You take out a home mortgage for $271,000 for 40 years. How much more total interest, in dollars, do you pay for a loan with an annual percentage rate of 7% than for a loan with an annual percentage rate of 5%? Round your answer to the nearest cent.

The solution is: I. ∠1 and ∠2 are same-side interior angles and,

III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.

Here, we have,

given that,

We have to find which two statements about angles on a transversal crossing parallel lines contradict each other.

we know that,

If a transversal intersects or crosses parallel lines, adjacent angles are supplementary.

Corresponding angles are those that are in the same relative position, between the crossing line and the parallel lines.

now, we have,

I. ∠1 and ∠2 are same-side interior angles it can be possible.

Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines.

Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary. If , then m ∠ 1 + m ∠ 2 = 180 ∘ .

so, if number-l is true, so, we get,

II. m∠1 = m∠2 may be true,

III. m∠1 + m∠2 = 90, never can be true.

so, we get,

if, l. holds then lll. contradicts that.

Hence, The solution is: I. ∠1 and ∠2 are same-side interior angles and,

III. m∠1 + m∠2 = 90, are the two statements about angles on a transversal crossing parallel lines contradict each other.

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Answer:

10

Step-by-step explanation:

If you multiply the width with the length and height , you will get nine, then add that lonely brick on top to get ten

The Sanjay method used  to calculate the median is an incorrect formula. The correct value of the median is 7.5 kilometers.

Given:

the distances traveled by the Sanjay on his recent walks - 5, 6, 6, 7, 8, 8, 9, 9

The Median which is calculated by Sanjay = 7 kilometers

We need to find the mistake that Sanjay made in calculating the median

Solution:

We have the following data

5, 6, 6, 7, 8, 8, 9, 9

There are an even number of values, the median is determined by determining the average of the n/2th term and {(n/2) + 1}th term, where:

n = total number of values

= n/2

= 8/2

= 4

= (n/2) + 1

= (8/2) + 1

= 5

The 4th value in the given data = 7

The 5thvalue in the given data = 8

The median is the average of 7 and 8 = (7 + 8)/2 = 7.5

Therefore, the median will be the 7.5

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Using the formula of compound interest, the number of years is 7.6 years

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula of compound interest is given as;

[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]

But in this case, the interest was compounded continuously

[tex]A = Pe^r^t[/tex]

Substituting the values into the formula;

[tex]7450 = 5500e^(^0^.^0^5^2^5 ^* ^t^)[/tex]

Solving for t;

t = 7.6 years

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The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).

The given system of equations can be solved using the substitution method. We can begin by solving the first equation,[tex]a^2 + b^2[/tex], for either a or b. Let's solve for a:

[tex]a^2 + b^2 = 0[/tex]

[tex]a^2 + b^2 = 0[/tex]

[tex]a^2 = -b^2[/tex]

[tex]a = \pm\sqrt(-b^2)[/tex]

We can substitute this expression for a into the second equation, [tex]3a^2 - 2ab - b^2 = 0[/tex], and simplify:

[tex]3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0[/tex]

[tex]3b^2 - 2b^2 - b^2 = 0[/tex]

0 = 0

Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation [tex]a^2 + b^2 = 0[/tex] will also satisfy the equation [tex]3a^2 - 2ab - b^2 = 0[/tex]

However, the equation [tex]a^2 + b^2 = 0[/tex] only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).

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The solution to the given problem of equation comes out to be quotient : x² +x+6+2/(x+2)  and remainder is 2.

We have to find the remainder and quotient

Given : synthetic division for

x³ + 3x² + 8x + 14

------------------------

x + 2

Write the problem in synthetic division format

-2  | 1 3 8 14

        -2 -2  

------------------------

    1   1  6

Carry down the leading coefficient, unchanged, to below the division symbol

-2  |    1 3 8 14

          -2 -2

---------------------------

        1  1   6

Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:

1(-2)=-2

-2 |  1 3 8 14

       -2 - 2

------------------

    1    1   6

=> We get:

As x² +x+6+ 2/(x+2)

and remainder is 2

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Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!

To start, let's quickly review what a trapezium is. A trapezium, also known as a trapezoid, is a four-sided geometric shape with two parallel sides (called the bases) and two non-parallel sides (called the legs). The distance between the two parallel sides is known as the height.
In order to find the area of a trapezium, we use the formula:
Area = (sum of bases x height) / 2
So for trapezium PQRS, we need to identify the length of its two bases and its height in order to use this formula.
Without any specific measurements given in your question, I'll assume we don't have any numerical values to work with. Instead, let's use variables to represent the length of each base and the height.
We can call the shorter base PQ, and the longer base SR. Let's say PQ has a length of 'a' units, and SR has a length of 'b' units. For the height, let's call it h.
So, the formula for the area of trapezium PQRS becomes:
Area = ((a + b) x h) / 2
This means that to find the area of the trapezium, we simply need to know the lengths of the two bases (a and b) and the height (h).
Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!

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Answer:

it is A

Step-by-step explanation:

def correct! a+ student

Answer: D

Step-by-step explanation:

The answer has to be A or D because they're the only ones that look like real box-and-whisker plots. The mean is the line in the middle of the "box", so calculating the mean should be easy enough.

Add all the numbers together and then divided by the number of numbers.

56+72+75+98+73+86+48+95+69+88+75+92 = 972

There are 12 numbers.

972/12 = 77.25

Only option D represents the proper mean.

The greatest common divisor of 120, 70, and 30 using prime factorization is 10.

To find the greatest common divisor (GCD) of 120, 70, and 30 using prime factorization  we need to first express each number as a product of its prime factors.

Prime factorization of 120

2³ × 3 × 5

Prime factorization of 70

= 2 × 5 × 7

Prime factorization of 30

= 2 × 3 × 5

common prime factors among the three numbers

common prime factors

= 2 × 5

= 10

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Answer:

300 per year??

Step-by-step explanation:

I'm not sure what you're trying to find...I'm guessing it's how many people it grew by per year

3000-1500 is 1500

1500/5 is 300

hope this helped

Answer:

Step-by-step explanation:

Since the given figure is a right triangle, we can use Pythagorean Theorem

where c² = a² + b²

c = 15

15² = a² + b²

Since 15 is the hypotenuse, we can then say that the possible legs of the triangle are less than 15.

225 - a² = b²

we will do trial and error

let a be 14

225 - 14² = b²

b = √29

a = 14cm, b = √29cm, c = 15cm

let a be 13

225 - 13² = b²

b = 2√14

a = 13cm, b = 2√14cm, c = 15cm

let a be 12

225 - 12² = b²

b = 9

a = 12cm, b = 9cm, c = 15cm

You can solve for other possible values using the same process as above. Since there are no conditions whether the lengths of the legs should be a whole number or not then the above dimensions can be considered. If you're looking for an answer that consists of whole numbers then the answer would be a = 12cm, b = 9cm and c = 15cm

The value of sin Ф is 72/97.

We have,

Since cos Ф = -65/97 and Ф terminates in quadrant III, we know that cos Ф is negative (since cosine is negative in quadrants II and III).

We can use the Pythagorean identity to find sin Ф:

sin² Ф + cos² Ф = 1

Substituting cos Ф = -65/97, we get:

sin² Ф + (-65/97)² = 1

Simplifying, we get:

sin² Ф = 1 - (-65/97)²

Taking the square root of both sides (since sin Ф is positive in quadrant III), we get:

sin Ф = √(1 - (-65/97)²)

sin Ф = √(1 - 4225/9409)

sin Ф = √(5184/9409)

sin Ф = 72/97

Therefore,

The value of sin Ф is 72/97.

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1. The location of point A  and B in complex (a + bi) form is 4 + 3i, B is -6 + 4i.

2. The modulus of point A is 5.

3. The length of AB is 10.

4. B in polar form is 2√13 × (cos(146°) + i sin(146°))

5. The product of two complex numbers in rectangular form is  -36 - 2i

6. z1/z2 in polar form is z1/z2 = 4 cis (7π/6 - π/4)

1. The location of each point A and B are as follows  Arrow A is at (4, 3) and arrow B (-6, 4). therefore the location in complex (a + bi) form is 4 + 3i, B is -6 + 4i.

2. The modulus of a complex number (a + bi) is represented as √(a² + b²) ⇒ √(4² + 3²) = √(16 + 9) = √25 = 5.

3. We can calculate the length of vector AB with √(x₂-x₁)² + (y₂-y₁)²)

AB = √((-6 - 4)² + (4 - 3)²)

AB = √((-10)² + 1)

AB = √(100 + 1)

AB = √101 ⇒ 10

4. The modulus of B, r = √((-6)² + 4²) = √(36 + 16) = √52 = 2√13

θ = 180° - arctan(|4/-6|) = 180° - arctan(2/3)

θ = 180° - 33.69° = 146.31°

5. The product of the complex number can be see as follows

(4 + 3i) × (-6 + 4i) = (4×-6 - 34) + (4×4 + 3×-6)i

= (-24 - 12) + (16 - 18)i

= -36 - 2i.

6. (7π/6 - π/4) = (14π/12 - 3π/12) = 11π/12.

11π/12 × (180/π) = 165°.

In Polar form z1/z2 = 4 cis (7π/6 - π/4)

= 4 cis 165°.

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Answer:

Step-by-step explanation:

The length of the AB in the curved road path comes out to be 98.2 feet

Given:

Radius = 88 feet

DE = 15 feet

CD is the radius of the circle

CD = CE + DE

88 = CE + 15

CE = 73 feet

Since the CD is the perpendicular bisector the AE and BE are equal in length

In triangle CBE,

It is right-angled at E,

By Pythagoras' theorem:

hyp² = height² + base²

88² = 73² + BE²

7744 = 5329 + BE²

BE² = 2415

BE = 49.1 feet

AB = BE + AE

AB = BE + BE

AB = 2BE

AB = 2 * 49.1

= 98.2 feet

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The complete question is:

The curved road at the right is part of circle C which has a radius of 88 feet. What is AB as shown in the figure? Round to the tenth

Answer:

Step-by-step explanation:

You want the formula that describes the decay of an insect population from 10000 by 9% per year, and the years it takes for the population to decline by half.

An exponential function will have the form ...

  f(t) = (initial value) · (growth factor)^t

where ...

  growth factor = 1 + growth rate

Here, the growth rate is -9% per year, so the growth factor is ...

  1 -9% = 1 -0.09 = 0.91

The population is then ...

  f(t) = 10000·0.91^t . . . . . formula for number of insects

We can solve for t when f(t) = 5000 (half the original population):

  5000 = 10000·0.91^t

  1/2 = 0.91^t . . . . . . . . . . . divide by 10,000

  ln(1/2) = t·ln(0.91) . . . . . take logarithms

  t = ln(0.5)/ln(0.91) ≈ 7.3496 ≈ 7.3 . . . . years

It would take about 7.3 years for the population to reduce to less than half its present size.

__

Additional comment

We have rounded the time period to the nearest tenth, 7.3 years. At the end of that period, the population is modeled to be about 5023, not quite "less than half." To get below half the original population would take almost 7.35 years.

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(a)  the probability of generating 999999 is [tex](1/10)^6[/tex]

(b) the probability of generating 703928 is [tex](1/10)^6[/tex]

(c) the probability of generating a sequence of six identical digits is [tex](1/10)^6[/tex]

(d)  the probability of generating a sequence with no identical digits is  15,120/1,000,000.

(e)  the probability of generating a sequence with exactly one repeated digit is[tex]10 * 6 * (9^4).[/tex]

Probability is described as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

The probability of generating a sequence with no identical digits is calculated as  (10/10) * (9/10) * (8/10) * (7/10) * (6/10) * (5/10) = 15,120/1,000,000.

We start by choosing  the digit to be repeated, which can be done in 10 ways and the next thing is to choose the position of the repeated digit, and can be done in 6 ways.

We then see that remaining four positions can be filled out with any of the other 9 digits and this can also be   done in [tex]9^4[/tex] ways.

So we can conclude that the number of possibilities in this case is [tex]10 * 6 * 9^4.[/tex]

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Answer:

10

Step-by-step explanation:

2 / 10 = 0.2

2 divided by ten is two-tenths.

Answer: 2 divided by 10 is 0.2

Answer:

Step-by-step explanation:

[tex]\frac{925!}{(925-3)!}= 923*924*925=788,888,100[/tex]

To determine the number of ways the first, second, and third prizes can be awarded in a contest with 925 contestants, we can use the concept of permutations.

For the first prize, there are 925 contestants eligible to win. After the first prize is awarded, there are 924 remaining contestants for the second prize. Finally, for the third prize, there are 923 remaining contestants.

The number of ways to award the prizes can be calculated as the product of the number of choices for each prize:

Number of ways = 925 * 924 * 923

Calculating this expression, we find:

Number of ways = 779,449,100

Therefore, there are 779,449,100 ways to award the first, second, and third prizes in the contest with 925 contestants.

The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.

The volume of a solid is the three dimensional space the solid occupies.

The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;

Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³

Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³

70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³

The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0

The number of times Johnny needs to use the wheelbarrow is about 41 times

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Answer: 27.3 inches

Step-by-step explanation:

Answer: (5x+6)(x+4)

Step-by-step explanation:

5x^2 + 26x + 24

5x^2 + 20x + 6x + 24

(5x^2 + 20x) + (6x + 24)

5x(x + 4) + 6(x + 4)

5x(x + 4) + 6(x + 4)

(5x + 6)(x + 4)

Answer:

x=20

Step-by-step explanation:

On line n, the two unknown angles are supplementary, so we need their sum to be 180° and we can find x that way:

(6x-4)°+(3x+4)°=180°

6x+3x-4+4=180

9x=180

x=20

The image polygon P'S'R'T' has vertices P'(-5, 1), S'(0, -1), R'(3, -2), and T'(-2, -4).

To determine the image vertices of P' when the preimage is rotated 90° counterclockwise, we can use the following formula:

(x', y') = (-y, x)

where (x, y) are the coordinates of the preimage vertex, and (x', y') are the coordinates of the image vertex after rotation.

Using this formula for each vertex of the polygon PSRT, we get:

For P(1, 5), rotating 90° counterclockwise gives us P'(-5, 1).

For S(1, 0), rotating 90° counterclockwise gives us S'(0, -1).

For R(-2, -3), rotating 90° counterclockwise gives us R'(3, -2).

For T(-4, 2), rotating 90° counterclockwise gives us T'(-2, -4).

Therefore, the image polygon P'S'R'T' has vertices P'(-5, 1), S'(0, -1), R'(3, -2), and T'(-2, -4).

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Rounding 473,615 to the nearest hundred gives us 473,600.

We have,

Rounding a number to the nearest hundred means that you are looking at the digit in the tens place of the number.

If that digit is 5 or greater, you round up the digit in the hundreds place, and if it is less than 5, you keep the digit in the hundreds place the same.

In the case of 473,615, the digit in the tens place is 1, which is less than 5. So we keep the digit in the hundreds place (3) the same and round the remaining digits to zero.

Thus,

Rounding 473,615 to the nearest hundred gives us 473,600.

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Answer:

64 - (6 x 8)

Step-by-step explanation:

"The product of 6 and 8" means 6 and 8 multiplied together, therefore this part can be expressed as 6x8. "Subtracted from 64" means that the product of 6x8 is being taken away from 64, therefore it is 64-(6x8).

That's quadratic.

y=x^2

It's a very simple version of y=ax^2+bx+c. Just in this case, a = 1, b = 0 and c = 0.

The solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

An exponential function is a mathematical function in the form of [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is a variable. The value of the function at a particular value of "x" is found by raising "a" to the power of "x". Exponential functions are characterized by their rapid growth or decay.

We can solve for x by taking the logarithm of both sides with base 5:

[tex]5^{(\frac{-x}{16})} = 5[/tex]

[tex]log_5(5^{(\frac{-x}{16}))} = log_5(5)[/tex]

(-x/16)log₅(5) = 1

-x/16 = 1/log₅(5)

x = -16/log₅(5)

Using a calculator, we get:

x ≈ -4.4431

Therefore, the solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex]  in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

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Answer: yes 2,0193-029712123,

Step-by-step explanation: