6. jessie and bob are financing $425,500 to purchase a house. they obtained a 30/8 balloon mortgage at 6.55%. what will their balloon payment be? (3 points)
o $379,659.89
0 $637,130.99
o $357,491.39
o $380,040.19

Answer

a=3/2

b=1/2

Step-by-step explanation:

let f(x)=ax+b

f(2x-3)=a(2x-3)+b

f(2x-3)=2ax-3a+b

3x-4=2ax-3a+b

3x=2ax

3=2a

a=3/2

b-3a=-4

b-3(3/2)=-4

b=1/2

The diameter of a circle with a circumference of 69.1 yds is 22.

What is circumference of a circle?

The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference . The radius of the circle is considered when applying the formula to determine the circumference of the circle.

Circumference of circle(C) = 2πR

where,

R represents the radius of the circle

We know that diameter of circle is twice of its radius i.e

Diameter(D) = 2R

Thus, C = πD

We are given Circumference(C) = 69.1yd and π= 3.14

So, using C = πD, we get

⇒69.1 = 3.14*D

⇒D = 69.1/3.14

⇒D = 22

Hence, the diameter of a circle with a circumference of 69.1 yds is 22.

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Answer:

n=3

Step-by-step explanation:

324/2^ n. = 30

324/30 = 2^n

Log 324/30 = Log 2^n = n x Log2

n = Log 324/30 ÷ Log 2

n = 3.43...

as n musg be an integer, thus

take n=3. or 4 will makd the midel height cliase to 30m

Listing of the angles and the sides in the order of smallest to largest is given by :

Side opposite to obtuse angle > Side opposite to acute angle and

side opposite to right angle > side opposite to acute angle.

As given in the question,

In the given triangle,

Ordering of the angles and sides from smallest to largest.

As per the property of the triangle:

Side opposite to the greatest angle is the largest side of the given triangle.

If the given triangle is obtuse angle triangle,

Then other two angles are acute.

Compare all the angles and sides arrange in ascending order.

Side opposite to obtuse angle  > Side opposite to acute angle

In the right angled triangle,

Other two angles are acute.

Same compare and write in ascending order.

side opposite to right angle > side opposite to acute angle

Therefore, the sides and angles can be written in smallest to largest order by comparison and is given by:

Side opposite to obtuse angle  > Side opposite to acute angle and

side opposite to right angle > side opposite to acute angle.

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Note if Tommy were to hire a car to drive 850 miles in 8 days under the price conditions given, it would cost him £575 to go with the cheaper company which is company B.

To compute the cheaper price, we need to work out how much it comes to if he went with either company.

Company A:

Daily Charge £20

Cost per mile 50p

Given that he goes 850 Miles ;

For 8 days,

His Total cost with Company A is

(20 x 8) + [ (50 *850)/100); recall that 100 pence (p) make 1 British Pound (£)

Thus, 160 + 425

= £585

Thus, to go with Company A, Tommy will spend £585

On the other hand, Tommy's Total cost with Company B is computed as follows;

Daily Charge £40

Cost per mile 30p

Total cost will come to: (40 x 8) + [(30 *850)/100)

= 320 + (25500/100)

= £575

Since Company will charge a total of £585 and Company B will charge a total of £ 575, we can conclude that the cheaper company is company B.

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Full Question:

Tommy wants to hire a car to drive 850 miles in 8 days how much would it cost him to hire a car from the cheaper side. See the attached for the pricing conditions.

Answer:

27π

Step-by-step explanation:

Volume = 1/3πr²h
=1/3*(3)²9π
=27π

Answer:

Step-by-step explanation:

4 m/s squared

The equation to find the amount the rental car company will charge for any number of days is y = 75+20(n-3).

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

Given that,

The charge per day for a 3-day rental = 75/3 = 25

The additional charge for an extra 4 days is (155-75)= 80 which is $20 per day.  

The charge for a period of n days (n>3) is then 75+20(n-3).

Thus, The equation to find the amount the rental car company will charge for any number of days is y = 75+20(n-3).

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Answer:

2√(13)= 7.21

Step-by-step explanation:

The formula for Pythagoras' theorem is a² + b² = c². In this equation, c is the longest side of a right-angled triangle. This line is also known as the hypotenuse. A and b represent the other two sides of the triangle.

so h = √(6²+4²) = 2√(13)= 7.21 (approximately)

The domain and range of the rational function in this problem are given as follows:

The domain of a function is the set that contains all the input values that can be assumed by the function.

The function in this problem is a fraction, meaning that the denominator must assume values different of zero, hence the value outside the domain is:

x - 1 = 0 -> x = 1.

The range of a function is the set that contains all the output values that can be assumed by the function.

The function in this problem can be simplified by x - 1, hence at x = 1 it would assume a value of y = 7. However, for the range, we suppose that the function cannot be simplified, hence it is given by all real values except y = 7.

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The inequality that describes the problem is: x*4 >= $14.

This inequality can be read as: "the cost of 4 cups of hot chocolate (x) multiplied by 4 is greater than or equal to $14."

We know that Beth expects to spend at least $14 on the hot chocolate in total, and she's buying 4 cups, so we can set up the inequality with the number of cups and the minimum amount she wants to spend.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

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The value of x (hypotenuse) by using trigonometry is 2√5.

What is trigonometry ?

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.

The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.

In the triangle height = √15  and hypotenuse as x

The value of the angle is  60°

by using trigonomtry we can write

sin60° = height/ hypotenuse

√3/2 = √15/ x

x = (√15 * 2)/√3

x = 2√5

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Answer:

Step-by-step explanation:

-10.9p + 3.9

-10.9p turns positive.

The (p) is isolated.

10.9 - 3.9= 9.18 = -9.18

Answer

-9.18

The values of a, b, c, and d are 1, 2, 3 and 4, though not necessarily in that order. The greatest possible value of ab + bc + cd + da is 25.

Greatest Possible Value:

For any number, whether decimal or integer, the leftmost non-zero digit is most significant. For decimals, this digit is the first non-zero digit to the right of the decimal point, and for integers it is the first digit in a series of numbers. For example, in the fraction 0.00163925, the most significant digit is 1. In the integer 2,473,981, the most significant digit is 2. Rounding off the most significant digit in these two examples gives a fraction of 0.002 and an integer of 2,000,000.

Given That:

The Values of a, b, c and d is 1 ,2 ,3 and 4

Therefore,

4× 2 + 2 × 1 + 1 × 3 +3 × 4

= 25

Therefore, the greatest possible value of ab + bc + cd + da is 25.

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The area of trapezoid ABCD is 98 square units.

Based on the data given, The area of  ΔDBA  = area of  ΔADE  + area of ΔABE  = 20 + 50  = 70. So  

area of Δ DBA  = 0.5 sin DBA (AB x DB)  = 70

sin DBA = 140 / ( AB x DB)

sin DBA = sin CDB

The area of  ΔCDB  would be 0.5 sin (DBA) (DB x DC)  

The area of  ΔCDB = 0.5 (140 / [(AB x DB] ) (DB x DC)

The area of  ΔCDB = 70 (DC/AB)  = 70 ( DE /BE)

The area of ΔAEB  would be 0.5 sin AEB ( AE * BE)

The area of ΔAEB = 50  (1)

Area Δ ADE  would be 0.5 sin DEA (AE * DE)  

Area Δ ADE  = 20  (2)

Because of  angle AEB  is  supplemental to angle DEA, their sines are equal. So  

sin AEB  = sin DEA

Let rearranging (1), (2). So we will have

sin AEB  =   sin DEA

100 / [ AE * BE] = 40 / [ AE * DE ]

DE / BE  = 40/100  = 2/5

Since area of ΔCDB  equal to  70 (DE / BE) then

ΔCDB = 70 (2/5)  =  28

So...area of trapezoid ABCD  = area of ΔDBA  + area of ΔCDB  

area of trapezoid ABCD =  70 + 28 = 98  

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The coordinates of its midpoint M are (0,6)

A line is an infinitely long object with no width, depth, or curvature.

Given that a line segment has the endpoints B(0, 2) and C(0, 10).

We need to find the  coordinates of its midpoint M.

Midpoint=(0+0/2, 2+10/2)

Midpoint=(0, 12/2)

Midpoint=(0, 6)

The coordinates of its midpoint M are (0,6)

Hence, the coordinates of its midpoint M are (0,6)

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The range, variance, and standard deviation are 8, 21.10, 445.21.

The range, variance, and standard deviation are 99, 40.14,1612

What is data?

Data is a collection of measurements or observations used as a source of information. There are numerous types of data and numerous ways to represent data.

Given data is

43, 41, 48, 47, 49

Arrange them in ascending order:

41, 43, 47, 48,49

The range is (49 - 41) =8

The mean is (41+43+47+48+49)/5 =45.6

Data      deviation from mean    square  deviation

41                         4.6                         21.16

43                         2.6                        6.76

47                         -1.4                        1.96

48                         -2.4                        5.76

49                         -3.4                        11.56

Total                                                  47.2

The standard deviation is s = √[(x-μ)²/N] = 21.10

The variance is s² = 445.21

Given data is

100, 1, 3, 95, 70, 4, 6, 10, 5

Arrange them in ascending order:

1, 3, 4, 5, 6, 10, 70, 95, 100

The range is (100 - 1) = 99

The mean is (1+3+4+6+5+10+70+95+100)/9 =32.67

Data      deviation from mean    square  deviation

1                         31.67                         1002.99

3                         29.67                       880.31

4                         28.67                        821.97

5                        27.67                         756.63

6                         26.67                        711.29

10                         22.67                      513.93

70                        -37.33                       1393.52

95                        -62.33                      3885.03

100                         -3.33                        4533.33

Total                                                     14508.0001

The standard deviation is s = √[(x-μ)²/N] = 40.14

The variance is s² = 1612

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The equation that models how many parts p each machine can manufacture in any number of minutes m is m = 1.5p

The term equation in math is defined as a mathematical sentence that has two equal sides separated by an equal sign

Here we have given that a machine manufactures a part in 11 minutes and here we have also know that a newer machine can manufacture the same part 1.5 minutes faster.

Let us consider that p refers the number of parts for old machine and m refers the time taken for manufacturing.

Then the equation can be written as,

=>  m = 1.5p

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Answer:

Step-by-step explanation:

x=2+2[tex]\sqrt{6}[/tex] or x=2-2[tex]\sqrt{6}[/tex]

The data set that represented by the dot plot given is:

D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}

In a dot plot, each data point in a data set is represented by a dot.

To find out the data set that is represented in the dot plot, list out the data points as plotted on the dot plot given.

In the given dot plot that is showing the pulse rates of runners after finishing a marathon, it can be seen that,

There are 1 dot on 145, 5 dots on 165, 6 dots on 175 and 1 dot on 185.

Thus:

Therefore, the data set that represented by the dot plot given is:

D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}

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(a) A larger random sample can potentially reduce the bias of the poll result and (b) a larger random sample will generally reduce the variability of the result.

(a) A larger random sample can potentially reduce the bias of the poll result. Bias in a poll refers to systematic errors in the sampling process that result in inaccurate or unfair representation of the population being polled. A larger sample size means that the poll is more likely to include a diverse range of perspectives and opinions, which can make the results more representative of the population as a whole. However, the sample size alone is not enough to guarantee unbiased results, it also depends on how the sample is selected and how the questions are phrased.

(b) A larger random sample will generally reduce the variability of the result. Variability refers to the degree to which the results of a poll can vary depending on the specific sample that is selected. A larger sample size means that there are more data points being included, which makes the results less susceptible to fluctuations caused by chance. However, the variability also depends on how the sample is selected, having a larger sample size does not guarantee less variability.

In summary, increasing the size of a random sample from 1500 to 4000 people can help reduce bias and variability in the poll results, but it is not a guarantee. Other factors such as the sampling method and question design also play an important role in determining the accuracy and fairness of the poll results.

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Answer:

a. $20,442.09

b. $47,981.82

c. Benny

d. $211,063.58

e. $9,583,450.63

f. Benny

Answer:

yes dont listen to anything isay because i just wants the points its to harda for me

Step-by-step explanation:

Substitute 2x+3y=6 into the first equation:

4x^2+4y^2=(2x+3y)^2

4x^2+4y^2=4x^2+12xy+9y^2

0=12xy+5y^2

Divide both sides by 5:

0=2.4xy+y^2

Subtract 2.4xy from both sides:

-2.4xy=y^2

Take the square root of both sides:

y=±√-2.4xy

Substitute y=±√-2.4xy into the equation 2x+3y=6:

2x+3(±√-2.4xy)=6

2x±3√-2.4xy=6

Add 2x to both sides:

4x±3√-2.4xy=6+2x

Subtract 4x from both sides:

±3√-2.4xy=6-4x

Divide both sides by 3:

±√-2.4xy=2-4/3x

Square both sides:

-2.4xy=(2-4/3x)^2

-2.4xy=4-16/3x+8/9x^2

8/9x^2-16/3x+4+2.4xy=0

Use the quadratic equation to solve for x:

x= (16 ± √(256+192y^2))/18

Substitute this back into the equation 2x+3y=6 to solve for y:

2(16 ± √(256+192y^2))/18 + 3y = 6

3y = 6 - 32 ± √(256+192y^2))/9

3y = -26 ± √(256+192y^2))/9

y = (-26 ± √(256+192y^2))/27

Therefore, the solution is:

x = (16 ± √(256+192y^2))/18

y = (-26 ± √(256+192y^2))/27

The probability that x equals 1 is 0.3151.

What are examples and probability?

The quantity of success-producing options. the total number of outcomes that could occur.

                     For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.

0.05x0.6302 1!(10-1)! =10x0.05x0.6302 = 0.3151 ">

Since the binomial distribution is a discrete distribution, it accepts discrete random variables. This shows that the random variable x can only accept integer values and cannot take the value 0.5000 because it is on an interval scale (continuous). Therefore, the statement that the maximum probability happens when x equals 0.5000 is false.

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The value of x  is 16 cm.

What is the equilateral triangle?

An equilateral triangle is a type of triangle that has three sides of equal length and three equal angles of 60 degrees each. All equilateral triangles are also equiangular and isosceles triangles. The sides of an equilateral triangle are congruent, and it is symmetrical in all ways, meaning that it has rotational and line symmetry.

We have given,

Lengths of sides:

16 cm,  16cm, and x cm,

we have to find the value of x.

The given triangle is an equilateral triangle,

so, The length of all three sides of an equilateral triangle is equal.

16 cm = 16cm =  x cm,

x = 16 cm

Hence, The value of x  is 16 cm.

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Based on the diagram presented, it can be concluded that for every 1 cup of fruit juice, 1.2 cups of iced tea and 0.6 cup of sugar are used.

The diagram shows the three ingredients required to prepare a pitcher of fruit tea and the amount of the ingredients required.

Ingredients required:

Fruit juce: 2.5 cups

Sugar: 1.5 cups

Iced tea: 3 cups

Let's use the rule of three to find the answer:

Sugar required:

2.5 cups = 1.5 cups

1 cup  = x

x= 1.5 / 2.5 = 0.6 cups

Iced tea required:

2.5 cups = 3 cups

1 cup  = x

x = 3 / 2.5 = 1.2

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Answer:

Here is a picture of it graphed

Step-by-step explanation: