Lamar is considering two loans

Which loan will have the lowest total payback?

The sum of squares of the lengths  of the triangle is 130 and the square of the length of the hypotenuse is 65

This is a triangle with 3 sides and one side is called the hypotenuse which faces one of the angles 90°

Analysis:

distance between two points = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

distance AB with coordinates A(-2,4) B(5,0) = [tex]\sqrt{(5 - -2)^{2} + (0 - 4)^{2} }[/tex] = [tex]\sqrt{65}[/tex]

distance AC with coordinates A ( -2,4) C(2,6) = [tex]\sqrt{(2--2)^{2} + (6-4)^{2} }[/tex] = [tex]\sqrt{20}[/tex]

distance BC with coordinates B(5,0)  C(2,6) = [tex]\sqrt{(2-5)^{2} + (6-0)^{2} }[/tex] = [tex]\sqrt{45}[/tex]

sum of squares of the lengths = [tex](\sqrt{45} )^{2}[/tex] + [tex](\sqrt{65}) ^{2}[/tex] + [tex](\sqrt{20}) ^{2}[/tex] = 65 + 45 + 20 = 130

the square of the length of the hypotenuse = 65

In conclusion, the sum of the squares of the three length is 130 and the square of the hypotenuse is 65

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The computation of the index shows that the value of 9 × 10² will be 900.

From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:

= 9 × 10²

Note that 10² simply means that you've to multiply 10 twice. This will be:

= 10 × 10 = 100

Therefore, 9 × 10² will be:

= 9 × 100

= 900

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Answer:

2 hours

Step-by-step explanation:

Mike has a six hour head start so he is    6 x 2 = 12 miles ahead

 their 'closing speed' is  8-2 = 6 m/hr

    it will take Kim   12 / 6  = two hours to catch Mike

Answer:

0.341

Step-by-step explanation:

Multiply the probabilities: 0.55 * 0.62 = 0.341

Answer:

Circumference: 25.12m

Area: 50.24 [tex]m^{2}[/tex]

Step-by-step explanation:

Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius

C=3.14*2*4=3.14*8=25.12

Formula for area of a circle: A=[tex]\pi r^{2}[/tex]

A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24

Answer:

Step-by-step explanation:

-5x+4y=-3

-6(-5x+4y)=-6×(-3)=18

When Leonardo and his wife file married filing jointly in 2021, the average tax rate will be 15.63 percent

In the question above, Leonardo's taxable income = $80,000

Theresa's taxable income = $15,000

Total taxable income for both of them will be:

$ 80,000 + $ 50,000 = $ 130,000

When you make use of the Schedule Y-1,

The amount of the tax on total income shall be said as:

Tax liability = $9,086 + (($130,000 - $78,950) * 22%)

= $9,086 +($51,050 * 22%)

= $9,086 + $11,231

= $ 20,317

To get the Effective tax rate, it will be:

= tax liability / Total taxable income Effective tax rate

= [tex]\frac{20,317}{30000}[/tex]  that is also written as $20,317/ $130,000

So, the  average tax rate is = 15.63%

Therefore, the average tax rate will be = 15.63 percent

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Answer:

1, 4, 5, 6

Step-by-step explanation:

to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).

you can also double check by plugging both into a calculator and see if they equal the same number.

Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

where:

Rewrite both equations into slope-intercept form:

a) 2x + 4y = 15

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

b) 6x + 12y = 45

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

New equations:

[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

No Solution: the same slope (both lines will be parallel)

One Solution: different slopes and different y-intercepts

Infinitely Many Solutions: the same slope and y-intercept

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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

Equation #1

Subtract 2x from both sides

Divide both sides by 4

Equation #2

Subtract 6x from both sides

Divide both sides by 12

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

The set of input of the function are {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }

The set of output of the function is a multiple of 40 from 200 to 640

The input of the function can be found as follows:

The camp can only run if we have at least 5 students.

The limits of student is 16.

Therefore, the input are  {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }

The output are the dependent variables or the range. They are gotten when we input the values of the input in the function.

Therefore,

R(n) = 40n

R(5) = 40(5) = 200

R(16) = 40(16) = 640

The output are multiple of 40 from 200 to 640

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Answer: 29, 31, 37, 41, 43, 47, 53.

Step-by-step explanation:

Answer:

Mean = 3.125 ≈ 3.13

Step-by-step explanation:

Mean = Sum of numbers =  1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13

           Amount of number                     8                             8

Answer:

Area of the circle = 227.0095 cm^2

Step-by-step explanation:

Given:

To Find:

Area of the circle

Soln:

We know that,

Area of the circle: πr²

where:

But we don't know the radius,as the diameter is given.We could use the formula of diameter & plug the value of it do find the radius.

[tex] \rm \: Diameter = 2(r)[/tex]

Where

Substitute the value of Diameter:

Diameter = 2r

17 = 2r

17/2 = r

8.5 = r

r = 8.5

Now we got the radius, so substitute radius onto the formulae:

[tex]\text{Area of circle} = \pi\cdot \text{Radius}^2\\\\\\~~~~~~~~~~~~~~~~~~=\pi~ \left( \dfrac{\text{Diameter}}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=3.142 \left(\dfrac{ 17}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=227.0095~ \text{cm}^2[/tex]

=================================================================

Explanation:

Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.

The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.

Multiply this floor area with the height of the room (22 m) to get the volume of the room.

volume = (floor area)*(height) = 84*22 = 1848 cubic meters

The total cost when 881 minutes is used is $477.50.

a + 480b = 277 equation 1

a + 990b = 532 equation 2

Where:

Subtract equation 1 from equation 2

510b = 255

b = 255 / 510

b = $0.50

In order to determine the flat fee, substitute for b in equation 1

a + 480(0.5) = 277

a + 240 = 277

a = 277 - 240

a = $37

Total cost = flat fee + (variable cost x number of minutes spoken)

$37 + (881 x 0.5) = $477.50

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Answer:

the class earned $722059884

Step-by-step explanation:

because each person sold 444 tickets and there was 232323 students

=232323×444

=103151412

because 103151412 tickets were sold and a ticket cost $7

=103151412×7

=722059884

Answer:

$2142.86

Step-by-step explanation:

The remaining part of her money, after spending 3/5 of it and depositing 1/8 of it is equal to $750.

===============================================================

Retracing the steps :

⇒ She put 1/8 of the remainder in the bank, which gives $750

⇒ R - R/8 = 750

⇒ 7R/8 = 750

⇒ R = 750/7 × 8

⇒ R = 107.142857 × 8

⇒ R = 857.142856

* Don't worry, we'll simplify at the end of the answer *

=============================================================

Now, this remainder is what was left after spending 3/5 of it.

⇒ T - 3/5T = 857.142856

⇒ 2/5T = 857.142856

⇒ T = 857.142856/2 × 5

⇒ T = 428.571428 × 5

⇒ T = $2142.86 (nearest cent)

A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x) and g(x) can be plotted as shown in the below image.

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The simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have an expression:

[tex]= 8 \dfrac{3}{8} + 3 \dfrac{3}{8} + 2 \dfrac{3}{8} + \dfrac{3}{8}[/tex]

After simplification:

[tex]= \dfrac{67}{8} + \dfrac{27}{8} + \dfrac{19}{8} + \dfrac{3}{8}[/tex]

[tex]= \dfrac{67+27+19+3}{8}[/tex]

= 116/8

= 29/2

[tex]= 14\dfrac{1}{2}[/tex]

Thus, the simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.

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Answer:

i dont understand your question

Step-by-step explanation:

The equation of the scatter plot is (a) y = 100x + 2

The line of best fit of the scatter plot passes through the points

(x,y) = (0,2) and (1,102)

Start by calculating the slope using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{102 - 2}{1 - 0}[/tex]

m = 100

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 100(x -0) + 2

Evaluate

y = 100x + 2

Hence, the equation of the scatter plot is (a) y = 100x + 2

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From the question given above, the ratio of L : W in simplified form is given as: 6 : 5. See the explanation below.

A ratio, simply, can be defined as the quantitative relationship that exists between two values which is indicative of the number of times one value can be obtained from the other.

Let X be the width of one of the rectangles and let its height be Y.

It is clear from the image that:

4X = 3Y

Hence

(4/3)X  = Y

Therefore,

Lenght (L) = 3Y

= 3 (4/3)X

= 4X

Width (W) = Y + 2X

= (4/3)X + 2X

= (10/3)X

Therefore,

L : W =  4X: 10/3X

= 4:10/3

To remove the fraction, multiply both sides of the ratio by 3

= 12 : 10, furhter simplify by halving each value, and we have

= 6:5

Hence, the ratio L: W in simplified form is 6 : 5.

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Answer:

[tex]\frac{1}{102}[/tex]

Step-by-step explanation:

1) Negative Power Rule: [tex]x}^{-a}=\frac{1}{{x}^{a}}[/tex].

[tex]\frac{1}{3}\div 34[/tex]

2) Use this rule: [tex]a\div \frac{b}{c}=a\times \frac{c}{b}[/tex].

[tex]\frac{1}{3}\times \frac{1}{34}[/tex]

3)  Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}[/tex].

[tex]\frac{1\times 1}{3\times 34}[/tex]

4) Simplify [tex]1\times 1[/tex] to [tex]1[/tex].

[tex]\frac{1}{3\times 34}[/tex]

5) Simplify  [tex]3\times 34[/tex] to [tex]102[/tex] .

[tex]\frac{1}{102}[/tex]

Finding the correlation coefficient, it is found that the regression line shows a:

negative trend line with a strong relationship.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is of -0.85, which is negative and strong.

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Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85,

The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.

Finding the correlation coefficient, it is found that the regression line shows a: negative trend line with a strong relationship.

It is an index that measures the correlation between two variables, assuming values between -1 and 1.

If it is positive, the relationship is positive, that is, they are directly proportional. If it is negative, they are inversely proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85, which is negative and strong.

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The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.

Conversion means to convert the same thing into different units.

Convert the degree measure to the radian measure.

⇒ 75°

We know the conversion is given as

180° = π radian

   1° = π/180°

Then we have

75° = 75° x π/180° radian

75° = 1.30899 radian

75° ≅ 1.31 radian

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well, the total amount of technicians employed is 100% and that is "x" amount, now, we also know that 3% of of that is 10800, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 10800& 3 \end{array} \implies \cfrac{x}{10800}~~=~~\cfrac{100}{3} \\\\\\ 3x=1080000\implies x=\cfrac{1080000}{3}\implies x=360000[/tex]

Answer:

O The value of f(2) is smaller than the value of f(1).

Step-by-step explanation:

First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)

Answer:

Step-by-step explanation:

Answer:

the function is only increasing.

Step-by-step explanation: