 on a number line.
Answer:
trying not to get too much
Step-by-step explanation:
j and
3x^2+16x+20 vertex form
Answer:
the vertex form of the given quadratic expression is:
y = 3(x + 8/3)^2 - 4/3
Step-by-step explanation:
To write the given quadratic expression 3x^2+16x+20 in vertex form, we need to complete the square.
Step 1: Factor out the coefficient of x^2:
3(x^2 + (16/3)x) + 20
Step 2: Take half of the coefficient of x and square it:
(16/3)/2 = 8/3
(8/3)^2 = 64/9
Step 3: Add and subtract the result from step 2 inside the parentheses:
3(x^2 + (16/3)x + 64/9 - 64/9) + 20
Step 4: Simplify inside the parentheses and factor:
3[(x + 8/3)^2 - 64/9] + 20
Step 5: Simplify the constant term:
3(x + 8/3)^2 - 4/3
Therefore, the vertex form of the given quadratic expression is:
y = 3(x + 8/3)^2 - 4/3
Sur un catalogue, les dimensions de l'image à l'échelle, d'un tapis rectangulaire, sont 12cm sur 20cm.
Nadine a acheté ce tapis et elle mesure la petite dimension, qui est de 2,4 m.
a) Quelle est l'échelle du plan ?
b) Quelle est la longueur de la grande dimension du tapis?
Answer:
b have a great day today and look in comments
A small manufacturing company makes $125 on each stereo sound bar produces, and $100 profit on each flatscreen TV it makes. Each sound bar and TV must be processed by cutting machine (A), a fitting machine (B), and a polishing machine(C). Each sound bar must be processed on machine A for one hour, machine B for one hour, and machine C for four hours. Each TV must be processed or machine A for two hours, Machine B for one hour, and machine C for one hour. Machine A is available for 16 hours machine B 49 machine C for 24 hours.
The optimal solution is to produce 4 stereo sound bars and 8 flatscreen TVs, which will result in a profit of $1800.
Define profit ?
Profit is the financial gain that is earned by a business or an individual after deducting all the expenses incurred.
Let's represent the number of sound bars produced by "x" and the number of flatscreen TVs produced by "y."
The objective function for profit can be represented as:
Profit = 125x + 100y
The constraints can be represented by the availability of each machine:
Machine A: 1x + 2y ≤ 16
Machine B: 1x + y ≤ 49
Machine C: 4x + y ≤ 24
Also, the number of sound bars and flatscreen TVs produced must be non-negative:
x ≥ 0 and y ≥ 0
To solve the feasible region using graphical method, we need to plot the constraints and find the intersection points.
First, let's plot the constraint equations:
A: x + 2y <= 16
B: x + y <= 49
C: 4x + y <= 24
To plot each constraint, we need to find two points that satisfy the equation. Then, we can draw a straight line passing through those two points.
For constraint A:
When x = 0, y = 8
When y = 0, x = 16
So the line for constraint A passes through (0,8) and (16,0).
For constraint B:
When x = 0, y = 49
When y = 0, x = 49
So the line for constraint B passes through (0,49) and (49,0).
For constraint C:
When x = 0, y = 24
When y = 0, x = 6
So the line for constraint C passes through (0,24) and (6,0).
Now, let's plot these lines on a graph and find the feasible region.
The feasible region is the shaded area that satisfies all three constraints. We can see that it is a triangle with vertices at (0,0), (6,0), and (4,8).
Therefore, the optimal solution will be at one of the vertices.
At vertex (0,0):
Profit = 0
At vertex (6,0):
Profit = 125(6) + 0(0) = 750
At vertex (4,8):
Profit = 125(4) + 100(8) = 1800
So the optimal solution is to produce 4 stereo sound bars and 8 flatscreen TVs, which will result in a profit of $1800.
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ABC Insurance offers an annuity with a minimum interest rate of 3.5% APR for the *
next 5 years. You decide to invest $2000 into this account. What type of annuity is
this?
OSingle-payment fixed annuity
OSingle-payment variable annuity
ORecurring-payment fixed annuity
O Recurring-payment recurring annuity
Answer:
Single payment Variable annuity
The diagram represents the net of a triangular prism. Calculate the TOTAL surface area for the image below using the net.
The total surface area of the triangular prism using the net is 640 square meters
Calculating the total surface area using the net.From the question, we have the following parameters that can be used in our computation:
The net of a triangular prism
The surface area of the triangular prism from the net is calculated as
Surface area = sum of areas of individual shapes that make up the net of the triangular prism
Using the above as a guide, we have the following:
Area = 2 * 8 * 17 + 8 * 16 + 2 * 1/2 * 15 * 16
Evaluate
Area = 640
Hence, the surface area is 640 square meters
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A train track through a mountain is 1600 feet long and makes an angle of 1.1 with the horizontal. What is the change in elevation from one end of the tunnel to the other?
Answer:
Please mark me the brainliest. It took me a lot of time to answer this question.
Step-by-step explanation:
To solve this problem, we can use trigonometry. We know that the length of the train track through the mountain is 1600 feet and that the angle it makes with the horizontal is 1.1. Let's call the change in elevation from one end of the tunnel to the other "h".
We can use the tangent function to find "h", which is defined as the opposite side (the change in elevation) divided by the adjacent side (the length of the train track through the mountain). In this case, the tangent of the angle 1.1 is equal to h divided by 1600:
tan(1.1) = h/1600
To solve for "h", we can multiply both sides by 1600:
h = 1600 * tan(1.1)
Using a calculator, we can find that tan(1.1) is approximately 0.0192. Therefore:
h = 1600 * 0.0192
h = 30.72 feet
So the change in elevation from one end of the tunnel to the other is approximately 30.72 feet.
Enter a number for y. Approximate to THREE decimal places (last digit should be 8). Thanks in advance!
Answer:
Step-by-step explanation:
try adding 18 and 60 the subtracting the answer from 180 :)
2s +3≤7 OR 3s +5> 26
Number 10
The solutions of the inequalities are s≤2 and s>7 respectively
The given inequalities are 2s +3≤7 OR 3s +5> 26
We have to find the solutions
2s +3≤7
Subtract 3 from both sides
2s≤4
Divide both sides by 2
s≤2
Now inequality 3s +5> 26
Subtract 5 from both sides
3s>21
s>7
Hence, the solutions of the inequalities are s≤2 and s>7 respectively.
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In your music collection, 75% are "burned" discs while 25% are CDs you purchased from a store. The CD player in your car is very particular...if there is the slightest irregularity in the disc it will not play. You have realized your car CD player will play 95% of the store purchased discs, but only 20% of the burned discs.
Let event B occur if the CD is burned and event P occur if the disc will play. Create a tree diagram starting with P(B) and P (-B)
on the far left.
a) What is the probability that a CD will not play in your car? Round to 4 decimal places.
b) What is the probability, given that the CD does not play, that it is store bought? Round to 4 decimal places.
ewdf
The probability that a CD will not play in your car is 0.76 and given that the CD does not play, the probability that it is store bought is 0.1053.
What is Probability?Probability is the study of the chances of particular outcomes in a set of given circumstances. It is used to measure the likelihood of an event occurring, and it is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability can also be expressed as percentages, fractions, or decimals. Probability is used in many fields, including mathematics, finance, engineering, and science.
P(B) = 0.20
P(-B) = 0.80
P(No Play | B) = 0.20
P(No Play | -B) = 0.95
a) P(No Play) = P(No Play | B)*P(B) + P(No Play | -B)*P(-B)
= 0.20*0.20 + 0.95*0.80 = 0.76
b) P(Store Bought | No Play) = P(No Play | B)*P(B) / P(No Play)
= 0.20*0.20 / 0.76 = 0.1053
From the tree diagram, the probability that a CD will not play in your car is 0.76 and given that the CD does not play, the probability that it is store bought is 0.1053.
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HELP ASAP OVERDUE!!!!!!!
R(3, 2), S(5, -2), and T(6, 0) are the coordinates of a triangle's vertices. If the triangle is reflected over the y-axis, what are the coordinates of the image?
R'(-3, 2), S'(-5, -2), T'(6, 0)
R'(-3, -2), S'(-5, 2), T'(-6, 0)
R'(3, -2), S'(5, 2), T'(6, 0)
R'(-3, 2), S'(-5, -2), T'(-6, 0)
R'(-3, 2), S'(-5, -2), T'(-6, 0) is the correct answer for the given problem.
To reflect a point over the y-axis, we negate its x-coordinate.
Using this rule, the coordinates of the image of R, S, and T after reflecting the triangle over the y-axis are:
R'(-3, 2) (negate the x-coordinate of R)
S'(-5, -2) (negate the x-coordinate of S)
T'(-6, 0) (negate the x-coordinate of T)
Therefore, the correct answer is: R'(-3, 2), S'(-5, -2), T'(-6, 0).
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6,075 / 450=
I need an answer pls
Answer:
13.5
Step-by-step explanation:
Answer: 13.5
Step-by-step explanation:
just use the calculator