Proper subset is a set that contains elements contained in another set but not equal
to that set.
True or false

Answer:

both sides are equal to: [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

Trigonometric functions are defined as the ratios between sides based on some angle. There's three main trig functions you want to remember which are defined as:

[tex]sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\\\\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex]

and then there are three other trig functions, which are simply the reciprocals:

[tex]csc(\theta)= \frac{\text{hypotenuse}}{\text{opposite}}=\frac{1}{sin(\theta)}\\\\sec(\theta) = \frac{\text{hypotenuse}}{\text{adjacent}}=\frac{1}{cos(\theta)}\\\\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}=\frac{1}{tan(\theta)}[/tex]

Now in our case we have the angle of 45 degrees and we have the hypotenuse with length 16, and we want to either solve for the opposite (x) or adjacent side (y)

Let's solve for the adjacent side, in which case we want a trig function defined using the hypotenuse and adjacent side, which is our cosine function.

[tex]cos(45)=\frac{y}{16}\implies cos(45)*16=y[/tex] and from here we can use a calculator or the unit circle which gives us an exact value. Using the unit circle, we can determine that: [tex]cos(45)=\frac{\sqrt{2}}{2}[/tex] and plugging that into our equation we get: [tex]y=\frac{\sqrt{2}}{2}*16=8\sqrt{2}[/tex] and we can use a calculator to approximate this: 11.313

Now we can also use the trig functions to find "x", which is the opposite side. In this case we want to use a trig function which is defined using the opposite and hypotenuse side, which is our sine function: [tex]sin(45)=\frac{x}{16}\implies sin(45)*16=x[/tex] and the cool thing about this, is that sin(45) and cos(45) are actually equal, so our "x" and "y' side are exactly equal: [tex]x=8\sqrt{2}[/tex]

We can verify this using the Pythagorean Theorem: [tex](8\sqrt{2})^2+(8\sqrt{2})^2=16^2\\\\(8^2*\sqrt{2}^2)+(8^2+\sqrt{2}^2)=256\\\\(64*2)+(64*2)=256\\\\128+128=256\\\\256=256[/tex]

The parameters for the home mortgage, and the monthly payment, PMT,  for the mortgage are as follows;

Part 1;

P = $175,000, APR = 7%, n = 12, Y = 30

Part 2;

The monthly payment for the mortgage, PMT ≈ $1,164.28

A mortgage is a loan agreement, with the possession of the collateral presented for the loan such as a house being bought with the loan amount, being relinquished by the debtor, upon default

Part 1

The value of the mortgage  = $175,000

The fixed Annual Percentage Rate, APR = 7%

The duration of the payment = 30 years

Part 2; The monthly payment PMT loan formula can be presented in the following format;

Therefore;

[tex]PMT = \frac{175000\times \frac{0.07}{12} }{1-\left(1+\frac{0.07}{12}\right)^{(-12\times 30)} } \approx 1164.28[/tex]

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By using the substitution method, the value of a is equal to 10 and the value of b is equal to -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2a + 7b = 13      .......equation 1.

8b = 2 - a          .......equation 2.

From equation 2, we have:

a = 2 - 8b         .......equation 3.

By using the substitution method to substitute equation 3 into equation 1, we have the following:

2(2 - 8b) + 7b = 13

4 - 16b + 7b = 13

4 - 9b = 13

9b = 4 - 13

9b = -9

b = -1

a = 2 - 8b

a = 2 - 8(-1)

a = 2 + 8

a = 10.

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The APY for the account would be 3.045%.

What is continuous compounding?

The formula for continuous compounding is given by:

A = P[tex]e^{(rt)}[/tex]

where:

A = final amount

P = principal amount

e = the mathematical constant e (approximately 2.71828)

r = annual interest rate

t = time in years

In this case, P = $1000, r = 0.03 (since APR is given), and t = 1 year.

Using the formula, we have:

A = 1000[tex]e^{(0.03*1)}[/tex]

A ≈ $1030.45

So the balance in the account after 1 year is approximately $1030.45.

To find the balance after 5 and 20 years, we simply need to plug in the corresponding values for t:

For t = 5:

A = 1000[tex]e^{(0.03*5)}[/tex]

A ≈ $1160.92

For t = 20:

A = 1000[tex]e^{(0.03*20)}[/tex]

A ≈ $1806.11

To find the APY, we use the formula:

APY = (1 + r/n)ⁿ- 1

where:

n = number of compounding periods per year

Since this is continuous compounding, we take the limit as n approaches infinity:

APY = eʳ - 1

APY = [tex]e^{0.03}[/tex] - 1

APY ≈ 0.03045 or 3.045%

Hence, the APY for the account would be 3.045%.

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Answer: The  range of f(x) is [tex]f(x)\geq -2[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)+2=\frac{1}{6}|x-3|[/tex]

It can be written as

[tex]f(x)=\frac{1}{6}|x-3|-2[/tex]                ...(1)

The function is in the form of

[tex]g(x)=a|x-h|+k[/tex]               ...(2)

Where, a is scale factor and (h,k) is vertex of the graph.

On comparing (1) and (2), we get

[tex]a=\frac{1}{6}[/tex]

[tex]h=3[/tex]

[tex]k=-2[/tex]

The value of a is [tex]\frac{1}{6}[/tex] . So, the graph compressed vertically. The value of a is positive, therefore the graph of f(x) opens upward.

We know the absolute value is always greater than or equal to 0.

[tex]|x-3|\geq 0[/tex]

[tex]\frac{1}{6}|x-3|\geq \frac{1}{6}(0)[/tex]

[tex]\frac{1}{6}|x-3|\geq 0[/tex]

[tex]\frac{1}{6}|x-3|-2\geq 0-2[/tex]

[tex]f(x)\geq -2[/tex]

hope you've understood...

The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Let 'x' be the amount of investment at a rate of 4.75%. Then the amount of investment at a rate of 2.75% is ($18,000 - x). Then the equation is given as,

(18,000 - x) × 0.0275 + 0.0475x = 579

495 - 0.0275x + 0.0475x = 579

0.02x = 84

x = $4,200

Then the value of ($18,000 - x) is given as,

$18,000 - x = $18,000 - $4,200

$18,000 - x = $13,800

The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.

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Selma needs to leave the money in the new account for at least one year, option A. 1 to recover the penalty paid.

Assuming Selma wants to recover the penalty paid using the extra interest earned in the new account, she needs to calculate the amount of time it will take for the new account's interest to make up for the penalty paid.

Let P be the initial amount of money in Selma's current account. The penalty for closing the account is 5% of P, which is 0.05P.

If Selma leaves the money in the current account for one year, she will earn simple interest of 5% of P, which is 0.05P. So at the end of the year, the balance in the current account will be P + 0.05P = 1.05P.

If Selma transfers the money to the new account, it will earn compound interest of 8% per year, compounded quarterly. The quarterly interest rate is 8%/4 = 2%.

After one quarter, the balance in the new account will be:

P*(1 + 2%/4) = P*1.02

After two quarters, the balance will be:

P1.02(1 + 2%/4) = P*1.02^2

After three quarters, the balance will be:

P1.02^2(1 + 2%/4) = P*1.02^3

After four quarters (i.e., one year), the balance will be:

P1.02^3(1 + 2%/4) = P*1.02^4

So at the end of one year, Selma will have 1.05P in the current account and P*1.02^4 in the new account.

To recover the penalty of 0.05P, Selma needs the balance in the new account to be at least 1.05P. That is,

P*1.02^4 >= 1.05P

Simplifying, we get:

1.02^4 >= 1.05

Taking the fourth root of both sides, we get:

1.02 >= 1.05^(1/4)

Using a calculator, we get:

1.02 >= 1.01298

So Selma needs to leave the money in the new account for at least one year to recover the penalty paid.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

y = f(x) represents a function with output value as y and x as an input in the function.

Therefore, f(2) represents value of function (y) at x = 2

so the correct choice here would be : " the output (y - value) when x = 2 "

Answer: $169.15

Step-by-step explanation: 15 percent of 199 is 29.85, and 199-29.85 is 169.15

The measurement closest to the area of the circle in meters is 379.94 sq. meters.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The word "area" refers to a free space. A shape's length and width are used to compute its area. The majority of forms and things have corners and edges. When computing the area of a certain form, both the length and width of these edges are taken into account.

Given that,

diameter = 22m

radius = 22/2 = 11m

The area of the circle is:

A = πr²

Substituting the value of π = 3.14 and r = 11 we have:

A = (3.14)(11)²

A = 379.94

Hence, the measurement closest to the area of the circle in meters is 379.94 sq. meters.

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The solution is,

(a) Output = 37

(b) Input = 9

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

Given

y=5x -3

Solving (a): Output, when input = 8

This means that, we solve for y when x = 8

So, we have:

y=5x -3

 =5*8 -3

 =40 - 3

 = 37

Solving (b): Input, when output = 42

This means that, we solve for x when y = 42

So, we have:

y=5x -3

5x = 42+3

    = 45

Collect like terms

Divide both sides by 5

x = 9

Hence, The solution is,

(a) Output = 37

(b) Input = 9

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Answer:

To solve this problem, we can use the formula for exponential growth:

V(t) = V0 * (1 + r)^t

where:

V(t) is the value of the equipment at time t

V0 is the initial value of the equipment ($15,000)

r is the annual growth rate (15.9% or 0.159)

t is the time in years

We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:

V(t) < 7500

Substituting the formula for V(t), we get:

V0 * (1 + r)^t < 7500

Substituting the given values, we get:

15000 * (1 + 0.159)^t < 7500

Simplifying and solving for t,

we get:(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

So the company's new equipment will be worth less than $7500 after about 2.64 years.

Step-by-step explanation:

The constant of proportionality for the given graph is 6.

The two sequences of numbers are proportional or directly proportional if the ratio between the corresponding elements of two sequences of numbers, typically experimental data, is constant and is known as the coefficient of proportionality or proportionality constant.

From the given graph the point is (5,30) from which the line is passing.

The equation for the constant of proportionality is written as below,

y = kx

Substitute the points in the above equation,

y = kx

30 = k x 5

k = 30 / 5

k = 6

Therefore, the proportionality constant for the displayed graph is 6.

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Answer:

Step-by-step explanation:

I do not know bro. If I was a robot i'd know. I don't. I'm different.

The domain and the range of the ordered pairs in interval notations are as follows: 1) Domain = [0,4], Range = [1,5]   ; (2) Domain [-1,-4], Range =[0,-3]

The domain of a function is the collection of all conceivable values that may be used as inputs, or alternatively, it is the whole array of possible values for independent variables.

The range of a function is the set of every possible value for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.

In a set of ordered pairs (x,y), the domain (input) refers to all the x-values and the range refers to all the y-values.

From the points on the graph given:

(0,1) (1,2) (2,3) (3,4) (4,5)

Domain: (0, 1, 2, 3, 4)

Range: (1, 2, 3, 4, 5)

(-1,0) (-2,-1) (-3,-2) (-4,-3)

Domain: ( -1, -2, -3, -4)

Range: (0, -1, -2, -3)

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On solving the provided question we can say that the expressions are    

a)  1000

b  10

c) 100000.001

d) 99000

In mathematics, it is pοssible to multiply, divide, add, or remove. The construction of an expression is as follows: Expressiοn, number, and mathematical operatοr Numbers, variables, and functions are the building blocks of a mathematical expressiοn (such as addition, subtraction, multiplicatiοn or division etc.)

Expressiοns and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic οperation between them is called an expression or an algebraic expressiοn. For instance, the expressiοn 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expressiοn, all of which are separated by the arithmetic sign +.

The expressiοns are

a)10¹⁵/10¹² = 10³ = 1000

b)10¹/10⁰ = 10/1 = 10

c)10⁵ + 10⁻³ = [tex]\dfrac{10^8 +1}{100}[/tex]= 100000.001

d)10⁵ - 10³ = 100000 - 1000 = 99000

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The value of x for the given circle will be going to be 50°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circle objects for example our bike wheel.

Area of circle = πr² and the perimeter of circle = 2πr

where r is the radius of the circle.

Angles of Intersecting Chords Theorem

When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

So, angle x = (190° + 40°)/2  = 115°

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Using the system of equations, we found the number of adult tickets sold as 82 and the number of child tickets sold as 42.

What is the system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Given,

Number of tickets sold = 124

Cost of one adult ticket = $ 12.50

Cost of one child ticket = $ 6.50

Total money received = $ 1298

We can write a system of equations using the above information.

Number of adult tickets sold = x

Number of child tickets sold = y

x + y = 124

12.5x + 6.5y = 1298

Solving the above equations, we can find x and y.

Multiplying the first equation by 6.5

6.5x+ 6.5y = 806

12.5x + 6.5y = 1298

Subtracting the equations,

-6x = -492

x = 82

Substituting the above value in any one of the equation

82 + y = 124

y = 42

Therefore from the system of equations, the number of adult tickets sold is 82 and the number of child tickets sold is 42.

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The demonstration of magnitude of power given by 80 kg monkey by climbing a 15 meter tree in half a minute is equal to option b.  392 J/S.

Weight 'm' of the monkey is equal to 80kilogram

Height 'h' of the tree is equal to 15 meter

Time 't' taken by monkey to climb a tree = half a minute

                                                                    = 30 minutes

g = 9.8 m/s²

Magnitude of power = ( m × g × h )/ t

⇒ Magnitude of power = ( 80 × 9.8 × 15 )/ 30

⇒ Magnitude of power = 784 / 2

⇒ Magnitude of power = 392 J/S

Therefore, the magnitude of the power for the given weight , displacement and time is equal to option b. 392 J/S.

The above question is incomplete, the complete question is:

A 80 Kg monkey climbs a 15 meter tree in half a minute. What is the magnitude of power the monkey demonstrated?

a. 13.1 J/S

b. 392 J/S

c. 784 J/s

d. 11760 J/s​

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Answer:

Step-by-step explanation:

The surface area of a rectangular box can be calculated as follows:

Surface area = 2lw + 2lh + 2wh

Where l is the length, w is the width, and h is the height.

We are given the surface area (500 ft2) and the length and width (16 ft and 7 ft respectively), so we can use these values to solve for the height:

500 = 2 * 16 * 7 + 2 * 16 * h + 2 * 7 * h

500 = 224 + 32h + 14h

500 = 238h + 224

276 = 238h

h = 276 / 238

h = 1.16 ft

So the height of the box is approximately 1.16 feet.

The correct solution to the problem is m = 92 and the error made was subtracting 7 from both sides of the equation instead of dividing both sides by 7

Incorrect Work/Solution:

m = the number of messages Nigel sent

644 = 7m

subtract 7 from both sides

644 - 7= 7m - 7

637 = m

Nigel sent an average of 637 messages

each day last week.

Correct solution:

644 = 7m

divide both sides by 7

m = 644/7

m = 92

Therefore, Nigel sent an average of 92 messages

each day last week.

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Answer:

96

Step-by-step explanation:

z-scores are defined as: [tex]z=\frac{x-\mu }{\sigma}[/tex], and this may look a bit confusing at first but by looking at the numerator and then denominator we can get a more understandable definition.

The numerator is first finding the difference between the statistic and the mean. It then divides by the standard deviation, so essentially it's telling us  how far the statistic is from the mean in terms of standard deviation.

We can actually rewrite the equation to express this:

[tex]z=\frac{x-\mu }{\sigma}\\\\z\sigma = x-\mu\\\mu + z\sigma=x[/tex]

So in essence, how many standard deviations the statistic is away from the mean.

Now this may seem very off topic compared to what the problem is asking, but we want to convert the top 5% to a z-score. Now let's first convert this top 5% to a percentile. To be in the top 5% you just need to be in the 95th percentile and using technology we can convert this into a z-score which is approximately 1.645.

So this means the 95th percentile is 1.645 standard deviations away and in this case above (since it's positive) from the mean.

The good thing is we know the standard deviation and mean, now let's just apply it: [tex]76+1.645(12)=95.74[/tex]. We now want to round this to the nearest integer of 96, and now we have our answer!

Answer:

416,`735

Step-by-step explanation:

Do inverse operations

Step-by-step explanation:

0.25c = 63.25

We would just get c alone by dividing by 0.25 on both sides of the equal sign

c = 253

Answer: C = 253

Step-by-step explanation:

No The triangles' are not congruent

The length of the corresponding sides should be equal and the length of sides is gotten using the equation:

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points A(2, -8), B(-5, -2), C(-7, 3); and ΔDEF: D(-9, 7), E(-11, 12), F(-2, 1) are calculated as follows:

AB =√{(-2 + 5)² + (-8 + 2)²} = 6.71

DE = √{(-9 + 1)² + (7 - 12)²} = 9.43

BC = √{(-5 + 7)² + (-2 - 3)²} = 5.39

EF = √{(-11 + 2)² + (12 - 1)²} = 14.21

AC = √{(2 + 7)² + (-8 - 3)²} =  14.21

DF = √{(-9 + 2)² + (7 - 1)²} = 9.22

Examining the figures showing the side lengths shows that the two triangles are not congruent

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Answer: The sales tax is $2.5 and her total cost of the shirt is $47.5.

Step-by-step explanation:

Answer: interest= 670

Step-by-step explanation:

(1+r)^t*principal