The distance from Point C to the tower at Point A is 1.2 miles, while the distance from Point C to the tower at Point
Bis 1.8 miles. If mZACB=81", what is the distance, to the nearest tenth of a mile, between the water towers?

The negative value indicates that the policy is providing a net benefit of approximately $9,742.21 over the 10-year period.

To calculate the net cost of insurance, we need to compare the return on investment from investing the premium elsewhere with the cash value of the policy.

First, let's calculate the amount of money you would have if you invested the $2,000 premium elsewhere for 10 years with a 5% annual yield. We can use the compound interest formula:

A = P * (1 + r)^n

Where:

A is the final amount.

P is the principal amount (premium).

r is the interest rate per period (5% or 0.05).

n is the number of periods (10 years).

Calculating the investment amount:

A = 2,000 * (1 + 0.05)^10

A ≈ 2,000 * 1.628895

A ≈ 3,257.79

Therefore, if you invested the premium elsewhere, you would have approximately $3,257.79 after 10 years.

Now, let's calculate the net cost of insurance:

Net cost of insurance = Annual premium - Cash value of the policy + Investment return

Net cost of insurance = 2,000 - 15,000 + 3,257.79

Net cost of insurance ≈ -$9,742.21

The negative value indicates that the policy is providing a net benefit of approximately $9,742.21 over the 10-year period.

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The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer:

\( \frac{9x { }^{2 } - 63x}{ 3x} \\ = \frac{3x(3x - 21)}{3x} \\ = 3x - 21 \)

hope it helps:)

Answer:3x-21

Step-by-step explanation:

\(\frac{9x^{2} - 63x }{3x}\) ⇒ \(\frac{3x * (3x - 21) }{3x}\) ⇒ cancel out 3x ⇒ 3x - 21

Answer:

Sure.

Step-by-step explanation:

ok, so you basically just count from 0 going left three spaces. and the same going 5 spaces. For positive numbers you go (starting at 0) from left to right. for negative numbers (starting from 0 on the line) you go right to left.

I will make a G for where the green dot goes and a P for the pink dot.

<--I--I--I--I--I--I--I--I--I--I--I--I--I--I--I--I-->

         P    G       0       3     5

Hope this helps.

- Mach Speed.

If you apply the changes below to the absolute value parent function, f(x) = |x|, the equation of the new function is option  A. g(x) = |x – 4| + 6

The mathematical function f(x) = |x|, commonly referred to as the absolute value parent function, yields the numerical value of a provided input in an absolute sense.

from the question,

\(f(x)= /x/\)

as well as the fact that  It shifted 4 units to the right end 6 units up.

So, we see that:

(0) 4 units to the right

(b) 6 units up

Hence, Equation f(x)= /x/ is one that have moved the vertex of the parabola 4 units to the right as well as 6 units up.

So,

\(f(x) = a(x-h)^{2} + k\\\\f(x) = /x/\)

So by moving right it implies one is adding 4 h= 4 and going up implies adding for example. k = 6

So:

\(f(x)= |x|\\\\g(x) = /x-4/ + 6\)

So, based on the equation above, the transformation that is correct is option (A).

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See full text below

If you apply the changes below to the absolute value parent function, f(x) = |x|, what is the equation of the new function?Shift 4 units to the right.Shift 6 units up.

A. g(x) = |x – 4| + 6

B. g(x) = |x – 6| + 4

C. g(x) = |x + 6| + 4

D. g(x) = |x + 4| + 6

Answer:

3

15: 1, 3, 5, 15

24: 1, 2,3,4,6,8,12,24

27:1, 3,9,27

(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.

(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.

(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.

(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.

Similar triangles have the same corresponding angle measures and proportional side lengths.

The triangle similarity criteria are:

(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.

12/8 = 9/6

1.5 = 1.5

(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.

(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.

14/10 = 21/15

1.4 =

(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.

SMK = 90⁰, 60⁰, 30⁰

QTR =  90⁰, 30⁰, 60⁰

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Answer:

x = 8 or x = -2

Step-by-step explanation:

x^2 - 6x + 9 = 25

x^2 - 6x - 16 = 0

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

with a = 1

b = -6

c = -16

substitute in the formula

x = [-(-6) +/- √(-6^2 - 4(1)(-16))]/2(1)

x = [6 +/- √(36 + 64)]/2

x = [6 +/- √10]/2

x = [6 +/- 10]/2

x1 = [6 + 10]/2 = 16/2 = 8

x2 = [6 - 10]/2 = -4/2 = -2

Answer:

x = 8,-2

Step-by-step explanation:

First, complete the square on LHS (Left-Handed Side).

\(\displaystyle \large{x^2-6x+9=(x-3)^2}\)

Make sure to recall the perfect square formula. Rewrite another equation with (x-3)² instead.

\(\displaystyle \large{(x-3)^2 = 25}\)

Square both sides of equation.

\(\displaystyle \large{\sqrt{(x-3)^2}=\sqrt{25}}\)

Because x² = (-x)² which means that it’s possible for x to be negative. Thus, write plus-minus beside √25 and cancel square of LHS.

\(\displaystyle \large{x-3=\pm \sqrt{25}}\\ \displaystyle \large{x-3=\pm 5}\\ \displaystyle \large{x=\pm 5+3}\)

Therefore, x = 5+3 or x = -5+3

Thus, x = 8,-2

The method above is called completing the square method.

Answer:

Quadrilateral: 20.5 units

Triangle: 8.6 units

Step-by-step explanation:

Quadrilateral:
We can use the following formula to find the perimeter of a quadrilateral.

Perimeter = AB + BC + CD + DA

where AB, BC, CD, and DA are the lengths of the four sides of the quadrilateral.

In your case, the coordinates of the vertices of the quadrilateral are A(-3,-1), B(-3,3), C(2,3), and D(4,-1).

Using the distance formula, we can find the lengths of the four sides of the quadrilateral as follows:

\(AB = \sqrt{(-3 - (-3))^2 + ((-1) - 3)^2} = \sqrt{16} = 4\)

\(BC = \sqrt{(-3 - 2)^2 + ((3) - 3)^2} = \sqrt{25}= 5\)

\(CD = \sqrt{(2 - 4)^2 + ((3) - (-1))^2} = \sqrt{4+16} = 2\sqrt{5}\)

\(DA = \sqrt{(4 - (-3))^2 + ((-1) - 1)^2} = \sqrt{49} =7\)

Therefore, the perimeter of the quadrilateral is:

Perimeter = AB + BC + CD + DA

= \(4+5+2\sqrt5+7=20.5\) units

Triangle

The perimeter of a triangle is the total length of all three sides of the triangle. To find the perimeter of a triangle, we can use the following formula:

Perimeter = AB + BC + CA

where AB, BC, and CA are the lengths of the three sides of the triangle.

In your case, the coordinates of the vertices of the triangle are

E(-4,1), F(-2,3), and G(-2,4). Using the distance formula, we can find the lengths of the three sides of the triangle as follows:

\(EF = \sqrt{(-4 - (-2))^2 + ((1) - (3))^2} = 2\sqrt{2}\)

\(FG = \sqrt{(-2 - (-2))^2 + ((3) - (4))^2} = 1\)

\(EG = \sqrt{(-4 - (-2))^2 + ((1) - (4))^2} = \sqrt{4 + 9} = \sqrt{13}\)

Therefore, the perimeter of the triangle is:

Perimeter = EF + FG + EG

= 4 + 1 + \(\sqrt{13}\)

=8.6 units

Therefore, the perimeter of the quadrilateral is 20.5 units and the perimeter of the triangle is 8.6 units

Answer:

L=30 W=15

Step-by-step explanation:

90 divided by 6 is 15. 15 is the Width. Multiply 15 by 2 and you get 30 which is the Length.

The probability of the area hit by the dart between the bigger square and the smaller square is equal to 0.7656.

As given in the question,

Total number of squares present = 2

Side length of the bigger square = 16 units

Side length of the smaller square = 14 units

Area of the bigger square = ( side length )²

                                           = ( 16 )²

                                           = 256 square units

Area of the smaller square = ( side length )²

                                           = ( 14 )²

                                           = 196 square units

Here favorable outcome is represented by small square and total outcome is represented by bigger square

Probability that the given dart hit the area between the square is

= 196 / 256

= 49/64

= 0.765625

≈ 0.7656

Therefore, the probability of the dart hitting the area formed by bigger square and smaller square is equal to 0.7656.

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The general pattern that these diamonds follow is that the top number is the result of multiplying the numbers in the middle; while the bottom number results from adding these numbers. This pattern can be used to find the numbers in the fourth diamond. Moreover, the numbers that complete the diamonds are A (15,8), B (2,-3), C (4,2), D(4,8.5), E (-3.-4)

Based on observation, you can determine in these diamonds the top number is obtained by multiplying the numbers in the middle, while the bottom number is obtained by adding these numbers.

Diamond A

Top number: 15 (3x5)

Bottom number: 8 (3+5)

Diamond B

Top number: 2 (-2x-1)

Bottom number: -3(-2+-1)

Diamond C

4, 2 because 4x2 = 8 and 4+2 = 6

Diamond D

Top number: 4( 8x0.5)

Bottom number: 8.5(8+0.5)

Diamond E

-3,-4 because -3x-4= 12, and -3+-4= -7

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Answer:a. 0.13% b. 2.28%

Step-by-step explanation:

Let x  denotes the useful life of batteries.

Given: \(\mu=56\) months, \(\sigma=6\)

Since X is normally distributed.

The probability that batteries with a useful life of less than 38 months

\(P(X<38)=P(\frac{X-\mu}{\sigma}<\frac{38-56}{6})\\\\=P(Z<-3) \ \ \ [Z=\frac{X-\mu}{\sigma}]\\\\=1-P(Z<3) \\\\=1- 0.9987\\\\=0.0013\)

The percent of batteries with a useful life of less than 38 months =0.13%

The probability that batteries will last longer than 68 months

\(P(X>68)=P(\frac{X-\mu}{\sigma}>\frac{68-56}{6})\\\\=P(Z>2) \ \ \ [Z=\frac{X-\mu}{\sigma}]\\\\=1-P(Z<2)\\\\=1-0.9772=0.0228\)

The percent of batteries that will last longer than 68 months =2.28%

Answer:

meter - yard

kilogram - 2 pounds

liter - quart

To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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Answer:

26,225.3 = 3.14(12^2)h + (2/3)(3.14)(12^3)

26,225.3 = 452.16h + 3,617.28

452.16h = 22608.02

h = 50 feet

26,225.3 = π(12^2)h + (2/3)π(12^3)

26,225.3 = 144πh + 1,152π

144πh = 26,225.3 - 1,152π

h = (26,225.3 - 1,152π)/(144π)

h = 49.97 feet = 50 feet

Answer:3 hours 20 mins

Answer:

3 hours 20 minutes is the length of the movie.

Answer:

y = -1/6x + 2

Step-by-step explanation:

Slope: (-6,3) and (6,1) = (1-3) / (6 - - 6)

= - 2/12 = -1/6

b = 3 - (-1/6)(-6)

b = 3 - 1

b = 2

Answer: 30%

Step-by-step explanation:
12/40 = 3/10 = 0.30

0.30*100 = 30%

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

the value of x is 150° because all are 150°

Answer:

The answer is 50.

Step-by-step explanation:

Use MDAS

Multiplication, Division, Addition and Subtraction

2 + 6 * 8 =

Multiply first then add

2 + 6*8 = ?

= 2 + 48

= 50

The approximate x-values for the local maximum and the local minimum are given as follows:

D) max ≈ -0.3 , min ≈ 2.3.

Hence the critical points of the graphed function are given as follows:

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The volume of an object that has small dimensions is 348.4 cubic centimeter

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Take the stack of 100 sticky notes and stack them on top of each other to create a single "block" of sticky notes.

Measure the length, width, and height (thickness) of this block.

Calculate the volume of a rectangular prism with the same dimensions as the block: length × width×height.

Volume=7.62×7.62×6

=348.38 cubic centimeter

Hence, the volume of an object that has small dimensions is 348.4 cubic centimeter

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Answer:

12 is the answer of this equation

the answer would have to be 465

Answer:

Weight of a pile of sand = 90 Kg

Ratio of weight of sand in three bags =

2 : 3 : 7

Let the weights be 2x kg, 3x kg and 7x kg respectively

A.T.Q.

=> 2x + 3x + 7x = 90

=> 12x = 90

=> x = 90/12

=> x = 7.5 Kg

___________________________

Weight of sand in small bag =

=> 2 × 7.5

=> 15 Kg ANS

Weight of sand in medium bag =

=> 3 × 7.5

=> 22.5 Kg ANS

Weight of sand in large bag =

=> 7 × 7.5

=> 52.5 Kg ANS

5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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Answer:

-1*-1= 2;2*-1=-1;-1*-2=2

Step-by-step explanation:

negative times neg equals positive

Because when you add negatives together it goes more down because you are adding negatives together. if you add 2 negatives it decreases in value but when you subtract 2 negatives from each other the number increases.