Question content area top
Part 1
In a different plan for area​ codes, the first digit could be any number from 0 through 6​, the second digit was either 2,3, or​,4 and the third digit could be any number except 0 or 3. With this​ plan, how many different area codes are​ possible?

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

Answer:

The answer should be P'(-3,-7), Q(-9,3), and R'(-4,1) which is D.

Step-by-step explanation:

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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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.

Answer:

Step-by-step explanation:

try adding 18 and 60 the subtracting the answer from 180 :)

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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Answer:

Single payment Variable annuity

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.

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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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]

Answer:

trying not to get too much

Step-by-step explanation:

j and

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.

The 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.

Answer: 185

Step-by-step explanation:

231-46=185

Answer: 185

Step-by-step explanation:

231-46

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.

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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In the figure given, rotation is the only single transformation that takes shape A to shape B.

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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answer:

a. 7/8

b.9

c.9

explanation:

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.

Answer:

13.5

Step-by-step explanation:

Answer: 13.5

Step-by-step explanation:

just use the calculator

Answer:

$886.47

Step-by-step explanation:

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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Answer:

b have a great day today and look in comments

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]

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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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

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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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

The probability from the t distribution is 0.8999 and the value of c is 1.77

From 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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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.

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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The total surface area of the triangular prism using the net is 640 square meters

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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Check the picture below.