Bob’s employer covers 23% of his family’s annual health insurance premium. The balance of the premium is deducted in equal amounts from bob’s paycheck 26 times over the calendar year. If $185. 30 is withheld from each of bob’s paychecks, what is his family’s annual health insurance premium? a. $805. 65 b. $4,817. 80 c. $6,256. 88 d. $20,946. 96.

[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ f(-4)=1\hspace{5em}1=ab^{-4}\implies 1=\cfrac{a}{b^4}\implies b^4=a \\\\[-0.35em] ~\dotfill\\\\ f(4)=69\hspace{5em}69=ab^4\implies \stackrel{\textit{substituting from the 1st equation}}{69=(b^4)b^4\implies 69=b^8} \\\\\\ \sqrt[8]{69}=b\implies (69)^{\frac{1}{8}}=b \\\\[-0.35em] ~\dotfill[/tex]

[tex]y=\sqrt{69}\left( (69)^{\frac{1}{8}} \right)^x\implies \boxed{y=\sqrt{69}(69)^{\frac{x}{8}}} \\\\\\ \textit{when x=6.5, what is "y"?}\qquad y=\sqrt{69}(69)^{\frac{6.5}{8}}\implies y\approx 1522.73[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x-2y=6\implies -2y=-x+6\implies y=\cfrac{-x+6}{-2} \\\\\\ y-\cfrac{-x}{-2}+\cfrac{6}{-2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]

so we're really looking for the equation of a line whose slope is -2 and that it passes through (-3 , -1)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-3)}) \implies y +1= -2 (x +3) \\\\\\ y+1=-2x-6\implies {\Large \begin{array}{llll} y=-2x-7 \end{array}}[/tex]

We may determine the option a) 15x - 12 by simply multiplying and adding them by the necessary terms.

A linear equation is an algebraic equation of the form y = mx + b. involving only a continuing and a first-order ( linear ) term, where m is the slope and b is the y-intercept.

5X ( 3 - 12 X) - 3 ( 4 - 20[tex]x^{2}[/tex] )

15X - 60[tex]x^{2} \\[/tex] - 3 ( 4 - 20[tex]x^{2}[/tex] )

15X - 60[tex]x^{2} \\[/tex] - 12 + 60[tex]x^{2}[/tex]

15X - 12 this is required solution .

Just by simply multiplying and adding them by required terms we can conclude 15x - 12.

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Answer:

[tex]-18x+20[/tex]

Step-by-step explanation:

We can simplify to find an equivalent expression

Take a look at the attachment...

Hope this helps! :)

The equation in point-slope form of a line that passes through the points (5, −3) and (−2, 9) is

y + 3 = -12/7(x - 5)

Given, a line that passes through the points (5, −3) and (−2, 9).

Now, we have to find the equation of the line in point-slope form.

As, we know to find the equation of a line,

(y - y1)/(x - x1) = (y1 - y2)/(x1 - x2)

Now, using the above formula, we get

(y + 3)/(x - 5) = (-3 - 9)/(5 + 2)

(y + 3)/(x - 5) = -12/7

On cross-multiplying, we get

y + 3 = -12/7(x - 5)

Hence, the equation in point-slope form of a line that passes through the points (5, −3) and (−2, 9) is

y + 3 = -12/7(x - 5)

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The sub contractor pays $0.94 per hour for the work .

In the question ,

it is given that ,

the amount paid by the contractor for 25 hours of work = $23.50

We need to find the amount paid by the contractor for 1 hour .

The per hour pay can be calculated using the formula ,

amount paid per hour = (amount paid for 25 hours)/( number of hours)

substituting the values ,we get

So , the amount paid by the contractor for 1 hour of work = 23.50/25

= $0.94

Therefore , The sub contractor pays $0.94  per hour for the work .

The given question is incomplete , the complete question is

A sub-contracted job pay $23. 50 for 25 hour of work. How much money does it pay per hour ?

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Answer:

The graph gets shifted up more

Step-by-step explanation:

Calculating the values of x^2    and then adding a constant 'c' to that value shifts the graph upward by the value of 'c'

Answer:

The vertex (or minimum) would move to a higher position on the y -axis

Step-by-step explanation:

Whatever the value of C is, will be where the vertex of the quadratic sits

Answer: Error

Step-by-step explanation: Its impossible to divide by zero.

Answer:

0

Explanation Anything divided by zero is zero

Answer:

Step-by-step explanation:

1/3(12) - 1/3(9w)

4 - 3w

At least 10 people or guests could go to a party and the second caterer is $250 cheaper to hire.

In the question we can use the equation :

  Y = mx + b ,  which is the slope-intercept form of the equation of a straight line. Here, m is the slope of the line and b is the intercept, x and y represent the distance of the line from the x-axis and y-axis, respectively.

For caterer A, the cost per guest is $15. This is the m value. The b value is the additional fee for setting up the tables, $100.

Here, the equation will be  y = 15x + 100     -------------------------(1)

For Caterer B, the cost per guest is $20. The b value is the additional fee for setting up the tables $50.

For this the equation will be : Y = 20X + 50.  --------------------- (2)

To find the number of guests that will result in an equal cost, set the equations equal to one another. Solve for x.

                    15x + 100 = 20x + 50        ---------------------- (3)

solving the equation (3),

   15x - 20x = 50 - 100

⇒ -5x = - 50

⇒ x = 10

Putting x = 10 in equation (1),

   15 × 10 + $100 = $250

Therefore, the cost of 10 people or guest will attend the party and the second caterer is $250 cheaper then the first caterer.  

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The rate  that is the best deal for a bottle of mustard is: C: $2.42 for 12 oz.

a. $1.26 for 6 oz

Unit rate = $1.26 / 6 oz

Unit rate = $0.21

b. $1.65 for 8 oz

Unit rate = $1.65 / 8 oz

Unit rate = $0.206

Unit rate = $0.21 (Approximately)

c.  $2.42 for 12 oz

Unit rate =   $2.42 /12 oz

Unit rate =  $0.201

Unit rate = $0.20 (Approximately)

d.  $3.30 for 16 oz

Unit rate = $3.30 / 16 oz

Unit rate = $0.206

Unit rate = $0.21 (Approximately)

Therefore the correct option is C.

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Answer:

slope = -1, y-intercept = is n/a. The line is vertical since the y intercept was not given.

Answer:

62, 78

Step-by-step explanation:

248:4

you want to know

x:1 (hour)

you can do that by dividing by 4 which gives

248/4 = 62

for 2 it's the same, divide by four

Answer:

1- 62 miles per our

2- 78 calories per serving

Answer:

Step-by-step explanation:

4a

The value of x in the isosceles triangle is 9.25.

An isosceles triangle is a polygon that has three sides. The opposite length have the same length and equal angles.  has two opposite sides. If the two angles are equal , it means the triangle is an isosceles.

Th perimeter of an isosceles triangle is the sum of the length of the three sides of the triangle.

Perimeter = (2 x length of leg) + base

43 = (2x x) + 2x - 6

43 = 2x + 2x - 6

43 = 4x - 6

43 - 6 = 4x

37 = 4x

x = 37 / 4

x = 9.25

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Answer:

Step-by-step explanation:

m n

Answer:

x = 8

Step-by-step explanation:

since the triangle is isosceles then the 2 legs are congruent, that is both 4x - 3

the perimeter is the sum of the 3 sides , that is

x + 4x - 3 + 4x - 3 = 66

9x - 6 = 66 ( add 6 to both sides )

9x = 72 ( divide both sides by 9 )

x = 8

Answer:15

Step-by-step explanation:

The mean is the sum of all the numbers divided by the amount of numbers

Step 1: Add

5+25+10+15+20 = 75

Step 2: Divide

Since there are 5 numbers divide 75 by 5

75/5 = 15

The answer is 15

Answer: The mean is 15

Step-by-step explanation:

   To find the mean, we add all the numbers together and divide by the number of numbers.

[tex]\displaystyle \frac{5+ 25+10+ 15+ 20}{5} = \frac{75}{5} = 15[/tex]

Answer:

13x-12y+6xy

Step-by-step explanation:

To  make this easier, we can rearrange these terms, and get

5x+8x-12y+2xy+4xy.

x and y just represent variables, so we can combine 5x and 8x to get 13x, and we can combine 2xy and 4xy to get 6xy.

Now we have 13x-12y+6xy, and nothing else can be combined.

Answer:I really like math

Step-by-step explanation:

Answer:

Step-by-step explanation:

a

The percent of chloride ion in a sample if 2. 500 g of the sample produces 1. 750 g of AgCl when treated with excess ag⁺  is 17.2%

The percent of chloride can be calculate as follow:

Mass of AgCl precipitated = 1.750 g

Molar mass of AgCl = 143.32 g/mol

Molar mass of Chlorine atom = 35.45 g/mol

Asume, all the chlorine in the sample is precipitated to silver chloride. So, the mass of chlorine in silver chloride will be equal to the mass of chlorine present in the sample.

To calculate the mass of chlorine in given mass of AgCl, we apply unitary method:

In 143.32 g of silver chloride, mass of chlorine present is 35.45 g

So, in 1.3487 g of silver chloride, mass of chlorine present will be =

35.45g/143.32 g * 1.750 g = 0.43 g

To calculate the percentage composition of chlorine in pure chloride compound, as follows:

Mass of pure chloride compound = 2.500 g

Mass of chlorine = 0.43 g

% Chlorine = 0.43/2.5 *100

% Chlorine = 17.2 %

Therefore, the mass percentage of chloride in pure chloride compound is 17.2%

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The expression represents the current price of milk is 3 + y in dollars

The initial price of a gallon of milk = $2.65

The price rose y dollars after the last hurricane

Then the expression will be

2.65 + y

Then the price dropped $0. 15

2.65 + y - 0.15

Add the terms

2.65 + y - 0.15 = 2.5 - y

later rose again by $0. 5

2.5 + y + 0.5

Add the terms in the expression

2.5 + y + 0.5 = (2.5 + 0.5) + y

= 3 + y

Current price of milk = 3 + y in dollars

Hence, the expression represents the current price of milk is 3 + y in dollars

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Answer:

Step-by-step explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm

Answer:

2.80112699842

Step-by-step explanation:

height = volume / (π × radius²)

220/25 pi

If the domain of the function f(x) = 2x + 1 is {-2 ≤ x ≤ 3}, an integer which is not in the range is: a) -4.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values (real numbers), which are shown on the y-axis of a graph.

When x = -2, the range of this function f(x) = 2x + 1 is given by:

f(-2) = 2(-2) + 1

f(-2) = -4 + 1

f(-2) = -3

When x = 3, the range of this function f(x) = 2x + 1 is given by:

f(3) = 2(3) + 1

f(3) = 6 + 1

f(3) = 7

Therefore, the range of this function is -3 ≤ y ≤ 7 and as such, -4 is an integer that is not within the range as shown in the number line attached below.

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Answer:

233

Step-by-step explanation:

The ordered pair that is not a solution to the inequality y ≥ 2x² - 4x + 2 is given as follows:

(-1,6).

The inequality is presented as follows:

y ≥ 2x² - 4x + 2.

Then for each pair, the numeric value is calculated, replacing x and y by it's respective coordinates, and when a false statement is generated, the ordered pair is not a solution to the inequality.

For the first ordered pair, (-1, 6), the numeric value of the inequality is given as follows:

6 ≥ 2(-1)² - 4(-1) + 2

6 ≥ 8.

Which is a contradiction, hence it is not a solution to the inequality.

For the pair (1,0), we have that:

0 ≥ 2(1)² - 4(1) + 2

0 ≥ 0.

Which is true, hence it is a solution.

For the pair (0,3), we have that:

3 ≥ 2(0)² - 4(0) + 2

3 ≥ 2

Hence it is also a solution.

For the pair (2,5), we have that:

5 ≥ 2(2)² - 4(2) + 2

5 ≥ 2

Hence it is also a solution.

The problem is given by the image shown at the end of the answer.

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The order from least to greatest is "forty percent, 0.5, eight-ninths, six-fifths".

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The given numbers are,

six fifths = 6/5 = 1.2

eight ninths = 8/9 = 0.9

0.5

40% = 0.4

Therefore, the order from least to greatest is "forty percent, 0.5, eight-ninths, six-fifths".

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Answer:

Divide the calories by 2 to get the amount for 1 mile the multiply that by 3 to get your answer which is 277.5 calories

Step-by-step explanation: