The measure of an angle is 103°. What is the measure of its supplementary angle?

Answer:

  a) 30 yr: $1597.75; 25 yr: $1773.75

  b) $43065.00

Step-by-step explanation:

The monthly payment for each loan can be found using the amortization formula, or a spreadsheet or calculator. The shorter 25-year loan has fewer and larger payments, but the net result is less interest paid.

The attached calculator shows the monthly payments to be ...

  30 year loan: $1597.75 monthly

  25 year loan: $1773.75 monthly

The number of payments is the product of 12 payments per year and the number of years. The total repaid is the monthly payment times the number of payments.

The difference in amounts repaid is the difference in interest charged.

  360×1597.75 -300×1773.75 = $43065 . . . . savings using 25-year loan

__

Additional comment

The monthly payment on a loan of principal P at annual rate r for t years is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

Some calculators and all spreadsheets have built-in functions for calculating this amount.

The total interest on the mortgage loan  is $219,249.60

What is a mortgage loan?

It is a loan taken in order to purchase a property that requires periodic repayments such as monthly repayment since most mortgages are repaid monthly.

Our first task is to determine the monthly repayment using the present value formula of an ordinary annuity because the monthly payment becomes due at the end of each month.

PV=monthly repayment*(1-(1+r)^-N/r

PV=loan amount=$210,000

monthly repayment=unknown(assume it is X)

r=monthly interest rate=5.5%/12=0.00458333333333333

N=number of monthly payments in 30 years=30*12=360

$210,000=X*(1-(1+0.00458333333333333)^-360/0.00458333333333333

$210,000=X*(1-(1.00458333333333333)^-360/0.00458333333333333

$210,000=X*(1-0.19277525234572900)/0.00458333333333333

$210,000=X*0.80722474765427100/0.00458333333333333

$210,000=X*176.12176312456800000

X=$210,000/176.12176312456800000

X=monthly payment=$1,192.36

total repayments(360 months)=$1,192.36*360

total repayments(360 months)=$429,249.60

Total interest=total repayments(360 months)-loan amount

Total interest=$429,249.60-$210,000

Total interest=$219,249.60

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Answer:

Austin earned a higher score

Step-by-step explanation:

47/50 (Austin's score) = 94/100 (denominator is now 100) = 94% (converted to percentage) > 92% (Marty's score)

Hope this helps!

Answer:

Austin earned a higher score.

Step-by-step explanation:

Marty 50 * 0.92 = 46 points

The next number in the series is 25.

Number is a fundamental concept in mathematics, used to represent a quantity. It can be represented in many forms, such as an integer, a fraction, a decimal, and a ratio. Numbers are used to measure and quantify almost every physical phenomenon in the world. They form the basis of scientific principles, such as Newton's law of gravitation, and are used in everyday life for activities such as counting and calculating. Number is also an important concept in other disciplines, such as philosophy, psychology, and sociology.

This series follows a pattern of adding the previous two numbers together. Therefore, the next number in the series is the sum of 25 and -7, which is 32. This pattern can be continued indefinitely, with the next number in the series being 39 (32 + 7) and so on.

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Answer:

The circumference of a circle is calculated using the formula: C = πd, where C represents the circumference and d represents the diameter of the circle.

In this case, the diameter of the circle is given as 24 inches.

Using the formula, we can substitute the values:

C = πd

C = 3.14 * 24

C ≈ 75.36 inches

Therefore, the circumference of a circle with a diameter of 24 inches (and using π = 3.14) is approximately 75.36 inches.

Step-by-step explanation:

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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Area of chalkboard = 4 feet x 6 feet = 24 square feet.

Total cost = 24 square feet x $7.21 per square foot = $173.04

Answer: $173.04

Answer:

Left-hand side: \(\displaystyle -\frac{1}{2}\, \ln(5)\).

Right-hand side: \(\displaystyle \frac{1}{2}\, \ln(5) - \ln(5)\).

Step-by-step explanation:

Apply the logarithm power rule: \(\ln \left(x^{a}\right) = a\, \ln (x)\) for all \(x >0\).

This property is not only true for logarithm to the base \(e\), but for other bases, as well.

Take the logarithm (to the base \(e\)) of the left-hand side of this equation:

\(\displaystyle \ln \left(5^{-1/2}\right) = (-1/2)\, \ln(5)\).

For the right-hand side of this equation, consider the logarithm quotient rule:

\(\displaystyle \ln \left(\frac{a}{b}\right) = \ln(a) - \ln (b)\) for all \(a> 0\) and \(b > 0\).

Indeed, on the right-hand side of this equation, \(\sqrt{5} > 0\) and \(5 > 0\). Therefore:

\(\displaystyle \ln\left(\frac{\sqrt{5}}{5}\right) = \ln\left(\sqrt{5}\right) - \ln(5)\).

This expression could be further simplified. Notice that \(\sqrt{x}\) is equivalent to \(x^{1/2}\) for all \(x \ge 0\). (Think about how \(\sqrt{x} \cdot \sqrt{x} =x\) whereas \(x^{1/2} \cdot x^{1/2} = x^{(1/2) + (1/2)} = x\).)

Therefore, \(\ln \left(\sqrt{5}\right)\) would be equivalent to \(\ln\left(5^{1/2}\right)\). Apply the logarithm power rule to show that \(\displaystyle \ln\left(5^{1/2}\right) = \frac{1}{2}\, \ln(5)\).

\(\begin{aligned} \text{R.H.S.} &= \ln\left(\frac{\sqrt{5}}{5}\right) \\ &= \ln\left(\sqrt{5}\right) - \ln(5) \\ &= \frac{1}{2}\, \ln(5) - \ln (5) = -\frac{1}{2}\, \ln(5)\end{aligned}\).

Indeed, the left-hand side of this equation matches the right-hand side.

Answer:

-4, -1/7,0.09,π/2,√3 ,√225,17

Step-by-step explanation:

π/2, is approx 1.5

-4,

0.09,

17,

√3 is approx 1.7

,-1/7, is approx -.143

√225 = 15

From most negative to greatest

-4, -1/7,0.09,π/2,√3 ,√225,17

Answer:

\(-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17\)

Step-by-step explanation:

So we have the numbers:

\(\pi/2, -4, 0.09, 17, \sqrt3, -1/7, \sqrt{225}\)

(And without using a calculator) approximate each of the values.

π is around 3.14, so π/2 is around 1.57.

17 squared is 289, so 1.7 squared is 2.89. Thus, the square root of 13 is somewhere between 1.7 and 1.8.

-1/7 can be divided to be about -0.1429...

And the square root of 225 is 15.

Now, use the approximations to place the numbers:

\(\pi/2\approx1.57; -4; 0.09;17;\sqrt3 \approx1.7; -1/7\approx-0.14;\sqrt{225}=15\)

The smallest is -4.

Next is -1/7 or about -0.14

Followed by the first positive, 0.09.

And then with π/2 or 1.57

And then a bit bigger with the square root of 3 or 1.7.

And then with the square root of 225 or 15.

And finally the largest number 17.

Thus, the correct order is:

\(-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17\)

Metric tons of soil lost during its formation \(2.96*10^-7\)

Gully is 2 meter deep 4 meter wide and 50 meters long.

So we know if Gully length = l width =w height =h

then volume of gully is l*b*h.

by same way volume of gully is 50*4*2 = 200 \(m^3\)

Bulk density of this soil is 1.48 mg/m^3.

How many metric tons of soil lost during its formation?

1000kg = 1 metric ton.

density  = 1.48mg/m^3 = \(1.48*10^-6\) kg/m^3

means for 1 m^3 volume we lost \(1.48*10^-6\) kg of soil.

for 200m^3 volume we lost \(200*1.48*10^-6\) kg of soil.

\(296*10^-6\) kg of soil.

to convert kg into metric ton we have to divide 1000.

\(296*10^-6\)/1000 = \(296*10^-9\) = \(2.96*10^-7\)

So  Metric tons of soil lost during its formation \(2.96*10^-7\)

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The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

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

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)

Answer:

1,500 pounds :>

Step-by-step explanation:

There are 2,000 pounds in 1 ton, take away 500 from 2,000 you get 1,500

Answer:

46666

Step-by-step explanation:

FALSE

7Y= 1 --> Y= ⅐ NOT 7

so it can't be it's solution

Answer:

48 cans must be sampled.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.99}{2} = 0.005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.005 = 0.995\), so Z = 2.575.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

The machine is calibrated so that the population standard deviation is 0.04 ounces.

This means that \(\sigma = 0.04\)

How many filled cans must be sampled so that we estimate the mean fill volume within 0.015 ounces with 99% confidence?

n cans must be sampled, and n is found when M = 0.015. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.015 = 2.575\frac{0.04}{\sqrt{n}}\)

\(0.015\sqrt{n} = 2.575*0.04\)

\(\sqrt{n} = \frac{2.575*0.04}{0.015}\)

\((\sqrt{n})^2 = (\frac{2.575*0.04}{0.015})^2\)

\(n = 47.2\)

Rounding up, 48 cans must be sampled.

The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.

To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.

Algorithm/Abstract Strategy:

Start with the numerator, which is 3.

Identify the denominator, which is 5.

Interpret the fraction as a ratio or comparison between the numerator and denominator.

Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).

Perform the division: 3 ÷ 5.

Simplify the division to its simplest form, if necessary.

The result of the division, in this case, is the decimal representation of the fraction.

If required, convert the decimal representation to a percentage or any other desired form.

For example, if we perform the division 3 ÷ 5, the result is 0.6.

So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.

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Answer:

he can rent the camera for 5 days and will have $5 left over

Step-by-step explanation: he only has $50 , and he has to pay 15 to register which will leave him with 35 left over and then he pays $6 each day and it would be 5 days of renting.

50-15+35

6x5=30 which means he pays $6 everyday for 5 days

which will leave $5 left over

Answer:

Domain= {x:x £|R}

|R=any real number

Answer:

a)  Commutative Property of Multiplication

b)  Associative Property of Multiplication

c)  Distributive Property of Multiplication over Addition

d)  Inverse Property of Multiplication

e)  Zero Property of Multiplication

Step-by-step explanation:

The Commutative Property of Multiplication states that the order of factors in a multiplication operation can be rearranged without changing the end result.

The Associative Property of Multiplication states that the grouping of factors in a multiplication operation by parentheses in a different way does not affect their product.

The Distributive Property of Multiplication over Addition states that multiplying a number by the sum of two other numbers is equivalent to multiplying the number separately by each of the two numbers and then adding the results.

The Inverse Property of Multiplication states that if a number is multiplied by its reciprocal (multiplicative inverse), the product is always equal to 1.

The Zero Property of Multiplication states that the product of any number and zero is always zero.

Answer:

\( \sf \large{m=−3}\)

Step-by-step explanation:

Let's solve your equation step-by-step.

10=7−m

Step 1: Simplify both sides of the equation.

10=7−m

10=7+−m

10=−m+7

Step 2: Flip the equation.

−m+7=10

Step 3: Subtract 7 from both sides.

−m+7−7=10−7

−m=3

Step 4: Divide both sides by -1.

−m/−1= 3/−1

m=−3

Answer:

n[total]=5

now

probability to Lisa and another girl are chosen to read=n[Lisa]/5×n[another girl]/4=1/5×1/5=1/25=0.04 is your answer

Step-by-step explanation:

Solution :

here ,

n= 5

then,

The probability that Lisa and another girl are chosen to read = n(Lisa)/5×n ( another girl ) /4

=1/5×1/5

=1/25

=0.04 answer

hope it is helpful to you ☺️

Answer:

which question?

Step-by-step explanation:

I'm confused on what your trying to solve

Answer:

The data provide strong evidence that young men weigh more on average than old men in the U.S

Step-by-step explanation:

Given :

The null hypothesis ; H0 : μ1 = μ2

The alternative hypothesis ; H1 : μ1 > μ2

T score = 5.3 ; Pvalue = < 0.0001

The decision region :

If Pvalue < α ; We reject the Null

If Pvalue > α ; We fail to reject the Null

When the α - level isn't stated, we usually assume a α - level of 5%

However, even at lower alpha level of 1% = 0.01 ;

The Pvalue < α

Hence, we can conclude that there is significant evidence that there is difference in the mean weight of young men and old men in the U.S

Equation for the perpendicular bisector of the line segment is  

2y = 3x +20.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

Given coordinates of the endpoints of a line segment  (-9, 3) and (-3,-1).

In order to find the equation of perpendicular line, we need to find the slope between given coordinates.

Slope between  (-9, 3) and (-3, -1). :

slope = \(\frac{-1-3}{-3+9} =\frac{-2}{3}\)

Slope of the perpendicular line is reciprocal and opposite in sign.

Therefore, slope of the perpendicular line = 3/2

Now, we need to find the midpoint of the given coordinates.

\(Mid points : \\x= \frac{ -9-3}{2} =-6\\ y= \frac{3-1}{2} = 1\\ pint = (-6,1)\)

Let us apply point-slope form of the linear equation:

y-y1 = m(x-x1)

y - 1 = 3/2 (x + 6)

2y = 3x +20

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Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

12

Step-by-step explanation:

144 divided by 12 is 12

1st row=x

2nd row=x+2

3rd row=x+2+2

1st row=x=28

2nd row=x+2=28+2=30

3rd row=x+2+2=28+2+2=32