Dmitry Mendeleyev and his wife obtained a 30-year, $210,000 mortgage loan from
Community Bank. The interest rate is 6.5%. Their monthly payment is $1,362.06. For the first payment, what is the amount of the interest, payment to principal, and new principal?

The length of each side of the tile with an area of 790 cm² correct to 3 significant figures is 28.1 cm.

Significant figures are the digits in a number that give a reliable accuracy of the quantity of a measurement.

The significant figures do not include the zeros immediately after the decimal place but those that occur between other numbers are regarded as significant.

The area of a square tile = Length x Length

= 790 cm²

The length of each side = √790 = 28.1069

= 28.1 cm

Thus, we can conclude that the length of each side of the square tile is 28.1 cm.

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The system of equations are t = 22.28 years , number of nickles and dimes are solved

Given data ,

a)

Let the number of years be represented as t

For truck A, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:

Total cost for truck A = 20345 + 1230t

For truck B, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:

Total cost for truck B = 16000 + 1425t

when the total costs are equal , we get

20345 + 1230t = 16000 + 1425t

On simplifying , we get

195t = 4,345

t = 22.28 years

b)

Let the number of nickels be n and number of dimes be d

The total value of nickels is 0.05n (since the value of one nickel is $0.05) and the total value of dimes is 0.10d (since the value of one dime is $0.10)

The total value of the coins = $ 2.05

And , the total number of coins = 56

0.05n + 0.10d = 2.05

And , n + d = 56

Hence , the system of equations are solved

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The planes that are parallel in the cube shown would be C. NOR and LMP.

Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.

From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.

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Answer:

N′(−5, −6), M′(−2, −5), O′(−3, −7)

Step-by-step explanation:

To reflect a point over a line, we can use the following steps:

Find the distance between the point and the line.

Construct a perpendicular line from the point to the given line.

Extend this perpendicular line to the same distance on the other side of the given line.

The intersection of the extended perpendicular line with the given line is the reflected point.

Alternatively, we can use the fact that reflecting a point over a line is equivalent to reflecting the coordinates of the point across the line. In this case, we are reflecting over the line y = -2, so we can simply negate the y-coordinate of each point to find its reflection.

Using this method, the reflected vertices are:

N'(-5, -4)

M'(-2, -3)

O'(-3, -1)

′(Therefore, the correct answer is option D: N−5, −6), M′(−2, −5), O′(−3,-7)

Answer:

∠ A ≈ 75.96°

Step-by-step explanation:

using the tangent ratio in the right triangle

tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then

∠ A = [tex]tan^{-1}[/tex] ( 4 ) ≈ 75.96° ( to the nearest hundredth )

The requried shading would appear above the solid line of the slope.

To graph the inequality 9x + 5y > 1, we first require to graph the equation 9x + 5y = 1, which is the equation of the line that separates the two regions determined by the inequality.

To graph this line, we can solve for y in terms of x:

9x + 5y = 1

y = (-9/5)x + 1/5

Although the slope of the line is negative, the shading should occur above the line, which means the correct answer is, the shading would occur above the solid line of the slope.

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Answer:

-4/3

Step-by-step explanation:

-1.33333333333 or -1 1/3

The equations are classified as follows

System A

consistent and independent this means that the system as a unique  solution at (3, 3)

System B

inconsistent this means that the system as a no  solution

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.

System C

consistent and dependent this means that the system as infinitely many solution

A consistent system is dependent if there are an infinitely many solutions. The two equations represent the same line when you graph them.

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The amount of tax and deductions from the income is $229.21

From the question, we have the following parameters that can be used in our computation:

Gross income = $1,568

Net income = 1,338.79

Using the above as a guide, we have the following:

Deductions = Gross income - net income

Substitute the known values in the above equation, so, we have the following representation

Deductions = $1,568 - 1,338.79

Evaluate the expression

So, we have

Deductions = $229.21

Hence, the amount of tax and deductions from the income is $229.21

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Answer: A

Step-by-step explanation: complementary is 180 that’s the angle is A. Supplementary is 90 so that’s incorrect.

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{8}\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{x} \end{cases} \\\\\\ x=\sqrt{ 8^2 - 2^2}\implies x=\sqrt{ 64 - 4 } \implies x=\sqrt{ 60 }[/tex]

Receiving a large tax refund is problematic because it means overpaying taxes and missing out on the opportunity to use that money throughout the year for paying down debt, building an emergency fund, or investing.

We have,

While receiving a large tax refund each year may seem like a positive thing, it actually means that Mia and Allen are overpaying their taxes throughout the year.

This means that they are essentially giving the government an interest-free loan by allowing them to hold onto their money instead of having it available to them throughout the year to use for things like paying down debt or investing in their future.

By overpaying their taxes,

Mia and Allen are essentially missing out on the opportunity to use their money in ways that could benefit them in the long run.

Additionally, the large tax refund they receive each year may create a sense of false security, leading them to believe that they are in a better financial situation than they actually are.

Rather than receiving a large tax refund each year, it may be more beneficial for Mia and Allen to adjust their tax withholdings so that they are receiving more money in each paycheck.

This way, they can use the extra money to pay down debt, build up their emergency fund, or invest in their future, rather than giving the government an interest-free loan.

Thus,

Receiving a large tax refund is problematic because it means overpaying taxes and missing out on the opportunity to use that money throughout the year for paying down debt, building an emergency fund, or investing.

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Тhе sum оf thе first 6 tеrms оf thе given sеquеncе is аpproximаtely 14.56.

First detеrmine thе common rаtio (r) аnd thе first tеrm (а1).

Eаch tеrm is obtаined by multiрlying thе prеvious tеrm by 1/3. Тherefоre, thе common rаtio is r = 1/3.

Тhe first tеrm is а1 = 12.

Now wе cаn use thе fоrmulа fоr thе sum оf а finite geоmetric series:

Sn = а1(1 - r^n) / (1 - r)

whеrе n is thе number оf tеrms.

Plugging in thе vаlues, wе gеt:

Sn = 12(1 - (1/3)^6) / (1 - 1/3) ≈ 14.55

Rounding to thе neаrest hundredth, wе gеt:

Sn ≈ 14.55 ≈ 14.56

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Answer:

The answer for Area is 189.29in²

Step-by-step explanation:

Area of compound =Area of semi circle +Area of rectangle

r=d/2=10/2=5in

A=1/2pir² + L×B

A=1/2×5² + 10×15

A=25pi/2+150

A=39.29+150

A=189.29in²

The two lines will intersect after 3 months.

We can set the two expressions for y equal to each other:

400x + 700 = 300x + 1,000

100x + 700 = 1,000

100x = 300

x = 3

So the two lines will intersect after 3 months. In this case, to find the corresponding value of y, we can substitute x = 3 into either of the equations:

y = 400x + 700

y = 400(3) + 700

y = 1,500

Therefore, the two lines will intersect after 3 months, at a point with coordinates (3, 1,500).

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The expression which has the greatest value is 1 7/8 divided by 1/12

• For the first question,  [tex]\frac{3}{4} /\frac{1}{3} =2 \frac{1}{4}[/tex]

• For the second question, [tex]\frac{3}{4} / \frac{1}{12} = 9[/tex]

• For the third question,  [tex]1 \frac{7}{8} =\frac{15}{8}[/tex] so [tex]\frac{15}{8} /\frac{1}{12} = 22 \frac{1}{2}[/tex]

• For the fourth question, [tex]1 \frac{7}{8} =\frac{15}{8}[/tex] so [tex]\frac{15}{8} /\frac{1}{3} = 5 \frac{5}{8}[/tex]

—————

Please remember to revise this and make it in your own words if you want! I tried to speed this up a lot! I hope this helps you. -Doodle

—————

Answer:

1 7/8 / 1/ 12 has the greatest value

Step-by-step explanation:

Answer:

Step-by-step explanation:

Quadratic form:

ax²+bx+c

>We are going to work backwards from getting an equation and then solving for the x's.

>From a graph, you are given your x's.

>Put those x's (x-intercepts)  into factored form.

Red:

x  = -7            >add 7 to both sides

x+7 = 0

x = -5            >add  5 to both sides

x+5=0

x+5   and x+7    are your factors

y= (x+5)(x+7)   >FOIL

y=x²+7x+5x+35

y=x²+12x+35     for RED

Blue:   follow same pattern as RED

x= -4               and                x=-2

(x+4)=0                                (x+2)=0

-(x+4)(x+2)              There is a negative in front because this one is facing

                               down

-(x²+6x+8)               FOILED and simplified, now distribut negative

y= -x²-6x-8       BLUE

Green:

x=-1      x=1

y=(x+1)(x-1)               FOIL and simplify

y=x²-1    GREEN

Orange:

x= 2   x=4

-(x-2)(x-4)

-(x²-6x+8)

y= -x²+6x-8      ORANGE

Purple:

x=5    x=7

(x-5)(x-7)

y=x²-12x+35    PURPLE

The volume of the composite solid is 980.2 cm³.

A composite solid is a solid made of two or more well-defined solid objects.

To calculate the volume of the composite solid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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B.

B, is the true comparison

The amount of money is 4000 was invested at 3%.

Let x be the amount of money invested at 3%.

Then, the amount of money invested at 5% is 6000 - x.

The interest earned on the amount invested at 3% is 0.03x.

The interest earned on the amount invested at 5% is 0.05(6000 - x) = 300 - 0.05x.

The total interest earned is given as $220.

So, we can write the equation:

0.03x + (300 - 0.05x) = 220

Simplifying and solving for x, we get:

0.03x + 300 - 0.05x = 220

-0.02x + 300 = 220

-0.02x = -80

x = 4000

Therefore, $4000 was invested at 3%.

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The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\mathrm{4(2y-4)-11y}[/tex]

Apply the distributive property:-

[tex]\mathrm{8y-16-11y}[/tex]

Combine like terms:-

[tex]\mathrm{8y-11y=\bf-3y}[/tex]

[tex]\mathrm{-3y-16}[/tex]

_________________________

Hope this helps! :)

The probability of flipping tails at least two times in three flips is 1/2.

When flipping a coin, there are two possible outcomes: heads or tails. Each flip is independent of the previous flips, so the probability of getting tails on any given flip is always 1/2 (assuming the coin is fair).

To find the theoretical probability of flipping tails at least two times in three flips, we can use the binomial probability formula:

P(x ≥ k) = 1 - P(x < k)

where P(x < k) is the probability of getting tails fewer than k times in three flips.

To find P(x < k), we can add up the probabilities of getting tails 0 times and getting tails 1 time:

P(x < 2) = P(0 tails) + P(1 tail)

P(0 tails) = (1/2)⁰ x (1/2)³ = 1/8

P(1 tail) = 3 x (1/2)  (1/2)² = 3/8 (since there are three ways to get exactly one tail: TTH, THT, HTT)

P(x < 2) = 1/8 + 3/8 = 1/2

Therefore, the probability of flipping tails at least two times in three flips is:

P(x ≥ 2) = 1 - P(x < 2) = 1 - 1/2 = 1/2

So the theoretical probability of flipping tails at least two times in three flips is 1/2 or 0.5 as a decimal.

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Answer: 9

Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:

10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.

Now lets try it with 1/9.

X divided by 1/9 = X times 9/1.

So dividing by 1/9 is equal to multiplying by 9.

The coordinates of the solution that lies in quadrant I are

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x² + 4y² = 100    ......equation 1.

4y - x² = -20  ......equation 2.

In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (6, 4).

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Answer:

60.96 meters per hour.

Answer:

3658.53658537 meter per hour

Step-by-step explanation:

[tex]\frac{100ft}{30sec}[/tex] · [tex]\frac{1meter}{3.28feet}[/tex] · [tex]\frac{60sec}{1min}[/tex] ·[tex]\frac{60min}{hour}[/tex]  You can cross cancel works like you can numbers

[tex]\frac{100}{30}[/tex] · [tex]\frac{1meter}{3.28}[/tex] · [tex]\frac{60}{1}[/tex] · [tex]\frac{60}{1hour}[/tex]

[tex]\frac{360000meters}{98.4hours}[/tex]

3658.53658537 meter per hour

The true population proportion of people with kids is between 0.0565 and 0.1835.

We are given that;

Number of people= 100

Percent= 95%

Now,

To construct a 95% confidence interval for the true population proportion of people with kids. Here are the steps to do so:

Find the sample proportion p. This is the ratio of the number of successes (people with kids) to the sample size. In this case, p = 12 / 100 = 0.12.

Find the z-value that corresponds to the 95% confidence level. You can use a table or a calculator to find this value. The z-value for a 95% confidence level is 1.96.

Find the standard error of the sample proportion. This is the standard deviation of the sampling distribution of p. You can use the formula √p (1-p) / n to find this value. In this case, the standard error is √0.12 (1-0.12) / 100 = 0.0324.

Plug these values into the formula for the confidence interval and simplify. You get:

Confidence interval = 0.12 +/- 1.96*0.0324 Confidence interval = 0.12 +/- 0.0635 Confidence interval = [0.0565, 0.1835]

Therefore, by proportions the answer will be 0.0565 and 0.1835.

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The angle is 47 degrees while the arc measure is solved to be 94 degrees

The arc measure of the figure labelled AC is solved using the relationship between arcs and inscribed angles.

The relationship goes with formula below

angle B = 1/2 arc measure AC

where

angle B is the inscribed angle and it is equal to 47 degrees

arc measure AC is the unknown

plugging in the values will result to

47 degrees = 1/2 arc measure AC

arc measure AC = 2 * 47 degrees

arc measure AC = 94 degrees

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